The Birmingham-CfA cluster scaling project - I: gas fraction and the M-T relation

27 Pages·0.74 MB·English

by  A. J. R. Sanderson

Mon.Not.R.Astron.Soc.000,1–27(2002) Printed2February2008 (MNLATEXstylefilev2.2)
The Birmingham-CfA cluster scaling project - I: gas
M − T
fraction and the relation
X
A. J. R. Sanderson1,5 ⋆, T. J. Ponman1, A. Finoguenov2,3, E. J. Lloyd-Davies1,4
and M. Markevitch3
1School of Physics and Astronomy, Universityof Birmingham, Edgbaston, Birmingham B15 2TT, UK
2Max-Planck-Institut fu¨r extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
3Harvard-Smithsonian Centerfor Astrophysics, 60 Garden Street, Cambridge, MA 02138
3 4Department of Astronomy, Universityof Michigan, AnnArbor, MI48109-1090, USA
0 5Department of Astronomy, Universityof Illinois, 1002 WestGreen Street, Urbana, IL 61801, USA
0
2

n
Accepted 2002??.Received2002??;inoriginalform2001??
a
J

3
ABSTRACT

1
v Wehaveassembledalargesampleofvirializedsystems,comprising66galaxyclusters,
9 groups and elliptical galaxies with high quality X-ray data. To each system we have
4 fitted analytical profiles describing the gas density and temperature variation with
0 radius, corrected for the effects of central gas cooling. We present an analysis of the
1 scaling properties of these systems and focus in this paper on the gas distribution
0 and M −TX relation. In addition to clusters and groups, our sample includes two
3
early-typegalaxies,carefullyselectedtoavoidcontaminationfromgrouporclusterX-
0
ray emission. We compare the properties of these objects with those of more massive
/
h systemsandfindevidence forasystematic differencebetween galaxy-sizedhaloesand
p groups of a similar temperature.
o- We derive a mean logarithmic slope of the M −TX relation within R200 of
r 1.84±0.06,althoughthereissomeevidenceofagradualsteepeningintheM −TX re-
t lation,withdecreasingmass.Werecoverasimilarslopeusingtwoadditionalmethods
s
a of calculating the mean temperature. Repeating the analysis with the assumption of
: isothermality,wefindtheslopechangesonlyslightly,to1.89±0.04,butthenormaliza-
v
i tion is increased by 30 per cent. Correspondingly, the mean gas fraction within R200
X changes from (0.13±0.01)h−23 to (0.11±0.01)h−23, for the isothermal case, with the
70 70
r smallerfractionalchangereflecting differentbehaviour betweenhotandcoolsystems.
a
Thereisastrongcorrelationbetweenthegasfractionwithin0.3R200andtemperature.
This reflects the strong (5.8σ) trend between the gas density slope parameter,β, and
temperature, which has been found in previous work.
These findings areinterpretedas evidencefor self-similaritybreakingfromgalaxy
feedback processes,AGN heating or possibly gas cooling.We discuss the implications
of our results in the context of a hierarchical structure formation scenario.
Key words: galaxies: clusters: general – galaxies: haloes – intergalactic medium –
X-rays: galaxies – X-rays: galaxies: clusters
1 INTRODUCTION potential. By studying the properties of groups and clus-
tersofgalaxies,itispossibletoprobethephysicalprocesses
The formation of structure in the Universe is sensitive to
whichshapetheevolutionandgrowth ofvirialized systems.
physical processes which can influence the distribution of
X-rayobservationsofthegaseousintergalacticmedium
baryonicmaterial,aswellascosmologicalfactorswhichulti-
(IGM) within a virialized system provide an ideal probe of
matelygovernthebehaviouroftheunderlyinggravitational
the structure of the halo, since the gas smoothly traces the
underlying gravitational potential. However, this material
is also sensitive to the influence of physical processes aris-
⋆ E-mail:[email protected] ing from the interactions between and within haloes, which
(cid:13)c 2002RAS
2 A. J. R. Sanderson et al.
are commonplace in a hierarchically evolving universe (e.g. temperature analyses of clusters. We include a large num-
Blumenthal et al.1984).Eveninrelativelyundisturbedsys- ber of cool groups in our analysis, as the departure from
tems, feedback from the galaxy members can bias the gas self-similarity is most pronounced in haloes of this size: the
distributionwithrespecttothedarkmatterinawaywhich non-gravitationally heated IGM is only weakly captured in
varies systematically with halo mass. N-body simulations theshallower potentials wells of these objects.
(e.g.Navarro, Frenk& White1995)indicatethat,intheab- To further extend the mass range of our analysis, we
sence of such feedback mechanisms, the properties of the include two galaxy-sized haloes in our sample, in the form
gas and dark matter in virialized haloes should scale self- of an elliptical and an S0 galaxy. Galaxy-sized haloes are
similarly,exceptforamodestvariation indarkmattercon- of great interest as they represent the smallest mass scale
centration withmass(Navarro, Frenk & White1997).Con- for virialized systems and constitute the building blocks
sequently, observations of a departure from this simple ex- in a hierarchically evolving universe. Great emphasis was
pectation provide a key tool for investigating the effects placedonidentifyinggalaxiesfreeofcontaminationfromX-
ofnon-gravitationalheatingmechanisms,arisingfromfeed- rayemissionassociated withagrouporclusterpotential,in
back processes. which they may reside, since this is known to complicate
Thereisnowclear evidencethatthepropertiesofclus- analysis of their haloes (e.g. Mulchaey & Zabludoff 1998;
ters and groups of galaxies do not scale self-similarly: for Helsdon & Ponman 2000). The most well-studied galaxies
example,theL T relationinclustersshowsalogarithmic aregenerallythefirst-rankedmembersingroupsorclusters,
X
−
slope which is steeper than expected (e.g. Edge & Stewart and it is known that such objects are atypical, as a conse-
1991;Arnaud & Evrard1999;Fairley et al.2000).Afurther quenceofthedensegaseousenvironmentsurroundingthem:
steepeningofthisslopeisobservedinthegroupregime(e.g. thework of Helsdon et al. (2001) has shown that brightest-
Helsdon & Ponman 2000), consistent with a flattening in groupgalaxiesexhibitpropertieswhichcorrelatewiththose
the gas density profiles, which is evident in systems cooler of the group as a whole, possibly because many of them lie
than3–4 keV(Ponman, Cannon & Navarro1999).Suchbe- atthefocusofagroupcoolingflow.ThestudyofSato et al.
haviourisattributedtotheeffectsofnon-gravitationalheat- (2000) incorporated three ellipticals, but any X-ray emis-
ing, which exert a disproportionately large influence on sion associated with these objects is clearly contaminated
the smallest haloes. An obvious candidate for the source byemissionfromthegrouporclusterhaloinwhichtheyare
of this heating is galaxy winds, since these are known to embedded.
be responsible for the enrichment of the IGM with heavy Throughout this paper we adopt the following cosmo-
elements (e.g. Finoguenov, Arnaud & David 2001). How- logicalparameters;H0=70 km s−1 Mpc−1andq0 =0.Un-
ever, active galactic nuclei (AGN) may also play a signif- lessotherwisestated,allquotederrorsare1σononeparam-
icant role, particularly as there is some debate over the eter.
amount of energy available from supernova-driven outflows
(Wu,Fabian & Nulsen2000).Recently,theoreticalworkhas
alsoexaminedtheroleofgascooling(c.f.Knight & Ponman 2 THE SAMPLE
1997), which is also able to reproduce the observed scaling
In order to investigate the scaling properties of virialized
properties of groups and clusters, by eliminating the low-
systems, we have chosen a sample which includes rich clus-
estentropygasthroughstarformation,thusallowinghotter
ters,poorerclusters,groupsandalsotwoearly-typegalaxies,
materialtoreplaceit(Muanwong et al.2001;Voit & Bryan
comprising 66 objects in total. Sample selection was based
2001).
