X-ray total mass estimate for the nearby relaxed cluster A3571

10 Pages·0.51 MB·English

by  J. Nevalainen

Accepted toApJ
PreprinttypesetusingLATEXstyleemulateapj
X-RAY TOTAL MASS ESTIMATE FOR THE NEARBY RELAXED CLUSTER A3571
J. Nevalainen1, M. Markevitch2 and W. Forman
HarvardSmithsonianCenter forAstrophysics,Cambridge,USA
Accepted to ApJ
ABSTRACT
We constrain the total mass distribution in the cluster A3571, combining spatially resolved ASCA
temperature data with ROSAT imaging data with the assumption that the cluster is in hydrostatic
0 equilibrium. Thetotalmasswithinr500(1.7h−501Mpc)isM500=7.8+−12..42×1014h−501M⊙at90%confidence,
0 1.1 times smaller than the isothermal estimate. The Navarro, Frenk & White “universal profile” is a
0 good description of the dark matter density distribution in A3571. The gas density profile is shallower
2 than the dark matter profile, scaling as r−2.1 at large radii, leading to a monotonically increasing gas
n mass fraction with radius. Within r the gas mass fraction reaches a value of f = 0.19+0.06 h−3/2
500 gas −0.03 50
a (90% confidence errors). Assuming that this value of f is a lower limit for the the universal value of
gas
J
the baryon fraction, we estimate the 90% confidence upper limit of the cosmological matter density to

0 be Ω <0.4.
m
1
Subject headings: cosmology: observations – dark matter – galaxies: clusters: individual (A3571) –

intergalactic medium – X-rays: galaxies
1
v
2 1. INTRODUCTION the universe,is largerthanthat derivedassumingisother-
6 mality whichfurther aggravatesthe “baryoncatastrophe”
Measuringclustermasseshassignificantimplicationsfor
1 (e.g. White et al. 1993, White & Fabian 1995, Ettori &
1 cosmology. Assuming that the cluster mass content rep-
Fabian 1999, Mohr et al. 1999).
0 resents that of the Universe, measured total and bary-
A3571 (z = 0.040) is suitable for measuring the dark
0 onic mass distributions in a cluster, combined with the
and total mass distributions, since it is bright and hot (∼
0 Big Bang nucleosynthesis calculations and observed light
7keV)allowingaccuratetemperaturedeterminationswith
/ element abundances, can be used to constrain the cosmo-
h ASCA.Indeed,theA3571temperatureprofileusedinthis
logicaldensityparameter(Whiteetal. 1993). Ameasured
p work(seeMarkevitchetal. 1998)isamongthemostaccu-
- clustermassfunctioncouldbeusedtoconstraincosmolog-
o ical parameters via the Press-Schechter formalism. How- rate for all hot clusters. The three ASCA pointings cover
r ever, the mass cannot be observed directly since most of theclustertor500 (theradiuswherethemeaninteriorden-
t sity equals 500 times the critical density, approximately
s the cluster mass is dark matter, and one must rely on ob-
a the radius inside which hydrostatic equilibrium holds, ac-
servedquantities like gas temperature or galaxy velocities
: cordingtosimulationsofEvrardetal. 1996). A3571hasa
v and assume the state of the cluster to derive the mass.
Xi In this paper, we estimate the total mass for the A3571 coolingflow (Pereset al. 1998),but it is weak enoughnot
to introduce large uncertainties in the temperature deter-
cluster under the assumptions of hydrostatic equilibrium
r mination.
a andthermalpressuresupport. Untilrecently,mosthydro- We use H ≡ 50h kms−1Mpc−1, Ω = 1 and report
staticX-raymassestimateshavebeenmadeassumingthat 0 50
90% confidence intervals throughout the paper.
the gas is isothermalat the averagebroadbeam tempera-
ture. However,the total mass within largeradiiis only as 2. ROSATANALYSIS
accurate as the local temperature at that radius. ASCA
We processed the ROSAT data, consisting of a PSPC
observations provide spatially resolved temperature data
pointing rp800287, using Snowden’s Soft X-Ray Back-
for hot clusters and yield their 2D temperature structure.
