**5.5 Other Distance Indicators using Novae**

Several other methods for using novae as distance indicators have been proposed in the literature. Here we give a brief discussion of some of these methods, and their limitations.

<*M*_{15}>:
Buscombe and de
Vaucouleurs (1955)
first showed that the mean magnitude of an ensemble of novae 15 days
after maximum light was a constant; from the most recent data on
Galactic novae,
Cohen (1985)
has shown that <*M*_{15}>
-5.60 ± 0.14, where the
quoted error is the 1 error
in the mean. The rough constancy of <*M*_{15}> is a
consequence of the MMRD relation, and has been explained theoretically
by Shara (1981a).
For Virgo cluster novae, <*B*_{15}>
+26 if *(m - M)* =
31.5; hence the <*M*_{15}>
distance indicator will be strongly affected by Malmquist bias at the
distance of the Virgo cluster unless the observational completeness
limit goes somewhat fainter than *B* > 26.
Note that there are exceptional objects (e.g., M31 novae
Arp 1, 2, and 3) that suggest this method be used with caution.

*Luminosity Function of Novae:* The luminosity function of novae at
maximum light is approximately Gaussian in the data of
Rosino (1973);
de Vaucouleurs (1978)
used the mean magnitude of this Gaussian to
determine the distance to M31. More recently,
Pritchet and van
den Bergh (1987a)
used this technique to determine the distance to the
Virgo cluster, and obtained a result that was
consistent with the MMRD
relation. The most recent compilation of M31 nova data by
Capaccioli et
al. (1989)
appears to show a double-peaked luminosity function;
Capaccioli et al. use the magnitude of the *minimum* between the two
peaks as a distance indicator. Yet another method is to use the
*integral* luminosity function of novae at maximum light; this function
is linear over a wide range of magnitude, and possesses a well-defined
intercept
(van den Bergh and
Pritchet 1986).

The use of the luminosity function of novae at maximum light as a
distance indicator demands large samples of novae that are essentially
complete at the faintest magnitudes; it is therefore unlikely that this
method will be useful for any but the nearest *luminous* galaxies (i.e.,
those with high nova rates). The
Capaccioli et
al. (1989)
technique of using the dip between two peaks in the luminosity function is not
completely reliable, because, as Capaccioli et al. demonstrate,
different samples of M31 novae have luminosity functions with very
different structure. (The very existence of this dip is in some
question - cf. Rosino 1973,
Capaccioli et
al. 1989.)

Finally, it should be mentioned that the luminosity function of
*all* M31 nova observations (i.e., random phases)
possesses no useful
information that can be used in determining extragalactic distances
(van den Bergh and
Pritchet 1986;
Ford and Ciardullo
1988).

*Period of Visibility:*
Van den Bergh and
Pritchet (1986)
show that
there exists a strong correlation between the mean period of visibility
of novae (down to some limiting magnitude *m*_{lim}, and
the absolute magnitude that this *m*_{lim} corresponds
to. Application of this correlation (calibrated using M31 data) to the
Virgo elliptical observations of
Pritchet and van
den Bergh (1987a)
yields a distance modulus that is similar to that obtained using the
MMRD relation. This method needs complete samples of novae down to some chosen
*m*_{lim},
but the samples do not have to be large. (With a large sample of novae,
it would in principle be possible to apply this technique at several
different *m*_{lim} values.)