The magnetic field of 4U 0115+63

Melanie Pfeuffersupervised by Prof. Dr. Jorn Wilms, Dr. Karl Remeis-Sternwarte,

astronomical institute of the University Erlangen-Nurnberg(Dated: April 11, 2007)

In this project the RXTE observations of an outburst of the binary X-ray pulsar 4U 0115+63,having taken place in 2004 September– October, are analyzed with respect to luminosity-dependentcyclotron resonance energies and compared to an former outburst in 1999 March–April. It can beshown that both outbursts are subject to the same behavior relating to all considered characteristics.

I. INTRODUCTION

Extraordinary importance has been attached to thestudy of the magnetic field of neutron stars. Since themagnetic flux is conserved during the collapse of theevolved progenitor star of the neutron star and the mag-netic field strength is proportional to

B ∝ R−3 (1)

a rough estimate leads to B-field strengths from 1012 Gup to 1014 G, which surpass the strongest magnetic fieldsobtained on earth a million times. Due to many obser-vations and examinations it is known that these B-fieldscannot decay spontaneously without external influencies[1]. Though this is not valid for neutron stars in bi-nary systems, where low magnetic fields have been ob-served in many systems. The reason therefore Geppertand Urpin (1994) suggested is accretion. Supposing ahigh enough accretion rate and further a long enoughaccretion phase, the neutron star is heated by the ac-cretion which yields to a decreasing conductivity of theneutron star. Thus it follows that the magnetic field isalso decreasing. Nevertheless there are also quite a fewneutron stars in binary systems with an enormously highB-field in the range given above. This simply means thatthese neutron stars are too young in comparison to thetime scale of magnetic field decay due to accretion, whichdirect one’s attention to the accretion process in orderto gain the time dependence of the B-field [1]. One ofthe methods of accurately measuring the present B-fieldsis analyzing the cyclotron resonance scattering features(CRSFs) in X-ray spectra since the line energy E0 ofthe fundamental CRSF is related to the magnetic fieldstrength of the neutron star as

E0 ∼ 11.57keV ·B12, (2)

whereas B12 is the magnetic field in units of 1012G. Therelation (2) is known as ’12-B-12 rule’ and after takinggravitational redshift into account can be used to calcu-late magnetic field strengths [1].

In this project I consider a neutron star in a transientBe/X-ray binary system (see IV): the X-ray source 4U0115+63 with 3.6 s pulsations [3] is an accreting X-raypulsar, whose distance is estimated to 7 kpc. The com-panion is a 09e star V635 Cassiopeiae with an orbital

period of 24.3 days [3, 4]. Its CRSF were first discov-ered (1979) at ∼ 20 keV by Wheaton et al. (1979) in theHEAO-1 A4 spectra and later an additional CRSF wasnoted at ∼ 12 keV during the analysis of data from thelower energy HEAO 1/A-2 experiment by White (1979).Furthermore, Heindl et al. (1999) found for the first timein any pulsar a third harmonic feature in the HEXTEdata of the outburst of 4U 0115+63 and were able toshow that the line spacing between the fundamental andsecond harmonic as well as between the second and thirdharmonics are not equal and further not multiples of thefundamental line energy. Because of these earlier out-bursts, the X-ray-spectrum of 4U 0115+63 was analyzedfor several times and thus is one of the most suitableobjects for studying the physics of cyclotron resonancein the polar caps of binary X-ray pulsars. Nakajimaet al. (2006) reported on the luminosity-dependence ofCRSFs, which was also discovered in the outburst in1999 using RXTE data. These authors confirmed thatthe cyclotron resonance energy of 4U 0115+63 increasesas the X-ray luminosity decreases, which might be a re-sult of a decrease in the accretion column height. In thisproject, RXTE data of 4U 0115+63 covering an outburstin 2004 September–October are analyzed. The main taskis once more to consider the resonance energy as contin-uous function of the luminosity. Hence one is able todecide whether the behavior of CRSFs in dependence ofluminosity and thus accretion is the same compared withthe former outburst in 1999 and so due to physical effectsor whether a hysteresis effect can be detected.

The outline of the project is as follows: First a short in-sight in the scientific instruments, namely High EnergyX-Ray Timing Experiment (HEXTE) and the Propor-tional Counter Array (PCA), aboard the Rossi X-RayTiming Explorer (RXTE) the observations of the out-burst were made with, is given. After that a rough insightin the topic of spectral fitting is given. Before attend-ing to the basic theory of CRSFs in Sect. V the reasonsas well as the mechanism of accretion are summarized.Then in Sect. VII C 1 I show that the behavior of theCRSFs during the outburst 2004 equals that one dur-ing the outburst in 1999 with respect to all consideredcharacteristics.

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II. OBSERVATION WITH RXTE

Observations were made in both in the project con-sidered outbursts (1999, 2004) with the ProportionalCounter Array (PCA) and High-Energy X-ray TimingExperiment (HEXTE) on board RXTE.

FIG. 1: RXTE spacecraft viewed from above. The five PCAproportional counters and the two HEXTE clusters A and Bare shown, whereas on the front side the ASM lies [7]

A. Instrument description

The Rossi X-ray Timing Explorer (RXTE) is a satel-lite, which was launched in 1995 December 30 by a DeltaII rocket from the Kennedy Space Flight Center into alow earth orbit (LEO) with 580 km altitude and 23◦ in-clination. Its orbital period is about 90 Minutes. RXTEwas named after the astrophysicist Bruno B. Rossi, whoworked in the field of solar X-ray emission [1]. RXTEcontains three scientific instruments (see Fig. 1), namely

• the Proportional Counter Array (PCA; [8])

• the High Energy X-Ray Timing Experiment(HEXTE; [7])

• the All Sky Monitor (ASM; [9]).

Since many events like the outburst of transient X-raypulsars cannot be predicted up to now, the ASM isof enormous advantage. It consists of three scanningshadow cameras (SSCs), which are independent. Eachof the cameras has a field of view of 90◦ × 6◦ and staysin the same position for ninety seconds and then moves

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51220 51230 51240 51250 51260 51270 51280 51290

301511511510

AS

M C

ount

Rat

e [c

ount

s/s]

MJD

1999 February 1999 March 1999 April

March 3

April 20

FIG. 2: RXTE/ASM light curve of 4U 0115+63 covering itsoutburst in 1999. The arrows indicate the first and the lastspectrum observed with PCA and HEXTE (data from [10]).

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31150115011501

AS

M C

ount

Rat

e [c

ount

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2004 August 2004 September 2004 October

Sept. 6Oct. 2

FIG. 3: RXTE/ASM light curve of 4U 0115+63 during itsoutburst in 2004. The arrows indicate the five with PCA andHEXTE observed spectra (data from [10]).

to a new position. Therefore ∼ 80% of the complete skyis scanned once a day. The ASM monitors the ∼ 100brightest sources in the sky in the energy range from 2to 12 keV. Whenever the ASM detects something un-usual or of otherwise great importance (e.g. the out-burst of 4U 0115+63 in 1999 March, see its lightcurvein Fig. 2), it is possible to abort the current observa-tion and point the satellite to the interesting positionin less than one hour, since RXTE’s high slewing speedof ∼ 6◦/minute. The only exceptions are areas next tothe sun, since these endanger the instruments, which forexample Fig. 3 shows during almost the whole August.Then in the week August 27 – September 2 the intensitysuddenly rose to ∼ 65mCrab and in the following weekup to ∼ 190mCrab so that one could be sure to observean outburst. Consequently it was decided to take five ac-curate measurements of the radiation of 4U 0115+63 (thefirst one taking place in September 6, also see Fig. 3).

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TABLE I:RXTE observations of 4U 0115+63 in the 2004 September–October outburst

PCA HEXTE

Date (2004) PCU No. Exposure (ks) Exposure (ks)

Sept 6 0, 2 1.60 0.83

Sept 14 0, 1, 2, 3 0.59 0.75

Sept 22 0, 2 16.8 13.6

Sept 24 0, 2 3.49 2.26

Oct 2 0, 2, 3, 4 3.44 2.32

For such pointed observations are the two other scientificinstruments responsible. In order to obtain the detectionof the energy range as broad as possible, in RXTE from2 keV to over 200 keV, PCA is sensitive at lower ener-gies (2–60 keV), while HEXTE is in charge of radiationat higher energies (15–250 keV).

