galaxies:
individual (M31)novae,
cataclysmic variables
L48, 1997 September 20
We use a Monte Carlo technique together with a simple model for the distribution of dust in M31 to investigate the observability and spatial distribution of classical novae in M31. By comparing our model positions of novae to the observed positions, we conclude that most M31 novae come from the disk population, rather than from the bulge population as has been thought. Our results indicate that the M31 bulge-to-disk nova ratio is as low as, or lower than, the M31 bulge-to-disk mass ratio.
Subject headings: dust, extinctiongalaxies:
individual (M31)novae,
cataclysmic variables
1 Department of Physics, Southwestern Oklahoma State University, Weatherford, OK 73096.
Opinions about the spatial distribution of classical novae in M31 and in our Galaxy have been undergoing an interesting evolution. The major searches for novae in M31 (Hubble 1929; Arp 1956; Rosino 1964, 1973; Rosino et al. 1989) showed that in a general sense novae are distributed like the light of the galaxy. Ciardullo et al. (1987) and Capaccioli et al. (1989) concluded that novae in M31 belong overwhelmingly to the bulge population. By analogy, it is often assumed that Galactic novae also come mainly from the bulge; for example, Della Valle & Duerbeck (1993) and Della Valle & Livio (1994) assume that three-fourths of the Galactic novae are from the bulge.
Doubts about the bulge dominance of the
M31 nova population arose when Ciardullo et al.
(1990) combined the results of their search for novae in NGC 5128 with
data on novae in the LMC, SMC, M33, M31, and a few elliptical galaxies in
the Virgo cluster. They found the nova rates per unit K-band
luminosity to be remarkably
similarapart
from a strikingly low rate for the M31 disk. They suggested that since the
M31 bulge has been more thoroughly searched for novae than its disk and
since disk novae may be preferentially obscured by dust, it is possible
that the nova rate in the M31 disk had been underestimated and that the
nova rate per unit mass of old stellar population may be approximately
constant. Recently, Shafter, Ciardullo, &
Pritchet (1996) report that their search for novae in three more
galaxies, M51, M101, and M87, has produced preliminary results that are
consistent with this proposition.
Another point of view that has developed recently is that young populations are better than old populations at producing novae. On the basis of observation, Della Valle et al. (1994) concluded that bulge-dominated galaxies (NGC 5128, M31, M81, and Virgo ellipticals) have a nova rate per unit H-band luminosity that is more than a factor of 3 lower than that of nearly bulgeless galaxies (LMC and M33). In addition, on the basis of a binary star population synthesis study, Yungelson, Livio, & Tutukov (1997) predict that the nova rate per unit mass of a young population should be much higher than that of an old population. Yungelson et al. find support for that prediction in the nova rates per unit K-band luminosity in the galaxies mentioned above, and they suggest that the apparent dominance of bulge novae in our Galaxy may be due to observational selection effects that favor the discovery of bulge novae over disk novae.
Recently we
(Hatano et al. 1997b) have used a Monte
Carlo technique together with a simple model for the distribution of dust
in the Galaxy to investigate the observability and spatial distribution of
Galactic classical novae. We concluded that most Galactic novae are indeed
produced by the disk, rather than by the bulge. More specifically, we found
the distribution of nova apparent magnitudes and positions on the sky to be
consistent with the proposition that the Galactic bulge-to-disk nova ratio
is equal to that of the overall Galactic bulge-to-disk mass ratio, which is
only about
1
7
(van den Kruit 1990). In this Letter we
report results of a study which set out to address the question of whether,
similarly, the M31 bulge-to-disk nova ratio is consistent with the M31
bulge-to-disk mass ratio.
Since about 1917, more than 300 novae have been discovered in M31. We concentrate on 191 novae that were discovered (or reported) in major surveys carried out at Mount Wilson (Hubble 1929; Arp 1956) and at Asiago (Rosino 1964, 1973; Rosino et al. 1989) and for which estimates of the peak apparent magnitude, B, are available.
