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           Distant stars Nearby star p p = ‘parallax’  0.76 arcsec 1 AU d 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 = 4πd 2 F. 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 R s 2  T s 4, if L, T s known. Can also define the effective temperature T eff of a star by: L  4π R s 2  T eff 4

Typical observed values 0.1 M  < M < 50 M  L  < L < 10 6 L  R  < R < 10 3 R  2000 K < T < 10 5 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 log 10 F, 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 log 10 (D/10pc). [We can hence also define the distance modulus m-M by: m - M = 5 log 10 (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  R 2 – 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  M 4 ) 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 T eff, 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, stars; in spherical halo around centre of Galaxy Galactic (or open) clusters: open, irregular, 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, 19 th century), then timescale ~ E/L where E = gravitational energy of star, L = luminosity: t KH = GM 2 /LR ~ 3  10 7 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: E N ~ 0.01Mc 2, so t N ~ 0.01Mc 2 /L ~ 1.5  yr for Sun. Over-estimate, because not all mass of Sun is hot enough to be transformed. Strong mass dependence, because L  M 4 – so, for 50 M , t N ~ 10 8 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.