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Extragalactic X-Ray Source Counts MAARTEN SCHMIDT California prostitute of Technology ABSTRAcr Extragalactic x-ray source counts carry information about the lumi- nosi~ function and cosmic evolution of galaxies, clusters of galaxies, BL Lac objects, Seyfert galaxies and quasars. We discuss two available x-ray source samples Ninth complete optical identifications and redshifts. We find evidence for instrumental bias in the detection of clusters of galaxies for cosmic evolution of quasars, and of absorption eDems in low-lu~mnosity Seyfert galaxies. Modest spectral and density evolution of Seyfert galaxies would allow the soft x-ray background to be made up entirely of discrete sources. We present a source count prognosis for the AXAF energy range 0.5 - 10 keV INTRODUCTION Extragalacdc x-ray sources are identified with galaxies, clusters of gal~es, BE L!ac objects, Seyfen gal~es and quasars. Optical studies of these objects have shown strong cosmic evolution only for quasars. For galaxies, evolution is suspected but there is no well documented variation of the luminosity function. Clusters of galaxies are difficult to find optically at high redshift and no reliable counts are available. There is no well defined optical sample of BL Lac objects. Only one complete optical sample of Seyfert gal~es, based on the CfA redshift suney, is available. Counts of extragalactic x-ray sources promise lo play an important role in studying evolution. We discuss a non-parametric procedure for the derivation of luminosity function and source counts. We apply this 336
HIGH-ENERGY ASTROPHYSICS 337 method to the two well defined x-ray samples that have complete optical identifications and redshifts. We find evidence for insturmental effects in the detection of clusters of gahies, for evolution of quasars, and for absorption effects in low-luminosi~ Seyfert galaxies. On the basis of the luminosity functions developed, we present an x-ray source count prognosis for the AXAF energy range 05 - 10 keV. DERIVATION OF LUMINOSllY FUNCTION Consider an x-ray sample that is complete over a given area of sky to a limiting 0= Slim in a given energy band. Since the luminosity function that is derived from such a sample is a linear combination of the contributions from the sample sources, we start by considering one single source. Hypothetically, we move this source radials away from us, maintaining all its absolute properties. As the redshift ~ increases, the flux S declines: let S(z) be the flwr-redshift relation for this source. We can invert this and derive z(S), which is the redshift at which the given source would have an observed flux S. Now let V (<z) be the co-moving observable volume out to redshift z, for a given cosmological model Substitution of z(S) in V(<z) produces V(>S), which is the volume over which the source will be observed to have a flux of S or greater. Since our sample was complete to flux S'`m, V(>S`im) is the volume over which the given source will be included in the sample. Since the luminosity function is the space density of sources, as a function of their luminosity, the one source provides a contribution of 1/V(>S'im) to the lu- minosity function at the source's luminosity L. The total luminosity function is the sum of the contn~ution of the n sources that comprise the complete sample, ~(L) = ~ Vans [2) DERIVATION OF SOURCE COUNTS We now derive the source counts corresponding to the luminosity function just determined. Let us return to the one source in the original complete sample, which yielded a space density of lJV(>S'im). At a flux larger than S. this source can be seen over a volume V(>S) and therefore we should obsene V(>S)/V(>S`im) of such sources brighter than S. The total source counts are again He sum of the n individual contn~utions, N(> S) = Ni(> S) i 1 Vs(> Slim)
338 AMERICAN AND SOVIET PERSPECTIVES We illustrate this procedure by considering the counts produced by just one source in the HEAO1 A-2 survey (Piccinotti et al. 1982~. We assume that it has a power law spectrum with energy spectral index-0.7. We employ a cosmological model with Hubble constant Ho = 50 km s-iMpc-i, and q0 = 0.5. We also assume that there is a redshift cutoff at Zmaz = 2. Figure 1 shows the counts generated by the source, depending on its x-ray luminosity ~ = L=~2-10 keV), in erg/sec. At the lowest luminosity illustrated, log HX = 41, the counts follow the-3/2 law expected in Euclidean space for fluxes larger than log S(2-10 keV) ~ -13. For sources of higher luminosity, the slope at a given flux becomes progressively smaller. Clearly, for most extragalactic x-ray sources, the -3n law is a very poor approximation. The