The PCA consists of five xenon proportional countersunits, called PCUs. Its total effective area is ∼ 6000 cm2

if all PCUs are operating. Since soon two of the fivePCUs, later followed by the other three, showed im-proper behavior including breakdowns, they were peri-odically switched off in order to let them rest. So itis common practice to use just a few of the five PCUsfor observations. Thus during the detection of the out-burst of 4U 0115+63 in 1999 only in eleven out of 34PCA observations on different days all PCUs were op-erating simultaneously [3]. Table I shows the observingPCAs during the 2004 outburst of 4U 0115+63. Aftervoltage changing in 1999, also in order to extend the life-time, the PCA has now a nominal energy range from 2to 100 keV. However the useful energy range is between2 keV and 30 keV, because on the one hand the XenonK edge at 34.6 keV reduces the effective area strongly,while on the other hand the response matrix for ener-gies in the range above the the Xenon K edge is not wellunderstood, although the effective area has increased upto 1000 cm2 again. Fig. 4 illustrates the efficiency ofboth of the instruments PCA and HEXTE. The XenonK edge can be seen very well. Also one recognizes thatabove 20 keV HEXTE is the more appropriate instru-ment. The HEXTE consists of two independent arraysof detectors, cluster A and B. Each of them contains fourNaI(Tl)/CsI(Na) phoswich scintillation counters, sensi-tive in an energy range of 15− 250 keV. All eight detec-tors are coaligned on source to gain together a 1◦ FWHMfield of view and a total net open area of ∼ 1600 cm2 [7].However early in the mission one of the four detectorsof clusters B failed, so the effective area of cluster B isreduced by ∼ 25%. One task to solve was the high back-ground of the detectors compared to PCA. Therefore themethod of Source Beam Switching is used and thus analmost real-time estimate of the background is possible.The HEXTE cluster rocking subsystem changes the ori-entation of the cluster between on- and off-source posi-

10 100

10−

30.

010.

11

1010

010

00

Effe

ctiv

e A

rea

(cm

2 )

Energy (keV)

pcaresp.rmf hxt.rsp

Total efficiency

pfeuffer 23−Mar−2007 11:16

FIG. 4: The two graphs show for the effective area (cm2)versus energy (keV) of the two instruments, PCA (black) andHEXTE (red). The data are obtained by the PHA files of anobservation of 4U 0115+63 in 2004-09-14.

tion every 32 s. Since the rocking axes of the cluster Aand B are adjusted orthogonal to each other, four back-ground regions are available. In order to interpret theshape of the effective area of HEXTE in dependence ofthe energy (once more see Fig. 4) one has to know thatat lower than 20 keV photoelectric absorption takes placein the housing above the detector, whereas at higher en-ergies finite NaI(Tl) thickness yields reduction of the ef-fective area. Interesting are also the sharp drops around30, 60, 100 and 110 keV. So for example that one near30 keV is due to the change in photoelectric cross sectionat the K edge of iodine.

Considering the effective areas of both instrumentsPCA and HEXTE and taking only the ranges with higheffective areas I have chosen to use PCA data in the en-ergy range from 4 keV up to 20 keV and HEXTE data inthe range 20–60 keV for analysis of the spectra.

Moreover one big problem every kind of satellites butespecially X-ray satellites are confronted with are the ra-diation and particle belts around the earth. Thus RXTEis in general lucky to be launched into LEO and there-fore far below the radiation belts in the altitude of about1000 km, called ’van Allen belts’ resulting from the spe-cific configuration of the magnetic field. However therestill remains one position in the south Atlantic south-east off the coast of Brazil, known as the South AtlanticAnomaly (SAA, see Fig. 5), where the configuration ofthe magnetic field of the Earth distinguishes. While highenergy particles usually cannot leave the van Allen belts,due to a dent in the magnetosphere above this area theycan enter this zone. Thus in order to protect the detec-tors from the very intense particle background the RXTEhas even to be shut off during its passing through theSAA-zone. Furthermore after the satellite has left the

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SAA the 25 minute half-life radioactive decay of 128I re-sults in an exponential decrease of additional backgroundradiation, which is evident for about half of its orbit [1, 7].

FIG. 5: South Atlantic Anomaly (SAA) in the south Atlanticsoutheast off the coast of Brazil (from [1])

III. SPECTRAL FITTING AND XSPEC

A. The basics of spectral fitting

Life would be easy if the detectors of RXTE are ableto supply people on earth with the real spectrum of thesource. However, this isn’t possible as it requires anunequivocal identification between each single energy ofthe incoming radiation and detector channel. Instead wehave to take for a fix photon energy the probability foreach channel to detect this photon into consideration.Therefore one introduces the function

R(I, E) (3)

called instrumental response, which is as mentionedabove proportional to the probability that an incomingphoton will be detected in channel I. Of course the in-strumental response (3) is tried to be found out accu-rately before missions in laboratories, but at the latestproblems arise if some detector devices have failed dur-ing mission or parameters are changed to values, thathave not been tested before (as the voltage change in thePCUs of the PCA).

Then the detector counts in dependence of each chan-nel I, C(I), is obtained by integration of the spectrum ofthe source f(E) weighed with the instrumental responseR(I, E) over all energies:

C(I) =∫ ∞

0

f(E)R(I, E)dE (4)

Mathematically, knowing C(I) and R(I, E), an inversionof equation (4) yields the wished spectrum f(E). Un-fortunately the problem is not unique in general. Thusone has to go the other way round: Suggest a model forthe spectrum f(E, p1, p2, . . .), which is usually dependenton several parameters p1, p2, . . ., and calculate due to (4)a predicted count spectrum Cp(I). Then compare it toC(I) and test whether the model ”fits” the data. In or-der to judge the goodness of a fit, usually χ2 is used asfit statistics:

χ2 =∑

(C(I)− Cp(I))2/σ(I)2, (5)

where σ(I) is the error for channel I, estimated by√C(I). After varying the parameters one obtains a best

fit due to (5). These parameters are called best fit para-meters and consequently its model best fit model. Theχ2 statistics provides a generally accepted goodness-of-fit criterion for a given number of degrees of freedomν, which is equal to the difference between the numberof channels and the number of model parameters. Onewants the reduced χ2

red,

χ2red = χ2/ν ∼ 1. (6)

So a reduced χ2 much greater than 1 shows that the fitisn’t good enough, while a reduced χ2 much smaller than1 is a sign for overestimated errors of the data [11].

B. A short description of spectral fitting withXSPEC

XSPEC is a command-driven, interactive X-rayspectral-fitting program (for a more detailed descriptionsee [11]). The software was developed with the additionalconstraint to be completely detector-independent. Thechallenge was to provide an algorithm finding the best fitparameters in a short time as possible. For the searchof the best fit parameters the Levenberg-Marquardt-algorithm (see [12]) is used, which solves minimizationproblems. It combines the Newton-Gauß-algorithm witha regulation technique that forces the function, which hasto be minimized, to decrease in each step. Thus the pro-cedure converges even with worse starting parameters incomparison to the Newton-Gauß-algorithm, but insteadconvergence speed decreases. However, having reacheda local minimum once, there is absolutely no chance toreach the global minimum. Hence one has to estimatethe starting parameters in the surrounding of the globalminimum in order to get the global minimum, which isassumed to yield the correct scientific parameters.

IV. ACCRETION IN X-RAY BINARIES

A. Accretion

As it is generally known the energy source of a neutronsource is accretion, which is by the way the most effi-cient way (at least for neutron stars) to gain energy froma particle with a certain mass. For this the companionin the binary is of big importance. Having two stars ina binary with masses M1,M2 each of them contributesa gravitational potential to the total potential, knownas Roche potential in a co-rotating frame of reference,whereas the stars are considered as point masses. Thisyields 5 Lagrange points (see in Fig.6 L1–L5) and theinmost equipotential surface encompassing both stars,called Roche surface, in which all gravitational forces nul-lify. Thus whenever material of the companion crosses

5

the Roche surface it can be accreted by the neutron staror expelled into interstellar medium. Due to the releaseof potential energy accretion of material with mass mtherefore results in an energy gain ∆Eacc of

∆Eacc =GMm

RNS= ηmc2, (7)

with η = GMRNSc2 . M designs the neutron star mass

and RNS is its radius. Taking typical values, M =1.4M¯, RNS = 10 km, leads to η = 0.2. Therefore theenergy release for the accretion of one electron is calcu-lated as 100 keV. So energy of this order at the surfaceof the neutron star is converted into radiation (X-rays)or it is used to heat the surrounding material.

