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On the Origin of the Diffuse X-ray Background DAVID J. HELFAND Columbia Un~versi~r ABSTRACT We report the first measurement of the intensity and spectrum of the diffuse X-ray background in the 0.1~3.5 keV band which is free from contamination by sources with fluxes greater than ~ 6 x 10-14 erg cm~2 sol. This result has been made possible by the development of a number of techniques for reducing cosmic ray contamination and instrumental artifacts in the data collected by the Einstein Observatory imaging proportional counter. Our analysis of the background data reveals a mean absolute intensity for the emission Is(0.16 - 3.5 keV) ~ 5.6 x 10~8erg cm~2s~isr~~. The intensity is dependent on galactic longitude even when only high galactic latitude data are used, allowing us to set a lower limit of 20% on the galactic contribution to the mean emission in this band. The spectrum of the total background is consistent with a power law of slope ~ 0.7 between 0.16 keV and 3.5 keV with evidence for a steep rise toward lower energies. This intensity is greater than that expected from extrapolation of the HEAO A-2 results at higher energies and the slope is steeper than Eat which obtains between 3 and 20 keV. A reanalysis of the faint end of the log N-log S distribution for X-ray point sources in the 1.~3.0 keV band reveals an extragalactic source surface density of only 6 to 10 per square degree at the Einstein Deep Survey limit of 4 x 10~~4erg cm~2s-i in this band; the integrated contn~ution of all detected sources above this limit to the observed diffuse intensity is ~ 12%. We also report preliminary evidence for the association of faint radio sources with Peale in Me arcminute-scale fluctuations of the diffuse X-ray surface brightness distribution and then 174

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HIGH-ENERGY ASTROPHYSICS 175 briefly consider some of the implications of these results for the origin of the cosmic X-ray background. INTRODUCTION The detection of an intense, apparently diffuse, isotropic flux of X-rays in the 2-10 keV band was one of the major discoveries of the 1962 rocket night which gave birth to X-ray astronomy (Giacconi e! aL 1962~. Measure- ments over the ensuing quarter century by a variety of instruments including those on OS0-3 and OSO-5, numerous rocket flights, and particularly the A-2 experiment on HEAD-1 (Rothschild et aL 1983) have established that the X-ray background rises above the radio-to-gamma-ray u-0-7 power law over the band 0.1-300 keV; its total energy density is ~ 4 x 10~5eV cm~3 or 0.02% that of the cosmic microwave background radiation. Between 3 and 100 keV, the spectrum of the radiation can be characterized by an optically thin thermal bremmstrahlung model with kT ~ 40 keV (e.g., Marshall et aL 1980~. The radiation is isotropic on scales ~ 5 to an accuracy of one part in 10-3, with the exception of a possible dipole anisotropy (Shafer and Fabian 1983) very similar to that seen in the microwave background which represents our motion with respect to the frame in which the microwave photons were emitted at z ~ 1500. A definitive review of the observational situation with respect lo the X-ray background measurements above 3 keV prior to 1986 is given by Boldt (1987~. Although the diffuse X-ray background was discovered several years before the cosmic microwave radiation, its origin remains a matter of con- siderable discussion and debate. One of the principle difficulties has been that only the brightest members of source classes which are potential con- tributors to the background have X-ray intensities and spectra which are measurable with the non-imaging detectors used to record the flux from the background itself. Although operating over the relatively limited bandwidth between 0.16 and 3.5 keV, the imaging proportional counter (IPC) onboard the Eu~sMin Observatory had the potential to remove this difficulty by mea- suring simultaneously the X-ray flux from both the background and the candidate sources of which it may be composed. While the ten years since the launch of the satellite has seen tremendous progress in characterizing the X-ray luminosity functions and spectra of potential point-source con- tributors such as active galactic nuclei (AGN), measurement of the diffuse emission in this band has remained relatively unaddressed. We report here me development of a number of techniques necessary for the analysis of diffuse X-ray emission observed by the IPC. Their application to six deep-exposure fields at high galactic latitudes (the Deep Surveys has allowed us to measure the intensity and spectrum of the background ~ the Gl~3.5 keV band with an accuracy of ~ 5%. We have

