148
THE MASS-LUMINOSITY RELATION
these supply M sin 3 i and a sin i as in the case of Capella (§ 11); but
whereas for Capella i was found from the visual orbit, for V Puppis it is
found by analysis of the light-curve. It can generally be inferred that i is
near 90° for eclipsing variables since otherwise eclipses would not occur;
but in V Puppis and some other systems the separation is not large in
comparison with the radii of the components and a more trustworthy
estimate is needed. The method of analysing the light-curve is due to
H. N. Russell; it enables the quantities i and R/a to be found. Combining
these with M sin 3 i and a sin i, we obtain the values of M and R given
above.
We have
L = 7 tclcR^T* = 2-62.10 37 ergs per second,
which corresponds to bolometric magnitude — 4 m -75. Table 16 gives
Am = 1-63, so that the visual magnitude is — 3 m -12.
For comparison with this we shall calculate the magnitude from M by
the present theory. For M = 19-2, we find 1 — ¡3 — *597. Then L is
conveniently found by comparison with Capella, using the relation
L oc M° (1 — £)* T e \
L for V Puppis /19-_2\* /-597\* /19000N* .
sothat L for Capella ~ U*18/ V283/ V 5200 )
= 72-9 = 4-66 magnitudes.
Hence the absolute bolometric magnitude of V Puppis determined
from the observed M is
_ o m -40 - 4 m -66 = - o m -06
in satisfactory agreement with the determination — 4 m -75 from the
observed R.
Other details are—
Pm = '0618,
Pa = 3-35,
T c = 4-24.10 7 .
The comparison of theory and observation for V Puppis is of special
interest because it takes us as far as is yet possible in the direction of high
mass. It is known, however, that greater masses occur. J. S. Plaskett*
has found for the spectroscopic binary B.D. 6° 1309
M x sin 3 i = 75-6 0, M % sin 3 i = 63-3 O.
Since i is unknown the masses cannot be determined, but they are
necessarily greater than 75 and 63. In fact the masses are greater than
87 and 73 because i must be such that the two discs never overlap-—other
wise eclipses would be observed.
* Monthly Notices, 82, p. 447. It is pointed out that 29 Canis Majoris also has
a mass at least as great as that of V Puppis.