In principal there are three methods the optical com-panion can donate material to the neutron star, whichare introduced in the following.

• Roche Lobe OverflowDue to stellar evolution the optical companion willexpand and once exceed its Roche volume (seeagain Fig. 6). As already discussed above, thenthe mass outside of the Roche surface isn’t bound tothe companion any more and thus can be accretedby the neutron star. However, the angular momen-tum of the material is too big for the possibility toaccrete the material directly. Instead, an accretiondisk forms. In this disk collisions take place anda part of the material escapes while the other partlooses step by step its angular momentum such thatit moves further inwards. Consequently, the densityin the disk grows with decreasing radius. Frictiondue to viscosity on the one hand supports the lossof angular moment and thus the movement inwards

FIG. 6: In the Fig. (from [1]) are shown the equipotentialsurfaces of the Roche potential. Of special interest is theRoche surface, the inmost equipotential surface encompassingboth stars.

FIG. 7: A neutron star in an eccentric orbit around a Bestar. 4U 0115+63 belongs to the transient Be/X-ray binaries,in which X-ray outbursts only can be observed after the ac-cretion disk of the neutron stars has filled by mass transferduring periastron passages. Otherwise luminosity is too lowto be observed. Figure from [1].

and on the other hand yields high temperatures inthe inner parts of the disk.

• Be Mechanism

Before explaining the accretion mechanism of Bebinaries it is reasonable to give a short insight inthe development of Be/X-ray binaries, especiallysince 4U 0115+63, which is of main interest in thisproject, belongs to these binaries.

Be/X-ray binaries are the result of the evolution ofa binary system of two B-stars, whereas the result-ing neutron star has been the more massive starinitially. First the progenitor of the neutron stardonates mass by Roche Lobe Overflow (cf. IV A)onto its companion due to hydrogen-shell-burning,which is resulting in a helium star orbiting a Be-star. Since the transferred material also inhabitsangular momentum, the angular momentum is alsotransfered and consequently the companion rotatesfaster, it is spun up. This, by the way, is assumed tobe the reason for the formation of a decretion torusaround the companion. Then again the helium-star transfers mass onto its companion, due to asimilar process, namely helium-shell-burning untilit undergoes a supernova explosion finally. Loos-ing mass and experiencing a velocity kick duringthe supernova explosion can lead to wide eccentricorbits (see in Fig.7)[13].

Due to these wide orbits the neutron stars in aBe binary are not able to accrete material fromtheir companions, whenever they are far away fromthe Be-star. Accretion only takes place when theneutron star approaches periastron and enters thedecretion torus around the Be-star (illustrated inFig.7). Once the accretion disk of the neutron starhas filled during the passage, material is accretedonto the neutron star, the released energy is con-verted at least partly to X-rays and thus an X-ray

6

FIG. 8: Accretion from the companion onto the compact ob-ject (neutron star) via stellar winds. It can be seen clearlyhow deep the object is embedded in the wind. In Be/X-raybinaries this accretion method becomes important outside theperiastron. Figure from [1].

outburst can be observed. Having left the decretiontorus again, mass transfer is aborted. For a shorttime the accretion disk is able to sustain accretiononto the neutron star but soon the luminosity willdecrease and stay at a very low level until the nextperiastron passage. Thus outbursts arise in suchsystems due to their orbital period.However, one can imagine systems, called transientsources, which are so dim outside periastrom, suchthat they are hardly observable. One prominentexample is once again 4U 0115+63. In some cases itcan even happen that though a periastron passagehas taken place, no X-ray outburst can be observed.The reason for this behavior is assumed to be thatthe Be-star has lost its torus, and consequently isunable to transfer mass onto the passing neutronstar.

• Stellar WindSince all stars have weak stellar winds, the thirdmethod for accretion remains for discussion: ac-cretion via stellar wind. In case of O or B starsbeing the optical companions the stellar wind canbe very intense. Knowing the fact that a neutronstar usually passes its companion with a distanceof less than one stellar radius (measured from sur-face to surface), it is obvious that the neutron staris really embedded in the stellar wind (see Fig. 8).In Be/X-ray binaries this accretion method is alsoattached importance, since outside periastron masstransfer can be obtained by stellar wind and thusremain observable.

Assuming accretion as single energy source the energygain depends only on the amount of accreted material

FIG. 9: One hat to distinguish between low (right) and high(left) accretion rates onto neutron stars: while at low ac-cretion rates the infalling plasma simply falls onto the sur-face, at high accretion rates the plasma is deccelerated oreven stopped due to photon-electron interactions as well asCoulomb-forces (electrons-protons). Figure out of [1]

per time, M . However, once a certain intensity of re-sulting radiation is reached, one can no longer ignore thepressure of the outgoing radiation since Thomson scat-tering becomes more and more important for the elec-trons. Although due to the low cross section Thomsonscattering for protons is still negligible, the protons stayat the electrons because of Coulomb forces. With in-creasing luminosity the radiation pushes more and moreagainst the infalling material and a shock front is form-ing (see Fig. 9). At a certain luminosity, the EddingtonLuminosity the impact of the radiation pressure and thegravitational forces are in equilibrium and the followingequation is valid:

GMmp =LσT

4πc(8)

Ledd = 4πGMmpcσT (9)

≈ 1.3× 1038 M

M¯ergs−1, (10)

whereas mp is the proton mass (mp À me). However, inthe ansatz above (8) a spherically symmetric accretionwas assumed. With the accretion taking place only in afraction f of the whole surface, the maximum luminosityis also reduced to f · Ledd. But this relation is againnot valid if the accretion area gets too small. Then theradiation is able to escape sideways and thus the pressureon the infalling material is reduced. Therefore the fluxeven can be Super-Eddington locally.

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B. Accretion geometry

Since we know that in binary systems a procedure ofmass transfer exists and that first this material is de-posed to the accretion disk and then accreted, we canhave a more detailed look on the mechanism of accre-tion. Here the fact becomes important that the neutronstar is not only a very compact object, but also exhibitsa strong magnetic field. Thus mass that’s going to beaccreted, not simply falls onto the neutron star surface,after having lost its angular momentum due to friction.Instead, it is influenced in the vicinity of the neutron starby the magnetic pressure Pmag, which can be stated asat a radius r:

Pmag =µ2

8πr6, (11)

where µ is the magnetic moment and the magnetic fieldgeometry of the neutron star is assumed to be equal todipole geometry with

B ∼ µ

r3. (12)

At a certain radius, the Alfven radius rm or also knownas magnetospheric radius (see Fig. 10), the magneticpressure and the ram pressure of the infalling materialwill be equal [1]:

µ2

8πr6m

=(2GM)1/2M

4πr5/2m

(13)

Using (13) one can calculate the Alfven radius for a typ-ical neutron star:

rm = 2.9× 108M1/71 R

−2/76 L

−2/737 µ

4/730 cm (14)

Mass at this radius is forced to follow the magnetic fieldlines and thus it is accreted onto one of the poles of theneutron star and therefore an accretion column arises.

However, today one is not sure about the geometry ofthe accretion column, whether it is a hollow or a ”solid”cylinder. Moreover its structure depends on the accretionrate, what is discussed later (in section VI).

V. CRSF FORMATION

The best way to obtain information about the geome-try of the accretion column is the analysis of CyclotronResonance Scattering Features (CRSF). The CRSFs areabsorption features in X-ray spectra of accreting neutronstars that arise due to high magnetic field strengths ofthe order B ∼ 1011−1013 Gauss. There is a lot of litera-ture concerning the physics of charged particles in mag-netic fields (e.g. , Harding and Lai, 2006) and thus onlythe most important relations are presented afterwards.Due to quantum mechanics the motion of the electrons(e.g. , Landau and Lifshitz, 1977) perpendicular to the

FIG. 10: At the Alfven radius rm the magnetic field gets sostrong, such that the material of the accretion disk has tofollow the magnetic field lines. Figure from [1].

magnetic field is quantized. Thus the energy of a freeelectron with the momentum p‖ is quantized in Landaulevels and can be obtained by solving the Dirac Equation(e.g. , Johnson and Lippmann, 1949):

En = mec2

√1 + (

p‖mec

)2 + 2nB

Bcrit, (15)

where n is an positive integer number and Bcrit =(m2c3)/(e~) is the critical magnetic field strength. Arelativistic treatment yields Landau levels that are notequidistant. Furthermore the angle between the mag-netic field and the path of photon θ is of importance:

En =mec

2

sin2θ(√

1 + 2nB

Bcritsin2θ − 1) (16)

Due to the energy gain by accretion, photons arise fromthe X-ray emitting region interact with the electrons.The quantization of the electron energies results in thephoton absorption of discrete energies that raises theelectrons exactly from into a higher Landau level. Inthe case of B ¿ Bcrit using Taylor expansion of (15)the energy difference Ecyc, that turn out to be equallyspaced, between two Landau levels can be calculated:

Ecyc =~eBme

(17)

Inserting the constants in (17) leads to the popular ’12-B-12 rule’ (see (2)) which is an important result since itconnects the fundamental cyclotron line energy with thestrength of the magnetic field of the neutron star.

