Nov. 1, Continuing to mine the H-R diagram: Spectral Types Recall, the H-R diagram gives the range of Luminosty, L, and radius, R, of stars as dependent on the stars’ surface temperature, T The systematic range of color and thus temperature, T, is also revealed in the absorption line (and emission line) spectra. Spectral Types (O, B, A, F, G, K, M) are classes (derived at Harvard ( ) on the basis of presence/absence of particular absorption lines: from H (only; and also emission) in very hottest stars (O stars), to molecular bands in the very coolest (M stars) Spectral types also reveal the chemical composition of the stars and Cecelia Payne’s epoch discovery: Hydrogen is dominant element. The forest of “metal” lines in cooler stars is due to lower energy levels (higher up) being excited at lower temp. At higher temps, these levels are ionized (electrons stripped off)

Nov. 1, Variation of spectral lines with Sp. Type As illustrated nicely in your text, Tf17-11 and Tf17-12 (below), the line content varies considerably from O to M stars: Abs. Lines then become the key discriminators of what Sp. Type a star is since its color will be affected by interstellar absorption: dust in space is like dust in Earth’s atmosphere – causes reddening! Relative strength of absorption lines vs. Spectral type. Ca II or Fe II denote once-ionized Calcium and Iron ions, respectively. Molecules like TiO can form in outer atmosphere of M stars since they are so cool (~3000K!)

Nov. 1, Absorption lines also reveal Luminosity Class Absorption lines are formed near surface of the star and so are sensitive to the force of gravity, GMm/R 2 on each mass m (e.g. a single H atom producing the abs. line spectrum below) Since Giants (upper right of H-R diag.) have larger radii for their given mass, their gravitational Force on H atoms is weaker and so lines formed in lower pressure atmosphere and thus narrower for same Temp star and thus same Sp. Type: B8 Ia star (supergiant) vs. B8 V star (main sequence)

Nov. 1, So H-R diagram shows Sp. Type and Luminosity class Spectra of star (alone) thus gives both T and L; so can get distance (luminosity class) from spectroscopic parallax But in practice this requires high resolution spectra to measure line widths… Luminosity classes range from Ia (supergiants) to II (giants) to IV (subgiants) to V (main sequence) Main sequence stars differ in that only they are “burning” H in their cores; vs. He and heavier “metals” in cores of giants and supergiants

Nov. 1, The last key parameter: Stellar Mass We can measure masses of stars all thru the H-R diagram by picking out star of given Sp. Type and Lum. Class that happens to be in a binary system Use Kepler’s Laws to derive masses for both stars, M 1 and M 2, if know the inclination of the binary orbit (tilt with respect to our line of sight: i = 90 o means edge-on orbit). Recall that M 1 + M 2 = a 3 /P 2 Get M 1 separately from M 2 by measuring Doppler shifts in spectra to measure velocities V 1 and V 2 of each star orbiting at radii a 1 and a 2 about the center of mass (see Tf17-22) since V 1 /V 2 = M 2 /M 1. So now have values for both M 1 + M 2 and M 2 /M 1 and can solve for M 1 and M 2 separately Measure radii R 1 and R 2 of M 1 and M 2 by timing the eclipse duration of each star by the other (see Tf17-24)

Nov. 1, Putting it all together: L vs. M relation for main sequenc stars With now masses M derived (from binaries), as well as stellar radii (which check validity of BB spectral determination), we can finally see how stellar luminosity varies with stellar mass for main sequence stars: L ~ M 3.5 (see Tf17-21): This in turn will allow us to measure stellar lifetime on the main sequence, since lifetime (as for Sun) must depend on both L and M since lifetime ~(amount available to burn)/(rate of burning): Lifetime ~ M/L ~ M/ M 3.5 ~ 1/ M 2.5 So lower mass main sequence stars live longer!