Giant H 11 Regions and the Quest for the Hubble ConstantJ. MELNICK, ESO

The search for yardsticks with whichto measure cosmic distances is one ofthe fundamental endeavours of obser­vational astronomy but this is a difficulttask and it was not until the beginning ofthis century, when astronomy was al­ready hundreds of years old, that thesize of our own Galaxy could be deter­mined. The yardstick which made thispossible was the discovery, by MissHenrietta Swan Leavitt, of a relation be­tween the period of pulsation of DeltaCephei stars and their luminosities. TheCepheid period-Iuminosity relation wassubsequently calibrated by HarlowShapley who then used it together withthe absolute magnitudes of RR Lyraestars to measure the Milky Way.

Soon after the galactic distance scalewas determined by Shapley, a greatcontroversy arose as to whether the spi­ral nebulae, wh ich were very weil knownat the time from the work of William andJohn Herschel and others, were galacticor extragalactic objects. The contro­versy was not settled until after the 100­inch Hooker telescope was brought intooperation at Mount Wilson, and Hubblediscovered cepheid variables in theGreat Andromeda Nebula (M 31) in 1924and later in other spiral nebulae. The"island universe" hypothesis of Kantwas thus proved and for the first time itwas observationally established that theUniverse extends far beyond the limitsof the Milky Way.

Soon after the work of Hubble, sever­al astronomers began to measure radialvelocities of galaxies and discoveredthat these velocities increased linearlywith distance. Thus, if R is the distanceof a galaxy and V its radial velocity, thetwo are related as,

V = Ho x R

where Ho is a universal constant. In1931, Hubble and Humason calibratedthis relationship in galaxies where theyhad previously found Cepheid variablesand obtained a value of Ho = 558 km/sec/Mpc for this constant which is nowknown as the Hubble constant. Almostten years before the work of Hubble andHumason, the Russian mathematicianAlexander Friedmann had found a solu­tion of Einstein's General Relativityequations which predicted that the Uni­verse should be either expanding orcontracting according to a linear relationbetween velocity and distance. Thus,immediately after Hubble's results werepublished, the idea that our Universe isexpanding gained universal accept­ance.

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The Friedmann solutions have asingularity where the radius of the Uni­verse is zero and mass density infinite.In fact the Hubble relation (V = HoR)implies that some time in the past allgalaxies were on top of each other. Forobvious onomatopoeic reasons the sin­gularity is called the "Big-Bang"; thusthe singularity is interpreted as a magni­ficent cosmic firework which marked thebeginning of time. Friedmann cos­mologies can be parametrized in termsof the expansion rate Ho, the mass den­sity Qo, and an elusive parameter calledthe cosmological constant, 1\., whichhas bedeviled cosmology since it wasfirst introduced by Einstein himself.

Einstein's theory allows for the exist­ence of this additive constant whichrepresents either an additional attractiveor repulsive "gravitational" force butthere is no compelling reason in thegeneral theory of relativity for this forceto exist in nature. It is merely allowed bythe mathematical structure of the equa­tions. Einstein found that in order toconstruct a statical model for the Uni­verse, he had to introduce arepulsionterm to balance gravity. Of course, in1917 everybody, including Einstein,thought that the Universe was static!

With no cosmological constant (I\. =

0), Friedmann's models give simple rela­tionships between the age of the Uni­verse (Ta, the time elapsed since theBig-Bang) and the Hubble constant andQo' In general Ta is always smaller thanHo-1 and it is equal to Ho-1 if the massdensity is zero (Qo = 0).

Thus, the calibration of the Hubblerelation provides not only the most pow­erful cosmic yardstick but also a meansof determining the age of the Universe. Itis not yet known how important the de­celeration and the gravitational repul­sion terms in Friedmann models are but,at least in principle, they can be deter­mined observationally and this is one ofthe major tasks of modern observationalcosmology. An important constraint onthe Hubble constant is that, for !\. = 0,Ho-1 must be larger than the age of theGalaxy. At the time of Hubble's work,this limit was the age of the earth, about4,000 million years. Today, from thetheory of stellar evolution and from ob­servations of globular clusters the age ofour galaxy is estimated to be more than16,000 million years.

