The mass distributions were determined of several clusters of galaxies by using X ray surface brightness data from the Einstein Observatory Imaging Proportional Counter (IPC). Determining cluster mass distributions is important for constraining the nature of the dark matter which dominates the mass of galaxies, galaxy clusters, and the Universe. Galaxy clusters are permeated with hot gas in hydrostatic equilibrium with the gravitational potentials of the clusters. Cluster mass distributions can be determined from x ray observations of cluster gas by using the equation of hydrostatic equilibrium and knowledge of the density and temperature structure of the gas. The x ray surface brightness at some distance from the cluster is the result of the volume x ray emissivity being integrated along the line of sight in the cluster

White, Raymond E., III

English

NASA Technical Reports Server

FINAL TECHNICAL REPORT
_o yzJW/Z ')
IPC "Two-COLOR" ANALYSIS OF )[-RAY GALAXY CLUSTERS
PI: RAYMOND E. WHITE III
Department of Physics and Astronomy
University of Alabama
Tuscaloosa, AL 35487-0324
NASA ADP Grant: NAG 5 1188
8/ /s9-1/31/9o
(NASA-CR-188980) IPC
X RAY GALAXY CLUSTERS
Report, 1 Aug. 1989 -
Univ.) 9 p
TWOCCOLOR ANALYSIS OF
Final Technical
31 Jan. 1990 (Alabama
CSCL 03A
G3/89
N92-I0724
Unclas
0048073
https://ntrs.nasa.gov/search.jsp?R=19920001506 2020-03-19T16:27:44+00:00Z

