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Spectroscopy Lecture 10 Chemical analysis Stellar radii & temperatures ● Stellar spectra ● Abundances ● The Sun ● Examples: peculiar stars etc. ● Measuring Radii and Temperatures of Stars • Direct measurement of radii • Photometric determinations of radii • Determining temperatures – Speckle – Interferometry – Occultations – Eclipsing binaries – Bolometric flux – Surface brightness – Absolute flux – Absolute flux – Model photospheres – Colours – Hydrogen lines – Metal lines Stellar Radii To calculate R: Observe: ● parallax p => distance d = 1 / p ● spectral type or colour index => T ● apparent magnitude, e.g. V Stellar Diameters ● ● ● Angular diameters typically measured in milliarcseconds (mas) Angular diameter (in radians) given by physical diameter divided by distance Some diameters: Vega (3.2 mas), Sirius (5.99 mas), Aldebaran (21.1mas) Typical radii: Sun: R = 700000 km main sequence stars: R ~ 0.1 ... 10 RSun giants: R ~ up to 100 RSun supergiants: red: R ~ up to 1000 RSun blue: R ~ 20 – 50 RSun white dwarfs: R ~ 0.01 RSun Accurate radii Most accurate radii ( < 1% ) from eclipsing binary stars ● interferometry (for nearby stars) ● lunar occultations (for a few stars) ● Accurate R improves T via Speckle Diameters ● ● ● ● ● The diffraction limit of 4m class telescopes is ~0.02” at 4000A, comparable to the diameter of some stars The seeing disk of a large telescope is made up of the rapid combination of multiple, diffractionlimited images 2d Fourier transform of short exposures will recover the intrinsic image diameter Only a few stars have large enough angular diameters. Speckle mostly used for binary separations Interferometry ● 7.3m interferometer originally developed by Michelson ● Measured diameters for a few K & M giants ● Until recently, only a few dozen stars had interferometric diameters Other Methods ● ● Occultations – Moon used as knifeedge – Diffraction pattern recorded as flux vs. time – Precision ~ 0.5 mas – A few hundred determined Eclipsing binaries Homepage of Joachim Köppen: http://astro.ustrasbg.fr/~koppen/JKHome.html Eclipsing binary Eclipsing binary Photometry use filters (e.g. U, B, V, R, I) measure flux densities: fB, fV, ... apparent magnitudes: (B, V, ...) colour indices: absolute magnitudes (d from parallax): colours => Teff , log g Bolometric magnitude Mbol = absolute bolometric magnitude total flux over the entire spectrum Difficult to measure Mbol, easy to measure MV. Why spectra differ ● Line strengths change mainly due to surface temperature hot: high ionization and excitation cool: neutral atoms and molecules ● some line widths and ratios change with luminosity very little range of abundances ( 74% H, 24% He, 2% everything else) ● ... BUT ... some stars show pronounced abundance anomalies ! Curves of Growth Traditionally, curves of growth are described in three sections ● ● ● The linear part: – The width is set by the thermal width – Eqw is proportional to abundance The “ flat” part: – The central depth approaches its maximum value – Line strength grows asymptotically towards a constant value The “ damping” part: – Line width and strength depends on the damping constant – The line opacity in the wings is significant compared to κ ν – Line strength depends (approximately) on the square root of the abundance Determining Abundances ● ● ● ● Classical curve of growth analysis Fine analysis or detailed analysis – computes a curve of growth for each individual line using a model atmosphere Differential analysis – Derive abundances from one star only relative to another star – Usually differential to the Sun – gf values not needed Spectrum synthesis – Uses model atmosphere, line data to compute the spectrum Abundances ● [m/H] = log N(m)/N(H)star – log N(m)/N(H)Sun • [Fe/H] = 1.0 is the same as 1/10 solar • [Fe/H] = 2.0 is the same as 1/100 solar ● [m/Fe] = log N(m)/N(Fe)star – log N(m)/N(Fe)Sun • [Ca/Fe] = +0.3 means twice the number of Ca atoms per Fe atom Solar Abundances (Grevesse and Sauval) CNO Log e (H=12) 8 Fe 5 S r , Y, Zr Sc 2 Ba Li, Be , B Eu -1 10 20 30 40 50 Atomic Number 60 70 80 Recall: Solar abundances Element log N ∆NLTE 6 C 8.592+/0.108 0.045 7 N 7.931+/0.111 0.032 8 O 8.736+/0.078 0.028 10 Ne 8.001+/0.069 … 12 Mg 7.538+/0.060 ~0 14 Si 7.536+/0.049 0.010 26 Fe 7.448+/0.082 +0.000 Holweger, H. (2001), AIP Conference Proceedings Details of Solar Abundances • Oxygen – Variations of 0.1 dex depending on which lines are included or not – Individual lines vary from 8.697 to 8.921 – NLTE effects generally strengthen the lines – Also affected by granulation • Carbon, Nitrogen dito • Magnesium – Use Mg II as dominant species • Neon – EUV spectra of emerging active regions • Iron – still controversial! – Values range from 7.42 to 7.51; ... 