Astr 2320 Tues. March 7, 2017 Today s Topics Chapter 13: Stars: Binary Stars Determination of Stellar Properties vi Binary Stars Classification of Binary Stars Visual Binaries Both stars visible Only one star visible Spectroscopic Binaries Radial Velocity Curves Mass Function Eclipsing Binaries Light Curves Stellar Radii Contact Binaries Interferometic Stellar Diameters and Effective Temperatures Lunar Occultations Stellar Interferometers 1
Chapter 13 & 14 Homework Chapter 13: #2, 3, 5, 6, 8 (Due Tues. March. 7) Chapter 14: #1, 3, 5, 6, 7 (Due Tues. March 21) 2
Importance of Binary Stars Binary stars provide the primary means for determining the physical properties of stars. Classification of Binary Stars Visual Binaries Based upon visible motion of the stars Spectroscopic Binaries Based upon radial velocity variations of the stars Eclipsing Binaries Based upon brightness variations of the stars 3
Motion of Binary stars Newton s form of Kepler s 3 rd law for planets: 2 2 4π P = GM a Modified form when mass of planet gets very large P 2 = G( M 3 2 4π 3 + a A M B ) 2 3 4π a M A + M B = 2 G P For binary stars we consider the motion of both stars about the center of mass. Note that the period and semi-major axis alone only give the sum of masses. From our text: Horizons, by Seeds 4
Visual Binaries Classes of Binary Stars Stellar mass determined via movement of both stars Spectroscopic Binaries Stellar motion inferred from radial velocity of one or both stars Eclipsing Binaries Orbital motion along line of sight such that stars undergo eclipses. 5
Visual Binaries Both stars visible: Ideal but rare Modeling to de-project orbits mass ratio from each orbit sum of masses from period. Two equations, two unknowns yield both masses Brightnesses + parallax give luminosities One star visible: More common Only sum of masses 6
Spectroscopic Binaries Only combined light visible Spectra reveal radial velocity variations Orbital projection is generally unknown but in principle: One set of lines yields sum of masses. Two sets of lines yields mass ratio: m 1 v 1 = m 2 v 2 m 1 /m 2 = v 2 /v 1 If also eclipsing (see below) the orbital inclination is ~ 90 o 7
Eclipsing Binary Stars Eclipses place strong constraint on orbital inclination All eclipsing binaries are also spectroscopic binaries Additional Info. Obtained: Radii of stars (relative to orbit, see text) relative surface brightness area hidden is same for both eclipses drop bigger when hotter star hidden ΔL = σt 4 8
Measuring Stellar Diameters - I Lunar Occultations Shape of diffraction pattern can be modeled to reveal stellar angular diameters Rare since star must be occulted and be close enough for parallax 9
Measuring Stellar Diameters - II Michaelson Interferometer Visibility of fringes falls as the interferometer resolves the star Only a few stars near enough for ground-based measurements Future space-based interferometers may provide considerably more Intensity Interferometer Two telescopes used to correlate fluctuations in the number of photons. Correlation falls if separation resolves star Many stellar diameters have been measured via this technique 10
Chapter 14: Stars The Hertzsprung-Russell Diagram Today s Topics Stellar Atmospheres Physical Characteristics Temperatures Spectral Line Formation Classifying Stellar Spectra Spectral Classification Sequence Temperature Sequence Hertzsprung-Russel Diagram Magnitudes vs. Spectral Type Magnitude vs. Color Luminosity Classification Elemental Abundance Effects Distances and the H-R Diagram 11
Stellar Atmospheres Radiative Transfer of photons from deeper layers must be modeled Scattering effects complicated Given density profile temp, pressure vs. depth Spectral Line Formation Given physical properties vs. depthsolve Boltzman and Saha Equations Most of the atomic elements» Requires huge list of ionization energies» Requires huge list of spectral lines and transition probabilities Compute strength and broadening for each line Result is a model stellar atmosphere 12
Classification of Stellar Spectra O B A F G K M scheme Originally in order of H strength A,B,etc Above order is for decreasing temperature Standard mnemonic: Oh, Be A Fine Girl (Guy), Kiss Me Use numbers for finer divisions: A0, A1,... A9, F0, F1,... F9, G0, G1,... From our text: Horizons, by Seeds 13
What Causes the Stellar Spectral Sequence? Saha Equation models the ionization state of the atomic elements. Boltzman Equation describes the collisional excitation of each element/ ion. Both depend on temperature and pressure. Atomic Physics describes the transition probabilities of each atomic level and strength of the corresponding spectral line. 14
Composition of Stars Atomic Physics (Quantum mechanics + Boltzman Equation) Regular pattern: More of the simplest atoms: H, then He,... Subtle patterns later related to nuclear fusion in stars 15
Stars of Different Temperature Hotter stars are bluer, cooler stars are redder. The temperature can be measured using only a small number of broad filters. The original Johnson system included the U, B, and V filters. Kron and Cousins extended these to redder colors detectable with CCDs. l Note that the B-V color is a good tracer whereas U-B is not. 16
Stellar Abundances Given an accurate stellar atmosphere model Lines of individual ions can be matched in a self-consistent way All ionization states of an element summed to yield abundance Abundance varied and the atmospheric model recomputed until lines are reproduced to yield elemental abundance 17
Hertzsprung-Russell (H-R) Diagram Plot of Luminosity and Temperature of Nearby Stars Reveals H-R Diagram Most stars found on the main sequence. Giants and Supergiants White dwarfs From our text: Horizons, by Seeds 18
Lines of constant Radius in the H-R diagram Main sequence not quite constant R B stars: R ~10 R Sun M stars: R ~0.1 R Sun l Betelgeuse: R~ 1,000 R Sun Larger than 1 AU White dwarfs: R~ 0.01 R Sun A few Earth radii From our text: Horizons, by Seeds What causes the main sequence? Why similar size, with precise R related to T? Why range of T? Why are a few stars (giants, 19 white dwarfs) not on main sequence?
Luminosity Classes Ia Bright supergiant Ib Supergiant II Bright giant III Giant IV Subgiant V Main sequence star white dwarfs not given Roman numeral Sun: G2 V Rigel: B8 Ia Betelgeuse: M2 Iab From our text: Horizons, by Seeds 20
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Masses and the HR Diagram Main Sequence position: M: 0.5 M Sun G: 1 M Sun B: 40 M sun Luminosity Class Must be controlled by something else From our text: Horizons, by Seeds 22
The Mass-Luminosity Relationship L = M 3.5 Implications for lifetimes: 10 M Sun star Has 10 mass Uses it 10,000 faster Lifetime 1,000 shorter From our text: Horizons, by Seeds 23
What fundamental property of a star varies along the main sequence? T and R vary smoothly (and together) along the main sequence B stars are ~4 times hotter and ~10 times Sun s mass M stars are ~2 times cooler and ~10 times lower mass Presence of a line implies that a single fundamental property is varying to make some stars B stars and some stars M stars That fundamental property then controls T, R A second property controls whether we get a giant or dwarfs Fundamental properties that determine stellar properties (Russell-Voit Theorm) Composition: Composition of stars varies Age: Will be important Mass: Turns out to be the most important parameter 24
H-R Diagram of the Brightest vs. the Nearest Stars 25
Chapter 13 & 14 Homework Chapter 13: #2, 3, 5, 6, 8 (Due Tues. March. 7) Chapter 14: #1, 3, 5, 6, 7 (Due Tues. March 21) 26