The location of the line forming region is unknown butassumed to be close to the surface of the neutron star,since high magnetic field strengths are required. Thusgravitational redshift has to be considered, which is atthe neutron star surface approximately

z =1√

1− 2GMRc2

− 1 (18)

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Taking typical neutron star parameters again, a redshiftof z ∼ 0.3 is derived [17].

As one knows from observational studies, the sec-ond harmonic is generally deeper than the fundamentalline. Furthermore, the profile of the fundamental line isclearly non-Gaussian, but sometimes features like emis-sion wings occur. Schoenherr et al. (2007) developed aconvolution model to simulate the fundamental line independence of different parameters like the optical depthand temperature and compared it to results from obser-vational data analysis [17].

VI. CYCLOTRON EMISSION INDEPENDENCE OF ACCRETION

As it was shown in Sect. V in eqs. (15),(17) the cy-clotron line energies depend directly on the magneticfield. Since the magnetic field strength is changing withthe distance between the electrons and the neutron star(NS) according to (12), the cyclotron line energy E inthe approximation of B ¿ Bcrit depends on the heighthr of the line forming region as E ∼ (RNS +hr)−3(1+z),where RNS is the radius of the NS and z the gravita-tional redshift (18). Neglecting the radius dependence ofz, the relation between E and the cyclotron line energyE0, obtained directly on the NS surface, can be stated as(E/E0)−1/3 = 1 + hr/RNS. Consequently one obtains

hr

RNS= (

E

E0)−1/3 − 1. (19)

Thus knowing E from spectral analyzing and an esti-mate of E0 yields the relative height of the line formingregion. Of course, the height of the this region also de-pends on the amount of plasma being accreted per time.So again the point is reached, where one has to distin-guish the case in which the plasma directly falls on thesurface of the NS (sub-Eddington accretion) and whenthe local Eddington rate exceeds a certain value inter-actions between the emerging radiation and the infallingplasma can not be neglected any more (super-Eddingtonaccretion). Here the decisive parameter that already wasdiscussed in IV A is the local Eddington luminosity givenby (see [18])

LE =2πGMcmp

σT(σT

σm)θ2

c ' 1036erg/s(σT

σm)(

θc

0.1)2,

(20)where M is the NS mass (again assumed to be 1.4M¯in the numerical estimation, σm is the photon-electronscattering crosssection in the magnetic field, σT is theThomson crosssection and θc represents the half-openingangle of the polar cap magnetic field lines. Since Staubertet al. (2007) suggested transient pulsars (as 4U 0115+63)to have evidence for a transition from super- to sub-Eddington accretion these different accretion regimes areof extraordinary interest for this project. The aim of thefollowing two sections is to introduce simple models for

the accretion procedure for each of the two cases thatyield relationships between the altitude of the line form-ing region and the luminosity. Since the luminosity L canbe calculated by means of the measured flux accordingto

L = flux · 4πR2, (21)

where R is the distance between the observer and theNS (in case of 4U 0115+63 approximately 7 kpc), it ispossible to compare the theoretical models to observeddata.

A. Sub-Eddington accretion

A low-luminosity accretion model was introduced byNelson et al. (1993). It is assumed that the accretionbeam enters the atmosphere at free fall velocity, suchthat the kinetic energy is given by the release of poten-tial energy according to (7). The atmosphere is mod-eled as an electron-proton plasma with a magnetic fieldin the z − direction. Thus the accreting ions enteringthe atmosphere are interacting with the plasma and loseenergy to atmospheric electrons via magnetic Coulombcollisions and exciting the plasma to plasma oscillations.However, one must also consider the impact of the mag-netic field. As it is shown in [18] the primary effect ofthe field is to reduce the plasma stopping power, sincethe transfer of proton energy to electron motion perpen-dicular to the magnetic field is suppressed. In order tofind a relationship between the position of the line form-ing region and the luminosity, one starts with a Taylorexpansion of (19) using r = RNS + hr and arrives at∆r/RNS = −1/3∆E/E. Staubert et al. (2007) identi-fied hr with the characteristic braking length for protonsl∗, which itself can be estimated by the mean free pathl∗ ∼ 1/neσ, such that now r = RNS + l∗. Using thelast relation and the density dependence of l∗ one gets∆r/l∗ = −∆ne/ne and consequently one obtains

∆r

RNS= −1

3∆E

E= − l∗

RNS

∆ne

ne. (22)

So a relation between the electron density and the lu-minosity has to be found. Nelson et al. (1993) deter-mined the electron density ne with the assumption ofa neutral electron-proton plasma by hydrostatic equi-librium P = 2nekT = gy, where P is pressure, Ttemperature and y the mass column density. Staubertet al. (2007) extended the model by considering also thedynamical pressure of accreting protons. The dynamicalpressure of the infalling protons, which can be obtainedfrom Euler-Equation, was added to the hydrostatic termP = gy + (ρ0v

20 − ρv2). Staubert et al. (2007) considered

the different terms more closely and finally obtained forthe electron density ne ' (M/A)(v0/2kT )(τ/4τ∗) (A isthe accretion area for one pole, τ is the Thompson opti-cal depth and τ∗ is the proton stopping depth) such that

9

FIG. 11: The figure (from [20]) shows the free falling plasma.It is decelerated in such a strong way that it is transformedinto subsonically settling plasma by the shock. Emerging pho-tons are able to escape sideways.

eq. (23) becomes

∆r

RNS= −1

3∆E

E= − l∗

RNS

∆M

M= − l∗

RNS

∆L

L. (23)

B. Super-Eddington accretion

In contrast to low-luminosity accretion the radia-tion pressure dominates the deceleration of the infallingplasma in the super-Eddington radiation regime, whatresults in the formation of a shock front above the NSsurface. This radiation-dominated shock transforms thefree falling plasma into the subsonically settling plasmaof the mound (see Fig. 11) [20]. Moreover, the accretioncolumn has more cylindrical geometry, since the emerg-ing photons escape from the sides of the mound [14, chap11]. Burnard et al. (1991) studied this dynamical modelin detail and found for the relative height of the peak ofthe mound the estimation

htop

RNS≈ L

LeddH‖(24)

Here, H‖ denotes the ratio of the Thomson cross sec-tion to the Rosseland averaged electron scattering crosssection for radiation flow along the magnetic field. Atypical value for an ordinary NS is H‖ = 1.23, which isalso used in the theoretical estimation of the height ofthe line forming region later. Ledd is given by (8).

10−

30.

010.

11

norm

aliz

ed c

ount

s/se

c/ke

V

hxta.pha hxtb.pha

data and folded model

50

−4

−2

02

χ

channel energy (keV)

28−Feb−2007 14:09

FIG. 12: Data of HEXTE cluster A and B of the observationin 1999 March 5. Fitting both data with the chosen modelyields same residuals, what justifies to add the data of botharrays of detectors. One sees also in the upper part of thefigure that HEXTE B has a lower effective area, since one ofits four detectors failed already (see again chap. IIA).

VII. ANALYSIS AND RESULTS

In this section the behavior of the CSRF energy of the2004 Sept–Oct outburst of 4U 0115+63 is analyzed. Thechosen model is tested before by using it for the 1999March-April outburst that has already been studied byHeindl et al. (1999) and Nakajima et al. (2006). Heindlet al. (1999) discovered a third CRSF in the spectrum ina narrow phase range and detected a non-equally spac-ing of the CSRFs. Furthermore, these people concluded

10 100

10−

30.

010.

1

keV

/cm

2 s

keV

Energy

pca.pha hxt.pha

Current model

14−Mar−2007 13:42

FIG. 13: An example for the resulting model the data (here1999-03-20) are fitted with.

