Requirements for Cosmological Studies in Radio Astronomy

SEBASTIAN VON HOERNER

Summary-Two types of world models and their main propertiesare discussed briefly: the steady-state model and the simplest rela-tivistic models. In some world models there is a horizon whichprincipally limits any observation within a certain distance. Thequestion investigated is what requirements must be met by ob-servation (and theory) in order to distinguish between differentworld models.

A comparison of various observational methods and their require-ments shows that the most promising method seems to be observingangular source diameters and distances between double sources bylunar occultations of radio sources. (The resolution given by theedge of the Moon is better than 1 sec of arc.) This method requires asingle, fully steerable dish of more than 300 ft diameter, and a fastcalculating machine.

Because of the traveling time of light, one must always look backinto the past if one wishes to look out into space; one would see themost distant sources almost at age zero with a large antenna. Thus,a theory is needed to describe the formation and development ofstrong radio sources. Without it, no conclusions about world modelscould be derived from observations.

INTRODUCTION

C< OSMOLOGY tries to understand and to describethe universe as a whole, its present state as wellas its evolution, and even its "beginning" if, in

fact, there was one. Since our actual knowledge is andalways will be limited, cosmology invariably means alarge extrapolation into the unknown. In general,scientists may have, and they actually show, three dif-ferent attitudes toward cosmology. First, one can ask,with a certain spirit of temerity, what kind of a worldis possible at all. This leads to the so-called "worldmodels," each model describing a world which might berealized from all we know; however, theory alone cer-tainly can never decide which, if any, of these models isthe true one. Second, one can keep more closely to whatone actually sees, trying to push his limits of observa-tion as far out into space as possible. The results donot encompass the world as a whole, but try to stay alittle closer to reality. Third, one can choose a markedscepticism, regarding the first attitude as a merespeculation, and the results of the second one as a mis-interpretation of observing errors. In the end, all threeattitudes are necessary and helpful, and only by theirconcerted action and counteraction might we approachthe truth. This paper will attempt to combine the firsttwo attitudes by the question, "What is required fordistinguishing between different world models fromobservation?" The third attitude is left to the reader.

Manuscript received March 9, 1964. This article is based in largepart on a paper presented by the author at the OECD Symposiumon Large Antennas for Radio Astronomy, Paris, Dec. 12-14, 1961.

The author is with the National Radio Astronomy Observatory,Green Bank, W. Va. (Operated by Associated Universities, Inc.,under contract with the National Science Foundation.)

I. COSMOLOGY

To begin, a somewhat vigorous short cut throughcosmology is appropriate to show where the worldmodels come from which are to be tested, in order tomention some of their main properties, and to discussthe principal limits of any observation. The followingwill be restricted to a special class of relativistic modelsand to steady-state theory.

A. World Models

Starting with Riemannian space and imposing theconditions of homogeneity and isotropy, it followsthat the space-time metric can be written as

ds = d - R2(t)du2 (1)

where t is the time, u represents three dimensionlessspace coordinates moving together with the expandingsubstratum, and R is a time-dependent scale factor ofthe dimension of a length. If properly normalized, Rmay represent the radius of curvature of the world. Butone more assumption is needed in order to get R asfunction of time.

In general relativity, it is assumed that each bodymoves along a geodesic line. This yields the differentialequation

2GMR~2 = - - sc2c

R(2)

where G= the gravitational constant, Al= the mass with-in 47rR3/3, and c= + 1, 0, -1 for hyperbolic, parabolic,or elliptic expansion. It is characteristic for general rela-tivity that the type of expansion also defines the curva-ture of space which becomes hyperbolic, flat (Euclidean)or spheric. In (2), another term has been omitted forsimplicity, and the pressure has also been neglected.

In steady-state theory, it is assumed that the worldoffers the same view at any time, which leads to

R(t) = Ro eHot (3)instead of (2). It also leads to the conclusion that newmatter is being created constantly.

B. Some PropertiesDefining the first two derivatives of R in a dimen-

sionless way, we have

H=RIR and q = -RR/R2 (4)

called the Hubble constant and the deceleration parame-ter respectively, their present values being Ho and qo.

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von Hoerner: Cosmological Studies in Radio Astronomy

Fig. 1 gives an illustration of the time development ofvarious models and it can be seen that an evaluation ofqo not only would define the type of model we live in,but also might yield information about the presentstate of development.