ground programs (Snowden et al. 1994), which reduced
A large number of ASCA clusters shows that the temper-
the total exposure by 25% to 4.5 ks. The spatial analy-
ature declines with increasing radius (Markevitch et al.
sis was restricted to the energy band of 0.73 - 2.04 keV
1998), in qualitative accordance with hydrodynamic clus-
(Snowden’s bands R6-R7) to improve sensitivity over the
ter simulations(e.g. Evrardetal. 1996,Bryan& Norman
X-ray background. The surface brightness contour map
1997,Burns et al. 1999). This implies that the totalmass
(smoothed by a Gaussian with σ = 1′) is shown in Figure
within small radii is greater,while at large cluster radii it
1a. Thedatashownoobvioussubstructuresandnodevia-
issmallerthanthatderivedassumingisothermality,which
tionsfromazimuthalsymmetry,exceptforaslightelliptic-
has also been observedin A2256 (Markevitch& Vikhlinin
ity. Fabricant et al. (1984) showed that for A2256, whose
1997b, A2029 (Sarazin, Wise & Markevitch 1998), A496
X-ray brightness distribution is more elliptical than the
andA2199(Markevitchetal. 1999)andA401(Nevalainen
oneofA3571,the trueellipticaltotalmassis verycloseto
et al. 1999a). Consequently, the gas mass fraction within
thehydrostatictotalmassderivedassumingsphericalsym-
a large radius where the cluster may be a fair sample of
metry. Furthermore, Vikhlinin et al. (1999) divided the
1Observatory, UniversityofHelsinki,Finland
2SpaceResearchInstitute, RussianAcad. ofSci.
1
2 X-ray total mass estimate for A3571
PSPCdataofA3571intoseveralsectors,fittedthebright- r =0.1−2h−1 Mpcradius,centeredattheclusterbright-
50
nesswithanazimuthallysymmetricmodelandfoundthat ness peak (r = 0.1 Mpc encompasses the cooling flow ex-
theazimuthalvariationofthegasdensitygradient(dueto cluded from all our analyses).
ellipticity) was 6% of the global value, which would indi-
cate a similar error in the total mass, which is negligi- 3. TEMPERATUREDATA
ble comparedto total mass errorsobtained with spherical
We used the temperature profile data presented in
model. Therefore,in the following analysiswe assume the
Markevitch et al. (1998), who combined three ASCA
cluster to be azimuthally symmetric.
pointings to derive the emission weighted, cooling flow -
We excluded point sources and generated a radial sur-
corrected temperature kT = 6.9±0.2 keV. Outside the
face brightness profile in concentric annuli of width rang-
ing from 15′′ at the center to 7′ at a radial distance of cooling radius, the temperature values were measured in
40′. In the radial range of ASCA pointings (r < 35′), we radial bins 2′-6′-13′-22′-35′ (0.13-0.39-0.85-1.43-2.28 h−501
Mpc). Thecentralbinthatisaffectedbyasignificantcool-
includedonlytheROSATdatafromtheskyareascovered
ingflowcomponentis notusedinthe analysisbelow. The
byASCA.Acoolingflowwithamassflowrateof40-130
temperature errors were determined by generating Monte
M⊙/yr and a cooling radius of 1.2 - 2.2 arcmin has been
- Carlo data sets which properly account for the statis-
detected in the center of A3571 by Peres et al. (1998).
tical and systematic uncertainties (including those of the
Our data show a significant centralbrightness excess over
PSF, effective area and background). As in most nearby
the β-model (Figure 2), in agreement with the reported
clusters,theASCAdatarevealatemperaturedeclinewith
cooling flow. Therefore we excluded the data within the
central r <3′ from the fit. radius. TheROSATPSPCdataonA3571inthe0.2–2keV
bandwerealsoanalyzedbyIrwinetal. (1999),whoderive
We fitted the observed profile with a β- model
atemperatureprofileconsistentwithaconstantupto20′.