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176 AMERICAN AND SOVIET PERSPECTIVES also undertaken a reanalysis of the X-ray point-source population at faint fluxes derived from these same fields and present a new assessment of the contn~ution of discrete X-ray emitters to the diffuse background. In the next section, we discuss in some detail the origin of "counts" detected by the IPC and then describe a set of algorithms we have developed to distill from these raw counts a measure of the true diffuse X-ray flux incident on the detector. These techniques include editing the data to remove solar X-rays scattered into the detector by the residual atmosphere, a source excision algorithm which removes the effects of photons scattered far from a source's centroid by imperfections In the telescope mirror surface, a flat-fielding algorithm for removal of spatial irregularities in the counter response, and, most importantly, a determination of the fraction of counts which result from the interaction of cosmic rays with the detector. We present our principal scientific result in the third section: a source e spectrum of the diffuse X-ray background in the 0.1~3.5 keV band, where "source-free" implies removal of the contribution of all discrete sources for which /= > 4 x 10~~4erg cm~2s~~. The galactic longitude dependence of the result determines an upper limit to the fraction of the flux in this band which is of cosmic ongin. The fourth section presents the application of our new source detection algorithms to the clean IPC data and concludes that there are only 6 to 10 sources per square degree at the Deep Survey threshold. In the final section we include a brief report on our search for radio counterparts to the background fluctuations and then summarize our conclusions regarding the origin of the X-ray background. DATA ANALYSIS What is an IPC count? The imaging proportional counter (IPC) at the focus of the Einstem Observatory X-ray telescope collected data in the 0.1 - 4.5 keV X-ray band from ~ 5000 1 x 1 fields scattered over the celestial sphere. The angular resolution of the instrument was ~ 1' and the spectral resolution scaled as R ~ 0.5(E/1 keV)~~; effective exposure times ranged from ~ 102 to ~ 105 seconds. Over the course of the Einstein mission, the IPC recorded the position (in 8" cells), energy (in 32 pulse-height bins), and time-of-arrIval of ~ 20 million "events" arising from the deposition of energy in the counter gas. These events result from a number of distinct stimuli: from cosmic ray interactions with the detector. Low-energy elec- trons and gamma rays may be directly detected, while higher energy cosmic rays produce spallation in the walls of the counter as well as neutron ac- tIvation of the detector and spacecraft, leading to secondary events in the instrument

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HIGH-ENERGY ASTROPHYSICS 177 o from a low-level leak of the iron fluorescence calibration source from detector and/or electronic malfunctions (e.g., breakdown or "sparing" in the counter gas) from solar X-rays scattered from the residual atmosphere above the satellite and collected by the mirror from cosmic X-ray sources. While the detection of such events was the primary purpose of most of the observations conducted with the IPC, these photons must be excised in a study of the background. In particular, the distribution of source counts outside the nominal instru- ment point-response function which results from photons which scatter off imperfections in the mirror surface must be treated with care. from diffuse X-rays of galactic origin the hot bubble of gas ~ 100 pc across which surrounds the sun (McCammon et at 1983), the ridge of emission along the galactic plane (Iwan e' at 1972; Koyama et at 1986), and the putative halo of hot gas surrounding the Galaxy. from the cosmic X-ray background, the principal object of this study. Additional complications in studying diQuse emission with the IPC include non-uniformities in the spatial response of the instrument, detector gain changes, and the off-axis response of the telescope mirrors which introduces an energy-dependent vignetting for X-rays but does not affect cosmic ray-induced events. A few of these problems are handled adequately by the standard IPC processing routines. Data from the small number of periods exhibiting anomalous detector behavior are excluded from all further analysis. The calibration source leak is confined to the high-energy pulse-height channels and Is said to contribute < 2% of the counts in channels below number 7 which corresponds, at nominal detector gain, to 1.5 keV For the higher energy channels, we adopt information from the Eu~stezn Software Specifi- cation document (Harnden e! at 1984), and fold this through our algorithm to find new estimates for the effect of the calibration source on our results (see ~ et at 1990 for details). Solar Scattered X-rays The fraction of the counts detected in an IPC image which are at- tributable to solar X-rays scattered into the optical path by the residual atmosphere is a function of solar activity and of the geometry of the Earth- Sun-satellite system. In the standard processing software, the latter factor is parametrized by viewing geometry (VG) flags where VG = 1 ("best") describes data collected with the satellite over the night-time side of the Earth (i.e., the sun is fully occulted by the Earth and the solar scattered flux should be essentially zero), VG = 2 and VG = 3 are the "better" and