Figure 1
shows the positions on the sky of these novae, on the coordinate system
of Capaccioli et al. (1989). At the adopted distance to
M31 of 725 kpc
(
=
24.3),
6
corresponds to about 1 kpc. We take M31 to be inclined by 77° and the
bulge to be an oblate ellipsoid with an axial ratio of 0.63
(Hodge 1992). The small oval in
Figure 1 has a semimajor axis of
18
(about 3 kpc) and defines
the 
apparent
bulge
;
apparent bulge novae are those for which the sky positions are within the
apparent bulge, and apparent disk novae are those for which positions are
not. As discussed below, some of the apparent bulge novae actually are disk
novae. The larger ellipse in Figure 1 corresponds to a
circle in the disk, of radius 8.8 kpc (where, as described below, the
density of the dust peaks in our model). We note that a great deal of disk
is projected within the apparent bulge. Open and filled circles denote
novae having B < 17 mag and B > 17 mag, respectively. The
top panel of Figure 2 shows the B
distributions for the 167 apparent bulge novae, the 24 apparent disk novae,
and the sum of the two. (For comparison, the shape of our model B
distribution, to be discussed below, also is shown in
Fig. 2, top.)
Fig. 1 
Fig. 2
The Monte Carlo technique that we have
developed was inspired by one that was used by
Dawson & Johnson (1994) in their study
of the observability of historical supernovae in our Galaxy. We
(Hatano, Fisher, & Branch
1997a) constructed an independent Monte Carlo code and used it to
extend the work of Dawson and Johnson by considering the observability of
hypothetical ultradim
supernovae in the Galaxy and to consider the observability of supernovae,
in the model, from an external point of view. Then Hatano
et al. (1997b) extended the technique to consider the observability of
Galactic classical novae. Here we give a brief description of the model as
it is used for this study of novae in M31.
In our previous papers, the Galactic dust
was assumed to follow a double exponential law, with a radial scale length
of 5 kpc and a vertical scale height of 0.1 kpc. In such a model, the
density of the dust peaks right at the center of the Galaxy. In M31,
however, the density of the dust is known to peak well out in the disk, not
far from where most of the current star formation rate is taking place
(Hodge 1992). Following Figure 3 of
Xu & Helou (1996), we adopt a simple
distribution for the radial dependence of the extinction in M31:
where AB is the total line-of-sight extinction
through the inclined disk of M31. This distribution is generally consistent
with the various evidence for the radial dependence of extinction discussed
by Hodge (1992). The vertical scale height of the dust
is again taken to be 0.1 kpc. In this model, the extinction at r =
8, z = 0 kpc is 1.85 mag kpc-1, similar to its value at
r = 8, z = 0 kpc in our Galactic model, 1.9 mag
kpc-1. The major difference between our adopted distributions of
dust in the Galaxy and in M31 is the low dust content in the central
regions of M31.
We assume that disk novae in M31 obey a
double exponential distribution, with radial and vertical scale lengths of
5 and 0.35 kpc, and the disk is truncated at r = 20 kpc. Bulge novae
are taken to be distributed as (R3
+ a3)-1, where R is a radial
coordinate, R2 = r2 +
z2 , and a = 0.7 kpc. Our conclusions do not
depend on the particular form of this distribution. The bulge is truncated
at r = 6.4 kpc, which gives an effective bulge radius of 2.1
kpc (Hodge 1992). For Galactic novae, we used
a bulge-to-disk nova ratio of
17,
based on the estimated bulge-to-disk mass ratio of the
Galaxy (van der Kruit 1990). For M31, a more reasonable
estimate of the bulge-to-disk mass ratio would
be 12
(Hodge 1992; Kent
1989), so we adopt this as our default value of the M31 bulge-to-disk
nova ratio.
The M31 nova luminosity functions are the
same as we used for novae in our Galaxy. They are Gaussian, with
dispersions 
(MB)
= 1, and the mean absolute magnitudes of disk and bulge novae are -8 and
-7, respectively.
Figure 2
(middle) shows our model B distributions for true bulge
novae, true disk novae (we do know which model novae are from the
disk and which are from the bulge), and the sum of the two. As can be seen
in Figure 2 (top), the total model B
distribution agrees well with the observed B distribution on its
bright side, to B
16.5.