2 (−3β+21) However,thoseauthorsdidnotinclude the PSPCcalibra-
b tionuncertaintiesthatdominatethe ROSAT temperature
I(b)=I 1+ +CXRB (1)
0 a errors for hot clusters such as A3571 (see e.g. Marke-
(cid:18) x(cid:19) ! vitch&Vikhlinin1997a);inclusionoftheseuncertaintines
should make their results consistent with the ASCA pro-
(Cavaliere & Fusco-Femiano 1976), where b is the pro-
file. TheASCAtemperatureprofileforA3571issimilarto
jected radius. We fixed the cosmic X-ray background
(CXRB) to 1.5×10−4 counts s−1 arcmin−2 found from profilesofalargesampleofnearbyASCAclusters(Marke-
vitch et al. 1998), when scaled to physically meaningful
the outer part of the image, and included 5% of the back-
unitsoftheradiioffixedoverdensity. Thereforeitappears
groundvalueasasystematicerror,duetovariationonthe
unlikely that the observed decline is due to an unknown
sky. We used XSPEC to convolve the surface brightness
instrumental effect. A more detailed discussion about the
modelthroughaspatialresponsematrix(constructedfrom
validity of the ASCA spatially resolved temperature data
the ROSAT PSF at 1 keV, for an azimuthally symmet-
can be found in Nevalainen et al. (1999a). Hydrodynamic
ric sourcecenteredon-axis)andto comparethe convolved
simulations predict a qualitatively similar radialtempera-
profile with the data. We find an acceptable fit in the ra-
dial range 3′-43′ (see Figure 2 and Table 1), with best fit ture behavior in relaxedclusters (e.g., Evrardet al. 1996;
Eke, Navarro, & Frenk 1997; Bryan & Norman 1997), al-
parameters a =3.85±0.35 arcmin (= 310±30 h−1kpc),
x 50 though there are differences in detail between the simu-
β =0.68±0.03 with χ2 = 74.1 for 87 degrees of freedom.
lations and observations as well as between the different
Our values of a and β are consistent with another study
x simulation techniques (e.g., Frenk et al. 1999).
oftheROSATPSPCdataofA3571(Vikhlininetal. 1999)
who also excluded the cooling flow area from the fit. In
4. VALIDITYOFTHEHYDROSTATICEQUILIBRIUM
yet another study of ROSAT PSPC data of A3571 (Mohr
et al. 1999) inconsistently smaller values were found for Quintana & de Souza (1993) report preliminary results
a and β. This is a consequence of including the data of of an optical study of the galaxies in A3571. They find
x
the cooling flow into the profile fit in that work. a suggestion that the galaxy distribution in A3571 is ir-
If we assume that the intracluster gas is isothermaland regularandformsseveralvelocitysubgroups,buttheydid
spherically symmetric, the best-fit parameters a and β notperformquantitative statisticalanalysesofthe galaxy
x
determine the shape of the gas density profile as: distribution,duetothe smallnumberofobservedgalaxies
(see Figure 1 for the distribution of A3571member galax-
r 2 −23β ies from the NASA Extragalactic Database). The central
ρ (r)=ρ (0) 1+ (2) giant galaxy MCG05-33-002has an extensive optical halo
gas gas (cid:18)ax(cid:19) ! with dimensions of 0.2 × 0.6 h−501Mpc, elongated along
the major axis of the core region of this galaxy (Kemp &
The observedtemperature variation in A3571 from 7 keV Meaburn 1991). The galaxy distribution of A3571 is also
to 4 keVwith radiuswillintroduceatmosta2%effecton aligned in the same direction (Kemp & Meaburn 1991).