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178 AMERICAN AND SOVIET PERSPECTIVES "good" data, respecter, implying increasing contributions of solar scat- tered flux, and VG > 4 data are excluded from all standard images. Since these parameters each represent a range of Earthen, Earth-satellite, and Sun-satellite viewing angles, and since the incident level of solar X-ray flux varies significantly with time, the contribution of solar-scattered flux to the IPC count rate in any given field is not simply a function of the fraction of VG = 1, 2, and 3 data in the image. 1b quantifir this contn~ution, we have examined data from 54 fields in the IPC survey of the Large Magellanic Cloud conducted by Columbia. Companug the mean, source subtracted count rates in the inner 30' of each field for the VG = 1 and VG = 2 ~ 3 data taken separately, we find a median solar-scattered component in the VG = 2 + 3 data of ~ 2.6 x 10-4ct s~iarcmin~2, in excess of the mean level of cosmic ray contamination found below; the total range of solar contamination Is from ~ O to ~ ~ x 10-4ct s~iarcmin~2. The spectrum of the solar scattered radiation is, as expected, extremely soft and, as a result of its steep energy distn~ution at the lower level cutoff for acceptable events, small gain variations over the face of the detector produce a greater level of spatial fluctuations for solar scattered X-rays than is observed for celestial X-rays or for cosmic ray particles. A quantitative analysis of this effect (Wu e' al l99O) has led us to conclude that, when studying sources near the detection threshold, the sytema tic errors introduced by including data contaminated with solar-scattered flux are significant; in addition, the presence of a time-variable component of counter illumination is clearly inimical to a precise measurement of the diffuse X-ray background flux. Thus, in all that follows, we have included only VG = 1 (satellite-night) data in our analysis. Source Excision By definition, a characterization of the "diffuse" X-ray background must include an analysis of only those photons not attributable to discrete sources. 1b eliminate point-source photons, it is necessary first to iden- tif,r the sources and then to subtract the system point response function, appropriately normalized, from the data. In the Eumein mirror/detector system, the point response profile Is energy dependent both as a result of a blur circle pulse-height dependence of the counter response (lower energy photons are spread over a greater area - Harnden et aL 19843 and as a result of scattering by imperfections on the surface of the grazing incidence mirror Higher energy photons scatter to larger distances from the source centroid - Mauche and Gorenstein 19843. We have modeled the instrument response function using the convolution of an azimuthally symmetric Gaus- sian core plus exponential wings and a constant underlying background (see wing and Helfand l99O for details). In the analysis reported here, all bright

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HIGH-ENERGY ASTROPHYSICS 179 sources are subtracted using this technique, while sources fainter than 0.1 IPC ct s~i have been eliminated by simply excluding from consideration regions within a radius proportional to en (intensity) (ie., within a contour of constant signal to noise ratio). This assures that < 1% of the photons in a field originate in point sources above the detection threshold. A ~lat-Field Image for the IPC Data collected with the Eu~stezn IPC possess two inherent, instrument- imposed symmetries: the radially symmetric X-ray sensitivity resulting from the (energy~ependent) mirror vignetting function, and the rectangular symmetry of the detector body, the window support ribs, and the crossed grids of position-sensing wires. In order to eliminate non-uniformities in the response of the instrument conforming to the latter symmetry, we have produced the first "flat field" unage for the IPC. We summed over four hundred individual paintings after 1) eliminating all fields with potentially significant extended emission (e.g., clusters of galaxies, SNRs, star formation regions, etc.), 2) excising all point sources as described above, and 3) rotating the fields to zero roll angle (referred to hereafter as "machine coordinates"~. The data selected were from the standard '`broad band" (PHI channels 2-10) and were binned in 64" x 64" pixels; the mean pixel contained nearly 1000 counts implying statistical errors at the 3% level. The two-dimensional, flat-field image with ~ 1' resolution formed from these data (corrected for vignetting) is shown in Figure 1. Highly significant features are clearly present in the detector response on scales from 0'5 to 5'. The amplitude of these features is a weak function of pulse-height channel and detector gain, although the overall morphology of the flat-field image is independent of these parameters. Note that here, and in all of the analysis which follows, we delete all data within +3'5 of the window support ribs as being unreliable for most purposes. The features are remarkably reproducible, appearing in all subsets of the data we examined: the Large Magellanic Cloud fields, the satellite-night-only Deep Survey fields, SO fields at the same galactic latitude as the LMC, and the remaining fields included in the final composite image. The fractional intensity of the features appears to be relatively independent of the ratio of X-rays to particles in the summed images: the LMC fields with their extensive diffuse emission shows structure of the same amplitude (measured as a percent of total count rate) as do the Deep Survey fields. 1b first order, then, it appears that both X-ray and cosmic ray-induced events respond similarly to these detector nonuniformities. The fluctuations have a peak-to-peak amplitude of .75 to 1.34 of the mean value and an Ens deviation of 9%. In order to obtain the particle

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- - - - - ~ AMERICAN AND SOVIET PERSPECTIVES . A_ __ a_ in ~ FIGURE 1 A flat-Seld image for the ~ IPC broad band with 64"x 64" pixels. Mamma deviations Tom the mean value are-0.26, +034; the nns deviation is Go. Each pixel contains > 900 photons for a statistical uncertain of ~3%. count rates derived below and in utilizing our source detection algorithms, we first apply this flat-field correction to all data by multiplying the flat-field image value in a given pixel by the exposure map used to turn raw count rate maps into fluxed images. A Determination of the Cosmic Ray Particle Contamination in the IPC From the flattened, source-free, night-only images, we proceed via two independent methods to estimate the cosmic ray-induced contamination in the IPC count rate. The first method relies explicitly on the radial symmetry imposed on all detected X-ray photons by the Obsenato~y's

