Neutral Hydrogen in External Galaxies

Arnold Rots

July 1 1975

For a topic like this there are two possible approaches

to consider one galaxy in cosiderable detail, or to consider just

global parameters of many galaxies. Limited by resolution the second

approach has been the prevailing one until recently. Now that de-

tailed studies of galaxies other than Andromeda or the Magelanic

Clouds are more or less available, it seems interesting to compare

the two approaches. In doing so, it is surprising how the same pa-

rameters and the same problems are popping up. It turns out that the

two methods are highly complementary and hence such a comparison is

very clarifying and fruitful.

I would like to start out with the integral properties

statistics on a relatively large number of galaxies. An excellent

reference which I include in these notes to cover this subject is

M. S. Roberts,1974, Interstellar Hydrogen in Galaxies, Science 183,

371.

Then I would like to discuss one galaxy in detail : M 81,

on the basis of Westerbork observations. This part is represented

in these notes by a paper given at the CNRS symposium Dynamics of

Spiral Galaxies (Paris 1974). Most of the figures of that paper are

slightly outdated at present. This, however, does not affect the

argument. Figs. 8a and 8b have been added. They contain M/L, B-V,

and relative HI surface density as functions of radius.

Reprinted fromi February 1974, Volume 183, pp. 37 1-378

Interstellar Hydrogen in Galaxi

Radio observations of neutral hydrogen yield valua

information on the properties of galax

Morton S. Rol

In the past 20 years radio spectralline techniques have been used to study.the interstellar hydrogen content of the.

nearer galaxies. .These isolated systemsof stars, gas, and dust typically havemasses in the range 10a4 to 1045 grams.They take second place on the massscale to the physical groupings and

clusters of galaxies which populate anddefine the universe.

The period during which the galax-ies themselves have been recognized asseparate entities rather than nebulouspatches located within our "Milky Wayuniverse" dates back only to 1924,when Hubble established that cepheidvariable stars, a powerful astronomicalyardstick, were present in the spiralnebula in Andromeda (1). He foundthat the nebula lay well beyond theconfines of our own Milky Way sys-tem-the "island universe" theory wasproved. An interesting and little-recog-nized sidelight was the derivation ofa similarly large distance for the An-dromeda galaxy by Opik a few yearsbefore Hubble's discovery of thecepheids (2). Opik employed a methodcommonly used today, that of assum-ing a constant ratio of mass to luminos-ity for galaxies. This assumption, to-gether with rotation and luminosityinformation on Andromeda and a regionin our own galaxy, enabled Opik toestimate the distance.

Developments of the following 30

The author is a member :of the. staff of theNational Radio Astronomy Observatory, Char-lottesville, Virginia 22901.

years included. recognittypes of galaxies, theThe discovery that theare receding. in a sysproportional to their di;velocity-distance correrelated Hubble constathe rate of expansionas well as a measure ofcounts were developedfully applied, to dernvof the universe. (Radiare being used in similawith widely differing c

The thrust of extralwas aimed at cosmolknown of the galaxiesbasic a parameter asknown for only a hanThe gaseous interstellaronly qualitatively descitical emission lines. Otof the, properties of gveloping slowly becausobservational data wobtain: spectrographphotographic emulsiophotoelectric techniqueinfancy; the number oifor extragalactic studiesurprisingly, the nummers working in thisparatively few.

The classificationstructural appearanceimportant clues to ouof these systems. Somflected an evolutionar,there was no agreeme

rection the evolution took. Figure 1summarizes in a series of sketches thedifferent galaxy types. Photographicexamples are given in. (3-5). Thereare two basic sequences: the ellipticais-es -which show no structural .features,only different degrees of apparent flat-tening-and the spirals. The latter are

ible further subdivided into regular andbarred. In the regular systems the spiral

ies. arms come from the central nuclearregion; the barred galaxies have theirspiral structure starting from the ends

berts of a central bar.As a matter of convenience, the

terms "early" and "late" are used torefer to the two ends of the sequence.

tion of different Thus, SO's are earlier than Sb's, and"Hubble types." irregular galaxies are late type systems.distant galaxies Hubble (6), in. introducing this nomen-

tematic manner clature, was careful to point out that

stance led to the no evolutionary or chronological sig-

:lation and the nificance was intended.nt, which gives The classification of galaxies is a

of the universe subjective procedure. The general fea-f its age. Galaxy tures of the different types are well

but .unsuccess-. described, and one can quickly learnre the geometry the classification scheme. But are thereo source counts any physical parameters that can be

ir analyses today associated with this subjective scheme?conclusions.) The color and the related quantity, the

galactic research integrated spectral type, are usually'ogy. Little was well correlated with structural .type.

themselves. As Another correlation, that of the ratio

total mass was of total mass to luminosity, was sug-

dful of galaxies. gested when relatively few galaxian

Scomponent was. masses were available (7). It does not

ribed by the op- appear to hold now, except for their understanding broad subdivision of ellipticals and

galaxies was de- spirals, the former having a higher;e the necessary ratio by about an order of magnitude.

ere difficult to No correlation among the variouss were slow; classes of spirals is indicated by thens were slow; larger 'sample of mass determinationses were in their now available (8).f telescopes used:s were few; and,ber of astrono- Hydrogen 21-Centimeter Emissionfield were com-

A significant correlation of a physi-of galaxies by cal parameter with structural -type isseemed to offer found in studies of the hydrogen emis-ar understanding sion at 21 cm. The fractional hydrogene felt that it re- content and the ratio of hydrogen massy sequence. But to luminosity both increase in -a.syste-nt on which di-. matic manner for later structural types

Copyright©1974 by the American Association for the Advancement of Science

EO

SO Sa Sb Sc Sd

Regular spirals

6 - ,.

SBO SBa SBb SBc SBd

Ellipticals Barred spirals

Fig. 1. Schematic representation of normal galaxy types. This is a composite of clcation systems proposed by Hubble (3, 6) and de Vaucouleurs (4).

(8). The significance of this correlationis not understood. When first found itwas thought to be the Rosetta stonewhich would aid in deciphering theHubble sequence; perhaps the clue toan evolutionary sequence was at hand.As will be discussed below, these hopeshave yet to be realized. But the corre-lation of hydrogen content and galaxytype must surely mark a significantstep in our description of galaxies..

Part of the importance of hydrogen.is that it is the most abundant, by far,of all the elements; it is nine timesmore abundant in number of atomsand twice as abundant in mass com-pared to second place . helium. Together,these two elements make up 99 percent,of the chemical mass of the universe.Within our own galaxy most of thismass is in the form of stars. Interstellar,material, dust and gas, represents abouta twentieth of the total mass of thegalaxy. It is, however, an importantcomponent for it is the stuff fromwhich new stars are made.

