Modelling stellar photospheres & winds. Paul Crowther

Transcription

1 Modelling stellar photospheres & winds Paul Crowther

2 Outline Part I (stellar photospheres) Stellar temperatures, luminosities, gravities, abundances.. Late-type supergiants; Early-type stars Part II (stellar winds) Wind densities, velocities for early-type stars

3 Stellar Photospheres Temperature Metallicity Mass Radius Luminosity Age gravity Jacoby ApJS

4 Teff (direct) Temperature directly follows from angular diameter of star ( via interferometry, lunar occultation) + integrated flux (ok except for v.hot stars) e.g. Code+ 1976, ApJ 203, 417 using angular diameters from Hanbury-Brown s Narrabri stellar interferometer) so If distance (from parallax) also known, luminosity and radius directly follow..

5 Atmospheric models For most stars with thin atmospheres, T eff, L, X/H follow from LTE* plane-parallel models accounting for metal line blanketing: ATLAS (Bob Kurucz, Harvard) or MARCS (Bengt Gustafsson, Uppsala) ATLAS ideal for early-type stars, MARCS for late-type stars *LTE=Local Thermodynamic Equilibrium

6 Atomic data

7 MARCS (solid) vs ATLAS (dotted) Dwarfs (log g = 4) (super)giants

8 Spectral synthesis ATLAS/MARCS models provide atmospheric structure but detailed spectral line comparisons requires additional codes (incl. line broadening mechanisms) e.g. TurboSpectrum, SURFACE, Synspec

9 Vega Kurucz ATLAS model comparisons (solid lines) with observed (dotted) optical & ultraviolet spectrophotometry for Vega, revealing Teff=9,550K (Castelli & Kurucz 1994, A&A ) fully consistent with direct approach (R=2.7 Rsun, L=55 Lsun -> Teff=9,600K).

10 Balmer jump in early-type stars For stars earlier than mid-a, H - absorption is negligible relative to H, so the Balmer jump is due to the ratio of absorption from H atoms in Paschen continuum (n=3 >3647A) to Balmer continuum (n=2, <3647A). From Boltzmann formula this is solely a function of T eff, so this can be determined from the Balmer jump (via e.g. Stromgren photometry).

11 Balmer jump in yellow stars For F & G stars the size of the Balmer jump is determined by the ratio of κ(3647+) due to just H - (negligible Paschen continua) to κ(3647-) due to Balmer continua and H -, i.e. From Saha eqn, with f(t) a slowly varying function of T so: Balmer discontinuity is sensitive to both T eff & n e, and can be used to measure temperature or density/pressure/ gravity

12 Teff & log g via Stromgren filters Moon+Dworetsky 1985 MNRAS ). Stromgren filter system permits a number of useful indices: (b-y) colour index (free of blanketing effects) c1=(u-v)-(v-b) Balmer jump m1=(v-b)-(b-y) blanketing at ~4100 Ang beta = H-beta strength

13 Teff & log g via Stromgren filters beta index (H-beta strength) useful Teff indicator in F&G stars Balmer jump strength c1=(u-v)-(v-b) sensitive to Teff and surface gravity Lester ApJS

14 Balmer jump vs Balmer lines For A&B stars (T eff > 8,000K), Balmer jump, (u-v) provides Teff, so Balmer lines may be used to derive surface gravities. For F & G stars (T eff < 8,000K), Balmer lines provide Teff due to nil gravity dependence, so Balmer jump (c1 index) may be used to derive gravity Neutral metal lines in Solar-type stars are useful Teff indicators since they are not pressure sensitive.

15 Surface gravities g=gm/r2

16 Surface gravities g=gm/r 2 log g = 3.95 (Castelli & Kurucz 1994) so from R=2.7 Rsun (measured angular diameter + Hipparcos distance) we obtain M = 2.4 Msun

17 Elemental abundances

18 Elemental abundances Spectral synthesis permits determination of elemental abundances - e.g. metal-poor star with [Fe/H]=-0.85 dex (upper) compared to ultra-metal poor [Fe/H]=-7.1 dex (lower) Figures courtesy Anna Frebel

19 Elemental abundances Various spectral synthesis tools available for determination of abundances (many exploit MARCS + TurboSpectrum code developed at Uppsala: details in Alvarez & Plez 1998 A&A ) as discussed by Jofre arxiv: for ESO-Gaia benchmark FGK stars Non-LTE correction factors need to be taken into account (affecting Mg, Si, Ca, Cr, Fe, Ni..). Exemplary study of abundances in early B stars use ATLAS + SURFACE/DETAIL accounting for non-lte corrections is Nieva & Przybilla (2013 A&A 539 A143)