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HIGH-ENER~ MTROP~ICS 181 mirror system. The mirror vignetting function was measured in ground calibrations; it is reasonably constant within the energy range 0.1~3.5 keV and our adopted function is shown in Figure 2a superposed on the radial distribution from the summed, night-only LMC data. The best-fit normalization clearly does not describe the data well. This discrepancy is attributable to a second component of the detected counts namely, cosmic-ray induced events ~ which do not follow the mirror vignetting function. As a working hypothesis we adopted a flat radial distribution for these so-called "particle" events. Any first-order departures from this assumption have been removed by the flat-fielding algorithm. (Note that the flat field was derived by normalizing each pixel to the adopted vignetting function to remove this lowest order Fourier component of the spatial fluctuations - see Wu e! al 1990 for details.) The two component fit to the radial distribution of EMC data (flat particle, plus vignetted X-ray contributions) is shown in Figure 2b. The result is both a substantial improvement in the fit to the radial surface brightness distribution of the IPC, and a direct measurement of the mean particle component in these fields: 1.39 it .03 x 10~4cts~iarcmin~2. Separate measurements of the particle rate for each of the six Deep Survey paintings yields a value of 1.41 + .03 x 10~4cts-iarcmin~2, consistent with the result based on the LMC fields and with an error in the mean of only 2%. 1b test the robustness of thus important measurement, we have made a completetr independent estimate of the mean IPC particle event rate by taking advantage of the large number of overlapping paintings which comprise the Columbia EMC survey. The essence of the approach is the fact that, for a given sly direction, two separate IPC observations with different field centers will receive the same number of diffuse X-rays, but will record different numbers of events because 1) a different distance from the field center results in a different diminution in X-ray intensifier from vignetting, and 2) the two data sew, recorded at different times, will have a different level of particle contamination. It is possible then, to construct from the original data a highly con- strained simultaneous solution for both the true X-ray intensity for each sly position and a particle contamination level for each observation by producing a x2 minimization solution for the equation CiJk = (FijTijkVijk + PkTijk] Smn where - C ilk represent the counts recorded in the sly pixel i (RA), j (Dec3 in Me kth field

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182 o c) a) o o cr En oO Cal AMERICAN AND SOVIET PERSPECTIVES o /ianett~na function Jiqnetting Function + Particle 10 20 30 Distance to the Center of Field (Arcmin) - 40 FIGURE 2 (a) The radial distribution of total counts in the summed VG=1 LMC data fitted to the nominal E - ein mirror vignetting function. (b) The same radial distribution fittedtothevignettingfunctionplusaconstantparticleIateof1.4XlO-4cts~larCmin~2.

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HIGH-ENERGY ASTROPHYSICS 183 - F ij represents the diffuse X-ray flux from that sly pixel Vijk represents the vignetting function value for that sly pixel in field k P k represents the particle value for field k T ilk represents the exposure time at sly position ij in field k (e.g., T ilk = 0 under a nab S mn represents the flat-field correction to the exposure time in the detector pixel labelled by mn which corresponds to the current pixel of interest. The mght-only EMC data includes 114 fields with exposure times > 500 s. The ~ 5 x 5 region covered by these fields has been divided into 4293 sly pixels 4'3 x 4'3 in size (corresponding to 32 x 32 8" IPC pixels); multiple overlaps (up to 12 fields covering a given sky pixel) result in a total of 20,908 C ilk values. Solving for the 4293 sly fluxes (F ij's) and the 114 particle fluxes (P k'S) yields a mean particle rate of (P) = 1.45 x 10~4cts~iarcmin~2 with a reduced x2 value for the fit of 0.99. This independently derived estimate is indistinguishable from the value obtained from the radial dis- tnbution of the Deep Survey fields and gives us considerable confidence in our understanding of particle contamination in the IPC. The fit also yields an estimate of the range of particle values in typical, short-exposure IPC fields for which direct fits to the radial distribution are compromised by poor statistics and me absence of an overlapping pointing renders a simultaneous solution (as in our LMC example) impossible. The range of values in the 114 LMC fields runs from ~ O to ~ 3 x 10~4cts~iarcmin~2 with an rms dispersion about the mean of ~ 35%. Finally, of incidental interest here, but of considerable scientific importance, the simultaneous fit yields a map of the absolute sly flux in the 0.16 - 3.5 keV band with ~ 4' resolution over the whole LMC; the implications of this result are discussed elsewhere (Wang e' aL 19901. In order to measure the spectrum of the X-ray background, it is necessary to extend this analysis to derive the spectrum of the particle contamination. Thus, we have repeated the radial profile fitting analysis on the summed Deep Survey fields for each pulse height bin independents. We find particle contamination levels which vary smoothly from 29% in channel 2 (0.15 0.3 keV) to 9% in channel 6 ~ 1.1 to 1.4 keV, the minimum particle background channel) to 30% in channel 10 (17 to 3.5 keV) although calibration source leakage contributes an additional ~ 50% of the total counts in this channel We are in the process of acquiring the entire Einstein data base so that we can construct flat fields and particle contamination