The Determination of Ho

Periods and luminosities of Cepheidscan be reliably determined from the

ground out to distances of about 5 Mpc.One of the major tasks of the HubbleSpace Telescope will be to extend theseobservations to larger distances. OurMilky Way is a member of a group ofgalaxies (the Local Group) of roughly1 Mpc in diameter of which the An­dromeda nebula is also a member. TheLocal Group is itself member of a largeragglomeration of galaxies known asthe Local Supercluster which is domi­nated by the Virgo cluster, distant15-20 Mpc from the Local Group.Thus, the expansion of the Universe isperturbed at small distances by thesemass concentrations and it is necessaryto measure velocites and distances togalaxies beyond the Virgo cluster in or­der to derive a meaningful value for theHubble constant. Hubble's own deter­mination was too large because of an'umber of errors, including a large errorin Shapley's calibration of the cepheidperiod-Iuminosity relation. But even to­day, almost 60 years after the pioneer­ing work of Hubble and Humason, as­tronomers have not yet agreed on theexact value of Ho although most agreethat it lies between 50 and 100 km/sec/Mpc. In fact, the opinions are divided intwo groups; the Ho = 50 camp cham­pioned by Sandage and Tammann, andthe Ho = 100 camp whose strongestadvocates are Aaronson and co-work­ers and G. de Vaucouleurs. Both campsdefend their cause with excellent obser­vations but the controversy is still farfrom being resolved. The discrepancy isalso philosophical; at Ho = 50, the Big­Bang age of the Universe is consistentwith the age of the oldest stars in ourGalaxy while for Ho = 100 that age is tooshort and, in order to maintain consis­tency with the Friedmann models, thecosmological constant must be revived.

In this article I would Iike to present anew method (in fact a new version of anold method), developed in collaborationwith Roberto Terlevich from the RGOand Mariano Moles from the IM inGranada, which uses the properties ofgiant H 11 regions as distance indicators.

Giant H 11 Regions as Distance In­dicators

In the early 1960s Sersic discoveredthat the diameters of the largest H 11regions in spiral galaxies increase withgalaxy luminosity. This correlation wasfurther developed by Sandage and ithas since been used by many workersas a cosmic yardstick. The correlation,however, is not useful much beyond

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obtained with the 3.6-m and 2.2-m tele­scopes at La Silla and the line-widthswith the Echelle spectrograph at the4-m telescope of Cerro Tololo.

The slope of the correlation is4.5 ± 0.3 and rms scatter is ologL (H rl) =0.32 but the dispersion is correlatedwith the chemical composition of thenebular gas. A Principal ComponentAnalysis of the data leads to the follow­ing relation.

Log L(Hß} = 5 logo - 10g(O/H} + constant

Figure 2 presents a plot of L(H rl} ver­sus the distance independent parameterMz = 05/(O/H} for 29 H 11 galaxies withaccurate metallicities.

The linear fit to the data has a slope of1.03 ± 0.05 and an rms scatter of olog(L(H fl)) = 0.21, which is comparable tothe scatter of the Tully-Fisher relation.Since H 11 galaxies can be easily ob­served out to very large distances, thecorrelation between L(Hß} and Mz can

_indeed be a very useful cosmicyardstick provided its zero point can beaccurately determined.

As I discussed above, the extragalac­tic distance scale is tied to the galacticscale via cepheid variables. Thus, in or­der to calibrate the zero point of the(L(H 1l), Mz} relation for H 11 galaxies wemust use giant H 11 regions in nearbyspiral galaxies. The properties of manysuch H 11 regions have been extensivelystudied mainly by Sandage andTammann who used the Sersic-San­dage correlation to calibrate distances.

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Giant HII regions

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or more extremely luminous giant H 11regions, others are essentially star-likeobjects where only the giant H 11 regioncomponent is visible and are probablytruly intergalactic, galaxy-size H 11 re­gions. Figure 1 presents a log plot ofL(H fl} versus 0 for a sampie of H 11 galax­ies for which the luminosities have been

..........'<"I

(f)

(f)CJ)L(1)

'-.../

1.2

Log () (km s-1)Figure 2: Logarithmic plot of the integrated HfI luminosities of giant HI/ regions in nearbygalaxies as a function of fine-profile width.