ontwocriteria:firstly,thata3-dimensionalgastemperature
Previous observational studies of the distribution of
profilewasavailable.Inconjunctionwiththecorresponding
matter within clusters have typically been limited by ei-
gasdensityprofile,thisallowsthegravitatingmassdistribu-
therasmallsamplesize(e.g.David,Jones & Forman1995),
tion to be inferred. Secondly, we reject those systems with
or have assumed an isothermal IGM (e.g. White & Fabian
obvious evidence of substructure, where the assumption of
1995);it appears that significant temperature gradients are
hydrostatic equilibrium is not reasonable; it is known that
presentinmany(e.g.Markevitch et al.1998),althoughper-
the properties of such systems differ systematically from
haps not all (e.g. White 2000; DeGrandi & Molendi 2002;
thoseofrelaxedclusters(e.g.Ritchie& Thomas2002).This
Irwin & Bregman2000)clustersofgalaxies.Anotherissueis
also favours the assumption of a spherically symmetric gas
therestriction imposed by thearbitrary limits of theX-ray
distribution, which is implicit in our deprojection analysis.
data; halo properties must be evaluated at constant frac-
tions of the virial radius (R ), rather than at fixed metric
v
radii imposed by the data limits, in order to make a fair
comparison between varying mass scales. In this work, we
deriveanalyticalexpressionsforthegasdensityandtemper-
aturevariation, which allow ustoextrapolate these quanti-
tiesbeyondthelimitsofthedata.However,wearecarefulto
consider the potential systematic bias associated with this
process. Our study combines the benefits of a large sample
with the advantages of a 3-dimensional, deprojection anal-
ysis, in order to investigate the scaling properties of virial-
ized haloes, spanning a wide range of masses. In this work
we have brought together data from three large samples,
comprisingthemajorityofthesuitable,radially-resolved3D
(cid:13)c 2002RAS,MNRAS000,1–27
c(cid:13) Name z Ta R200 ρ(0) rc β αb γ CF radiusc Sampled Datae
20 (keV) kpc ( 10−3cm−3) (arcmin) keV/arcmin (arcmin)
0 ×
2
RA NVGirgCo1553† 00..00003366 02..5505+−+000...201173 1200836+−[phone]..246+−+020...222154 21..2004++−000...032906 00..4653++−000...000297 0.01–+0.00 1.44–+−00..1154 8.–00 FS PP,S
S,M NGC 1395 0.0057 0.84+−−000...210486 556+−−1925300 14.1−+−1502..4.2624 0.35+−−000...210199 0.43+−−000...000322 − –−0.00 1.05+−00..0076 0.24 S P
N NGC 5846 0.0058 1.18+0.07 683+37 57.18+0.67 0.42+0.02 0.55+0.02 – 1.06+0.01 3.00 F P,S
R −0.07 −33 −0.67 −0.02 −0.02 −0.01
A HCG 68 0.0080 0.67+0.19 497+104 14.6+6.31 0.37+0.12 0.46+0.02 – 1.07+0.07 – L P
S0 NGC 5044 0.0090 1.25−+−000...010656 798−+−833363 10.66−+−432...243252 1.66+−−000...521181 0.49+−−000...000112 – 0.97+−−000...000226 3.97 L P
,100 NICG4C2936258 00..00019253 21..5074+−+000...111282 755209+−[phone]..3926+−+000...000262 120..6840++−000..1.44133 00..3321+−+000...000111 –– 11..6108+−+000...010747 32..3237 FF PP,,SS
– −0.15 −49 −0.06 −0.11 −0.01 −0.14
27 Abell 1060 0.0124 3.31+−00..111 1587+−6490 3.74+−00..0023 7.49+−00..0061 0.72+−00..0010 – 0.97+−00..0012 5.51 L P+G
NGC 6482 0.0131 0.56+0.37 361+181 25.0+13.5 0.22⋆ 0.48+0.03 – 1.23+0.15 1.20 S P
† −0.22 −105 −5.41 −0.04 −0.15
HCG 62 0.0137 1.48+0.18 559+35 1.25+0.02 2.26+0.09 0.30+0.01 – 1.46+0.08 2.17 F P,S
−0.16 −31 −0.02 −0.09 −0.01 −0.08
Abell 262 0.0163 2.03+0.36 998+146 8.41+0.80 1.49+0.17 0.40+0.01 – 0.80+0.07 0.41 L P
−0.27 −113 −0.73 −0.16 −0.01 −0.08
NGC 2563 0.0163 1.61+0.02 627+6 1.41+0.02 2.07⋆ 0.42+0.003 – 1.36+0.01 1.02 S P
−0.03 −8 −0.01 −0.003 −0.01
NGC 507 0.0164 1.40+0.11 738+28 142.39+12.4 0.10⋆ 0.43+0.01 0.02+0.01 – 0.90 L P
−0.08 −23 −9.91 −0.01 −0.01
IV Zw 0381 0.0170 2.07+0.56 892+104 1.36+0.13 2.77+0.40 0.38+0.03 0.04+0.03 – – L P
−0.42 −86 −0.11 −0.38 −0.03 −0.02
AWM 7 0.0172 4.02+0.75 2207+641 5.22+0.05 5.28+0.23 0.59+0.00 – 0.67+0.09 4.77 L P
−0.62 −420 −0.06 −0.07 −0.00 −0.09
Abell 194 0.0180 2.07+0.43 1126+246 0.66+0.02 8.64+0.35 0.60+0.02 0.01+0.04 – 1.67 F P,S
−0.43 −199 −0.02 −0.35 −0.02 − −0.04
MKW 4 0.0200 2.08+0.05 842+18 1.50+0.04 5.45+0.22 0.64+0.03 – 1.29+0.02 1.51 F P,S
−0.06 −17 −0.04 −0.22 −0.03 −0.02
HCG 97 0.0218 1.00+0.13 620+45 140+205 0.04+0.03 0.41+0.01 0.02+0.03 – – L P
−0.12 −37 −61 −0.01 −0.01 −0.03
Abell 779 0.0229 3.57+0.94 1075+203 1.48+0.05 1.42+0.06 0.34+0.01 – 1.02+0.13 5.26 F P,S
−0.76 −148 −0.05 −0.06 −0.01 −0.14
NGC 5129 0.0233 1.54+0.41 567+71 1.56+0.04 2.46+0.10 0.60+0.02 – 1.48+0.09 3.85 F P,S
−0.35 −54 −0.04 −0.10 −0.02 −0.10
NGC 4325 0.0252 0.90+0.07 678+81 44.7+11.0 0.21+0.07 0.54+0.02 0.00+0.02 – 0.78 S P
−0.07 −68 −15.0 −0.07 −0.01 −0.02
HCG 51 0.0258 1.38+0.04 610+15 0.96+0.02 1.81+0.07 0.30+0.01 0.01+0.01 – 1.16 F H,S
−0.04 −15 −0.02 −0.07 −0.01 − −0.01
NGC 6329 0.0276 1.60+−00..5423 859+−213523 1.17+−00..0077 2.61+−00..1100 0.53+−00..0022 – 1.06+−00..1167 2.17 F P,S G
NGC 6338 0.0282 2.64+1.92 893+121 4.44+0.68 1.93+0.30 0.53+0.04 – 1.25+0.09 1.02 S P a
−1.55 −278 −0.50 −0.26 −0.03 −0.25 s
MKW 4S 0.0283 2.46+0.23 978+74 1.42+0.03 2.64+0.11 0.51+0.02 – 1.14+0.06 2.12 F P,S
Abell 539 0.0288 2.87−+00..2221 1305−+61524 2.42+−00..0063 5.21+−00..2111 0.69+−00..0032 – 1.04+−00..0066 – F P,S fra
−0.21 −104 −0.06 −0.21 −0.03 −0.06 c
