N O T I C E
THIS DOCUMENT HAS BEEN REPRODUCED FROM MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE Nr%W% Technical Memora►idum 82168
^V A Complete X-Ray Sample of the High Latitude (W > 20 0 )Sky from HEAD -1 A-2: Log N - Log S and Luminosity Functions
G. Piccinotti, R. F. Mushotzky, E.A. Boldt, S. S. Holt F. E. Marshall, P. J. Serlemitsos and R. A. Shafer
(NASA-TH- 82168) A COMPLETE X-RAY SAMPLE OF N82-18787 THE HIGH LATITUDE SKY FROM HERO-1 A-2: log N 10 S AND LUMINOSITY FUNCTIONS (NASA) 51 p HC A04/MF A01 CSCL 04A Unclas G3/46 13871 c AUGUST 1981
National Aeronautics and Space Administration Godord Spne FUpht Gunter ^ftla^'t^82 20771
0 SA PJ/SA Technical Memorandum 82168
4
A Complete X-Ray Sample of the High Latitude (IbI > 200 )Sky from HEAO -1 A,-2: Log N -Log S and Luminosity Functions
GI. Piccinotti, R. F. Mushotzky, E.A. Soldt, S. S. Holt F. E. Marshall, P. J. Serlemitsos and R. A. Shafer
AUGUST 1981
National Aeronautics and Space Administration Goddrd Spa* FIipht center Greenbelt, Maryland 20771 I
A COMPLETE X-RAY SAMPLIC OF THE NIGH LATITUDE (I b l > 20 0 )
SKY FROM HShOP- 1 A-2t LOG N LOG S AND LUMINOSITY FUNCTIONS
G. Piccinottil , R.F. Mushotsky, E.A• Boldt, S.S. Holt,
F.E. Marshall, P.J. Serlemitsos and R.A. Shafer2
'geboratory for Nigh Energy Ast rophysics
NASA/Goddard Space Flight Censer
Greenbelt, Maryland 20771
ABSTRACT
The HRA0-1 experiment A-2 has performed a complete X-ray survey of the
8.2 steradtans of the sky at JbI > 20 0 down to a limiting sensitivity of t 3.1
x 10-11 ergs/cm2 sec in the 2-10 keV band. of the 85 detected sources
(excluding the LMC and SMC sources) 17 have been identified with galactic
objects, 61 have been identified with extragalactic objects and 7 remain
unidentified. The log N log S relation for the non-galactic objects is well
fit by the Euclidean relationship. we have used the X-ray spectra of these
objects to construct log N log S .in physical units. The complete sample of
identified sources has been used to construct X-ray luminosity functions,
using the absolute maximum likelihood method, for clusters of galaxies and. active galactic nuclei. + 1
Xeywordst X-Ray Sources, Luminosity Function, Cosmic X-Ray Background
1 NAS/NRC Research Associate ^l 2Also Dept. Physics ,6 Nitronomy, Univ. of Maryland r ;E 4 2
I. INTRODUCTION
The HEAD-1 satellite experiment A-2 (Rothschild at al. 1979) with its extended energy range, complete sky coverage, low and stable .internal background and moderate spatial resolution has enabled us to create a complete catalog of X-ray sources at galactic latitudes Jbi > 20 0 down to a limiting
,sensitivity of 3.1 x 10 -11 ergs/cm2 sec In the 2-10 keV band. Recent
identifications of these sources by modulation collimator experiments on
HERO-1 and SAS-3 as well as imaging detectors on HEAD-2 has resulted in
certain identifications of all sources of flux c 4.0 x 10-11 ergs/cm2 sec, pending confirmation of two clusters and NGC 7172, and reasonable
Wentif ications for 78 out of the 85 (92+x) sources in the sample. All but 9
of these :identifications are extremely likely or certain. This identification
ratio for the extragalactic sources compares to identification of 45 out of 67
(674) sources in the sample of Warwick and Pye (1979).
The completeness of this sample enables construction of the
number-intensity distribution (log N - log S) for X-ray sources as well as
developing X-ray luminosity functions for clusters of galaxies and actbre
galactic nuclei. In addition the body of X-ray spectral data returned 'by A -2
allows us to cast the log N - log S distribution in absolute rather then
instrument dependent units which enables comparison with the log N - log S
relation in different X-ray energy bands (cf. Giacconi at al. 1979).
Analysis of this data shows that the source counts are well fit by a
"Euclidean" law with
5/2 1 sr-1 = 16.5 S (R15 cts/sec)_
consistent with previous results despite the quite different samples (Warwick
3
and Pye 19781 Schwartz 1979). The luminosity functions are well fit by power
law representations with
dN -7 -2.15 44 -1 -3 3.5 10 L44 (10 erg/sec) - Mpc 44
for clusters of galaxies, and
dN c -1 • 2.7 x 10 (10 44 erq/sec) Mpc 3 dL 7 L aa75 44
for active galactic nuclei,, similar to previous results (McKee at Al- 19801
Pye and Warwick 1979). Integration of the luminosity functions over
the c 1042.5 _ 1045 erg/sec range within which they are well determined
results in estimates of the contribution of clusters and active galactic
nuclei to the integral. 2-10 keV unresolved X-ray background of 4 4% for
clusters and c 20% for active galaxies. Using these luminosity functions,
with no evolution, we estimate that 4 30% of the sources seen in the Einstein
Observatory deep survey (Glaccont at al. 1979) should be relatively low ^ j luminosity (L < 1 x 10 44ergq/sec)/sec) nearb (x 0.5) obj ects.
II. DATA ANALYSxa AND SOURCE SELECTION
The HERO- 1 A-2 experiment, desar.:ibeJ in detail by Rothschild et al.
(1979), provided two independent, low background, high sensitivity surveys of
the entire sky six months apart. We have analyzed the A-2 data in order to
obtain a complete flux limited sample of extragalactic X-ray sources. The
region between -200 and +200 in galactic latitude has been excluded to
minimize contamination from galactic sources, A circle of 6 degrees radius
around the LMC sources has been also excluded to prevent confusion problems.
Therefore, we remain with 65.5 % of the sky (8.23 star). The statistical 4
significance of the existence of the sources is tested by determining the decrease in X2 when the new source is adde.i to the model. All sources in the sample give a decrease in X2 of at least 30. The probability of having, by chance, a decrease of 30 in X2 with two degrees of freedom (scan angle and intensity) is 3 x 10 -7 0 This probability is almost the same as the one ansoc.iated with a deviation of So in a Gaussian distribution (6 x 10`7).
