4.3. X-ray spectra
Observations of the X-ray spectra of clusters of galaxies have played a
critical
role in establishing the primary emission mechanism (thermal emission from
diffuse hot intracluster gas) and in testing models for the origin of
this gas. Models in which the emission comes from diffuse thermal gas
predict (1) that the
spectrum will be roughly exponential (the intensity
I
(erg / cm2-s-Hz) varies as
exp(-h
/
kTg) where Tg is the gas
temperature); (2) that the gas
temperature will be such that the thermal velocity of protons in the gas
(k Tg / mp)1/2 be
comparable to the velocity of the galaxies in the cluster, as
both are bound by the same gravitational potential; (3) that there will
be no strong low energy photoabsorption; and (4) that emission lines
will be present if the gas contains a significant contamination of heavy
elements like iron. Alternatively, models in which the emission is due to
relativistic nonthermal electrons predict a power-law spectrum
I
-
,
which implies an excess at low and high energies when compared to an
exponential spectrum; no line emission would be expected for a nonthermal
emission process. As another possibility, the emission might be thermal
emission from a number of compact sources, such as galactic nuclei or the
binary stellar X-ray sources which dominate the X-ray sky within our own
galaxy; however, such sources are generally optically thick at low X-ray
energies (
1
keV). The theories for each of these classes of emission
processes and the basis for these predictions are discussed in
Section 5.1.
The first three of the predictions given above concern the broad-band form of the spectrum (the continuum), while the last prediction concerns lines. Accordingly, the properties of the continuum spectra will first be reviewed, and then those of the line spectra. Reviews devoted primarily to the observations of the X-ray spectra of clusters have been given recently by Canizares (1981) and Mushotzky (1980, 1984, 1985), while Holt and McCray (1982) review all of X-ray spectroscopy.
4.3.1. Continuum features in the spectrum
If the X-ray emission from clusters is due to a diffuse plasma of either
thermal or nonthermal electrons, the optical depth of the gas should be
quite low. On the other hand, compact X-ray sources (such as galactic
nuclei or binary stellar X-ray sources) often contain significant
quantities of relatively cool neutral gas, which absorbs soft X-rays
through photoionization. Because the fluorescent yield of the
light elements is low, the absorbed X-rays are not reemitted and are
lost from the
spectrum. This low energy photoabsorption occurs in a series of edges which
correspond to the absorption edges of cosmically abundant elements. The
opacity of a solar abundance, low density, cold neutral gas has been
calculated, for example, by
Brown and Gould (1970).
It is conventional to parametrize the
absorption observed in an X-ray spectrum by the column density of hydrogen
Nh in a gas with assumed solar abundances required to
produce the observed
absorption. Typically, compact sources have Nh
1022
cm-2. Even the earliest
X-ray spectra of clusters suggested that they had rather weak low energy
absorption
(Catura et al.,
1972;
Kellogg, 1973;
Davidsen et al.,
1975;
Kellogg et al.,
1975;
Margon et al.,
1975;
Avni, 1976),
with column densities Nh
1022
cm-2, which were generally consistent with the amount of
neutral
hydrogen in our own galaxy along the line of sight to the cluster. This
indicated that the emission from clusters comes from a diffuse, ionized
plasma.
Initially, there were two competing models for the nature of this ionized
plasma (see Section 5.1). It could be a
hot, thermal plasma with a temperature
Tg
108 K, or it could be a relativistic, nonthermal plasma with
a power-law
electron energy distribution, such as the plasma responsible for the radio
emission observed in clusters (see
Section 3.1). In the first case, the
X-ray continuum would be primarily due to thermal bremsstrahlung (see
Section 5.1.3),
with a spectrum given by equation (5.11). If the frequency variation of
the Gaunt factor
gff(
,
kTg) is ignored and the gas is all at a single
temperature, the spectrum is exponential
I
exp(-h
/
kTg). In the second
case, the emission is primarily due to the inverse Compton process (the
scattering of low energy photons to X-ray energies by the relativistic
electrons; see Section 5.1.1), and the
expected spectrum is a power-law
I
-
.
Unfortunately, proportional counters have rather poor spectral resolution,
and it is therefore difficult to distinguish between thermal and nonthermal
spectra. Moreover, any sufficiently smooth and monotonic spectrum can
be produced by the combination of the thermal spectra with varying
temperatures, or nonthermal spectra with varying spectral indices
; thus the
distinction between thermal and nonthermal spectra cannot be made
unambiguously. It is not surprising, therefore, that the early proportional
counter spectra of clusters could be fit consistently by either thermal
(exponential) or nonthermal (power-law) spectra (for example,
Kellogg et al.,
1975).
However, spectra over a large energy range were better fit by the
thermal model
(Davidsen et al.,
1975;
Scheepmaker et
al., 1976).
The first large surveys of cluster spectra came from observations with OSO-8 and Ariel 5. These satellites observed individual clusters for longer periods of time than had been possible with previous sky survey instruments, and had detectors that were optimized for spectral resolution. The spectra of clusters observed with OSO-8 and Ariel 5 were significantly better fit by the thermal bremsstrahlung model than by the nonthermal model (Mushotzky et al., 1978; Mitchell et al., 1979). The required temperatures for the cluster gas were found to range from about 2 × 107 to 2 × 108 K from cluster to cluster, and some of the clusters required gas at several temperatures to fit the spectrum. Recently, a more extensive survey of X-ray cluster spectra was made with the A-2 experiment on the HEAO-1 satellite (Mushotzky, 1980, 1984, 1985; a href="Sarazin_refs.html#345" target="ads_dw">Henriksen, 1985; a href="Sarazin_refs.html#346" target="ads_dw">Henriksen and Mushotzky, 1985, a href="Sarazin_refs.html#347" target="ads_dw">1986).