Interstellar hydrogen occurs in bothatomic and molecular states and atvarious levels of excitation. The firstdiscovered radio spectral line and theonly one known for 12 years arisesfrom a hyperfine transition of neutral,atomic hydrogen (HI). The wave-length corresponding to this transitionis ,21 cm. It was predicted by van deHulst (9). in 1944 and detected fromngalactic hydrogen radiation in 1951.The first extragalactic detection of 21-cm line radiation was made 2 yearslater. The source was the MagellanicClouds, the two galaxies nearest theMilky Way (10).

This year, the 20th anniversaryof such extragalactic observations, isa convenient mark for the beginningof a new era--one of high angular.

resolution studies of extragalacticdrogen through beam synthesis.first Magellanic Cloud observawere made with an antenna 36(11 meters) in diameter, with a bwidth at 21 cm of 1.5 degrees.two largest filled-aperture telescopesrently used for extragalactic line stihave beam widths of 10 by 104 by -24 arc minutes. The firobtained with the 300-foot (91telescope at the National Radiotronomy Observatory in Green BWest Virginia. The other is fortiltable plane-standing parabola ant(of the Paris Observatory locatesNancay, France. The north-south bof this instrument is dependentdeclination: at approximately 30'less the beam width is 24', at rthan 60 0 it becomes larger thana degree.

The beam

2

* 109 .

0E

SOb.

areas of these telesc

0.2 0.4 1.0 2 4Distance (Mpc)

10 .20

Fig. 2. Interstellar atomic hydrogentent for spiral galaxies plotted agairisdistance of the system. Note the r2abrupt upper limit which applies rejless of structural type.

con- Two assumptions are generally madet theather in relating the observed brightness tem-

gard- perature, TI, to the column density(projected surface density) of neutral

2 "% "*'

. . .. .* , * . .

** *

2-

*

0 'Se

E ,I , .,, ,,

+ " : " '

-+;

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I 1 1 1 1-rT Tr

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ii

are about 10-2 times that of the 36-foot telescope. Beam synthesis will give

4 an additional improvement of about10-3. The procedure involves using

Ir an interferometer (or groups of inter-ferometer pairs) at several spacings.These, combined with the earth's rota-tion, give the equivalent of an antennabeam corresponding to the separation

"4% of the interferometer elements. For21-cm line work, spacings are generally

1Ir in the range of a few hundred metersto over a kilometer. In this mannerresolutions of about 2' to 4' have been

assii- achieved at the California Institute ofTechnology, Pasadena, and at Cam-bridge, .England. The array of tele-scopes at Westerbork in the Nether-

hy- lands is synthesizing a beam of 25 arcThe seconds at 21 cm.tions A large body of information mayfeet be derived from studies of the 21-cm.Seam hydrogen line radiation from galaxies.The This includescur- 1) The total hydrogen content.idies 2) The distribution of hydrogen..and 3) The systemic radial velocity; that

st is is, the red shift of the galaxy.m) 4) The radial velocity field; that is,As- a map of loci of constant radial veloc-

lank, ity as seen on the projected image ofthe the galaxy,

enna . 5) An estimate of the total mass ofd in the system from (i) its global velocityeam profile or (ii) its rotation curve.

on Assuming that 21-cm line radiation0 or is detected, then the determinations ofnore 1, 3, and 5(i) are essentially inde-half pendent of the antenna beam size. The

ability to determine the other pa-opes rameters, 2, 4, and 5(ii), is directly'-

related to the ratio of galaxy size (or,more specifically, hydrogen extent) to

' beam size. We would like this ratio,the relative resolution, to be as largeas possible. The new era of high angu-lar resolution (small beam size) willgreatly increase and improve on therather small sample of galaxies for

SWhich good relative resolution is pres-ently available.

The past 20 years have given us.extensive data on those parameters

derivable from the lower resolutionSstudies. It is primarily this material

which will be reviewed here.

40 Hydrogen Content

hydrogen: (i) that the hydrogen isoptically thin, and (ii) that there is nointeraction with any continuum radia-tion. Under these conditions the columndensity N(0,4), in atoms per squarecentimeter, at position 0,4 is given by

N(O,€,) = 1.823 X 10" X.

fT(0,f,V)dVr (1)

where the integration is over all radialvelocities (Vr) expressed in kilometersper second. Typical beam-averagedvalues of N lie in the range 1020.to1021 atoms per square centimeter.

The total hydrogen mass in solarunits, Mt11 /M 0 , is obtained by inte-grating over the galaxy

Mn/M --= 1.236 X 10$ D2 x

fff T(o,',,V,) do de dV, (2)

where D is the distance to the galaxyin megaparsecs and the coordinatesare expressed in arc minutes. Theintegration is over all radial velocities(kilometers per second) and the con-volution of the main beam and thesource, for example, the observed con-

tour diagram. Hydrogen masses aretypically 10" ME.

A convenient form of Eq. 2, especi-ally for estimating an upper limit, is

MmH/M 0 = 1.5 X 108 D'T V 1 02 (3)

where T is the peak brightness tempera-ture, V is the half-intensity width of:an assumed Gaussian velocity distribu-tion, and 0~ and 02 are the half-inten-sity widths of the beam-averaged HIspatial distribution (taken. here asGaussian in shape). For an upper limit.01 and 0, refer to the beam size.

The neutral hydrogen content for130 spiral and irregular galaxies isshown in Fig. 2, where the derivedhydrogen mass is displayed as a func-tion of distance. (The distances arefrom a variety of sources; many arefrom systemic velocities and a Hubbleconstant (H) of 100 km sec-1Mpc-1.) The diagonal boundary inthe lower right of this figure reflectsthe observational constraint of the in-verse square law. Of more interest isthe strikingly sharp boundary along thetop of the figure. To within less thana factor of 2, the upper boundary tothe neutral hydrogen content of agalaxy is 1010 Mo. The upper bound-

ary cannot be explained as a selectioneffect, for observational selection gen-erally favors galaxies having a highhydrogen content. Rather it reflects areal boundary. Galaxies appear to havea self-regulating mechanism; givenmore than 101o Mo of hydrogen theywill convert it to some other form.Possibilities include molecular hydro-gen, regions of high optical depth, orstars. If galaxies with more than 1010Mo of hydrogen exist, they have notyet been recognized.