the gas mass (e.g. Mohr et al. 1999), which is negligible As discussed by Quintana & de Souza (1993), the optical
compared to other components in our error budget. data suggests that the cD galaxyformed during the origi-
We obtained the normalization of the gas density pro- nal collapse of the centralpart of the cluster and that the
file (as in Vikhlinin et al. 1999) ρgas(0) = 1.5×1014M⊙ cluster may not yet be virialized. However, as Quintana
Mpc−3, or 1.0 ×10−26 g cm−3, by equating the emission & de Souza (1993) state, their galaxy distribution results
measure calculated from the above equation, with an ob- are only tentative. Furthermore, galaxies are not the best
served value of 8.1 ×1067 cm−3 inside a cylinder with measure of the relaxation since clusters form within in-
Nevalainen J., Markevitch M. and Forman W. 3
tersecting filaments in larger scale and superpositions can at large radii, and those models that are convectively un-
givetheappearanceoftheasymmetries,substructure,and stable (that is, correspond to polytropic index > 5 in the
3
superposed groups. radial range of the temperature data, outside the cool-
In X-rays, the ROSAT PSPC data of A3571 (Figure 1) ing flow region r = 3′-35′). From the distribution of the
show that the gas is azimuthally symmetric (except for a acceptable Monte - Carlo models, we determine the 1 σ
slight ellipticity, see Section 2) and that there is no sub- confidence intervalsofthe mass values asa function ofra-
structure and no correlation between the galaxy and gas dius. We convert these values to 90% confidence values,
distributions at large radii. Furthermore, the ASCA gas assuming a Gaussian probability distribution. We cannot
temperaturemapofA3571(Markevitchetal. 1998)shows constrainalldarkmattermodelparametersindependently
no asymmetric variation that would indicate dynamic ac- duetothelimitedaccuracyofthetemperaturedata. How-
tivity. ever, the models with steeper dark matter density slopes
Neumann & Arnaud (1999) found evidence in their (higherα)requirelargerdarkmattercoreradii(highera )
d
ROSAT cluster sample that cooling flows are a recurrent toproducesimilarshapesoftemperatureprofileanddueto
phenomena that may be turned off by mergers, in accor- thiscorrelationthecorrespondingmassvaluesvarywithin
dancewithahierarchicalclusteringscenario(Fabianetal. arelativelynarrowrange. We alsopropagatetheestimate
1994). Since A3571 has a considerable cooling flow (Peres of the uncertainty of the local gas density gradient to the
et al. 1998), any merger must have been either not very total mass values, as in Nevalainen et al. (1999a).
strong or sufficiently in the past for the gas to reestablish In Figure 3 we show representative density profiles of
equilibrium and a cooling flow. forms (3) and (4), and the corresponding model temper-
A3571 is a member of the Shapley supercluster (Ray- ature profiles. Both functional forms give acceptable fits
chaudhury et al. 1991) and therefore likely to have more to the data and yield masses consistent within 90% con-
frequent mergers and may not be typical of more isolated fidence errors. Our final 90% confidence intervals of total
clusters. However, all the X-ray evidence consistently mass,at eachradius, include the 90% confidence intervals
argues against any significant ongoing merger in A3571. ofboth models, andthe averageofthe two models is used
Sincetheopticalevidencedoesnotcontradictsignificantly as the best value. As can be seen in Figures 3c and 3d,
theX-rayevidencefornon-merger,weassumethatthehy- in the radialrange 3′−15′, the Monte-Carlo densities are
drostatic equilibrium is valid in A3571. lower than the best fit values. This asymmetry is due to
the fact that the polytropic index criterion effectively re-
5. MASSFITTING jects themostmassivemodels,aswasalsofoundforA401
5.1. Method (Nevalainen et al. 1999a).
For the details of the mass calculation, we refer to our
5.2. Results
similar analysis of cluster A401 (Nevalainen et al. 1999a).
Briefly,we modelthe darkmatter density witha constant The final mass profile is shown in Fig. 4. The over-
core model density, or the mean interior density in units of the criti-
r2 −α/2 cal density, calculated from our best fit models, is 240 at
ρ ∝ 1+ , (3) r = 35′, the largest radius covered by the ASCA data.
dark a2
(cid:18) d(cid:19) Simulations (e.g. Evrard et al. 1996) suggest that within
and with the central cusp profile: r500,wheretheoverdensityis500,hydrostaticequilibrium
is valid. For A3571,
−η η−α
r r
ρ ∝ 1+ . (4) r =25.9′ =1.7 h−1 Mpc (6)
dark a a 500 50
(cid:18) d(cid:19) (cid:18) d(cid:19)
and the mass within this radius
We fix η = 1 in the cusp models, as suggested by numer-
ibcuatl vsaimryultahteioontshe(Nr apvaarrarmoeetteras.l.W1e99so7l,vehetrheeafhteyrdrNosFtWati)c, Mtot(≤r500)=7.8+−12..42×1014h−501 M⊙. (7)
equilibrium equation The mass values within several interesting radii are given
in Table 1.
