Searching for the missing baryons in clusters Bilhuda Rasheed, Neta Bahcall1, and Paul Bode Department of Astrophysical Sciences, 4 Ivy Lane, Peyton Hall, Princeton University, Princeton, NJ 08544 Edited by Marc Davis, University of California, Berkeley, CA, and approved January 10, 2011 (received for review July 8, 2010) Observations of clusters of galaxies suggest that they contain few- fraction in the richest clusters, it is still systematically below er baryons (gas plus stars) than the cosmic baryon fraction. This the cosmic value. This baryon discrepancy, especially the gas frac- “missing baryon” puzzle is especially surprising for the most mas- tion, is observed to increase with decreasing cluster mass (14, 15). sive clusters, which are expected to be representative of the cosmic This raises the questions: Where are the missing baryons? Why matter content of the universe (baryons and dark matter). Here we are they “missing”? show that the baryons may not actually be missing from clusters, Attempted explanations for the missing baryons in clusters but rather are extended to larger radii than typically observed. The range from preheating or other energy inputs that expel gas from baryon deficiency is typically observed in the central regions of the system (16–22, and references therein), to the suggestion of clusters (∼0.5 the virial radius). However, the observed gas-density additional baryonic components not yet detected [e.g., cool gas, profile is significantly shallower than the mass-density profile, faint stars (10, 23)]. Simulations, which do suggest a depletion of implying that the gas is more extended than the mass and that cluster gas in the inner regions of clusters, do not yet contain all the gas fraction increases with radius. We use the observed density the required physics [stellar and Active Galactic Nuclei (AGN) profiles of gas and mass in clusters to extrapolate the measured feedback, cosmic ray heating, magnetic fields, etc.] for providing baryon fraction as a function of radius and as a function of cluster accurate comparisons to the data. Therefore, we use only obser- mass. We find that the baryon fraction reaches the cosmic vations in this work; the collective data should help shed light on value near the virial radius for all groups and clusters above which physical processes are most essential. ∼ × 13h−1M In this paper we investigate the possibility that the “missing 5 10 72 ⊙. This suggests that the baryons are not missing, they are simply located in cluster outskirts. Heating processes baryons” are not missing at all, but are rather located in the out- (such as shock-heating of the intracluster gas, supernovae, and skirts of clusters where few detailed observations have yet been Active Galactic Nuclei feedback) likely contribute to this expanded made. The missing baryons problem is typically observed within distribution. Upcoming observations should be able to detect these the central regions of clusters, generally within a radius of R500 baryons. (where the enclosed mass-density is 500 times the critical den- sity). This radius is ∼0.5 of the virial radius of the cluster [where cosmology ∣ hot intracluster gas the enclosed density is ∼100 times the critical density for the current Lambda Cold Dark Matter (LCDM) cosmology (24, 25)]. Thus for a virial radius of ∼1.5 Mpc, the typical missing baryon lusters of galaxies, the largest virialized systems in the uni- ∼0 75 Cverse, are powerful tools in constraining cosmology and tra- problem is observed only at . Mpc from the cluster center. ASTRONOMY cing the large-scale structure of the universe (1–4, and references Observations show that the gas density profile in the outer 14 15 −1 parts of clusters decreases with radius slower than the mass therein). The large mass of clusters (∼10 to 10 h72 M⊙) implies that their contents—dark and baryonic matter—have been profile in these regions. Using gravitational lensing, the latter accreted from very large regions of ∼10 comoving Mpc, and has been observed out to large radii (11, 26, 27) and is consistent therefore should be representative of the mean matter content with the expected Navarro, Frank, White (NFW) profile (28). of the universe; on these large scales there are no clear mechan- Whereas the cluster mass density declines with radius approxi- mately as r−2.6 in these outer regions, the gas density declines only isms to separate dark and baryonic matter (e.g., refs. 5 and 6). r−2.2 The strong gravitational potential of clusters also implies that as . This implies that the gas is more extended than the total mass, and therefore the gas fraction increases with radius beyond baryons cannot easily escape from these systems. Therefore, clus- R ters are expected to retain the cosmic baryon fraction, the relative the observed radius of 500. A shallow slope of the gas profile fraction