Stellar Structure

Section 1: Basic Ideas about Stars

Lecture 1 – Observed properties of stars

Relationships between observed properties

Outline of the life history of a star

Introduction

A star is: a “vast mass of gas”

self-gravitating

supported by internal pressure

self-luminous

Some questions:

source of pressure?

energy source?

do they stay hotter than surroundings?

how long do they live?

Real and ideal stars

Ideal stars are:

• isolated

• Spherical

Real stars may be:

• Embedded in gas and/or dust

• In a double or multiple star system

• Connected to surrounding gas by

magnetic field lines

• Rotating rapidly

Factors affecting observational properties of stars

Observed appearance depends on:

• Distance (and any gas/dust in the way)

• Initial mass

• Initial chemical composition

• Current age

How do we measure observed properties?

Distance measurement

Direct: trigonometric parallax

Earth (January)

Earth (July)

Sun

Distantstars

Nearby

starp

p = ‘parallax’ 0.76 arcsec

1 AUd

d = 1 parsec (pc) when p = 1 arcsec

d(in pc) = 1/p(in arcsec)

Light output

Deduce luminosity L (total power output) from

flux density F (Wm-2) measured on Earth and

distance d (when known): L = 4πd2F.

Spectrum gives surface temperature (from

overall shape of continuum – best fit to a black

body) and chemical composition (from relative

strengths of absorption lines).

Mass and Radius

Mass:

• Directly, only from double star systems

• Indirectly, from surface gravity (from spectrum) and radius

Radius:

• Interferometry

• Eclipse timings

• Black body approximation: L = 4π Rs2 Ts

4, if L, Ts known.

Can also define the effective temperature Teff of a star by:

L 4π Rs2 Teff

4

Typical observed values

0.1 M < M < 50 M

10-4 L < L < 106 L

10-2 R < R < 103 R

2000 K < T < 105 K

Stellar magnitudes

Hipparchus (~150 BC):

6 magnitude classes (1 brightest, 6 just visible)

Norman Pogson (~1850): defined apparent magnitude m by

m = constant – 2.5 log10F ,

choosing constant to make scale consistent with Hipparchus.

Absolute magnitude M is defined as the apparent magnitude a star

would have at 10 pc. If D = distance of star:

M = m – 5 log10(D/10pc).

[We can hence also define the distance modulus m-M by:

m - M = 5 log10(D/10pc).]

Relationships: Hertzsprung-Russell diagram (HRD)

Relation between absolute magnitude and surface temperature

(Handout 1):

• Dominated by main sequence (MS) band (90% of all stars)

• Giants & supergiants (plus a few white dwarfs): ~10%

• L R2 – so most luminous stars are also the largest

Either:

• 90% of all stars are MS stars for all their lives Or

• All stars spend 90% of their lives on the MS

Relationships: Mass-luminosity relation (MS stars)

• Strong correlation between mass and luminosity (Handout 2)

• Main-sequence stars only

• Calibrated from binary systems

• Slope steepest near Sun (L M4)

• Less well-determined for low-mass stars (hard to observe) …

• … and high-mass stars (rare)

Indirect ways of finding stellar properties

• Spectrum: absorption line strengths depend on

Chemical composition

Temperature

Luminosity

• Chemical composition similar for many stars …

• … so Teff, L can be deduced

• Variability:

• some pulsating variables show period-luminosity relation

• Measure P L M; plus measure m distance

Star clusters

Gravitationally bound groups of stars, moving together

Globular clusters:

• compact, roughly spherical, 105-106 stars;

• in spherical halo around centre of Galaxy

Galactic (or open) clusters:

• open, irregular, 102-103 stars;

• concentrated in plane of Galaxy

Small compared to distance all stars at ~same distance

Apparent magnitude/temperature plot gives the shape of the HR

diagram

Globular cluster HR diagrams(Handout 3)

All globular cluster HR diagrams are similar:

• short main sequence

• prominent giant branch

• significant horizontal branch (containing RR Lyrae variables)

Find distances by comparing apparent magnitudes of

• main sequence stars

• red supergiant stars

• RR Lyrae variable stars

with those of similar nearby stars of known absolute magnitudes

Galactic cluster HR diagrams(Handout 3)

Much more variety, but all diagrams show

• Dominant main sequence, of varying length

• Some giant stars, in variable numbers

If all main sequences are the same (i.e. have the same absolute

magnitude at a given temperature), then can create a composite

HR diagram (Handout 3) – plausible if all stars formed at same

time out of same gas cloud same age and composition

Then find distances to all, if know distance of one, by this “main-

sequence fitting” procedure

Mean MS is narrow – suggests it is defined by a single parameter

– the mass increases from faint cool stars to hot bright ones

Life history of stars: Birth

Interstellar cloud of dust and cool gas:

• Perturbed by external event: self-gravity starts contraction

• If spinning, contraction leads to faster spin

• High angular momentum material left behind in disc

• Disc may form planets, and may also eject jets

• Central blob radiates initial isothermal collapse

• When blob opaque, radiation trapped and temperature rises

• Thermal pressure slows collapse

• “Proto-star” – hot interior, cool exterior

• Contraction releases just enough energy to balance radiation

Life history of stars: Energy sources

Gravitational energy, from contraction – if sole energy source for

Sun (Kelvin, Helmholtz, 19th century), then timescale ~ E/L where

E = gravitational energy of star, L = luminosity:

tKH = GM2/LR ~ 3107 yr for Sun.

But geology requires much longer timescale – only nuclear fuel

provides this; nuclear binding energy releases up to ~1% of rest

mass energy: EN ~ 0.01Mc2, so

tN ~ 0.01Mc2/L ~ 1.5 1011 yr for Sun.

Over-estimate, because not all mass of Sun is hot enough to be

transformed. Strong mass dependence, because L M4 – so, for

50 M, tN ~ 108 yr – massive stars were born recently.

Life history of stars: Life and death

• Proto-star contracts until centre hot enough for hydrogen to fuse to helium

• Nuclear energy source enough to balance radiation, and contraction ceases (no more need for gravitational energy)

• Very little change for a nuclear timescale – i.e. until nuclear fuel exhausted

• Series of phases of alternating contraction (releasing gravitational energy until centre hot enough) and further nuclear reactions (helium to carbon, etc, possibly up to iron)

• After all possible nuclear fuels exhausted, star contracts to a dead compact object: white dwarf, neutron star or black hole.