HII Galaxies

•.......... •~

I(f) 41 • •(f) ••CJ) • •L •(1) •• •

'-.../ •.......... 40Q::l..:r: ... •'-.../ • •--l ••••CJ)0

--l 39

•1.1 1.2 1.3 1.4 1.5 1.6 1.7

Log () (km s-1)Figure 1: Logarithmic plot of the integrated Hf, luminosities of H 11 galaxies as a function of theirline-profile widths in velocity units. Ho = 100 km/sec/Mpc is assumed.

20 Mpc where the angular diameters ofeven the largest giant H 11 regions be­come comparable with the seeing disks.However, the linear diameters of giantH 11 regions correlate very weil with thewidths of the nebular emission lines,which in these bright H 11 regions areextremely easy to measure.

Thus, replacing H 11 region diametersby line-widths in the Sersic-Sandagecorrelations, a new powerful distanceindicator is obtained. However, theemission line profile widths also corre­late extremely weil with the luminositiesof giant H 11 regions and this correlationhas the advantages (over the previousones) that it does not require inclinationcorrections for the magnitudes of theparent galaxies and that the reddeningcorrections to the giant H I1 regionluminosities can be done in a self-con­sistent way using the Balmer decre­ments. Thus, the method I am going todiscuss here relies on the correlationbetween Hfl luminosity (L(H 1l)), the emis­sion line-profile widths (o) and the Oxy­gen abundances (O/H) of giant H 11 re­gions.

Since, to obtain a meaningful value ofHo, we must observe galaxies beyondthe Virgo cluster we have applied themethod not to giant H 11 regions in dis­tant spiral galaxies (which would be toofaint) but to the so-called "intergalacticH 11 regions" or "H 11 Galaxies" whichmay be defined as being dwarf galaxieswith the spectrum of giant H 11 regions.In fact, while some H 11 galaxies areclearly dwarf irregular galaxies with one

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HII Galaxies

o

o

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luminosities predicted by this equationto the observed fluxes corrected for ex­tinction. Before discussing the results,however, I must say a few words aboutradial velocities and about Malmquistbias.

Corrections ...

(a) The Radial Velocities

If one knows velocities and distances,Ho is simply obtained as Ho = V/R. Theradial velocity of almost any galaxy canbe easily obtained with present-day in­strumentation from the Doppler shift oftheir spectral features. In the case of H 11galaxies, for example, even at large dis­tances the Doppler shifts of the emis­sion lines can be obtained with expo­sures of only a few seconds. However,the Earth, the Sun and the Galaxy aremoving and therefore we must subtractfrom the observed velocities the motionof our frame of reference. Thus, we mustremove the motions of the Sun aroundthe centre of our Galaxy, of the Galaxy inthe Local Group, of the Local Grouptowards the Virgo Cluster and of theVirgo Cluster relative to the Cosmic Mi­crowave Background. In addition, thegalaxies themselves may be falling intoVirgo or drifting relative to the CosmicMicrowave Background and thesepeculiar velocities must also be re­moved to extract the purely expansionalvelocities. Our radial velocities incorpo­rate all these corrections with the ex­ception of streaming motions relative tothe Microwave Background which at

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05

Log L{H f1) = Log (O/H) + 41.32

The distances for H 1I galaxies canthen be obtained by comparing the

Log Mz = 5 Log (J - Log (OjH)Figure 3: Logarithmic plot of integrated H,! luminosity as a function of the distance indicatorMz. O/H is the oxygen abundance of the nebular component.

galaxies, the global luminosities of giantH 11 regions are a function only of theirvelocity dispersion, radii and chemicalcomposition. Moreover, the RC 02 de­pendence is strongly reminiscent of theVi rial theory and Terlevich and I haveproposed that giant H II regions aregravitationally bound objects, in whichcase the correlations would have a verysimple physical interpretation. But, as

.almost everything in astronomy, this in­terpretation is controversial and its dis­cussion will take us far from our presentgoal of getting to Ho.