I = Ru (5)

is now introduced as the "physical distance" of twopoints. If the expansion of the world could be stoppedfor a while, and then the distances by the travelingtime of light would be measured, we would get just this1. In a spherical world, traveling along a "straight line"as defined by the path of a light ray, we have

u

07r/27r

27r

5 le

Sk -10

S

p

,

44,

5.00 ~ ~ O

q = 0.5

Fig. 1-The time dependence of R and q for different models.

a

I

startequatorantipolehack again

U

0 if 2w

Fig. 2-Angular diameter and distance in spherical world models.

If one could see beyond the antipole, one would seethe most distant galaxies twice, at exactly oppositedirections, with equal angular diameter, but with dif-ferent brightness and redshift.Another quantity of interest is the angular diameter

6. If we have objects of equal linear diameters, theirangular diameters would vary with distance as shownin Fig. 2 for spherical models. There is a minimumdiameter 63m which would occur at the equator in a staticworld but nearer to the observer in an expanding world.

C. Limitations

Rindler1 has defined three types of horizons, but onlywhat he calls the "particle horizon," defined as theboundary between things observable and things not

observable (at present for an observer at rest in thesubstratum) will be used here. This definition impliesthat objects at the horizon have infinite redshift andthat they can be seen at age zero;

Z =cat horizon. (6)

T =0O]

Some world models have no horizon, for example, therelativistic model, with q0 =0 and the steady-statemodels.Cosmology is concerned mainly with two things: the

structure of space, and the creation and development ofobjects. Thus one might want to ask space questions ortime questions. Observationally, however, it is neces-

sary to look back into the past if one looks out into spacebecause of the traveling time of light. One thing cannotbe done without the other, and it will be a difficult task

1 WV. Rinder, Alonthly Notices Roy. Astron. Soc., vol. 116, p. 662;

1956.

to disentangle the answers to both kinds of questionswhich we will get simultaneously.

If one builds extremely large instruments, one willclosely approach the horizon, thus becoming able toanswer the time questions (at least if qo>O), becausethe full history of the world lies within the horizon.However, in order to answer the space questions, anappreciable amount of curvature must lie before thehorizon, which might not be the case. The question,then, is this: which comes first, the equator or thehorizon? This is illustrated in Fig. 3, where an equatoris defined for the elliptical case by u =7r / 2.The result is the following. Tinme answers can be

forced by building extremely powerful instruments, butone might be principally limited with respect to spaceanswers if the equator of the world lies behind thehorizon; this is the case for

0.285 < qo < 1. (7)

Finally, one other difficulty should be mentioned. Ifone observes at very large distances, one will get veryhigh redshifts. The well known part of the spectrumthen will be driven out of the observable range, andcompletely unknown parts of the spectrum will be seen.instead. The redshifts to be expected are shown in Fig. 4for five different observational limits: 1) optical limitof spectroscopy at a magnitude2 m = 19, 2) optical limitof detection at m = 22, which coincides with the 3Ccatalogue of radio sources, 3) the new measurements ofScott, Ryle, and Hewish3 (taking a flux density of

2 Editor's Note: The brightest stars have a magnitude of 1.Magnitude increases with decreasing stellar lutminosity by 1 magni-tude per 4 db. Thus, a sixth magnitude star is 20 db fainter than afirst magnitude star.

3 P. F. Scott, M. Ryle, and A. Hewish, Monthly Notices Roy.Astron. Soc., vol. 122, p. 95; 1961.

9 -1 I NW

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-1 0 +1 +2 +3

Fig. 3-The distance I as a function of qo, illustrating the questionof which comes first, horizon or equator?

20

10

5

2

0.2

Fig.

a

f;

S=140-

of any two of these three quantities; however, in orderto use m, one has to know the absolute magnitude M,and to use 6, the linear diameter D is needed. Anotherapproach to the cosmological problem is to count num-bers N above various limits, thus getting the frequencydistribution of one of the quantities. Here, the luminos-ity function or the distribution of linear diameters oughtto be known.

In optical astronomy, the z(m) correlation seems tobe the most promising one and might yield good resultswithin the next years. The number-magnitude countN(m) has been given up completely, and angular di-ameters never were used. (For more details, see Sand-age.4) This picture might be changed by observationsfrom outside the atmosphere.

