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 Distant stars Earth (January) Nearby 1 AU d Sun p star Earth (July) p = ‘parallax’ 0.76 arcsec 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 Ts4, if L, Ts known. Can also define the effective temperature Teff of a star by: L 4π Rs2 Teff4 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 “mainsequence 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.