Three sources of error or uncertaintyare present in hydrogen mass determi-nations. (i) Observational errors in-clude poor signal-to-noise ratio, incom-plete mapping of the source, calibrationuncertainties, and so forth. When theresults of various observers are inter-compared and zero-point differencesare corrected, the typical scatter is 20to 30 percent, although much largerindividual differences are found. (ii)The distance to the galaxy is uncertain(see Eq. 2). This is an all too commonproblem in astronomy, especially in ex-tragalactic studies. For this reasonparameters which are independent ofdistance are of particular interest. Theseinclude hydrogen surface density and

Number 8 20 28 20 10

Type SO - Sab Sb - Sbc Sc - Scd Sd - Sm r

Number2 2 4 10 10 16 12 10 10 10

SO SOa Sa Sab Sb Sbc Sc Scd Sd Sdm Sm Jr

Structural type

a,

>1

0

0

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C

,0

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4)

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1.0

0.8 --

0.6 -

0.4

0.2 -

Number 17 31 39 24 130.0 - e _ - -- + s ++ -Type SO -Sab Sb - Sbc Sc -Scd Sd - Sm Ir

1.0

0.8

0.4

0.2

0.0

6 3 4 14 17 23 16 13 1 10 13SO SOa Sa Sab Sb Sbc Sc Scd Sd Sdm Sm Ir

Structural type

Fig. 3 (left). Fractional hydrogen content for galaxies of different structural type. The upper panel represents averages overseveral structural classes. Fig. 4 (right). Ratio of hydrogen mass to photographic (pg) or blue luminosity for galaxies of dif-ferent structural type. The upper panel represents averages over several structural classes.

0.20

0.15

0.10

S0.05

M 0.00

o

o 0.15

I 0.05

E

o

0 .!5

• 0.05

0.00

SEast

Fig. 5. Isometric projection of the integrated brightness temperature contours for M 31,the Andromeda Nebula; the units are *K x kilometers per second. These contours aredirectionly proportional to the projected surface density of hydrogen with 100 0 *K kmsec-1 - 1.8 X 101 atoms per square centimeter. The beam size is 10'.

the ratio of hydrogen mass to opticalluminosity. (iii) The validity of theassumption of small optical depth isuncertain. This assumption appears tohold in general for our galaxy, althoughthere are many regions of high opticaldepth. Because of the assumption ofsmall optical depth, the hydrogen con-tent of a galaxy is underestimated. Theexact amount is not known but is mostlikely less than a factor of 2. This un-certainty may be described as intrinsic.to the system and reflects local regionsof high density. Another optical deptheffect enters through the inclination, i,of the galaxy. The line of sight will belonger through an edge-on system thanthrough a face-on one. Countering thisis the greater radial velocity range inthe former case. By using suitably nor-malized hydrogen masses for a largenumber of galaxies, an inclination ef-fect has been found. Galaxies with igreater than 600 have a lower observedHI mass. This may be allowed forthrough a statistically derived correc-tion (11).

The fractional hydrogen mass con-tent of a galaxy, MIll/Mr (T = total),varies with structural type. It is about1 percent in the earliest type spirals,SO, and teaches 18 percent for thelatest type spirals, the irregular sys-tems. This variation is displayed inFig. 3. The systematic variation of thisratio with type is one of the few cor-relations of a quantitative parameterwith structural type.

No elliptical type galaxies are in-cluded in Figs. 2 and 3. Only one posi-tive detection has been reported (12)and this has been questioned by morerecent observations which set upperlimits of several times 108 M® for themass of optically thin neutral hydro-gen (13). This gives typical values ofMi/MT of less than 10-3. This verylow upper -limit is puzzling, for webelieve that stars, as they evolve, returnmaterial to the interstellar matter andthat detectable amounts (that is, wellabove the observed limits) should soonaccumulate. There have been severalsuggestions to explain this discrepancy(13). These include sweeping out of thegas by an intergalactic wind, or collec-tion of the material in the centralregion of the elliptical galaxy with aresultant triggering of the formation ofeither a star or a very massive object.

The helium content of the interstellarmedium for different regions within agalaxy, as well as for different types ofgalaxies, appears to be remarkably con-stant (14). The number ratio of heliumto hydrogen atoms is 0.11. Thus, thefraction of the total mass in theform of interstellar gas (HI and He)for the average irregular t :pe galaxy isone-fourth. In our own galaxy it isabout one-twentieth.

The hydrogen content of a galaxymay also be compared to its opticalluminosity, L o. A convenient and com-mon measure of the latter is the magni-tude in the photographic or blue part

of the spectrum, appropriately cor-rected for inclination and foregroundgalactic extinction. The ratio Mnu/Loin solar units is shown in Fig. 4 as afunction of structural type. It is inde-pendent of distance since both the hydro-gen radiation and the luminosity radia-tion depend in the same manner ondistance. The steady increase in thisratio with later type systems is evidentin the upper panel of Fig. 4. In thelower panel the apparent drop for typeSm may reflect uncertainty in the opticaldepth-inclination correction mentionedabove. This correction is most likely de-pendent on galaxy type, but there aretoo few data at present to make sucha subdivision. Most of the sample often Sm's are of high inclination andthe correction may have been underesti-mated for this structural class.

The ratio of hydrogen mass to lu-minosity is another physical parameterthat is well correlated with structuraltype. This ratio also implies a character-istic time scale for galaxies in whichthey may maintain their present lu-minosity Lo by converting their hydro-gen into stars (7). After applying vari-ous corrections to allow for mass re-tuined to the interstellar medium andto obtain the bolometric magnitude of.the young stars within a galaxy (ratherthan the total photographic magnitude),one finds that all types of spirals maymaintain their present rate of star 'for-mation for a few times 1010 years. Thisargument may be inverted to show thatan approximate doubling of the inter-stellar mass will allow galaxies to havemaintained their present rate of starformation for about a Hubble time(1/H). Thus, the large amounts of gasin late type systems (and more specif-ically the sample of late type systemsrepresented by the data in Figs. 2, 3,and 4) need not imply that they areyoung. All spirals studied in this mannermay be of the same age. The variationin hydrogen content may only reflectthe efficiency of converting interstellargas into stars, the irregulars being leastefficient and the early type spirals mostefficient.

Hydrogen Distribution

Two criteria describe the ability tomap details in another galaxy: (i) therelative resolution given by the ratio ofsource size to beam size, which wewant as large as possible, and (ii) thelinear scale of the beam at the distance

of the source. As examples consider theAndromeda galaxy at a distance of 0.69Mpc and a member of the Virgo clusterof galaxies at 12 Mpc. In Virgo, thelarger spiral systems are about 10' indiameter. For the 10' beam of the 300-foot telescope the relative resolutionsare about 30 and 1, respectively. Thelinear scale is 10' equals 2 kpc and 24kpc for the two examples. These linearscales refer to distances measured onthe plane of the sky; any nonzero in-clination will have a foreshortening forpositions off the major axis., the linedefined by the intersection of the planeof the galaxy and the plane of thesky.