Therefore, we can also state that the Lowest statistical significance for the existence of the sources included in our sample is 5a, as required by the maximum likelihood methods we use to determine the log N log S parameters
(see Section IV-1). Taking into account this statistical significance requirement we estimated the completeness level of the first and the second scan as 1.25 and 1.8 R15 counts/sac respectively, see Figure 1. one R15 count/sec c 2.17 erg cm-2 sec-1 in the 2-10 keV energy band for a power law spectrum with photon ,index 1.65. R15 in a counting rate derived using the
1.50 x 30 FWHM fields of view of the second layer of the argon counter and both layers of a xenon counter. This combination has a FWHM for the quantum efficiency from s 3 to C 17 keV'(Marshall at al. 1979).
The second pass is less sensitive on average, because much more time was spent in pointing at sources. We shall be more concerned with the first pass data in deriving best fit parameters and use the second pass ones mostly as an independent confirmation.
Ill. OBSERVATIONS
A. The Sample
Table 1 contains all the relevant data for the 68 sources either brighter than 1.25 R15 c/o in the first scan which corresponds to days 248-437 of 1977, or brighter than 1.8 in the second scan, days 73-254 of 1978. Source names are listed in column 1. Column 2 contains previous catalog names. 5
First pass f.'luxgps and /a errors are in column 3, while the second pass ones iI are in colamn 4. Some fluxes may differ slightly from previously reported results, as different procedures have been useds e.g., in the recent paper by
McKee at al. (1980) fluxes have Teen obtained fixing the X-ray position at the optical position, .instead here we have used the best fit X-ray position to . , derive the flux. Available identifications are listed in column 5. The type of object is in column !. one * in column 7 indicates firm identifications
(i.e. as provided by the SAS-3 or HMAO-1 modulation co111mator4 or by the
Einstein X-ray telescope), two * indicates possible identification consistent with larger error boxes. Redshift values and references are given in column
8. Spectral ,information is now available for more than half of our sources
(Mushotzky at al. 1980; Worr'all at al. 19801 Mushotzky 19791 bolt ` 19801 Holdt
1980), we quote in column 9 conversion factors between R1,5 counts/s and ergs
n-2 s-1 . Wen spectral information is lacking we assumed a 6 kev thermal bremestrahlung spectrum for all ►'sources identified with clusters and a 1.65 photon index power law for all sources identified with active galaxies. An average conversion factor value of 2.5 x 10 -11 ergo cm-2 s-1/R15 counts s-1 was assumed for the few unidentified sources. Columns 10 and 11 contain the first and second pass luminosities in units of 1044 erg s-( calculated for Ho
50 km/s/Mpc and qo 0.5. Column 12 contains notes.
B. Classes of Sources Sixty of the 82 sources brighter than 1.25 counts s- 1 in the first scan and not definitely associated with galactic objects have been associated with extragalactic objects. Only 7 remain unidentified at the present time. These
60 identified sources subdivide almost equally between clusters of galaxies.
(30) and single galaxies (30). Most of the 30 galaxies are Seyfert galaxies
of class 1 or 2, but we have also 1 Q80 (3C 273), 4 BL Lac objects, and 1 "ncs^mal" galaxy (NGC 7172). Note that M3) and the Magellanic Cloua sources are not included in our uxtragalattc sample because they represent a local
inhomogensity as part of the local group of galaxies. Table 2 lists the 17 high galactic latitude sources not included in our extragalactic sample because they have been identified with galactic or "local" objects. The second pass sample contains only 37 sources brighter than 1.8 Rl5 counts/sec, all but one Identified. The source classification is consistent with the
first pass. Assuming Poisson errors, 'cluouers contribute 50 1 9e of the
identified sources in the first pass and 61 J 13% tit tho second. Galaxies contribute 50 t 9% in the first scan and 39 # 10% in the second.
C. New Sources and Sample Completeness
H0328+025 and H0917-075 are the only entirely new sources in Table 1.
Figure 2 shows their error boxes. All the other sources in Table 1 have been listed somewhere else before. The improvement in our sample, as compared to previously reported ones, is due to a better rejection of non-extragalactic sources, made possible by the recent identifications, and to a uniform sky coverage to a relatively low limiting flux.
As the instrument has a fairly large (1.50 x 3.00 ) angular resolution the possibility of source confusion must be considered. The total area of the sky included in this survey is approximately 2.7 x 10 4 square degrees, therefore there are about 6 x 10 3 independent positions on it. As the high galactic latitude X-ray sources bright enough to give confusion problems at our sensitivity level cannot be more than a hundred using the log N-log S relation derived later (taking into account also the possibility that two weaker sources can simulate a source bright enough to be included in our list) we therefore expect negligible confusion. That is using d c 16.5 S-1.5 there are roughly 65 resolution elements per source, of S > 1.25 cts, well above the 7
confusion level of 25 beam areas per source often quoted in the literature. in addition the uniform sky coverage at the chosen sensitivity levels provided by this experiment and the availability of two .independent sets of data for cross-checking purposes support our confidence in the completeness of our sample.
D• Space Distribution of Sources Since the pioneering work of DeVaucouleurs (1958) much attention has . n been devoted to findinq evidence of a supercluster centered in the Virgo cluster of galaxies. We plotted the positions of our sources in supergalactic coordinates looking for some kind of anisotropy. Figure 3 shows the lot pass sample. Obviously, no anisotropy is observed as most sources lie beyond the supercluster. If we restrict our attention to the 12 sources with redsh.ifts less than .01 (In boxes in Figure 3), we see that 9 are in the center region of the supercluster while 3 are in the anticenter and that all but one have supergalactic latitude less than 30 degrees in absolute value This result, which is significant at the few percent level, suggests that close X-ray galaxies may lie preferentially in the supergalactic plane. But no conclusion can safely to shade from such a small number of objects at present. IV. THE NUMBER--FLUX FUNCTION
The usual power law form
N(S) = KS-0 (R15 counts/sec) -1 sr-1 (1) has been assumed for the number-flux relation. The various methods applied to estimate the coefficient K and the differential exponent a as well as to evaluate the goodness of the fit are outlined in the next section.
A. Statistical. Methods 9
1. Maximum Likelihood
Crawford, Jauncey ar„d Murdoch applied the maximum likelihood method to unbinned data In order to estimate the slope of the number-flux relation of radio ,sources. in the first paper (Crawford et al. (1970) a solution is worked out for error free data. in the second paper (Murdoch at al. 1973) the method to extended to include errors on the measured fluxes. Numerical corrections to the error free answers were calculated for the special case of Gaussian distributed errors. In the same paper it was pointed out that a minimum signal-to-noise ratio of five is required so that the uncertainty in
the correction factor due to weaker sources does not dominate the correction
itdelf. This is why we excluded from our sample sources with statistical
significance less than 5o. In both Tapers I and iI the Kolmogorow-Smirnov test (here after: K-S test) was suggested to evaluate the goodness of the fit
obtrined. In the remainder of this paper we will refer to this method as to
the Maximum Likelihood (ML) method.
