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OCR for page 174
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
OCR for page 175
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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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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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
OCR for page 179
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
OCR for page 180
- -
- -
- ~
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
OCR for page 181
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
OCR for page 182
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.
OCR for page 183
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
OCR for page 185
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
OCR for page 187
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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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 < 1°20 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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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
OCR for page 191
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.
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Representative terms from entire chapter:
kev band