Klemola 442 0.0290 3.40+0.28 1513+180 4.74+0.05 3.40+0.14 0.61+0.02 – 0.94+0.06 – F P,S t
−0.26 −148 −0.05 −0.14 −0.02 −0.05 i
Abell 2199 0.0299 3.93+−00..0066 1223+−1185 12.09+−00..0011 2.1400..000011 0.60+−00..00000055 – 1.15+−00..0011 2.20 L P on
Abell 2634 0.0309 3.45+−00..2287 1189+−18054 0.99+−00..0022 8.62+−00..3344 0.69+−00..0033 – 1.29+−00..0099 – F P,S a
AWM 4 0.0318 2.96+0.39 1540+343 3.52+0.08 1.93+0.08 0.62+0.02 0.07+0.07 – 3.51 F P,S n
−0.39 −290 −0.08 −0.08 −0.02 − −0.07 d
Abell 496 0.0331 6.11+0.35 1540+94 7.24+0.31 2.85+0.14 0.62+0.01 – 1.16+0.03 3.44 L P+G
2A0335+096 0.0349 3.34+−−000...32473 1596+−−11653989 17.46−+−000...344422 1.40+−−000...001662 0.65+−−000...000331 – 0.95+−−000...000333 2.63 F P,S the
Abell 2052 0.0353 3.45+0.39 1507+281 10.03+0.17 1.75+0.07 0.64+0.03 0.02+0.07 – 3.51 F P,S M
Abell 2063 0.0355 4.00+−00..142 1493−+25377 3.75+−00.0.117 3.79+−00..1057 0.69+−00..0033 −0.05+−0.00.207 – – F P,S
−0.12 −56 −0.01 −0.15 −0.03 −0.02 −
Abell 3571 0.0397 7.31+0.28 1870+101 5.91+0.35 4.14+0.31 0.69+0.01 – 1.12+0.04 2.15 M P,G,S
−0.38 −120 −.34 −0.31 −0.01 −0.03 T
MKW 9 0.0397 2.88+−00..6585 1246+−228142 4.86+−00..1111 0.83+−00..0033 0.52+−00..0022 – 0.97+−00..0099 1.54 F I,S X
Abell 2657 0.0400 4.53+−00..6415 1251+−118088 1.97+−00..0088 5.68+−00..3311 0.76+−00..0022 – 1.34+−00..0192 2.15 M P,G,S re
HCG 94 0.0417 4.02+0.46 1151+94 5.32+0.10 1.10+0.04 0.48+0.02 – 1.17+0.05 – F P,S l
−0.43 −83 −0.10 −0.04 −0.02 −0.05 a
Abell 119 0.0444 6.08+−00..4497 1720+−118355 1.68+−00..0022 6.74+−00..3399 0.66+−00..0022 – 1.14+−00..0089 1.97 M P,G,S tio
MKW 3S 0.0453 4.42+0.57 1218+176 2.51+0.21 4.13+1.38 0.71+0.07 – 1.32+0.10 2.05 M P,G,S n
−0.67 −123 −0.20 −1.38 −0.07 −0.11
Abell 3558 0.0477 6.28+0.37 1598+124 5.94+0.08 2.46+0.36 0.55+0.03 – 1.13+0.04 1.82 M P,G,S
−0.3 −87 −0.07 −0.36 −0.03 −0.05
continuedoverleaf 3
Name z Ta R ρ(0) r β αb γ CF radiusc Sampled Datae 4
200 c
(keV) kpc ( 10−3cm−3) (arcmin) keV/arcmin (arcmin)
×
A
Abell 4059 0.0480 5.50+−00..546 1313+−116116 4.23+−00..3353 2.85+−00..6655 0.67+−00..0022 – 1.29+−00..0078 1.82 M P,G,S .
Tri. Aus. 0.0510 11.06+1.04 1963+266 4.85+0.15 4.41+0.25 0.67+0.01 – 1.26+0.08 1.71 M P,G,S J
−0.96 −188 −0.15 −0.24 −0.01 −0.09 .
Abell 85 0.0521 8.64+−00..6249 1684+−16610 3.56+−00..1111 4.82+−00..2244 0.76+−00..0022 – 1.32+−00..0037 1.69 M P,G,S R
Abell 3391 0.0536 5.39+0.72 1671+306 3.05+0.19 2.44+0.12 0.53+0.01 – 0.99+0.10 1.63 M P,G,S .
Abell 3266 0.0545 9.53+−−000...955757 1880+−−112601531 2.85+−−000...001338 5.72+−−000...441662 0.74+−−000...000441 – 1.29+−−000...001571 1.60 M P,G,S Sa
Abell 2319 0.0555 10.99+0.81 1882+140 7.45+0.11 2.37+0.79 0.54+0.06 – 1.23+0.04 1.58 M P,G,S n
−1.14 −113 −0.16 −0.79 −0.06 −0.05 d
Abell 780 0.0565 4.63+0.25 2032+152 10.09+0.25 1.68+0.04 0.67+0.01 – 0.90+0.03 0.45 L P+G e
−0.24 −133 −0.25 −0.04 −0.01 −0.03 r
Abell 2256 0.0581 8.62+0.55 1814+124 3.18+0.03 5.02+0.11 0.78+0.01 – 1.27+0.07 1.53 M P,G,S s
−0.51 −145 −0.03 −0.11 −0.01 −0.05 o
Abell 1795 0.0622 8.54+1.66 2000+628 4.30+0.05 4.01+0.20 0.83+0.02 – 1.17+0.10 1.44 M P,G,S n
−1.05 −290 −0.05 −0.21 −0.02 −0.14
Abell 3112 0.0703 7.76+1.65 1311+237 14.82+0.87 1.03+0.69 0.63+0.02 – 1.32+0.14 1.29 M P,G,S e
−3.08 −295 −0.86 −0.69 −0.02 −0.09 t
Abell 644 0.0711 11.68+1.52 1660+299 7.76+0.45 2.18+0.18 0.73+0.02 – 1.35+0.11 1.27 M P,G,S a
Abell 399 0.0722 7.97+−01.6.299 1734+−124492 4.14+−00..4413 1.89+−00..3168 0.53+−00..0052 – 1.16+−00..0190 1.26 M P,G,S l.
−0.73 −190 −0.41 −0.36 −0.05 −0.06
Abell 401 0.0739 9.55+0.45 1851+113 6.11+0.20 2.37+0.09 0.63+0.01 – 1.22+0.05 1.23 M P,G,S
−0.5 −123 −0.20 −0.09 −0.01 −0.04
Abell 2670 0.0759 5.64+0.4 1647+122 6.20+0.16 0.97+0.04 0.55+0.02 – 1.04+0.04 – F P,S
−0.39 −111 −0.16 −0.04 −0.02 −0.04
Abell 2029 0.0766 9.80+0.4 2266+111 6.34+0.10 2.37+0.09 0.68+0.03 0.20+0.06 – 1.69 F P,S
−0.42 −103 −0.10 −0.09 −0.03 −0.06
Abell 1650 0.0845 8.04+1.75 1816+756 5.51+0.55 2.25+0.78 0.78+0.12 – 1.19+0.15 1.09 M I,G,S
−1.14 −376 −0.55 −0.78 −0.12 −0.17
Abell 1651 0.0846 6.18+0.55 1777+170 6.25+0.41 2.02+0.23 0.70+0.02 – 1.10+0.04 1.09 M P,G,S
−0.36 −116 −0.40 −0.23 −0.02 −0.05
Abell 2597 0.0852 6.02+0.47 1841+161 6.47+0.29 1.40+0.06 0.68+0.03 – 1.05+0.04 1.55 F P,S
−0.45 −144 −0.29 −0.06 −0.03 −0.04
Abell 478 0.0882 10.95+2.15 1723+587 6.98+0.21 2.34+0.23 0.75+0.01 – 1.34+0.17 1.06 M P,G,S
−1.82 −332 −0.21 −0.23 −0.01 −0.18
Abell 2142 0.0894 11.16+1.54 2216+544 5.21+0.13 3.14+0.22 0.74+0.01 – 1.18+0.10 1.05 M P,G,S
−1.15 −292 −0.13 −0.22 −0.01 −0.13
Abell 2218 0.1710 8.28+1.82 1904+180 6.17+0.15 0.90⋆ 0.59+0.01 – 1.11+0.02 – L P+G
−1.33 −149 −0.16 −0.01 −0.02
Abell 665 0.1818 8.60+1.27 2273+268 6.32+0.17 1.21+0.04 0.65+0.01 – 1.02+0.08 – L P+G
−0.94 −279 −0.16 −0.04 −0.01 −0.06
Abell 1689 0.1840 12.31+1.19 2955+135 33.61+0.64 0.60+0.02 0.73+0.06 0.00⋆ – 2.40 L P+G
−0.93 −112 −1.92 −0.00 −0.00
Abell 2163 0.2080 16.64+3.36 2104+794 7.77+0.53 1.63+0.08 0.73+0.02 – 1.38+0.11 0.54 M P,G,S
−1.55 −253 −0.52 −0.08 −0.02 −0.22
Table 1: Some key properties of the 66 objects in the sample, listed in order of increasing redshift. Redshifts are taken from
Ebeling et al. (1996, 1998); Ponman et al. (1996) and NED. Columns 3–9 are data as determined in this work. All errors are 68%
confidence.
