a r X i v :a s t r o -p h /0305296v 2 9 J u l 2003
Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 2February 2008
(MN L A T E X style ?le v2.2)
Are we missing baryons in Galaxy Clusters?
European Southern Observatory,Karl-Schwarzschild-Str.2,D-85748Garching,Germany
The recent constraints on the cosmological parameters put from the observations of the
WMAP satellite limit the cosmic baryon fraction in a range that is larger than,and marginally consistent with,what is measured in galaxy clusters.This rises the question whether or not we are considering all the ingredients of cluster baryonic budget.Carefully weighing the baryons in X-ray emitting plasma and stars in cluster galaxies,I conclude that the cluster baryonic pie is made by 13(with a 1σrange of 8–19)per cent of stars,70(56–89)per cent of intracluster hot medium and 17(0–33)per cent,and a probability of 73per cent of being larger than 0,of “other”baryons,presumably in the form of warm (105?107Kelvin)material.
Key words:galaxies:cluster:general –galaxies:fundamental parameters –intergalactic medium –X-ray:galaxies –cosmology:observations –dark matter.
The recent analysis of the angular power spectrum of the Cosmic Microwave Background (CMB)obtained from WMAP (Bennett et al.2003)has provided constraints on the cosmological parameters (Spergel et al.2003)that con?rms with greater accuracy the current energy density of the Universe to be comprised by about 73per cent of dark energy and 27per cent of matter,mostly non-baryonic and dark.In particular,the quoted constraint on the baryon den-sity,?b ,is 0.0224±0.0009h ?2
100,and on the total matter density,
?m ,is 0.135+0.008?0.009h ?2
100.Consequently,the cosmic baryon fraction,
?b /?m ,is equal to 0.166+0.012
?0.013and the ratio between baryon and
cold dark matter density,?c =?m ??b ,is equal to 0.199+0.017
?0.019.These values are expected to be maintained in regions at high over-densities that collapse to form galaxy clusters.
The clusters baryon budget is composed mainly from the X-ray luminous baryons,M gas ,of the intracluster medium (ICM)that becomes hotter upon falling into the cluster dark matter halo by gravitational collapse.Other contributions come from the baryonic stellar mass in galaxies,M gal ,and from other “exotic”sources,like intergalactic stars and a still poorly de?ned baryonic dark mat-ter.Given the large uncertainties on the relative contribution from baryons that are not accounted for in either M gas or M gal ,I qual-ify these as “other baryons”,M ob ,as already done in a previous work (Ettori 2001)in which I discussed the constraints on clus-ter baryon budget from BOOMERANG and MAXIMA-I data.The tighter constraints on the cosmological parameters provided from WMAP allow now more ?rm conclusions.
Therefore,one can put the following relation between the rel-ative amount of baryons in the Universe and in clusters with total gravitating mass,M tot :?b
Figure 1.Gas (dots )and baryon (diamonds )fractions estimated at an overdensity of 200for a cosmology ?xed to the best-?t WMAP results (Spergel et al.2003).These results constrain the cosmic baryon budget to the shaded region.The central (±1σ)value of the observed distribution is obtained with a Bayesian method (see Press 1996)and is indicated with a dashed (dotted )line.The thickest dashed line indicates the estimate of the baryon fraction corrected by the depeletion parameter Y =0.92.(Left)Low (z <0.1)redshift sample of galaxy clusters observed with BeppoSAX .The best-?t spectral results were deprojected to recover the gas density and temperature pro?le and to infer the gas and gravitating mass (see Ettori,De Grandi,Molendi 2002).The f gal is estimated from B-band luminosities in Girardi et al.(2002),assuming M gal /L B =4.5±1.0h 100M ⊙/L ⊙(Fukugita et al.1998).Where L B is not available,the median value of measured f gal =0.022obtained from six nearby systems is used [Lin et al.(2003,Fig.7)measure f gal between 0.01and 0.02from K-band luminosity].(Right)High (z >0.7)redshift sample of objects observed with Chandra (see Ettori,Tozzi,Rosati
Figure 2.Constraints as function of the depletion parameter Y on the gas (dashed line ),stellar (dotted line )and “other baryons”(solid line and probabil-ity contours at 1,2,3sigma con?dence level)mass fraction normalized to the cosmic value.The shaded region indicates the range of Y permitted from hydrodynamical simulations (Frenk et al.1999).
low ?z and high ?z sample,respectively.Note that these values do not include any correction by the baryonic depletion that is ex-pected to raise the gas/baryon fraction by about 8/6per cent at this overdensity.See also Fig.1and text that follows).These estimates are consistent with other,independent,recent determinations (e.g.Allen et al.2001,Pratt &Arnaud 2002)and consistently lower than the baryon budget required from WMAP results.It is worth notic-ing that only the highest estimates of the gas (baryon)mass fraction (e.g.A426,A2142,RXJ1350)are perfectly consistent with WMAP results,whereas the other clusters are systematically below them.
To investigate the systematics that could affect this estimate,I change the values of the factors B and C and study their in?u-ence on the baryon fraction.The factor B ,which parametrizes the uncertainties on M tot is expected to be between 1and 1.15from the cluster mass pro?les recovered from both X-ray and lensing data (e.g.Allen et al.2001).The factor C represents the level of clumpiness that affects the estimate of M gas in X-ray analysis and that simulations show to be lower than 1.2(Mathiesen et al.1999).Figure 2shows that higher values of B and C require a more relevant role to be played by f ob ,giving a 2σpositive detection for
Are we missing baryons in Galaxy Clusters?
