If the FP is universal (or the deviations from universality are known to be within certain limits), it can be used to determine distances.
If the FP is established for a given cluster of galaxies and in addition the distance to the cluster is known from some other method, the intrinsic FP zero point can be calculated, cf. Eq. (). A recent example of this is Hjorth & Tanvir (1997), who calibrated the intrinsic FP zero point using the observed FP zero point for 5 E and S0 galaxies in the Leo-I group and the HST cepheid distance to the Leo-I galaxy M96.
Without knowing the intrinsic FP zero point ,
the FP can be used to determine relative distances.
For example, if we have two clusters HydraI and Coma,
it follows from Eq. () that
their relative distance is related to their observed FP zero point difference as
The subscript ``A'' on the distances d
in Eq. ()
indicates that they are so-called
angular diameter distances, cf. Weinberg (1972).
is defined as
where D is the linear diameter
is the angular diameter of the object.
Another distance is the luminosity distance
which is defined as
where L is the (intrinsic) luminosity
and l is the apparent luminosity of the object.
In Euclidian geometry the two distances agree with each other
and with the true distance.
In an expanding universe (here given by the Robertson-Walker metric),
this is not the case.
are related through the redshift z as
Later (in Sect. ) we will
determine the distance to Coma and HydraI in the following way.
The distance to Coma will be derived from the redshift,
assuming Coma to be at rest in the CMB frame.
The distance modulus can then be found from
Eq. () and ().
The distance to HydraI relative to Coma
will be calculated from the observed FP zero point difference.
Eq. (), (), and (),
we get the following equation for
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo Milvang-Jensen (firstname.lastname@example.org)