Optical astronomy has already reached a funda-mental limit, set by scintillation and sky background.This noise level is equal to an object of m= 22. Buteven from above the atmosphere a second and finallimit soon will be reached, set by the high energy of asingle optical photon. From an object of m = 22 we getonly about

1 nn) h1,r+rt,c! /ona- v2 _b~~~~~~/1tJV~~~~~~~~UPnLOSllJSl/sec;m-11

___ / in the whole optical region, but in order to observe withan accuracy of 1 per cent, we must wait for 10,000photons. Radio astronomy still is far away (by many

powers of ten) from both of these limits, and the onlyM |9 limit effective at present is the financial one. Thus,

radio astronomy has a great and unique chance incosmology. But one of the most urgent tasks is the de-

%------ velopment of new ideas for the design of extremely large

1 0 lI

antennas within reasonable price limits. The success-I 0 1 2 3 45

A , in this direction will be called the first requirement of sixElliptic discussed in the paper.

Paabolic Radio astronomy reaches extremely far out intoStua*stata space and time, but it yields very little information. At

bl- atisticse , -present, there is no way of measuring redshifts of dis-p =, A=o tant objects, and no way of telling their absolute

4-The redshifts to be expected for different observational limits luminosities. This is a terrible handicap; more and moreLnd different world models. The optical limits have been calc.u- spectral observations of extragalactic sources shouldated for the brightest galaxies in clusters, and the radio limitsor Cyg A-type sources. definitely be provided over a large range of frequencies

and at many points in order to eventually find indicatorsfor redshift and luminosity. Powerful multichannel re-

0ftXdiametW/m cpservi as limi 4)wavround dish ceivers might facilitate this task. This will be called-ft d1ameter, observing wength ith the second requirement.

I1!aSer 01 Lu , 0) VC1 y iaig1 UMV11cX.IlIcA, iU Uliig OA1V/

sources/steradian. Ryle must already have reachedsources with redshifts between 2 and 6, depending on

the actual world model, and with the very large an-

tenna, one would observe redshifts between 5 and 30.

II . OBSERVATIONA. GeneralThe observational quantities used for cosmology are

the redshift z, the apparent magnitude m, and perhapsthe angular diameter 8. One may ask for the correlation

B. The Number-Magnitude CountOn the theoretical side, there are various world

models to be compared with observation. These modelsare concerned with the metric (1), and with its changewith time (2) or (3). Their effects on observation may

be called "world effects"; they can be calculatedtheoretically and checked against observation. But ob-

4 A. Sandage, Astrophys. J., vol. 133, p. 355; 1961.

V'AZ

_/ / / = ~~~22; kc- Catelope

I a a

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11 1

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von Hoerner: Cosmological Studies in Radio Astronomy

jects will actually be observed which will have a historyof their own, comprising the frequency of their occur-rence as well as their individual development. Effectsof this type may be called "object effects." Any ob-servation will contain both types simultaneously.

Unfortunately, no theory whatsoever is available forthe object effects and, therefore, no detailed observa-tional requirements can be given. If Scott, Ryle, andHewish3 are right, we already see these effects verysignificantly. But to understand these findings a theoryof peculiar galaxies is needed which might be called arequirement concerning the theoreticians. This theoryis also needed for subtracting the object effects fromthe observed ones in order to get the world effects sep-arated. This will be called the third requirement.The observational requirements for getting signif-

icant world effects can be given, provided that theabove separation becomes possible. In two recentpapers5 6 there has been an attempt to estimate: 1) upto which limiting number of sources per steradian, Niim,one ought to go in order to see the differences betweenvarious world models, 2) what instrumental propertiesare needed for reaching this limit, and 3) which is thecheapest way to meet these requirements.Two independent estimates gave the limiting number

as about

Niiim = 3 X 105 sources/steradian. (8)

In optical astronomy, this would mean countinggalaxies up to m = 28. In radio astronomy, it meansobserving sources down to a flux density S =2 X 10-28W/m' cps (at 158 Mc). Every radio telescope has twolimits: its sensitivity or brightness limit (flux densityof the weakest observable source), and its resolutionlimit (distinction between neighboring sources). Thefirst limit is given by the total collecting surface; thesecond one by the baseline between different parts, forexample, by the separation between two antennas of aninterferometer, or by the length of a Mill's cross. Bothlimits are illustrated in Fig. 5 for various wavelengths.The brightness limit of an antenna-receiver system

can be written in a simple form. If, for the present pur-pose, the atmospheric limitations on both sides of thespectrum aie neglected, and if it is assumed that thenegative slope of the log N-log S diagram is not too dif-ferent from 1.5 and that the flux densities go aboutwith the power 0.8 of the wavelength, it is found thatfor the number of visible sources per steradian

= O .45

JVvis = 524-~A1l5

8-

7-

6-

5-

4.