For Andromeda there is a good coin-cidence between the optical featureswhich define the spiral arms and theregions of high surface density of hy-drogen (15). This coincidence is mostmeaningful along the major axis wherethe linear resolution in the plane of thegalaxy is highest. Coincidence with 10'beam radio observations are also foundoff the major axis, but the foreshort-ening ratio of more than a factor of 4makes such comparison less meaningful.Observations with higher resolution arerequired.

The highest linear resolution with afilled aperture was obtained with thecombination of the 210-foot (64-m) an-tenna at Parkes, Australia, and theMagellanic Clouds-the linear resolu-tion is 0.25 kpc. At first sight bothclouds are irregular in nature, clearlydefined optical spiral features are notpresent. A more careful study of theLarge Cloud shows that its luminousfeatures define a "one-armed" spiraland it is a prototype of the Sm categoryof spiral (16). Good coincidence in bothposition and velocity is found betweenthe extensive small-scale clumps of neu-tral hydrogen and ionized hydrogen(HII) (17).

The following picture is emergingfrom the results obtained with bothfilled-aperture and aperture synthesistelescopes. All galaxies showing spiralstructure, including our own, show aminimum in the projected surface den-sity of hydrogen in the center of thegalaxy. This is evident in the integratedbrightness temperature map for M'31shown in Fig. 5. Synthesis results forthe galaxy M 33 (18) which are in con-flict with this conclusion appear to bein error (19, 20). The surface densityreaches a maximum at some distancefrom the center. For Andromeda thismaximum occurs at about 10 kpc, for

430

Fig. 6. Two contourlevels of integratedbrightness tempera-ture superimposedon a photograph ofM 31. The inner,heavier contour isfor peak values. Theouter, lighter con-tour is 200°K kmsec-' and is one-sixthto one-eighth thepeak values. A hy-drogen concentra-tion in the southwestis outlined by a con-tour of 600°K kmsec'. The beam sizeis 10'. The year1950 is the epoch ordate to which thecoordinates are re-ferred.

420

41°

0p

e-

40*

390

0 0 h5 0 m 46m 42

m 38 m'

Right ascension (1950)

our galaxy at about 12 kpc. The hydro-gen distribution decreases from thismaximum value with increasing dis-tance from the center. A gross over-simplification of the distribution is todescribe it as a "ring."

For the early type galaxies, the spiralarms are embedded in this ring-in theregion of highest HI surface density.For later type galaxies significant partsof the prominent spiral arms are foundinterior to the region of maximum HIsurface density. Much confusion hasoriginated over this point because partsof spiral arms and, at times, wholearms-but of low surface brightness-are found in the region of maximum.hydrogen density. There is as muchcorrelation as anticorrelation betweenmany of the bright optical and HI con-centrations in late type spirals. What isof importance here is that so much ofthe prominent arms is not located inregions of greatest hydrogen distribu-tion. In the latest type systems-the ir-regulars-the central minimum is gone,replaced by a central maximum withthe prominent optical features distrib-uted throughout this maximum.

The depth of the central minimumvaries, possibly with total mass of thegalaxy. It is the small contrast betweenthe central minimum and the maxi-mum HI region in M 33 that has re-sulted in the conflicting results men-tioned above.

No satisfactory explanation for thisHI distribution is available although

34 m

several have been suggested (21). Thedata are few (only ten galaxies) and asubdivision by type makes each cate-gory woefully small. Additional infor-mation can only come from synthesistelescope observations.

The decrease in hydrogen columndensity (and hence brightness tempera-ture) at large distances from the cen-ter of a galaxy places a severe signal-to-noise limitation on the determinationof the extent of hydrogen. This is es-pecially so for synthesis observationsunless unusually long integration timesare employed. Filled-aperture observa-tions are more favorable, but the beamsize limitation restricts such studies togalaxies of large angular size. Becausethe signals are weak, special attentionmust be directed to the beam shapeand to beam side-lobes.

The 300-foot telescope has beenused to study all of the larger galaxiesahd they all show hydrogen dimensionssignificantly larger than optical dimen-sions measured to a sky-limited surfacebrightness. Such an effect was first de-scribed by Dieter (22). At a radial dis-tance of 28 kpc, Andromeda has acolumn density of about 1020 atomsper square centimeter (see Fig. 6). Thegalaxy M 81 is surrounded by a hydro-gen "envelope" which includes its com-panion galaxies M 82 and NGC 3077(14). At 30 kpc the hydrogen columndensity is also about 1020 atoms persquare centimeter. Generally this great-.est extent in hydrogen is found near

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but not on the major axis. A prominentexample is M 33 where Gordon (20)has mapped two "wings" of hydrogenat about 400 from the major axis. Hisresults have been extended with latermeasurements and the northern winghas been mapped to 75', or approxi-mately 15 kpc; the optically measuredradius is about one-half this value. The.hydrogen along the major axis has anextent of about 50' or 10 kpc.

If the mean surface density of hy-drogen is determined by using optical-ly derived dimensions a strong correla-tion with type is found, in the sensethat later type galaxies have highersurface densities (11). In an extensivestudy of moderate-sized galaxies (inangular extent) Bottinelli (23) concludedthat the ratio of hydrogen size to opticalsize varies with type, with the latergalaxies having larger ratios (23). Thesurface density-type correlation is nolonger present when hydrogen ratherthan optical dimensions are employed.Bottinelli's conclusions are importantand warrant independent confirmation.

Red Shifts

The red shift, or the systemic radialvelocity, as measured by observations ofthe 21-cm emission, is available forwell over 100 systems. The major frac-tion of these come from Green Bankand Nancay and there is excellent agree-ment between values for galaxies incommon. Comparisons between 21-cmand optical determinations give a pow-erful test of the form of the Dopplerexpression over a wavelength ratio ofhalf a million. It is important to notethat optical and radio astronomers usedifferent conventions for computing thevelocities (V). In the optical case,wavelengths are measured and thequantity cA/ A, = Vop t is employed (cis the velocity of light, A the observedwavelength, and Ao the wavelength atrest). In radio astronomy frequencies(v) are the measured quanti.ty and veloc-ities are given as cAv/ v0 = Vra i;o. Theseare not equal, rather

cAX/Xo= cV/v (5)

Optical cd (km/sec)

Fig. 7. Comparison of red shifts of galaxies measured at 21 cm and at optical wave-lengths. The inset shows the region of discrepancy. (1200 to 2200 km sec') whichoccurs with optical measurements made in the blue part of the spectrum. Only valuesderived from the red part of the spectrum are used in this velocity range in the mainbody of the diagram. Filled circles are points of normal weight and open circles pointsof low weight. The large plus signs are added for convenience in reading the co-ordinates.