The two properties that can be derived most easily from the continuum X-ray spectrum are the gas temperature Tg and the emission integral
![]() | (4.3) |
where np is the proton density, ne
is the electron density, and V is the volume
of the gas in the cluster. The X-ray luminosity of a cluster is
proportional to EI
(equation 4.11). The X-ray luminosity (or EI) and gas temperature
are found to be strongly correlated
(Mitchell et al.,
1977,
1979;
Mushotzky et al.,
1978).
The HEAO-1 A-2 sample (Figure 11) gives
Lx
Tg3
(Mushotzky, 1984).
The OSO-8, Ariel 5, and HEAO-1 A-2 spectral surveys established a
number of correlations between these X-ray spectral parameters and the
optical properties of X-ray clusters, which are discussed in
Section 4.6 below.
![]() |
Figure 11. The correlation between the gas temperatures derived from X-ray spectra with HEAO-1 A-2 and the cluster X-ray luminosities, from Mushotzky (1984). |
There was also some evidence from the OSO-8 survey that the gas in clusters was isothermal; that is, the range of temperatures within the gas in a single cluster was relatively small. However, in many cases the OSO-8 and Ariel 5 temperatures were not in agreement within the errors; if these differences are real, they suggest that there are multiple temperature components to the emission. If that were the case, the OSO-8 and Ariel 5 detectors, which have different spectral and spatial sensitivities, might give different weights to the different components, and produce different average temperatures.
The HEAO-1 A-2 detector has provided much more data on the spectra of
clusters in the photon energy range 2-60 keV
(Mushotzky, 1980,
1984,
1985;
Henriksen, 1985;
Henriksen and Mushotzky,
1985,
1986).
There is now evidence
that most clusters contain a range of gas temperatures, with typical values
between Tg
2 ×
107 and 8 × 107 K. These multiple temperature
components appeared to be most significant in clusters with low X-ray
luminosities, although
it is possible that similar low-luminosity cool components might remain
undetected if hidden in the spectrum of clusters with high-luminosity
high-temperature emission. The information on the spatial distribution
of the X-ray emission in clusters
(Section 4.4) suggests two locations for this
cool gas.
First, in low luminosity clusters, the X-ray emission is often
inhomogeneous, with
clumps of emission being associated, in some cases, with individual
galaxies.
These clumps may contain cooler gas. Second, in some clusters there are
enhancements in the X-ray surface brightness at the position of the cD
or other centrally located dominant galaxy in the cluster. X-ray line
observations suggest that these are regions at which the hot
intracluster gas
is cooling and being accreted by the central dominant galaxy
(Section 5.7).
The Einstein X-ray observatory had two instruments capable of
providing
information on the continuum spectra of clusters. First, there was the
Imaging Proportional Counter (IPC), which provided low resolution
spatial and spectral information. Initially there were problems with the
calibration of the energy
scale of the spectra due to gain variations. These problems have now
apparently been resolved, and a few cluster spectra from this instrument
are available at the present time
(Fabricant et al.,
1980;
Perrenod and Henry,
1981;
Fabricant and
Gorenstein, 1983;
White et al., 1987).
The second instrument was the Solid State Spectrometer (SSS), which had
considerably better spectral resolution, but had no spatial resolution
and less
sensitivity than the IPC. Because of its small field of view (6 arc min),
it could only observe a small portion of nearby clusters. Thus it was
used primarily to determine spectra for the central regions of nearby
clusters. It provided strong evidence for the presence of cool gas at the
centers of a number of clusters
(Mushotzky, 1980,
1984,
1985;
Mushotzky et al.,
1981;
Lea et al.,
1982);
these observations are discussed further
below. One problem with Einstein as an instrument for X-ray cluster
spectroscopy is that the telescope was only sensitive to photons with
energies of
about 0.1 - 4.0 keV. With the typical temperatures of the gas in clusters
being kTg
8 keV, observations
with Einstein could not determine the
thermal structure in this hot gas. However, the Einstein
detectors were very sensitive to the presence of low temperature
components of the emission.
Detections or limits on the hard X-ray spectrum and flux of clusters have
been useful in limiting the contribution of nonthermal processes to their
luminosity. As mentioned above, spectra extending into the hard X-ray region
(h > 20 keV) gave
the first direct, strong indication that the primary emission
mechanism was thermal, rather than nonthermal
(Davidsen et al.,
1975;
Scheepmaker et
al., 1976).
Subsequently, stronger limits on the hard X-ray
emission have shown that nonthermal emission makes at most a very small
contribution to the X-ray luminosity of clusters
(Mushotzky et al.,
1977;
Lea et al.,
1981).
When combined with observations of the diffuse radio emission in the
cluster (Section 4.4), these hard X-ray
limits can be used to give lower
limits on the magnetic field in the cluster, because the synchrotron radio
emissivity is proportional to the product of the density of relativistic
electrons and the magnetic field strength, while the inverse Compton X-ray
emission depends only on the density of relativistic particles (see
Section 5.1.1 for a more detailed
discussion of this point). Typically, these limits
are B
10-7G
(Lea et al.,
1981;
Primini et al.,
1981;
Bazzano et al.,
1984).
In the Perseus cluster, a power-law hard X-ray component with
2.25 has
been detected; it varies on a time scale of about a year, and the X-ray
variations
are correlated with variations in the radio flux of the compact radio
source at the nucleus of the galaxy NGC1275
(Primini et al.,
1981;
Rothschild et al.,
1981).
Much weaker power law sources may also have been detected in the
M87/Virgo, A2142, and 3C129 clusters
(Lea et al.,
1981;
Bazzano et al.,
1984).