2. Absolute Maximum Likelihood
The ML method assumes the same underlying error distribution for
all the souces In the sample, i.e. it assigns the same to error to all the
sources. As we deal with sources of greater than 5o significance the error
assumed is one fifth of the minimum flux in the sample, or .25 R15 counts s_1
In the first scan and .36 R15 counts s-1 in the second. Table 1 shown that
these values are not very fax from the actual orrors. However Lightman et al.
(1980) have developed a, refinement of the ML method in connection with the K-S
test capable of handling sources with their own experimental_ error. Following
those authorn we will call this new statistical method the "Absolute Maxly4um
Likelihood" (AML) method. Lightman et al. (1980) worked out the AML method on
general grounds and then applied it to the evaluation of globular cluster
A 9
X-ray source masses. As this is the first application of the AM method to the number flux function, we give a short outli ne of the method below.
Assuming the form (1) for the numb •c-flux relation and a: Gaussian form P(F i ,Qi,$) for the error dixtritrition of the measured fluxes we evaluated numerically the .integral probabilities i (a) as
F idF d5 N(Sra) Woo Iss) Co Pi(a) (2) dF as N(S,a) P(rjoits) min cc
where S is the true flux, F,i and o f are the measure % fiux and error of the i-th source. F;co is a cutoff value used to avoid the apparent dtvergence at P
0. As in Murdoch et al. ().-.1)73) the particular choice of the cutoff value does not affect the value of the integral as long as the stat i stical significance of the sources is at least 5o. Fmin is the :sensitivity limit c of the sample. For every assumed a we computed the Pi ( a) for all the sources. The PI (a) should be uniformly distributed 'between 0 and 1.
Following Lightman et al. we evaluated the maximum deviation from the uniform distributions
(D I N ^) D max (a) - max (a)] max O PI(a) (3) i=1,N i=1,N
c where N is the number of sources in the sample and the P I (a) have been sorted in ascending order. Then we calculate the probability P(DMAX (a)) of observing deviations gre*ter than DM (a) from the formula for the K-S statistic given by Birnbaum and Tingey (1951) The (a,P(D (a)) function is max then plotted. The best fit value of a is the one corresponding to the maximum 10
value PMhX of the P(D,,X (a)) Mmtribut ion. obviously PMAX aust be greater than some minimum value ( say 10%) in order to accept the model. The range in a for results given below on a are evaluated from the values a^ and a2 of a, which reduce P(Dmax(a)) to PM X/2•
3.Chi-Square
Both the ML and the AML methods are independent of the coefficient x of the number-- flux relation, as K in lost in normalising the probabilities. Therefore, we used the X2 method to determine K. Dins with equal expected number of sources for a - 2.5 have been used for
the X2 calculations, of course, in calculating confidence bounds, we have
assumed that the functional form of the distribution is the "truo" one. If
better data later shows that this is not true our confidence values are not applicable.
V LOG N - LOG S RESULTS
The ML method applied to the 60 non-galactic sources brighter than 1.25
Ri5 counts 6" 1 in the first pass gives (In this section we use R15 counts 8-1
as the unit)
a - 2.67 t .23
with a goodness of fit probability ( evaluated using the KS test) of 39.5
percent.
For the 37 non- galactic sources brighter than 1 . 8 R15 counts s-1 in the
second pass the ML result is
a - 2.74 # .32 I
with a probability of 17.5 percent.
The AMR, results are
4 w 2.63 t •2
. , in the first pass, sea figure 4a, and
G * 2.74 * .22
in the seccndo see Figure, 0.
'rho 68 and 95 percent probability contours for the lot pass values of K and a evaluated with the X2 method are plotted in Figure 4c The X2 best fit values and la errors for the number-flux function parameters are
. - a .. 2 72 +115 (4)
K R 20 +4.0 (Rl5 counts/sec) o-1 or•^.
The differential ;number-flux data as well as the best fit function
N(S) - 20 8- 2672 (R15 counts/sec) -1 or-'
are plotted irs F. qure 51 the X 2 value of the fie is 2.79 for 6 degrees of
freedom, corresponding to a probability P( > X2) c 83%. The limited size of
the second scan sample does not allow a good estimate of the probab ility but
the results are consistent with the first pass ones.
C. Number Flux Relation in Physical Units
Using theconversions factors listed in column (9) of Table 1 we can
r :c 12
4 i kk `x l express the fluxes in ergs co-2 1 and evaluate the number- flux relation
accordingly. Conversion factors range approximately from 2 . 0 x 10 -11 to 2.9 x
10" 11 ergs cm72 s-1 ( R15 counts -1^ -1 r the highest values referring to soft
spectra sources whose emission peak lies below our instrument energy window.
An a consequence of the different conversions factors the completeness level
I of the samples when fluxes are in ergs cm-2 s-1 is equal to the former
completeness level in R15 counts s-1 times the maximum conversion factor: that is s 3.6 x 10-11 ergs cni 2 8-1 for the first pass and 5.2 x 10-11
ergs/cm2 sec in the second pass. The lot scan sample with this flux
restriction contains 51 sources: 25 clusters 22 "galaxies" and 4
unidentified sources. The best fit values and 1 a errors for the number-flux
function parameters obtained with the three methods agree with
a c 2.85 t .3 (5.65-1.3) x -19 ) a-lsr-1 (5) K 10 (ergs cm 2 -1 +1.9
The 32 second scan sources brighter than 5.2 x 10 -11 ergs cm 2 8-1 give us a
best fit of slightly steeper slope a 4 3.1 t .4.
VI. DISCUSSION OF THE RESULTS
All the first pass samples #-whether fluxes are expressed in R15 counts
0-1 or in ergs cm7 2 s-1 are consistent with the five halves Euclidean slope
(see Figures 6 and 7). The slight preference for a steeper than Euci.edian
slope is due to the distribution of the brightest few sources in calculating
the likelihood functions. It is these sources that are most sensitive to
changes in a by virtue of the relativel y small statistical error in their
measured intensity. our Euclidean best fit for the lot pass data is 13
S-2.5 -t 1 N(S4) • 16.5±3 (R15 C0UAts/s) or-
with a X2 of 5.S for 7 degrees of freedom# p(X2 > 5.5) i 60%. The AMID probability for am 2.5 is 42.4%. Assuming an average conversion factor of 204 x 10-11 ergs cm 2 s`1 (R15 counts s) -1 the relation (4) becomes ., S-2.5 2e-1)-1 N(S) ,^ (1.9+:325) x 10-15 (ergs cm or-1 . ,
In agreement with the exact result
S-2.1 s 1) N(S) ` (2 . 2+ :12) x 10-15 (ergs cm 2 1 or "I
obtained from the let pass complete sample for fluxes In ergs cn 2 s-1 and
using the conversion factors In Table 1.