IPC "Two-COLOR:' ANALYSIS OF X-RAY GALAXY CLUSTERS
Background
I have determined the mass distributions of several clusters of galaxies by using X-ray
surface brightness data from the Einstein Observatory Imaging Proportional Counter
(IPC). Determining cluster mass distributions is important for constraining the nature of
the dark matter which dominates the mass of galaxies, galaxy clusters and the Universe.
Galaxy clusters are permeated with hot gas in hydrostatic equilibrium with the gravita-
tional potentials of the clusters. Cluster mass distributions can be determined from X-ray
observations of cluster gas by using the equation of hydrostatic equilibrium and knowledge
of the density and temperature structure of the gas:
M(r) - #raG d _n r + -d-_n T(r)r. (1)
Here M is the total mass within radius r from the cluster center, p and T are the gas
density and temperature, and k, #m and G are the Boltzmann constant, mean mass
per gas particle and the gravitational constant, respectively. Note that the logarithmic
derivatives of p and T in this equation are simply the respective local slopes of density and
temperature profiles.
The X-ray surface brightness at some distance r from the cluster is the result of the
volume X-ray emissivity being integrated along the line-of-sight in the cluster. The X-ray
surface brightness profile S,(r) can be deprojected to give the local volume emissivity
e_(r) = p2(r)Ax(T(r)), which is a function of the local gas density and the radiative
cooling function A,(T) (the latter of which has been convolved with the spectral response
of the detector). Because the spectral response of the Einstein Observatory IPC was
rather insensitive to temperature variations, accurate gas density profiles can be extracted
from such deprojected volume emissivities: that is, Ax(T) is fairly constant for the bulk
of the temperature range expected in clusters. Thus, the slope of the density profile and
its contribution to the total mass determination in equation (1) is well-constrained by
the high spatial resolution surface brightness profiles provided by the IPC. However, the
poor spectral resolution of the IPC has prevented temperature profiles T(r) from being
extracted with similar accuracy.
Analysis
To estimate the temperature structure of the hot gas in several galaxy clusters, I divide
IPC surface brightness data into two different energy bands: 0.56-1.5 keV and 1.5-3.5 keV.
Only two broad bands are chosen in order to maximize the counts in each band, reducing
their statistical uncertainty. Although the Einstein IPC was sensitive to photons softer
than 0.56 keV, they were excluded from consideration because they are most subject to
uncertainties in the column density of intervening X-ray-absorbing matter.
Volume X-ray emissivities are extracted from the surface brightness profiles, after back-
ground subtraction and vignetting correction. A ratio of emissivities in the two energy
2
bands provides a temperature estimate when compared to theoretical emissivity ratios
for these two bands. Theoretical emissivity ratios are derived from the XSPEC software
(Sharer, Arnaud, Haberl, Tennam 1990), which can convolve thermal spectra with the
spectral response of the IPC. The photon statistics remain poor, nonetheless, so there is a
considerable tradeoff to be made: 1) one can derive reasonably well-constrained tempera-
tures at very few (maybe only one) positions, leading to no or very coarse mass profiles;
or 2) one can try to retain high spatial resolution, but lose accuracy in the temperature
profile, leading to poorly determined mass profiles.
I first tried to derive reasonably smooth mass profiles by retaining considerable spatial reso-
lution with a Monte Carlo approach to the data analysis. Synthetic surface brightness data
were generated from the original data by assuming Poisson errors. Smooth fits were made
to the resulting synthesized surface brightness profiles in each energy band. The chosen
forms of the surface brightness fits a/lowed emissivity profiles to be deduced analytically.
The subsequent ratio of the emissivity profiles in the two energy bands allowed smooth
temperature profiles, and therefore smooth mass profiles, to be deduced. Errors were esti-
mated from the dispersion in the temperature and mass profiles after 20-100 realizations
of the surface brightness data were processed.
Initial analysis of the X-ray data for clusters A496 and A2199 seemed promising, in that
smooth and reasonable mass profiles were derived from fits to the raw data. Howeyer,
the subsequent Monte Carlo synthesis and error analysis showed that the uncertainties in
the derived temperature and mass profiles were so large that the temperature and mass
profiles could not be interestingly constrained.
I then turned to a straightforward, non-synthetic analysis Of the data in order to deter-
mine the maximum spatial resolution for which I could still obtain reasonably constrained
temperatures. I started by combining all of the data in one spatial bin (resulting in no
spatial resolution) in order to derive the most accurate temperature. I then deprojected
the data into successively smaller spatial bins until the temperature uncertainty in each
bin grew to make the temperature estimates uninteresting.
The deprojection routine I developed to extract volume emissivities from surface brightness
data also calculates the errors in the emissivities so derived. Temperatures were derived
from a comparison of the ratio of deprojected count emissivity in the two energy bands
to theoretical ratios derived from XSPEC spectral synthesis. The metal abundances and
column densities of intervening, X-ray absorbing matter were held fixed in deriving tables
of temperature vs. hardness ratio. Abundances were taken from Ginga observations of
Hatsukade (1989) or EXOSAT observations of Edge (1989). Column densities of inter-
vening X-ray absorbing matter were taken from the same sources. I have been able to
derive reasonably well-constrained temperatures for at least two and as many as four spa-
tial bins in four clusters: A262, .-k1060, A2199 and A496. The temperature profiles for
these clusters are shown in Figures la - d. The temperatures are plotted against angular
distance from the cluster centers. The spatial conversion (assuming q0 = 0.5 and H0 = 50
km/s/Mpe) for each cluster is indicated in the lower right of each panel.
The global temperatures I derive for A262 and A1060 are in excellent agreement with
temperaturesderived from other spectroscopicinstruments (seeTable 1). However, the
temperatures of A496 and A2199 are respectively hotter and cooler than those derived
from other instruments (seeTable 1). Thesesystematic differencesare probably due to
the fact that I am deriving a temperature from only onehardnessratio, rather than from
fits to the the full complementof energyresolution elementsof the IPC. Nonetheless,even
in the two clusterswhich have systematic temperature differences,I can still accurately
assessthe isothermality of their cluster atmospheres. If the clusters are isothermal to the
outermost radii investigated, a systematic offset in the absolute temperature calibration