str~ing differences in the predicted source counts for different luminosities are also reflected in the contribution to the x-ray background. In our example, the source counts corresponding to a single source of luminosity log HX = 41 contribute 13% to the observed background at 2 keV. For log HX = 43 the contn~ution Is 1% and for log HX = 45 it is only 0.1%. The non-parametric procedure for the derivation of luminosity function and source counts, described above, takes into account cosmology, in terms of S(z) and V(<z), as well as the shape of the spectral energy distribution, through S(z). No assumptions are needed about the shape of the luminosity function. If there is a need to account for luminosity or density evolution, then the luminosity or number density can be varied as a function of redshift for each of the n sources contributing to the luminosity function. The r.m.s. error of the predicted source counts (due to the sampling error in the sample used to generate the source counts) can be estimated by assigning an r.m.s. error of +100% to each of the n contributions. For further details about the non-parametric derivation of the lunninosipr function, the reader is referred to Schmidt and Green (1986~. IWO COMPLKlE X-RAY SAMPLES There are two x-ray samples for which optical idenitifications and redshifts are essentially complete. These are the HEAO1 A-2 survey (Piccinotti et al. 1982) and the Einstein Medium Sensitivity Survey (MSS) (Maccacaro et al. 1982; Gioia e! al. 1983; Stocke e! al. 1984~. Sky coverage, energy bands, flux limits and numbers detected in the two surveys are given in liable 1. The MSS has a distn~ution of flux limits versus sly coverage. The flits limit given in Able 1 is an effective limit; this limit would produce the observed number of sources if it applied uniformly to the entire area of the survey. Since the two surveys differ in flow limit by a factor of around 100, a
HIGH-ENERGY ASTROPHYSICS 339 HEAO] A-2 ~ source 3 2 1 - o En A - - 1 o / q0 = 0~5 ME =-0.7 Zmax = 2 -2 ~ -3 _ log HX = 41 , it/ -11 // // // / l ~1 45 1 1 1 -13 -15 log S(2 - joked FIGURE 1 Source counts based on one single source of luminosity HA hypothetically observed in the HEAO1 A-2 suney. detailed comparison of their content is of interest. In malting the compar- ison, we generally use the sample with the larger number of objects of a given class to predict the expected number in the other sample, following the procedure described in the preceding sections.
340 AMERICAN AND S0~7ET PERSPECTIVES TABLE 1 X-RAY SURVEYS WITH COMPLETE IDENTIFICATIONS HEAO] A-2 EINSTEIN MSS Area 27, 000 deg-2 89.1 deg-2 Energy 2-10 keV 0.3-3.5 keV Limit 3 x 10-11 cgs 3 x 10-13 cgs BE Lacs 4 4 Galaxies 1 3 Clusters 30 20 Quasars 1 23 AGNs 20 32 BL Lacs: The two samples, both very small, are consistent with each over for a uniform space distribution. Gak~s: Based on the three galaxies in the MSS, we expect one galaxy in the HEAO1 A-2 for a uniform space distnbutiom Numbers are very small so there is large uncertainty. Quasars: We define as quasars those active galactic nuclei with optical absolute magnitude MB < -23. Besides the one quasar (3C 273) in the A-2 sample, there is the BOX sample, a small subsample of the Bright Quasar Survey (cf. Schmidt and Green 1986~. Both of these samples contain fewer objects than are predicted from the 23 quasars in the MSS for a uniform space distribution. This constitutes pure x-ray evidence for the evolution of quasars, independent of optical evidence. We invoke luminosity-dependent density evolution to fit both the x-ray counts, as well as the total surface density of quasars with z < 2 of around 70 deg~2. This evolution is somewhat different from that used by Schmidt and Green (1986~. Casters of galaxies: Schmidt and Green (19863 found that there was a large difference between the luminosity distnbutions of clusters in the two samples. Further study shows that there is only a discrepancy at the bright end: based on the A-2 sample, we expect 25 clusters with log HX > 44.4 in the MSS, but none are observed. Part of He explanation is probably that