indicates thetwo galaxies.
†
⋆ denotes noerrors available, as parameter poorly constrained.
1 also known as NGC 383.
c(cid:13)
2 also known as Abell 4038.
2
0
02 a The cooling-flow corrected, emission-weighted temperatureof thesystem within 0.3R , as determined in thiswork.
200
RA b Temperature gradient; positive values mean T decreases with radius.
S, c Cooling flow excision radius (M sample) or radius within which a cooling flow component was fitted (F,L,S samples)
M d F = Finoguenov et al., L = Lloyd-Davies et al., M = Markevitch et al., S = Sanderson et al. (this work)
N
R e P = ROSAT PSPC, H = ROSAT HRI,G = ASCA GIS, S = ASCA SIS,I = Einstein IPC; + denotes simultaneous fit
A
S
0
0
0
,
1
–
2
7
Gas fraction and the M −T relation 5
X
By combining three samples from the work of Marke- 3.1 Cluster models
vitch, Finoguenov and Lloyd-Davies (described in detail
In order to evaluate the gas temperature and density in
in sections 3.3, 3.4 & 3.5, respectively) together with new
a virialized system, as well as derived quantities such
analysis of an additional six targets (also described in sec-
as gravitating mass, at arbitrary radii, we require a 3-
tion 3.5), we have assembled a large number of virialized
dimensional analytical description of these data. A core in-
objects with high-quality X-ray data. From these data, we
dex parametrization of the gas density, ρ(r), is used, such
have derived deprojected gas density and temperature pro-
that
filesfor each object, thusfreeing ouranalysis from thesim-
plistic assumption of isothermality which is often used in r 2 −23β
studies of this nature. The large size of our sample ensures ρ(r)=ρ(0) 1+ , (1)
(cid:20) (cid:16)rc(cid:17) (cid:21)
a good coverage of thewide range of emission-weighted gas
temperatures, spanning 0.5 to 17 keV. Thus, we incorpo- where rc and β are the density core radius and index pa-
rate the full range of sizes for virialized systems, down to rameter, respectively. The motivation for the use of this
the scale of individual galaxy haloes. The redshift range is parametrization is essentially empirical, although simula-
z=0.0036–0.208 (0.035median),withonlyfourtargetsex- tionsofclustermergersarecapableofreproducingacorein
ceedingaredshiftof0.1.Somebasicpropertiesofthesample the gas density, despite the cuspy nature of the underlying
are summarised in Table 1. darkmatterdistribution(e.g.Pearce, Thomas & Couchman
Asanumberof systemsarecommon totwoormore of 1994). However, in the absence of merging, N-body simula-
thesub-samples, weare able todirectly compare data from tionsoffer noclear explanation for thepresenceof asignifi-
differentanalyses, allowing ustoinvestigate anysystematic cantcoreintheIGMprofile,evenwhentheeffectsofgalaxy
differencesbetweenthetechniquesemployed.Wepresentthe feedback mechanisms are incorporated (Metzler & Evrard
results of these consistency checksin section 4. The diverse 1997).
natureof oursample, with respect to thedifferentmethods The density profile is combined with an equivalent ex-
usedtodeterminethegas temperatureanddensityprofiles, pression for thetemperaturespatial variation, described by
insulatesourstudytoanextentfromthebiascausedbyre- one of two models; a linear ramp, which is independent of
lyingonasingleapproach.However,wearestillabletotreat thedensity profile, of theform
thedatainahomogeneousfashion,giventheself-consistent
T(r)=T(0) αr, (2)
manner in which the cluster models are parametrized (see −
section 3.1). whereαisthetemperaturegradient.Alternatively,thetem-
perature can be linked to the gas density, via a polytropic
equation of state, which leads to
r 2 −32β(γ−1)
T(r)=T(0) 1+ , (3)
(cid:20) (cid:16)rc(cid:17) (cid:21)
3 X-RAY DATA ANALYSIS whereγ is thepolytropic indexand rc and β are asdefined
previously.
The X-ray data used in this study were taken with the Together, ρ(r) and T(r) can be used to determine the
ROSAT PSPCandASCAGIS&SISinstruments.Although cluster gravitating mass profile as, in hydrostatic equilib-
now superseded by the Chandra and XMM-Newton obser- rium, thefollowing condition is satisfied
vatories, these telescopes have extensive, publicly available
kT(r)r dlnρ dlnT
dataarchivesandaregenerally well-calibrated. Inaddition, M (r)= + , (4)
thePSPCandGISdetectorshaveawidefieldofview,which grav − Gµmp hdlnr dlnri
isessentialfortracingX-rayemissionouttolargeradii,par- (Sarazin1988),whereµisthemeanmolecularweightofthe
ticularly for nearby systems, whose virial radii can exceed gas and m is the proton mass. This assumes a spherically
p
onedegreeonthesky.Theuseofthreeseparatedetectors,on symmetric mass distribution, which has been shown to be
twodifferenttelescopes,enhancestherobustnessofouranal- a reasonable approximation, even for moderately elliptical
ysis,byreducingpotentialbiasassociated withinstrument- systems (Fabricant, Rybicki& Gorenstein 1984).
related systematic effects. Since the X-ray emissivity depends on the product of
Sincethisworkbringstogetherdatafromseparatesam- the electron and ion number densities, we parametrize the
ples, there is considerable variation in the form in which gas density in terms of a central electron number density
thosedatawereoriginallyobtained.Thisnecessitatedasup- (i.e. at r=0), assuming a ratio of electrons to ions of 1.17.
plementary processing stage to convert thedata into a uni- We base our inferred electron densities on the X-ray flux
fied format, in order to treat them in a homogeneous fash- normalized to the ROSAT PSPC instrument, as there is a
ion. In the case of the Finoguenov sample, analytical pro- known effective area offset between this detector and the
fileswerefittedtodeprojectedgasdensityandtemperature ASCA SIS and GIS instruments. In those systems where
points(seesection3.4fordetails);fortheMarkevitchsample theoriginal density normalization was defined differently, a
it was necessary to calculate the gas density normalization conversion was necessary and this is described below.
for such an analytical function, from the fitted data (sec- Oncethegravitatingmassprofileisknown(from equa-
tion 3.3).However,ourchosen model parametrization –de- tion4),thecorrespondingdensityprofilecanbefoundtriv-
scribedbelow–wasfitteddirectlytotherawX-raydatafor ially, given the spherical symmetry of the cluster models.