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184 AMERICAN AND SOVIET PERSPECTIVES spectra as a function of gain with the highest possible statistical precision, but we do not expect the basic results reported here to change significantly. ~1~ SPEClllUM OF THE X-RAY BACKGROUND Having measured or eliminated all extraneous sources of IPC counts and minim wed to the extent possible sources of systematic error, we are now In a position to measure the intensibr and spectrum of the low-energy diffuse X-ray background. We present the result in Figure 3. The integrated flux in the 0.1~3.5 keV band as measured by Eu'- stezn is 35 ph cm~2s~isr~~. This is clearly in excess of the extrapolation of the power law with a slope of-0.4 observed in the ~30 keV band. The amount of the excess is unclear, however, because of a long-standing but little-known discrepancy between the normalization of the ~10 keV background spectrum. The HEAD-1 A-2 experiment medium energy de- tectors measure a flux of 8.3E-i 4ph cm~2s~isr~~keV~i whereas a series of several rocket flights by the Wisconsin group (Nousek 1978; Fried 1978; Burrows 1982) designed specifically to study the diffuse X-ray background obtained precisely the same slope but a normalization which is 30~O higher in the same band. Both used the Crab Nebula as a calibration source and obtained consistent values for its flux, and both claim errors in the normalization of < 10%. Apart from an error in the calibration of the collimator responses of the two experiments, it is difficult to imagine the cause of this discrepancy. At present, the situation is unresolved, and we have plotted both 3-10 keV spectra in Figure 3. An extrapolation of the HEAD-1 spectrum to the 0.1~3.5 keV band implies an expected intensity of 28.5 ph cm~2s~isr~i, ~ 25% below the measured value. The complex shape of the low-energr spectrum of the background is apparent in the figure. There is a steep rise at the lowest energies ~ ~ .3 keV) which is consistent with emission from the ~ 106K plasma filling the ~ 100 pc caviar around the sun (McCammon et at 1983~. Between .5 and 3.5 keV, the slope of the spectrum is ~ 0.7, significantly steeper Han mat at higher energies, but similar to that of the spectra of nearby AGN in the 2-10 keV band as measured by HEAD-1 (Mushotsly 19823 and Ginga (Tanaka 1989~. The limited information we have on the spatial distribution of the diffuse background in the Einstein band demonstrates that at least part of this emission is galactic in origin A plot of the diffuse mtensibr in each of the 35 high galactic latitude (30 < ebb < 70) fields as a function of galactic longitude shows a significant increase between longitudes 300 < ~ < 60: the mean intensity for 12 fields between 120 and 240 is 3.1~.2 x 10-4ct s~iarcmin~2 while the value for 10 fields with 330 < ~ < 30 is 6.7~.5x 10-4ct s~:arcmin~2. This substantial excess is clearly a large-scale

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HIGH-ENERGY ASTROPHYSICS 60 50 40 30 20 c o - o ~0 2 3 - 1 of N 10 185 1 1 1 1 1 1 1 1 1 IPC o Wisconsin Extrapolation - t o - I o o 1 I ~ 1 12 4 5 6 7 8 9 IPC PHI Number 10 11 slope = -0.7 \ ,HEAO-2IPC 10.0 _ Diffuse or ~ 103 5t Sources Deg~2 From Granularity 25%. Directly Ob served 12% ~ _ 1-3 keV Wisconsin HEAO A-2 Slope = -0.7 Slope =-0.4 \ 1.0 10.0 Energy ( keV ) 100.0 FIGURE 3 (a) The photon spectrum of the X-ray background as measured in the Ems~ Observatory IPC compared to an extrapolation of the Wisconsin ~9 keV background spectrum folded through the IPC response The integrated contribution of discrete sources with 1-3 keV fluxes > 6 X 10~14 erg cm~2 s-1 has been subtracted Cam the Wisconsin results to provide an app~pnate comparison with the source-free Epstein data. (by A schematic representation of the X-ray Background spectrum with various measured and potential contributions indicated.

