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The ~rge-Scale Surface Brightness Distribution of the X-Ray Background RICHARD MUSHOTZKY NASA/Goddard Space Flight Center INTRODUCTION The X-ray background and the micro-wave background are the dom- inant "isotropic" radiation fields available for measurement. While there has been a convergence of opinion on the origin of the p-wave background and the measurement of its dipole variation and upper Emits on higher order multipole terms (Klypin e! al. 1987, Strukov et al. 1987) there has been no such agreement on the X-ray background. However, because of its relative uniformity (Schwartz and Gursky 1974; Schwartz 1979; Turner and Geller 1980) its seems fairly clear that the bunk of the E > 2 keV background is also of "cosmological" origin (e.g., due to objects or truly diffuse radiation originating at z > 0.~) and as such, is of great interest. At lower energies much of the observed flux is due to a galactic component. (For a recent extensive review on the cosmic X-ray background see Boldt 1987~. Inhere has been extensive work on trying to determine the physical origin of the background. That is, whether it is due to a superposition of numerous faint '~well-known" sources such as active galaxies (Giacconi et al. 1979), an early unidentified population of AGN at high redshift (Boldt and Letter), a new population of objects, or to Ouly diffuse processes (Guilbert and Fabian 19863 or to a superposition of these. However while of great intrinsic interest these studies have not been aimed at using the XEtB to provide the cosmological information that has been gleaned from the p- wave background. Our group has been attempting an alternate approach, to use the available information on the large, > 5, scale distn~ution of the sky flux to see if the ORB can provide such constraints. 285

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286 AMERICAN AND SOVIET PERSPECTIVES As opposed to the p-wave background, much of the X-ray background is presumabb,r due to sources at z < 3 (if it is due primarily to active galax- ies) or z < 10 (as a very general limit). For the determination of large-scale motions the X-ray and ,u-wave backgrounds are thus complementary, both defining "distant" reference frames with respect to which one can measure motion. However, the X-ray background can provide information not con- ta~ned in the ,u-wave background; the distribution of matter perturbations at intermediate (0.1 < z < 3) redshifts; (see the detailed discussion in Rees 1979 of how the optical galaxy counts, ,u-wave background measures and X-ray surface brightness measurements complement each other).) Warwick et al. (1~79), and Rees (1979) have pointed out how measurements of the variation of the X-ray sly surface brightness on moderate angular scales can get the tightest constraints available on density perturbations in the universe on scales from 100-1,000 Mpc at redshifts < 1. If the sources of the X-ray background are distributed roughly like matter, variations in the X-ray surface brightness are tracers of the matter distribution on large scales. Even if most of the sources responsible for the background are not distributed in such a fashion the best estimates are that ~ 30-40% of the X-ray background comes from objects such as Seyfert galaxies, normal galaxies and clusters that are distracted like matter.2 While, potentially, this information resides in the distribution of X-ray sources (in the way that the IRAS counts were used lo examine the distribution of matter in the local universe), it is very difficult to obtain all of it from source counts alone because In of the sly surface brightness comes from sources dimmer than 3 x 10-~5 ergs/cm2-sec or two orders of magnitude below the Rosat all-sly survey limit Thus very deep surveys are required to "resolve out" the background (see below). Cataloging and identifying the ~ 1 x 106 sources/sr, most of which will be quite faint optically (M', > 20 mag), will be difficulty In addition such surveys have ~ Of course, the X-ray background does not contain the same information as the p-wave back- ground on the spectrum and amplitude of primordial perturbations. 2 In particular, Giacconi and Zamorani (1987) have estimated based on the optical-X-ray ratio of low redshift normal galaxies and the deep optical counts of Orson (1988) that ~ 13~o of the X-ray background at 2 keV is due to normal galaxies. Persicet al. (1989b), based on the local luminosity function of Seyfert galaxies, have calculated that they contribute ~ 25~o of the background and various authors have calculated that clusters contribute ~ 5-10% of the 2 keV X-ray background. ache best such use of an all-sky catalog to obtain cosmological information has been from the IRAS all-sly survey. However, there are substantial differences between an X-ray and IR sur- vey. The X-ray sources tend to be much more distant and have fainter optical counterparts. In addition, the X-ray source counts at high latitutde will be dominated by active galaxies rather than the star forming galaxies which dominate the IRAS counts. Perhaps the most fundamen- tal difference is that the IR background is dominated by local, solar system, and galactic effects while the X-ray background is dominated by effects originating at z ~ 0.5.