VII. COMPARISON WITH PREVIOUS ERPHRIMENTS
Both the Uhuru (Schwartz 1979) and Ariel 5 data (Warwick and Pye 1978)
gave a flux-number function consistent with the Euclidean model. Their beat
fit values for the coefficient K with a - 2.5 and S in R15 counts s-1 are
respectively
K - 16.5 t 3.9 using l Uhuru ct/s - 1.0 R15 ct/sec
and
K _ 15.8 j 4.2 using 1 Ariel- 5 ct/seo 2.12 R15 ct/sec
In agreement w1.th our results at the la level,. These conversion factors
assume a mean 1,115 conversion factor of 2.4 x 10 -11 ergs/sec, 1 Uhuru ct/sec = 2.4 x 10-11 erg/sec, and 1 Ar.iel-5 count/ sac - 5.1 x 10- 11 erg/sec. if we use the calibration of Marshall et a1. (1979) appropriate for the active galaxies
of 1 R15 ct/ sec - 2.17 x 10- 11 etrg/cm2 sec, we find KUhuru 4' 20 and 14
Kkri.el-S a 19, The best fit slope of Warwick and Nys of 2,7 1 .2 is also
consistent with our result,
VXXX, LUMXNOSITY rUNCfXQN
P4 0 Method and Data bane Many authors (Schwartz 19781 Mollardy 19781 McKee at al, 19801 Elvin at
al, 19771 Pye and Warwick 19791 Tananbaum at al. 19781 noldt 1980) have
reticently considered the problem of evaluating the X-ray luminosity functions
for different classes of sources principally # clusters of galaxies and active
galaxies. rll of them with the exception of Vye and Warwick had to rely upon optical elate to aelect complete samples. Wei present her* X-ray luminosity functions evaluated from X-ray .flux liPited samples. Ae we remain with a few untdonttfted sources# our results have some uncertainty, but we believe that the residual incompleteness should not be very important. 1. The samples The first pass sample of clusters of galaxies contains 30 objects- The second pass one includes 22 sources, Thirty "galaxies" are observed in the
first ;Naas, but we excluA,,e from our sample the QSQ 3C273, the 4 BL Lae objects, the peculiar galaxy M82 and the "normal" galaxy NGC 7172 as they are not homogeneous with the hulk of the sample which consists of Seyfert galaxies. 'Therefore we remain with 23 active galactic nuclei.. The second pass sample contains only 12 objects (after excluding 30 273 and PKS 2155-34d). The compl,ateness of the sample is checked using the Schmidt test and with a K-S test on the distribution of the 'Vi/V Mt as suggested by Avn;i and bahcall (1990). The results are listed in Table 3,
TABLE 3 0 OBJECTS KS TEST
CLASS OP OBJECTS SCAN w IN SAMPLE tV > POW
Clusters of Galaxies 1 30 .4711.054 18.1
Clusters of Galaxies 2 22 .5521.062 11.8
Active Galaxies 1 24 05231.059 50.4
Active Galaxies 2 12 .557*.083 56.8
The 1v error quoted for incompleteness due to the unidentified sources. 2. Methods of ?analysis Of the three methods outlines in Sec (IV-A) only the AML to suited for the determination of the luminosity function parameters. The relatively small sizes of the samples do not allow an efficient use of the X 2 square method or of any other binned method. Moreover the ML method in the form developed by Crawford, Jauncy and Murdoch cannot be used because of its assumptions of a single underlying error distribution. This laot hypothesis was :reasonably satisfied by the flux data in the evaluation of the log N log S parameters, as we already pointed out, but is not satisfied at all by the luminosity data, as the errors are proportional to the square of the redshi.ft of the sources: 2 OL 'i OP (6) On the contrary the AML method is well suited for the task. The description of Section IV-A still applies. However, .instead of calculating the probabilities of eq (2) we evaluated the probabilities: 16 L max LiW Lin d=* f(L,q) P L Vmax (LjFmin) (L,Q , L ) ~ L dL f "dL f(L,q) Vma^r (L^Fmin) p(L,cL • L ) min i Eq. (7) gives the .integral normalized probabilities of observing a source with measured luminosity less or equal to L i# assumi)iq as Gaussian error distribution with standard deviation a , and for the differential, luminosity i function the form f(L,q) where L is the true luminosity and q represents the functional parameters to be determined. Lmin and Lmax are: the lower and upper boundaries of the luminosity function. V MhX is the maximum volume at which one could detect the 'source and depends on the sensitivity limit of the sample. For a source of luminosity L in a sample of minimum sensitivity FMIN the maximum visibility volume VMAX is proportional to ( L 'min) 3 Note that Eq. (7) does not take in account errors on the redshift z. The AML method can determine the form of the luminosity function but not its absolute value. Therefore we have used a least squares fit to the unbinned data to evaluate the multiplicative coefficient. B. Results 1. Clusters of Galaxies Luminosity Function We considered two different forms for the luminosity function: the power law form 17 f(L) = Ke L/Lo between the minimum (1,44min) and maximum (L44max) observed luminosities, expressed in units of 10 44 ergs sec-1 . The normalization for a power law luminosity function scales as No-1. Clusters of Galaxies Figure 9 represents the AML probabilities for the slope of the cluster of galaxies power law luminosity function. The lot pass best fit values for the power law parameters are Y = 2.15 +.12 -.17 -7 Y-1 Mpc-3. K - (3.5 t 1.1) x 10 (1044 erg/a)rg/ )Y-1 K has been evaluated with the least squares method. The error on K has been determined by letting Y assume the 10 extreme values of 2.03 and 2.32. Figure 8r gives a binned representation of the data with the best fit luminosity function. Each bin contains three sources, except for the highest luminosity bin which contains five. The second pass results are +.16 Y 2.13-.24 Mpc-3 K = (3.8 t 2) x 10 -7 (10 44 ergs/s)Y-1 Figure 8b give the binned representation. The minimum luminosity object in both the let and the 2nd pass at 2.4 x 10 43 (ergs/s) is the Virgo cluster. The highest luminosity cluster is Abell 2142 with 2.8 x 10 45 (ergs/s). The exponential form of the luminosity function has also been considered, but the quality of the fit is poorer, see Figure 10. 