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186 AMERICAN AND SOVIET PERSPECTIVES galactic component since it is not confined to local features such as the North Polar Spur, a region of enhanced soft X-ray and nonthermal radio emission thought to be a piece of an old supernova remnant. Further analysis of the spectrum and the spatial distribution of the excess using the entire database Is required before the relative contributions of local emission, a thick galactic ridge (e.g., Iwan e! aL 1982; Koyama e' at 1986; Watson 1989), and a bulge or coronal component can be assessed. In the discussion that follows we use the 1-3 keV background flux derived from high galactic latitude fields in the longitude range 120 < e < 240 as our best estimator of the cosmic background intensity, although a residual galactic contribution cannot be excluded; the adopted value in this band is 2.5 x 10~8erg cm~2s~isr~~. THE POINT SOURCE CONTRIBUTION A number of extragalactic source classes contribute to the integrated surface brightness of the X-ray sly; the most important known sources are galaxy clusters, Seyferts, BL Lac objects, and quasars. Considerable effort has been expended in attempting to derive a total discrete source contribution by extrapolating from the relatively small number of known examples in each class. These determinations are limited by selection effects in the X-ray data, uncertainties in the optical luminosity functions and X- ray-to-optical luminosity ratios, poorly-~own broad-band X-ray spectra, and the imponderables of source luminosity and density evolution. It is beyond the scope of me present work to review these calculations. Rather, we will adopt a strictly empirical approach in which we apply an optimized source detection algorithm to the edited, flat-fielded data of the six Deep SuIvey fields to define the faint end of the log N-log S distribution of discrete X-ray sources. We have developed a method of identifying sources in Einstein IPC data which relies on a statistical interpretation of flux enhancements but then uses morphological fitting techniques for the determination of source locations and fluxes. The specific parameters of our algorithm were deter- mined by running the program with a wide variety of parameters on several sets of real and artificial data. The final parameters were then chosen so that the program detected real sources with maximum efficiency and spurious sources in an evenly distributed manner. This second goal is fairly difficult to achieve with IPC data because calculating a reasonably accurate background for a potential source requires collecting photon events from an area of ~ 100 arcmin2 and the IPC detector has significant structure, from ribs and mirror vignetting, on these scales. Before searching a data set for sources we constructed two maps: one, a record of the number of events per pixel (usually 32 or 64 arcseconds on

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HIGH-ENERGY ASTROPHYSICS 187 a side), and a second recording the adjusted exposure time determined by taldng the total integration time for the observation and applying correc- tions for the effect of mirror vignetting and counter flat-fielding as discussed above. We then inspected every pixel in the field lo determine the proba- bility that a source lies within it. ~ measure the statistical significance of flux enhancements F. we construct a local background model by comput- ing weighted (by adjusted exposure time) average flux over a background annulus. This annulus is centered on the point which is being analyzed and excludes areas which are either adjacent to the pixel of interest, under the IPC ribs, or near another source (this latter facet obviously requires multiple iterations; see below). The expected background counts B for the central source region is, then, the computed flux times the adjusted expo- sure tune for the candidate central source. The expected statistical width of the background AB is also computed by taking the counting statistics of the background annulus and weighting the result by the ratio of adjusted exposure tunes. A signal to noise measure is calculated as S/N = (F-B)/(F-~ BE ~ . (1) We determined the optimum values for the algorithm parameters the inner and outer radii of the annulus and the outer radius of the central candidate region by analyzing real and Monte Carlo generated fields with a vanety of values and parameters. Increasing the size of the background annulus has the desirable effect of reducing the statistical error in the background model and the potentially undesirable effect of enabling diffuse sources of emission (which cannot be readily eliminated from the data) to degrade the accuracy of the background calculation. A somewhat more difficult problem arises when the statistics of faint point source detections is considered in detail. Because increasing the size of the candidate region adds an amount of noise which scales linearly with the area while adding a signal contribution which drops exponentially, the optimum Size of the candidate region is considerably less than the size which includes almost all of the true source flux. Consider a case ~ which the candidate region is increased in area by a factor of 2. Equation (1) would then read (F(1 + ~)-B(1 + ay~2 . ,,, ~ _ F(1 ~ a) + B(1 _ a) ~ 4~2B2 (2) where c' is me percentage increase in flux gained by going to the larger area. The optimum value for the flux in the candidate region was determined by applying the algorithm to Deep Survey and Monte Carlo-generated fields and was found to be 70% of the total power. As a result of this strategy, our candidate region is immediately surrounded by a region containing a

