x-ray astronomy and sco x-1

X-Ray Variability in Astrophysics

s tudy of the variability of x-rayand gamma-ray sources is a rel-atively mature field. providingastrophysicists with a wealth of

information about the workings of binarystellar systems and the internal structureof the component stars. Recently, interestin these rapidly changing systems hassoared as a result of new data gathered bythe European Space Agency’s satellite EX-OSAT, launched in 1983. EXOSAT hasbeen able to gather invaluable data onrapid and repeating transients as well as onperiodic behavior and more subtle effectssuch as frequent, small shifts in the periodof an oscillatory phenomenon. Orbitalperiods and partial eclipses in binary sys-tems, x-ray bursts. and even changes in thedirection of flow of accreting matter ontoneutron stars are among the new detailsthat can now be studied.

Until recently, luck has been a big factorin discovering transient behavior. But thatwill change when the new JapaneseASTRO-C satellite is launched in 1987and the new American XTE satellite islaunched in the early 1990s (see “The NextGeneration of Satellites”). The plan is toequip these satellites with all-sky sensorsthat will be able to discover and monitortransient behavior anywhere in the sky. Inaddition, the satellites will carry large-areadetectors that will allow the spectral andtemporal behavior of cosmic x-ray sourcesto be studied with unprecedented pre-cision. Moreover, the satellites will bespecially designed so that observers canquickly turn the large-area detectorstoward sources showing unusual behavior.Both the quantity and quality of informa-tion about transient systems should there-fore increase dramatically in the comingyears.

It was thus felt that the summer of 1985would be an opportune time for a work-shop to review the accomplishments of thelast decade, to discuss plans for the newsatellites, and to prepare for the expectedwave of new, more detailed data onvariable x-ray and gamma-ray sources.

The timing of the workshop could not

4

have been more fortunate. During theweeks preceding the workshop, unex-pected new results from EXOSAT keptpouring in, requiring repeated overhaul ofthe schedule to accommodate reports ontwo newly discovered phenomena. Onewas quasiperiodic oscillations in the x-rayoutput of some neutron-star binaries (See“Quasiperiodic Oscillations”); these os-cillations provide the first direct probe ofthe transition region between the neutronstar and the accretion disk present in thesesystems. The other was evidence that thefamous neutron star in Hercules X-1 (HerX-1) is freely processing, which could ex-plain the origin of its enigmatic 35-daycycle (see “Her X-1: Another Window onNeutron-Star Structure”).

In view of the importance and con-troversial nature of the evidence on HerX-1, a special effort was made to gather forthe first time those scientists with majorinterest in the 35-day cycle. Almost allwere able to attend the workshop, makingpossible in-depth discussions of the dra-matic new evidence for precession in thissystem. It became apparent that severalpossible stumbling blocks to acceptance ofthis interpretation could be set aside.

Similarly, the workshop was the firstmeeting at which almost all the scientistsinvolved in the discovery and interpreta-tion of quasiperiodic oscillations werepresent. Participants stayed up late intothe night, discussing the new data and

arguing over its interpretation.Many commented that the workshop

was one of the most exciting scientificmeetings they had ever attended. Not onlydid the workshop pave the way for plan-ning use of the next generation of x-ray

satellites, but it served as a forum fordiscussing the startling discoveries beingmade with present instruments.

This report summarizes many of thediscoveries and developments discussedin the sessions of the workshop, to whichall participants contributed. The illustra-tions and tables arc adapted from materialpresented at the workshop. The selectionof topics and the views expressed arc ob-viously those of the authors alone. Theparticipants and the subjects of theirscheduled talks are listed on page 37.

X-Ray Astronomy and Sco X-1

The brightest stellar x-ray source in oursky, Scorpius X-l (Sco X-1), has beenstudied since the beginning of x-ray as-tronomy. The story of this object, dis-covered early but not easily understood,illustrates the development of x-ray as-tronomy,

Sco X-1 shines so intensely that it de-livers to earth about a thousand x-rayphotons per square centimeter per second,ten times more than the next brightest x-ray star, It was detected during a 1962

Spring 1986 LOS ALAMOS SCIENCE

rocket experiment led by Riccardo Giac-coni that was designed to look for solar xrays scattered from the moon. The dis-covery of such a bright x-ray sourceoutside the solar system came as a greatsurprise. Sco X-1 was found to radiate xrays with ten thousand times the totalpower of our sun.

What sort of object could be such apowerful source of x rays? One suggestionwas that Sco X-1 is a neutron-star systemin which matter is heated to millions ofdegrees as it falls into the enormous gravi-tational potential of the neutron star,producing x rays. Without direct evidenceof a neutron star in Sco X-1, this accretionmodel remained highly speculative untilthe early 1970s when similar but pulsed x-ray sources were discovered. The rapid

regular pulsing of these sources signaledthe presence of a rotating magnetic neu-tron star. Many of these pulsed x-raysources were found to be neutron-starbinaries in which a close companion star isthe source of the accreting matter. Al-though Sco X- I exhibits no strong x-raypulsations. regular variations in the Dop-pler shifts of its spectral lines and in thebrightness of its optical light, discoveredin 1975, show that it too has a compan-ion—one that circles it every 0.787 days.

Sco X-1 has revealed its nature onlygrudgingly. The system is too small and faraway for its components to be resolved:

LOS ALAMOS SCIENCE Spring 1986

what little we know is deduced from theshapes of its x-ray and optical spectra andtheir variations with time. For example,the existence of an accretion disk aroundthe neutron star in Sco X-1 was confirmedby the discovery in 1981 of simultaneousrapid changes in the optical and x-rayintensity. The lack of delay between thetwo signals meant that the x rays are gener-ating optical light in an accretion disk nearthe neutron star as opposed to generatingoptical light by traveling to and heating thecompanion star.

Even an old friend can surprise you. ScoX-1 did just that early in 1985 when it wasshown to exhibit quasiperiodic oscilla-tions in its x-ray intensity. This phenome-non is a variation of several per cent in thex-ray output that is not perfectly periodic,

..


that is, the period of the intensity variationalso varies. As a result, the Fourier trans-form of intensity squared versus time,namely, the power-density spectrum, givesa broad rather than a sharp peak. Thecentroids of the observed peaks lie in theregion of the spectrum between 6 and 50cycles per second (Hz). The cause of theoscillations cannot be simply rotation ofthe neutron star—-a very preciseclock—but could be produced by interac-tion of the magnetosphere of the neutronstar with the surrounding disk—a sloppyclock. These quasiperiodic oscillations arethe first direct evidence of what is happen-ing near the neutron star and confirm ourexpectations that study of x-ray variabilitywill reveal the detailed dynamics of thesebinary systems. continued on page 8

5

The Next Generation of Satellites


w ithin the next few years twoplanned satellites, one Japaneseand one American, should

begin gathering data vital to a deeper un-derstanding of x-ray sources and theirvariability, The instruments aboard thesatellites will allow both detection ofpreviously invisible sources and muchmore detailed studies of bright sources.

The Japanese satellite, ASTRO-C (Fig.1), which is being designed by the JapaneseInstitute of Space and Astronautical Sci-ence, will be launched in 1987. Its keyinstrument will be a proportional counter,called the large-area counter (LAC), withan effective area of 0.45 square meter. Aproportional counter, the workhorse of x-ray astronomy, was chosen as the maininstrument because it can be made with alarge effective area, is rugged, and hasgood background rejection. It has mod-

Signals from extraneous sources and thediffuse glow of the x-ray sky will be ex-cluded with mechanical vanes that restrictthe field of view to 0.8 by 1.7 degrees. TheLAC will be sensitive to energies from 1.5to 30 keV, a range that includes most ofthe output of neutron-star x-ray sources,

NASA’S X-Ray Timing Explorer (XTE)(Fig, 2) will be larger than ASTRO-C andis planned to be launched from the SpaceShuttle in the 1990s. Its kcy instrumentwill be a proportional counter array com-posed of eight separate detectors with atotal effective area of a full square meter,The individual fields of view of the eightd e t e c t o r s w i l l t y p i c a l l y b e n e a r l ycoaligned, but it will be possible for ob-servers to command two detectors to anoffset position to permit simultaneous ob-servations of source and background in-tensititcs. This feature will make itpossible to separate variations in faint orweakly varying x-ray sources from varia-

6

tions in the background. The field of viewwill be similar to that of ASTRO-C, butthe use of xenon rather than an argon-xenon mixture will allow detection ofhigher energy x rays (2 to 60 kcV).

XTE will also carry a large-area (0.2-square-meter) hard x-ray te lescopesensitive to energies from 20 to 200 kcVand pointed in the same direction as theproportional counter. In combinationwith the proportional counter array, thisinstrument will allow simultaneous spec-tral and variability measurements over theentire energy range from 2 to 200 keV.This capability will make possible detailedstudy of a host of kcy phenomena, such asthe spectra of transient x-ray sources,cyclotron features in accretion-poweredpulsars, the energy output from active ga-lactic nuclei, and changes in the state of’certain galactic sources, such as the black-hole candidate Cygnus X-1.

Fig. 2. ASTRO-C, Japan’s third x-ray as-tronomy satellite. The large-area counter(LAC) will consist of eight proportionalcounters containing a mixture of argon(70%), xenon (25%), and carbon dioxide(5%) and will be sensitive to x rays with

energies from 1.5 to 30 keV. The gamma-ray burst detector will be a two-detectorsystem: a 60-square-centimeter NaI(Tl)scintillation counter sensitive to photonenergies from 15 to 480 keV and a 100-square-centimeter proportional countersensitive to the same photon energies as theLAC. The all-sky monitor (out of view onthe side opposite the LAC) will consist oftwo proportional counters. Also shown isthe star sensor used to determine the orien-tation of the satellite.

The square-meter class of detector onthe two satellites will allow the study of



Fig. 2. NASA’S X-Ray Timing Explorer, orXTE. The observational objective of thissatellite will be to measure photons from 2to 200 keV on time scales ranging from 10microseconds to months. To accomplishthis objective, XTE will carry a 1-square-meter proportional counter (PCA), a 0.2-square-meter hard x-ray telescope(HEXTE) consisting of twelve scintillationdetectors, and two ail-sky monitors thatwill scan the sky continuously. ➤

very faint sources and of changes insources on very short time scales that havepreviously been inaccessible. Sources 1Os

times fainter than Scorpius X-1, for exam-ple, will be detectable in 100 seconds, al-lowing extensive study of active galacticnuclei and faint galactic binaries. Featuresof bright sources, such as fast variations inintensity, pulse frequency changes, andspectral changes during x-ray bursts. willbe resolved without parallel. For example,XTE will be able to collect 2000 photonsduring a single pulse from the accretion-powered pulsar Hercules X-1, 200,000photons during a bright x-ray burst. andeven 45 photons during a 600-micro-second flare of the fascinating source ofCygnus X-1.

The x-ray transients discovered by EX-OSAT, Tenma, and other recent satellitesfrequently turn out to be key examples forelucidating the physics of such systems.However, they are discovered mostly byluck because there is no all-sky coverageby these satellites. The transients wereeither detected by another satellite or weredetected while the telescope was movingfrom one known source to another. Bothof the new satellites will carry all-skymonitors. ASTRO-C will be able to scanthe sky by executing a slow pirouette onceeach orbit, during the time the source be-ing observed by the LAC is hidden by theearth. The monitor on XTE will con-tinuously scan from two rotating plat-forms and will detect sources 1000 timesfainter than Scorpius X-1 in a single 90-minute orbit. Data from these monitors


can be used to redirect the main arraystoward sources showing unusual activity,The monitors will also provide un-precedented information on the day-to-day behavior of hundreds of sources.

ASTRO-C will carry a gamma-ray-burstdetector, designed in collaboration withLos Alamos, whose viewing angle is halfthe sky. What is unusual about this instru-ment is the juxtaposition of a proportionalcounter sensitive to x-ray photons andscintillation counters sensitive to gamma-ray photons; such an arrangement meansthe critical spectra of burst events will bemeasured to lower energies than before.

ASTRO-C will be a free-flying satelliteand will operate, with luck, for at leastthree to four years. The expectations forXTE are less clear. Its nominal designlifetime is that typical of NASA satel-lites—two years-but past NASA satel-lites have often functioned productively

tor five or more years. (NASA’S interna-tional Ultraviolet Explorer, launched in1978 with a similar design lifetime, is stillpouring out results, and competition byscientists for its use has hardly eased. )Even though the XTE instruments canfunction almost indefinitely, NASA maychoose to operate XTE aboard a re-coverable platform and terminate itsoperation when the two-year design life-time has elapsed. If so, the initial dis-coveries of XTE could not be followed up.Especially for the all-sky monitor, twoyears would provide only a tantalizingglimpse compared to the 10-year Vela 5Bmission and the 5-year Ariel-5 studies ofvery long term changes in the x-ray sky. ■

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continued from pages

An Overview of Compact Sourcesof X Rays

In all accretion-powered x-ray sourcesthe bulk of the energy for emission issupplied by the fall of matter into the deepgravitational well of a compact object,either a degenerate dwarf, a neutron star,or a black hole. The kinetic energy of thefall is converted to heat and then to x rayseither during the fall or when the matterstrikes the surface of the star.

X-Ray Stars. Accretion-powered x-raybinaries are distributed through galaxiessuch as our own (Fig. 1). Almost in-variably, such compact x-ray sources areclose binary systems in which a compactobject with a mass 1/2 to 10 times that ofthe sun strips matter from a companionstar. Frequently, the matter spirals slowlytoward the compact object, forming a hotdisk (opening figure). The known x-raystars fall into several different classes.