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HIGH-ENERGY ASTROPHYSICS 287 strong selection effects due to source spectra and extent. However, it Is clear that the Rosat all-sky data can be analyzed in a fashion similar to the IRAS data base to obtain another measure of our local velocity vector. The simplest way to see the usefulness of measuring "lumps" in the X-ray surface brightness observation is to assume a Euclidian universe and that the sources of the X-ray background are d~stnbuted roughly like matter. Then (Rees 1979), the amplitude variation in the X-ray background (AI/I)2 due to perturbation in matter (^p/p) on a scale ~ compared to the Hubble scale, AH, is roughly (~Id)= = (~p/p) (~/>H)f; where f is a parameter that describes cosmological effects and X-ray source evolution. Rees (1979) estimates that f ~ 1/2 (see Goicoechea and Martin-Mirones 1990 for a more detailed calculation). If we assume (~p/p) ~ 2, as seems appropriate for the largest scale perturbation claimed to date (the Great Attractor) and similarly (~/)H) ~ 0.~ (~ l~h-~50 Mpc3 then the predicted variations in the X-ray surface brightness on angular scales from 1/2 sterradian (z ~ 0.01) to 1-2 degrees (z ~ 1) should be of the order of 1-2% (see Shafer 1983 for a detailed discussion). Similarly interesting results can be obtained by searching for a 24 effect in the distribution of the all-sky flux (Warwick and Fabian 1979) due to velocities induced by matter perturbations on scales ~ << AH (the Compton-Getting effect). The expected peak amplitude is (^I/I)2 ~ (3 + <'jVpec/C ~ (^P/p)~/)H)Q; or more exactly (Peebles 1980) (^I/I)~ = (1 + Ct/3~^p/p)~/>H)QO 6, where c', the effective energy index in the 2-20 keV X-ray band, is ~ 0.4 (Boldt 1987~. Using the micro-wave dipole velocity of the sun as a scaling parameter we expect (^I/I)~~3 ~ 0.4%. As opposed to the fluctuation amplitude, which is confined to a small region of the sky, the "dipole-like" term is an all sky effect and thus needs a large solid angle for its measurement. If the perturbations exist on larger scales ~ ~ AH, (Warwick and Fabian 1979; Warwick et al. 1980) then one no longer has a dipole-like term but an ablate variation dominated by a 12-hour term. However the relative amplitude compared lo the micro-wave dipole term is expected to be small, < 0.6, for reasonable (bM < 102 solar masses on scales Liz ~ 1), large-scale perturbations. ~ summanze, the X-ray diffuse background should show a large-scale effect Spherical and harmonic) (3 + a) times larger in (^I/I) than the p- wave background and an effect due to the clumping of sources-which does not have a simple dipole-like shape, larger yet by a factor (f/Q). The fact that the amplitude of any 24 hour-like variation in the X-ray background is smaller than 2% (see below, Boldt 1987; Shafer 1983; Gatwick e' al. 1980) gives a lower bound on the closure ratio and the relative contribution of sources (which are distn~uted like matter) to the XRB.

