Sulkanen wrote:
I think that this dimensional analysis for the x-ray luminous mass
and gravitational mass may overestimate M(p)/M(g) compared to the
actual method of doing some of this (Fabricant et al.); e.g.,
since cluster plasma is centrally condensed the effective
luminosity radius is smaller than 3 Mpc (it’s more like a few core
radii at most – see Sarazan Rev Mod Phys ’86 p.78). A good
estimate of M(g) for radii much larger than the core radius of the
cluster gives M_g(r) = 1.08 x 10^14 B T (keV) R (Mpc) Msol
(Mushotzky, preprint X-Ray 94-8), where B is a parameter related
to the exponent of the King-like profile of the cluster x-ray
surface brightness, and is in the range of 0.6 – 0.8. When the
smoke clears the error could easily be an order of magnitude for
M(p)/M(g). You also need to demonstrate the egregious error that
x-ray observers are now making in their data analysis that leads
to many clusters with a gravitational mass in large excess
compared to the x-ray luminous mass. I doubt that all of them are
making systematic errors like the one that plagued the analysis of
the ROSAT observation of N2300.
My reply:
My simple formula for the plasma mass, which assumes an even
distribution, does overstate plasma mass, but not by that much. I
compared the sum of the plasma masses for 20 clusters cited by
Sanders, with masses determined by Jones and Forman on the basis
of detailed data, with the sum of the masses derived from my
formula M(p) = .37 T^-.25 R^1.5 L^.5, where L is x-ray luminosity
in units of 10^44 ergs/s T is kev and R is Mpc(assumed to be
3Mpc). The Jones and Forman mass was smaller than mine by a
factor of 1.7, although in individual cases the ratio was as great
as 5 or as little as 0.7. In the case of Coma, where there were
several estimates available in the literature, they ranged from
3.1-4.8 x10^14 solar masses as compared with the formula value of
4.0.
The Mushotzky formula for gravitational mass quoted above is just
about twice the formula I gave. But this is a bit strange, since
my formula M(g)=.34 TR should also overestimate gravitational mass
since it assumes a constant T out to R, while in reality T will
fall with R. When I compared the masses of Coma, Centaurus and
A2256 from my formula with those of detailed models, I get a sum
of 24(in units of 10^14 s.m.) for my formula and a range of 25-78
in the detailed estimates. So in these few cases, mine are within
the limits set by more detailed models.
I had previously, using known empirical correlations of T and L,
estimated that the ratio of visible mass (plasma plus stars)
gravitational energy to plasma kinetic energy(or visible mass to
gravitational mass) was .75-.95 for an average cluster going from
L=1 to 100. The ratio of magnetic energy to kinetic energy varied
over the same range from .57-.02. With a 1.7 smaller plasma mass
and twice as big gravitational mass we get .22-.28 for M(v)/M(g)
and .97–.03 for E(m)/E(k). So, even with these corrections, the
typical fraction of gravitational mass that is "missing" is about
1/3 and for the brightest clusters, 2/3, not .9 or .95. And I
doubt that in the general case the factor of two increase in
gravitational mass is real.
There’s no real disagreement between my results and the more
detailed ones. I was talking about averages. In individual
clusters, the ratio of gravitational mass to visible mass is going
to be greater or less. But there were other simplifying
assumptions that I used, such as the magnetic field being always 2
microgauss and the radius begin 3 Mpc. To get a better idea of
the fraction of confining field that can be explained by visible
matter or magnetic fields would involve measuring magnetic fields
in many more clusters.
But the key point remains. For the average of all clusters, at
least half and probably a lot more of the confining field is
observable as due to visible matter and magnetic fields. I don’t
see how the "best" case individual clusters can be used as
evidence for non-baryonic matter, since it is really difficult to
imagine a process that would separate this stuff into some
clusters and not others. And if we use an average value, it’s
nowhere near the 95% required by the need to fill up an omega
equal one universe. Moreover, I don’t see how, given the
uncertainties of all these estimates, and given the certainty
that some baryonic matter is dark, how a factor of two (at most)
discrepancy can be used to justify the need for non-baryonic
matter.
posted by admin in Uncategorized and have
Comment (1)