Mtot(≤r)=3.70×1013M⊙T(r) r −dlnρgas − dlnT , At large radii our mass errors are quite large because
keV Mpc dlnr dlnr theycoverthevaluesallowedbytwodifferentmodels,and
(cid:18) (cid:19)
(5) include the uncertainty of β. Therefore the isothermal
(e.g. Sarazin 1988, using µ = 0.60), for temperature, in mass is consistent with our results, but compared to our
terms of dark matter and gas density profile parameters. best values, the isothermal ones are greater by factors of
We fix the gas density to that found from the ROSAT 1.1and1.3atradiiofr and35′(seeFigure4). Thisdif-
500
dataabove,calculatethe3-dimensionaltemperaturepro- ference is a natural consequence of the real temperatures
filemodelcorrespondingtogivendarkmatterparameters, being lower than the average temperature at large radii,
project it on the ASCA annuli, compare these values to similarly with other clusters with measured temperature
the observed temperatures and iteratively determine the profiles (Markevitch & Vikhlinin 1997b, Nevalainen et al.
dark matter distribution parameters. To propagate the 1999a, Markevitch et al. 1999). However, at small radii
errors of the temperature profile data to our mass values, (r = a ), differently from the other above clusters, the
x
we repeat the procedure for a large number of Monte - isothermal mass in A3571 is about equal to the value ob-
Carlotemperatureprofileswithaddedrandomerrors. We tained with the observed temperature profile, due to the
reject unphysical models that give infinite temperatures nearly constant temperature up to 13′ in A3571.
4 X-ray total mass estimate for A3571
The deprojection method, with the isothermal assump- deed be universal.
tion, gives a total mass value of 6.22×1014h−501 M⊙ in-
side a radius of 0.91 h−1 Mpc (Ettori et al. 1997), 6.2. Gas mass fraction
50
whereas our value at that radius is significantly smaller, Thedarkmatterdensityinthebestfitmodelfallsasr−4
4.9+−00..69×1014h−501 M⊙. This behaviour is similar to that at large radii, whereas the gas density falls as r−2. This
found for A401 (Nevalainen et al. 1999a). causes the gas mass fraction to increase rapidly at large
The frequently used mass - temperature scaling law ob- radii, to a value of
tained in cosmological simulations (Evrard et al. 1996)
predictsthatA3571,whichhaskT=6.9±0.2keV(Marke- f (≤r )=0.19+0.06h−3/2. (8)
vitchetal. 1998),willhaver =2.1±0.14h−1 Mpcand gas 500 −0.03 50
500 50
Mtot(≤r500)=1.3±0.19×1015h−501M⊙,whereasourmea- (see Figure 4). This value is consistent with those for
sured values above are smaller by factors of 1.2 and 1.6. A2256(Markevitch&Vikhlinin1997b),A401(Nevalainen
Similarbehaviourhasbeenfoundinseveralotherhotclus- et al. 1999a), A496 and A2199 (Markevitch et al. 1999)
ters with temperature profiles measured with ASCA, i.e. obtained using ASCA temperature profiles implying that
A2256(Markevitch&Vikhlinin1997b),A401(Nevalainen the gas and dark matter distributions are similar in dif-
et al. 1999a), A496 and A2199 (Markevitch et al. 1999). ferent clusters. Our value is also consistent with results
Also temperature profiles of cooler groups NGC5044 and for samples of clusters analyzed assuming isothermality:
HCG62 and a galaxy NGC507, measured with ROSAT, f (≤ r ) = 0.168+0.065h−3/2 (Ettori & Fabian 1999)
gas 500 −0.056 50
give similarresults (Nevalainen etal. 1999b). These com- and f (≤ r ) = 0.212±0.006h−3/2 (for clusters with
parisons suggest that the above simulations produce too gas 500 50
kT > 5 keV Mohr et al. 1999). At larger radii the tem-
small temperature for a given mass.