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288 AMERICAN AND SOVIET PERSPECTIYES RECENT RESULTS ON "STRUCTURES" IN TEE X-RAY BACKGROUND HEAD-1 A-2 Capabilities We have used HEAD-1 A-2 data, which is the only available all sk r data base with sufficient sensitivity, to look for effects at < 5% level on angular scales > 200 square degrees. The limits on this data base are set by Poisson noise, sky fluctuations due to unresolved point sources and residual systematic errors. For the smallest field of view available from this detector (3 x 1.5 degrees) the sk r fluctuation variance is, using a point source estimator (Persic et al. 1g89), ~ 5.5 x 10-~2 ergs/cm2sec ~ the 2-10 keV band and the error due to Poisson noise is ~ 4 x 10-12 for a total variance of ~ 8% of the sky flux in the beam. Using an estimator appropriate for the fluctuations (Shafer 1983) the variance due to fluctuations is ~ 6.3 x 10-~2 for a total variance of ~ 10%. In the absence of variance due to other causes (such as background variations) the absolute value of the noise due to the sly fluctuations scales as solid angled/2 as does the Poisson error. Estimates of the variance in the internal background (Shafer 1983) are on the order of 2-3 x 10~~2ergs/cm2sec, which is not significant. Thus beam sizes of > 75 square degrees are necessary to examine surface brightness variations of < 2% with the HEAD-1 data. Galactic Component Previous studies using this data base (Shafer 1983; Twan et al. 19~) have shown that the strongest large-scale feature in the sky at galactic latitudes greater than 10 degrees is due to the galaxy. This component has an effective scale height of < 15 degrees (Figure 1 and Iwan et alp. This emission is not symmetric about the galactic plane or the galactic center and has a "softer" spectra than the "extra-galactic" background. Because it is bright? roughly 7% of the diffuse X-ray background flux at b ~ 10, 1~ 45, it has been mapped by HEAD-1 A-2 with the full resolution of the detector. At lower latitudes this component has been studied in detail by Exosat (Warwick et al. 1985) and Ginga (Koyama 1988) and it is clear from the Tenma spectroscopy that most of the emission is due to thermal processes from plasmas of T < 10 keV but as of yet its physical origin has not been determined (Koyama 1988~. It is the presence of this strong spatially complex Galactic component that makes determination of the X- ray surface brightness dipole moment in the direction of the micro-wave dipole diffictlL

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HIGH-ENERGY ASTROPHYSICS 289 FIGURE 1 The 2-20 keV surface brightness of the sly in galactic coordinates boxcar smoothed By 10 . The contour levels represent -2.5%, O. +2.5% and +5% of the mean high galactic latitude surface bnghtness. The Great Attractor Region The next strongest feature in the high latitude sly is a "bright" spot at b ~ 20, 1 ~ 330 (Figure 1) which is located in the direction of the "Great Attractor" (GA) (Lynden-Bell et al. 1988) and the large concent~adon of clusters (Scaramella et al. 1989) located at v ~ 14,000 km/sec. This region has an enhancement of ~ 4-5% of the average sky flux (^IGA ~ 7.8 x 10-~3 ergs/cm2sec/deg2, Jahoda and Mushotzly 1989) and subtends a solid angle of ~ 1,000 square degrees for a total flux of ~ 10-9 ergs/cm2-sec. If it were at the distance of the GA it would have a luminosity of ~ 3 x 1044 ergs/see and if it were due to the superposition of objects at the distance of the large concentration of clusters Lo ~ 3 x 1045 ergs /cm2-sec. We have visualtr compared our map of X-ray surface brightness with a smoothed map of the Abell cluster d~stn~ution (Figure 2), and this region appears to be the only place where an X-ray surface brightness enhancement at this level may be due to "superclusters" at z < 0.1. There is another region, a factor of 2 dimmer than may be associated with supercluster 12A in the list of Bahcall and Soneira (1984) at 1 = 30, b = 70 and z ~ 0.07. If this is a real association, and the lack of other "detections" places this ~ doubt, Lx ~ 1044, roughly consistent with the Persic et al. upper limits. We may assign an upper limit to (Ap/p) in the GA or similar region from the X-ray data of (~p/p) < (^I/I)~)Q- 6~/)H) ~ fat: using (~\I/I)~) < 0.05 and (~/AN) ~ 0.02 we find (^p/p)Q 6 < l.Sf-i, very similar to the values obtained