From the (L{HIIL Mz) relation for giantH 11 regions we obtain a zero point of41.32 ± 0.08 and therefore the cosmicyardstick for H 11 galaxies is the equa­tion,

TABLE 1: The local distance scale

Galaxy Number ot Distance (Kpc) NotesHII regions adopted ST

LMC 1 50.1 52.2 Local GroupSMC 1 60.0 71.4 Local Group

NGC 6822 2 457 616 Local GroupM 33 4 682 817 Local GroupNGC 2366 3 3160 3250 M81 groupNGC 2403 3 3160 3250 M81 groupHolmb 11 1 3160 3250 M81 groupIC 2574 2 3160 3250 M81 groupNGC 4236 2 3160 3250 M81 group

M101 3 6920 6920

We have studied the correlations be­tween internal parameters for 22 giantH II regions in galaxies whose distanceshave been determined trom studies ofCepheid variables. Table 1 summarizesthe relevant parameters of these galax­ies together with the distances we haveadopted. Also listed in the Table are thedistances adopted by Sandage andTammann (ST) in their calibration of theHubble constant.

In a few cases there are differencesbetween the scale adopted here, whichis essentially the scale adopted byAaronson and co-workers in their cali­bration of the Tully-Fisher relation, andthe Sandage-Tammann scale. Thesediscrepancies have to do with the way inwhich the Cepheid luminosities arecorrected for extinction in their parentgalaxies and, although the local dis­tance scale is still the subject of consid­erable controversy, its discussion is farbeyond the scope of this article.

Figure 3 shows a logarithmic plot ofL{H rj) versus 0 for giant H I1 regions. Theslope of this relation if 4.2 _ 0.5 and therms scatter is olog (L{H fj)) = 0.23.

A Principal Component Analysis(PCA) for H I1 regions shows again thepresence of 3 parameters of the form,

Log L{H r1) = Log RC 02 - Log{O/H) +constant

where Rc is a measure of the radius ofgiant H II regions introduced by San­dage and Tammann which they calledthe core radius. This relation cannot bedirectly compared with H II galaxies be­cause we lack core radii for these dis­tant objects. However, in giant H II re­gions, the core radii corelate with veloci­ty dispersion approximately as Rc - 03.

Thus, the parameter Rc 02 is equivalentto the parameter 05 which we found forH II galaxies. Indeed, the PCA analysisof H 11 galaxies in the (L{HrIL 05

, O/H)domain and of giant H 11 regions in the(L{H 1l), Rc02, O/H) domain give essen­tially identical eigenvalues and eigen­vectors.

This leads us to conclude that, inde­pendently of the mass of the parent

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Redshift <Ho> Malmquist Numberrange km/sec/Mpc correction of galaxies

Full sampie 94 ± 5 -11 29Excluding Virgo 97 ± 5 -12 24Redshift > 2000 99 ± 5 -14 21Redshift > 4000 102 _ 6 -16 16

present are very poorly understood. The TABLE 2: The Hubble eonstant

most recent results tend to show that asfar as they can be observed, all galaxiesmove relative to the CMWB with a ve­locity of several hundred kilometres persecond in the direction of Centaurus.Thus, it is not clear at what distance oneshould start correcting the velocities forthis effect or if one should correct themat all!

(b) Malmquist Bias

This is an unpleasant effect wh ich hascaused and continues to cause endlesstroubles to those who engage in thequest for the Hubble constant. Malm­quist bias occurs because all correla­tions used to determine distances haveconsiderable cosmic scatter. So if oneselects galaxies which are brighter thana certain limiting value, close to thisvalue one tends to observe galaxieswhich are systematically brighter thanthe luminosities one would predict fromthe distance indicator in the absence ofbias. This causes the distances to bebiased towards lower values.

I am very fortunate to have EdmondGiraud ("Mr. Malmquist Bias") nextdoors who showed me how to correctmagnitude limited sampies for thiseffect. Because at any distance H IIgalaxies span a very large range ofluminosities, and because there areluminous H I1 galaxies at small dis­tances, the Malmquist effect on the dis­tance indicator is, as we shall see, verysmall.

The Hubble Constant from GiantHII Regions

The resulting values for Ho are given inTable 2 for different redshift cuts of thedata.

The errors quoted are 1 a deviationsfrom the mean of all galaxies and donot include the zero point errar. Whenthis is included, our best estimate isHo = 85 ± 10 km/sec/Mpc. this valuecompares very weil with the value of Ho= 92 _ 1 found by Aaronson and co­workers using the Tully-Fisher relation(the error they quote does not includezero point uncertainties). Gur value dis­agrees with the value of Ho = 50 ± 7 km/sec/Mpc obtained by Sandage andTammann. If we use the Sandage­Tammann local distance scale (Table 1)we obtain a value of 78 ± 10 which stilldisagrees at the 3 a level with Ho = 50.