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188 AMERICAN AND SOVIET PERSPECTIVES flux level enhanced by the excluded photons from the source. This region must, in turn, be excluded from consideration in calculating either the source flux or background. Clearly, this method is not a reliable way to measure the flux or position of ~ source. We use it merely to establish a source's existence. Each source falling above a specified significance level is later analyzed in detail using more realistic models for the point response function. Thus, our procedure cannot be completed in less than three iterations. First we identity the relatively bright sources in a field. Then using this source list as a basis for excluding regions from background annul), we search the field again, this tune finding the faintest sources. Finale, we look at the data a third time to calculate fluxes and positions of each identified source. The results of our application of this procedure to the six Quested: Deep Survey fields are described in detail in Hamilton et al. (19901. We detected a total of 29 sources at a significance level of > 3~. The faintest detected sources have an X-ray flux in the 1-3 keV band of 4 x 10~~4erg cm~2s~i if a power law spectrum with a slope of 0.7 is adopted and the absorbing column density is assumed to be negligible (i.e., N H < 120 5 cm~2~. Preliminary analysis of three of these fields have appeared in the literature (Giacconi e' al 1979; Griffiths et at 1983) and considerable work aimed at optical identification of the candidate X-ray sources has been undertaken. From this partially complete optical program we find that 6 of the sources we detect in the three fields common to this earlier work are foreground galactic stars. In fact, all 11 of the optically identified sources listed in the earlier analysis are found in our survey, whereas only 6 of the 38 other source candidates found earlier are now detected. The other three Deep Survey fields show a similar surface density of sources. These results agree well with recent work by Primini et al (private communication), and lead to a log N-log S amplitude of 6 (counting only the sources Lath ex~agalactic optical IDs) to 10 (including all unidentified sources as extragalacitc) sources deg~2 at a Deep Survey threshold of 4 x 10-~4 erg am~2 S-i (1-3 key. Adopting a log N - log S slope of-1.5, consistent with the results of the data from the Medium Sensitivity Survey (viola et al 1984), and integrating the contribution of all e~nragalactic source detected in the Einstem band, we find that they comprise ~ 12% of the diffuse X-ray background flew detected in this same band by this same instrument. THE ORIGIN OF THE X-RAY BACKGROUND The 6= thesthold for detectable sources in the Deep SuIvey is set by the photon counting statistics of the images and our adopted significance cntenon. Clearly, however, sources fainter than this theshold commute to

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HIGH-ENERGY ASTROPHYSICS 189 the flux observed in each field, and the characteristics of the log N-log S below the significance cutoff can be studied by analyzing the arcminute- scale fluctuations In the images. No years ago, we published such an analysis (Hamilton and Helfand 1987), concluding that the log N-log S of discrete X-ray emitters must extend below the Deep Survey limit by at least a factor of 3 to explain the graininess of the images, but that the entire background was too smooth to be explained completely by such a population. The upper limit to the contribution of discrete sources was set at ~ 50%, with the remainder of the emission requiring a source surface density of greater than several thousand per square degree. These i factional contributions were based on an assumed background level derived from an extension of the high energy ?~-0 4 power law. As indicated in Figure 3b, the percentages of the observed background in the 1-3 keV band are now 12% from resolved discrete sources, ~ 255to from a fainter extension with the same log N-log S slope of the observed population, and ~ 65% from either truly diffuse emission or a very numerous population of objects. Given the evidence cited above that a population of objects other than AGN is required to explain the background, we have undertaken a search for such objects utilizing the VITA in conjunction with our X-ray fluctuation analysis. The results are presented in detail in Helfand and Hamilton (1990~. Briefly, we obtained a deep (24 hours) integration of the Draco Deep Survey field utilizing the C configuration of the VLA at 20 cm. A total of ~ 100 discrete radio sources was detected down to a limiting flux density of ~ 150pJy. We then compared the positions of these sources (accurate to ~ 1") with the positions of the brightest ~ 5% of the ~ 300 independent pixels making up the X-ray image. The expected rate of chance associations was 4, while the observed number of radio/X-ray coincidences was 9. One of the matches was with an optically identified X-ray source, whereas the remainder represent coincidences between l 3.0a positive fluctuations in the X-ray background and 0.2-2 mJy radio point sources. We are currently pursuing optical, infrared, and radio followup observations of these faint radio sources in an attempt to establish the nature of this potential new contributor to the X-ray background. The quest for an understanding of the origin of the X-ray background remains frustrated by the simple fact that the bunk of the energy density which we must explain is contained in photons above 4 keV, while the best data on the spatial distribution of the background and the characteristics of the sources which contribute to it are measured below this energy. Nonetheless, the constraints on the intensity, spectrum, and fluctuation statistics derived from the Einstein data as well as the telescope's faint threshold for discrete source detection have added considerably to our knowledge of this cosmic radiation. For example, we require a very strong evolution in the X-ray-to-optical luminosity ratio for quasars if they are to