Accretion-powered pulsars are stronglymagnetic rotating neutron stars in closebinary systems (Fig. 2). Most are found in

of the sun) systems, although a few have

When accreting material from the com-panion star enters the neutron star’s mag-netosphere, it falls toward the magneticpoles along field lines, causing emission ofx rays from the magnetic poles. If thesepoles do not coincide with the rotationaxis, the spinning star will emit two broadbeams of x rays that can repeatedly sweepacross the earth as the star rotates so thatthe x rays appear to be pulsed. In addition,the flow of accreting matter to the stellarsurface may be partially modulated at therotation frequency of the star. Typical fre-quencies are in the mHz to Hz range.

In contrast to accretion-poweredpulsars, rotation-powered pulsars are pow-ered by conversion of the rotationalenergy of a strongly magnetic neutron starinto electromagnetic radiation. This con-

8

version takes place as the result of theexistence of extremely strong electric fieldsnear the star that accelerate charged parti-cles to high energies. These neutron starslack a companion or one close enough toserve as a source of accreting matter. Someof the youngest and fastest rotation-pow-ered pulsars radiate predominately in xrays. The pulsed emission is thought to bethe result of misaligned rotation and mag-netic-field axes.

Much of the variation in intensity ofbinary x-ray sources on time scales ofhours to days is due to the orbital motionof the binary, which can produce eclipsesand so-called dips—short episodes ofpartial obscuration. However, in somesources the x-ray intensity is observed tochange regularly with a period longer thanthe orbital cycle. The cause of these long-term periodic variations is at present un-known, although a variety of explanationshave been proposed.

Galactic-bulge sources are so called be-cause the majority are located in a bulgeabout the center of our galaxy. Althoughsome may be black holes, most are thought

to be weakly magnetic rotating neutronstars in relatively old low-mass binary sys-tems. Our old friend Sco X-1 is in thiscategory. These systems flicker on a widevariety of time scales but do not producestrong regular pulsations. Those of mod-erate luminosity exhibit x-ray burstscaused by thermonuclear explosions of ac-creted matter. The bursts, which occurepisodically at intervals ranging from min-utes to days, last a few seconds and standout above the flickering emissionproduced by the continuous rain of matteronto the surface of the star. Some bulgesources exhibit the quasiperiodic oscilla-tions that were the subject of such intensediscussion at the conference.

Cataclysmic variables are low-massclose binary systems containing a stronglyor weakly magnetic degenerate dwarf andare highly variable in both visible light andx rays. They are much more numerousthan binary systems containing neutronstars.

Gamma-Ray Bursters. A long-standingpuzzle are the sources observed to emit

COMPACT X-RAY SOURCES IN OUR GALAXY

Fig. 1. A recent map of compact x-ray the HEAO-1 satellite. The radius of thesources in our galaxy prepared using data dot representing a source is proportional tofrom the A-1 x-ray experiment on board the logarithm of its intensity.



Fig. 2. The neutron-star orbit and esti-mated companion-star mass (in terms of

systems. The mass of the neutron star isbetween ½ and 3 solar masses.

intense bursts of gamma rays lasting afraction of a second to a few seconds.Accompanying these gamma rays is arelatively weak flux of x rays. Unlike thegalactic x-ray stars, which are largely con-fined to the Milky Way, gamma-raybursters appear to be randomly dis-tributed over the sky. They are believed tobe neutron stars, although the mechanismunderlying their bursts remains anenigma.

Active Galactic Nuclei. The nuclei ofsome galaxies are extremely luminoussources of hard x rays. These sources arebelieved to be black holes with masses of

from the surrounding galaxy itself.

All the sources described above varydramatically on human time scales—adirect result of the fact that the x rays areproduced near compact objects. For galac-tic sources dynamical time scales can be asshort as milliseconds, mass-accretion ratesas high as 10–8 of a solar mass per year,and luminosities 105 times that of the sun.In active galactic nuclei, dynamical timescales are as short as 102 seconds, accretionrates are believed to be as much as a solarmass per year (a billion times greater thanin typical galact ic sources) , andluminosities are as great as 1013 times thatof the sun. Because the sources are socompact, these high luminosities comefrom very small areas (a few square kilo-meters for pulsars) and the effective tem-perature of the emitting region is thereforevery high. Thus, the photons producedhave energies predominantly in the rangeof 0.01 to 20 kilo-electron-volts (keV) for

cataclysmic variables, 2 to 20 keV forpulsars and bulge sources, and 100 keV ormore for gamma-ray bursters and activegalactic nuclei.

High-Mass X-Ray Binaries

Twenty-three of the twenty-six knownaccretion-powered pulsars are found inhigh-mass binary systems (Fig. 2). As dis-cussed above, the stable, periodic pulsa-tions we see from these sources areproduced in large part by rotating beamsof x rays, Since black holes in such systemswould be axisymmetric, stable pulsationsare strong evidence that these sources arenot black holes. Moreover, the x-rayluminosities of most exceed the maximumluminosity given by radiative-transfer cal-culations for degenerate-dwarf x-raysources (about 2 X 1036 ergs/second).

Evidence that accretion-poweredpulsars are indeed neutron stars comesfrom observed changes in their pulsation

LOS ALAMOS SCIENCE Spring 1986 9


44

Days

Fig. 3. The orbital period and eccentricity then used to remove the effects of thefor the 4U0115+63 binary system are motion of the neutron star around itsobtained from a fit of time-delay data companion, yielding the residuals (red).(black) after the effects of the motion of An analysis of the residuals may uncoverthe satellite around the earth and the variability in the intrinsic spin rate of themotion of the earth around the sun have neutron star.been removed. The orbital parameters are

Table 1

Orbital parameters for some neutron-star x-ray binaries. The estimated mass of thecompanion star Mc, which is relatively uncertain, the radius of the companion star Rc,and the allowed range of the mass of the neutron star M are in solar units; the inclinationangle i is the angle in degrees between the orbital angular-momentum vector and the lineof sight.

System M c R c M 1

SMC X-1 17 16 0.8- 1.5 57 to 77Cen X-3 20 12 0.5- 1.7 >634U0900–40 23 31 1.6-2.2 >734U1538–52 20 16 1.0-3.2 >60LMC X-4 20 9 1.0- 1.8 >58Her X-1 2 4.0 1.1-1.8 >80

frequencies, which agree quantitativelywith the changes predicted by the theory ofaccretion by neutron stars having mag-netic fields of 1011 to 1013 gauss (G). Otherevidence comes from the discovery ofwhat appear to be cyclotron scatteringlines in the x-ray spectra of two of thesesystems, indicating magnetic fields in thesame range. Such magnetic field strengthsare expected for neutron stars. Several ac-cretion-powered pulsars show thermal soft(about 0.5 keV) x-ray emission that isinferred to be coming from a region about1 03 kilometers (km) in radius, just theradius of the magnetosphere of a neutronstar with the appropriate luminosity andwith surface magnetic fields of about1012 Finally, the x-ray spectra and pulsewaveforms of these pulsars agreequalitatively with those predicted by neu-tron-star models.

A few high-mass binary systems arethought to contain black holes. These arediscussed later (see the section in thisarticle entitled “Black Holes,” page 26).

10 Spring 1986 LOS ALAMOS SCIENCE


Pulse Timing. During the past few years,the interplay between theory and observa-tions of pulsars has led to fundamentalchanges in our understanding of thedynamical properties of neutron stars (see“Internal Dynamics of Neutron Stars”)and has uncovered surprising features ofthe accretion flow patterns in massive x-ray binaries. These advances have beenmade possible by extremely precisemeasurements of the intrinsic pulse fre-quencies of pulsars, carried out with x-rayinstruments on satellites such as SAS-3,Ariel-5, HEAO-1, Hakucho, Tenma, andEXOSAT and by the development of newmethods of analysis (see “New AnalysisTechniques”).

Determining the intrinsic pulse fre-quency of the neutron star from the ob-served pulse frequency requires removingthe systematic effects of the motion of theobserving satellite around the earth, themotion of the earth around the sun, andthe motion of the pulsar around its stellarcompanion. Determining the binary orbit,a major task in itself (Fig. 3), providesvaluable information about the mass ofthe neutron star (Table 1), as well as re-vealing the structure of the companionstar and, over time, the evolution of thebinary system.

After the effects of the orbital motionhave been removed, the intrinsic pulsefrequency can be examined for variations,which are due primarily to changes in therotation rate of the neutron-star crust. (Inprinciple, changes in the x-ray beamingpattern can also cause variations in theobserved pulse frequency. However,where observations have been made thatcan determine the size of such variations,they appear to be small compared to varia-tions caused by changes in the rotationrate of the crust.) In accretion-poweredpulsars, variations approaching 0.01 percent of the spin rate have been seen tooccur within a few days, and changes aslarge as a few per cent have been observedover the course of a year (Fig. 4).

These variations in the rotation rate ofthe crust could be caused by internal ef-


INTRINSIC PULSE-FREQUENCYVARIATIONS

GX 1+4

70 74 78

Cen X-3.

74 78 82

Year

Fig. 4. Pulse-timing results for severalaccretion-powered pulsars, showingvariations in the intrinsic pulse frequencythat are most likely due to changes in therotation rate of the neutron-star crust.

fects, such as changes in the moment ofinertia of the crust or in the torque exertedon the crust by other components of thestar. Examples of such internal changesinclude temperature fluctuations, fractureof the star’s crust, and unpinning of super-fluid neutron vortices in the inner crust(discussed in “Internal Dynamics of Neu-tron Stars “).

Analysis of relatively small variationsin the rotation rates of both accretion-powered and rotation-powered pulsars hasled to a new picture of the dynamicalproperties of neutron stars (also discussedin “Internal Dynamics of Neutron Stars”).In particular, it had been thought that thecrust of the neutron star was only weaklycoupled to the neutron superfluid thatforms most of the core of the star. It is nowthought that neutron stars are essentiallyrigid—that all but 1 per cent of the star iscoupled to the crust on time scales longerthan a few hundred seconds. According tothis new picture, the effect of internaltorques on the rotation rates of accretion-powered pulsars can be neglected.

Variations in the rotation rate of thecrust can be caused by fluctuating externaltorques, which reflect changes in the star’scoupling to its environment. Examples areelectromagnetic torque fluctuations, re-versals in the flow of accreting material, orfluctuations in the magnetic brakingtorque that occur when a rapidly rotatingstar accretes from a disk.

Accretion Torque Variations. If therotation rate of the crust in accretion-pow-ered pulsars is not significantly affected byinternal torques as argued above,measurements of the pulse frequencyprovide direct evidence of the accretiontorque on the crust. What do suchmeasurements say about spin-rate fluctua-tions in accretion-powered pulsars? Analy-sis of the fluctuations in the spin rate ofVela X-1 over an eight-year period sup-ports the idea that the fluctuations arecaused by changing external torques andalso reveals interesting properties of theaccretion flow.

11


(a)

(b)

ANALYSIS OF INTRINSICPULSE-FREQUENCYVARIATION FOR Vela X-1

76 78 80 82Year

Fig. 5. Pulse-timing results for Vela X-1.(a) Although the change is small (0.5%overall), the pulse frequency, or angularvelocity, of the neutron star appears tohave increased from 1975 to 1979 andthen decreased from 1979 to 1982. (b)The power-density spectrum of fluctua-tions in the pulse frequency of the star isapproximately flat for periods rangingfrom 5 to 2600 days, which is character-istic of random forces acting on an ap-proximately rigid star. Thus, the long-term rise and fall of the pulse frequencyshown in (a) is consistent with torquevariations and does not indicate a changein the character of the accretion flowonto the star.

12

The original pulse-timing data for VelaX-1 (Fig. 5a) appear to show a relativelyslow increase in the rotation rate over afour-year period followed by a relativelyslow decrease. However, the power-den-sity spectrum of the pulse-frequency vari-ations derived from the same data (Fig. 5b)shows that the long-term rise and fall inpulse frequency is consistent with whatwould be expected as the result of a fluc-tuating torque. The spectrum is relativelyflat and therefore consistent, for periodsranging from 5 to 2600 days, with whitenoise in the star’s angular acceleration;that is, the behavior is equivalent to arandom walk in pulse frequency. The ob-served noise strength implies an ac-cumulated offset in pulse phase greater

days, showing that the observed variationsin pulse frequency are due primarily tochanges in the rotation rate of the neutron-star crust and not to variations in theradiation beaming pattern.

The rapidity of the changes in the pulsefrequency or angular velocity of Vela X-1is also significant. Average angular ac-celerations over 3 days are as large as 6 X

quency. Moreover, the sign of the accelera-tion reverses on the 3-day temporal resolu-tion of the observations. These large ac-celerations and reversals in sign rule outmost mechanisms for altering the angularvelocity. The simplest conclusion, alreadysuggested by theoretical considerations, isthat the random walk in angular velocity isdue to fluctuations in the external accre-tion torque.

If the external torque is indeed responsi-ble for these changes in the rotation rate ofthe neutron-star crust, then pulse-timingmeasurements can be used to probe theflow of accreting matter near the star. Forexample, the sign and magnitude of theaccretion torque depend on the accretionrate, the pattern of the exterior flow, andthe structure of the star’s magnetosphere.Precise observations of changes in therotation rate can thus provide informationabout these properties of the flow. In

particular, variations in the amount ofmatter falling on the neutron star shouldproduce simultaneous variations in x-rayluminosity and in the angular accelerationof the star’s crust. Thus, one of the mostdirect ways to probe the accretion flow isto plot the observed angular acceleration aas a function of the observed x-ray flux F.