cannot prevent that from being determined. However, if temperature structure exists, the
actual shape cannot be accurately deduced without knowing whether the systematic errors
in the derived temperatures are temperature-dependent. A262 and A1060 (see Figs. la, b)
appear to have roughly isothermal temperature profiles outside a cooler central bin. A496
also seems to be isothermal, but only two spatial bins proved feasible. A2199 seems to
have a substantial temperature peak at intermediate radii. The cooler centers of A262 and
A1060 are a signature of cooling flows and are also refiected in the fact that the central
cooling times in these clusters is less than 101° yrs (see Fig. 4).
I derived gas densities from the deprojected total emissivity (the full energy bandwidth
of the prior two energy bands) using count-to-flux conversions derived from XSPEC mod-
elling. I adopted the global temperatures derived above in determining the local gas
density. The resulting distribution of gas mass are shown in Figures 2a, b for A262 _and
A1060, for which the global temperature determination proved accurate. Also shown in
these figures are the total mass distributions I derive for A262 and A1060 using equation
(1). I took the cluster gas to be isothermal at the derived global temperature (neglecting
the temperature drop in the innermost region) and the slope of the density distribution
was derived from the deprojected density profile. The gas mass to total mass ratio is shown
in Figure 3, where it is clear that Mg_s/Mtot rises outward to about 10% by ",,500 kpc.
The cooling time distributions inferred from the local density and the (assumed constant)
global temperature in A262 and A1060 are shown in Figure 4, where it is apparent that
the cooling time is less than 101° yrs in the central parts. This indicates that the central
gas can radiate away its pressure support in a Hubble time, leading to a cooling flow. If
the cooling flow is long-lived, the central temperature should be cooler, as is indicated in
Figures la, b.
These results, with some additional analysis, will be submitted to The Astrophysical
Journal for publication.
The Energetics and Metal Abundances of Intracluster Gas
I was able to use some of the surface brightness data analyzed in the previously described
investigation in an entirely different project, as well. I recently showed that various galaxy.
formation scenarios can be tested and distinguished by their relative impact on the physical
state of intracluster gas. Intracluster gas gains a certain amount of energy in the course of
galaxy cluster collapse. Additional energy may (or may not) be injected into intracluster
gas through processes associated with galaxy formation before or during cluster collapse.
If galaxy formation was truncated by galactic winds, then such winds would deposit metals
and energy into intracluster gas. Clusters with low velocity dispersionsshould be most
affected by this additional energy deposition. If galaxies did not blow winds, then no
suchenergy would be deposited. In the latter case, the high metal abundancesobserved
in intracluster gasmay be attributed to the stripping of metal-rich gas from galaxies:a
processwhich doesnot add net energyto intracluster gas. Thus, thesetwo galaxyformation
scenarioscanbe distinguishedby their relative impact on the energeticsof intracluster gas.
If intracluster gaswereenergizedsolely by cluster collapse,then the gas should have the
same specific energy (temperature) as the cluster massand galaxies. The gas density
should then have the sameprofile as the massdensity if both are isothermal. In the
galactic wind hypothesis,intracluster gasshouldhavemorespecific energythan expected
if the intracluster gaswasenergizedsolely by cluster collapse.Thus the gas temperature
should exceedthe kinetic temperature (velocity dispersion)of the galaxies, and the gas
density profile should be shallower than the total massdensity profile. A shallowergas
density profile leadsto a shallowerX-ray surfacebrightnessprofile. Theseeffectsshould
be more pronouncedfor clusterswith low velocity dispersions,becausethe depthsof their
potential wells are more comparable than those of high dispersion clusters to the depths of
individual galaxies' potential wells. I showed that X-ray spectral observations of the gas in
cool and hot clusters indicate that cool clusters have preferentially higher specific energy
than the galaxies in such clusters. Furthermore, I showed that the surface brightness
profiles of cool clusters tend to be shallower than those of hot clusters. To help fo/'tify
this latter point, I used some of the surface brightness data acquired and analyzed in the
course of the previously described investigation of intracluster temperature profiles. Both
the temperature and surface brightness observations are consistent with galaxies having
blown energetically significant galactic winds in the past.
I presented these results at a meeting on "Superclusters and Clusters of Galaxies and
Environmental Effects" held in July 1990 in Sesto, Italy. Reprints of the publication
associated with this work ("The Metal Abundance and Specific Energy of Intracluster
Gas," White, R. E. III 1991, Astrophysical Journal, 367, 69-77) axe included with this
final report.
References
Edge, A. C. 1989, Ph.D. Thesis.
Hatsukade, I. 1989, Ph.D. Thesis, ISAS Research Note 435.
Sharer, R., Haberl, F., Arnaud, K. A., and Tennant, A. 1990, XSPEC.
Publications generated by this grant
"The Metal Abundance and Specific Energy of Intracluster Gas"
White, R. E. II! 1991, Astrophysical Journal, 367, 69-77.
"Temperature and Mass Profiles for Several Clusters of Galaxies"
White, R. E. III 1991, to be submitted to Astrophys. J.
5
Table I
Ten_erature Temperature other
Cluster (this study) (other) Instrument
A 262 EXOSAT
+0 37
1.86
-0 21
+0 31
2.42
-0 27
+0 22
2.53
-0 19
A 1060 Ginga
+1 20
5.44
-0 85
+0 04
2.55
-0 04
A 496 Ginga
+0 06
3.91
-0 06
+0 25
2.60
-0 20
A 2199 EXOSAT
+0 41
4.71
-0 35
Temperatures in keY. Ginga temperatures from Hatsukade
(1989); errors are 90% confidence. EXOSAT temperatures
from Edge (1989); errors are 90% confidence. Temperature
errors for this study are 1 sigma.
I t
II1
I
I t , , F-r-r--r-_
o
"7
O_
u_
-i
end-
(A_t) .+.
ml
v
m
- I
- I
C_ -
I" _
-
123 -
p..
II
o
,i.-,I
,i-.4
u+
-+
P.
o
f I i
(A_) j.
I I I I , I I I I I
T
II
o
i I
o
(A++t)± (A++t)±
@0
0
0
14
13
12
11
10
t I ; t I
- ,A. 262
D
m
14 j
- i i060
13 --
12 --
11 --
10 --
9 t
-1
] I '"J I
1 [ t I 1 I
I I I I 1 [.
0 .5
log R (arcmin)
i J i I I I
1 I I ] I I I 1 J
0 .5
log R (arcmin)
I I i
]
I I I
I I J
I I I
I I I I 1
I
(a)
J I J J
(b)
I I 1 ] I
1
q
i
m
m
w
t I
1,5
I !
1
1.5
Figure 2
:m
I4
bJ8
0
h_
V
bJD
0
.15
.05 --
0
-1
11.5
11--
10.,5 --
10----
9.,5--
I I I I I i I....I I I ' I I I I i I I I I I
A 262
[ ,, [ I l J _ , I
-.5 0
I
i
I I l I I
.`5
log R (arcmin)
I
I
I
I
I
I
I I I ] 1 I
A 1060-
I I I
' 1.`5
9
-1
'' I' ' ' ' I ' I I I
A 1060
I I l,J,] i l,_ i I
0 .`5
log R (arcmin)
I I t I I j I I I I
1 I
1.5
I
I
I
I
I
I
t
I
I I 1 I I
Figure 4


IPC two-color analysis of x ray galaxy clusters

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server