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290 AMERICAN AND SOVIET PERSPECTIVES ...=: -.~..~ .,, .'.:..-.2, ~ . ".. A... .. .-. . it. - ..~; I. I ... W~ FIGURE 2 Me surface density of D < 4 Abell clustem smoothed by a 10 boxcar in Galactic coordinates on the same scale as Figure 1. from model fitting the optical velocity data for the GA (Lynden-Bell et al. 1988) of (f~p/p)Q0 6 ~ 0 4. Because the GA is located close to the galactic plane it Is quite difficult to conduct an optical search for clusters of galaxies. It is thus not clear if, like other superclusters, the GA contains numerous rich Abell clusters. X-ray surveys at E > 2 keV are much less affected by reddening and sly confusion at ~ by > 5 and thus are an efficient way of searching for X- ray luminous rich Abel1 clusters. We have searched for "pointlike" X-ray sources (clusters of galaxies and active galaxies) which could be associated with the GA (Jahoda and Mushotzly 1989) and have not found any down to a luminosity limit of ~ 3 x 1~3 ergs/see, which Is considerably below the mean luminosity of Abell richness O clusters. We thus conclude that the GA if "real" it is not similar to other superclusters, which, by construction, are composed of rich Abell clusters. This raises the interesting question of whether other superclusters are similar to the GA in being composed primarily of "field" galaxies and poor groups and has important implications for studies of large-scale structures. If the X-ray surface bnghmess enhancement detected in the region of the GA is due to hot gas located in the potential well of the supercluster we may estimate its core mass as: M(gas) < 1.2 x 10l6Mo(AIGA)l/2(Tlo)ll4(Ds602o)5l2; where 4320 is the radius of the GA in units of 20 degrees, D86 is the distance in units of 86 Mpc, and T:o is the temperature in uIiits of 10 keV.

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HIGH-ENERGY ASTROPHYSICS 291 Superclusters Persic et al. (1989b) have used the same data base to place tight upper limits on diffuse radiation from optically selected "pointlike" superclusters (e.g., they have assumed that the superclusters were of angular size < 2~. They find that for a sample of ~ .046 an upper limit of Fir < ~ x 10-~2 ergs/cm2-sec. Using the HEAD-1 luminosity function of clusters of galaxies, they estimate that the Abell clusters in the superclusters would contribute an expectation value of ~ 4 x 10-~2 ergs/cm2-sec. Whey conclude that, on average, the X-ray luminosity of diffuse emission due to hot gas associated with superclusters is < 4 x 1043h250 ergs/cm2-sec, on the order of the detected diffuse emission in the direction of the Gig A uniform volume of hot gas of total mass 10~6M16 solar masses, temperature TO keV and linear size lOh-~50 R,o Mpc would have a luminosity of ~ the 2-10 keV band of L,a5 ~ 3 x lO45(M:6~2(T~ o)~/2(R~ o)-3 h50 ergs/sec. The HEAD-1 data thus indicate that the non-cluster associated mass in hot gas associated with optically identified superclusters is < 1.5 x 10~4 solar masses, on the order of the mass in hot gas associated with rich clusters. This limit already places tighter constraints (Persic et al. 1988) on the possible ba~yonic mass density than can be associated with superclusters or the fraction of supercluster mass that can be in hot gas. The all-sly X-ray surface brightness data already indicate that en- hancements of (^I/I)= > 2% on scales greater than 300 square degrees are rare. lDen using the same formalism as tor me QA and using a askance of 200 Mpc and an angular radius of 10 (scaling from the GA) we can already place upper bounds of M(gas) < 8 x 10~5(D2ooO~o)5l2 solar masses for any supercluster-like object of size > 35 Mpc whether or not it has been previously cataloged. If we assume superclusters to have a scale of 20 Mpc (Babcall 1988) and properties similar to that of the GA (CHILI) ~ 3% of the X-ray background, L ~ 1044 ergs/cm2-sec, (^p/p) ~ 2) then to detect such objects at z < 0.5 one needs a system capable of measuring the X-ray surface brightness at the level of 1-2% on scales of > 1 . Thus an appropriately sensitive X-ray surface bnghtness survey might be the best way of searching for "non-Abel! cluster" superclusters or any other vinalized concentration of banyans which might make a significant contn~ution to the mass of the universe. It is also of interest to determine whether the "voids" studied by Batuski and Burns (1985) (regions devoid of rich clusters of galaxies) have a systematically different X-ray surface brightness than the rest of the sly. If a considerable fraction of baryons in these regions did not form clusters and galaxies, the only place for this material to "hide" would be in the form of hot gas. Thus one might elect that the '~voids" might be systematically brighter than the rest of the sky. Alternatively if the difference signal is