As an example of an expected correla-tion, consider the case in which matterspilling from the atmosphere of the com-panion star has sufficient angular momen-tum to form an extensive accretion diskoutside the neutron star’s magnetosphere.The torque on the star is then independentof the detailed flow far away but is depen-dent on the radius r0 separating Keplerianflow in the disk from the flow of matteralong field lines of the star’s magneto-sphere. Suppose that the star is rigid andhas a constant moment of inertia. Then, ifthe flow is steady, the angular accelerationof the star is given by

a = n Mm (GM ro)1/2/I,

where Mm is the mass flow rate into themagnetosphere, M and I are the mass andmoment of inertia of the neutron star, G isthe gravitational constant, and n is adimensionless quantity of order unity thatdepends on the structure of the transitionzone between the disk and the magneto-sphere. In fact, n may be positive ornegative, depending on such parameters asthe neutron star’s rotation rate and themass-accretion rate.

What correlation does this equation im-ply between a and F? Suppose the ob-servable x-ray flux F is proportional toM m. Now, the torque—and hence theangular acceleration—depends on thelever arm ro, which becomes smaller asM m increases. Thus, for disk flow, theexpected correlation between a and F is

A second case is wind-fed sources inwhich matter is captured from a stellarwind with a high enough velocity that it



THEORETICAL a-F CORRELATIONS

Radial FlowFast or Slow Rotator

Fig. 6. Theoretical plots of angular ac- sents the case in which the circulation is expanded 40 times that of the other twocelebration versus x-ray flux (a-F) for counter to the rotation, and the shaded panels (disk flow). These plots were ob-various orientations of the angular region represents a random distribution tained by assuming that the time duringmomentum of the accreting matter. In all of directions for the angular momentum which the angular momentum of the flowpanels the red curve represents the case in of the accreting matter. Note that the a changes direction is much shorter thanwhich the circulation of the accreting scale for the left panel (the case of radial the time between changes, so that the flowmatter has the same sense as the rotation flow of accreting matter onto either a may be considered stationary most of theof the neutron star, the black curve repre- rapidly or slowly rotating neutron star) is time.

does not have enough angular momentumto form an extensive accretion disk. Inthese sources the radial velocity of theaccreting plasma outside the magneto-sphere is large, The theory of such radialflows has not advanced sufficiently topredict the precise relation between a andF. However, it is known that the sign andmagnitude of the torque is quite sensitiveto variations in the flow velocity and den-sity across the capture surface. Thus, cor-related changes in a and F are to be ex-pected.

Flow Reversals. Returning to the pulse-timing data from Vela X-1 (Fig. 5a), theobserved reversals in angular accelerationimply reversals in the sign of the accretiontorque. There are only two known ways forsuch torque reversals to arise. For diskflow near a rapidly rotating neutron star,


the reversal could be caused by a change inthe mass flow rate since this results in achange in the size of the magnetosphereand hence in the relative sizes of the mate-rial spin-up torque and the magnetic spin-down torque. For radial flow it could becaused by a reversal in the direction ofcirculation of the accreting matter. A com-parison of the simulated a-F correlationfor the wind-fed source Vela X-1 (similarto the left panel of Fig. 6) with the correla-tion derived from data taken with theHakucho satellite indicates that there is noextensive disk in this system and hencethat flow reversals are the cause of thetorque reversals.

Such flow reversals are not predicted bythe standard model of capture from awind. Moreover. the measured angular ac-celerations are some 70 times larger thanthose predicted by models in which matter

is captured from a homogeneous wind.The indicated circulation of the accretingmatter is so large that the azimuthal com-ponent of the flow velocity at the magneto-sphere of the neutron star must be com-parable to the Keplerian velocity there(that is, the matter is almost in orbit). Butas already pointed out, the sign and mag-nitude of the torque produced by radialflow is sensitive to spatial variations in theflow velocity and density. Thus, the VelaX-1 observations are consistent with atorque that is produced by capture from aninhomogenous wind. Although the x-rayflux variations appear random on timescales longer than 0.25 days, the directionof circulation of the accreting matter ap-pears to persist for much longer times.Evidently, the wind contains coherentstructures that are at least as large as theradius of the companion star.

13


The evidence that the accretion flow inVela X-1 changes its sense of circulationon time scales as short as 3 days hasstimulated theoretical work on accretionflows (Fig. 6). Previous work has assumedthat the angular momentum of the accret-ing matter always has a direction more orless parallel to the orbital angular momen-tum of the binary system. Obviously, thisassumption is wrong. In the case of moregeneral flows, one would like to know boththe direction and magnitude of the angularmomentum of the flow as a function oftime. The spin rate of the accreting starsamples only the component of theangular momentum that is parallel to thespin axis. To sample the perpendicularcomponent, it might be possible to ob-serve changes in the spin axis of the neu-tron star relative to the axis of rotation ofthe binary system.

Accretion-Flow Puzzles. The resultspresented at the workshop show that theflow of accreting matter in x-ray binaries ismuch more complicated than previouslyimagined. Many basic questions, such asthe cause of the relatively small variationsin spin rate of rotation-powered pulsars,are not yet settled. The substantial timevariability in the Vela X-1 data pose anumber of new and challenging problemsfor theorists. What is the origin of the veryhigh specific angular momentum of theaccreting matter? What are the essentialfeatures of rings or disks formed bystrongly circulating flows that continuallychange direction? What causes the re-versals? Meaningful answers may requiremulti-dimensional numerical simulationsof the kind that are just now becomingpossible.

Low-Mass X-Ray Binaries

As discussed above, almost all of theknown accretion-powered pulsars arefound in high-mass systems. In contrast,the low-mass x-ray binaries, which aremostly found in the galactic bulge, typi-cally do not contain pulsars but exhibit

14

dips, bursts, and quasiperiodic oscillationsthat reveal new aspects about the physicsof the accretion process. In particular, thenewly discovered quasiperiodic oscilla-tions in the x-ray flux from low-mass ga-lactic-bulge sources (see “QuasiperiodicOscillations”) promise to be a powerfulprobe of conditions near the neutron star.

A typical galactic-bulge source consistsof a low-mass star spilling matter into thegravitational potential well of a weaklymagnetic neutron star. Because the mattercaptured in the gravitational well of theneutron star has too much angularmomentum to fall directly to the stellarsurface, it swirls around in nearly circularorbits as the slow transfer of angularmomentum outward allows it to inch in-ward. In contrast to accretion-poweredpulsars with their extensive magneto-spheres, there may be little or no funnelingof material onto the magnetic poles ofbulge sources.

The angular momentum transportprocesses that allow the material to flowinward also heat it. By calculating theenergy generated per unit area of the diskas a function of the mass-accretion rate, itcan be shown that the inner disk, if it isoptically thick, is heated enough to be astrong source of relatively soft (about 1keV) x rays. However, this heating ac-counts for only half the kinetic energyacquired by material as it falls into thegravitational potential well of the neutronstar. The remainder is lost when the mat-ter interacts with the star, producing veryintense emission of harder (about 2 to 7keV) x rays from the surface.

Inner-Disk Coronae. This simpledivision into soft x rays from the disk andhard x rays from the neutron-star surfaceis clouded by the fact that the inner diskmay have a diffuse gaseous corona, withradius of order 102 km, that can alter theenergy spectrum of radiation from the diskor the star or both. The corona may formbecause of thermal instabilities in the in-ner disk if the rate of cooling is propor-tional to the square of the gas density

whereas the rate of viscous heating varieslinearly with gas density. Thus, regionsthat are slightly less dense than the densityat which heating equals cooling arepreferentially heated, which causes ex-pansion, a lower gas density, and an evengreater excess of heating over cooling. Thisprocess continues until the hot diffuse re-gions balloon into a corona.

Compton scattering by the hot electronsin the corona can alter the energy distribu-tion of the photons passing through it. Ifthe electron temperature is significantlyhigher than the energy of the photons, thescattering will, on the average, “blueshift,” or increase, the photon energy.When the mean number of scattering fora given electron temperature is not toolarge, such Comptonization will modifythe incident photon spectrum onlyslightly. As the number of scatterings in-creases, however, the photons are broughtto near thermal equilibrium with the hotelectrons. Such “saturated Comptoniza-tion” distorts the photon distribution into

h is Planck’s constant, v is the photonfrequency, k is the Boltzmann constant,and T is the electron temperature).

Recent work on the time variability ofthe x-ray spectra of galactic-bulge sourcesthat takes into account the effects ofComptonization in the corona promises tohelp unravel the structure of the inner diskand its interaction with the stellar surface.By taking the difference between spectra atdifferent times, a temporally varying hardx-ray component was separated from aconstant soft x-ray component (Fig. 7).Although this analysis was done withoutrecourse to a specific model, it is thoughtthat the harder component arises verynear the neutron star whereas the softercomponent arises farther out in the disk.Further interpretation, however, is uncer-tain, with two alternative models currentlyable to explain the data.

In model A (left half of Fig. 8) the disk isoptically thick far from the neutron starbut expands vertically into a low-densityoptically thin but geometrically thick disk



X-RAY SPECTRA FOR GX 5-1

1

Fig. 7. X-ray spectrum (black) of thegalactic-bulge source GX 5-1 decom-posed into a softer (red) component (witha 1.4-keV blackbody fit) and a harder(blue) component (with a 1.96-keV fit).The fact that the softer x-ray componentis constant in time whereas the hardercomponent is variable allowed the two tobe separated by taking the difference ofspectra obtained at different times.

Fig. 8. Model A for the bright galactic-bulge sources has an optically thin innerdisk and no magnetosphere; materialfalls onto the star in a narrow equatorialband. If the mass flow rate increases, theinner disk and the band of x-ray emissionthicken. In this model the direction ofemission of harder x rays is slightly aboveor below the plane of the disk. Only asmall fraction of the photons comingfrom the star, and none from the op-tically thick disk, are Comptonized.Model B features optically thick diskmaterial extending inward to a smallmagnetosphere. A geometrically and op-tically thick corona of less dense plasmasurrounds both star and disk. Radiationpressure spreads accreting material overthe star, resulting in emission of harder xrays from the entire surface, but the in-ner-disk corona makes it harder for themto escape in the equatorial direction. Thethick corona Comptonizes a large frac-tion of the photons emitted from the in-ner disk and the star.

near the star. Because the star has nomagnetosphere, accreting matter” falls on abelt around the equator. In this model thesource would therefore appear brightest inharder x rays if viewed from slightly aboveor below the plane of the disk. The softer xrays are assumed to come from the op-tically thick disk without being scattered.A fit to the observed spectrum—assumingthe harder component originates from thestar and the softer component from thedisk—accounts for the entire observedflux except for a high-energy tail. WeakComptonization of a small fraction of theharder x-ray photons that pass through thelow-density inner disk explains the tail.

In Model B (right half of Fig. 8) opticallythick material extends inward until thedisk is broken up by the magnetospherevery near the stellar surface. The star’smagnetic field tends to focus the accretingmaterial toward the magnetic poles, but,

radiation pressure cause the accreting ma-terial to spread throughout the magneto-sphere as it falls, heating much of the star’ssurface. The inner disk has an opticallyand geometrically thick toroidal corona; inaddition, a larger diffuse central coronasurrounds the inner disk and neutron star.Thus, softer x rays originating in the op-tically thick inner-disk material would bescattered as they pass outward through thecorona. This type of source would bebrightest in harder x rays if viewed alongthe polar directions where the x rays canleak out without being heavily scattered.Unlike the previous model, a large frac-tion of the hard x-ray photons emittedfrom the neutron star and its magneto-sphere would be Comptonized by theirpassage through the large central and in-ner-disk coronae. In addition, the softer xrays from the inner disk would have aspectrum characteristic of unsaturated

since the field is too weak to confine it, Comptonization.



Although both models are consistentwith present data, observations that deter-mine the fraction of Comptonizedphotons and the best viewing angle fordetecting the harder x rays will surely dis-tinguish between them.

Outer-Disk Coronae and Dippers.Strong observational evidence ac-cumulated within the last few years in-dicates that, besides an inner-disk corona,many low-mass x-ray binaries have anextensive outer-disk corona. This outer-disk corona is thought to be produced byradiation from the central x-ray sourcethat falls on the accretion disk at a radialdistance of 104 to 105 kilometers and heatsit. Such heating evaporates plasma, form-ing an extensive, hot, optically thick coro-na above and below the disk. X radiationfrom the central source is able to heat thedisk surface over a substantial annulusbecause the disk flares, becominggeometrically thicker at greater distancesfrom the x-ray source.

Because of the geometrical and opticalthickness of the outer disk and the ex-istence of an extensive outer-disk corona,the character of the observed variation inx-ray flux with orbital phase is verysensitive to the tilt of the binary system, asillustrated by the collection of x-ray fluxcurves in Fig. 9. Figure 10 showsschematically how such differences areproduced naturally by differences in ourviewing angle.