1.8 As the Virgo Cluster of galaxies has a "local" character, we evaluated the cluster of galaxies luminosity function without the Virgo cluster. The lot .pass sample to reduced to 29 sources, the Mean V/V,. is 0.486 * 06055 and the 'K-S text on the uniformity of the V/VMAX distribution gives a probability r of 24.7%. The 2nd pass sample contains 21 sources, the mean V/VMAX is 0.576 .063 and the K-S probability is 6.1%• Figure 9 given the usual (y,P(Y)) probability curves for the power law slope. The best fait value@ for the parameters are lot scan Y - 2.03 t .18 +1. 28 ) 1 3 K= (2 x 10 -7 (10 44 ergs/s)Y Mpc +.2 2nd scan Y " 2'07-.25 Mpc-3 K - (3.2 j 2) rt 10-7 (1044 ergo/s) Y-1 The minimum luminosity is now t 3.6 x 10 43 ergs/s (Abell 1060) in both first and second scan. The exponential fit is again poorer, see Figure 10. 2. Active Galaxies i. Luminosity Function The insert in Figure 11 represents the AML probability for the power law slope of the active galaxies differential luminosity function calculated from the lot pass data. The best fit values for the power law parameters are: Y - 2.75 1 .15 -7 44 1Mpc-3 K = (2.7 t .15) x 10 (10 ergs/s) Y - NGC 3227 is the weakest source in the sample with 1.75 x 10 42 ergs/s and 19 1IIZw2 is the brightest with 1.3 x 1045 ergs/s. Figure 11 shows the binned representation (3 sources/bin)„ This result is similar, to that of Boldt (1980) and Pye and Warwick (1979). The exponential form for the luminosity function is not acceptable as the probabilities are always less than 2%. The second pass sample is too small for a good determination of the luminosity function, however we find power law slopes steeper but consistent with the first pass ones it. A Lower Limit to the Active Galaxy Luminosity Function The active galaxies contribution to the cosmic X-ray background depends strongly on the lower luminosity limit of the luminosity function. The lower luminosity limit for which the function can represent the data, i,44MIN , can be calculated by noting that the luminosity function must be consistent with the log N log S observations. Namely, we can set a lower limit on L44MIN by requiring that the number of active galaxies brighter than 1.25 R15 counts/sec expected from the luminosity function does not exceed the observed number plus 1 or 2 times the square root of the expected number. From eq (14.7.35) of Weinberg (1972), and assuming a power law luminosity function we have (for Y 0 2.5 and y * 3) 2.5-Y LMAX -3/2 3-Y LMAX -2 1 B EL 2.5-y 3-Y _MIN LMIN where: S is the flux in ergs cm-28-1 K and Y are the parameters of the differential power law luminosity function in Mpc-3 (erg/sec)-(Y-l) the upper and lower limit of the luminosity function LMAX and i'MIN are (actually N(>S) depends strongly on L MIN and very weakly on LMT) j X ,r 20 all the luminosities aree in ergo/* A s 3.20 x 10-75 B e 4.7 x 10 -29 (assuming Ho - 50 km/s/Mpc) NOS) is the total number of sources in the sky uncorrected for sky coverage. The second term of this equataion represents a first order cosmological correction to the Eucledian result.") (1) Foot-notes For L in units of 1044 erg/sec equation (8) has constants A - 3.2 x 10-9 B - 2.3 x 10 -7 (Ho/50) (1+P) where r is the spectral index of the source (here chosen to be .7) Assuming an average conversion factor of 2.17 x 10 -11 ergs cm-20-1 per R15 counts s-1 we find that the 10 lower limit on LMIN is 4 x 10 d2 When Y 3s 2.75 and K is 2.68 x 10 -7 (1044 ergs/s) -1 Mpc-3 and LMAX varies between 5 and 15 x 10 44 ergs/sec. In Table 4 we show the 1 and 20 limits on LMIN as a function of LMAX and Y. We note that we have not included in Table 4 the possibility that all (or some) of the unidentified sources could be Seyfert galaxies. However, considering the distribution of identified sources with flux < 3 R15 cts/sec, we would expect, at most, 3 of these unidentified objects to be active galaxies. TABLE 4 APPROXIMATE LKIN FOR VALUES OF LMAX AND Y 1.5 x 1045 "MAX - LMAX - 3 x 1045 Y Y 2.6 2.75 2.9 2.6 205 2.9 10 1.5x1042 2.5x1042 4.5x1042 1.5x1042 3.ox1042 4.5x1042 20 4.5x1041 1.5x1042 2.5x1042 5.5x1041 1.Sx1042 3.0x1042 C. Discussion . a I. Clusters of Galaxies We note that our luminosity function for clusters of galaxies is very similar to the result of McKee et al. (1980). This .indicates that, whatever selection effects are operating in making a X-ray or optically complete sample, they do not strongly bias the result. However there is a strong overlap in the individual objects between this sample and McKee's. The method we have used has allowed us in principle to discriminate between exponential and power law luminosity functions for clusters. It is somewhat surprising that a power law is favored, since it requires a change in form at low luminosities in order not to exceed the space density of all clusters (Bahcall 1979). However, the contribution of clusters to the diffuse X-ray background (DXRB) depends only weakly on the lower limit chonen. We do remind the reader that an exponential form is not excluded. Our data are not capable of rejecting the exponential form. They are also not capable of determining well the three constants in Bahcall's (1979) suggested form of the luminosity function. Keeping in mind that the mean X-ray spectrum of clusters differs significantly from the diffuse X-ray background we shall, for historical reasons, compare the 2-10 keV volume emissivity of clusters to that of the diffuse X-ray background. For qo - 112, Ho 50 km/sec/Mpc the 2-10 keV background has a volume emissivity of 4 2.4 x 10 39 erg/sec/Mpc3 . The 2 contribution of clusters is t^'MIN f(TA) LdL 1 1 x 10 38 ergs/soc/Mpc3 J LMAX (for LMAX w 3 x 1OA5 erge/sec, LMT, - l x 1043 ergo/sec, where we have used the lot pass cluster power law luminosity function without the Virgo clveter). Therefore, in an average sense, clusters contribute 1; 4% of the 2-10 kev background. (For a more accurate treatment of the problem which .includes the effect of the spectral differences of clusters from the background see McKee et al. 1980 and Marshall et a1. 