10

FIG. 14: Top: The figure shows the pointing observation dataof 1999-03-20, compared with the folded model after fittingthe continuum model. Middle: Note that the huge residuumnear 10 keV indicates the fundamental cyclotron line. Bottom:Big improvement is achieved when fitting with the funda-mental cyclotron line around 10 keV. However, new residualsaround 20 keV arise that give rise to a second CRSF.

from a strong variability of the continuum and CRSFswith pulse phase a complex emission geometry near theneutron star polar cap. Nakajima et al. (2006) utilizedthe pulse-phase averaged data of this outburst and foundluminosity-dependent changes of the cyclotron resonanceenergies. This dependence was interpreted as change inthe accretion column height. Like Nakajima et al. (2006),in this project only pulse-phase averaged data were con-sidered. First the data of HEXTE cluster A and B werecompared and it was shown that by fitting a continuummodel with two gaussian absorbtion lines that representthe fundamental and the 1st harmonic CRSF (see Fig.12), residuals appeared at the same positions. Thus inthe following analysis the data of cluster A and B wereadded and analyzed together. Furthermore the PCA andHEXTE data were fitted simultaneously with the samemodel besides a constant factor to equalize the relativenormalizations. This factor was in both outbursts out ofthe range (0.8 : 1.4) and in most spectra close to 1.0.

A. Spectral Models

The calculation of the the emission of a accretion pow-ered neutron star is because of its complex geometryquite complicated. As was suggested by several peo-ple (see [1, chap 5.3.1]), the dominating process is as-sumed to be resonant Compton scattering, what results

FIG. 15: The best-fit model (spectrum of 1999-03-20) aftertaking the 1st harmonic CRSF into consideration. The acces-sory residuals (the top of the χ-plots) emphasize the presenceof the third line (bottom) and show the special hump around10 keV, which is modeled with a Gaussian (middle).

in a roughly power-law continuum with exponential cut-off at an energy Ec that is characteristic for the scat-tering electrons. Thus, in general continuum spectra ofaccreting binaries are modeled with a power-law with ex-ponential cutoff. Following Nakajima et al. (2006), whoused the Negative Positive Exponential Model (NPEX)NPEX(E) = (A1E

−α1 + A2E+α2)exp(−E/kT ), in this

project the sum out of a positive and a negative power-law was multiplied with the hightecut model, given by

highecut(E) =

{exp(Ec−E

Ef) E ≥ Ec

1 E ≤ Ec

was chosen to approximate the continuum. Here Ec is thecutoff energy and Ef the e-folding energy, both in keV(see [11]). The total continuum model M(E) is writtenas

M(E) = (A1E−α1 + A2E

+α2) · highecut(E), (25)

where A1, A2 denote the norm in units photonss−1cm−2keV−1 at 1 keV and α1, α2 are the photon in-dices. In the following α2 was fixed at 2.0, as did Naka-jima et al. (2006), so that the positive power-law de-scribes a Wien peak.

CSRFs were modeled with a Lorentzian shape by us-ing the multiplicative model component cyclabs. To allow

11

also non-equidistant line-spacing, as discovered by Heindlet al. (1999), the depth of the additional harmonic linewas fixed at zero. So each CRSF with energy Ecycl, widthW and depth τ is described itself by one cyclabs compo-nent and contributes to the shape of the resulting modelthe factor:

cyclabs(E) = exp(−τ(WE/Ecycl)2

(E − Ecycl)2 + W 2) (26)

An interesting phenomenon in the spectrum analysisof many accreting neutron stars occurs at energies be-tween 8 and 13 keV [1]: A small hump that cannot beexplained yet can be seen in the spectrum. This featurewas approximated with an additive gaussian componentgaussian(E) = K/σ

√2πexp(−(E − El)2/2σ2) with line

energy El, line width σ (both in keV) and norm K.

B. Analysis

During the 1999 outburst 44 pointing observations of4U 0115+63 were made with PCA and HEXTE. In thisproject 36 spectra out of these were chosen and fittedwith a model consisting of (mostly) three CRSFs influ-encing the continuum model and an additional gaussianfeature to describe the hump around 10 keV (see Fig.13).The occurring residuals after first fitting the data withthe continuum model alone (see fig. 14 and fig. 15), thentaking step by step one additional feature into account,justify this procedure. The main interest of the projectlies in the 2004 outburst. However, there were onlyfive pointing observations of PCA and HEXTE available.The same model used for the 1999 outburst was also ap-plied to the 2004 outburst.

C. Results

First one has to test whether the derived results, listedin table ?? and table ??, of 1999 outburst are consistentwith the previous analysis of Nakajima et al. (2006). Thefundamental cyclotron energies of the 1999 outburst areslightly below the results of Nakajima et al. (2006). Thedifference could arise from taking into account the un-known feature around 10 keV in this paper, what couldresult in a small shift of the harmonic CRSF to lower en-ergies. Furthermore Nakajima et al. (2006) used equidis-tant spacing for the CRSFs. Thus the data can be consid-ered to be consistent with those of Nakajima et al. (2006).

1. Comparison of 2004 outburst with 1999 outburst

As the data as well as the plots show the fundamen-tal cyclotron line energy during the 2004 outburst of 4U0115+63 behaves exactly in the same way as during theformer outburst (see Figures (16)-(19)). No hysteresiscould be observed.

6

8

10

12

14

16

18

20

0.01 0.1 1

E_0

L/L_edd

outburst 1999outburst 2004

FIG. 16: Obtained fundamental cyclotron energies for 1999outburst and 2004 outburst of 4U 0115+63. There is no dif-ference in the behavior of the two outbursts. Besides, note thestrong change in slope around L/Ledd ≈ 0.1, what indicatesdifferent behavior of the accretion column.

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

E_1

L/L_edd

outburst 1999outburst 2004

FIG. 17: Dependence of the first harmonic cyclotron energyon luminosity, again plotted for both outbursts. Except forquite low luminosities the energy remains constant.

In all of the plots the luminosity L is calculated at7 kpc and plotted in units of Ledd, assuming a mass ofthe neutron star of 1.4M¯.

Fig. (16) and Fig. (17) show the dependence of thefundamental and 1st harmonic cyclotron energy on theluminosity. While the fundamental cyclotron energy de-creases strongly with increasing luminosity , the 1st har-monic cyclotron energy remains constant (for L/Ledd >0.1). One clearly recognizes that the slope of both ener-gies is changing around L/Ledd ≈ 0.1, what gives rise tothe assumption that the physics of the accretion columnis changing within this range.

Nakajima et al. (2006) emphasized the correlation of τand the W/E ratio among all the correlations of other pa-

12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2

w_0

/ E

_0

depth of fundamental cyclotron line

outburst 1999outburst 2004

FIG. 18: A positive correlation can be found between theW0/E0 ratio of the fundamental cyclotron line and its depthτ0.

0

0.5

1

1.5

2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

T_0

(de

pth)

L / L_edd

outburst 1999outburst 2004

FIG. 19: The plot shows the depth of the fundamental CRSFversus luminosity. The minimum around L/Ledd > 0.1 mightalso be a sign for a change in the accretion column. However,since the results of Nakajima et al. (2006) show a contradic-tory behavior, one has to examine it more closely.

rameters and so this relation is also presented in Fig. 18.Besides the huge errorbars one recognizes like Nakajimaet al. (2006) a positive correlation between the funda-mental width and its depth.

An interesting feature occurs when plotting the depthof the fundamental CRSF versus luminosity. It looks as ifa minimum arises just around L/Ledd ≈ 0.1. This mightalso indicate a change in the behavior of the accretion col-umn. However, the results of Nakajima et al. (2006) showa contradictory behavior, the values of τ0 are even in-creasing in this region. Thus, one has to examine it moreclosely. In this paper as well as by Nakajima et al. (2006)simple Lorentzians are used for approximating CRSFs,although generally it is known that the profile of the fun-

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

26/02 04/03 11/03 18/03 25/03 01/04 08/04 15/04 22/04

L / L

_edd

day/month 1999

L / L_edd

FIG. 20: The luminosity directly depends on the accretionrate at the NS. Here, the luminosity dependence on time isplotted.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

26/02 04/03 11/03 18/03 25/03 01/04 08/04 15/04 22/04

h_r

/ R_N

S

day/month 1999

outburst 1999 E_0 = 20 keVoutburst 1999 E_0 = 18 keV

FIG. 21: Another hint for a possible change from super- tosub-Eddington accretion gives the rough change of the calcu-lated height of the scattering region.

damental line exhibits a complex shape [17]. So perhapsusing the results of Schoenherr et al. (2007), who devel-oped a model for CRSFs, one is able to find about thereal dependence of the depth on luminosity.