the remaining systems, including the Lloyd-Davies sample This can then be converted to an overdensity profile, δ(r),
(furtherdetailsofthedataanalysisaregiveninsection3.5). given by
(cid:13)c 2002RAS,MNRAS000,1–27
6 A. J. R. Sanderson et al.
δ(r) = ρtot(r), (5) 3.2 Cooling flow correction
ρ
crit
TheeffectsofgascoolingarewellknowntoinfluencetheX-
rayemissionfromclustersofgalaxies(Fabian1994).Cooling
flows may be present in as many as 70 per cent of clusters
(Peres et al. 1998) particularly amongst older, relaxed sys-
tems,wheremerger-inducedmixingofgasisnotasignificant
where ρ (r) is the mean total density within a radius, r,
tot
effect. Consequently we expect cooling flows to be common
and ρ is the critical density of the Universe, given by
crit
3H2/8πG. in a sample of this nature, as we discriminate against ob-
0
jects with strong X-ray substructure, which is most often
It is theoverdensity profilewhich determinesthe virial
associated with merger events. It is possible to infer mis-
radius (R ) of the cluster; simulations indicate that a rea-
v leading properties for the intergalactic gas, both spatially
sonableapproximationtoR isgivenbythevalueofrwhen
v and spectrally, if the contamination from cooling flows is
δ(r)=200(e.g.Navarro et al.1995)–albeit for ρ (r)cal-
tot not properly accounted for. Specifically, gas density core
culatedattheredshiftofformation,z ,ratherthanthered-
f radii – and, consequently, the β index in equation 1 (see
shift of observation, z – and we adopt this definition in
obs Neumann& Arnaud 1999, for example) – can be strongly
this work. Strictly speaking, the approximation R = R
v 200 biased, as can the temperature profile, particularly as cen-
is cosmology-dependent but, in any case, the implicit as-
tral cooling regions havethe highest X-rayflux.
sumption z = z is a greater source of uncertainty. In
f obs In all of the sub-samples the effects of central cooling
particular, there is a systematic trend for the discrepancy
were accounted for in the original analysis using a variety
between these two quantities to vary with system size, in
ofmethods,whicharedescribedintheappropriatesections
accordancewithahierarchicalstructureformationscenario,
below. The final cluster models therefore parametrize only
inwhichthesmallest haloesformfirst.Theconsequencesof
the ‘corrected’ gas density and temperature profiles; thus,
thiseffectareaddressedinsection7.4.Giventhelocalnature
we have extrapolated the gas properties inward over any
ofoursample,theassumedcosmologyhaslittleeffectonour
cooling region, as if nocooling were taking place at all.
results.Forexample,comparingthevaluesofluminositydis-
tanceobtainedforq =0andq =0.5:thedifferenceisless
0 0
than 5% for our most distant cluster (z =0.208), dropping 3.3 Markevitch sample
to less than 2% for z<0.1 (i.e. for 94% of our sample).
The sub-sample of Markevitch (hereafter ‘M sample’) was
Length scales in the cluster models are defined in a compiled from several separate studies and comprises spa-
cosmology-independentform,withthecoreradiusofthegas tial and spectral X-ray data for 27 clusters of galaxies
densityexpressedinarcminutesandthetemperaturegradi- (Markevitch et al.1998;Markevitch1998;Markevitch et al.
entin equation 2measured inkeVperarcminute. Thecon- 1999; Markevitch & Vikhlinin 1997; Markevitch 1996). Of
tributions to the cluster X-ray flux, in the form of discrete these datasets, 22 are included in our final sample, the re-
lineemissionfromhighlyionizedatomicspeciesintheIGM, maining systems being covered by one of the other sub-
are handled differently between the different sub-samples. samples (the factors affecting this choice are described in
However, in all cases the gas metallicity was measured di- section 4).
rectly in theanalysis and hence thisemission has, in effect, To measure the spatial distribution of the gas, X-ray
been decoupled from the dominant bremsstrahlung compo- images of the clusters were fitted with a modified version
nent,whichwerelyontomeasurethegasdensityandtem- of equation 1; undertheassumption of isothermality, equa-
perature. tion 1 leads to an equivalent expression for the projected
Thekeyadvantageofquantifyinggas densityandtem- X-raysurface brightness, S, given by
perature in an analytical form, is the ability to extrapolate r 2 −3β+21
and interpolate these and derived quantities, like gas frac- S(r)=S(0) 1+ p , (6)
tion and overdensity,toarbitrary radius.Consequently,the (cid:20) (cid:16)rc(cid:17) (cid:21)
virialradiusandemission-weightedtemperaturecanbeeval-
in terms of projected radius, r as well as the density core
p
uated in an entirely self-consistent fashion, and thuswe are
radius,r ,andindex,β.ThisisamodifiedKingfunctionor
c
able to determine the above quantities at fixed fractions of
isothermalβ-model(Cavaliere & Fusco-Fermiano1976).For
R ,regardless of the datalimits.
200 allbutoneoftheclusters,datafromtheROSAT PSPCwere
Clearly, where this extrapolation is quite large (e.g. used for the surface brightness fitting, as this instrument
at R ) there is potential for unphysical behaviour in the providesgreatlysuperiorspatialresolutioncomparedtothe
200
gastemperature,whichisnotconstrained tobeisothermal. ASCAtelescope(forAbell1650,noPSPCpointeddatawere
This is particularly true when steep gradients are involved available and an Einstein IPC image was used instead).
(i.e. large values of α in equation 2 or values of γ very Although strictly only appropriate for a uniform gas
different from unity in equation 3). A linear temperature temperature distribution, this approach is valid since, for
parametrizationismostsusceptibletounphysicalbehaviour the majority of the clusters in this sub-sample, the expo-
asitcan extrapolatetonegativevalueswithinthevirialra- nential cutoff in the emission lies significantly beyond the
dius. To avoid this problem, we have identified those linear ROSAT bandpass( 0.2–2.4 keV).Consequently,theX-ray
∼
T(r) models where the temperature within R becomes emissivityinthisenergyrangeisratherinsensitivetothegas
200
negative. In each case the alternative, polytropic tempera- temperature,andthereforescalessimplyasthesquareofthe
ture description was used in preference, where this was not gasdensity.These images were also useddirectly asmodels
already thebest-fittingmodel. of the surface brightness distribution in order to determine
(cid:13)c 2002RAS,MNRAS000,1–27
Gas fraction and the M −T relation 7
X
therelativenormalizationsbetweenprojectedemissionmea- 3.4 Finoguenov sample
sures in the different regions for which spectra were fitted
using ASCA data. The sub-sample of Finoguenov (hereafter ‘F sample’)
comprises X-ray data compiled from several sources, incor-
Gas density data for this sub-sample were provided
porating a total of 36 poor clusters and groups of galaxies
in the form of a King profile core radius and β index,
(Finoguenov & Ponman 1999; Finoguenov & Jones 2000;
as derived from PSPC data, using equation 6. However,
Finoguenov, David & Ponman 2000; Finoguenov et al.
the density normalization was only available in the form
2001) which were subject to similar analysis. Of the corre-
of a central electron number density for a small num-
sponding fitted results, 24 were used in the final sample,
ber of clusters: Abell 1650 & Abell 399 (Jones & Forman
withtheremaindertakenfromoneoftheothersub-samples
1999) and Abell 3558, Abell 3266, Abell 2319 & Abell 119
(thefactors affectingthischoicearedescribed insection 4).