The model distribution contains a larger proportion of faint novae than the
observed distribution. This is due at least in part to observational
selection against faint novae (many faint observed novae had to be excluded
from our sample because no estimate of peak B was available), but it
may also be that our adopted luminosity functions contain too many
intrinsically dim novae; in any case, this will not affect our main
conclusion because it will be based only on the brighter novae. We note
that in the mean, the true disk novae are brighter than the true
bulge novae. Figure 2 (bottom) is like the middle
one, except that now the model novae are divided into apparent disk
and apparent bulge novae. Because of the presence of true disk novae
masquerading as apparent bulge novae, the difference between the B
distributions of the apparent disk and apparent bulge novae is smaller than
the difference between the B distributions for the true disk and
true bulge novae. In Figure 2 (middle) almost all
of the bright novae are true disk novae, but in the lower panel, many of
those true disk novae become apparent bulge novae. In addition, even though
our input model bulge-to-disk nova ratio is
only 12,
the number of apparent bulge novae rivals the number of apparent disk
novae. Therefore, according to our model, a substantial fraction of the
apparent bulge novae in M31 actually are disk novae.
Some insight into what is going on (at least in the model) can be gained from Figure 3, which shows a side view of the spatial distribution of model novae having B < 20 mag; for clarity, the vertical scale is expanded by a factor of 5. First, many true disk novae having r < 10 kpc are seen as apparent bulge novae. Second, while true bulge novae on the top side of the bulge are practically unextinguished, from our vantage point, true bulge novae on the bottom are significantly extinguished by dust that is well out in the disk, where the extinction is largest. This means that true bulge novae projected onto the top of the bulge are, in the mean, brighter than those projected onto the bottom. As can be inferred from Figure 3, the B distributions of true disk novae (top and bottom) show a much milder difference.
Fig. 3
Figure 3 suggests that
the actual M31 bulge-to-disk nova ratio can be estimated by looking at the
bottom-to-top ratio (the BTR) of apparent bulge novae
and
thus avoiding the issue of the extent to which the bulge has been searched
more thoroughly than the disk. Because Figure 2 shows
that our model B distribution only fits the observed
B distribution on its bright side, we now confine our attention to
novae having B < 17 mag. The BTR of observed apparent bulge
novae having B < 17 mag (see Fig. 1) is 0.83
± 0.15, where the uncertainty is
from N12
statistics. The bottom panel of Figure 4
shows the model distribution of the sky positions of novae having B
< 17 mag. As expected, true disk novae show a mild asymmetry with
respect to the major axis, while true bulge novae are strongly concentrated
to the top. The top panel of Figure 4 is for an adopted
bulge-to-disk ratio of nine, instead of
12, i.e.,
for the case in which M31 novae are overwhelmingly from the bulge. For the
model bulge-to-disk ratio of
12 (Fig.
4, bottom), the BTR of apparent bulge novae is 0.63. For the
bulge-dominated case (Fig. 4, top) the BTR ratio
of apparent bulge novae is only 0.33, and the disagreement with the sky
positions of observed novae having B < 17
mag (Fig. 1) is obvious.
Fig. 4
The assumption that M31 novae come overwhelmingly from the bulge, together with our simple model, produces results that are inconsistent with observation. Instead, adopting an M31 disk-to-bulge nova ratio that is like the M31 disk-to-bulge mass ratio produces results that are acceptable. This would be consistent with the proposition that the nova rate per unit K-band luminosity is approximately constant (Ciardullo et al. 1990; Shafter et al. 1996).