2. The height of the scattering region versus luminosity

Many authors (e.g. Staubert et al. (2007), Nakajimaet al. (2006), Nelson et al. (1993))gave attention to thephysics in the accretion regime. As already mentionedin chap. VI it must be distinguished between sub- andsuper-Eddington accretion, whereas the decisive parame-ter is the local Eddington rate at the neutron star [19].Since clear changes of parameters like the energies ofCRSFs with the luminosity (see Fig. s (16), (17)) or the

13

0.01

0.1

0.001 0.01 0.1 1

accr

etio

n co

lum

n he

ight

h_r

/ R

_NS

L / L_edd

outburst 1999 E_0 = 20 keVoutburst 2004 E_0 = 20 keVoutburst 1999 E_0 = 18 keVoutburst 2004 E_0 = 18 keV

FIG. 22: Relative accretion column height hr in dependenceof luminosity. Clearly visible is a change in the accretioncolumn at L/Ledd = 0.1.

height of the scattering region with time (see Fig. 21)and therefore with luminosity (compare Fig. 20) arise inthe analysis of the 1999 outburst, one could take a pos-sible transition from super- to sub-Eddington accretioninto consideration. Therefore the height of the scatter-ing region is examined more closely, because this valuehas to depend sufficiently on a possible relevant radia-tion pressure. It can be calculated approximately withthe formula (19), derived in chap. VI:

hr

RNS= (

E

E0)−1/3 − 1. (27)

Since the cyclotron line energy E0 directly at the NSsurface is not known at all, it is followed Nakajimaet al. (2006) and thus also two different values of E0,18 and 20 keV are employed. As predicted, the heighthr (see Fig. 22) changes its slope around L/Ledd ≈ 0.1,where the possible transition point is assumed to be.

This luminosity-dependence of the hr is comparedin the following with the theory of super- and sub-Eddington accretion, presented in chap. VI. In the caseof super-Eddington accretion Burnard et al. (1991) foundthe relation (24):

htop

RNS≈ L

LeddH‖≈ L

1.23Ledd(28)

Staubert et al. (2007) derived the relation (23) in thesub-Eddington accretion regime:

∆r

RNS= −1

3∆E

E= − l∗

RNS

∆M

M= − l∗

RNS

∆L

L. (29)

Thus Staubert et al. (2007) predicted that the fractionalchange in cyclotron line energy is directly proportionalto the fractional change in luminosity. Testing this rela-tion on the data of the 1999 outburst with the fractional

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1

-l_*/

R_N

S

L/L_edd

l_*/R_NS

FIG. 23: Staubert et al. (2007) predicted a constant fractionalchange in the cyclotron line energy with a fractional changein luminosity. l∗/RNS = 1/3 ·∆E/E ·L/∆L is plotted againstluminosity.

0.01

0.1

0.001 0.01 0.1 1

h_r

/ R_N

S

L / L_edd

sub-Eddington

super-Eddington

E_0 = 20 keVE_0 = 18 keV

FIG. 24: hr in comparison with the theoretical models forsub- and super-Eddington accretion

changes relating to the luminosity Lr and energy Er ofthe observation in April 20 (∆L = L−Lr, ∆E = E−Er,Er, Lr of observation in April 20) yields Fig. 23. The pre-diction is verified at low luminosities, |l∗/RNS| ≈ 0.05 isconstant until L/Ledd ≈ 0.1, then deviations occur sincel∗/RNS is increasing. For Her X-1 Staubert et al. (2007)derived l∗/RNS ∼ 0.01. Using −l∗/RNS ≈ 0.05 and (29)the height of the scattering region can be expressed by:

hr

RNS= h0 + 0.05

∆L

L, (30)

where h0 = hr(Lr) calculated with (19) denotes theheight of the scattering region on April 20.

Equations (28) and (30) are expressions for a theo-retical approach for the height of the scattering regionfor super- and sub-Eddington accretion. Except for a

14

FIG. 25: Some spectra of 1999 outburst seem to have anexcess at the energy of 6.4 keV that might indicate a Fe-K-line. The spectra in the figure are from top to bottom fromobservations of March 24, April 2, March 19.

saturation toward the highest luminosity (see also [3])the two theories describe the height, calculated out ofobserved quantities, very good. This strengthens on theone hand the assumption that the observed cyclotron en-ergy changes are due to changes of the scattering heighthr and on the second hand the transition from super- tosub-Eddington transition.

D. Observation of a Fe-K-line?

Although Nakajima et al. (2006) as well as Heindlet al. (1999) reported no detection of a Fe-K-line in thespectra of 1999 outburst, the residuals of some spectraexhibit at least a little excess around 6.4 keV (see Fig.25, as well as Fig. 26 for the 2004 outburst) after fittingwith the model described in the chapter above. To judgewhether the spectrum contains a Fe-K-line one wouldhave to do Monte Carlo simulation. However, withinthe scope of that project only the F-statistic of the newbest-fit-models of spectra with the clearest excess wascalculated and listed in table II and table III. The F-statistic gives the probability that the new best-fit χ2

is achieved statistically [11]. But one has to be carefulwith interpreting the value, since Protassov et al. (2002)warned that the F-statistic is not sufficient good to testthe presence of an emission or absorption line.

Taking on the one hand the hight F-statistic results,but on the other hand the number of spectra with a littleexcess at the Fe-K-line energy into consideration, onereally will have to do Monte Carlo simulation to be sureabout the line.

FIG. 26: Also the residuals of some spectra of the September–October outburst in 2004 show a little hump at 6.4 keV. Thespectra in the figure are from top to bottom from observationsof Sept. 6, Sept. 14 and Oct. 10.

FIG. 27: The figure shows a counterexample for the observa-tion of a Fe-K-line in all spectra (spectrum from 1999-03-06).

VIII. CONCLUSION

This project shows that the 2004 outburst of 4U0115+63 behaves in exactly the same way as the 1999outburst. No hysteresis effect could be observed. Fur-thermore the theoretical approach for sub- and super-Eddington accretion describes the data of the March-April 1999 outburst of 4U 0115+63 very well, such thatthis indicates a transition from super- to sub-Eddingtonaccretion during the 1999 outburst. However, it remainsto be diagnosed whether there is a Fe-K-line present.

TABLE II:F-statistics of spectra taking an eventual Fe-K-line into ac-count during 1999 outburst

EFe ftest

Date (1999) (keV) probability

Mar 19 6.56 0.35

Mar 24 6.1 1.7E-05

Apr 2 6.38 0.78

15

TABLE III:F-statistics of spectra taking an eventual Fe-K-line into ac-count during 2004 outburst

EFe ftest

Date (2004) (keV) probability

Sept 6 6.39 5.3E-04

Sept 14 6.40 0.23

Oct 2 5.9 0.61

Acknowledgments

I would like to thank Prof. J. Wilms for taking muchtime for motivations, discussions, many explanations,constructive annotations, for answering trivial questionsand for showing astronomy makes really fun. I am alsograteful to all people working in the observatory in Bam-berg for the great atmosphere during the three weeks ofthis project. Furthermore thanks to my parents for show-ing interest and especially thanks to my brother Tobiasfor demonstrating that even a seven-year-old boy is ableto ask nontrivial questions about the sun and neutronstars.