(Mohr, Mathieson & Evrard 1999). In the original Marke-
A combination of ROSAT and ASCA SIS instrument data
vitchanalyses,densitynormalizationdatafortheremaining
was used to determine the spatial and spectral properties
systemsweretakenfromVikhlinin, Forman & Jones(1999),
of theX-ray emission respectively.
in the form of values of the radius enclosing a known over-
density with respect to the average baryon density of the Values for the King profile core radius and index pa-
Universe at the observed cluster redshift. It was therefore rameter were taken from surface density profile fits (using
necessary,forthiswork,toconvertthesevaluesintocentral equation 6) to PSPC images of the clusters, with the ex-
electron densities, to provide the necessary normalization ception of HCG 51 and MKW 9, where no such data were
component in thecluster models. available and a ROSAT HRIand Einstein IPC observation
Radii of overdensity of 2000, R′, were taken from wereusedrespectively.Acentralregionofthesurfacebright-
Vikhlinin et al.(1999)andwerecombinedwiththegasden- ness data was excluded for all systems, to avoid thebias to
sity core radii, rc, and β indices to determine the density rc and β caused by emission associated with central gas
normalization, ρ(0),given that cooling.Thebest-fittingparameterswereusedtodetermine
the3-dimensionalgasdensityandtemperaturedistribution,
R′ r 2 −23β 4πR′3 viaananalysisofASCASISannularspectra,byfittingvol-
ρ(0)Z0 (cid:20)1+(cid:16)rc(cid:17) (cid:21) 4πr2dr= 3 2000ρ(zobs), (7) ushmelelsa,nadlloluwminignofsoirtyt-hweeeigffhetcetds ovfalpureosjeinctaionse.rIinestohfisspsthaegreicoafl
where ρ(z ) is the mean density of the Universe at the the analysis the central cooling region was included and an
obs
observed redshift of the cluster. The integration was per- additional spectral component was fitted to the innermost
formed iteratively using a generalisation of Simpson’s rule bins,allowingthisextraemissiontobemodelled.Aregular-
to a quartic fit, until successive approximations differed by isation techniquewas used to stabilise the fit by smoothing
less than one part in 108. out large discontinuitiesbetween adjacent bins.Furtherde-
The fitted gas density and temperature data for the tailsofthismethodcanbefoundinFinoguenov & Ponman
M sample were corrected for the effects of central gas cool- (1999).
ing in the original analyses: the cluster models based on Togenerateclustermodelsfortheseobjects,itwasnec-
these data parametrize only the uncontaminated cluster X- essary to infer a central gas density normalization, as well
rayemission.Thiswasachievedbyexcisingacentralregion as an analytical form for the temperature profile. Density
of the surface brightness data in the original analysis and, normalization wasdeterminedbyacoreindexfunction(see
for the temperature data, by fitting an additional spectral equation 1) fit to the data points, using the β index and
component in thecentral regions (whererequired),to char- core radius values from the PSPC surface brightness fits.
acterisethepropertiesofthecoolinggasflux.Fulldetailsof Thiswasachievedbynumericallyintegratingequation1(as
these methods can be found in Vikhlinin et al. (1999) and described in section 3.3) between the radial bounds of the
Markevitch et al. (1998). spherical shells used to determine the fit points, weighted
Temperaturedataforalltheclustersinthissub-sample by r2 to allow for the volume of each integration element.
were provided in the form of a polytropic index and a nor- The core radii and β index were fixed at their previously
malization evaluatedat 2r (asdefinedin equation3).This determined values and ρ(0) was left free to vary. A best
c
radiuswaschosenasitlaywithinthefitteddataregion(i.e. fit normalization was then found by adjusting ρ(0) so as
outside of any excised cooling flow emission) in all cases. to minimize the χ2 statistic. Confidence regions for ρ(0)
These fits results are based on the projected temperature were determined from those values which gave an increase
profile,buthavebeencorrectedfortheeffectsofprojection. in χ2 of one. Fitting was performed using the MIGRAD
To construct cluster models, it was necessary to calculate method in the minuit minimization library from CERN
T(0)fromthesenormalizationvalues,byre-arrangingequa- (James 1998) and errorswere foundwith MINOS,from the
tion 3 and substituting r=2r to give same package. For the core radius and β index parameters,
c
a fixed error of four per cent was assumed, based on an es-
3
T(0)=T(2r ) 5+ β(γ 1) . (8) timate of the uncertainties in the surface brightness fitting
c 2 −
h h ii (Finoguenov, Reiprich & B¨ohringer 2001).
These central normalization values were combined with the Sincetheoriginaldensitypointsweremeasuredinunits
corresponding polytropic indices and density parameters to of proton numberdensity,it was necessary to convert them
comprisea3-dimensionaldescriptionofthegastemperature toelectronnumberdensityforconsistencybetweentheclus-
variation.Errorsonallparametersweredetermineddirectly termodels.Itwasalsonecessarytoallow foraknowneffec-
from theconfidenceregions evaluated in theoriginal analy- tive area offset between the ASCA SIS and ROSAT PSPC
ses. instruments. This adjustment amounts to a factor of 1.2
(cid:13)c 2002RAS,MNRAS000,1–27
8 A. J. R. Sanderson et al.
multiplication to convert from proton number densities in- The data reduction and analysis for the S sam-
ferred usingtheformer, toequivalentvaluesmeasured with ple was performed in a similar way to the study of
thelatter. Lloyd-Davieset al.(2000)andadetaileddescriptioncanbe
An analytical form for the gas temperature profile was foundthere.Themethodusedinvolvestheuseofaspectral
obtained from a mass-weighted (i.e. density multiplied by ‘cube’ofdata–aseriesofidenticalimagesextractedincon-
theintegration element volume,usingequation 1)fit tothe tiguousenergybands–whichconstitutesaprojectedviewof
3-dimensionaldatapoints,excludingthecoolingcomponent. theclusteremission.Athreedimensionalmodelofthetype
For5ofthecoolestgroups(IC4296,NGC3258,NGC4325, described in section 3.1 can be fitted directly to these data
NGC 5129 & NGC 6329), the cold component was not suf- in a forward fitting approach (Eyles et al. 1991), in order
ficiently separated from the bulk halo contribution and so to ‘deproject’ the emission. The gas density and tempera-
thosecentralbinsthatwereaffectedwereexcludedfromthe tureareevaluatedinaseriesofdiscrete,sphericalshellsand
analytical fit. The best fit temperature values were subse- theX-rayemission in each shelliscalculated with amekal
quently found for both a linear and polytropic description, hotplasmacode(Mewe, Lemen & van den Oord1986).The
again based on theχ2 criterion. emission isthen redshifted andconvolvedwith thedetector
Theparametrization whichgavetheoptimum(i.e.low- spectral response, before being projected into a cube and
est)χ2fittothedatapointswasused,exceptwherethisgave blurred with the instrument point spread function (PSF).
risetounphysicalbehaviourinthemodel;forthreesystems Theresultcanbecompareddirectlywiththeobserveddata
(Abell 1060, HCG 94 & MKW 4) thelinear T(r) model led and the goodness-of-fit is quantified with a maximum like-
to a negative temperature within R , when extrapolated lihood fit statistic (Cash 1979). The model parameters are
200
beyondthedataregion; in thesecases a polytropic descrip- then iteratively modified, so as to obtain a best fit to the
tion was used in preference. data.