7.448 'best' value – If Fe II is used, NLTE effects very small – Disagreements about choice of lines, fvalues Summary for the Sun • Departures from LTE occur in all lines formed above τ c=1 • Cores of lines with welldeveloped wings show strong departures from LTE • Weak, lowexcitation lines of trace elements are likely to show departures from LTE • Weak, highexcitation lines of abundant elements are less susceptible to NLTE • Far wings of strong lines are less susceptible to NLTE Basic Methodology for “ SolarType” Stars ● ● ● Determine initial stellar parameters – Composition – Effective temperature – Surface gravity – Microturbulence Derive an abundance from each line measured using fine analysis Determine the dependence of the derived abundances on – Excitation potential – adjust temperature – Line strength – adjust microturbulence – Ionization state – adjust surface gravity Different spectra ... what do these spectra have in common ... ? Different spectra Examples: peculiar stars etc. The Lower Main Sequence ● Flare Stars – M dwarf flare stars – About half of M dwarfs are flare stars (and a few K dwarfs, too) – A flare star brightens by a few tenths up to a magnitude in V (more in the UV) in a few seconds, returning to its normal luminosity within a few hours – Flare temperatures may be a million degrees or more – Some are spotted (BY Dra variables) – Emission line spectra, chromospheres and coronae; xray sources – Younger=more active – Activity related to magnetic fields (dynamos) – But, even stars later than M3 (fully convective) are active – where does the magnetic field come from in a fully convective star? – These fully convective stars have higher rotation rates (no magnetic braking?) WolfRayet Stars ● Luminous, hot supergiants ● Spectra with emission lines ● Little or no hydrogen ● 105106 Lsun ● Maybe 1000 in the Milky Way ● Losing mass at high rates, 104 to 10 5 Msun per year ● T from 50,000 to 100,000 K • WN stars (nitrogen rich) • Some hydrogen (1/3 to 1/10 He) • No carbon or oxygen • • • • WC stars (carbon rich) NO hydrogen C/He = 100 x solar or more Also high oxygen Outer hydrogen envelopes stripped by mass loss WN stars show results of the CNO cycle WC stars show results of helium burning Do WN stars turn into WC stars? Red Giants ● Miras (long period variables) – Periods of a few 100 to 1000 days Amplitudes of several magnitudes in V (less in K near flux maximum) Periods variable “ diameter” d epends greatly on wavelength Optical max precedes IR max by up to 2 months Fundamental or first overtone oscillators Stars not round Pulsations produce shock waves, heating photosphere, emission lines Mass loss rates ~ 107 Msun per year, 1020 km/sec – Dust, gas cocoons – – – – – – – – More Red Giants ● ● ● Normal red giants are oxygen rich – TiO dominates the spectrum When carbon dominates, we get carbon stars (old R and N spectral types) Instead of TiO: CN, CH, C2, CO, CO2 M Dwarf Spectral Types ● ● ● ● Molecular species switch from MgH to TiO CaOH appears in later M dwarfs Prominent Na D lines Spectral types determined in the blue M Dwarf Spectra Are a Mess ● ● ● ● Observed spectrum of M8 V dwarf VB10 Black body and H continuum spectra shown as dashed lines Real spectrum doesn’t match either Spectrum dominated by sources of opacity Later Spectral Classes ● ● ● TiO disappears to be replaced by water, metal hydrides (FeH, CrH) Alkali metal lines strengthen (note K I in the L8 dwarf) Spectral types determined from red, far red spectra (blue too faint!) Ltype Spectral Sequence ● ● K I line strength increases with later spectral type Li I appears in some low mass stars (m < 0.06 solar masses) ● Appearance of FeH, CrH ● Strength of Ca I ● Strength of water ● Disappearance of TiO ● Absence of FeH, CrH in T dwarf, much increased strength of water Brown Dwarfs ● Many L and T dwarfs have now been found – Improved IR detectors – Better spatial resolution (seeing improvements, AO) – IR and multicolor surveys (2MASS, DENIS, and Sloan) – Breakthrough in understanding appearance of spectra ● Significant progress in modeling low mass stellar and substellar objects ● Understood in the late ’50s that – low mass stars must be fully convective – Electron degeneracy must play a role – H2 formation also important (change in slope of main seq. at 0.5 MSun) ● early ’60s: a minimum mass is needed for H burning (0.08 Msun) ● early '70s: deuterium burning included in models ● Recent improvements include better equation of state and grain formation Li in Brown Dwarfs ● ● ● Li I appears in about a third of L dwarfs EQW from 1.5 to 15 Angstroms Li I can be used to distinguish between old, cooled brown dwarfs and younger, lower mass dwarfs History of White Dwarfs ● ● ● ● ● Bessell (1844) – Proper motions of Sirius and Procyon wobble – Suggested they orbited “d ark stars” Alvan Clark (1862) – Found Sirius B at Northwestern’s Dearborn Observatory Procyon B found in 1895 at Lick – Was it a star that had cooled and dimmed? Spectrum of 40 Eri B observed – an A star! – It must be hot – Must have small radius to be so faint – The first “w hite dwarf” Adams found Sirius B is also an A star in 1915 – From luminosity, R~ 2 x Earth (actually ¾) – From orbit, about 1 solar mass – Density 105 x water (actually 106) 20th Century History ● ● ● ● ● ● ● Eddington – Gas must be fully ionized so that nuclei could be compacted together – as the white dwarf cools, the atoms should recombine, but they can’t because the star can’t swell against gravity R. H. Fowler (1926) – Recognized the role of degeneracy pressure in supporting the star Chandrasekhar (1935) – Upper limit to mass supported by electron degeneracy pressure due to limit of velocity of light (1.4 solar masses) Zwicky (1930’s) Degenerate Neutron Stars Schatzman (1958) – chemical diffusion in strong gravity (plus radiative levitation, winds and mass loss, convective mixing, accretion) Greenstein and Trimble (1967) Gravitational redshift Hewish and Bell (1967) Pulsars White Dwarfs ● ● ● ● ● White Dwarfs – DO, DB, DA, DF, DG, DM, DC Classifications NOT analogous to MS – reflect compositions, not temperature – DA – hydrogen lines (no other lines, pure H atmosphere) – DB – neutral He lines (no hydrogen at all, pure He) – DO – ionized He lines (no hydrogen at all, hotter DBs) – DC – continuous spectrum, no lines – DF, DG, DM ... Heavier atoms sink in gravitational field Above 15,000 K, 15% are nonDA, below 15,000 K, half are nonDA. How do the stars do that? NO DB stars between 30,000 and 45,000 K Chemically Peculiar Stars of the Upper Main Sequence ● ● Ap stars – SrCrEu stars – Silicon Stars – Magnetic fields – Oblique rotators – Slow rotators AmFm stars – – – Ca, Sc deficient Fe group, heavies enhanced diffusion HgMn stars ● The λ Boo stars ... Vega is a l Boo star ! ● NLTE in O & B Stars • Low atmospheric density • High temperature • LTE not valid • Methods for NLTE in O stars date from the late ’60’s • NLTE effects not subtle – observable even at low spectral resolution Model atoms O I 29 levels, 71 transitions (Hempel & Holweger 2003) Diffusion ... important in B, A, F mainsequence stars and white dwarfs Diffusion Precondition: atmosphere stable, i.e., no convection, low rotational velocity (meridional circulation!) gravitational settling <=> selective radiation pressure radiation pressure is large for ● atoms / ions with many lines near flux maximum ● Elements with complex term structures ● rare earths small for ● noble gases ● saturated lines => overabundances of Mn, Sr, Y, Zr, Ba, ... underabundances of He, Ne, Ca, Sc, ... timescales 104 – 106 a < mainsequence evolution of a B star Diffusion in late Bstars – results (Hempel & Holweger 2003) Effects of weak stellar winds (Landstreet et al.1998) Certain elements can be used as tracers for weak stellar winds (1014 ... 1012 MSun/yr) Assumption: outward radial mass flux Behaviour of abundant elements He, O, C, Fe, Ne, N, ...) : Ne interesting in the case of late Btype stars (Teff = 11000 ... 16000K) Ne II from layers below atmosphere is pushed outwards with the stellar wind ↓ Ne becomes neutral in stellar atmosphere ↓ Ne I has a smaller crosssection than Ne II ↓ enrichment of Ne I in stellar atmosphere Weak stellar winds from late Bstars results LTE NLTE overabundances are artefacts of the assumption of LTE ! necessity of NLTEcalculations Some spectra ...