APPENDIX: BEST-FIT RESULTS

16

TA

BLE

IV:

The

bes

t-fit

para

met

ers

ofth

edate

-sort

edsp

ectr

aof2004

Sep

tem

ber

–O

ctober

outb

urs

t

conti

nuum

spec

trum

fundam

enta

lC

RSF

1st

harm

onic

CR

SF

2nd

harm

onic

CR

SF

gauss

ian

HE

XT

EP

CA

Ef

E0

W0

E1

W1

E2

W2

El

σE

xposu

reE

xposu

reχ

2 red

Date

A1a

α1

A2b

(keV

)(k

eV)

τ 0(k

eV)

(keV

)τ 1

(keV

)(k

eV)

τ 2(k

eV)

(keV

)(k

eV)

Kc

L/L

eddd

(ks)

(ks)

Sep

t6

1.1

32.1

06.1

65.2

5+

0.0

9−

0.0

19.9

6+

0.0

6−

0.2

50.8

8+

0.1

1−

0.0

110.2

0+

0.4

7−

0.0

122.5

2+

0.1

3−

1.1

00.6

211.1

239.2

00.5

81.0

010.0

00.7

30.0

40.2

10.8

31.6

00.8

6

Sep

t14

2.3

32.3

311.7

85.0

7+

0.1

6−

0.1

69.7

5+

0.0

9−

0.8

70.9

0+

0.0

2−

0.0

26.3

8+

1.1

3−

1.1

319.7

8+

0.2

3−

0.0

11.0

611.4

337.0

80.5

02.8

110.0

50.8

20.1

70.3

50.7

50.5

91.0

5

Sep

t22

1.1

91.8

80.9

45.4

8+

0.1

0−

0.1

09.9

7+

0.4

6−

0.0

31.0

7+

0.0

1−

0.0

16.1

8+

0.4

4−

0.0

121.0

6+

0.1

5−

0.1

51.0

75.8

732.9

91.2

213.7

29.4

20.6

00.0

10.3

313.6

216.7

71.6

5

Sep

t24

3.7

52.7

88.9

75.3

8+

0.1

1−

0.0

19.8

5+

0.4

1−

0.0

31.0

1+

0.0

1−

0.0

75.7

1+

0.0

1−

0.5

220.2

8+

0.4

3−

0.0

11.2

78.1

335.7

10.9

99.9

19.2

90.4

80.0

60.2

92.2

63.4

91.3

0

Oct

10

5.6

83.3

90.0

74.6

5+

0.0

6−

0.0

611.3

0+

4.0

0−

4.0

00.9

7+

0.0

1−

0.0

68.7

0+

0.9

4−

0.9

421.3

3+

4.0

0−

4.0

00.6

38.8

30.0

09.2

90.4

80.0

00.1

82.3

23.4

40.8

7

ain

unit

sphoto

ns

s−1cm

−2keV−

1

bin

unit

s10−

3photo

ns

s−1cm

−2keV−

1

cin

unit

sphoto

ns

s−1cm

−2

dca

lcula

ted

wit

hM

=1.4

M¯

,R

=7

kpc

acc

ord

ing

toeq

.s(2

1),

(8)

17

TA

BLE

V:

The

bes

t-fit

para

met

ers

ofth

edate

-sort

edsp

ectr

aof1999

Marc

h–A

pri

loutb

urs

t

conti

nuum

spec

trum

fundam

enta

lC

RSF

1st

harm

onic

CR

SF

2nd

harm

onic

CR

SF

gauss

ian

HE

XT

EP

CA

Ef

E0

W0

E1

W1

E2

W2

El

σE

xposu

reE

xposu

reχ

2 red

Date

A1a

α1

A2b

(keV

)(k

eV)

τ 0(k

eV)

(keV

)τ 1

(keV

)(k

eV)

τ 2(k

eV)

(keV

)(k

eV)

Kc

L/L

eddd

(ks)

(ks)