20 Late-type stars (+ brown dwarfs) Spectral features in latetype stars and brown dwarfs dominated by molecules (VO, TiO in M stars, H2O, CH4 in brown dwarfs). Synthetic spectra of L- type brown dwarfs for range of Teff and log g shown here (Cushing ApJ 678, 1372) based on Burrows+ (1997 ApJ 491, 856):

21 Late-type supergiants MARCS models (Teff=3700K, log g=0) for various metallicities (0.2 to 3 Solar) MARCS models (Gustafsson+ 2008, A&A 486, 951) favoured for Red Supergiants, owing to treatment of H2O, TiO & VO opacities + application to stars with extended atmospheres (spherical or planeparallel geometry)

22 Teff for red supergiants Davies+ (2013 ApJ 767, 3) have reevaluated Teff for RSG based on TiO bands vs full Spectral Energy Distribution (SED). They find TiO method systematically underestimates Teff (likely as a result of adopting 1D models).

23 Early-type stars Radiation field of hot stars is so intense that populations are only weakly dependent on local Te, Ne Crowther (1997) IAU Symp 189 ATLAS/MARCS models adopt LTE, so non-lte models required (e.g. TLUSTY: Hubeny & Lanz 1995, ApJ ), involving solution of complete set of equations of statistical equilibrium (computationally demanding, iterative solution).

24 Departure coefficients In O stars, LTE profiles are much too weak (Auer & Mihalas 1972 ApJS ). Departure coefficients (= non-lte/ltepop) shown here for n=1,2,3,4 for HeII can differ greatly through atmosphere, making HeI & HeII lines much stronger.

25 Temperatures of OB stars For O stars continuum techniques become unreliable Teff indicators. Why? The Balmer jump disappears so photometrically all O stars practically look identical. Cartoon from Conti, IAU Symp 116 (1986)

26 Temperatures of OB stars For O stars continuum techniques become unreliable Teff indicators. Why? The Balmer jump disappears so photometrically all O stars practically look identical. Cartoon from Conti, IAU Symp 116 (1986)

27 Temperatures of OB stars Photospheric absorption lines provide diagnostics for temperatures (SiII-IV for B stars, HeI-II for mid-late O stars, NIII-V for early O stars) T eff

28 Summary of Part I O-type stars: TLUSTY (non- LTE, plane parallel) Late-type supergiants: MARCS (LTE spherical) A&B-type stars: Kurucz/ ATLAS (LTE plane parallel) Late-type dwarfs: MARCS (LTE plane parallel)

29 Outline Part I (stellar photospheres) Stellar temperatures, luminosities, gravities, abundances.. Late-type supergiants; Early-type stars Part II (stellar winds) Wind densities, velocities for early-type stars

30 Stellar winds All massive stars possess strong winds (L>10 5 Lsun), low & intermediate mass stars in postmain sequence evolutionary phase also have powerful winds Red giants & supergiants possess slow (tens of km/s), dense (~10-6 to 10-4 Msun/yr) outflows, diagnosed via far-ir dust excesses (Mdust -> Mgas) & mm emission lines (1.3, 2.6mm CO) Early-type stars possess fast (thousands of km/s), dense (~10-7 to 10-5 Msun/yr) outflows, diagnosed via UV, optical or IR wind lines

31 Formation of P Cygni profile Observer Flux P-Cygni Line Profile = Symmetric Emission + Blue-Shifted Absorption } } V V=0 V V=0 Velocity ; Wavelength

32 Wind velocities 1% of c! Wind velocities of early-type stars measured from saturated troughs of P Cygni profiles in resonance CIV, NV, SiIV lines observed to range from hundreds km/s (B stars) to thousands km/s (O stars) (Prinja ApJ 361, 607)

33 SEI method Unsaturated UV lines (weaker winds, less abundant elements) are less amenable to direct wind velocity measurements, so Sobolev with Exact Integration = SEI (Groenewegen A&AS ) technique may be applied to derive wind velocity and acceleration exponent beta, where v(r) = vinf(1-r/r) beta

34 Mass-loss diagnostics Primary diagnostic of mass-loss in hot stars is Hα in the visual, which may be used to derive O, B and A supergiant wind massloss rates. Photospheric Hαlpha absorption line is contaminated by wind emission. H-alpha profile in O4 supergiant vs photospheric absorption (Crowther ApJ )

35 Mass-loss diagnostics Historically, rate of mass-loss obtained via core-halo approach by Leitherer (1988, ApJ 326, 356) based on H-alpha equivalent width or specific wind-only atmospheric models (Puls A&A 305, 171) Now, spherically extended non-lte models including metal-line blanketing are widely applied for hot stars with winds: FASTWIND (Puls A&A ) - widely applied to O stars CMFGEN (Hillier & Miller 1998 ApJ ) applied to OBA, WR stars, SNe, CSPNe PoWR (Grafener A&A ) applied to O and WR stars, CSPNe with winds