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292 I: ,~., it; , W ax, .,.-~-~ . of. .~ AMERICAN AND SOVIET PERSPECTIVES Hi - . eS~ - :~ -a At ....... ~ .- .. ~. ~ .... .. FIGURE 3 Abe ~20 keV surface brightness of the sly in supergalactic coordinates smoothed by a 10 boxcar. The axis has been rotated so that the supergalactic 1 = 180 is at the center of the diagram. dominated by the fluctuations due to unresolved sources such as clusters and active galaxies which tend to be missing from the voids one might expect a deficit of weak unresolved sources which will slighter lower the background intensity. A preliminary analysis of the HEAD-1 A-2 data is underway. OTHER SlllUCl~URES It is apparent to the eye (Figure 1) that there are several "bright" and "dim" regions in the X-ray with relative differences of 1-2%. While visual inspection is always risky, comparison of the HEAD-1 data with the Uhuru data Corner and Geller 19803 and the Ariel -V results Chadwick et al. 1979) shows fair overall agreement in both the location and amplitude of the surface brightness distribution. As indicated above, these are not associated with Abell clusters or "obvious" voids in their distnbutions. Projection of the HEAD-1 data in supergalactic coordinates (Figure 3) shows that most of the large-scale structure (other than in the GA regions is not directly assignable to the local supercluster. At the present time we do not know the physical origin of these "lumps," whether they are due to galactic or extragalactic effects or their possible relationship to other astrophysical objects. We are in the process of correlating our data with galaxy catalogs (I>hav 1987) and are trying to determine the two-point correlation function

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HIGH-ENERGY ASTROP~ICS 293 of our data on scales > 10. On smaller angular scales the HEAO- 1 data have already placed tight bounds on the two-point correlation function (Persic et al. 1989a; deZotti et al. 1989) which constrain the two- point correlation function of clusters and active galaxies. The HEAD-1 fluctuation data already constrain models of the sponge-like or shell-like structure of the universe (Meszaros and Meszaros 1988~. Limits on the dipole in the X-ray background were obtained by Shafer (1983) from the HEAD-1 A-2 data using detectors with an effective beam size of ~ 20 square degrees. He found that the X-ray data were consistent with the same velocity and direction as the ,u-wave an~sotropy. The major uncertainty was due to emission from the much larger galactic component, the small number of independent sky elements due to the dominance of sky fluctuation noise and the lack of information about structures like the GO Boldt (1987) gives a nice graphic representation of the problem. We are flying to see if we can improve on his results using data with better angular resolution and different approaches to modeling the galactic contribution and the effects of the large-scale structures. F[rrURE WORK As indicated above, recent studies of the X-ray surface brightness dis- tnbution of the sly have been able to make interesting statements about our galaxy, the Great Attractor, the two-point correlation of clusters, the topol- ogy of the large-scale structure of the universe and nearby superclusters. In addition, a "new,' unidentified component of the sly has been detected. The HEAD-1 A-2 data base is severely limited in angular resolution and sensitivity for future studies. The question is how to proceed further. The Ginga satellite with a 2 square degree field of view and ~ 6 times the collecting area of the A-2 experiment can be a very powerful tool for the study of selected regions of the sky. There are already indications (Hayakawa et al. 1989) that it is capable of achieving sensitivity levels of ~ 5% of the sly on angular scales of ~ 2 square degrees, e.g., 1/10 the beam size of the HEAD-1 experiment, and is only limited by the sly fluctuation signal. If there exist larger regions of the sly with surface brightness differences about this level Ginga can search for them. However, because Ginga is primarily a pointed satellite and the scanning mode is quite limited, the solid angle to be examined will only be a small fraction of the sky and thus it will have to search in "interesting" selected areas (such as optically selected superclusters) for such vanations. 1b obtain even better limits on even smaller solid angles will require an independent, simultaneous measurement of the weak sources responsible for the fluctuation signal in the 2-10 keV band. For a log N-log S slope of 1.5, most of the variance due lo unresolved sources comes from objects of