perature profile analysis would probably yield still higher
Thevirialtheoremanalysisofthegalaxyvelocitydistri-
values compared to the isothermal ones.
butioninA3571(Girardietal. 1998)givesR =4.18h−1
vir 50 Following the method of White et al. (1993; see also
MpcandMvir =1.63+−00..7792×1015h−501M⊙,whereasourval- Nevalainen et al. 1999a for its application to A401), us-
uesextrapolatedtothisradiusare1.2±0.7×1015h−501M⊙, ing the fgas value above, we compute an estimate for the
consistent within the large errors. cosmologicaldensity parameter Ω =<ρ>/ρ as
m crit
6. DISCUSSION Ω =ΥΩ f + Mgal −1, (9)
m b gas
M
6.1. NFW profile (cid:18) tot(cid:19)
With η = 1 and α = 3 the cusp model (Eq. 4) corre- atr500 forA3571,whereΥisthelocalbaryondiminution,
sponds to the NFW “universal” mass profile. For A3571 for which we use a value 0.90 as suggested by simulations
there is a significant detection of a cooling flow in the (Frenk et al. 1999). Due to the lack of a reliable esti-
center and the polytropic γ ≤ 5 constraint is applica- mate of the total galaxy mass in A3571 within r500 we
ble only beyond the cooling flow3region. At those radii compute only the upper limit for Ωm using Mgal =0. We
the temperature gradient of the cusp model is not strong, take Ωb = 0.076±0.007 (Burles et al. 1998). Using a
and the model is convectively stable. This model also reasonable lower limit for the Hubble constant H0 > 60
gives an acceptable fit to the A3571 data, and is consis- km s−1 Mpc−1 (e.g. Nevalainen & Roos 1998) we obtain
tent with our mass profile within the errors (see Figure Ωm <0.4, consistentwith severalindependendent current
4). Using the best fit NFW profile for A3571, we ob- Ωm estimates (Freedman 1999, Roos & Harun-or-Rashid
tain the concentration parameter c ≡ r /a = 5.3 and 1999).
200 d
M200 = 1.3×1015h−501 M⊙. These values are consistent 7. CONCLUSIONS
with the NFW simulations in SCDM and CDMΛ cosmo-
logical models. We have constrained the dark matter distribution in
In the hydrostatic equilibrium scheme, since the ob- A3571, using accurate ASCA gas temperature data. The
served gas density and temperature profiles are similar in dark matter density in the best fit model scales as r−4 at
different clusters, when scaled by their estimated virial large radii, and the NWF profile also provides a good de-
radii (Vikhlinin et al. 1999 and Markevitch et al. 1998, scriptionofthedarkmatterdensitydistribution. Thetotal
respectively), a similar total mass distribution is implied, masswithinr500 (1.7h−501Mpc)is7.8+−12..42×1014h−501M⊙at
and that is what we observe. The shapes of the total 90% confidence, or 1.1 times smaller than the isothermal
mass profilesatlargeradiiinother hotclusterswith mea- value,or1.6timessmallerthanthatpredictedbythescal-
sured ASCA temperature profiles for A2256 (Markevitch inglawbasedonsimulations(Evrardetal. 1996),whichis
& Vikhlinin 1997b), A2029 (Sarazin, Wise & Markevitch qualitatively similar to the results for other clusters with
1998),A496andA2199(Markevitchetal. 1999)andA401 accurate temperature profiles. The gas density profile in
(Nevalainen et al. 1999a) are also consistent with the A3571, proportional to r−2.1 at large radii, is shallower
NFW model. NFW profile also describes well the mass thanthatofthe darkmatter. Hencethe gasmassfraction
profilesofcoolgroupsNGC5044andHCG62andagalaxy increases with radius, with f (r ) = 0.19+0.06h−3/2
gas 500 −0.03 50
NGC507 that are derived using ROSAT PSPC tempera- (90 % errors) at r , consistent with results for A2256,
500
ture profiles(Davidetal. 1994,Ponman&Bertram1993, A401, A496, and A2199. Assuming that this is a lower
Kim & Fabbiano 1995, respectively, see the discussion of limit of the primordialbaryonic fraction, we obtain Ω <
m
NFWmodelsfortheseobjectsinNevalainenetal. 1999b). 0.4 at 90% confidence. However, f is still strongly in-
gas
These consistencies suggestthat the NFW profile may in- creasingatr ,sothatweobviouslyhavenotreachedthe
500
Nevalainen J., Markevitch M. and Forman W. 5
universal value of the baryon fraction, which would make his help. WF and MM acknowledge support from NASA
Ω even smaller. contract NAS8-39073. This research has made use of the
m
NASA/IPAC Extragalactic Database (NED) which is op-
JNthanksHarvardSmithsonianCenterforAstrophysics erated by the Jet Propulsion Laboratory, California In-
for the hospitality. JN thanks the Smithsonian Institute stitute of Technology, under contract with the National
foraPredoctoralFellowship,andtheFinnishAcademyfor AeronauticsandSpaceAdministration. We thanktheref-
asupplementarygrant. WeareindebtedtoDrA.Vikhlinin eree for a careful report on our paper.