1980). We ;rote that the present value agrees well with the estimate made by Marshall et al. (1980) of the maximum possible contribution of clusters If they were not to distort the thermal br+3mostrahlung fit to the spectrum of the DXRB in the 3-50 keV band. We note that the relatively soft spectra of clusters should result in an increase in their contribution to the DXRB in the Einstein Observatory energy range* 2. Active Galaxies The luminosity function derived here is in reasonable agreement with those derived previously by Pye and Warwick (1979) and Boldt (1980) in both slope and normalization. Using a lower bound of 3.0 x 10 42 ergo/sec and a upper bound of 1.5 x 10 45 erg/sec for our luminosity function results in a volume emissivity of c 4.9 x 1038 ergs/sec Mpc3 or a contribution of 208 to the 2-10 keV DXRB. If the lower limit is ln2 x 10 42 (see Table 4) the contribution to the DXRB is 4 40e. In tact, in order not to exceed the DXRB the luminoeltty function of AGN's must flatten at L < 3 x 10 41 ergs/sec (De Zotti 1980). There is a strong indication of such a flattening in the optical luminosity function (Huchra and Sargent 19731 Huchra 19771 Huchra 1980) at 23 My 4 - 21.5 (Ho #50) equivalent to a optical bolometric luminosity of 4 1.2 x 1044 ergs/sec. since the slops of the optical luminosity function, at higher luminosities, is the same, within errors, (Muchra and Sargent 19731 Woodman 1979) as the X-ray functioo it is tempting to associate the bend in the optical luminosity function with the bend in the x-ray function and therefore derive a Lopt/Lx 4 35. This value in rather larger than that found by examing Individual objects (Kriss at al. 19901 Elvis at al 1978). This may be due to the fact that most of the optical flux from low luminosity active galaxies does not come from the nucleus but from the stellar population. The total space density of X -ray emitting active galaxies in the luminosity range 3 x 10 42 - 1.5 x 1045 is 4 7 x 1:0-5 Mpc 3 which is < 1.5• of all galaxies of M < -19 (Huchra 1977)• This compares to a space density of active galaxies of M. < -19 of t 5 x 10 -5 Mpc 3 (Huchra 1977, 1980). It thus seems, to first order, their all active galaW,es of MP < -19 emit X-rays at Lx > 3 x 1042 ergs/sec. For a flat universe there are (assuming no evolution) < 4 x 10 7 X-ray emitting active galaxies with L x > 3 x 1042 with z4 3.5. We can also estimate, the number of sources per square degree expected in the Einstein deep survey if the luminosity function used in this paper does not evolve strongly in either slope or norm and that spectral effects, such as low energy absorption, are not important. With q o - . 50 Lmin - 3 x 10 42 in the 2-10 keV band and, Smin : 5 x 10-14 ergs/cm2sec in the 2 . 10 keV band, (which corresponds to the Einstein "deep survey" limit for a a - 0.7 source we predict t b active galaxies per square degree and < 1.3 clusters per square degree, compared to the 19 t 8 total sources per square degree , seen by the Einstein observatory (Giacconi et al. 1979). DeZotti (1980) has performed a similar calculation and finds c 5 active galaxies per square degree for Lmin = 24 9 1 x 1041 and Loax • 2.9 x 1044 ergs/sec in the 2-6 keV band and assuming that the slope of the luminosity function is 2.5. Oince most of the objects are noar Loin we would expect many of the Einstein survey objects to be seyfert galaxies of Lx 5 x 1042 erg/sec and z i 4 0. This is a consequence of the well known fact that if the luminosity function is steeper than 2.5, and barring strong evolution, when one looks at fainter objects one is looking primarily lower in the luminosity function rather than at higher redshift objects. A simple way to look at tho problem is to examine the number of objects predicted by our best fit luminosity function which would have redshifts (z) 1 0.5 and would have luminosities high enough to have been included in the Einstein Deep Survey. (We shall use qo - .5 or 0 geometry for simplicity). For Smin 5 x 10-14 ergs/cm2 sec in the 2 -10 key' band and qo . . 5 that we predict < 1 . 4 x 10 4 sources/star due to active galaxies and < 1.4 x103 sources/star due to clusters compared to the 6.312 . 6 x 104 sources/ster seen in the deep survey (Giacconi at al. 1979). We therefore predict that 4 251+1^ of the sources in -the deep survey are low (L ^ 4 x 1043) close by (z .5) active galaxies or clusters of galaxies of luminosity > 1 x 10 43 erg/sec. That this was a likely oituation was noted by Fabian and Rees ( 1978). (If qo - 0 the number of sources increases to 2. 