of baryons to total matter on large scales. This basic (as compared with the mass profile) is indeed expected if gas heating occurs in the clusters (e.g., from shock-heating of the expectation of a representative baryon fraction in clusters was gas, supernovae, and AGNs). The heating makes the gas less used in 1993 (6) to suggest that the mass-density of the universe bound relative to the dark matter potential, and spreads it out must be low, since the observed baryon fraction in clusters was to larger radii. considerably larger than expected for a critical density universe. Here we use the observed slopes of the gas-density and mass- Most of the baryons in clusters reside in the X-ray emitting hot density profiles in the outer regions of clusters to extrapolate the intracluster gas, which approximately traces the cluster gravita- observed gas fraction from R500 to larger radii, up to the virial tional potential dominated by dark matter. The rest of the bar- radius [R ¼ R100 (24, 25)]. We add the observed stellar fraction yons are in the luminous galaxies and in isolated stars that vir to the extrapolated gas fraction to find the baryon fraction at comprise the small amount of faint diffuse intracluster light large radii. We perform this extrapolation as a function of cluster (ICL). mass from groups to rich clusters, and as a function of radius from A puzzle has been raised, however, over the last few years: R500 to R . Note that this analysis is based entirely on obser- Detailed X-ray observations from Chandra, XMM-Newton, vir vations. and ROSAT suggest that the cluster baryon fraction (gas plus We find that the baryon fraction increases systematically with stars relative to total mass) is considerably lower than the cosmic radius, and show that there is no missing baryon problem in rich value. The cosmic baryon fraction is well determined both from Big-Bang nucleosynthesis (7, 8) and from observations of the cos- mic microwave background to be f b ¼ 0.1675 Æ 0.006 (WMAP7: Author contributions: B.R., N.A.B., and P.B. designed research, performed research, 9). The cluster gas fraction has been reported by observations contributed new reagents/analytic tools, analyzed data, and wrote the paper. (10–15) to be only 60–80% of the cosmic value, with stars con- The authors declare no conflict of interest. tributing only a small (∼10%) additional amount of baryons. This article is a PNAS Direct Submission. Whereas the baryon fraction appears to approach the cosmic 1To whom correspondence should be addressed. E-mail: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1009878108 PNAS ∣ March 1, 2011 ∣ vol. 108 ∣ no. 9 ∣ 3487–3492 Downloaded by guest on October 1, 2021 clusters when the data is extrapolated to near the virial radius, bins, from groups to rich clusters (15). (We do not include 13 −1 where the baryon fraction becomes consistent with the cosmic the lowest mass bin at 10 h72 M⊙ that contains only two groups value. Most of the missing baryons are therefore expected to with large error bars.) Our cluster sample has a mass range of R R 3 × 1013h−1M M 1015h−1M be in the outskirts of clusters, between 500 and vir. This result 72 ⊙ < 500 < 72 ⊙ and a redshift range of can be tested with upcoming observations of the Sunyaev–Zeldo- 0.012 < z < 0.23. The mean observed gas fraction for each mass vich (SZ) effect in clusters [e.g., South Pole Telescope (SPT) (29); bin is listed in Table 1 and shown in Fig. 1.p Theffiffiffiffiffiffiffiffiffiffiffiffi error on the mean Atacama Cosmology Telescope (ACT) (30)] as well as with more is the rms standard deviation divided by N − 1. The horizontal sensitive X-ray observations. bars are the mass ranges for the bins. Also presented in Fig. 1 is Observations have shown that the missing baryon problem at the cosmic baryon fraction observed by the WMAP7 microwave R500 becomes more severe for lower mass clusters and groups of background measurements. One can see that the cluster gas galaxies than for rich clusters; the observed gas fraction decreases fraction at R500 is significantly lower than the cosmic baryon frac- considerably with decreasing cluster mass. This too would be tion. The gas fraction decreases significantly from rich to poor expected if the heating processes expand the gas: the lower grav- clusters; whereas rich clusters contain about 12% gas within itational potential of the smaller systems will not be able to hold R500, the gas fraction in poor clusters and groups is only ∼6–7%. on to their gas as well as the higher mass clusters. The gas-density profile in small groups is indeed observed to be shallower than Stellar Fraction. The galactic stellar fraction has been measured in the gas-density profile in massive clusters, suggesting that the nearby clusters using multiband optical and infrared surveys com- gas in low-mass systems is more spread out.