3.

2-

I.-

0 -

-1 -

I4ZzoN

x 100 0 0000000I

100 *000 10000 100000 Mc

loom 10 1 0.1 0.01

Fig. 5-The number of observable sources per steradian for tubereceivers. a= diameter of round dish (in m) with surface equal tothe total collecting surface of the antenna. b=diameter of basearea (in m) over which the antenna system is spread.

noise temperature of receiver and background in °K,and A is the effective collecting surface of the antennain m2. In (9) it is assumed that a signal/noise=5, in-tegration time-= 10 sec, and bandwidth = 5 per cent offrequency. In order to meet (8), the surface must be atleast

A > 69T/XO'3. (10)

A rediscussion of the resolution limit showed thatthere must be at least

75 beam areas/source. (11)

In order to meet (8), the beamwidth then must be

, . 49 seconds of arc (12a)

or the base line must have at least the length

b > 5040X.(9)

where X is the wavelength in meters, T is the over-all

5 S. von Hoerner, National Radio Astronomy Observatory, GreenBank, W. Va., NRAO publ. No. 2; 1961.

6 S. von Hoerner, National Radio Astronomy Observatory, GreenBank, W. Va., NRAO publ. No. 4:1961.

(12b)

If an instrument were to be designed for this verypurpose, it then should operate exactly at both bright-ness limit and resolution limit (with no waste of antennasurface or base area). But then both disturbances,noise and background, add up, and the numerical valuesof the last equations need to be changed slightly;

a- l

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I a I I 2 3 4 5

Hypetolic Elliptic

Skudy sb* Panblic

40

X0

20

1S

Fig. 6-The distances I reached by the same observational means asin Fig. 4, compared with horizon, equator and antipole. Thedotted line shows the distance at which the angular diametershave their minimum.

,'

\ VLA

_\_

\

10\

5

m = 19

q0

-l J 1 2 3 4

Fig. 7-The traveling time of light r for the most distant objectsobservable, compared with the "expansion age" of the world.Hubble constant of 75 km/sec Mpc is used.

A = 110 T/X0 3

0 = 35 seconds if working at both limits. (13)b = 7100X

Eqs. (8), (10), (12), and (13) are summed up as thefourth requirement. The Benelux Cross will be high abovethe brightness limit and will just meet the resolutionlimit of this requirement.An antenna meeting the fourth requirement is ab-

breviated as VLA (very large antenna). Fig. 6 showshow far out into space a VLA would reach; the otherobservational limits of Fig. 4 are also shown. The VLAwould reach to the equator of the world if qo .1.6,which means one half or more of all Cygnus A-typesources would be seen. On the other side, if qo is closeto zero, there is a good chance that the curvature ofspace, this time a negative one, would be seen.

If the type of expansion is connected with the curva-

ture of space as postulated in general relativity, thenthe horizon will cross the antipole at qo = x (at themaximum of the oscillation). Thus, distant sources willbe seen twice at exactly opposite directions not beforethe world begins to collapse. But nevertheless, a trialmight already be risked in order to check this postulate.

Observations with this VLA will contain significantworld effects, but these might be completely blurred byobject effects; how serious this is going to be is shownin Fig. 7. Even the present observational limits reachalarmingly close to the "beginning of the world," andthe VLA will see her most distant objects at an age ofonly 108 years. Besides blurring the world effects, theobject effects might become extremely interesting fortheir own sake.

C. The A ngular Diameters

Hoyle7 has pointed out that the minimum feature ofangular diameters may provide a good test for worldmodels, but Sandage4 has shown that a minimum occurs

only if the measured angular diameters belong to metricdiameters (same linear diameter for objects at all dis-tances) but not for isophotal diameters (same measuredsurface brightness). The following is restricted to metricdiameters only.The minimum occurs at finite redshift only if qo>0,

and the distance at which it occurs is shown in Fig. 6.The present radio observations should have crossed thisdistance if qo>0.1. Table I gives the values of redshift,distance, flux density (for Cygnus A-type sources, at100 Mc), and the minimum diameter (belonging to a

linear diameter of 20 kpc).5 The relativistic model withqo=0 and the steady-state model approach a minimum

I F. Hoyle, presented at Paris Symp. on Radio Astronomy, Paris,France; 1958.