Mar

31.4

62.4

47.2

34.8

3+

0.0

5−

0.3

010.7

1+

0.2

3−

2.0

41.1

8+

0.0

1−

0.3

76.0

6+

0.8

8−

0.0

121.1

8+

1.4

0−

1.4

00.9

36.1

832.3

10.7

77.9

512.4

12.1

41.9

20.2

20.3

40.5

90.7

8

Mar

41.8

42.5

17.3

95.1

7+

0.3

8−

0.0

110.3

8+

0.1

2−

2.4

41.1

9+

0.0

1−

0.0

16.1

5+

4.5

0−

0.5

021.0

6+

1.6

6−

0.0

11.0

96.0

633.3

60.9

510.2

812.0

52.1

41.7

80.2

40.5

81.0

61.0

6

Mar

50.8

32.1

27.2

75.1

6+

0.0

9−

0.3

210.2

5+

0.0

1−

0.1

70.9

1+

0.0

2−

0.0

17.3

1+

1.9

3−

1.9

319.7

3+

0.0

1−

0.0

11.0

49.2

836.0

30.4

86.9

49.7

20.5

50.1

20.2

30.8

40.0

80.9

7

Mar

610.1

23.9

910.3

5.4

1+

10.0

0−

10.0

09.0

9+

1.6

0−

0.0

10.9

8+

0.2

0−

0.1

17.0

3+

1.2

2−

1.0

819.6

0+

0.0

1−

3.6

71.0

48.9

632.6

10.7

014.1

59.5

50.9

50.2

20.2

80.3

70.0

80.8

1

Mar

711.4

14.1

010.7

5.1

8+

0.3

1−

0.3

18.5

9+

3.1

1−

0.0

20.9

1+

0.0

1−

0.3

77.2

3+

10.6

2−

0.0

120.0

3+

0.0

6−

1.6

11.2

210.0

937.7

40.5

16.0

711.2

51.7

91.7

20.2

80.5

90.1

40.7

6

Mar

92.6

82.5

712.1

5.3

4+

1.0

8−

0.1

49.7

1+

0.8

2−

0.0

10.9

9+

0.1

4−

0.1

47.0

3+

0.1

3−

1.1

620.7

5+

0.0

1−

0.0

11.1

18.7

338.7

30.7

68.4

79.7

70.6

20.1

00.3

60.3

70.8

30.5

6

Mar

11

3.0

42.6

513.1

5.6

2+

0.0

4−

0.0

39.4

1+

0.6

8−

0.0

90.9

9+

0.1

0−

0.0

26.3

2+

0.1

1−

0.0

119.6

1+

0.1

8−

0.0

11.2

710.2

338.1

90.8

211.5

69.8

50.9

60.2

80.3

90.8

91.8

40.7

3

Mar

11

20.7

74.2

913.9

5.4

5+

10.0

0−

10.0

08.9

5+

0.0

9−

0.0

61.0

4+

0.0

4−

0.0

38.0

1+

0.1

0−

0.0

121.1

1+

0.0

1−

0.4

70.7

76.8

433.0

60.8

513.2

69.8

40.9

60.2

60.3

75.3

22.3

80.8

7

Mar

12

17.6

94.1

313.8

5.6

5+

0.0

1−

0.1

08.7

3+

0.8

2−

0.0

21.0

3+

0.0

1−

0.0

79.0

1+

0.0

5−

0.6

821.9

3+

0.0

1−

0.0

10.6

35.0

933.3

20.9

313.1

69.6

70.8

00.1

70.3

715.4

15.5

81.1

9

Mar

15

2.5

42.5

42.1

35.5

6+

0.3

9−

0.0

19.8

4+

0.0

5−

0.0

41.1

1+

0.0

1−

0.0

85.4

7+

0.0

1−

0.4

319.9

2+

0.0

1−

0.3

81.1

77.0

932.1

01.2

414.2

210.0

01.1

50.3

10.3

90.8

50.9

40.7

7

Mar

16

1.1

71.8

713.4

5.1

6+

0.0

1−

0.0

19.7

7+

0.0

1−

0.1

30.9

9+

0.0

1−

0.0

16.1

0+

0.0

1−

0.0

221.0

4+

0.0

1−

0.0

81.1

98.4

035.0

30.7

59.2

810.0

01.0

90.2

30.4

10.4

20.5

01.1

2

Mar

18

1.1

11.7

912.4

4.7

7+

10.0

0−

10.0

010.2

9+

0.0

6−

0.3

50.8

7+

0.0

1−

0.0

14.7

6+

0.3

4−

0.0

119.5

9+

0.7

9−

0.0

11.1

79.4

034.7

50.4

81.8

310.0

00.7

20.1

60.3

90.5

20.6

40.9

8

Mar

19

0.9

91.8

41.1

05.3

8+

2.0

0−

0.5

09.9

9+

0.4

2−

0.0

21.0

6+

0.2

0−

0.0

56.0

2+

0.4

8−

0.4

820.9

9+

0.0

2−

0.0

11.1

76.6

734.0

31.0

912.6

59.6

10.6

70.1

30.3

62.4

72.9

90.7

1

Mar

20

0.9

61.7

99.8

65.4

6+

0.0

1−

0.0

110.1

2+

0.5

4−

0.0

50.9

9+

0.1

3−

0.1

35.2

4+

0.0

7−

0.7

319.8

2+

0.1

1−

0.0

11.3

08.9

835.5

90.9

212.0

49.6

80.8

00.1

30.3

40.5

40.8

81.0

4

Mar

21

0.7

11.5

89.7

95.4

5+

0.1

9−

0.1

910.1

8+

0.4

5−

0.0

10.9

9+

0.0

8−

0.0

85.6

5+

0.0

0−

0.5

720.4

3+

0.4

7−

0.0

11.2

58.1

935.8

50.9

812.3

19.6

80.6

60.1

00.3

53.2

43.1

70.5

8

Mar

23

0.6

71.8

69.8

75.7

9+

0.0

9−

0.0

48.7

3+

1.1

2−

0.1

10.8

7+

0.0

1−

0.0

18.9

8+

0.0

8−

0.0

222.3

4+

0.0

2−

0.0

10.6

13.0

732.6

90.9

713.0

69.0

20.4

30.0

30.3

63.0

42.5

31.3

7

Mar

24

0.4

01.7

58.2

75.6

9+

0.1

1−

0.5

69.3

7+

1.7

7−

0.8

90.9

5+

0.0

6−

0.0

17.2

1+

2.5

2−

0.0

122.1

3+

2.1

7−

2.1

70.8

45.8

734.6

61.0

011.8

011.9

31.9

90.6

30.3

31.4

40.1

90.9

0

Mar

25

0.5

01.7

77.2

25.4

3+

0.0

1−

0.1

29.5

7+

0.0

8−

0.1

00.9

2+

0.0

1−

0.0

17.9

5+

0.6

3−

0.0

122.1

5+

0.0

1−

0.0

20.8

25.1

634.6

60.8

58.6

79.1

70.4

70.0

30.2

63.8

84.9

61.4

8

Mar

26

0.7

32.0

00.5

76.1

4+

0.8

9−

0.8

910.4

0+

0.9

3−

0.1

10.9

7+

0.0

1−

0.0

15.3

7+

0.4

8−

0.0

120.1

7+

0.0

5−

0.2

21.4

67.8

636.4

61.5

312.9

011.9

67.0

70.9

40.2

70.5

40.3

01.5

1

Mar

27

49.6

85.7

04.0

85.8

5+

0.0

2−

0.4

510.7

3+

0.0

6−

0.0

60.9

0+

0.0

1−

0.0

15.5

1+

2.5

6−

0.0

120.6

4+

0.6

3−

4.5

51.2

26.9

234.1

81.1

014.4

510.1

27.0

21.6

20.2

33.2

40.8

81.0

2

Mar

29

1.0

72.4

50.3

95.7

4+

4.9

7−

0.0

110.6

5+

0.0

7−

0.0

90.8

7+

0.2

1−

0.0

15.5

5+

3.0

6−

0.0

119.5

2+

8.7

7−

0.0

51.2

27.7

533.2

41.0

214.1

111.5

96.8

80.9

90.2

13.2

64.0

61.1

0

Mar

31

1.1

62.8

43.0

85.3

1+

2.8

3−

0.3

411.3

2+

0.0

1−

0.1

30.6

8+

1.7

7−

0.0

15.6

2+

0.0

2−

0.0

119.8

7+

6.5

2−

6.5

21.2

39.3

837.6

30.5

94.5

811.5

96.6

11.7

00.1

83.4

22.6

41.1

0

Apr

11.4

63.1

12.9

75.0

7+

3.9

9−

5.0

711.8

8+

1.5

0−

1.5

00.6

8+

0.0

1−

0.0

15.4

1+

12.0

6−

0.0

119.4

3+

0.2

0−

0.0

11.0

88.5

036.5

70.4

07.8

211.4

76.7

81.8

30.1

80.4

40.7

21.1

2

Apr

21.1

32.8

40.1

66.8

4+

10.0

0−

0.0

111.8

4+

4.2

1−

0.3

10.8

3+

13.6

9−

0.3

96.6

3+

36.6

1−

0.0

119.5

7+

0.0

1−

0.0

11.2

39.0

735.7

51.7

417.0

89.7

66.6

41,0

00.1

72.9

71.8

40.7

7

Apr

32.3

13.4

81.8

45.6

1+

6.1

8−

4.6

012.8

2+

0.1

9−

0.0

10.5

1+

0.0

2−

0.0

17.1

5+

91.1

4−

0.0

116.3

8+

0.0

1−

0.0

10.8

313.6

440.4

60.5

73.5

410.7

75.7

31.5

60.1

60.5

30.3

71.1

7

Apr

41.3

53.0

62.2

75.3

7+

0.7

9−

5.3

713.2

6+

1.5

1−

0.2

30.8

4+

0.0

1−

0.0

16.6

6+

4.3

6−

0.0

120.7

0+

0.0

5−

0.0

11.0

09.1

034.9

50.8

48.9

89.7

26.6

20.9

50.1

42.9

31.7

10.7

3

Apr

51.8

33.4

90.1

35.7

2+

2.2

7−

2.2

712.6

4+

4.5

3−

2.5

70.4

4+

0.0

5−

0.0

16.7

4+

19.7

6−

0.0

216.9

6+

0.1

2−

0.5

00.9

413.8

636.9

41.0

81.2

111.6

45.8

51.6

70.1

20.6

20.9

10.7

3

Apr

60.9

82.9

31.7

05.1

+0.6

4−

0.7

013.0

7+

2.4

7−

0.0

10.6

4+

0.0

1−

0.0

16.7

0+

35.1

4−

0.0

119.1

0+

4.3

2−

0.0

10.7

79.1

030.2

10.6

49.0

09.9

25.5

10.9

50.1

23.0

92.6

20.9

1

Apr

80.6

62.7

21.7

44.5

5+

1.7

3−

0.3

514.5

3+

0.0

7−

0.0

20.6

6+

0.4

6−

0.0

16.7

0+

5.0

0−

2.0

019.0

6+

6.0

3−

0.0

10.6

59.0

10

19.9

25.5

20.8

80.1

03.3

53.7

01.1

1

Apr

10

0.5

82.8

40.2

44.3

4+

1.6

7−

1.6

715.0

7+

0.1

4−

0.7

30.5

8+

0.1

9−

0.0

15.2

6+

0.5

0−

0.0

121.7

0+

0.8

5−

0.8

60.7

67.3

00

19.4

65.5

00.8

90.0

83.0

84.3

00.7

3

Apr

12

0.4

22.7

00.1

34.0

1+

1.5

8−

0.4

014.7

7+

0.1

1−

0.1

10.5

6+

0.0

1−

0.0

15.1

1+

2.6

0−

0.0

121.2

1+

0.0

1−

4.4

10.6

55.9

90

19.2

06.4

50.6

40.0

63.5

14.7

70.9

2

Apr

14

0.1

71.4

60.4

93.8

+0.0

8−

0.0

114.9

2+

0.0

1−

0.3

50.9

1+

0.0

1−

0.0

17.3

6+

0.0

1−

0.1

322.8

5+

0.7

8−

0.7

80.6

02.9

80

10

0.0

42.9

74.0

80.8

5

Apr

16

0.1

21.4

70.0

13.9

3+

10.0

0−

0.4

915.0

2+

0.6

9−

0.0

80.9

5+

0.0

1−

0.1

67.3

9+

1.7

4−

1.4

329.5

4+

5.7

0−

5.7

02.1

03.9

20

10

0.0

20.5

40.8

51.1

1

Apr

18

0.0

01.4

70.0

34.2

4+

0.1

1−

0.1

016.3

5+

0.0

1−

0.5

51.1

4+

0.0

1−

0.0

17.3

9+

3.4

7−

0.0

729.5

4+

0.0

1−

0.0

10

10

10

0.0

10.5

40.8

30.9

9

Apr

20

0.0

11.4

74.3

E-0

34.5

+0.0

1−

0.6

916.8

8+

0.5

5−

0.5

51.2

5+

0.0

1−

0.2

46.4

6+

2.0

7−

0.0

129.5

4+

0.0

1−

0.0

10

10

10

4.9

1E

-03

0.3

90.6

60.8

4

Apr

22

8.3

E-0

51.5

36.6

E-0

43.1

8+

10.0

0−

10.0

017.3

8+

92.0

1−

3.9

60.9

9+

65.0

1−

19.2

211.1

9+

0.0

1−

96.4

029.5

4+

0.0

1−

0.0

10

10

10

1.0

3E

-04

0.8

71.3

30.5

0

ain

unit

sphoto

ns

s−1cm

−2keV−

1

bin

unit

s10−

3photo

ns

s−1cm

−2keV−

1

cin

unit

sphoto

ns

s−1cm

−2

dca

lcula

ted

wit

hM

=1.4

M¯

,R

=7

kpc

acc

ord

ing

toeq

.s(2

1),

(8)

18

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