36 Line blanketing Analysis of hot luminous stars with strong winds requires non-lte + spherical geometry (CMFGEN, FASTWIND) rather than non-lte + plane parallel (TLUSTY). Inclusion of blanketing is CPU demanding Blanketed (solid) vs unblanketed (dashed) CMFGEN model (Puls A&A Rev)

37 Hot stars without winds TLUSTY model (T=46kK, log g=3.7) via photospheric HeI/HeII lines in an O4 supergiant + wind-affected lines Crowther ApJ

38 Hot stars with winds CMFGEN model (T=40kK, log g=3.6, dm/dt=8e-6 Msun/yr) fit to photospheric and wind lines in O4 supergiant. Crowther ApJ

39 Wind density Spectral analyses of O stars derive Teff, log g, H/He and wind density Q (for recombination line based processes) where: so if wind velocities are known (or estimated) and distances (allowing log L and R) are known, then mass-loss rates can be calculated. By way of example, the short runtime of FASTWIND allows large grids of models to be calculated from which robust parameter searches can be conducted..

40 FASTWIND Credit: S.Simon-Diaz

41 FASTWIND Credit: S.Simon-Diaz

42 More on mass-loss Wind contribution to H-alpha is a recombination process (so dependent upon ion density * electron density or density^2 diagnostic). Alternative methods are available: Free-free continuum emission at IR/radio wavelengths (also density^2 diagnostic) introduced by Wright & Barlow (1975 MNRAS ) Unsaturated UV wind profiles (linear density dependence) eg. Fullerton+ (2006 ApJ 637, 1025) Current issues focus on clumped nature of outflows. Winds from hot luminous stars are intrinsically unstable.. if optically thin clumps, lower mass-loss rates are implied..

43 Hot Star Winds are intrinsically unstable Wind velocity log r/r Wind density Simulation Courtesy: Stan Owocki

44 OB star ages/masses Complicated since high initial rotation rate can strongly affect evolution..

45 OB star ages/masses Complicated since high initial rotation rate can strongly affect evolution..use more info to break degeneracy!

46 OB star ages/masses HR diagram + rotational distribution prior -> probability distribution of initial masses (Bayesian approach BONNSAI: Schneider A&A )

47 Wolf-Rayet stars, Supernovae Wolf-Rayet stars are hot stars exhibiting strong emission lines due to dense (10-5 M sun yr -1 ), fast (2,000 km s -1 ) outflows

48 WR analyses Spectral analyses of WR stars involve more parameters than O stars since atmospheric structure is v. sensitive to elemental abundance of He (WN stars) and C, O (WC stars) - see Crowther (2007) ARA&A Similar spectra are predicted if wind densities are similar, parameterised by transformed radius Rt: so if wind velocities are known (usually measured from WR lines) and distances (allowing log L and R*) are known, then mass-loss rates can be calculated (D is clumping factor >1, while equivalent filling factor f = 1/D)

49 Wolf-Rayet stars Spectra of Wolf-Rayet stars are dominated by wind lines. CMFGEN fits provide T, L, dm/dt, abundances.. Crowther+ (2002 A&A )

50 Wolf-Rayet stars Spectra of Wolf-Rayet stars are dominated by wind lines. CMFGEN fits provide T, L, dm/dt, abundances.. Crowther+ (2002 A&A )

51 WC stars: Hot with cool winds Atmosphere of WC4 star (Crowther A&A ) illustrates highly stratified ionisation structure (effectively cooled since dense, C+O rich winds)

52 Supernovae Interpretation requires model comparisons..

53 Supernovae Dessart MNRAS CMFGEN fit to spectral evolution and light curve of SN1999em (II-P) allowing for non-thermal excitation, γ-ray deposition.

54 Multi-dimension models ATLAS/MARCS/TLUSTY/ CMFGEN/FASTWIND are all 1D models. Magic+ (2013 A&A 557 A26) have calculated 3D radiative MHD models for late-type stars. 3D models show subtle differences with 1D MARCS results (Davies+ 2013). PHOENIX was initially developed for time-dependent evolution of SNe, but has also been applied to dwarf, giant stars, brown dwarfs, CVs and AGN disks. 1D spherical symmetry is usually adopted, but a prescribed 3D structure can also be adopted (Hauschildt & Baron 2010, A&A 509 A36).

55 Summary of Part II SNe: CMFGEN (non-lte extended) Wolf-Rayet, blue supergiants: CMFGEN, PoWR (non- LTE, extended) O stars: FASTWIND (non-lte, extended)

56 Textbooks? Theory of Stellar Atmospheres (Ivan Hubeny & Dimitri Mihalas) Stellar photospheres (David Gray) Introduction to Stellar Winds (Henny Lamers & Joe Cassinelli)

57 Omitted topics? Rotational velocities, Magnetic fields, Binarity, Departures from spherical symmetry, (stay tuned for Ian Howarth s contribution..)