For small velocities, less than 1000 kmrsec-1, the difference is 3 km sec- 1,but at 5000 km sec - 1 the differencereaches 85 km sec-1. The importanceis that it represents a systematic effectand must be allowed for in comparingoptical and 21-cm determinations. Sucha comparison is made for 136 galaxiesin Fig. 7, where both axes are expressedin the optical convention.

Over the range of about -400 to5200 km sec- 1 there is excellent agree-ment. The two regression solutions forthese data agree to within the thicknessof the line drawn in Fig. 7. However,there is a systematic difference of about100 km sec- 1 in the range of about1200 to 2200 km sec - 1, as shown bythe inset in Fig. 7. An analysis of thevarious optical data shows that thiseffect is present only when the opticalmeasurement was made from blue-sen-sitive spectra. Red spectra, where theHa line of hydrogen and the forbidden[NII] line of nitrogen are generallymeasured, do not show the systematicdifference. The cause has not been def-initely established, but it is most likelycontamination of the galaxian Fraun-.hofer H and K lines by similar absorp-tion lines in the night sky. In the mainbody of Fig. 7 only optical values mea-sured in the red have been used in therange of disagreement. The rest of thedata are based on any optical mea-surements available (14).

Velocities greater than those indi-cated in Fig. 7 have recently beenmeasured at 21 cm. Hydrogen has beenobserved in emission at 6600 km sec-'and in absorption at 8120 km sec- 1

.In both cases (galaxies NGC 7319 andNGC 1275, respectively) there is good.agreement with.. optically measuredvalues (24).

We may conclude that the form ofthe Doppler expression holds over awavelength range of 5 x 0I and overan equivalent velocity range of -400to 8000 km sec-1. Such measurementsserve as a test of the constancy, withtime, of the ratio of magnetic momentsof the proton and the electron (25). Theequality of the 21-cm and optical veloc-ities indicate, within large errors, aconstancy in this ratio over the rangeof velocities available.

A significantly larger 21-cm red shifthas been measured in absorption in thespectrum of the quasar 3C 286 (26).The line is shifted from 1420.4 to 839.4-megahertz, corresponding to z21,abs=Ahl/Ao = 0.692. The velocity profile isshown in Fig. 8. The red shift of theoptical emission line is zem = 0.849.

This difference between Zabq and zem-follows the usual pattern for opticalmeasurements where, nearly always,Zabs < Zein. The 21-cm line is quite nar-row, corresponding. to a half-width of8.2 km sec- 1 in the rest frame. Sucha narrow line is difficult to measureoptically in a faint object (the visualmagnitude of 3C 286 is 17.25). How-ever, if optical absorption lines areeventually detected in 3C 286 and havered shifts corresponding to Z21,abs thena stringent test on the above constancycomparisons becomes available. Suchoptical absorption lines together withthe 21-cm line will also yield informa-tion on the ionization state of the ab-sorbing gas.

Because of the narrowness of theline and the difference between zem andZ21,abs it seems likely that an interveninggalaxy along the line of sight to 3C286 is responsible for the absorptionline (26).

Radial Velocities and Dynamics

The Doppler shift of. the 21-cmline reflects the systemic motion of agalaxy as a whole as well as the radialcomponent of motions of the hydrogen.within the system. For galaxies signif-icantly larger than the telescope beamsuch data can be used to construct aradial velocity map of the galaxy. Com-parison with computer-generated modelsyields such galaxian parameters as theinclination of the plane, the positionangle of the major axis, the rotationcurve, and the systemic velocity. Ob-servationally, the data are influencedby the beam size, hydrogen distribution,and velocity field, and the model mustinclude all of these parameters for arealistic comparison with the observeddata. This approach has been employedin varying degrees of complexity atGreen Bank, Nancay, and Pasadena.

Most of the galaxies studied so farare comparable in size to the beamwidth, and radial velocity maps cannotbe derived. Instead the basic observ-able parameter is the global velocityprofile, a display of signal strengthversus radial velocity. The area underthis curve yields the hydrogen contentof the galaxy (see Eq. 2), The midpointof the profile is a measure of thesystemic radial velocity. The width ofthe profile may be used to derive anestimate of the total mass of the galaxy.This width is primarily determined bythe ordered motion within the galaxy,that is, rotational' and possible radial

9

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839.80 83960 839.40 83920 839.00-- Observed frequency (Mhz)

(Wavelength and velocity--.)

Fig. 8. Absorption profile in the directionof the quasi-stellar object 3C 286. The 21-cm hydrogen line has been shifted from1420 to 840 Mhz, corresponding to z =0:692.

streaming. The profile would havesharp, vertical edges for the case ofno random motions and infinitely• nar-row filters. Random motions and finitefilter widths act to broaden and taperthe edges of the profile. For a purerotational model, the half-width of theprofile (after correction for randommotion and filter width) measures thepeak of the rotation curve. This parame-ter, together with a statistically derivedvalue of the location of the peak, interms of the optical dimensions of thegalaxy, yields a good estimate of thetotal mass of a highly concentratedmass model (11).

A distributed mass model may be ac-counted for by an additional parameter,n, which is related to the shape of therotation curve (which, in turn, reflectsthe mass distribution). At present, thesame value of n is used for all spiralgalaxies, regardless of structural type.A systematic error as a function ofstructural type will occur if n varieswith type. There is a suggestion thatthis may be the case, as shown below.A comparison between galaxies whosemasses have been determined by. both

Distance to center (kpc)

Fig. 9. Observed rotation curves for threespiral galaxies of different structural type.The rotation curve for our galaxy isshown as a dashed line. At distancesgreater than 10 kpc the galactic curve isbased on an assumed mass distribution.

could. account for the necessary mass.The total luminosity of these starswould be about 1 percent of the skybrightness in the blue and would thusremain undetected in usual photomet-

21-cm and optical methods shows nodependence on type. In the mean, theradio determinations yield a total massestimate Which is twice that of theoptical determinations (11). This is asurprisingly good agreement consideringthe uncertainty in both types of deter-minations. Further, it is not clear whichapproach is responsible for the "error."Most of the optical determinations arelower limits because they refer to themass within the last measured point. Incomparing masses determined by bothmethods an attempt is made to correctfor this underestimation, but little isknown of the form of the rotation curveat large distances from the center.

