VARIABLE STARS
191
i
Using (129-11) and (129-12) this becomes
Y — 1 P ° T ° ( pl + + = (p““! Po T o + Pi (129-3).
Or since N Po T 0 = pp 0 , i a T 0 * = ( 1 - ft P 0 ,
jp ]_ + 12 (1 — /2)j T x = {/2 -f- 4 (1 — /2)} pj (129-4).
Also by (129-11)
A = ß (Pi + T x ) + 4 (1 - /3) T x
= ßPi + (4 — 3/2) T x .
Hence by (129-4) P x = yp 1
where 7 = £ +
This can be reduced to
(4 - 3ft) 2 (F - 1)
/5 + 12 (F — l) (l-/3)
.(129-51),
.(129-52).
r-f
We have also
4 - 3 _j8
1 + 12 (F - 1) (l-ß)lß
y — ß
Ti =
(129-6).
Pi (129-7).
4—3/2
If we write by analogy with the usual equation for matter without
radiation
T 1 = (y'-l) Pl (129-75),
we have y' - f = (y - f)/(4 _ 3/2) (129-8).
Here y is the effective ratio of specific heats for the pressure-density
relation and y for the temperature-density relation. As the mass of the
star increases and /2 diminishes, y approaches f more rapidly than y.
In considering a star compressed by pulsation our first impulse is to
compare it with a star which has undergone slow contraction in the course
of evolution; but in the latter case T varies as p%, whereas in the former
Table 28.
Effective Ratio of Specific Heats.
l-ß
Values of y
Values of (ya)t
r=i|
r=4
r=if
r=4
r=if
r=i|
•20
1-410
1-467
1-511
•478
•632
•730
•30
1-398
1-443
1-476
•439
•573
•655
•35
1-392
1-433
1-462
•421
•546
•621
•40
1-387
1-423
1-449
•401
•519
•589
•45
1-382
1-414
1-437
•382
•493
•558
•50
1-377
1-406
1-426
•363
•466
•527
•60
1-368
1-390
1-405
•321
•412
•464
•70
1-359
1-375
1-386
•277
•353
•397
•80
1-350
1-361
1-368
•225
•286
•321