If the line of sight is in the orbital planeof the system (Fig. 10, view C), the thickaccretion disk will block any direct view of

Fig. 9. X-ray light curves for five dipperswhose orbital periods range from 0.83 to4.4 hours. The bottom panel is an exam-ple of what is seen when the line of sight isclose to the plane of the disk (view C inFig. 10), whereas the upper panels illus-trate what is seen when our sight line isabove the disk (view B in Fig. 10). Sev-eral of these binaries (see especially4U1323–62) also exhibit x-ray bursts. ➤

16

125 L Dip

15 17 19 21

60

Hours



Fig. 10. Low-mass x-ray binaries havesuch a geometrically thick accretion diskand corona that two different types ofperiodic variat ions in the x-rayflux-eclipses and dips-can occur. Athigh viewing angles (A), the source isseen directly and no flux variations dueto orbital motion occur, However, atsomewhat lower angles (B), relativelycold gas clumps near the outer rim of thedisk periodically swing across the line ofsight, generating absorption dips in theflux. For viewing angles close to the diskplane (C), the source cannot be seendirectly, and only x rays scattered fromthe outer-disk corona are observed. Asthe companion star crosses this line ofsight, an eclipse occurs, hut the corona isso large that the scattered x rays are onlypartially blocked. Absorption dips arealso usually evident in this type of lightcurve. ➤

the x rays from the neutron star. For thisreason there are almost no bright eclipsinglow-mass x-ray binaries. However, some xrays scattered by the outer-disk corona areable to reach us. Even though we arecheated of most of the x rays, the wealth ofinformation they provide compensates fortheir paucity. When the companion passesacross our line of sight we observe aneclipse, but because the companion doesnot cover all the outer-disk corona theeclipse is partial rather than total, that is,the x-ray flux decreases but never reacheszero.

Clumps of relatively cold plasma nearthe outer edge of the thick disk, such as thesplash where the accretion stream fromthe companion hits, can also block the lineof sight. Periodic obscuration by suchgaseous structures causes absorption dips,and sources exhibiting such dips are calleddippers. The clumps are literally imagedby x rays just as bodily structures are inmedical radiography, the varying trans-mission of the x rays revealing the com-plex density structure near the outer rim ofthe disk.


LOW MASS X-RAY BINARY

Corona FlaredDisk

Dip/

When our viewing angle of a low-mass viewing angles (view A), there is little orbinary is just high enough not to be no obscuration, and any variation of the x-blocked by the companion star (view B), ray flux must be due to changes in thewe can usually see the central source of x luminosity of the central source. For ex-rays directly. Thus, there will be no ample, the regular change in the flux fromeclipses, but a highly flared disk may still Sco X-1, probably viewed at an angle of 30result in absorption dips. At even higher degrees from the normal to the disk, is less

17


than 1 percent.4U1822–37 (Fig. 11) is a good example

of a partially eclipsing source. The smoothvariation through the orbital cycle isthought to be due to the varying height ofthe rim of the accretion disk: as we movearound the system, we see more or less ofthe central coronal cloud over the rim.The secondary minimum is thought to bedue to obscuration by a vertically thickerregion produced where the accretionstream from the companion star collideswith the disk.

Several of the dippers shown in Fig. 9exhibit sudden bursts of x rays, supportingthe idea that x-ray bursters (discussed

next) are close, low-mass binaries. Theexceptional transient EXO 0748–676 is anexample of such a system. Not only is it anx-ray burster, but it also exhibits bothabsorption dips and a total x-ray eclipsewith a 3.82-hour period, confirming thatthe period of the absorption dips is indeedthe orbital period. The relative phase be-tween the dips and eclipses puts the fatregion of accretion splash just where itwould be expected on the disk for an accre-tion stream that curves between the twomoving components of the binary. Thesame phase relationship holds for dippersin which optical measurements give thephase of the system: the dips occur just

4U1822–37: A PARTIALLY ECLIPSING SOURCE

SecondaryMinimum

PartialEclipse

14 22Time (hours)

SecondaryMinimum ,

Star

18

before the companion star occults the neu-tron star.

X-Ray Bursts. Until now we havefocused on x-ray variability that has beenfairly gentle, that is, changes in the x-rayflux by, at most, factors of order unity,caused by variable accretion rates, orbitalmotion, or geometric effects. Low-massbinary systems also show sudden, extremebursts in x-ray flux.

One type of x-ray burst, called Type I,has been explained with great success as athermonuclear flash on the surface of theneutron star. The details of such bursts,however, still present some enigmaswhose solutions may tell us much aboutthese binary systems and the structure oftheir neutron stars.

Only one star has been observed toexhibit Type II bursts, which are thoughtto be the result of some type of accretioninstability. Although the nature of the in-stability is unknown, the great regularityof the Type II bursts suggests that somefundamental property of low-massbinaries has yet to be grasped.

Figure 12 shows the hundred-fold in-crease in x-ray flux and the three-fold in-crease in emission temperature typical of a

Fig . 11 . X - ray l i gh t curve fo r4U1822–37, a low-mass binary. Thesecondary minima in the data are mostlikely due to obscuration of the line ofsight to the x-ray source by a thick regionwhere the stream of accreting materialhits the disk; the partial eclipse is causedby blockage of the line of sight by thecompanion star. The fact that the fluxdoes not diminish to zero during theeclipse means that the x rays come from aregion larger than the companion star.Since we know of no way to generate thex-ray energy in such a large region, weinfer that we are seeing x rays scatteredby a large outer-disk corona. As thebinary rotates, more or less of this flux isblocked by the structure of the outer disk



X-RAY BURST DATA FOR 4U1636–53

1 0– 8

o 15 30

Time (s)

F i g . 1 2 , X - r a y b u r s t d a t a f o r4U1636–53, showing the hundred-foldvariation in flux typical of such bursts(top) and the spectral temperature of theemission (middle), These two sets of datacan be used to calculate the radius of thephotosphere of the source (bottom),which, except for the initial rise and fall,remains of the order of 10 km, implyingthat roughly the entire surface of theneutron star is emitting,

Type I burst. During most of the burst, thesize of the radiating area, deduced fromthe flux and temperature, is of the order of10 kilometers, consistent with emissionfrom the entire surface of the neutron star.

The accepted mechanism for Type Ibursts is that newly accreted gas, rich inhydrogen and helium, ignites under condi-tions of high pressure and density andexplodes. Although the details of the proc-

ess are intricate and are still being workedout, we can illustrate the relevant physicsby assuming steady-state accretion and aparticular stellar luminosity, which, inturn, fixes the internal temperature gra-dients (averaged over many bursts).

Fig. 13. The temperature and column-density histories (black) of elements ofaccreting matter being buried deeper anddeeper on the surface of a neutron star

6.6 km). The hydrogen ignition curve isshown in blue; the helium ignition curveis shown in red. If the slope of either ofthese curves is positive (solid lines), burn-ing is stable, This happens because thetemperature and column-density changescaused by the burning keep the element ofmatter from departing significantly fromthe ignition curve. If the slope of the

As a given element of accreted matter isburied deeper in the star by subsequentaccretion, its temperature rises accordingto a predictable curve until eventually thetemperature becomes high enough that thematter ignites (Fig. 13). Depending upon

the opposite happens, and burning is un-stable. Low accretion rates result in un-stable hydrogen burning followed by arise in temperature and a hydrogen-helium explosion. Moderate accretionrates result in either stable hydrogenburning or unstable but bounded hydro-gen burning. High accretion rates causethe helium to ignite first, resulting inunstable burning and a hydrogen-heliumexplosion. Also shown (dashed black) isthe temperature and column-density his-tory of an element of matter accreted atthe maximum rate permitted by the Ed-

ignition curve is negative (dashed lines),

1 09

H-He Explosion

/

TEMPERATURE AND COLUMN-DENSITYHISTORIES OF ACCRETING MATTER

106

I I I I

104

Column Density (g/cm2)



the accretion rate, four outcomes arepossible. At the lowest rates, the hydrogenignites, the burning is unstable, and thetemperature rises until a combined hydro-gen-helium explosion occurs. At mod-erately low rates, the hydrogen burning isunstable but bounded, and only smallflashes are generated that are impercep-tible to distant observers. At moderatelyhigh rates, the hydrogen burning is stable.In the latter two cases, a helium explosionoccurs after the hydrogen is consumed andthe temperature has risen enough to ignitethe heavier element. At high accretionrates, the helium ignites first, and theburning is unbounded, resulting, again, ina combined hydrogen-helium explosion.

The maximum accretion rate is limitedby the fact that the rate of energy release byaccretion cannot exceed the Eddingtonluminosity. At the Eddington luminositythe outward force on the accreting elec-trons due to radiation pressure just equalsthe inward gravitational force on the ions.Above this critical luminosity, matter fall-ing inward that would have been accretedis instead expelled. The radiation pushesmainly on the electrons, whereas gravityacts more strongly on the ions. Thus, theEddington luminosity depends on thecomposition, in terms of the number ofelectrons per unit mass, of the star’s at-mosphere: a composition of helium andheavier elements has a luminosity limitabout 1.75 times that for a solar at-mosphere composition (75 per cent hydro-gen).

These steady-state models introducemany of the ideas thought to be relevant toType I bursts but are not, in fact, in goodagreement with all the data. These modelsexplain well the rise and decay times ofindividual bursts but do not give theproper ratio of time-averaged burst energyto total energy. (Only a few per cent of theaverage luminosity can be due to nuclearburning; most is due to the release of thegravitational energy of the accreted mate-rial.) Relaxing the steady-state assumptionmay resolve this problem. Moreover, anon-steady state is more consistent with

20

evolutionary ideas since the time neededfor the neutron star to come to thermalsteady state is many thousands of years,whereas there is good evidence that themass-accretion rate varies much morerapidly.

For Type I x-ray bursts, the Eddingtonlimit not only sets an upper bound on themass-accretion rate but also constrains themaximum x-ray flux during a burst. Whenthe luminosity of a star whose atmosphereis initially static rises slightly above theEddington limit, the outer layers are ex-pelled and luminous energy is convertedto kinetic energy of the matter being flungoutward. Further increases in totalluminosity impart more energy to theejecta but do not increase the amount ofescaping electromagnetic radiation.

The peak luminosities of Type I x-raybursts show evidence of reaching Ed-dington luminosity saturation and cantherefore be used to infer the surface com-position of the neutron stars and the in-trinsic luminosities of the bursts. Considera neutron star with an atmosphere consist-ing of a hydrogen-rich layer on top of ahelium-rich layer (the product of earlierhydrogen burning). When the luminosityreaches the Eddington limit for the hydro-gen layer, that layer is expelled, pushingthe photosphere to a larger radius (Fig.14). After most of the hydrogen is ex-pelled, the electromagnetic luminosity canrise further to the Eddington limit forhelium. If the total rate of energy outputrises beyond this limit, the excess powerwill cause the helium atmosphere to ex-pand. As the burst wanes, the star radiatesat this upper limit while the radius de-creases to its original value. Finally, theluminosity falls below the helium Ed-dington limit, and the atmosphere returnsto its hydrostatic configuration. This ex-planation is strongly supported by the factthat peak-flux-distribution data show thegap predicted by the 1.75 factor that dis-tinguishes the Eddington limit for a hydro-gen-rich atmosphere from that for ahelium-rich atmosphere.

By assuming that the peak luminosities


of Type I bursts are accurately determinedby the Eddington limits, the observed x-ray flux density has been used to calculatethe distance to these sources. Since x-raybursters, like other galactic-bulge sources,should be distributed symmetrically aboutthe galactic center, their mean distance, socalculated, provides a new, independentmeasure of the scale of our galaxy. Thisanalysis gives the distance to the galacticcenter as 6 to 7 kiloparsecs, as opposed tothe 8 to 9 kiloparsecs derived by oldermethods. Since the scale of our galaxy hasbeen used as the standard ruler for allextragalactic scales, cosmological dis-tances may have been overestimated by 30per cent. Further studies are required toprove that the peak luminosities are gener-ally Eddington, as shown in individualcases by data like those in Fig. 14, and thatthe bursters we see are not biased to ourside of the galaxy.

Type H x-ray bursts, which occur in onex-ray burster that also emits Type I bursts,have a time-averaged power that is toolarge by at least a factor of 25 to be causedby thermonuclear explosions. The time-averaged power in the Type II bursts iscomparable to the total luminosity of thesource. This fact means the bursts mustdraw on nearly all the gravitational energyreleased by the accreting matter (about 10per cent of the rest-mass energy of theaccreted material). These bursts are clearlycaused by an accretion instability.

Figure 15 shows the recently discoveredregularities in the decay curve of Type IIbursts. These regularities may provide thekey to the nature of the instability. Wheneach burst is scaled according to the char-acteristic time for structure in its decay, allbursts are seen to go through the samecycle of rises and falls. Moreover, the char-acteristic time appears to increase withtotal energy output. This type of behavioris reminiscent of a simple mechanical ar-rangement of springs with a spring con-stant that changes from event to event;however, we do not know what cor-responds to the springs in the burster andwhat tightens and loosens them.


TYPE II X-RAY BURSTS

5 s

40

0

Scaled Time

Fig. 15. Observed x-ray intensity curvesfor Type II bursts. Each of these curveshas been normalized to the characteristictime for the rising and falling structurein the decay (note the 5-second indicatorin each curve), showing the similarity ofthe oscillations during the decay. Suchtime histories are reminiscent of a me-chanical arrangement of springs withspring constants that change with totalenergy output. The event depicted by thetop curve has the highest total energyoutput and the longest oscillation period;the event depicted by the bottom curvehas the lowest total energy output and the

Long-Term Periodic Variability

X-ray flux variations due to the orbitalmotion of the two stars in an x-ray binary,such as eclipses, dips, and smooth varia-tions at the orbital period, are expected.Occasionally, however, variations are ob-served that have a period longer than thebasic orbital cycle.

The moderate-mass system Her X-1,with its 35-day variation, is the mostfamous example. Some massive x-raybinaries with bright, young companionstars have similar cycles. In the LargeMagellanic Cloud LMC X-4 shows a 30.5-day cycle that varies in period by no morethan 3 per cent per cycle (top panel of Fig.16). The supergiant systems SMC X-1 (inthe Small Magellanic Cloud) and Cen-taurus X-3 have very sloppy 60- and 130-day cycles—the variation in the period is15 to 20 per cent per cycle. A long-termperiodic variation is also seen in theprobable black hole system Cygnus X-1,whose flux changes by 25 per cent every294 days.