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294 AMERICAN AND SOVIET PERSPECTIVES

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HIGH-ENERGY ASTROPHYSICS 295 and large ~ 50' at z' ~ 2 ~25 iS the diameter of the pancake in units of 25 Mpc ). Their luminosity is uncertain, but if at least 1% of their total mass is in gas (as is necessary for them to collapse and form galaxies), L(x) > 1045 ergs/sec. SODART and XMM with their great sensitivity to surface brightness should see these systems as large, > 20', (Ho = 50, q0 = 1/23 diffuse objects with a surface brightness of ~ 1/10 of the diffuse X-ray background. Pancakes which have not collapsed or which have formed late might be visible as X-ray emitting larger objects at smaller redshifts. ACKNOWLEDGEMENTS Most of all I would like to thank Keith Jahoda who has done all the really hard work and without whose efforts I would have had no results to present. I thank M. Persic for discussion of results before publication and E. Boldt for continuing and enlightening discussions. I also thank E. Boldt and the entire HEAD-1 A-2 team for their care and attention to detail 15 years ago that has made this data set available for analysis. REFERENCES Bahcall, N. 1988. Ann. Rev. Astron. and Astrophys 26: 631. Bahcall, N., and R Soneira. 1984. Ap. J. 277: 27. Batusld, D., and J. Burns 1985. A. J. 90: 1413. Boldt, EN 1987. Physics Reports 146: 216. Boldt, E^, and D. Leiter. 1987. Ap. J. Lett 322. L1. De Zotti, G.F. et al. 1989. in preparation. Giacconi, R. et al. 1979. Ap. J. Letters 234: L1. Giacconi, R., and G. Zimorani. 1987. Ap. J. 313: 20. Goicoechea, LJ., and J.M. Martin-Mirones. 1990. M.N.R^S. submitted. Guilbert, P., and A Fabian. 1986. M.N.RA S. Ad. 439. Hayakawa, S. et al. 1989. prepnat. Jahoda, K. 1989. B.A^S. 20: 1086. Jahoda, K, and R Mushotzky. 1989. Ap. J. 346 in press Klypin, AA, M.V. Sazhin, IN Stn~kov, and D.P. Skulachev. 1987. Postma Astron. Zb. 13: 259 Koyama, K 1988. In: ~naka, Y. (ed.~. Physics of Neutron Stars and Black Holes. Universal Academy Press, Tolyo, Japan. Koyama, K 1989. PAS J. 41: 679. Lahav, 0.1987. M.N.RNS. 225: 213. Lynden-Bell, D. et al. 1988. Ap. J. 326: 19. Meszaros, A., and P. Meszaros. 1988. Ap. J. 325: 25. Peebles, J. 1980. Physical Cosmology. Persic, M., Y. Rephaeli, and E. Boldt. 1988. Ap. J. Letters 327: L1. Persic, M. et al. 1989a. Ap. J. Letters 336: L47. Persic, M. et al. 1989b. in preparation. Rees, M. 1979. In: Giacooni, R., and Setti feds. X-ray Astronomy NATO Advance Study Institutes Series. Scaramella et al. 1989. Nature 3~: 562. Schwartz, D. and H. Gursky. 1974. In: Giacconi, R., and H. Gursky (eds.~. X-ray Astronomy.

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296 Saw, D. 19~. ID: Bail, and Pele~D Ads.). X-~ WIDOW (COST). Pe~amon Pan. Sedemi~ ~ 1~. 1. ~ Brim Opd=. By: 1~. Sba~ R. 1~3 Spada1 Bu~uabons ~ the Dig <~ Ba~muDd. Pb.D Un-~ of ~and. Saga, I^., D.R 3~1a~e~ ~.N Age, and AN. ^~ 1~. Puma Stan. Ah. 1~ 1e. Ames A, and ad. Gelled 1~. Ha. J. go: 1. ~1~1` ~ ~~1~, R., and ~ Fabian. 1~. ~mm ~ A. Brig, R., 1. go, and A. gun. 19~. ~.~.R.~.3. 1~ ~6. Wile, S., hi. Dog, and C. Ark. 19~. ~.~.R^S. ~ alp.