Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mso.anu.edu.au/~wood/lectures2009/Pulsation_1.pdf Дата изменения: Thu Mar 26 12:54:24 2009 Дата индексирования: Tue Oct 2 05:06:02 2012 Кодировка: Поисковые слова: 3

ASTR 3007 - STELLAR PULSATION COMPONENT P e ter W o o d Research School of Astronomy & Astrophysics

TOPICS COVERED · Main types of variable stars · Linear adiabatic pulsation theory => periods of pulsation · Linear non-adiabatic pulsation theory => stability - will a star pulsate? · Some application of pulsation theory to real stars


LITERATURE SOURCES Cox, J P & Giuli, R T 1968, Principles of Stellar Structure, Volume 2 (most of this can be obtained via ADS in: Cox, J P 1974, Reports on Progress in Physics, 37, 563 ADS is at: http://adsabs.harvard.edu/abstract_service.html) Bowers, R L & Deeming, T 1984, Astrophysics (Vol 1, Chapter 11)


An example of pulsating stars: One night in the life of the globular cluster M3 - RR Lyrae variables Light varies by a factor of ~2. Brighter <=> bluer.


Hertzsprung-Russell diagram for the globular cluster M3 (very old, Population II)

RR Lyrae variables

Corwin & Carney (2001)


Two years in the life of the galaxy M33. Here we see Cepheids and long-period variables (LPVs) (movies from Hartman: http://cfa-www.harvard.edu/%7Ejhartman/)


WHY STUDY VARIABLE STARS? 1) Distance determination in the universe From Period - Luminosity laws 2) Mass determination a) Period - Mass - Radius relation From theory e.g. P = constant*R3/2M1/2 => Mass (P observed, R from photometry or spectra) b) Period ratios in multiperiodic pulsators c) Light curve shape e.g. bumps on light curves Can also give Luminosity, Radius, Reddening 3) Determination of rate of evolution From rate of P change 4) Determination of interior structure Asteroseismology (Helioseismology) - a rapidly growing field


The Hertzsprung-Russell diagram Where are the variable stars?


Variable stars in the HR-diagram
The Instability Strip

From Cox (1974), with modifications.


From Cox (1974)


What could cause the pulsation period to vary from star to star?
Think of a vibrating string: longer string => longer oscillation period more taught => shorter oscillation period What are the analogs of these properties in stars?


What could cause the pulsation period to vary from star to star?
Think of a string: longer string => longer oscillation period more taught => shorter oscillation period What are the analogs of these properties in stars? Radius


What could cause the pulsation period to vary from star to star?
Think of a string: longer string => longer oscillation period more taught => shorter oscillation period What are the analogs of these properties in stars? Radius Mass


PROPERTIES OF CEPHEIDS
Light and velocity curves Bumps Factor of 2 in light

40 - 60 km/s

Bersier (2002)


Cepheids occur where core He burning loops pass through the instability strip => Period - Luminosity relation Most evolutionary time spent at ends of loops => most common Cepheids M ~ 5 Msun Udalski et al (1999) Cox (1974) Two pulsation modes: fundamental (FU) & first overtone (FO)


How is distance determined from a period-luminosity (PL) law?
Galaxy 1 (m1, d1)

Magnitude

Galaxy 2 (m2, d1)

Log P Flux at distance d from a source is F(d) = f0/d2 apparent magnitude = constant - 2.5 log(F(d)) = constant - 2.5 log(f0/d2) = constant + 5 log(d) = M + 5 log(d(pc)/10) m1 ­ m2 = 5 log(d1) ­ 5 log(d2) = 5 log (d1/d2) We measure m1 ­ m2 from the observed PL relations. Knowing d2 => d1. We get relative distances.


Properties RR Lyrae variables
Corwin & Carney (2001)

RRab - sawtooth shape (FU) - amplitude ~1 mag Bailey types => RRc - more sinusoidal (FO) - amplitude ~0.2 mag RRd - simultaneous modes Blazhko effect - variable amplitude, beating of modes

B 50 - 70 km/s

Phase

Storm et al (1992)


Globular cluster M3 (very old, Population II) RR Lyraes occur where the Horizontal Branch (core He burning) lies in the Instability strip => NO Period - Luminosity relation. Instead, MV(RR Lyrae) ~ constant.

Corwin & Carney (2001)


The pulsating white dwarfs
T ype Other names Periods(s DAV ZZ Ceti variables 30-1200 DBV 30-2000 GW Vir PG 1159 stars 300-5000 ) T eff 11000-12500K 25000K 75000-200000K Atmosphere H He He, C, O

Multiperiodic => multiple simultaneously-excited modes The periods can only be those of nonradial g-modes (white dwarfs are so small that radial p-mode periods are too short)


The DB white dwarf GD358

Winget et al. (1982)


Pulsating red giants - the spectacular Mira variables
Omicron Ceti (Mira)

The first pulsating stars discovered (o Ceti ­ Fabricius 1596) The last to be explained (pulsation mode, stability,...)


Properties of Long Period Variables (LPVs) Wood et al (1999)
Wide variety of light curve shapes and amplitudes Mira variables Visual amplitude up to 8 mag

40 km/s Hinkle et al (1984)


They are Red giants Occur on the Asymptotic Giant Branch, and at small amplitude at the tip of the First (or Red) Giant Branch. Responsible for large amounts of mass loss (gas and dust in Planetary Nebulae). Wide age (mass) range.

Wood & Lattanzio (2004)

K

Ita et al (2002)

J-K


Red giants in the Large Magellanic Cloud

AB

C Mira variables C' D

Variable red giants show multiple period - luminosity sequences. Fundamental mode First overtone ? Binaries

E

Wood (2006), data from Fraser et al (2005)


Planetary Nebulae

Abell 39

Ring Nebula (M57)