© CAMBRIDGE UNIVERSITY PRESS 1999

1.4.5 Cluster Baryons vs. Big Bang Nucleosynthesis

A review (Copi, Schramm, & Turner 1995) of Big Bang Nucleosynthesis (BBN) and observations indicating primordial abundances of the light isotopes concludes that 0.009h^-2 _b 0.02h^-2 for concordance with all the abundances, and 0.006h^-2 _b 0.03h^-2 if only deuterium is used. For h = 0.5, the corresponding upper limits on _b are 0.08 and 0.12, respectively. The recent observations (Songaila et al. 1994a, Carswell et al. 1994) of a possible deuterium line in a hydrogen cloud at redshift z = 3.32 in the spectrum of quasar 0014+813, indicating a deuterium abundance D/H ~ 2 ~ 10^-4 (and therefore _b 0.006h^-2), are inconsistent with D/H observations by Tytler and collaborators (Tytler et al. 1996, Burles & Tytler 1996) in systems at z = 3.57 (toward Q1937-1009) and at z = 2.504, but with a deuterium abundance about ten times lower. These lower D/H values are consistent with solar system measurements of D and ³He, and they imply _b h² = 0.024 ± 0.05, or _b in the range 0.08-0.11 for h = 0.5. If these represent the true D/H, then if the earlier observations were correct they were most probably of a Ly forest line. Rugers & Hogan (1996) argue that the width of the z = 3.32 absorption features is better fit by deuterium, although they admit that only a statistical sample of absorbers will settle the issue. There is a new possible detection of D at z = 4.672 in the absorption spectrum of QSO BR1202-0725 (Wampler et al. 1996) and at z = 3.086 toward Q0420-388 (Carswell et al. 1996), but they can only give upper limits on D/H. Wampler (1996) and Songaila et al. (1997) claim that Tytler et al. (1996) have overestimated the HI column density in their system, and therefore underestimated D/H. But Burles & Tytler (1996) argue that the two systems that they have analyzed are much more convincing as real detections of deuterium, that their HI column density measurement is reliable, and that the fact that they measure the same D/H ~ 2.4 x 10^-5 in both systems makes it likely that this is the primordial value. Moreover, Tytler, Burles, & Kirkman (1996) have recently presented a higher resolution spectrum of Q0014+813 in which ``deuterium absorption is neither required nor suggested,'' which would of course completely undercut the argument of Hogan and collaborators for high D/H. Finally, the Tytler group has analyzed their new Keck LRIS spectra of the absorption system toward Q1937-1009, and they say that the lower HI column density advocated by Songaila et al. (1997) is ruled out (Burles and Tytler, private communications, 1997). Of course, one or two additional high quality D/H measurements would be very helpful to really settle the issue.

There is an entirely different line of argument that also favors the higher _b implied by the lower D/H of Tytler et al. This is the requirement that the high-redshift intergalactic medium contain enough neutral hydrogen to produce the observed Lyman forest clouds given standard estimates of the ultraviolet ionizing flux from quasars. The minimum required _b 0.05 h₅₀^-2 (Gnedin & Hui 1996, Weinberg et al. 1997) is considerably higher than that advocated by higher D/H values, but consistent with that implied by the lower D/H measurements.

It thus seems that the lower D/H and correspondingly higher _b 0.1 h₅₀^-2 are more likely to be correct, although it is worrisome that the relatively high value Y_p 0.25 predicted by standard BBN for the primordial ⁴He abundance does not appear to be favored by the data (Olive et al. 1996, but cf. Sasselov & Goldwirth 1995, Schramm & Turner 1997).

White et al. (1993) have emphasized that X-ray observations of clusters, especially Coma, show that the abundance of baryons, mostly in the form of gas (which typically amounts to several times the mass of the cluster galaxies), is about 20% of the total cluster mass if h is as low as 0.5 (see also Section 4.4). For the Coma cluster they find that the baryon fraction within the Abell radius (1.5h^-1 Mpc) is

(1.4)

where the first term comes from the galaxies and the second from gas. If clusters are a fair sample of both baryons and dark matter, as they are expected to be based on simulations (Evrard, Metzler, & Navarro 1996), then this is 2-3 times the amount of baryonic mass expected on the basis of BBN in an = 1, h 0.5 universe, though it is just what one would expect in a universe with ₀ 0.3 (Steigman & Felten 1995). The fair sample hypothesis implies that

(1.5)

A recent review of X-ray measurements gas in a sample of clusters (White & Fabian 1995) finds that the baryon mass fraction within about 1 Mpc lies between 10 and 22% (for h = 0.5; the limits scale as h^-3/2), and argues that it is unlikely that: (a) the gas could be clumped enough to lead to significant overestimates of the total gas mass - the main escape route considered in White et al. 1993 (cf. Gunn & Thomas 1996). The gas mass would also be overestimated if large tangled magnetic fields provide a significant part of the pressure in the central regions of some clusters (Loeb & Mao 1994, but cf. Felten 1996); this can be checked by observation of Faraday rotation of sources behind clusters (Kronberg 1994). If = 1, the alternatives are then either: (b) that clusters have more mass than virial estimates based on the cluster galaxy velocities or estimates based on hydrostatic equilibrium (Balland & Blanchard 1995) of the gas at the measured X-ray temperature (which is surprising since they agree: Bahcall & Lubin 1994); (c) that the usual BBN estimate of _b is wrong; or (d) that the fair sample hypothesis is wrong (for which there is even some observational evidence: Loewenstein & Mushotzky 1996). It is interesting that there are indications from weak lensing that at least some clusters (e.g., for A2218 see Squires et al. 1996; for this cluster the mass estimate from lensing becomes significantly higher than that from X-rays when the new ASCA satellite data, indicating that the temperature falls at large radii, is taken into account: Loewenstein 1996) may actually have extended halos of dark matter - something that is expected to a greater extent if the dark matter is a mixture of cold and hot components, since the hot component clusters less than the cold (Kofman et al. 1996). If so, the number density of clusters as a function of mass is higher than usually estimated, which has interesting cosmological implications (e.g. ₈ is higher than usually estimated). It is of course possible that the solution is some combination of alternatives (a)-(d). If none of the alternatives is right, then the only conclusion left is that ₀ 0.3.

Notice that the rather high baryon fraction _b 0.1 (0.5/h)² implied by the recent Tytler et al. measurements of low D/H helps resolve the cluster baryon crisis for = 1 - it is escape route (c) above. With the higher _b implied by the low D/H, there is now a ``baryon cluster crisis'' for low-₀ models! Even with a baryon fraction at the high end of observations, f_b 0.2 (h/0.5)^-3/2, the fair sample hypothesis with this _b implies ₀ 0.5 (h / 0.5)^-1/2.