5.4 Uncertainties

Existing problems with calibrating the MMRD relation in M31 have already been discussed above. The role of internal absorption in the M31 MMRD is probably small; more serious is the calibration uncertainty for the brightest M31 novae (has maximum light been observed?), and the inconsistency between Galactic and M31 MMRD relations (is it due to shell geometry?)

An additional problem is the existence of so-called ``anomalous'' novae. These novae, which represent roughly 10% of all novae in M31, are unusually bright or faint for their observed decay rate mdot. At least one faint nova (Arp 4) was unusually red and hence probably heavily obscured (Arp 1956). However, most anomalous novae in M31 are 1 mag brighter than other novae with the same mdot; nova 2 in the west field of the Virgo cluster elliptical NGC 4472 (Pritchet and van den Bergh 1987a) and Nova LMC 1991 (Della Valle 1991) may also be examples of such novae. Anomalous novae stand out clearly in the M31 MMRD relation (because of the small scatter in this relation), and hence can be ignored. But for Virgo cluster galaxies, the existence of anomalously bright novae has the potential to strongly bias distance determinations, for at least two reasons. (1) Data on novae in the Virgo cluster are affected by an apparent magnitude cutoff, so that only the brightest novae are observed. (2) m<sub>max</sub> and mdot are not well-determined for novae at the distance of the Virgo cluster; anomalous novae may be confused with normal novae because of scatter in the MMRD relation. Luminous variable objects of unknown type, such as the red ``nova-like'' variable discovered by Mould et al. (1990a) in the bulge of M31, may also be confused with normal novae in MMRD diagrams of distant galaxies.

An even more severe (logistical) problem is that of scheduling observations. Because bright novae are so fast, repeated observations are required each night to estimate m_max and mdot. But the nova rate per CCD field is only ~ 0.1 - 0.2 d^-1 for typical Virgo cluster ellipticals (Pritchet and van den Bergh 1987a), and lower than this for the brightest novae - i.e., the yield per night of observing is low. The need for large amounts of observing time on 4 m-class (or larger) telescopes to observe novae in the Virgo cluster means that the observations of Pritchet and van den Bergh (1987a) are unlikely to be repeated in the near future.

For fainter, slower novae (say M_B^max -8.5, mdot 0.2 mag d^-1), observations spaced one night apart suffice, so that a number of galaxies can be observed on a single night; observing faint novae also avoids uncertainties in the calibration of the bright end of the MMRD relation. But a nova with M_B^max -8.5 in the Virgo cluster (m - M 31.5) reaches B +23 at maximum light; novae much fainter than this cannot be followed the requisite 2 mag of fading, because of the bright background against which they are observed.

Nova light curves show a wealth of detail, and few if any are characterized by a simple linear decrease in magnitude. This irregularity poses several problems. Novae frequently have secondary outbursts; such outbursts can be confused with primary maxima if only a limited time series of observations is available (as is the case for most observations of distant novae). Unusual objects (such as the Mould et al. [1990a] object) might be flagged with an extensive time series of data; but with limited observations, such phenomena may be misidentified as normal novae.

To illustrate the internal errors that result in using novae to determine the distance scale, we take the specific case of the determination of the distance modulus of the Virgo cluster (Pritchet and van den Bergh 1987a) as an example.

(ii) Photometric errors: typically ± 0.05 to ± 0.10 mag, (3.6 meter telescope, 0.9 arcsec seeing, 1 hour exposures).

(ii) Errors in the determination of mdot: generally less than 10%, resulting in errors in distance modulus less than 0.1 mag.

(iii) Errors due to missed maximum light: A correction is made to remove the systematic bias resulting from missing maximum light. This correction is typically in error by ± 0.05 to ± 0.5 mag, depending on the speed of the nova.

(iv) Errors in absorption towards Virgo: ± 0.04 mag (blue light) is assumed throughout this entire review.

(v) Errors in d(M31): ± 0.1 mag assumed throughout this article.

The most important external error is the bias that is introduced because of the way in which the Virgo cluster light curves are sampled (compared with the M31 light curves). This bias has been estimated by Pritchet and van den Bergh (1987a) to be about 0.2± 0.1 mag on the basis of extensive Monte Carlo simulations.

It is difficult to know how to combine the above errors into a meaningful total error, since some of the errors are rms deviations, whereas others are``estimated'' peak-to-peak errors. A reasonably conservative total uncertainty appears to be ± 0.4 mag (cf. Pritchet and van den Bergh 1987a).