Thecontributionstotheplasmaemissivityfromhighly
ionizedspecies,intheformofdiscretelineemission,ishan-
3.5 Lloyd-Davies & Sanderson samples
dledbyparametrizingthemetallicityofthegaswithalinear
Thesub-sampleofLloyd-Davies(hereafter‘Lsample’)com- ramp(assumingfixed,Solar-likeelementabundanceratios),
prises 19 of the 20 clusters and groups of galaxies anal- normalized totheSolarvalue.However,thepoorerspectral
ysedinthestudyofLloyd-Davies,Ponman & Canon(2000) resolutionofthePSPCrequiresthatthemetallicitybecon-
(Abell400 was omitted asit isthoughttobealine-of-sight strained tobeuniform whereonlyROSAT datawerefitted
superposition of two clusters). Of the corresponding fitted (asforallsixextrasystemsintheSsample).Forthoseclus-
results, 14 were used in the final sample, with the remain- ters where ASCA GIS data were additionally analysed in
der taken from either the M or F samples (see section 4). theLsample(denotedbya‘+’intheright-most columnof
ROSAT PSPC data were analysed for all the objects, with Table 1), the gradient of the metallicity ramp was left free
data from the wider passband ASCA GIS instrument in- to vary.
cluded to permit theanalysis of certain hotterclusters. The use of maximum likelihood fitting avoids the need
Toextendthesampletoincludeindividualgalaxiesand tobinupthedatatoachieveareasonableapproximationto
also to improve the coverage at low temperatures, an addi- Gaussian statistics: aprocess which would severely degrade
tionalsixobjectswereanalysed–fourgroupsandtwoearly- spatialresolutionintheouterregionsoftheemission,where
typegalaxies(thissub-sampleishereafterreferredtoasthe thedataaremostsparse.Theonlyconstraintonspatialbin
‘S sample’). The galaxy groups were drawn from the sam- size relates to blurring the cluster model with the PSF; a
ple of Helsdon & Ponman (2000) and were chosen as being process which is computationally expensive and a strongly
fairly relaxed and having high-quality ROSAT PSPC data varying function of the total number of pixels in the data
available. Cooler systems, in particular, were favoured, in cube.AlthoughtheCashstatisticprovidesnoabsolutemea-
order to increase the number of low mass objects in the sure of goodness-of-fit, differences between values obtained
sample. The extra objects include two early type galaxies; fromthesamedatasetareχ2-distributed.Thisenablescon-
an elliptical, NGC 6482 and an S0, NGC 1553. fidence regions to be evaluated, for determining parameter
Genuinely isolated early-typegalaxies are rare objects, errors (c.f. Lloyd-Davieset al. 2000).
given thepropensity for mass clustering in theUniverse.In FortheSsample,twodifferentminimizationalgorithms
addition, findinga nearby example of such a system, which were employed to optimise the fit to the data. A modified
possesses an extended X-ray halo that has been studied in Levenberg-Marquardtmethod (Bevington 1969) was gener-
sufficient detail to measure T (r), severely limits the num- ally used to locate the minimum in the parameter space.
X
ber of potential candidates. Although NGC 1553 lies close Although very efficient, this method is only effective in
toanellipticalgalaxyofsimilarsize(NGC1549)thereisno the vicinity of a minimum and is not guaranteed to lo-
evidencefrom thePSPCdataofanyextendedemission not catetheglobalminimum.Inseveralcasesthisapproachwas
associated with either of these objects, which might other- unable to optimise the cluster model parameters reliably
wise point to the presenceof a significant group X-ray halo andasimulatedannealingminimizationalgorithmwasused
(see section 3.5.1). NGC 6482, by contrast, is a large ellip- (Goffe, Ferrier & Rogers 1994). However, the disadvantage
tical (LB 6 1010LB⊙) which clearly dominates thelocal of this technique is the computational cost associated with
∼ ×
luminosity function and which is embedded in an extensive the very large number of fit statistic evaluations required:
X-ray halo ( 100 kpc). Its properties indicate that this is once the global minimum was identified, the Levenberg-
∼
probably a ‘fossil’ group (see section 3.5.2) and as such, its Marquardtmethodwasusedtodetermineparametererrors,
propertiesareexpectedtodifferfromthoseofanindividual in an identical fashion to Lloyd-Davieset al. (2000).
galaxy halo. Inordertodetermineerrorsonderivedquantities,such
(cid:13)c 2002RAS,MNRAS000,1–27
Gas fraction and the M −T relation 9
X
as gravitating mass and gas fraction, we adopt the rather magnitudes fainter within 1 h−1 Mpc. However, its X-ray
50
conservative approach of evaluating the quantity using the luminosity is in excess of 1042h−2 erg s−1, which is very
50
extremevaluespermittedwithintheconfidencerangesspec- large for a single galaxy. These properties classify this ob-
ified by the original fitted parameters. However, although ject as a ‘fossil’ group – the product of the merger of a
thismethodtendstoslightlyoverestimatetheerrors,ascan number of smaller galaxies, bound in a common poten-
be seen from the intrinsic scatter in our derived masses in tial well (Ponman et al. 1994; Mulchaey & Zabludoff 1999;
section 7.2, it is not liable to introduce a systematic bias Vikhlinin et al. 1999; Jones, Ponman & Forbes 2000). Cor-
into any weighted fittingof thesedata. respondingly,thissystemismorecloselyrelatedtoagroup-
ForthosesystemsintheLandSsampleswhereacool- sized halo – albeit a very old one (c.f. Jones et al. 2000)
ingflowcomponentwasfitted,apowerlawparametrization – than to that of an individual galaxy. The X-ray over-
wasusedtodescribethegastemperatureanddensityvaria- luminous nature of this galaxy (L /L = 0.048) implies
X B
tionswithinthecoolingradius(alsoafittedparameter).To that the vast majority of the emission originates from its
avoidunphysicalbehaviouratR=0,thesepowerlawswere large (>100 kpc) halo, with a negligible contribution from
truncatedat10 kpc,wellwithinthespatialresolutionofthe discrete∼sources.
instrument (for NGC 1395 a cut-off of 0.5 kpc was used to Approximately 1500 counts were accumulated in an
reflect themuch smaller size of its X-rayhalo). 8.5ks pointing with the PSPC. During the fitting process
it was found that there was a significant residual feature in
the centre of the halo, which may indicate the presence of
3.5.1 NGC 1553
an AGN. It was not possible to adequately model this fea-
The X-ray spectra of elliptical galaxies comprise an emis- ture with either a point-like or extended component and it
sion component originating from a population of discrete was necessary toexcise a central region (radius1.2 arcmin)
sources within the body of the galaxy, as well as a possi- of the data to obtain a reasonable fit. As a result, the core
blecomponentassociated withadiffusehaloofgastrapped radius was rather poorly constrained and hence was frozen
in the potential well. The contributions of these differ- at its best-fitting value of 0.2 arcmin for the error calcu-
ent spectral components vary according to the ratio of lation stage. In addition, the hydrogen column could not
the X-ray to optical luminosity of the galaxy (L /L ) be constrained and had to be frozen at the galactic value
X B
(Kim, Fabbiano & Trinchieri 1992). Since we are interested (7.89 1020 cm−2), as determined from the radio data of
×
onlyintheX-rayhaloofthesystemsinthiswork,wefavour Stark et al. (1992).
those galaxies with a high L /L , where the emission can
X B
betracedbeyondtheopticalextentofthestellarpopulation.
A 14.5ks PSPC observation was analysed, in which
4 CONSISTENCY BETWEEN SUB-SAMPLES
the S0 galaxy NGC 1553 appears quite far off axis, al-
though within the ‘ring’ support structure. Some 2000 As a consequence of converting the data from the different
counts were accumulated in the exposure and the emission sub-samples into a uniform, analytical format, we are able
is detectable out to a radius of 4.8 arcmin (21 kpc). Al- toadoptacoherentapproachinouranalysis.Byextrapolat-
though its LX/LB, of 1.53 10−3, does not mark it out as ing the gas density and temperature profiles, it is possible
×
a particularly bright galaxy, its X-ray halo is clearly vis- to determine the virial radius and mean temperature (see
ible and uncontaminated by group or cluster emission. In below) self-consistently, and thus independently of the ar-
fact, this ratio is typical of non-group-dominant galaxies bitrary data limits. Of course, this process of extrapolation
(c.f. Helsdon et al. 2001). However, for this reason we ex- can potentially introduceotherbiases, andthisis discussed
pect a reasonable contribution to the X-ray flux from dis- in section 7.5 below. In some systems, emissivity profiles
cretesources;Blanton, Sarazin & Irwin(2001)haverecently areaffected bysignificant centralcooling andweemphasize
foundthatdiffuseemission onlyaccountedfor 84percent that in our analysis we have eliminated this contaminating
∼
of the total X-ray luminosity in therange 0.3–1 keV, based componentinallofourtargets,inordertomaintainconsis-
on a 34ks observation with the ACIS-S detector on board tency between the different sub-samples. In this section we
theChandra telescope. presenttheresultsofaninvestigationintotheconsistencyof
The PSPC data show evidence of central excess emis- oursampleandtheagreementbetweenthedifferentanalysis
sion, which is adequately described by a power law spec- involved.