Caveats

Recently, a well-known cosmologisttold me: "Your results are very nice,so ... what's wrong with them?" Whathe meant, of course, was that I had

obtained the wrang value for Ho. Thisillustrates the philosophical prejudicesinvolved in cosmology; this is onlynatural because Cosmology reaches theboundary between science and religion.Personally, I find the story of Adam andEve more elegant and easier to believethan the Big-Bang!

Nevertheless, observers must forsakephilosophical and theoretical prejudicesin the analysis of the weak points of ourown data. In the case of giant H II re­gions, the caveat is that the Hfl lumi­nosities of same H 11 galaxies may comefrom more than one giant H II regionsuperimposed along the line of sight.This would not only bias the luminositiestowards larger values but also introducethe gravitational potential of the parentgalaxies as an additional parameter. Asfar as we can tell from deep CCD pic­tures and spatially resolved spectros­copy, the effect of multiplicity in oursampie is small. The fact that the scatterof the H II galaxy correlations is similar tothat exhibited by the giant H II regionsampie lends strang support to thisconclusion.

It is clear, however, that if the emis­sion-line component of all H II galaxiesconsisted of four identical giant H 1I re­gions of exactly the same redshiftsuperimposed along the line of sight wewould not distinguish them from singleobjects but our value of Ho would beoverestimated by a factor of 2!

Epilogue

A large value of Ho is only one of anumber of new observations which arebeginning to erade the old edifice ofBig-Bang cosmology. Inflation, darkmatter, superstrings and other scaffold­ings are being used to save the "stan­dard" Big-Bang but in the end it willsurely fall. This should not worry us, forwe know that new buildings are alwaysmore solid than old structures. Unfortu­nately, however, there are very fewmodern buildings that are nicer than theold ones they replace.

References

For the sake of brevity I have notincluded formal references to the work Iquoted. I have based the discussion on

the following works where completelists of references can be found:

(1) R. Kippenhahn: Light from the Depths ofTime (Springer) for the history of the Hub­ble constant.

(2) A. Sandage: "The Dynamical parametersof the Universe", in First ESO/CERN Sym­posium, Large Seale Structure ofthe Uni­verse, Cosmology and Fundamental Phy­sies, p. 127, for a modern account of thequest for the Hubble constant and thedefence of Ho = 50.

(3) M. Aaronson and co-workers in As­trophysical Journal Vol. 302, p. 536(1986) for a detailed discussion of theTully-Fisher method, the various radialvelocity corrections and a defence of theHo = 100 view.

(4) J. Melnick and co-workers in ESO pre­print number 440 (1986) for a discussionof the use of giant H I1 regions as distanceindicators.

VisitingAstronomers(April 1- October 1, 1987)

Observing time has now been allocated forPeriod 39 (April 1-0ctober 1, 1987). Thedemand for telescope time was again muchgreater than the time actually available.

The following list gives the names of thevisiting astronomers, by telescope and inchronological order. The complete list, withdates, equipment and programme titles, isavailable from ESO-Garching.

3.6-rn Telescope

April: MartineVJarvis/Pfenniger/Bacon,Franx/illingworth, 1I0vaisky/Chevalier/v. d.Klis/v. Paradijs/Pedersen, Mathys/Stenflo,Frangois/Spite M/Spite F, Jeffery/Hunger/Heber/Schönberner, Hunger/HeberlWerner/Rauch, Miley/Macchetto/Heckman, Kollat­schny/Fricke, MaccagniNettolani.

May: MaccagniNettolani, Keel, Ortolani/Rosino, Cacciari/Clementini/Pn§voVLind­gren, Barbuy/Ortolani/Bica, Gratton/Ortolani,Lub/de Geus/ Blaauw/dc Zeeuw/Mathieu,CacciarilClementini/Pn§voVLindgren, Moor­wood/Oliva, Danziger/Oliva/Moorwood,Tapia/Persi/Ferrari-Toniolo/Roth, Lacombe/Lena/Rouan/Slezak.

June: Lacombe/Lena/Rouan/Slezak,Chelli/Reipurth/Cruz-G., Richichi/Salinari/Lisi, Zinnecker/Perrier, Perrier/Mariotti, Hab­ing/van der Veen, Sicardy/Brahic/Lecacheux/

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