This problem has been tackled by21-cm techniques, where observationsat such large distances are more feasiblethan they are for optical measurements.Three rotation curves extending to largedistances have been derived so far, andthe available data from optical, aperturesynthesis, and single dish measurementsare combined and displayed in Fig. 9(27). The sample, although small, is afortunate one, for three different typesor subtypes are represented: Sab, Sb,and Scd. Although the total masses ofthese systems are similar (approximately1011 Mo) their rotation curves andhence the mass distribution within thesystems differ quite significantly. Thedetermination of specific values of themass distribution depends on the modelused since only three of the six neces-sary phase space quantities are availablefrom observation. But it is simple toshow (and model calculations confirm)that the mass distribution varies withstructural type for these three galaxies.The earliest type is more centrally con-densed. This conclusion has generallybeen assumed to hold--on the basis ofthe distribution of luminosity within thedifferent types of galaxies--but it hasnever, to my knowledge, been demon-strated.

Another aspect of the rotationcurves in Fig. 9 is their great extent,well beyond the usually adopted opti-cal boundaries (see Fig. 6). Theremust be significant mass at these greatdistances. It is not in the form ofneutral hydrogen. Thus, at 28 kpc inAndromeda (M 31) only about 3 per-cent of the projected surface densityis in the form of hydrogen. Stars ofthe most common type, M dwarfs,

ric studies. If the mass is indeed inlate type dwarfs, observations in thefar-red or infrared should uncoverthem.

Keeping in mind the various uncer-tainties and assumptions involved inderiving the total mass of a galaxy, wewill proceed to examine the availabledata. Figure 10 shows "total" massesfor different types of spiral galaxies.They have been derived from opticaland from 21-cm studies.

As a statistical sample they must beconsidered with extreme caution forserious selection effects are presentwhich favor intrinsically massive sys-tems. This sample is not representativeof galaxies per unit volume of space.Several conclusions may be drawnfrom Fig. 10: (i) Among the mostmassive spirals, the late type systems(Sm and Ir) are, on the average, lessmassive than earlier type ones. (ii)There is no clear-cut difference ineither the mean or the maximummass for types SO to Sd. This conclu-sion is affected by the uncertainty inindividual mass determinations and bythe small sample size for the veryearliest types. (iii) Intermediate andearly type spirals with masses less than1010 M . are either exceedingly rareor this group has been seriously un-dersampled. (iv) There appears to bean upper bound of about 1012 M) tothe total mass of a spiral.

Summary

Measurement of the 21-cm lineradiation originating from the interstel-lar neutral hydrogen in a galaxy yieldsinformation on the total mass and

total hydrogen content of the galaxy.The ratio of these two quantities, iscorrelated with structural type in thesense that the later type galaxies con-tain a higher fraction of their totalmass in the form of interstellar hydro-

.:: gen. This ratio is one of the few physi-cal parameters known to correlate withstructural type. It need nbt, however,reflect an evolutionary sequence, suchas more hydrogen implying a youngergalaxy. Efficiency of conversion of hy-drogen to stars can just as easily ex-plain the correlation.

, 1010 -

E 2

10

.SO-SOa iSabi !Sbc I Scd Sm 1

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Fig. 10. Total masses of spiral galaxies ofdifferent structural types. The. data arefrom both optical and 21-cm determina-tions.

Except for the very latest systems,the total mass of a spiral does not ap-pear to be correlated with type.

Red shifts of galaxies measured atoptical wavelengths and at 21 cm arein excellent agreement. The form ofthe Doppler expression has been shownto hold over a wavelength range of5 x 105.

All spirals earlier than type Ir whichhave been studied with adequate res-olution show a central minimum intheir hydrogen distribution. The regionof maximum projected HI surfacedensity occurs at some distance fromthe center. In the earlier type spirals.the optical arms are located in theregion of this maximum surface den-sity. In the later type spirals the maxi-mum HI density and prominent opti-cal arms are less well correlated and,at times, are anticorrelated.,

Detailed studies of the HI distribu-tion and motions within a galaxy re-quire the high relative resolution ofbeam synthesis arrays. We may ex-pect significant new information fromsuch studies, which are now in prog-ress. Filled-aperture telescopes willsupply the necessary observations atzero spacing and vital statistical in-formation on large numbers of galax-

ies, peculiar systems and groups andclusters of galaxies. The two types oftelescope systems will complement oneanother. In the near future we should.have a much better description of spiralgalaxies and, we hope, a better under-standing of these systems.

References and Notes

1. E. Hubble;. paper read at the 33rd meetingof the American Astronomical Society, heldin affiliation with the American Associationfor the Advancement of Science, 30 December1924 to 1 January 1925, Washington, D.C.;abstracted. in Pop. Astron. 33, 252 (1925).

2. E. Oepik (now spelled Opik), Astrophys. J.55, 406 (1922).

3. A. Sandage, The Hubble Atlas of Galaxies(Publ. No. 618, Carnegie Institution ofWashington, Washington, D.C., 1961).

4. G. de Vaucouleurs, in Hanbuch der Physik,S. Fliigge, Ed. (Springer-Verlag, Berlin, 1959),.p. 275.

5. H. Arp, Atlas of Peculiar Galaxies (California.Institution of Technology, Pasadena, 1966).

6. E. Hubble, The Realm of the Nebulae (Dover,New York, 1958), p. 38.

7. M. S. Roberts, Annu. Rev. Astron. Astrophys.1, 149 (1963).

8.. -- , in Stars and Stellar Systems: Galaxiesand the Universe, G. P. Kuipcr and B. M..Middlehurst, Eds. (Univ. of. Chicago Press,Chicago, in press), vol. 9.

9. H. C. van de Hulst, Ned. Tijdschr. Natuurk.11, 201 (1945).

10. F. J.. Kerr and J. V. Hindman, Astron. I.58, 218 (1953); F. J. Kerr, J. V. Hindman,B. J. Robinson, Aust. J. Phys. 7, 297 (1954).

11. M. S. Roberts,t Astron. J. 74, 859-(1969).12. B. SJ. "Robinson and J.. A Koehier, Nature

(Lond.) 208, 993 (1965).13. J. S. Gallagher III, Astron. 1. 77, 568 (1972).14. M. S. Roberts, in External Galaxies and

Quasi-Stellar Objects, IAU Symposium No.44, D. S. Evans, Ed. (Reidel, Dordrecht,Netherlands, 1972), p. 12.