These intriguing periodicities might bedue to precession of the accretion disk orof the spinning neutron star, variations inthe shape of the accretion disk, the pres-ence of a third star in the system, periodicchanges in the wind flowing from the com-panion star, or some combination of these

21


0 120 2 4 0 360 480Days

Disk Precession Neutron-Star Precession

Disk Instability Presence of Third Star

LONG-TERMPERIODIC

VARIABILITYStellar-Wind Variation

(Fig. 16). Study of these variations mayprovide crucial evidence concerning thenature of the binary system. For example,conclusive evidence that the compact ob-ject is processing would rule out the possi-bility that it is a black hole because such anobject would be axisymmetric.

Some neutron stars may have an accre-tion disk with a twisted, tilted pattern thatrotates slowly, periodically blocking the x-ray flux received at earth. One popularexplanation for a tilted disk is that theouter layers of the companion star itself

22

are tilted so that the tug of the neutron starcauses these layers to precess, altering the

direction from which material flows intothe disk. On the other hand, the masstransfer may itself be asymmetric, causingthe disk to tip and thus to precess.

Neutron-star precession causes thecones swept out by the rotating x-raybeams to cycle up and down with respectto the spin axis of the star, which is almostfixed in space. Recent evidence from HerX-1 (see “Her X-1: Another Window onNeutron-Star Stucture”) suggests that the

Fig. 16. The observed periodic long-termvariation of the flux of LMC X-4 (top)and possible causes of such variation inthis and other x-ray binaries. These causesinclude precession of a tilted disk,precession of the neutron star itself, a diskinstability that periodically blocks part ofthe x rays, modulation of the flow of ac-creting matter by the tug of an orbitingthird star, and variation in the stellar wind

neutron star in this system is processingwith a 35-day period, changing the il-lumination of the companion star. Thischanging illumination is thought to pro-duce asymmetric mass flow from the com-panion to the outer rim of the disk, caus-ing the outer rim to be tilted. Precession ofthis tilted outer rim then causes it toperiodically obscure the neutron star, giv-ing rise to the observed 35-day variation inx-ray intensity.

The stars in our galaxy are not onlysingle or double systems; they often are inclose systems of three or more. The reg-ularly changing gravitational tug of a thirdstar moving in a distant eccentric orbitabout a close x-ray binary could modulatethe flow of matter between the inner twostars, producing long-term variability inthe x-ray flux. However, no directevidence has yet been found for the pres-ence of a third star in the systems knownto exhibit long-term periodicity.

The outward flow of material fromsolitary stars with stellar winds clearlywaxes and wanes, with one possible causebeing a solar-type magnetic cycle. In abinary system, such a cycle on the com-panion star might regularly modulate themass flow. A change in the mass-flow ratedirectly changes the x-ray brightness bychanging the rate at which gravitationalenergy is released as matter falls towardthe neutron star. Perversely, though, toomuch flow toward the x-ray source mightactually cloak it, increasing x-ray absorp-tion and causing a net decrease in the x-rayflux seen at the earth.



Time➤

Instabilities in the accretion disk that moving through dense, low-velocity mate-might cause it to fatten periodically andobscure the x rays emitted from the neu-tron star could also result in long-termvariability. A persistent fat disk may haveobscured Her X-1 during a period in 1983and 1984, causing its apparent disap-pearance in x rays (we know the x-raysource remained on because it continuedto heat the near face of its companion, asusual).

Some sources vary over a long timeperiod simply because they take a longtime to travel around a wide orbit. A goodexample is some Be stars with a neutron-star companion in an eccentric orbit (Fig.17). A Be star is a hot young star that isspinning so rapidly that it expels matter,creating a massive wind, a disk of ejectedmaterial around the rotation equator, orboth. The x-ray signature of this type ofbinary system is periodic outbursts thatoccupy only a small part of the cy-cle—presumably that part when the neu-tron star is closest to its companion and is

rial that it can accrete voraciously. Theperiod of the outbursts, which has beenobserved to range from less than 10 daysin some systems to almost 200 days inothers, should thus be the same as theorbital period. This is the case for manysystems, especially those with longperiods, but not for some, such as4U0115+63, which has an outburst periodof about 30 days. In systems in which theperiod of the outbursts differs from theorbital period, cyclical activity of the Bestar may be the dominant effect.

If interaction of a neutron star with anequatorial disk around the Be star is thecause of outbursts, then the neutron star isa splendid probe of the Be star’s mass loss.However, before we can exploit this tool inany particular system, we need to confirmthat we are indeed seeing the orbital periodand not an activity cycle on the Be starthat, because of some underlying clock,periodically expels matter. This may bestbe done with precise timing measurements

Fig. 17. An x-ray binary system consist-ing of a young, hot Be star and a neutronstar in eccentric orbit may show periodicx-ray flares that occur once an orbitwhen the neutron star is closest to the Bestar and its equatorial wind or disk of

as the pulsing neutron star moves aroundits orbit; however, changes in the spin rateof the neutron star driven by the varyingaccretion rate confuse such analyses. Wealso need to understand why the shapesand commencement times of certaingigantic outbursts are not controlledsimply by the orbital motion. Do someevents, for example, the 1973 eruption ofV0332+53 and the 1975 and 1980 erup-tions of A0535+26, simply choke at amaximum flow rate? Or is there a mini-mum acceptable accretion rate such that,near the threshold, a small variation inmass supply switches the source on andoff, whereas, at higher accretion rates, theluminosity vanes smoothly? Most impor-tant, we need to know the physics of theflow of matter from the Be-star disk to theneutron star. It is not yet clear whether adisk forms around the neutron star,whether matter from the Be star accretesdirectly into the neutron star’s magneto-sphere, or whether, as is likely, both occur.

We should also include in long-termvariations certain semi-regular cycles,with periods of 0.5 to 2 years, detected inseveral low-mass x-ray sources, such as thebursters 4U1820-30 and 4U1915–05.These are probably caused by changes inthe rate of mass flow from the companionto the neutron star, with the enhanced rateof mass transfer lasting for 50 to 100 days.The reasons for the enhancement are notwell understood, though analogousbehavior has been seen in close binariesthat contain degenerate dwarfs rather thanneutron stars.

Gamma-Ray Bursters

A bewildering category of violent events

23LOS ALAMOS SCIENCE Spring 1986


that is even more spectacular than the x-ray burst is the gamma-ray burst. Thesources of these events have never beenclearly observed during their quiescentperiods because they are extremely faint inall parts of the electromagnetic spectrum.However, during an outburst, which typi-cally lasts a few seconds, each of thesesources is by far the brightest gamma-raysource in the sky, outshining everythingelse combined, including the sun.

Despite the dramatic nature of gamma-ray bursts, little has been deduced aboutthe characteristics of their sources. Twofeatures in the observed radiation give usclues: one appears to be emission frompositron-electron annihilation that hasbeen gravitationally redshifted; the secondappears to be cyclotron lines from plasmain magnetic fields of the order of 1012 G.Either of these interpretations, if correct, isa strong indication that the sites for thebursts are neutron stars and not, say, blackholes. Beyond this one point, however,there is no general agreement about thenature of the bursts. Current proposalsinclude asteroids falling onto the neutronstar, thermonuclear explosions, and sud-den adjustments in the angular-momen-tum distribution of the neutron star.

Recent simultaneous x-ray and gamma-ray observations of gamma-ray burstshave shown the bursts to be extremelyclean sources of gamma rays. Even thoughother objects produce copious fluxes ofgamma rays, no other object producessuch a high ratio of gamma rays to x rays(Fig. 18). Evidently the radiation fromgamma-ray bursters is extremely non-thermal and does not degrade into manylower-energy photons. This constraintraises strong doubts about many previousassumptions about the nature of gamma-ray burst sources.

For example, it has been assumed thatthe gamma rays are produced by electronslosing most of their energy as synchrotronsradiation, a process that takes only about1 0-15 of a second in a 1012-G magneticfield. However, the spectrum from thisprocess would have too much x radiation

1 0,000

100

100 10,000Photon Energy (keV)

Fig. 18. Spectra of various high-energy 1980. The pulsing sources are the rota-sources showing the relative deficiency of tion-powered pulsar in the Crab Nebulax rays in gamma-ray bursts. The spectra (upper curve) and the accretion-poweredof the black-hole candidates are those of pulsar Vela X-1 (lower curve). The x-rayLMC X-1 when its spectrum is softest burster is XB1724–30 at its hardest. The(upper curve) and of Cyg X-1 when its gamma-ray bursts were recorded (left tospectrum is hardest (lower curve). The right) on May 14, 1972, July 31, 1979,solar flare is one that occurred on June 7, October 16,1981, and January 25,1982.

by at least a factor of 10. Likewise, if, as is considerations suggest that the gammagenerally assumed, the gamma rays are radiation in a burst may be collimatedemitted in all directions from a region near away from the stellar surface. Gamma-raythe stellar surface, the surface would heat bursters remain one of the great unsolvedup and radiate too many x rays. Such mysteries of our time.

24 Spring 1986 LOS ALAMOS SCIENCE


o 2 4 6 8 10 12

Time (thousands of seconds)

Cataclysmic Variables tions. Besides their evolutionary and phe-

The x-ray binaries discussed so far aresuch rare objects (only about two hundredof them exist in our galaxy) that thestatistical distributions of, say, theirperiods, masses, and galactic positions aredifficult to determine. Also, because eventhe closest one is a long way away, they aredifficult to observe at optical and radiowavelengths. Fortunately, we can supple-ment our understanding of neutron-starbinaries in important ways by observingthe more numerous and less distantcataclysmic variables.

These systems are low-mass closebinaries—often x-ray sources them-selves—in which the compact object is adegenerate dwarf rather than a neutronstar. Although the masses of degeneratedwarfs are comparable to those of neutronstars, degenerate dwarfs are much lesscompact—in fact, the gravitational energyrelease per gram of accreting matter is athousand times less than for matter fallingonto a neutron star. Thus, cataclysmicvariables tend to be less luminous. Evenso, many cataclysmic variables will beeasily observed by the high-sensitivity in-struments being built for the XTE andASTRO-C satellites (see “The Next Gen-eration of Satellites”).

Cataclysmic variables exhibit behavioranalogous to the various neutron-starbinaries: there are systems with large mag-netic fields (106 to 107 G) that pulsestrongly, systems that do not pulse, andeven systems with quasiperiodic oscilla-


nomenological similarities to neutron-starsources, cataclysmic variables are interest-ing in their own right as examples of thebehavior of matter under very differentconditions of magnetic field, density, andspat ial dimension. For example,cataclysmic variables show a “periodgap’’ —there are no systems with periodsbetween 2 and 3 hours—a fact that hasbeen attributed to the absence of magneticbraking of the orbital motion once themass of the companion star falls below acritical value. It is not clear whether low-mass neutron-star binaries also show astatistically significant period gap, since sofew such systems are known, but there are,indeed, no observed neutron-star systemswith periods between 2 and 2.9 hours. Incontrast to cataclysmic variables, how-ever, there are also few neutron-star x-raybinaries with periods less than 2 hours.

Strongly magnetic degenerate dwarfsare the analogues of accretion-poweredpulsars: rotation of the degenerate-dwarfstar causes the radiation to sweepperiodically across the observer. One ex-ample is the cataclysmic variable GK Per,observed by EXOSAT during a largebrightening. It has an x-ray flux curve thatlooks much like that of an accretion-pow-ered pulsar (Fig. 19). Even the period of itspulsations, 351 seconds, is within therange of neutron-star sources. However,GK Per and other strongly pulsingcataclysmic variables have simpler x-rayflux curves than their neutron-starcounterparts. The pulse waveform is

ray light curve for the cataclysmicvariable GK Per. The curve is approx-imately a modulated sinusoid with aperiod of 351.341 seconds.

nearly sinusoidal, lacking the high har-monic structure typical of accretion-pow-ered neutron-star pulsars.

This simplicity is a result of the physicalconditions at the degenerate dwarf. Theradiating region is bigger, the plasma thereis less dense, and the emission takes placein a much weaker magnetic field. Thus,the observed radiation beams are duesolely to the shadowing of the emissionregion by the degenerate dwarf itself andnot to the effect of magnetic fields. (Somecataclysmic variables-called AM Herstars—do have magnetic fields of about107 G and show more highly structuredperiodic flux curves that are probably dueto anisotropic absorption and emission inthe magnetized plasma.)

Quasiperiodic oscillations, just dis-covered in bright neutron-star binaries(see “Quasipenodic Oscillations”), havelong been seen in the visible light fromcataclysmic variables (Fig. 20) and haveeven been seen in the x-ray flux from someof these sources. The oscillations observedin cataclysmic variables span a muchwider range of frequencies, exhibit verydifferent coherence times, and show awider variety of frequency-intensity rela-tions than do those observed in neutron-star binaries. As a result, interpretation ofthese oscillations is difficult, and no con-vincing explanation for them has yetemerged. Indeed, the different types ofoscillations observed probably have dif-ferent origins.

Comparison of quasiperiodic oscillat-ions in neutron-star and degenerate-dwarf systems may help to shed light onthe mechanisms at work, since the twotypes of systems provide different infor-mation. For example, analysis of oscilla-tions in the visible light from cataclysmicvariables is complicated because visible

25


light represents only a small fraction of theenergy output of the system (most appearsas ultraviolet radiation). Moreover, thevisible light comes partly from conversioninto light of x rays falling on the disk andpartly from radiation of heat generatedinside the disk by shear. Thus, the visiblelight is not a good indicator of the accre-tion rate. In contrast, the x radiation fromneutron-star sources is produced near theneutron star, is the dominant form ofemission from the system, and is a goodindicator of the accretion rate.