HIGH-ENERGS: ASTROPHYSICS 341 the MSS detection efficiency for clusters is low. If part of the discrepancy is due to cluster evolution, it would have to be very steep. For clusters of lower luminosity log HX < 44.4, the two samples are consistent with a uniform space distnbution. AGNS: We define as AGNs (or Seyfert galaxies) those active galactic nuclei with MB > -2~. Bow samples contain substantial numbers of AGNs. There is a discrepancy opposite in sign from that found for clusters: based on the A-2 sample, we expect 25 AGNs with log HX > 43.5 in the MSS, but only 9 are observed. Following Reichert et al. (1985), we explain this as a consequence of absorption by clouds of 6X1022 H at cm~2 with a coverage of 70%. SOURCE COUNT PROGNOSIS We have derived a source count prognosis for the AXAF energy range 0.5-10 keV, based on the evaluation of the HEAO1 A-2 and Enstein MSS samples, discussed in the preceding section. The x-ray counts for the different classes of objects are shown in Figure 2. It is essential to keep in mind the uncertainty associated with this prognosis. As we saw in the preceding section, the reconciliation of the contents of the HEAO1 A- 2 sample and the Einstein MSS sample require invoking evolution (for quasars), instrumental effects (for clusters), and absorption (for AGNs of lower x-ray luminosity). There is considerable uncertainty associated with each of these interpretations. In addition, we have assumed a uniform space distribution for galaxies, BL Lacs, clusters of games and AGNs. Each of these objects probably elicits some cosmological evolution. The predicted number of x-ray sources with log S(0.5-2.0 keV) > -15 is 800 deg~2, of which AGNs contribute 500 deg~2. At this flux, total counts vary approximately as S~0 9. The total x-ray background produced by descrete sources in this prognosis is 52% of the observed background at 2 keV, and 30% at 10 keV. We also consider an alternative scenano, in which the entire back- ground is accounted for by discrete sources. We postulate that the AGNs evolve in number and spectrum such Hat the background at 2 keV and at 10 keV is entirely due to discrete sources. This is achieved if the AGNs show density evolution e2 i57 and have an energy spectral index of ~.7 + 0.6T, where ~ is the light-travel time in terms of the age of the universe. In this scenano, the number of AGNs with log S (0.5- 2.0 keV) > -15 increases to 2500 deg.-2. The median redshift of these AGNs would be around 1.0. While there is no physical basis for this AGN evolution scenario, it does illustrate, that AXAF may provide important clues to He composition and the nature of the x-ray background.
342 __ cn A 0 - o - 1 AMERICAN AND SOVIET PERSPECTIVES 3 WkAGN/.' /' Gel / ./ / /' 1 _ - !. i' ';/Wk Cl <; '' .4 11 _r Cl BLLac J - 13 109 S(0.5 - 1 OkeV) 15 FIGURE 2 Source count prognosis for the AXAF energy band 0.5-10 keV. See text for a discussion of the uncertainties associated with this prognosis DISCUSSION The study of the evolution of extragalactic x-ray sources is clearly in its infancy, win only two samples available that have complete optical identifi- cations and redshifts. Complications arise as a consequence of the reduced detection efficiency for clusters of galaxies and the internal absorption in low-luminosity Seyfert galaxies. These ejects can be incorporated in the non-parametric derivation of the luminosity function and associated source counts described above.
HIGH-ENERGY ASTROPHYSICS 343 Only for quasars can the effect of evolution be seen clearly in the available samples. We may hope that evolution of other x-ray sources such as clusters of gal~es and Seyfert galaxies may be derived from surveys to be earned out with ROSAT, AXAF and other missions. This would be of great interest, since no other in particular, optical~vidence for the evolution of these objects exists at the present time. REFERENCES Gioia, I.M., 1: Maccacaro, R.E. Schild, J.T Stocke, J.W. Iiebert, IJ. Danziger, D. Kunth, and J. Lab. 1983. The medium sensitivity survey: A new sample of x-ray sources with optical identifications and the revised extragalactic log N - log S. Astrophysical Journal 283: 495-511. Maccacaro, I, E.D. Feigelson, M. Fener, R. Giacconi, I.M. Gioia, R.E. Griffiths, S.S. Murray, G. ~morani, J. Stocke, and J. Liebert 198Z A medium sensitivity x-ray survey using the Einstein Observatory: The log N-log S relation for extragalactic x-ray sources. Astrophysical Journal 253: 504 511. Picanotti, G., RF. Mushot~ly, EN Boldt, S.S. Holt, F.E. Marshall, PJ. Serlemitsos, and RN Shafer. 198Z A complete x-ray sample of the high-latitude (| b 1>20°) sly from HEAO1 A-2 Log N-log S and luminosity functions Astrophysical Journal 253: 485-503. Reichert, GN, RF. Mushotzly, R. Petre, and S.S. Holt. 1985. Soft x-ray spectral observations of low-luminosity active galaxies. Astrophysical Journal 296: 69~9. Schmidt, M., and R.F. Green. 1986. Counts, evolution, and background contribution of x-ray queers and other intragalactic x-~ay sources. Astrophysical Journal 305: 68~. Stocke, J.1:, J. Liebert, I.M. Gioia, IRE. Griffiths, 1: Maccacaro, IJ. Danziger, D. Kunth, and J. Lub. 1983. The Einstein Observatory medium sensitivity surrey: Optical identifications for a complete sample of x-ray sources. Astrophysical Journal 273: 458~77.