15. , Astrophys. J. 144, 639 (1966); in RadioAstronomy and the Galactic System, IAUSymposium No. 31, H. van Woerden, Ed.(Academic Press, London, 1967), p. 89.

16. 0. de Vaucouleurs, Astrophys. . . 131, 265(1960).

.17. R. X. McGee, Aust. 1. Phys. 17, 515 (1964);and J. A. Milton, ibid. 19, 343 (1966).

18. M. C. H. Wright, P. J. Warner, J. E.Baldwin, Mon. Not. R. Astron. Soc. 155, 337(1972).

19. D. Rogstad, I. Lockhart, M. Wright, un-published results of observations with theinterferometer at the California Institute ofTechnology, communicated by D. Rogstad.

20. K. J. Gordon, Astrophys. J. 169, 235 (1971).21. G. S. Shostak, thesis, California Institute of

Tehnology (1972).22. N. H. Dieter, thesis, Harvard University

(1958); Astron. J. 67, 317 (1962).23.. L. Bottinelli, Astron. Astrophys. 10, 437

(1971).24. For NGC 7319: C. Balkowski, L. Bottinelli,

P. Chamaraux, L. Gouguenheim, J. Heidmann,ibid., in press; G. Shostak, Astrophys. J., inpress. For NGC 1275: D. S. DeYoung, M. S.Roberts, W. C. Saslaw, ibid., in press.

25. A. Yahil, in History of the Interaction Be-tween Science and Philosophy, SamburskyFestschrift, Y. Elkans, Ed, (Humanities, NewYork, 1972).

26. R. L. Brown and M. S. Roberts, Astrophys.. 185, 809 (1973).

27. M. S. Roberts and A. H. Rots, Astron.Astrophys. 26, 483 (1973).

28. The National Radio Astronomy Observatoryis operated by Associated Universities, Inc.,under contract with the National ScienceFoundation.

DISTRIBUTION AND KINEMATICS OF NEUTRAL HYDROGEN IN M81

Arnold H. RotsKapteyn Astronomical Institute

University of Groningen, The Netherlands

Messier 81 is a large, early-type (Sab) spiral galaxy in Ursa Major. Ishall assume it .to be at the same distance as NGC 2403 which has been reckonedby Tammann and Sandage (1968) to be 3.25 (+0.20) Mpndistant.

This contribution reports on neutral hydrogen line observations of M81obtained with the Westerbork Synthesis Radio Telescope as a joint project ofLeiden Observatory and of the Kapteyn Institute at Groningen. The work in Lei-den has- been directed by Dr. W.W. Shane. The present data are in a sense stillincomplete, since probably the large spatial components of the HI distributionare lacking. From the previously published observations it is not clear howmuch HI there really is in and around M81.

However, here I shall confine myself to those aspects which are sup-posed to be the least affected by this incompleteness, namely the spatial dis-tribution of HI and its kinematics. I shall not attempt to compare the presentdata with previously obtained results (e.g. Roberts, 1972; Gottesman andWeliachew, 1975). For a more thorough discussion I may refer to Rots (1974).

ObservationsThe observations were carried out with the Westerbork Synthesis Radio

Telescope employing its 80 channel filter spectrometer. The halfwidth of thefilters is 27 km/s. The angular resolution is 23.9" x 25.6"; this correspondsto 380 x 400 pc at the distance of 3.25 Mpc, or 400 x 800 pc in the plane of-the galaxy.

Distribution of neutral hydrogenFig. 1 shows the distribution of HI in the form of a "radiograph". It

shows the spiral structure of the HI distribution very clearly. These spiralarms line up very well with the optical arms.

In the central regions there is a distinct deficiency of HI. In thevery outer regions of the galaxy, at the eastern side two large hydrogen com-plexes are present; concentration I at a = 9 h5 4m, 6 = 69018', and concentrationII at a = 9n53m, 6 = 69033'. These concentrations line up very well with athird concentration just south of M82, as revealed by a preliminary inspectionof HI data in that area. Fig. 2 is an overlay of the hydrogen distribution overa 48-inch Schmidt photograph. Concentration I is close to, but not coincidentwith the irregular dwarf galaxy DDO 66/Ho IX.

In Fig. 3 the surface density distribution of neutral hydrogen as seenfrom a face-on position is simulated. The scale along the minor axis has beenexpanded such that the linear scales along the major and minor axes in the

plane of the galaxy are equal. The column densities have been multiplied by cos590. This figure clearly shows the symmetry of the spiral pattern which can beapproximated (as indicated in the figure) by a logarithmic spiral with a pitchangle of 15 . The spiral arms persist from 3 to 13 kpc distance from the centreof the galaxy, although they are most prominent between radii of 3 and 10 kpc.Beyond 10 kpc two outer spiral arms develop close to the line of nodes.

The spiral structure of the HI is displayed more quantitatively inFig. 4 which shows the surface density of neutral hydrogen (= approximatedcolumn density along a perpendicular to the plane of the galaxy) averaged overspiral sectors, as a function of the azimuthal displacement of these spiralsectors in the plane of the galaxy with respect to the eastern spiral arm.The sectors extend over 2 kpc in radius and the average surface density isshown for three such ranges in radius. The peak around spiral phase = 0° cor-

responds to the eastern arm, the peak around 1800 to the western arm.

Fig. 5 shows the same for the color index B-V as obtained from the ob-servations by Brandt et al. (1972). The spiral arms show up as blue dips inthis figure. There is a time lag between the regions with the bluest color andwith the highest HI surface density. Assuming a pattern speed of 20 km/s/kpcthis lag is of the order of 10 million years, according to the rotation curve.

DynamicsThe velocity field within a radius of 10 kpc as obtained from the HI

observations is displayed in Fig. 6. The lines of equal line-of-sight velocityhave been dashed in regions where the signal-to-noise ratio was poor. In thenorthern half apparently anomalous velocities occur in the region of the nor-thern outer arm.

From this velocity field I derived values for the position angle ofthe receding half of the major axis (3320+3), 'for the inclination angle betweenthe plane of the galaxy and the plane of the sky (590+2), and for the (helio-centric) systemic velocity (-40 km/s+5).

The resulting rotation curve. is shown in Fig. 7. Within 3 kpc there isnot enough HI to determine the curve reliably. Between 3 kpc and 10 kpc thereis general agreement between the northern and southern halves of the galaxy.Outside 10. kpc the two.halves deviate from each other. This discrepancy is con-nected with the anomalous velocities in the northern outer arm region and mightbe caused by tidal effects due to M82. One would then also expect non-circular.motions in the corresponding region in the southern half. At present, however,it is not yet possible to clarify the influence of tidal effects; this requiresa study of M81 and all its companions which will be done in the near future.

