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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
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Representative terms from entire chapter:
luminosity function
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 (
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(
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
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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.
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