1 x 104 sources/ster and the calculated contribution to the Einstein source counts to 35+24 Both the contribution of active galaxies to the DXRB and their contribution to the Einstein source counts depend sensitively on the lower limit, Lmin , of the luminosity function used. It is possible that the luminosity where the flattening of the luminosity function takes place could be higher than our calcuated value if we allow a two slope model of the luminosity function rather than our simple single slope power law model with a 25 . cutoff. However our data are not good enough to constrain such a model. ►Rs therefore strongly caution the rea4er that these results are Mod l dependent and should be treated as such. IX. CONCLUSIONS we have performed an all sky survey of X-ray sources complete to a limiting sensitivity of 3.1 x 10 -11 ergs/cm2 sec in the 2-10 keV band. Of the 85 detected sources only 7 remain without reasonable Idantifications. The log N log s relation for extragalactic sources is well fit by a tucltdean law N 16.5 S"`2.5 where S is in R15 ct/sec 15 or a - 2.Z x 10 S 2.5 (erg/cm2s) - 1 sr-1 where S is in erg/cm2s in the 2-10 keV band. This complete sample has allowed construction of luminosity functions based on a flux limited sample for clusters of galaxies and active galactic nuclei. These functions are well represented by power laws of slope 2.05 and 2.75 respectively. The sample enables us to estimate that the luminosity function for active galaxies should flatten at L J3 x 10 42 erg/sec in the 2-10 keV band. The cpace density of X-ray emitting active galaxies is approximately the same as that of optically selected Seyfert galaxies. Integration of the best fit luminosity functions indicates that clusters of galaxies contribute { 4% of the 2-10 keV diffuse X-ray background and active galactic nuclei c 201. 'rne sum of these contributions is very similar to the 26111% contribution due to .resolved duet to sources seen in the 'Einstein deep survey. We also predict that many of the objects seen in the deep survey should be local, (z 4 0.5), relatively low luminosity active galactic nuclei and clusters of galaxies. In order to determine more accurately the contribution of low ium.indsity active galaxies to the diffuse X-ray background one would have to sample the luminosity range 1041-42.5 over large solid angles. This would require a complete sky survey with 1 30 tines the 26 sensitivity of the present one and a angular resolution S 20 times better. Such a survey would also extend the luminosity function up to luminosities of 1047 ergs/sec. We stress the importance of a complete unbiased X-ray survey with good identifications in determining log N - log S and luminosity functions since there are various classes of sources of widely varying X-ray to optical luminosities. We feel that this strategy rather then deep observations over small solid angles will determine log N - log S and the luminosity functions most accurately for the local epoch since for a given observing time and fixed instrumental parameters the number of observed sources greater than some statistical limit is maximized when the solid angle is maximized at a given completeness level for a photon limited experiment. ACKNOWLEDGMENTS We thank J. Swank for extensive discussions and her major contribution to the HEAD-1 analysis program. We thank J. Huchra, D- Schwartz, W.H.M. Ku and C. Forman-Jones for communicating results prior to publication and G. DeZotti and T. Maccacaro for interesting discussion and D. Schwartz for a careful reading of the manuscript. ^ 1 1 t 3 .•t ^ / 1 ! 1 1 1 N•+ I 1 1 1 1 1 1 1 1 1 1 1 1 ^ 1 1 1 1 1 1 1 I N 1 1 1 1 w •+ t 1• 1 If 1' 1 ++ 1 +•/ I N I A I N I 1 1 It1i IM S' i • t ^+ 1 1•+ 1•IH 1 1+ 1• v 1 1 I r 1 I N 1 1 ^1 1 !7 1 I r 1 .+ I0 I2 N r 1 1 ••• ^ N ± .+ 1 I 1 t 1 1 I 1 1 I 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 4 1 1 1 ^ I 1 1 1 1 1 1 ^ 1 i 11 I 1 1 1 1 1 1 1 1 1 1 1 1 1 IN Itll 1 JM 10 ++ 1 I 1 N 1 ^► N ^ I ^I I • 1. • 1 1 10 I h I h 1 N I N 10 1 N * i ++ 1 10 W 1 • •~+ ININ I(•1 1 1N 1 + ^ W M N 11 a v I I 1+W+ I N 1~ N I I~ I "y l 1 1 1 1 1 I 1 1 1 1 1I 1 I 1 1 t 1 1 I' 1 1 1 I I 1 f 1 1 N 1 4 1 to 1^ 1 N i in I In 1 In N 1 ('^ 1 1N 1 ^. !. ^ I A W 1 h N ^! 11♦ •r o♦ ( In 1. 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M i ^_ 1+1 i 1 1 1 1 1 1 1 ^ ,i 1 1 1 . 1 1 1 1 1 !A I 1 P" 1 1 IM+1 f ^+ 1 r 11• In i+•+f lLir1.flO 1••I II 1 in 1.11 01 i 1 + 1 • • 1 + i • 1 r 1• 1 . 1 + 1 irl I 1+1 t INI ^ 1 ~ i 1 1 1 1 1 N 1 t 1 1 1 1 1 1 f 1 il:W j + i 1 i 1 t 1 1 1 1 1 O ^ 1 i 1 1 i 1 1 i i i N t1 1 1 inl l N! in I N 1 N I N 1 1 1N th11^11^11^11^fYI1 IA Ifni Y 1i ^+ + • i+ 1 + + 1 i+ 1 • 1+ i •► 1 i I N ININININtN 1N ININ I N .^I ^, 4v 1 1 1 ^. ! i 1 1 1 1 1 Io^o1Q1o1^ Ia i o 1 = 1 0 P• 1 1• I N f W I N I m i a l v 0 Y•.+ 1 011 M 1 W I in I w i ?% !• f- I 1•^Ir 1\ftpIWINir-+INIpIg1^1q 1^1W IAIA11s I 14 J^ a, J Y. 1 1 1 1 1 + i •( l i 4. 1 f1 1 L i 1 1 11 1 1 10.1= O I A I :i t i l i I i 1 i l i ! i t i 1 1 1 1 I 1 1 1 1 1 1 ^ ,,,^ ! ID 1 3 ! r3 ! N ! N ! _^ t c! t N ! !Q ! ^ I N 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t N 11 1 > Nmw 1 1D 1 1 1 1! 1 IN 1 1RI 1K O •mW 1 1 1 1 1 1' 1 1 1 1 1 N 1 < . N u 101 1NIMI i • I01 10 INi11gq I J I N 1^ 1 w 1 1 +-• 1 1D 1 W 1 m 1 N 1 < ..• w 9 1 • 1.+INIm 1 M1 1 1 1In1 J1 D1 I N► I P I A 1 9 l 1 R I N I n I J I Y .+1 hi` vwa< • A N w r r M i • H • w .n P w M V4M H u s N YI uM i • ^. • CI t b N • 0wV1 > t M W • WU u: a. 7 IN 1^0 H z t ► d T ► VI Z 131C- tr O W W W •.1 .at = aL M w J . • M Y w O • c m. m rynm • .JW U u p-M .r •m>f Mo og • .r.cm ..t . d •S ao z 4 m L. 1lu-1 i tUd.1W .t rr 0- w i aC t f U - _3i A O 01 It1 . U t= ai i a• .+.^N . M N .OIr UWO W W W .i .q`.Wt40 -IL J«+ a. N • •i 7< iii 4 U ^ i IL O 'm• a.M tJ JJ•+ :t09wSO •U01-W WN ^ ^ > 4c 64 u u y tv fdm !vtw " 0W N W W t.+ _ a. awr1'ONU O1!1"M • • OUOWZ taC • rppZ WU \N \ OO1Z•W w psNua -0 %D •a.UaC >1- Km e. N N Wr-+ u «01 CO ►..Out1Nr t0 1- w0H a% w V •^ O .pp^l/>1^IC - U~ z W W +•r^i[ •NN ' ►•z S "•1% nary ZZO • W 1- IS 19 M 10 0 t • a.etrNSa w w y ^ m N N .^ ^ 14 ^ riCI-ofno Nd f- W to- W u NU me In t9 O^" C-0 O §ZW"= W OL M z .