On the other hand, the visible light fromsome cataclysmic variables shows bothquasiperiodic oscillations and periodicpulsations at the rotation frequency of thedegenerate dwarf (Fig. 20). Thus, the studyof cataclysmic variables may offer a test ofthe beat-frequency model in whichquasiperiodic oscillations are attributed tothe difference between the rotation fre-quencies of accreting matter in the innerdisk and the rotation frequency of the star.Clear evidence of the rotation frequency ofthe underlying star in the bright neutron-star x-ray binaries that show quasiperiodicoscillations has yet to be seen.

Black Holes

Are the compact objects in x-raybinaries all neutron stars and degeneratedwarfs or could some of them be blackholes? The search for black holes in ourgalaxy has been disappointing. During thelast ten years there has been a successionof black-hole candidates, most of whichturned out to be strongly magnetic neu-tron stars, as eventually shown by thediscovery of periodic pulsations. More re-cently, the source V0332+53, whichshowed the rapid flickering long thoughtto be a reliable signature of a black hole,was discovered to be a 4-second accretion-powered pulsar. Evidently, such flickeringis a feature of neutron-star x-ray binariesas well. Though x-ray observations havenot proved definitive, they can direct ustoward black-hole candidates. For exam-ple, several candidates show, at least part

26

Periodic

\

RandomFlickering

I II

OPTICAL POWER-DENSITYSPECTRUM FOR AE Aqr

Quasiperiodic

—

0.04 0.08Frequency (Hz)

Fig. 20. Power-density spectrum of the and smaller peaks at lower frequenciesoptical emission from the cataclysmic that represent concentrations of quasi-variable AE Aqr showing narrow spikes periodic power. The power density at verythat represent the first two harmonics of low frequencies varies greatly and arisesthe degenerate-dwarf rotation frequency from random flickering of the source.

of the time, an ultra-soft x-ray spectrumnot seen in other objects. So far, the meas-urement of the masses of compact objects,using optical techniques, is the only re-liable diagnostic for black holes (withreasonable assumptions, three solarmasses is the theoretical maximum massfor a neutron star).

Currently, Cygnus X-1 and A0620–O0are the only strong black-hole candidatesin our galaxy: GX0339—4 is a more ques-tionable one. The best candidate for ablack hole at present is LMC X-3, a sourcein the Large Magellanic Cloud.

Active Galactic Nuclei. In contrast tothe paucity of stellar-mass black holes,supermassive black holes are thought to bethe engines powering most or all activegalactic nuclei and quasars. X-ray andgamma-ray variability provide one of thefew ways to probe the central regions ofthese objects. Interpreting the variability

is much more difficult, however, becausethese systems are much less well under-stood.

Over 108 to 109 years an active galacticnucleus can radiate energy equivalent to arest mass of 107 or more solar masses inthe form of beams and clouds of rel-ativistic particles. Even if energy con-version is very efficient, the mass of theengine driving this process is expected tobe of the order of 108 solar masses.

One characteristic time scale for thevariability of emission produced by mat-ter swirling into a black hole is the time ittakes light to travel across the innermoststable orbit—about 103 seconds times themass of the black hole in units of 108 solarmasses. If energy was generated by anyother mechanism, the region emitting xrays would necessarily be much larger andsuch rapid variations might be unex-pected. Figure 21 shows variations of thex-ray luminosity from the galaxy NGC


Fig. 21. The x-ray light curve for theactive nucleus of the galaxy NGC 6814showing fluctuations that vary rapidlyenough to suggest that a black hole is the

6814. Large fluctuations appear within afew hundred seconds, suggestive of thepresence of a large black hole.

The instruments to be placed aboardASTRO-C and XTE will be better able tomeasure variability and thus more fullyelucidate the nature of the energy sourcesin active galactic nuclei. In addition, XTEwill be able to measure the spectra of hardx rays up to 200 keV. These measure-ments will help clarify the nature of therelativistic plasma in the central regions of

active galactic nuclei and the emissionmechanisms operating there. This workwill complement planned research at otherfrequencies, such as the radio-wave inter-ferometry studies (using the Very LargeBaseline Array) of the angular structureand variability of these systems.

Remaining Puzzles

The progress discussed here is en-couraging, but there is no shortage of prob-lems for XTE and ASTRO-C to tackle.The increased sensitivity, rate of data ac-quisition, extended spectral coverage, all-sky monitoring capability, and flexibilityof the instruments aboard these spacecraftare essential for solving numerous un-answered questions. Here are a few.

What is the internal structure and tem-perature distribution of a neutron star?

Just how fast are the reversals of thetorque in accretion-powered pulsars suchas Vela X-1, and what do the reversals tellus about the accretion flow?

How do the spins and magnetic fields ofthe neutron stars in low-mass binary sys-tems evolve? Are these neutron stars theprogenitors of millisecond rotation-pow-ered pulsars?

Since the brightest galactic-bulgesources have no known binary periods. are


x

o 4 0 0 800

Time (s)

they really binaries?What is the cause of the quasiperiodic

oscillations in bright bulge sources? Dothese neutron stars have magnetospheres?

Will a non-steady-state approach to theaccretion of matter onto a neutron starexplain the ratio of the mean luminosity ofType I x-ray bursts to the total luminosityof the sources? What fundamental prop-erty of low-mass binaries is yet to be re-vealed by the remarkable scaling behaviorof Type II bursts?

What causes the periodic long-termvariations seen in a variety of galactic x-

ray sources? Are any of the modelsproposed so far correct?

Is free precession common among neu-tron-star x-ray sources? If so, what drivesit and how?

What is the nature of the gamma-raybursters? Do they have companions? Doesaccretion play a role?

What is the range of degenerate-dwarfmagnetic fields in cataclysmic variables?What role does magnetic braking play inthe evolution of such systems?

Where are the black holes of stellarmass?

What mechanisms are responsible forthe x-ray and gamma-ray emission fromactive galactic nuclei and quasars?

Discovery in this field has hardlypaused for twenty-three years. New instru-ments will sample many more sourceswhile allowing us to study known sourcesin much closer detail. There is everypromise that studies of time variabilitywill further elucidate the nature of cosmicx-ray sources. Most exciting will be thediscoveries we cannot anticipate but canonly expect. ■

Support for the workshop was provided byNASA and IGPP (Institute, for Geophysicsand Planetary Physics). Grant support forFrederick Lamb was provided by NASA,NSF, and the John Simon GuggenheimMemorial Foundation.

27

New Analysis Techniques

New Analysis Techniquesc oupled with the new satellites (see

“The Next Generation of Satel-lites”), new analysis techniques will

help reveal the underlying astrophysics inever greater detail. Recently, for example,new methods of data handling havesubstantially improved the precision withwhich the orbits of pulsars in binary sys-tems can be determined. As discussed inthe section entitled “Pulse Timing” in themain text, precise determination of theorbit yields valuable information aboutkey astrophysical questions, such as themasses of the pulsar and its companion,

rate of the neutron star.The large-area x-ray detectors on the

next generation of satellites will providevery high counting rates (20,000 countsper second from bright sources) and makepossible microsecond time resolution.This will greatly reduce fluctuations in themeasured pulse shape caused by photonstatistics and the imprecision in arrivaltimes introduced by the finite time resolu-tion of the detectors.

New analysis methods in which thepulse waveform is filtered have substan-tially reduced the uncertainty in pulse-

the internal structure of the companion, arrival times caused by pulse-shape varia-and the evolution of the system.

The principal method used to deter-mine the orbit of a pulsar relies on measur-ing the changes in the arrival times at earthof pulses emitted by the pulsar as it movesaround its orbit (Fig. 3 of the main text).The precision of such measurements islimited by fluctuations in the measuredpulse shape caused by photon-countingnoise and variations in the emission proc-ess, by the limited time resolution of thedetectors, and by fluctuations in the spin

tions associated with the emission process.In a recent study of the accretion-poweredpulsar Vela X-1, for example, filtering in-creased the precision of pulse-arrivaltimes by a factor of two—equivalent to anincrease in the area of the x-ray detector bya factor of four.

As the precision of pulse-arrival times isincreased—by enlarging the detector areaand filtering the pulse waveform—arrival-time variations caused by fluctuations inthe rotation rate of the neutron star be-

28

come more apparent (figurc). These spin-rate fluctuations can then be studied bet-ter, providing valuable tests of our under-standing of neutron stars (see “InternalDynamics of Neutron Stars”).

For sources with unknown orbits, newalgorithms will be needed to search effi-ciently for periodic and quasiperiodic os-cillations in the x-ray flux. This is becausethe power in such oscillations is spreadover a range of frequencies by the Dopplershift associated with the orbital motion ofthe source, making the oscillations dif-ficult to detect. Thus, to find oscillationsefficiently, new search algorithms must bedeveloped that can quickly and system-atically remove the effects of orbital mo-tion for a wide variety of possible orbits.

New analysis techniques are alsoneeded to uncover the origins of the largebut erratic (aperiodic) variability seen inmany compact x-ray sources. For exam-ple, fresh insights into the physical causesof this variability may be gained by apply-ing the techniques recently developed toanalyze nonlinear dynamical phenomenaand chaos. ■

Schematic angular-acceleration power-density spectrum P.(f), showing the con-tributions made by spin-rate fluctuationsand measurement noise. Here f is the analy-sis frequency. This example illustrates howa reduction in measurement noise can re-veal a physically important peak in thespectrum of neutron-star spin-rate fluctua-tions. Measurement noise—caused by, say,the random nature of photon counting inthe detectors—can be reduced by increasingthe area of the detector or by using morepowerful analysis methods, such aswaveform filtering. Any such reduction un-covers more information about intrinsicfluctuations in the spin rate of the star andthus reveals more about their physicalcause.

log fSpring 1986 LOS ALAMOS SCIENCE

Internal Dynamics of Neutron Stars

Internal Dvnamics of Neutron StarsThe central element of many binary

x-ray sources is a neutron star. Ad-vances in the theory of dense mat-

ter, spurred by precise measurements ofchanges in spin rates of both rotation-powered and accretion-powered pulsars(see, for example, the section entitled“High-Mass X-Ray Binaries” in the maintext) has made it possible to build detailedmodels describing the properties of thesestars. The latest work has led to a dramaticreversal of earlier views.

Theory

From theoretical considerations, neu-tron stars are thought to consist of severaldistinct regions (Fig, 1). Immediatelybelow the surface. the matter consists of asolid lattice of more or less ordinaryatomic nuclei. As one moves inward tohigher densities, however, the protons inthe nuclei capture electrons to form neu-tron-rich nuclei. Above a certain criticaldensity (about 4 x 1011 grams per cubiccentimeter), called the neutron drip point..it is energetically favorable for some neu-trons to be outside nuclei. At these densi-ties the lattice of nuclei is therefore inter-penetrated by neutrons, which are be-

Fig. 1. The outer crust of a neutron starconsists of a solid lattice of nucleiembedded in a sea of relativistic degenerateelectrons. The surface of the crust may besolid or liquid, depending on the tempera-ture and the strength of the surface magnet-ic field. The inner crust is a solid lattice ofnuclei embedded in a sea of superfluid neu-trons and relativistic electrons. The core islargely a superfluid neutron liquid with aslight admixture of degenerate electronsand superfluid protons. In heavier starsthere may also be a distinct inner core thatconsists of a pion condensate or perhaps aquark soup. Character is t ic d imen-sions are shown. ➤

lieved to be superfluid. At still higher den-sities (above about 2.4 X 1014 grams percubic centimeter—a lithe below normalnuclear density) the nuclei dissolve com-pletely, leaving a dilute plasma of elec-

trons and superfluid protons in the denseneutron liquid of the core.

In a rotating neutron star the neutronand proton superfluids are expected tobehave differently. In both the inner crustand the core the neutron superfluid isthought to rotate by forming arrays ofmicroscopic vortices. These arrays tend torotate at the same speed as the core. In theinner crust i t may be energet ical lyfavorable for the neutron vortices to passthrough the nuclei of the solid lattice. Ifthis arrangement is sufficiently favorable.the array of vortices will remain fixed inthe lattice and will not be able to adjust tochanges in the rotation rate of the cure. Inthis case the vortices arc said to be pinnedto the lattice. If the rotational dise-quilibrium becomes large enough, the con-stant jiggling of the vortices will causesome to jump from one nucleus to an-other. This process

Surface

As the rotational disequilibrium builds up,the dynamical forces on a vortex line mayexceed the pinning force, causing it tosuddenly unpin and move closer to itsequilibrium position.

Unlike the neutron superfluid. theproton superfluid is affected by mag-netic flux. The magnetic flux in thissuperfluid is confined to microscopicflux tubes around which proton currentscirculate, These flux tubes are muchmore numerous than the vortices thatform due to fluid rotation.

How these various components of aneutron star couple is not well understood,but such coupling determines how the starresponds to changes in the rotation rate ofthe crust. The coupling of the electron andproton fluids in the core to each other andto the solid lattice is thought to be rel-atively strong, so that one of these compo-nents responds to changes in the rotationrates of the others within hundreds ofseconds, depending on the rotation rate ofthe star and whether a strong magneticfield threads the crust and the core. On theother hand, a long-standing view; has been

NEUTRON-STAR STRUCTURE



that the neutron superfluid in the core isonly weakly coupled to the rest of the star,taking days to years to respond to changesin the rotation rate of the crust. To theextent that this is true, a neutron star canbe idealized as consisting of just two com-ponents: the crust plus electron and protonfluids in the core, and the neutron super-fluid in the core. This idealization hashistorically been called the two-componentmodel. Recent theoretical work and ob-servational data, which we will discussshortly, has caused astrophysicists to dra-matically revise this model.