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190 AMERICAN AND SOVIET PERSPECTIVES contribute more than ~ 30% of the background at energies below 4 keV; furthermore, the spectra of quasars in this band Awakes and Elvis 1987) are often steeper than the integrated spectrum of the background, setting an additional constraint on their contribution. Shaeffer and Sink (1988) have shown that, by invoking rather extreme evolutionary assumptions, a major (even dominant) contribution to the 1-3 keV background can arise from hot gas in clusters and groups of galaxies, although such sources would not add significant flux at higher energies. Models for galaxy formation which invoke superconducting cosmic strings have recently been used to make a prediction about the structure of the 1-3 keV background (Ostriker and Thompson 1987~; to wit, that as such strings "explode" they create superbubbles in the intergalactic medium at z ~ 10 - 30 which should lead to correlated structure in the background on scales of ~ 3 - 100 arcminutes. Unfortunately, it appears that the Einstein data are not quite sufficient to provide a quantitative test of this prediction. Primordial galaxies themselves are a potential background contributor and the high-source surface density our fluctuation analysis requires plus the tantalyzing evidence for associated faint radio sources makes this an attractive option to pursue. The most obvious explanation for a diffuse background a hot diffuse medium has not been excluded, although it suffers from severe problems on energetic grounds (Field and Perronod 1977) and may also have difficulties matching the observed broad-band spectrum once the known discrete contributors are removed (Giacconi and Zamorani l987~. It is clear that what is needed is data which can reach fainter flux levels and can measure the properties of contributing source populations with greater prounion and over a broader bandwidth. The ROSAT Observatory, to be launched next year, will allow us to push the log N-log S curie tO somewhat lower flux levels, albeit only in the band below 2 keV. Major progress should be forthcoming a few years hence when the higher energy imaging missions Astro-D and, particularly, Spectrum-RG, are launched. The extremely high throughput and broad spectral coverage of the Sodart telescopes on Spectrum-RG will provide qualitatively new data on the spectrum and spatial structure of the background itself as well as on the characteristics of sources which contn~ute to it down to fluxes an order of magnitude below the Eutstein Deep Survey limit Perhaps then, three decades after its discovery, we will finally understand fully the origin of the X-ray background and will be able to exploit this understanding for the constraints it will set on the evolution of the Universe and its contents. ACKNOWLEDGMENT S The author acknowledges the major contributions to this work of his collaborators T.T. Hamilton, K-Y. Wu and Q. Wang, as well as the support

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HIGH-ENER~ ~TROP~ICS 191 of the National Aeronautics and Space Administration under grant NAG8- 497, me U.S. National Academy of Sciences for making attendance at this worlo;hop possible, and the Academy of Sciences of the U.S.S.R. for their warm and gracious hospitality during the meeting. This is contribution number 397 of the Columbia Astrophysics Laboratory. REFERENCES Boldt, E. 1987. Physics Reports 146: 216. Burrows, D. 1982. Ph.D. Dissertation. University of Wisconsin. Field, G., and S. Perronod. 1977. Ap. J 215: 717. Fried, P.M. 1978. Ph.D. Dissertation. University of Wisconsin. Giacconi, R., et al. 1979. Ap. J. (Lettered 234: L1. Giaconni, R. and G. Zamorani. 198~7. Ap. J. 313: 20. Gioia, I.M., 1: Maccacaro, R Schild, J.l: Stocke, J.W. Liebert, IJ. Danziger, D. Kunth, and J. Lub. 1984. Ap. J. 283: 495. Gnffiths, IRE., et al. 1983. Ap. J. 269: 375. Harnden, F.R., D.G. Fabncant, DN Hams, and J. Schwartz. 1984. SAO Report 393. Hamilton, 111:, and DJ. Helfand. 1990. Ap. J. Attend Submitted. Hamilton, T.1:, and DJ. Helfand. 1987. Ap. J. 318: 93. Hamilton, 1:1:, DJ. Helfand, and X-Y. Wu. 1990. In preparation. Iwan, D., F.E. Marshall, E.A Boldt, RF. Mushotzly, MA Shafer, and A Stottlemyer. 198Z Ap. J. 260: 111. Koyama, K, K Makishima, Y. Tanaka, and H. Tsunemi. 1986. PASJ 38: 121. Marshall, F.E., E.A Boldt, S.S. Halt, R.B. Miller, R.F. Mushottly, LN Rme, R.E. Rothschild, and PJ. Serlemitsos 1980. Ap. J. 235: 4 L1. Mauche, COO., and P. Gorenstein. 1986. Ap. J. 302: 371. McCammon, D., D.N. Burrows, W.T. Sanders, and W.L. Kraushaar. 1983. Ap. J. 269. 107. Mushotzly, R. 1985. Ap. J. 256: 9Z Nousek J. 1978. Ph.D. Dissertation. University of Wisconsin. Ostnker, J.P., and ~ Thompson. 1987. Ap. J. (Letters) 323: L97. Shaeffer, R and J. SilL 1988. Ap. J. 333: 509. Tanaka, Y. 1989. In Proceedings of 23rd ESIAB Symposium in press Wang, Q., and DJ. Helfand. 1990. Ap. J. Submitted. wing, Q., 121: Hamilton, DJ. Helfand, and JAY. Wu. 1990. Ap. J. Submitted. Watson, h1. 1989. Windows on Galaxies. Ence Summer School in press Polkas, B., and M. Elvis. 19~37. Ap. J. 323: 243. Wit, X-Y., AT Hamilton, DJ. Helfand, and Q. Wang. 1990. Ap. J. Submitted.