8 Kiloparsecs (1 parsec=3.26 light years).

I

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diameter, too, but only so for infinite redshift and zeroflux density.Having no redshifts and absolute magnitudes in radio

astronomy, the best use of angular diameters might beto count numbers above a fixed flux density and abovevarious diameters. The result to be expected for qo 1and for steady state is shown in Fig. 8. If diameters ofsingle sources (about 20 kpc) are used, a resolution isneeded of about 2 inches, but if the distances betweendouble sources (about 100 kpc) could be used, about10 inches of resolution would do. Taking the scatter oflinear diameters into account, the picture of Fig. 8would be smeared out, indeed, but the Inain featureswould stay, and a distinction still seems possible.

If one wants to use angular diameters, one must meetthe fifth requirement, i.e., a resolution of 2 seconds of arcfor single sources or of 10 seconds for double ones. Thismeans a base line of 2.5 X 104 wavelengths for 10 secondsor of 1.25 X 105 wavelengths for 2 seconds.

D. Occultations of Sources by the Aloon

The above requirement seems to be a very difficultone, especially if very large numbers of sources areneeded. One possible method of meeting it might beto use the occultations by the moon in a systematicway, following the moon with a larger beam and wait-ing for occultations to occur. Time and duration of anoccultation would yield two possible positions of thesource, but this ambiguity will be removed the follow-ing month if the samne source is covered again. A fairlylarge antenna is needed to make it worth while, buta very high resolution gratis is obtained, and thiswithout any side lobes. During an observation time ofmany months, the moon will cover 90 per cent of thesky near to the ecliptic at least twice, and 96 per centat least once. At a distance from 3° to 5.60 from theecliptic, the coverage is complete.

In the light from a distant point source, the moon'sshadow on the earth has no sharp edge but is slightlysmeared out. The width of this diffraction pattern maybe given in seconds of arc (as seen from the moon), orin seconds of time (during which this pattern movesover the antenna, from a constant flux density oversome oscillations to about zero).

A3= 9.li \\

T = 16. 6 -v/X03 in sec of arc

r in sec

X in m

(14)

TABLE IMINIMUM DIAMETERS

qo

_~~~~~~

Steady State -1

0.00.10.25

Relativistic 0.551.02.05.0

* Megaparsecs.

N(8)

I

00

2.201.591.251 .000.810.64

103 MpC*

00

00

4.23.32.62.11.61.1

S a,.

10-26 sec of arcW/nm2 CpS

0.0 1.02

0.0 2.052.5 2.247.6 3.04

17.5 3.4639.2 4.187.0 5.1

239.0 6.8

10 a 30 X 10 kpc

Fig. 8- The number-diameter count to be expected for two world mod-els. Counting limit: S=0.25X10-26 W/m2cps (at 100 Mcp). Atthis limit, one would have 2 X 104 sources/steradian, suimmarizedover all diameters.

TABLE IIRESOLUTION AND WAITING TIME FOR OCCULTATIONS

x

m

0.20.51.01.352.05.0

0

sec of arc

4.16.49.110.612.920.4

sec

7.411.716.619.323.537.1

85 ft

692514131583

t (in hours)

140 ft 330 ft

15.2 1.255.6 0.443.1 0.252.9 0.233.3 0.2618.4 1.44

has its minimum at 1.35 m wavelength, and the rangeof 0.3 m<X<3 m could be used. The antenna must befairly large but needs only a moderate accuracy forthese longer wavelengths. The limit of the inethod isreached if more than, e.g., four sources are behind theMoon at a time, giving then 2.3 per cent of overlappingrefraction patterns. At this limit, we have

5 X 104 sources/steradian (15)

Table II gives f3 and r for various wavelengths, andthe average time t between occultations of two sources(waiting time) for round dish antennas of various di-ameter, operating with vacuum tube receivers.The waiting time is given by the brightness limit and

which is enough for the number-diameter count, seeFig. 8. It is not enough, however, for the number-magnitude count, see (8). The total number of sourcesobserved is

