Astronomy Lecture number 16

Physics 321

Astrophysics II: Lecture #16

Prof. Dale E. Gary
NJIT

Pulsating and Variable Stars

Naming Variable Stars

Intrinsic Variables - Stars whose output actually varies (pulsating stars, erupting or explosive stars)
Extrinsic Variables - Stars that only appear to vary due to geometric effects (eclipses, etc.)

We will study intrinsic variables in this lecture, but variables of all types are lumped into a single naming scheme using capital letters within each constellation until they run out, then numbers, as follows, in order of discovery:

R - Z

RR, RS, ..., RZ, SS, ST, ..., ZZ First three give 334 names

AA, AB, ..., AZ, BB, BC, ..., QZ

V335, V336, ...

Some examples, R Monocerotis, T Tauri, RR Lyrae, UV Ceti, AG Pegasi, BF Cygni, V378 Orionis, V999 Sagitarii. Up to 1925, novae were given a name consisting of constellation and year, but after 1925 they are given variable names. (Why?) Thus, RR Pic and DQ Her are examples of nova names. Finally, a few variable stars are bright enough to have been given greek-letter or proper names, e.g. b Lyrae, Algol, Mira, d Cephei (well-known prototypes).

Some variable star light-curves (from the Hipparchos web pages)

R Cru Cepheid Variable
XX Ant Eclipsing (Algol-type) Variable
R Hya RR Lyra Variable

A Good Place to Read About Variable Stars

Pulsating Stars

The most important (i.e. useful) stars are Cepheid variables, named for prototype d Cephei. They show regular, periodic brightness changes, and spectral changes.

Observing d Cephei

The spectral changes show that the surface temperature and radius changes. The spectral lines also show doppler shifts, from which we can measure radial velocity changes--actually measure the star's outer layers expand and contract. Cepheids and other variables (RR Lyra stars are another important type) lie in a particular region in HR diagram. As low mass stars (0.5 to 0.7 M_sun) evolve and cross through this region, they become RR Lyrae variables. As high mass stars (3-18 M_sun) cross it, they become Cepheid variables. Properties:

RR Lyrae	Cepheid
mass 0.5 - 0.7 M_sun .	mass 3-18 M_{sun .}
Pop II	Pop I
Core He burning	Core He burning

Cause of pulsations--lack of hydrostatic equilibrium beneath surface. Here is the cycle:

Start with point of greatest compression, when T is greatest.
He is doubly ionized due to high T, i.e. is He⁺⁺ (He III).
Ionized He is transparent, so UV photons escape easily, but have overpressure.
Atmosphere expands and cools. He⁺⁺ becomes He⁺.
Opacity shoots upward and atmosphere absorbs UV photons.
UV photons "push" envelope outward, overshoots equilibrium.
Atmosphere falls back, temperature rises.
Before it reaches equilibrium, He⁺ becomes He⁺⁺, and extra source of support vanishes.
Atmosphere falls back rapidly, overshoots equilibrium--starts cycle over again.

Radius can change by up to 2-3 x 10⁶ km.

Table of Classes of Pulsating Variable Stars
(from Zeilik & Gregory--Intoductory Astronomy & Astrophysics)

Type	Prototype	M_V	Spectral Class	Pulsation Period Range	Characteristic Period
Classical Cepheids	d Cephei	-0.5 to -6	F6 to K2	1d to 50d	5d to 10d
Population II Cepheids	W Virginis	0 to -3	F2 to G6	2d to 45d	12d to 28d
RR Lyrae stars	RR Lyrae	0.5 to 1	A2 to F6	1.5h to 24h	0.5d
Long-Period variables	o Ceti (Mira)	1 to -2	M1 to M6	130d to 500d	270d
RV Tauri stars	RV Tauri	-3	G, K	20d to 150d	75d
Beta Canis Majoris stars	b Canis Majoris	-3	B1, B2	4h to 6h	5h
Semiregular red variables	a Herculis	-1 to -3	K, M, R, N, S	100d to 200d	100d
Dwarf Cepheids	d Scuti	4 to 2	A to F	1h to 3h	2h

Period-Luminosity Relationship

Why is any of this useful? The period of this cycle, from 1 to 50 days for Cepheids, is very precisely related to the luminosity (or absolute magnitude) of the star. For Pop I Cepheids (the kind in the disk of our galaxy)

M_V = -2.76(log P - 1.0) - 4.16

Thus, by careful measurement of the period, any Cepheid's absolute magnitude, and hence its distance, can be measured. Cepheid variables are a major link in the distance scale! Problems: Cepheids are rare, and none are nearby. Before Hipparchos, not a single one could be determined using trigonometric parallax.