trum, blurred by the instrument PSF, with a photon in- Mean temperatures were calculated for each system,
dex consistent with unity. This was modelled as a separate by averaging their gas temperature profiles within 0.3R ,
200
component, so as to decouple its emission from that of the weightedbyemissivityandexcludinganycooling flowcom-
halo.Blanton et al.(2001)findevidenceofacentral,point- ponent (hereafter referred to as T ; see column 5 in ta-
ew
likesourcewhichtheyfitwithanintrinsicallyabsorbeddisk ble 1). Fig. 1 shows the temperatures determined in this
blackbody model. The spatial properties of the X-ray halo way,fromtheF&Msamples,comparedtothecorrespond-
arenotaddressedintheiranalysis,butinanycasetheemis- ing values taken from the original analyses. The F sample
sion is only partly visible, dueto the small detector area of (left panel) shows good agreement, although some discrep-
theACIS-S3CCD chip. ancy is expected, due to differences in the prescription for
obtaining T . However, two clusters are clearly anomalous
ew
–Abell2670 andAbell2597. Thecase ofA2670 isaknown
3.5.2 NGC 6482
discrepancy, arising from an unusually high background in
The elliptical galaxy NGC 6482 is a relatively isolated the SIS observation. A2597 is an example of the compli-
object, which has no companion galaxies more than two cations of a large cooling flow, which is more readily re-
(cid:13)c 2002RAS,MNRAS000,1–27
10 A. J. R. Sanderson et al.
solvedintheSISobservationthantheGISdata.Thevalues clusters show evidence of a radially increasing temperature
of T quoted in Finoguenov et al. (2000) for these clus- profile in their central regions, it is unlikely that this will
ew
ters are actually based on PSPC and GIS data respectively continueouttothevirialradius.Thispresentsafundamen-
(Hobbs& Willmore 1997 and Markevitch et al. 1998) and tal problem for a monotonic analytical profile, which must
not on the SIS data analysed in that paper. However, to inevitably findacompromise: in general thefitis drivenby
maintainconsistencywehaveusedjusttheSISdatatocon- the central regions, which have a greater flux weighting. In
struct our model for these clusters. the case of A780, the difference in T(r) leads to a factor
The agreement between Tew values for the M sample of 3 difference in the total mass within R200, between the
(right panel) is less good, but here differences are to be models, although thisdiscrepancy is reducedto60 percent
expected: the method used in this work weights the tem- forthemasswithin0.3R200.Thecorrespondingeffectonthe
perature profile, between 0.3R and zero radius, by the gas fraction is also less severe, since the total gas mass in-
200
emissivity of the gas as determined by extrapolating ρ(r) creases with R200. However, for A496 – whose temperature
and T(r) inwards from beyond the cooling flow region. In profile is more typical of the systems in our sample – the
contrast, Markevitch et al. (1998) determine a flux weight- agreementbetweenthegravitatingmasswithinR200 forthe
ing for their mean temperatures based on their estimate of differentmodelsismuchbetter,varyingbyonly40percent.
the emission measure from the non-cooling gas within the
coreregion.Forstrongcoolingflows,thisgivesalowweight-
ing to the central values of T(r) compared to those values
5 FINAL MODEL SELECTION
justoutsidethecoolingzone.Sincealmostallthesystemsin
thissamplehavepolytropicindicesinexcessofone,theirgas Inordertoarriveatasinglemodelforeachsystem,wedeter-
temperaturesincrease towardsthecentre,sothedifferences minedan orderofpreferencefor thesub-samples,tochoose
in the spatial weighting give rise to a systematic difference betweenanalyses, whereoverlapsoccurred.Aninitial selec-
between values of Tew determined with the two methods. tion was made on the basis of unphysical behaviour in the
Theoveralleffectofouranalysisisactuallytocorrectforthe models; the linear temperature parametrization is prone to
consequences of gas cooling, rather than simply to exclude extrapolatetonegativevalueswithinR ,andsoanumber
200
thecontributionfromthecoldcomponenttotheX-rayflux. ofmodels wererejected on thesegrounds.Oftheremaining
This amounts to a simple normalization offset – the mean overlaps, we preferentially select those cluster models from
of thevaluesof Tew from theMsample is18 percentlower theLsample,asthisrepresentsthedirectapplicationofthe
than that of thevalues determined in this work. modelto theraw X-raydataand henceshould bethemost
To assess the consistency between the different initial reliablemethod.Applicationofthiscriterionleavesjustfour
analyses in our sample, we studied the models derived for remaining systems, where an overlap occurs between the F
fourclusterswhichwerecommontotheM,FandLsamples and M samples. These were resolved on an individual ba-
(Abell 2199, Abell 496, Abell 780 & AWM 7), providing a sis; in each case the analysis of the data which covered the
directcomparisonofmethods.Fig.2showsthetemperature largest angular area was chosen. Since the ability to trace
and densityprofiles for each of these systems– in each plot halo emission out tolarge radii is critical in this study,this
the different lines correspond to a different analysis result. amountstoselectingthemorereliableanalysis.Theparam-
Itcanbeseenthatthedensityprofilesshowexcellentagree- eters for each of thefinal models are listed in table 1.
ment in all but the very central regions. At the redshift of
themostdistantcluster(z=0.057,forA780),1arcmincor-
responds to roughly 60 kpc and hence these differences are
6 COMPARISON WITH CHANDRA AND
confinedtotheinnermost partsofthedata.Sincetheseare
XMM-NEWTON
all cooling flow clusters, any discrepancies in the core can
beattributed to differences in theway thecooling emission To provide a further cross-check on our results, we present
ishandled.Inanycase, theeffectsof thesediscrepancieson here a comparison of our temperature profiles with those
theglobalclusterpropertiesaresmall.Thetemperaturepro- measured using the recently launched Chandra and XMM-
filesshowconsiderablymoredivergence,andfortheclusters Newton satellites. A2199 has been observed with Chandra
A780 and AWM7, theL sample temperaturerises with ra- andananalysisofthesedatahasrecentlybeenpresentedby
dius,incontrasttotheMandFsamplemodels.Inthecase Johnstone et al. (2002). The projected temperature profile
of A780, data from a recent Chandra analysis (David et al. shows a increasing T(r) from the core out to 2.2 arcmin
∼
2001; McNamara et al. 2000) indicate that T(r) does in- (78 kpc),whereitturnsoverandflattenssomewhat– albeit
deed show evidence of a rise with radius within the inner with only 2 data points. This turnover radius is identical
200 kpcintheACIS-Sdetectordata,althoughtheACIS-I to our own “cooling radius” as determined in the L sample
∼
temperature profile exhibits a drop in the outer bin, in the analysis (see column 11 of Table 1). Johnstone et al.’s de-
range 200–300 kpc. projected T(r) rises continually with radius, but is limited
The discrepancy between the temperature profiles of to thecentral 4 arcmin of the cluster.
∼
A780 and AWM 7 is exacerbated by the rise with radius An XMM-Newton observation of A496 was recently
seen in the L sample models, which has the compounding analysed by Tamura et al. (2001). The projected temper-
effects of increasing the size of R , as well as steepening ature profile rises from the core and turns over at roughly
200
the gravitating mass profile. However, these clusters have 3.5 (137 kpc) arcmin, in good agreement with our “cool-
two of the most extreme rises in T(r) of any system in our ingradius”of3.44arcmin.AlthoughTamura et al.’sdepro-
sample, and only 5 other systems show any significant in- jectedT(r)peaksataslightlylargerradius(of 5arcmin),
∼
creaseintemperaturewithradius.Whileitisclearthatsome it clearly indicates that the temperature drops significantly
(cid:13)c 2002RAS,MNRAS000,1–27