Figure4.Cluster baryonic pie.The1σrange from the Bayesian calcula-tions applied to the eight nearby clusters is shown in parenthesis.A deple-tion factor Y=0.92±0.06is assumed.The factors B and C are?xed to 1.We expect larger values of the warm ingredient if either B or C are>1. It is worth noticing that the hot component,f gas,scales as h?1.5and the cold component,f gal,is here independent from h.
typical value of Y when B and C are15per cent larger than the null hypothesis of reliable estimates of both M gas and M tot from X-ray analysis.
Moreover,I can estimate from the observables the ratio R gas=(?b/?m?f gal/B)/f gas×(Y BC)≈(f ob/f gas+1) and to evaluate the probability that R gas>1and a no-zero value of f ob is required from the data(see Fig.3).I obtain values of R gas between1.3(B=1,C=1)and1.7(B=1.15,C=1.15), with an interval accepted at the95per cent con?dence level of0.5–2.7.More signi?cantly,this ratio has to be larger than1at76.6 (B=1,C=1)and92.5(B=1.15,C=1.15)per cent con-?dence level.This result gives a high con?dence to the conclusion that a signi?cant amount of baryons has to be present apart from what is observed both at X-ray and optical wavelength.
By comparing the recent cosmological constraints from measure-ments of the angular power spectrum of the temperature anisotropy in the CMB done with WMAP with the observed distribution of the gas mass fraction in clusters of galaxies,I conclude that
(i)galaxy clusters with the highest observed gas/baryon frac-tion are well in agreement with the WMAP estimate of the cosmic baryon budget.On average,however,a disagreement in the order of 15–20per cent is present,the observed cluster baryon fraction be-ing a lower estimate of the cosmic one.This implies that estimates of the cold dark matter density,?c,done by applying mean results from large sample of objects tend to overestimate it.In this perspec-tive,a more“realistic”result is provided from the highest estimate in the distribution of the cluster gas(baryon)mass fraction;
(ii)this dark baryonic component appears to be between a frac-tion,and up to2times,the measured gas fraction.Values of R gas=(f WMAP?f gal)/f gas larger than1are required from the data with a level of con?dence of about80per cent and more,if we are underestimating(overestimating)the total(gas)mass.The most probable values are f ob/f gas=R gas?1=0.3(B=C=1)and 0.7(B=C=1.15),and lower than1.7at95per cent con?dence level.
It is very unlikely that galactic objects,such as“colored”(red, brown,white,beige)dwarfs,stellar remnants and other species of MACHOs(see review in Gilmore1999and Evans2003),or in-tergalactic ones formed from tidal disruption of cluster dwarfs,like planetary nebulae(e.g.Ciardullo et al.2002),red-giant-branch stars (e.g.Ferguson et al.1998)and supernovae(Gal-Yam et al.2003), can be responsible for such amount of baryons.It is reasonable to believe that they can contribute by about0.2times f gal,or0.04f gas.
The most plausible suspect to give so large contribution is then a X-ray warm(105K
Intriguingly,the stronger soft excess detected in Rosat data from Bonamente et al.(2002)is measured in objects like A85and A1795,that are the ones lacking most of the baryons with respect to the cosmic budget as plotted in Fig.1.Signi?cant detection is also present in A2029,A2199and A3571,whereas a marginal detection is associated to A2142.Nevalainen et al.(2003;see also Kaastra et al.2003)con?rm with XMM the excess in the soft X-ray emission in A1795and that this excess is best?tted by a thermal compo-nent with a characteristic temperature of0.8keV,which is about an order of magnitude higher than what required from Rosat data but still consistent with our energetic http://www.sodocs.net/doc/2591e5d9a58da0116c1749c4.htmling their esti-
Figure 3.Bayesian distribution (Press 1996)of the ratio R gas =(f WMAP ?f gal )/f gas for B =C =1(left)and B =C =1.15(right).
mation of the atom density of the W-ICM in the core of A1795,and assuming that it is broadly distributed like the ICM,one can infer a f W ?ICM /f gas =R gas ?1≈0.43.In general,values of f W ?ICM /f gas between 0.1and 0.5are expected.
To summarize,clusters seem to have similar behavior in ac-cumulating the same relative amount of baryons.It is then their peculiar thermal history due to the interplay of merging actions and/or activity of the central active galaxy that provides the bary-onic ingredients and cook the baryonic pie that we taste and show in Figure 4.To prepare it,I have considered only the eight nearby clusters which provide a more reliable estimate of f gal and are less affected from systematics in the determination of f gas (see discus-sion in Ettori et al.2003).I have also corrected the gas fraction by the depletion factor Y ≈0.92.The baryonic pie is then made of 70per cent of hot ICM,with 1σrange between 56and 89per cent and a distribution of the calculated f gas /f WMAP that spans between 28and 143per cent at 2σcon?dence level (higher upper limit ob-served in A426that has a most probable f gas /f WMAP value of 115per cent).The cold ,stellar component is responsible for 13(1σ:8–19)per cent,with an observed distribution in the sample between 2and 37per cent (2σlower and upper limit,with the latter reached in A2199,which has a central value of 21per cent).Finally,a third ingredient,probably a warm ICM,contributes by about 17(0–33)per cent (and a probability to be larger than 0of 73per cent)with a distribution that goes from –29±15per cent in A426to 40±12per cent in A1795,one of the objects with the largest detected soft excess (Bonamente et al.2002,Kaastra et al.2003).
I am grateful to Hans B¨o hringer and Andy Fabian that pointed out a relevant weakness in the assumptions done in the original manuscript.
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