For fitting a mass model I decided to extend the rotation curve beyond10 kpc with points from the southern half, rather than from the northern halfor the mean of the two halves, because it produces the simplest mass model. Themodel I fitted is of the type described by Shu et al. (1971), consisting offlattened inhomogeneous spheroids and a thin disk component. The rotation cur-ve produced by this model is also shown in Fig. 7.

Fig. 8 shows the mass surface density from this model, together withthe blue and yellow surface luminosities. These luminosities were derived fromthe observations by Brandt et ai. (1972), corrected for galactic and internalextinction, and averaged in circular rings, 250 pc wide in the plane of thegalaxy. The mass-to-luminosity ratio remains between 2.5 and 6, except perhapsfor the central regions where the mass model and the internal absorption aremuch less well known.

Linear density-wave theoryI attempted to fit a model velocity field based on linear density-wave

theory, as described by Lin et al. (1969), and according to the formulae givenby Burton (1971) and Rogstad (1971), to the residual velocity field. This resi-dual field was obtained by subtracting the circular motions according to themass model from the observed line-of-sight velocities.

For this fit I used the rotation curve and the epiclyctic frequenciesas derived from the mass model. Because the HI spiral arms are unperturbed be-tween 3 and 10 kpc, I assumed a pattern speed of 20 km/s/kpc which puts theinner Lindblad resonance at 2.6 kpc and corotation at 10.1 kpc. For the densi-ty contrast (the amplitude of the density perturbation in the gas) I assumed0.75. A good fit could be obtained using a logarithmic spiral with a pitchangle of 150, and invoking a phaseshift of 20 between the maximum of the HIsurface density and the potential minimum.

Fig. 9a shows the "observed" residual velocities along the minor axis,averaged over its western and eastern halves (allowing for the sign reversal)as dots. The full drawn curve represents the linear density-wave model, i.e.the line-of-sight component of the radial motions. Fig. 9 shows the same forthe major axis and the tangential motions.

The agreement between the theoretical and observed velocities is goodfor the radial component of the density-wave streaming. For the tangential com-ponent it is much less pronounced. This may be caused, however, by the assumedrotation curve, since it is difficult to separate circular motions and non-cir-cular tangential motions, whereas the separation of circular and radial motions(along the minor axis) is trivial and beyond question.

Non-linear effects and the phase shift which had to be invoked, aswell as the conditions around the resonances should be considered in a moredetailed study. We may conclude that density-wave theory is consistent with thepresent observations if the phase shift can be explained.

The Westerbork Radio Observatory is operated by the Netherlands Foun-dation for Radio Astronomy with financial support from the Netherlands Organi-zation for the Advancement of Pure Research (Z.W.O.).

References:

Brandt, J.C., Kalinowski, J.K., Roosen, R.G. 1972, Astrophys. J. Suppl. 24, 421Burton, W.B. 1971, Astron. and Astrophys. 10, 76Lin, C.C., Yuan, C., Shu, F.H. 1969, Astrophys. J. 155, 721Roberts, M.S. 1972, IAU Symp. No 44, Ed. D.E. Evans, p. 12.

Rogstad, D.H. 1971, Astron. and Astrophys. 13, 108.Rots, A.H. 1974, Dissertation, Groningen UniversityShu, F.H. Stachnik, R.V., Yost, J.C. 1971, Astrophys. J. 166, 465Tammann, G.A., Sandage, A.R. 1968, Astrophys. J. 15P?, 825

Figure CaptionsFig. 1. Radiograph of the density distribution of HI in M81. The half

power beam width (FWHP) is shown in the lower right hand corner which containsalso an indication of the linear scale in the plane of the galaxy; 64" corres-ponds to I kpc. The coordinates are right ascension and declination (1959.0).The thin features which look like pieces of large circles in the north-easternquadrant of the figure are due to uncancelled parts of grating rings relatedto M82, and are thus spurious. The crosses indicate star positions and the cen-ter of M181. (Photo by University of Princeton Observatory).

Fig. 2. A contour map of the density distribution of HI superimposed ona 48-inch Schmidt photograph. The dashed full, and thick contours correspondto column densities of 5, 10and 20 x 10 0 atom/cm2, respectively. (Photo byHale Observatories).

-4-

Fig. 3. Contour map of approximate surface density of HI (= observedcolumn density times cos 590) deprojected to a face-on orientation of the planeof M81. Note that this figure does not display the true surface density in theplane of the galaxy, since there is no information on the HI distribution alongthe line of sight. The contour interval is 1.6 Mo/pc 2 ; different shading beginsat 3.2, 4.8 and 6.4 Me/pc 2 . Superimposed is-a two armed logarithmic spiral witha pitch angle of 15° . The dashed circles have radii of 2.6 and 10.1 kpc. Theline of nodes has the same orientation as in Figs. I and 2.

Fig. 4. HI surface density as a function of spiral phase (with respectto the eastern spiral arm). The surface density has been averaged over (loga-rithmic) spiral sectors 20 wide in spiral phase and stretching over 2 kpc inradius. The three panels show different radius ranges.

Fig. 5. B-V color as a function of spiral phase. The color index hasbeen averaged over sectors 40 wide in spiral phase and extending from 4 to 6kpc radius. It can be directly compared with the upper panel in Fig. 4.

Fig. 6. Lines of equal line-of-sight velocity superimposed on a 200-inch photograph. The contours are labeled by their heliocentric velocities (km/s). The coordinates are right ascension and declination (1950.0). Dashed linesconnect the contours over areas where the signal-to-noise ratio is poor. (Pho-to by Hale Observatories).

Fig. 7. Rotation curve derived for M81. Within 3.5 kpc there is notenough HI to define the curve reliably. Between 3 and 10 kpc the northern andsouthern halves agree reasonably well. The full curve corresponds to the massmodel in Fig. 8.

Fig. 8. Surface densities of matter, and of blue and yellow luminosi-ties (Brandt et al., 1972) as functions of radius in the galaxy.

Fig. 9. Observed residual velocities (dots) and line-of-sight compo-nents of theoretical density-wave motions (drawn in full). a) Along the minoraxis. b) Along the major axis. The data have been averaged over both halves ofthe axes (allowing for the sign reversal), since in both cases there is closeagreement between the two halves. The signs of the velocities shown in thisfigure are correct for the western and northern halves of the axes. The abcis-sa is R, the distance to the center in the plane of the galaxy.

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