Population II Cepheids

The Population I Cepheids that we just discussed are stars with relatively high metallicity (like our Sun) and so are "second generation" stars. Stars in globular clusters are low-metallicity "first generation" stars, and since the composition is different, the period-luminosity relation is also slightly different. These so-called Population II Cepheids are about 4 times less luminous than Population I Cepheids.

Measuring the distance to a nearby galaxy.

First determination that spiral "nebulae" are external galaxies.

RR Lyrae Variables
Another important type of variable is RR Lyrae stars. Their period-luminosity relationship is even simpler--they all have L ~ 100 L_sun, (that is, M_V = 0.5 = constant) regardless of period. They are fainter, and they are Pop II--important for globular clusters, but cannot be seen in external galaxies. They have relatively short periods of 1.5 - 2.4 h

Mira Variables
Large, irregular variations in brightness, due to cool (2000 K) atmosphere veiled by dust and molecules (absorption bands). Locally higher T dissociates the molecules and allows great increases in L. Periods are P ~ 100 to 700 days, and stars fall in HR diagram where He-shell burning is taking place. The exact mechanism is unknown.

Nonpulsating Variables

There are several other types of nonpulsating variables:

T Tauri stars - PMS objects of 0.2 to 2 M_sun with large winds, associated with dark clouds (link). Young objects that are rapidly rotation and nearly fully convective, with strong magnetic fields. Has strong "flares." The T Tauri phase of star formation is one limitation on formation of planets.
Flare stars - "solar-like" stars, rapid rotation plus deep convection -> magnetic fields. However, flares are a million times larger than solar flares, so not understood.
Magnetic variables - Ap stars (spectral type A, peculiar) show strong magnetic fields with average up to 0.1 T. Relatively small brightness changes may be star spots.
RS CVn (Canum Venaticorum) stars - double stars, very close together (orbital periods of 0.5 day to several months), probably magnetically interacting--strong flares, starspots. One of the stars is luminosity class V (main-sequence) and the other is IV (sub-giant).

Extended Stellar Atmospheres

Several types of stars show mass outflow. This outflow, coupled with stellar rotation in some cases, causes distinct spectral features due to doppler shifts. P-Cygni profile.

Cataclysmic Variable Stars

Table of Classes of Cataclysmic Variable Stars
(from Zeilik & Gregory--Intoductory Astronomy & Astrophysics)

Type	Time	Example	M_max	Dm	Energy per Outburst (J)	Cycle	Mass Ejected per Cycle (M_o)	Velocity of Ejection (km/s)	Mass of Star (M_o)
Supernova I		Tycho's	-20	>20	10⁴⁴		< 1	10,000	1
Supernova II			-18	>20	10⁴³		?	10,000	>4
Novae	Fast	GK Per = Nova Per	-8.5 to -9.2	11 to 13	6x10³⁷	10⁶ y ?	10^-5 to 10^-3	500 to 4000	1 to 5
	Slow	DQ Her	-5.5 to -7.4	9 to 11				100 to 1500	0.02 to 0.3
	Recurrent	T Cr B	-7.8	8	10³⁷	18 to 80 y	5 x 10^-6	60 to 400	2
Dwarf Novae		U Gem SS Cyg	+5.5	4	6x10³¹	40 to 100 d	10^-9		~0.4

We will talk about novae and supernovae next time, in connection with close binary systems. Some links to web pages that describe or give examples of these objects
are below.

Gamma Ray Bursts (Hypernovae?)