Relative distance estimators.IV.
The
relation
Elliptical galaxies also follow scaling
laws which relate their size, velocity dispersion and luminosity (or surface
brightness).
The most useful relation to measure distances to elliptical galaxies is
the
relation.
The parameter Dn
is the diameter within which the mean surface brightness
is
In= 20.75 mag/arcsec2 in the blue.
is the central velocity dispersion.
The relation represented by a straight line in the above (log-log) plot
is
To obtain the distance we only need to compare the
angular size of Dn to the scale predicted by this equation.
There is a 15% scatter in the relation from galaxy
to galaxy, which will imply a 15% intrinsic uncertainty in the distance.
However, if one is interested in measuring the distance to a cluster of galaxies,
the uncertainty to the cluster distance can be reduced by observing large
numbers of elliptical galaxies.