+ U rt -• z W x U m Z O J CW m -^v N"'-(AW 1Dv F- UZOWMI> J O D1 '0 4 x to - re .J ^ O - S mw ^ t y- W Ce -Z w Z I/1► ►.J W .^ v tp 1- Z• =S N W F- Z me V) W S W= a M1- -ry Wm W= S4.N 01- _! F-0O-yh M t/! 0 X: Z w= 0 X>" J O Z m CC Z J •wy h W -I vW ZJ OWE 7 Z'O-J ZW • f%N WW O4. M Z U >0.+ vU Om.-.... 1 oc'su W=N M 0E-I jLL r O x x v— I X v .+ Ww ON •"" ► e^ W WERENCES Avni, Y., Bahcall, J.N. 1980 0 Apo J. 235, 694x. Bahcall, N. 1979, Apo J. 232, 639, Birnbaum, Z.W., Tingey, F.M. 1951, Ann. Math, Stat 22, 592. Boldt, E. 1980, Invited Talk at AAS Meeting, NASA TM 80659. Bradt, H., Doxsey, R.E., and Jernigan, J.G. 1979, Advances in Space Exploration. Charles, P. Thorstensen, J., Bowyer, S., and Mi.ddledi.tch, J.19791 Apo is (Letters) 231, L131. 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'heinberg, S. 1972, Gravitation and Cosmology West, R.M., and Frandsen, S. 1980, ES4 Scientific Preprint, No. 110. White, N.E., Sanford, P.W•, and Weiler, E.J. 1978, Nature 274, 569. worrall, D•, Boldt, E., Holt,S., Mushotzky, R., and Serlemits0s, P. 1981s Ap. J. 243, 53. F'IGURS ChPTIONS Figure 1. The completeness level of the present survey vs ecliptic latitude. The diamonds are for they first pass and the crosses for the second pass. The lower histogram is the sky fraction in each ecliptic latitude bin (right hand scale). The centre of the diamonds and crosses is 5 times the mean error for a source located in that scli.ptic latitude bin and the since of the error bar is the standard deviation of this error. Since we truncate at 1.25 R15 counts all of our sources at ecliptic latitude greater than 30 0 lie well above the 5d level. We estimate that residual :incompleteness of sources at levels less than 1.4 cts is less than 3 sources and zero uources greater than this limit. Figure 2. The error boxes for H0328+025 and H0917-074. The inner and outer boxes are the 908 confidence boxes as described in Marshall et al. 1979. The inner box assumes that the source was roughly constant during our period of observation. Figure 3. The distribution of the non-galactic sources detected in this survey in supergalactic coordinates. Figure 4. The probability distributions for K and a. The top panel shows the AML probabil„tty vs. a in the first pass data, the Middle panel shows the } AML probability vs. r in the second pass. The bottom panel shows the 66 and 95% joint probability contour for K and a for the first pass data. The + MEN log 5 distribution for our sample, The Figure 5. The ditfere►ntial log N - best fit is indicated. The highest flux point is indicated by a dashed crone because its upper flux bound is not well defined. (lot pass data) 4 Figure 6. The AML Kolomogorov- smirnov test distribution for an a - 2.5 model. The 50 and 95% probability bounds are .indicated. (lot pass data) Figure 7. The ratio of the number of observed sources No bs to the number of expected sources for a . 2.5 loci K - log S law. (lot pass data) F.gsre 8a. The cluster of galaxies differential luminosity function for the first pass data. 8b. The same information for the second pass data. The best fit power 1tw models are indicated on both panels. Figure 9. the AML probability vs. Y the slope of the power law differential luminosity function for clusters of galaxies for the first and second passes including and excluding the Virgo cluster. Figure 10. Same as Figure 9 but for the exponential luminosity function.. Figure 11. The Seyfert galaxy luminosity function for the first pasts data. The best fit power law differential model Is .indicated. The .insert shows the AML probability vs. Y the slope of the luminosity function. w ''SENSITIVITY AND SKY COVERAGE 2.0 2"o PASS COMPLETENESS LEVEL 1.6 N i COMPLETENESS 8 LEVEL in 1.2 F9 1.8 ca l 0.8 1.25 cos l 15 co ao 0.4 10' W a o °D ca = 5 tja coW 0 O N T 9 0 20 40 60 80 MOD ( ECLIPTIC LAT.) * rises 4.000 H0321+025 8 -1.000 L-- 49,00 57,00 10.000 H0917-074 s 6.000 , 1 136.00 144.00 a r^ t m t a ^ vs Fw k , W t t € O{ Y p= JO 14 i `^ r tititiFFF...tti 10 ^ .^ 'R' • p 0 • In y^ a ^ 1 ^ i ^. v. O; 1 L1Q°^ ,i.tt 0 N go W ix f •^ 1 ^K Q 1 ``l M D D ^ A i 8 t , 0 ^Pi ^ n 4 J ' k 1 T^^. ^ f Y A ^^ { I ^ f CLO ^ oi l ^. 1 t r ^ f ^ pWp,, ji t ^^, r i t [ ^: N j ^ \fit Y ^A^ ^ ^ :. r FO `^ ^', *^^Al ! 1^1 : ^ 3 i s i t. ^Iy,11 '1111^^(^^ ` f(^ ZO 1' sy ^ 0" yyyyyy ^0 to ^i •^ ^^ t y ^ 4. ! ^ { lyA 1 `j Y e3. Q A t 1 i x fc f s k y f _ N k. ^- r 2 ST 60 I 'PASS J I > 1.25 ao 40 m FWNY O a 20 ^ 0 2N° PASS 40 I >1.8 20 ma FWHM ^ o X2 PROBABILITY CONTOUR 32 I ST BASS I > 1.25 0 28 24 Y 68% 95% 20 4 16, 12 2.1 2.5 2.9 a I RATIO OF OBSERVED TO EXPECTED 5.0 NUMBER OF SOURCES N106s 1.0 NEXP 0.5 10 1 0.1 5 10 50 R15 COUNTS SEC i N - I I I w i M^ a O2 F! i Qn W co I tri to i p "I •I O t0 co V .I tc^ hy- E a 1 c d' V J tC^ ' V N W — i^ Al M i O C/'1 l •1' .s N H Cf) N i Lo J N r Q^ d 4 10 "I 1 .ww W 1.0 G7 F- Z 8 WI) W ... 0.1 10 100 R 15 COUNTS SEC" W !N ^r Z ^ V x O ti Ni ^ O O H v ,^ z La. Z .J1 ' V! 1-- co -j Z H Z `/ D .^J Z w VO W_ W t/7 T Q ^J O c^^ V W 4. W In CJ qp Z W H 1 J^ V I J~ O H O sc y V M cr_ V ul L1. M Z ---0 N J H Z J o_ O O IQ Q O 140 ^_(ONO33S/S983 y`01) ^_OdYV(wl) N Q. N W O c©^ N ^ OG N a^ 0 N W F=.. 3 OD co v J N W O N CD N a>3cr- J NG W33 CL OD tCo q N CAD ^ N M AIIII9d80Hd R O CD O 1-+ Z O in VQ F- Cn H O ^ Z Cn Z w V ^? o ^> L J^ et J QJ O= F-1-- W32 O i M WK O D N O O C N O C CV O c z ui Oct zQ c.) v N M cn o ^ Z C V O cr- W J0 i F 0 M O N O O ^O N O ON' M JllIl18V80^d .: SEYFERT GALAXIES LUMINOSITY FUNCTION 10 — op% 60 ACTIVE GALAXIES ..at FIRST SCAN 40 16-1 FWHM m c,4 20 y= 2.T5t.15 16,4 02.4 2.6 2.8 3.0 r N (1-44 ) = 2.68 x 10 ' L;4» cnW 16-5 cn w w FIRST SCAN xo I > 1, 25 R 15 COUNTS / S ^ ^ ME 106 qw z 10 7 Id" • 3! 16*1 L 0.01 0.1 1.0 w IOU L44 (1044 ERGS / SECOND)