If we take our model literally we can
derive the bulge-to-disk nova ratio that actually reproduces the observed
BTR of 0.83 ± 0.15. Figure 5 shows the
dependence of the model BTR on the percentage of true bulge novae for three
different degrees of
dustinessour
standard case, as described by equations (1) and (2); twice as dusty; and
half as dusty. Our standard model does not require any bulge novae to
reproduce the observed BTR of 0.83; within the statistical uncertainty of
the observed BTR, the upper limit on the percentage of bulge novae is
about 25%, i.e., a bulge-to-disk nova ratio of 0.33. This would
be consistent with the proposition that young populations are better
at producing novae than old populations (Della Valle et
al. 1994; Yungelson et al. 1997). However,
Figure 5 shows that if M31 is only half as dusty as we
have assumed (see Han 1996), then our upper
limit on the percentage of bulge novae would be about 60%, i.e., a
bulge-to-disk nova ratio of 1.50. In view of the statistical uncertainties
associated with the observed BTR and with our simple model, it probably
would be premature to draw any conclusion other than that the M31
bulge-to-disk nova ratio is at least as low as the M31 bulge-to-disk mass
ratio.
Fig. 5
Now, in order to advance our knowledge of the spatial distribution of novae in M31, what is needed is a carefully controlled search for novae that includes parts of the disk that are unambiguously outside the bulge. It is interesting that of eight M31 novae that were discovered in a recent search by Sharov & Alksnis (1996), only three qualify as apparent bulge novae. As we completed this study we learned that another major search for novae in the disk of M31 is planned (A. Shafter 1997, private communication).
We are grateful to Eddie Baron, Darrin Casebeer, Dean Richardson, and Lev Yungelson for discussions, and to Allen Shafter for correspondence. This work has been supported by NSF grants AST 9417102 and 9417242.
. 1973,
A&AS, 9, 347 First citation in article | NASA ADS Note added in proof.We
are indebted to George Jacoby for asking a question that led us
to recognize that equations (1) and (2) apply not to the B band but
to the V band. This means that we used only three-fourths of the
extinction implied by the results of Xu & Helov
(1996). Using the full amount only would have strengthened our
conclusion that the bulge-to-disk nova ratio is low.
Full image (23kb) | Discussion in text
FIG.
1.Sky
positions of 191 novae observed in M31, for which estimates of
peak B are available. The M31 major and minor axes are along
the X and Y axes, respectively. The large ellipse represents
a circle in the inclined disk, of radius 8.8 kpc. Open and filled circles
denote novae having B < 17 mag and B > 17 mag,
respectively.
Full image (22kb) | Discussion in text
FIG.
2.Top:
the B distribution of observed novae in M31; long-dashed line is for
apparent disk novae, short-dashed line is for apparent bulge novae, and
solid line denotes the sum of the two. The highest curve is our model
B distribution. Middle: the model B distributions for
true disk novae (long-dashed line), true bulge novae
(short-dashed line), and their sum. Bottom: as in the middle
panel, but for apparent disk and bulge novae.
Full image (24kb) | Discussion in text
FIG.
3.Side
view of the model spatial distribution of novae in M31. For clarity, the
vertical scale is expanded by a factor of 5. The ellipse shows where the
bulge is truncated. Filled and open circles denote true bulge and true disk
novae, respectively. Large, medium, and small symbols denote B <
16 mag, 16 
B
18 mag, and B
18 mag,
respectively. The widths of the diamond-shaped figures indicate the adopted
radial dependence of the dust density (not its vertical scale height). Our
view is from the upper right; the apparent bulge is within the outermost
slanted lines. True bulge novae in the bottom of the bulge are extinguished
by dust that is located well out in the disk.
Full image (34kb) | Discussion in text
FIG.
4.Bottom:
sky positions of model M31 novae having B < 17 mag, for our
standard bulge-to-disk nova ratio of
12.
Filled and open symbols denote true bulge and true disk novae, and large
and small symbols denote B < 16 mag and B
16 mag.
Top: as in the bottom panel, but for a bulge-to-disk nova ratio
of 9.
Full image (14kb) | Discussion in text
FIG.
5.The
model BTR is plotted against the percentage of bulge novae, for
our standard dust model (central slanted line), for twice as
dusty (lower slanted line), and half as dusty (upper
slanted line). Solid horizontal line represents the observed BTR of
0.83, and dashed horizontal lines represent the statistical lower and
upper limits, 0.68 and 0.98.