Download Ast 405, Pulsating Stars The following is based Chapter 14 of the

Ast 405, Pulsating Stars
The following is based Chapter 14 of the book.
• 1. Stars whose brightness varies regularly due to some internal mechanism.
• 2. Examples are Miras, Cepheids, RR Lyraes, W Virginis, BL Her stars.
You shouyld be familiar with Table 14.1 in the book.
• 3. The Cepheid Period-Luminosity relation, or PL relation is of crucial
importance in Astrophysics.
• 4. The brighter the star, the longer its period of oscillation.
• 5. First observed in the LMC/SMC where the ”depth” of the LMC/SMC
is negligible compared to the distance of the LMC/SMC from Earth, i.e.
m − M = 5log(d) − 5.
Here since all the stars are at the same distance, d, then observing m, the
apparent magnitude, is like observing the absolute magnitude.
• 6. The absolute magnitude M is a logarithmic measure of the luminosity.
• 7. Examples of PL relations are
Mv = −2.81 log10 Pd − 1.43.
• 8. Note which is the slope and which is the intercept. The PL relation slope
and intercept varies with wavelength. So an example of the PL relation in
the H band is
MH = −3.234 log10 Pd − 16.079.
• 9. The PL relation is a simplified version of the Period-Luminosity-Color
(PLC) relation e.g.
MH = −3.428 log10 Pd + 1.54(J − K) + 15.637.
• 10. The pulsation hypothesis was developed by Arthur Eddington. The
Stefan Boltzmann law states that the luminosity of a star is
L = 4πσR2 Te4 ,
where σ is the Stefan-Boltzmann constant, R is the radius and Te is the
effective or surface temperature.
• 11. Hence the luminosity changes of a pulsating star are caused by surface
temperature and radius changes. Of these the temperature variation is
more important.
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• 12. Contracting gases heat up and expanding gases cool down according to
the ideal gas law. This is what is to be expected during an adiabatic change.
But pulsating stars generally are brightest when they are expanding through
their equilbrium radius. This is the phase lag for classical Cepheids and
RR Lyraes and is due to non-adiabatic effects in the outer parts of these
stars.
• 13. Stellar pulsation is an acoustic phenomenon relaying on the motion of
sound waves in the star. The speed of sound is
vs =
q
γP/ρ.
• 14. Thus an approximation to the period of oscillation in a pulsating star
is
Z R
dr
Π=2
,
0 vs
which simplifies to
Π ≈ ρ−0.5 .
• 15. Stars which have a high average density have shorter pulsation periods
than stars which have a low average density. Cepheids have a low average
density compared to RR Lyraes and thus pulsate with longer periods.
• 16. Stars pulsate when they go through the instability strip (IS) in the HR
diagram.
• 17. The blue and red egde of the IS refer to the hot and cool sides of this
strip respectively.
• 18. Parts of the horizontal branch are found in the IS.
• 19. Revise the terms fundamental and first overtone pulsators.
• 20. Pulsation amplitdues decrease toward the center of the star.
• 21. You can predict the existence of the Cepheid PL relation from the
Stefan Boltzmann law, the period-mean density theorem and the existence
of a mass-luminosity relation.
• 22. Cepheids are very important as distance indicators through the Cepheid
PL relation.
• 23. For some calibrating galaxy A, know Mv = a + b log P.
• 23. Assume this is universal.
• 24. Observe mv for Cepheids in galaxy B, the target galaxy.
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• 25.
mv − Mv = 5 log(d) − 5,
mv = a − 5 + 5 log(d) + blogP.
• 26. This is a linear relation, same slope but different intercept.
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