Imagine forces on the neutron star crustthat cause changes in its spin rate (see thesection entitled “Pulse Timing” in themain text). Whether the forces are externalor internal, whether the crust slows downor speeds up, the stellar interior musteventually adjust. This adjustment can bestudied by monitoring the behavior ofpulsars after the occurrence of suddenchanges in the crust rotation rate. In somerotation-powered pulsars, isolated, rel-atively large jumps in the rotation rate,called macroglitches, have been observed.In both rotation- and accretion-poweredpulsars, relatively small fluctuations in therotation rate have also been seen. Thestatistical properties of these relativelysmall fluctuations have been modeled suc-cessfully as a series of frequent, smalljumps in the rotation rate called micro-glitches (microglitches are thought to betoo small to be seen individually withcurrent instruments). The sizes and ratesof occurrence of these glitches and thebehavior of the rotation rate followingthem provide tests of models describingthe dynamical properties of neutron stars.

Twelve macroglitches have been ob-served. The largest have occurred in theVela pulsar (six events) and in three otherrotation-powered pulsars (one eventeach). The smallest macroglitches wereone-thousandth the size of the largest Velamacroglitch and occurred in the famouspulsar in the Crab Nebula (two events)and in another rotation-powered pulsarcalled 0525+21. No isolated events like

30

these have been seen in accretion-poweredpulsars.

Disturbing Results

For a decade, the model used to explain

the behavior of the star following a macro-glitch was the two-component model. Thismodel attributes the slowness of the ob-served recovery of the crust rotation rate,which takes days to months, to the rel-atively small torque exerted on the crustby the weakly coupled neutron superfluidin the core.

The two-component model appeared toexplain the initial data on the post-macro-glitch behavior of both the Vela and Crabpulsars. Although model parameters de-rived from fits to the data were differentfor the two stars, the parameters were ap-proximately the same for macroglitchcs inthe same star. However, recent detailedanalyses of new observations of macro-glitches have revealed complex post-glitchbehavior not adequately explained by thismodel.

Further troubling evidence wasprovided by a detailed study of micro-glitches in the Crab pulsar. Like itsresponse to macroglitches, a star’sresponse to microglitches can be used toprobe its internal dynamical properties.This is because the microglitches, whichcan be described as a random noise proc-

ess, disturb the crust-superfluid systemand may be considered an input noisesignal applied to this system. The outputnoise signal, represented by changes in therotation rate of the crust, is the input noiseas filtered by the crust-superfluid system.In other words, the observed power at theanalysis frequency f is given by

Pobs(f) = F(f) Pin(f),

where Pin(f) is the power-density spectrum(Fourier transform) of the forces disturb-ing the crust, F(f) is the power-transferfunction, which reflects the dynamicalproperties of the neutron star, and Pobs(f)is the observed power-density spectrum offluctuations in the rotation rate of thecrust.

Compared to the response times of thesystem, input forces are expected to bespiky, delta-function-like disturbances.The power-density spectrum of the fluc-tuating input forces is then a power-law

analysis frequencies of interest. In fact,one can make Pin(f) a constant (a= O) bychoosing to work with the power-densityspectrum of the fluctuations in the rightvariable (which may be the phase, angularvelocity, or angular acceleration of thecrust). The shape of the key function F(f) isthen given directly by Pobs(f). The shape ofF(f) can be used to distinguish betweenneutron-star models, for example, be-



tween a rigid-star model, in which thecoupling between the crust and the core isstrong, and the two-component model, inwhich the coupling is weak (Fig. 2). Inparticular, if a power-density spectrum ofthe fluctuations in the appropriatevariable is flat, this indicates that the starrotates as a rigid body, or, if not, that anyinternal components are completely de-coupled, for disturbances at the analysisfrequencies observed.

Unfortunately, at high frequenciesnoise produced by measurement errorsdominates (see the figure in “New Analy-sis Techniques”), making it difficult to tellwhether or not the spectrum remains flat.At low frequencies the spectrum obviouslycannot be extended to time scales longerthan the observing time. Thus, data from agiven experiment can constrain the mo-ments of inertia of components withcoupling times only in a certain range.Moreover, power-density estimatesalways have some uncertainty. Thus, evenif the observed spectrum appears to be flat,only an upper bound can be placed on theinertia of components with coupling timesin the range studied.

A recent analysis of optical timing dataon the Crab pulsar showed that the spec-trum of micro-fluctuations in angular ac-celeration is relatively flat over more thantwo decades in frequency. This result in-dicates that the neutron star is respondingto microglitches approximately like a rigidbody: for a coupling time of 10 days, nomore than 70 per cent of the star’s mo-ment of inertia can be weakly coupled.These values are sharply inconsistent withthe older values derived from fits of thetwo-component model to macroglitches.These older values implied that 95 percent of the star’s inertia is coupled to thecrust with a coupling time of about 10days. Thus, the two-component modelcannot be an adequate description of thefull dynamical properties of this neutronstar.

Analysis of relatively small-scale fluc-tuations in the rotation rates of accretion-powered pulsars also shows no evidence of


THEORETICALPOWER-TRANSFER FUNCTIONS

log f

Two-ComponentModel with

Internal ResonantVibration

Two-Component

Rigid Star

weakly coupled components. The mostcomplete power-density spectrum is thatrecently obtained for Vela X-1 (see Fig. 5bin the main text), which covers periodsfrom 0.25 to 2600 days. This spectrumimplies that, for coupling times in therange of 1 to 30 days, no more than 85 percent of the moment of inertia of the starcan be weakly coupled.

New Ideas

The inability of the two-componentmodel to account for the response of theCrab pulsar to both macroglitches and

Fig. 2. Logarithmic plots of theoreticalpower-transfer functions F(f) for three dis-tinct neutron-star models: a rigid star(dashed line), a two-component model(dotted line), and a two-component modelin which the vortex array in the superfluidneutron core can be set vibrating (solidline). The shape of the power-transfer func-tion depends on the coupling of the crust tothe other components of the neutron starand therefore provides information on thenature of the star’s interior.

microglitches and the absence of evidencefor any weakly coupled component in themicroglitch data from the Crab pulsar andVela X-1 have stimulated theorists to re-examine the view that coupling between

31


the crust and the neutron superfluid in thecore is weak. They found that a previouslyoverlooked quantum liquid effect may ac-count for the inability to detect a weaklycoupled component.

As discussed above, the neutron super-fluid in the core is expectcd to rotate byforming arrays of vortices, whereas theproton superfluid in the core is expectcd torotate uniformly. Even though the neu-trons are superfluid, their motion dragssome protons around each neutron vortex.generating a proton supercurrent. (Be-cause the drag coefficient is negative, theproton current actually circulates in thedirection opposite to the neutron current.)At the very high proton densities in thecore, this induced proton supercurrentgenerates a magnetic field of 1015 gauss (G)near each neutron vortex (even though themean field in the star generated by thiseffect is only 10–7/P G, where P is therotation period in seconds). Because ofthis strong magnetization, the magneticfields threading the neutron vortices scat-ter electrons very cffectively. causing astrong coupling between the core neutronsand electrons. The resulting short couplingtime between the crust and the superfluidneutrons in the core (of the order of 400 Pseconds) rules out gradual spin-up of theseneutrons as the explanation of the longpost-macroglitch relaxation times in theCrab and Vela pulsars.

If these theoretical results are correct.the only remaining candidate for a weaklycoupled component is the neutron super-fluid in the inner crust, where there is noproton fluid and the neutron vortices arctherefore unmagnetized. But the momentof inertia of this component is expected tobe only about 10 -2 that of the rest of thestar. Thus, a neutron star in which onlythis component is weakly coupled wouldbehave almost like a rigid body. consistentwith the previously puzzling observationsof the Crab pulsar and Vela X-1.

What then is the explanation of themacroglitches and the long post-glitch re-laxation. which first suggested the idea ofweak coupling between the crust and the

32

core of neutron stars? One possibilitybuilds on the fact that the neutron vorticesin the inner crust arc expectcd to bcpinned to the lattice of nuclei there. Amacroglitch could be a sudden unpinningand movement of many vortices. causinga rapid transfer of angular momentumfrom the superfluid to the rest of the starand a jump upward of the rotation rate ofthe crust. If the neutron vortices in theinner crust are dynamically coupled to thecrust by vortex creep, then the long relaxa-tion could be explained as the response ofthis creep process to the macroglitch. Thismodel differs from the two-componentmodel in important ways. Only the neu-tron superfluid in the inner crust is in-volved and the superfluid response is fun-damentally nonlinear, unlike the linearresponse given by the frictional couplingof the two-component model.

With relatively few parameters thevortex-unpinning model can explain thepost-macroglitch behavior in the Crab andVela pulsars as well as that in 0525+21.Because post-macroglitch relaxation isthermally activated in this model andhence the relaxation time is proportionalto the internal temperature of the star, thistemperature can be estimated from post-glitch timing observations.

Now if a neutron star is nearly rigid (thetheoretical results described above implythat only one per cent of a neutron star isloosely coupled to its crust), the interpreta-

tion of the large pulse-frequency varia-tions seen in accretion-powered pulsarsbecomes much simpler. Because internaltorques can have only a small effect, anysubstantial fluctuations in the rotation fre-quency of the crust must be due to varia-tions in the external accretion torque, thatis, must be due to fluctuations in thetorque exerted on the star by materialfalling onto it.

T h e t h e o r e t i c a l a r g u m e n t s s e e mpersuasive, but it is important to keep inmind that so far we have only a verymodest amount of observational evi-dence. Although analyses of about twodozen rotation-powered pulsars are inprogress. detailed microglitch power-den-sity spectra have been published for onlyone rotation-powered and two accrction-powered pulsars, These spectra only ex-clude weakly coupled components withmoments of inertia greater than 70 to 85per cent of the star as a whole, for couplingtimes in the range of 2 to 20 days. Detect-ion of a weakly coupled component with amoment of inertia as small as that ex-pected on the basis of theory (about 1 percent of that of the star) appears out ofreach currcntly, but the upper bounds onthe size of any weakly coupled componentcan be reduced substantially by more ex-tensive observations using the large-areadetectors planned for the near future (see“The Next Generationa of Satellites”).Moreover, measurements of a larger num-ber of pulsars are essential before wc canbe sure that our conclusions about neutronstars are not based on atypical examples.And, of course, there is always the possi-bility of yet another surprise. ■


Her X-1

Her X-1: AnotherWindow on Neutron-Star Structureo fall the x-ray binaries, none shows

a more complex pattern of regularvariability than Hercules X-1 (Her

X-l). In this system, as in many others, alow-mass normal star transfers mass to aneutron star via a thin accretion disk.What makes Her X-1 so curious is itsvariability, which exhibits no less thanthree concurrent periodicities.

The general picture has been knownsince the first extensive observations weremade by the x-ray astronomy satelliteUhuru over a decade ago. The fastest pe-riodic variation is a stable 1.24-secondpulsation. Two effects related to the rota-tion of the star probably play a role inproducing this pulsation. First, becauseaccreting matter funnels down the stellarmagnetic field lines toward the magneticpoles. the emitted x rays are preferentiallybeamed in certain directions. The star’srotation sweeps these beams past us every1.24 seconds in a manner analogous to theway the light from a lighthouse seems topulse as the lamp assembly rotates. Sec-ond, because the orientation of themagnetic field with respect to the diskchanges as the star rotates, the inward flowof mass, and hence the luminosity of thestar, is likely to vary at the rotation fre-quency.

The pair of stars in the Her X-1 binaryorbit each other with a 1.7-day period.This motion also modulates the x rays atearth by periodically obscuring them onceper orbit when the neutron star is eclipsedby its companion.

The most interesting cycle is the 35-dayone. The source follows a slightly irregularpattern in which it is bright for about 9days and then relatively dim for about 26days (figure). For years the most popular

explanation for this 35-day cycle has beenperiodic obscuration by a tilted, twisted,and processing accretion disk. However,the cause of the tilt and precession has notbeen well understood. One popular expla-nation, that the companion star is process-ing (see the section entitled “Long-TermPeriodic Variables” in the main article),has been questioned because the requiredprecession of the fluid companion star hasyet to be modeled successfully.

New studies by the EXOSAT satellite,reported at the Taos workshop, stronglysupport an alternative suggestion. In thisstudy Her X-1 was monitored for hun-dreds of hours and approximately thirtytimes more x rays were recorded than inall previous studies put together. As aresult, the pulse shape and its variationwith the 35-day cycle were measured withunprecedented accuracy. These observa-tions indicate that the neutron star itself isprocessing with a 35-day period.

The neutron star is expected to havetwo x-ray beams emanating from the twomagnetic poles. If the neutron star doesnot precess, then the orientation of thesebeams relative to the rotation axis doesnot change, and the observed pulse patternis constant. However, if the neutron starprecesses, the magnetic poles, and hencethe beams, drift with respect to the rota-tion axis, causing the corresponding peaksto appear or disappear from the observedpulse waveform.

The EXOSAT data indicate such a driftin Her X-1. During the bright phase of the35-day cycle, we see a main peak at phase0.3 coming from the pole that swingsalmost directly toward us. Six-tenths of asecond later at phase 0.8, we see a hint of apeak from the edge of the opposite pole.