forseveralhelpfuldiscussions. WethankProf. M.Roosfor
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6 X-ray total mass estimate for A3571
Table 1
Mass of A3571 ∗
Parameter Value
a a[arcmin] 3.85±0.35
x
a a[h−1 kpc] 310±30
x 50
β a 0.68±0.03
ρ (0) [10−26 h1/2 g cm−3] 1.0
gas 50
M(<3.85′ =ax) [M⊙] 6.2+−42..16×1013
M(<15.2′ = 1 Mpc) [M⊙] 5.4+−01..61×1014
M(<25.9′ =r500) [M⊙] 7.8+−12..42×1014
M(<35′) [M⊙] 9.1+−24..84×1014
f (<25.9′ =r ) × h3/2 0.19+0.06
gas 500 50 −0.03
∗usingH ≡50h kms−1Mpc−1. Allerrors
0 50
are 90% confidence errors.
aFromROSATPSPCdataexcludingthecen-
tral r ≤3′ cooling flow region.
Nevalainen J., Markevitch M. and Forman W. 7
Fig. 1.— ROSAT PSPC contour map of the surface brightness of A3571 in 0.73-2.04 keV energy range, smoothed by
a Gaussian with σ = 1′. The contour level values are 0.0005, 0.001, 0.002, 0.004, 0.008, 0.016 and 0.032 counts s−1
arcmin−2. Galaxies from the NASA Extragalactic Database are plotted as filled circles.
8 X-ray total mass estimate for A3571
Fig. 2.— ROSAT PSPC radialsurfacebrightness profilein 0.73-2.04keVrangetogether withthe PSF-convolvedbest-fit
β model. The data with r <3′ are not included in the fit, due to central cooling flow.
Nevalainen J., Markevitch M. and Forman W. 9
Fig. 3.—In(a)and(b),crossesshowprojectedASCAtemperatureswith1σerrors. Thinsolidlinesshowarepresentative
setoftemperaturemodelsoftheconstantcoreform(a)andthecuspform(b),beforeprojection,allowedbytheconvective
stabilityconstraint(seetext). Thicksolidlineshowsthebestfitmodel(beforeprojection). Inthecaseofcuspmodel,the
thickdottedlineshowsthevaluesofthisbestmodelprojectedtothe 2DASCAbins,whicharecomparedwiththe ASCA
data. In (c)and(d), the correspondingdensity models are plotted, togetherwith the gasdensity model. For comparison,
values assuming isothermality (kT = 6.9 keV) are also shown.
10 X-ray total mass estimate for A3571
Fig. 4.—(a)showstheenclosedmassprofile(solidline)with90%confidenceerrors(shadedarea),obtainedcombiningthecoreandthecusp
model fitresults. Alsothe model assumingisothermality(dotted line), together withthe gas mass profile(dash-dot) are shown. The best fit
“universal” darkmatter profile, suggested by NFWsimulations, is plotted as dashed line. In (b), the gas mass fractionwith errorsisshown.
Massesareevaluated usingH0=50km−1 Mpc−1 (total massscalesasH−1 andgasmassasH−5/2).