THE MISSING MASS PROBLEM IN GALAXY CLUSTERS
AND THE MODIFIED NEWTONIAN DYNAMICS
Sandro Mendes
Instituto
de Astronomia, Geofísica e Ciências Atmosféricas
Universidade
de São Paulo, Brasil
Recent estimates of
dynamical masses of galaxy clusters show that dark matter is needed even when
the analysis is performed in the MOND (Modified Newtonian Dynamics) context.
Although the mass discrepancy is reduced by a factor of 2 in the MONDian
analysis, the mere existence of small amounts dark matter is completely against
the MOND premises. Thus we should have an undetected component of baryonic
matter in clusters if the phenomenology is correct. It has been argued that
another, more radical, possibility of reconciling MOND with the observational
data would be a variation in the Hubble parameter H from h = 75 locally to h = 50 at the distance scale of the
clusters (H = 100h km s-1
Mpc-1). The idea is that the MOND parameter a0 has a
certain dependence on h and is
determined from rotation curves of nearby galaxies. Its value would therefore
be different for distant clusters if the Hubble parameter were significantly
different from the local value. We emphasize in this work that such behavior of
H would imply a deceleration
parameter q < -1 if the the change is interpreted as a time variation. This
is obtained when one constrains H to
be an increasing function of time, and is marginally consistent with the
MONDian universe of McGaugh. However when one adds the extra constraint that
the variation in H must be DH = 15 h km s-1 Mpc-1 in a redshift range Dz = 0.2, we conclude that,
respecting big bang nuclesynthesis constraints, the vacuum contribution to the
density parameter should be WL » 2.3 (assuming a universe containing baryons
and vacuum energy only). Such value is obviously ruled out by all observational
constraints on WL. We therefore conclude that
the most natural hypothesis in the MOND context remains that the source of the
mass discrepancy is really the presence of undetected baryonic material,
possibly deposited in the cluster centers by cooling flows.