(a) Changes in the x-ray flux from Her X-1(averaged over its 1.24-second pulse period)during one-and-a-half periods of the 35-day cycle. The bright state (red) lasts about9 days. Midway between the bright peaksthere is a smaller rise in intensity for sev-eral days (blue). (b) During the bright peak(red), the hard (1 to 30 keV) x rays showone large pulse every 1.24 seconds, reveal-ing the neutron star’s rotation. During thesmaller, dim peak (blue), a second hard x-ray peak occurs half a cycle later. This isevidence that the neutron star has precessedso that both magnetic poles sweep into view.

X-RAY FLUX FOR HER X-1

o 20 40Days


Quasiperiodic Oscillations

During the dim phase of the cycle, thereare two almost equal peaks in the pulsepattern. In this case, it is thought that themagnetic poles have precessed so thatboth swing equally near us during the 1.24-second rotation. Neithercomes as close asthe pole producing the main peak didearlier, so neither resulting peak is as largeas the main peak during the bright phase.

Precession of the neutron star alsocauses the pattern of x-ray flux falling onthe near side of the companion star to varywith the 35-day period. This variation inthe illumination of the companion starmay introduce an asymmetry in thestream of material leaving the companion,causing the accretion disk to be tilted.Such a tilt leads naturally to precession ofthe outer rim, resulting in periodic ob-scuration of the x rays from the neutronstar.

The idea that the neutron star in HerX-1 might be processing has major im-plications for two key aspects of neutron-star structure. First, it would imply thatthe super-fluid vortices in the inner crust(see “Internal Dynamics of NeutronStars”) are unpinned; otherwise, theirgyroscopic motion would cause the star toprecess far too rapidly. Second, it wouldindicate that the neutron star has a thickcrust; otherwise, the star would not besufficiently rigid to maintain its oblatenessand hence could not precess fast enough.Detailed measurements of the 35-day cy-cle thus give us new insight into one of themost hidden parts of our universe-theintenor ofa neutron star. ■

34

QuasiperiodicOscillationsI n the spring of 1985, the phenomenon

of Quasiperiodic oscillations was dis-covered by EXOSAT in the bright ga-

lactic-bulge sources GX 5-1, Cygnus X-2(Cyg X-2), and Scorpius X-1 (Sco X-l).Such oscillations have now been lookedfor in more than a dozen other galactic-bulge sources, and four more exampleshave been found. Quasiperiodic oscilla-tions are revealed in a power-density spec-trum as a broad peak covering many fre-quencies rather than a sharp spike at onefrequency. Moreover, in the bulge sourcesthe position of this broad peak is seen tovary with time. and the changes seem to becorrelated with changes in the source in-tensity.

For example, GX 5-1 has a broad peakin its a~cragcd power-density spectrawhose central frequency systematically in-creases from 20 to 36 Hz as the sourceintensity increases from 2400 to 3400counts per second (Fig. 1 ). The peaks inCyg X-2 and Sco X-1 change in frequencyfrom 28 to 45 Hz and from 6 to 24 Hz,respectively.

All the GX 5-1 and most of the CygX-2 data for 1- to 18-kcV x-ray photonsshow a strong positive correlation be-tween the peak frequency and the sourceintensity. In Sco X-1 the oscillation fre-quency, at t imes, shows a strongpositive correlation with the intensity ofthe 5- to 18-keV photons but, at othertimes, exhibits a weak rzegaliw correla-tion (Fig. 2). Whether the oscillations inSco X-1 have the same origin as those inGX 5-1 and Cyg X-2 is not yet clear.

A variety of physical mechanisms havebeen discussed for the Quasiperiodic os-cillations in these bright galactic-bulgesources, but, at the moment, the heat-frequetzc} model appears the most promis-ing. If this model is correct, theQuasiperiodic oscillation frequency is a

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measure of the difference between therotation frequency of the neutron star andthe orbital frequencies of the plasma in theinner disk.

The model assumes that a c/umpedplasma is accreting from an accretion diskonto a weakly magnetic neutron star. Suchclumping can be caused by magnetic,thermal, or shear instabilities. Onceformed, clumps drift radially inward andare stripped of plasma by interaction withthe magnetospheric field. Plasma strippedfrom the clump is quickly brought intocoronation with the neutron star and fallsto the stellar surface, where it produces xrays.

Inhomogeneities in the stellar magneticfield cause the rate at which plasma isstripped to vary with time, which, in turn,changes the intensity of the x-ray cmis-sion. Unless the stellar magnetic field isaxisymmetric, aligned with the rotationaxes of the disk and star, and centered inthe star, the interaction of’ a given plasma:Iump in the disk with the magnetosphereis greater at some stellar azimuths than atothers. Because the clumps of plasma andthe magnetosphere arc rotating at different ifrequencies, the strength of the magnetic iheld seen by a given clump will vary at thebeat frequency or one of its harmonics.:ausing the x-ray emission to vary at the$ame frequency,

A simple version of the beat-frequencymodel predicts power-density spectra thatme very similar to the spectra observed for3X 5-1 and Cyg X-2 (Fig. 3), The theorydso predicts that changes in accretion rate;hould cause a shift in beat frequencyJim ilar to that actually observed for these.WO bright galactic-bulge sources (Fig. lb),Moreover, the neutron-star rotation rateabout 100 Hz) and magnetic field strengthabout 109 G) inferred from the beat-fre-luency model are consistent with previ-

Spnng 1986 LOS ALAMOS SCIENCE

ous theories that binary systems like GX5-1 and Cyg X-2, when disrupted, producethe observed millisecond rotation-pow-ered pulsars.

The most direct evidence in favor of thebeat-frequency model would be detectionof weak x-ray pulsations at the predictedspin rate. Though several sources havebeen examined carefully and pulsationssmaller than 1 per cent would have beenobserved, regular pulsations in the sourcesthat exhibit Quasiperiodic oscillations areyet to be seen. One explanation for theabsence of strong pulsations is that themagnetic fields of these neutron stars aretoo weak (less than 107 G) to channel theaccretion flow onto the magnetic poles.This, however, does not agree with thestrength of 109 G inferred from the beat-frequency model, which is large enough toproduce some channeling and x-ray beam-ing.

In the context of the beat-frequencymodel, there are three distinct physicaleffects that could prevent observation ofpulsations at the rotation frequency of thestar. Radiation pressure within the mag-netosphere could be supporting the accret-ing plasma, causing it to settle over a largefraction of the star’s surface. Evidence forthis effect comes from analyses of the hardx-ray components, which yield emittingareas comparable to the star’s surface area.The resulting broad x-ray beam wouldproduce only weak modulation and thenat relatively high harmonics of the rota-tion frequency. Any modulation might befurther weakened by bending of thephoton paths in the strong gravitationalfield of the neutron star.

Fig. 1. (a) The Quasiperiodic oscillations ofGX 5-1 are seen as a broad peak inaveraged power-density spectra that shiftsfrom 20 to 36 HZ as the intensity of thesource increases. (b) A strong positive cor-relation exists between the centroid fre-quency of the Quasiperiodic oscillations andsource intensity. The dashed line is thebehavior predicted by the beat-frequencymodel. ➤


(a)

Quasiperiodic Oscillations

QUASIPERIODIC OSCILLATIONS OF GX 5-1

ShiftHigh Intensity

o 20 40 60 80 10Frequency (Hz)

2400 2800 3200X-Ray Counts/s

35

Quasiperiodic C)scillations

The second efTcct has to do with thethick central corona that may be surround-ing each bright galactic-bulge source. Anal-yses of the x-ray spectra indicate that thesecoronae may have dimensions on the or-der of 100 kilometers (about 10 neutron-star radii) and electron-scattering opticaldepths on the order of 10, which shoulddrastically reduce the modulation due tox-ray beaming. In contrast, Quasiperiodicoscillations produced according to thebeat-frequency model would not be af-fected if the mean time for photons topropagate through the corona is less than

Fig. 2. Power-density contours for Sco X-1as a function of time and frequency withhigh power in red, medium power in yellow,and low power in blue. The curve at the leftis x-ray intensity as a function of time andshows flaring episodes (bottom) followed bjran extended low-intensity state (top). Theregions of concentrated color are the 6-Hz

the oscillation period. (’calculations for atypical system show that pulsations at the1OO-HZ rotation frequency arc stronglysuppressed. whereas the amplitude of’Quasiperiodic oscillations at 30 Hz is unaf~fected and is therefore equal to the mod-ulation in the accretion rate.

Finally, there is evidence that the innerand outer parts of the disks of bright galac-tic-bulge sources are both geometricallyand optically thick. Such disks would pre-vent us from seeing x-rays that comedirectly from the neutron star cxccpt whenour line of sight is close to the star’s rota-

POWER DENSITY CONTOURS FOR SCO X-1

oscillations present during the extendedlow-intensity state. Power is spread over therange of 14 to 24 HZ between jlares and atthe start of the extended low-intensity state(horizontal clusters of blue circles). Thegap in the data occurred when the detectorwas shut off for fear the intensity of theflare might damage the detectors. V

2000 5000 8000 0 10 20 30

Intensity (counts/s) Frequency (Hz)36

tion axis. X rays cmerging near the rota-tion axis would. at most, be only weaklymodulated.

W o r k currcn t] y u n de rway o nQuasiperiodic oscillations in galactic-bulgesources has benefited from previous workon th is phenomenon in ca tac lysmicvariables, In turn, the new observationsand theoretical work may,, when scaledappropriately, help us understand the os-c i l l a t i o n s o b s e r v e d i n some of thecataclysmic variables. ■

I o r—-- ‘-----–--—---------–OBSERVED GX 5 1

SPECT”RUMI

IL___

\\ THEORETICAL\\ \ SPECTRA

5,-~m50532

L__J0.01 1 100

Frequency (Hz)AFig. 3. An observedpower-density spectrumfor GX 5-1 (top panel) compared to twotheoretical power-density spectra (bottompanel) calculated for the beat-frequencymodel using diflerentparameter values. Be-cause the low-frequency behavior of the twocalculated spectra differ markedly, futureobservations should be able to constrain thevalues of the model parameters.


WORKSHOP PARTICIPANTS

Jonathan Arons (University of California, Berkeley)Paul Boynton (University of Washington) “Pulse Timing Analysis”Hale Bradt (Massachusetts Institute of Technology)Lynn Cominsky (University of California, Berkeley)France Cordova (Los Alamos National Laboratory)John Deeter (University of Washington)Richard Epstein (Los Alamos National Laboratory) “Gamma-Ray Bursts”Doyle Evans (Los Alamos National Laboratory)Paul Gorenstein (Harvard-Smithsonian Center for Astrophysics)Josh Grindlay (Harvard-Smithsonian Center for Astrophysics) “Other Variability”Gunther Hasinger (Max Planck Institute for Extraterrestrial Physics, Garching bei Munchen)

“Quasiperiodic Oscillations”David Helfand (Columbia University)Steve Holt (NASA-Goddard Space Flight Center)James Imamura (Los Alamos National Laboratory)Hajime Inoue (Institute of Space and Astronautical Science) “X-Ray Bursters”Richard Kelley (NASA-Goddard Space Flight Center)Richard Klein (Lawrence Livermore National Laboratory)Julian Krolik (Johns Hopkins University)Donald Lamb (Harvard-Smithsonian Center for Astrophysics)

“X-Ray Bursts and CV Time Variability”Frederick Lamb (University of Illinois) “Quasiperiodic Oscillations, ” “Pulse-Timing Theory”Frank Marshall (NASA-Goddard Space Flight Center)Keith Mason (Mullard Space Science Laboratory, University College, London)Richard McCray (University of Colorado)Peter Meszaros (Pennsylvania State University)John Middleditch (Los Alamos National Laboratory) “Quasiperiodic Oscillations”Kazuo Makishima (Institute of Space and Astronautical Science) “Galactic Bulge Sources”Sigenori Miyamoto (Osaka University)Jacobus Patterson (West Georgia College)William Priedhorsky (Los Alamos National Laboratory) “Long-Term Variability”Saul Rappaport (Massachusetts Institute of Technology) “X-Ray Binaries”Richard Rothschild (University of California. San Diego)Frederick Seward (Harvard-Smithsonian Astrophysical Observatory)Jacob Shaham (Columbia University)Noriaki Shibazaki (University of Illinois)Luigi Stella (European Space Operations Center)Jean Swank (NASA-Goddard Space Flight Center) “XTE Scientific Capabilities”Ronald Taam (Dearborn Observatory)Yasuo Tanaka (Institute of Space and Astronautical Science) “ASTRO-C Scientific Capabilities”Allyn Tennant (University of Cambridge) “Active Galactic Nuclei”Joachim Trumper (Max Planck Institute for Extraterrestrial Physics, Garching bei Munchen)

“Her X-1”Ian Tuohy (Mt. Stromlo and Siding Springs Observatory)Michiel van der Klis (European Space Agency, ESTEC, the Netherlands)

“Quasiperiodic Oscillations”Jan van Paradijs (University of Amsterdam) “Quasiperiodic Oscillations”Michael Watson (University of Leicester) “EXOSAT Observations, Cataclysmic Variable Systems”Martin Weisskopf (NASA-Marshall Space Flight Center)

“Searches for Periodic and Aperiodic Variability”Nicholas White (European Space Operations Center) “EXOSAT Results, X-Ray Binaries”Kent Wood (U. S. Naval Research Laboratory) “Fast Timing Experiments”

Richard I. EpsteinLos Alamos National Laboratory

Frederick K. Lamb, University of Illinois andVisiting Scholar, Stanford University

William C. PriedhorskyLos Alamos National Laboratory

37Spring 1986 LOS ALAMOS SCIENCE

x-ray astronomy and sco x-1

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