3000 sources/year. (16)

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A dish of 330 ft diameter has 8000 m2, and the sixthrequirement then is an antenna of 8000 m2 for wave-lengths of about 1 m, steerable in both directions. (SeeTable III for a summary of requirements.) This gives0=9 seconds, but it is much better to achieve a resolu-tion by a more sophisticated way of data reduction.Scheuer9 has suggested a method of restoring the bright-ness distribution across the source from the observeddiffraction pattern; further details have been worked outby the author.10 Observations have been made, and therestoring method, in fact, gives a resolution betterthan one second of arc. It really seems worthwhile tobuild a special, large antenna just for occultations.An antenna of the required dimension and wavelength

would have a beam area six times the solid angle of themoon, thus the noise contributed by the moon may beneglected against receiver noise.

I P. G. Scheuer, Australian J. Phys., vol. 15, p. 133; 1962.10 S. von Hoerner, Astrophys. J., vol. 140, p. 65; 1964.

TABLE III

SUMMARY OF REQUIREMENTS

Requirement Reason

1) New ideas for design of various No physical limits for radioextremely large antennas at astronomy for a long time.moderate price.

2) Increased effort on spectral ob- To find indicators for redshiftservations over long range at and absolute magnitude.many points of spectrum.

3) Theory of peculiar galaxies, Separation of world effectstheir radiation and development. from object effects.

4) Surface area, A =69 T/I0 3 To reach N=3X105 sources/Beamwidth, 3=49 sec of arc steradian for number-magni-

tude count.

5) ,B=2 sec of arc to 10 sec of arc For number-diameter count.N= 2 X 104 sources/steradian

6) A =8000 m2 fully steerable Moon occultations, for num-X=1 m ber-diameter count.

The Structure of the Galaxy from Radio Observations

GART WESTERHOUT

Summary-The appearance of our Galaxy at radio wavelengthscan be described as follows: The Milky Way stands out as a brightband of emission, at both long and short wavelengths. Above 50 cm,radio emission from the rest of the sky can also be observed. Thebrightness distribution is highly irregular. It can be interpreted asbeing due to the following sources: 1) Emission from ionized gas inthe galactic plane, prominent at short wavelengths. 2) Synchrotronemission from the galactic disk and the Halo, prominent at longwavelengths. It is proposed that the sources of this nonthermal emis-sion are clouds of relativistic particles and magnetic fields, possiblysupernova remnants, distributed through the spiral arms and up tosome distance from the galactic plane.

The 21-cm line emitted by neutral hydrogen permits the as-tronomer to obtain a picture of the spiral structure and to study themotions of both the gas and the Galaxy as a whole.

The galactic center and its surroundings poses a problem in itself,showing structure remarkable in both the continuum emission andin the neutral hydrogen distribution. Its structure suggests thepossibility of an explosion of the galactic nucleus in the past.

O UR GALAXY is a flat disk formed by billionsof stars, clouds of gas, and small solid particles.Stars and clouds describe circular orbits around

the center of this disk. The Sun is one of these stars.It is at a distance of about 33,000 light years from thecenter and it describes its orbit in about 250 million

Manuscript received June 2, 1964.The author is Director of Astronomy, University of Maryland,

College Park, Md.

years. The diameter of the Galaxy is approximately150,000 light years.Apart from the objects in the disk, which one can

subdivide into several groups according to their con-centration near the plane of symmetry, there are alsostars, star clusters, and gas more or less sphericallydistributed around the disk. The gas and dust cloudsform the flattest part of the disk. The thickness of thislayer is no more than about 600 to 800 light years, lessthan one hundredth of its diameter. The flatness is evenmore extraordinary; within a radius of 30,000 lightyears from the galactic center, the deviations from aflat plane are no more than 100 light years. We findthat the young stars, those which have recently beenformed from the gas and dust clouds, are concentratedvery near this galactic plane. The older the stars, thewider is their distribution around the galactic plane;the objects which are believed to be the oldest, globularclusters and RR Lyrae variables, are distributed in thespherical halo.The size of the dust particles is of the same order as

that of the wavelength of light, and the absorption ofstarlight by the clouds of interstellar dust is so strongthat it is impossible for the optical astronomer to seefurther than approximately 4000 to 6000 light years inthe plane of the Galaxy. Of course, looking away from

288 July-October