4 all massive hot stars with L/Lsun > 10 Æ highly supersonic, strong winds 1 M˙ v R− 2 L1.8[Z]0.8 ∞ ∗ basic properties explained by ∝ phot 0.15 v 3vesc [Z] ∞ ≈ M (1 Γ) 1 theory of line driven winds phot 2 vesc = 2G ∗R − { ∗ }
Kudritzki & Puls, 2000, ARAA 38, 613
How to explain metallicity dependence?? Hydrodynamics of stationary line driven winds
M˙ =4πr2ρ(r)v(r)
dv(r) 1 dPgas(r) v(r) =- g(r)+grad(r) dr ρ(r) dr −
Th bf,ff lines grad(r)=grad + grad + grad Contribution by one line i at νi
i photon momentum absorbed by line i grad = time mass
1 τi 1 = Lν (1 e− )dν 2 c i − 4πr ρdr τ i dv dν = νi c
Th neσeL grad(r)= c4πr2ρ
ν L i Th 1 i νi τi 1 dv g =g (1 e− ) rad rad c L − neσe dr Mi lines Th grad = gradM(t) line force multiplier
ν L vth 1 i νi τi M(t) = c t i L (1-e− ) P τi(r)=kit(r) line optical depth
χi(r) nlower ki= fluλi line strength neσe ∝ ne
vth t= neσe dv/dr optical depth parameter depth dependence of line force M(t)
ν L τi(r)=kit(r) vth 1 i νi τi M(t) = c t i L (1-e− ) vth t= neσe dv/dr P
2 extreme cases: kmax = max {ki}, kmin = min {ki}
1 νiLνi t ts = k− M (t) = Mmax ki = const. ≤ max ⇒ ∝ i L
1 1 1 dvP t tm = k− M (t) = ≥ min ⇒ t ∝ ne dr
optical thickness of lines is crucial ! line strength distribution function atomic line lists, NLTE: α 2 {k } for some 106 lines n(k,ν)dνdk k − dk i ∝ Æ power law
Teff = 40000 K
α = 0.65
see Puls et al. 2000, A&AS 141, 23 for detailed discussion depth dependence of line force ν L α 2 1 i νi kit n(k,ν)dνdk k − dk M(t) (1-e− ) ∝ ∝ t i L P 1 kmax tk α 2 M(t) Neff 1 e− k − dk ∝ t 0 { − } R log n(k) log M(t)
α Mmax slope: M(t) Neff t− α -2 ∝ · slope: -α α Neff Mmax k − ∝ max log k log t 8 t kmax ~ 10 s dv(r) 1 dPgas(r) α v(r) =- g(r) 1+ΓM (t− ) dr ρ(r) dr − { } non-linear
vth eq. of motion t= neσe dv/dr
1 1 1 ˙ α α 1 α analytic solutions, M Neff L M (1 Γ) − ∝ { ∗ − } scaling relations α phot v 2.24 1 α vesc ∞ ≈ − M (1 Γ) 1 phot 2 vesc = 2G ∗R − { ∗ } Castor, Abbott, Klein, 1975 Kudritzki et al. 1989, 1 1 1 ˙ − 2 α α Puls, Kudritzki et al., 1996, Mv R Neff L ∞ ∝ ∗ Kudritzki & Puls, 2000 Hα fits with hydrodynamic NLTE models M˙
Variation ofM˙ by ± 20%
Kudritzki & Puls, 2000, AARA 38, 613 fit of v∞ ± 5% accuracy
Kudritzki & Puls, 2000, AARA 38, 613 Kudritzki & Puls, 2000, AARA 38, 613 data from Prinja & Massa (1998), Lamers et al., (1995) Stellar wind momenta: O-stars and CSPN
Kudritzki & Puls, 2000 Kudritzki et al., 1997 New WLR: O-stars and CSPN (blanketing)
Repolust, Puls, Herrero, 2004 Markova, Puls, Repolust, Markov, 2004 Kudritzki, Urbaneja, Puls, 2006 theoretical wind momenta observed regressions calculated
calculations by Kudritzki, 2002, ApJ 577, 389 Rome 2005 relationship (WLR) idmmnu luminosity Wind momentum – M ˙ v ∞ R α ∗ 2 1 ≈ = 3 2 con s t.L α 1 Kudritzki &Puls, 2000 Kudritzki etal., 1999 etal.,96 Puls Kudritzki etal., 89 empirically calibrated confirmed and slope alpha zero pointand theory Predicted bywind Stellar wind momenta: B and A supergiants
Kudritzki & Puls, 2000 Kudritzki et al., 1999 Concepcion 2007 WLR forA-supergiants Æ distances rslnet al.,2001 Bresolin Kudritzki et al.,1999 Z metallicity k=k Z ¯ ¯ log M(t) log n(k) Z M kmax = kmax¯ Z max Z=Z ¯ sun Z=Zsun
Z Z 1 α M˙ = M˙ −α ¯ Z Abbot, 1982 { ¯ } Kudritzki et al., 1989 Puls, Kudritzki et al., 1996 curvature of line strength distribution function log n(k) contribution to M(t) mostly from lines with τ = k•t = 1 α-2 real distribution α(k= 1 ) M(t) t t average α-2 − power law fit ∝ for lower metallicity log k • weaker winds larger k contribute α smaller α smaller ! • k ~ Z/Zsun distribution shifts α smaller Z x v Z but no unique consequences: ∞ ∝ { ¯ } ˙ Z m exponent ! M Z ∝ { ¯ } Complication: M (t, ne/W) Teff = 50000K, Z = Z_sun ne/W ne(r) δ ionization changes through wind: Neff ∝ { W (r) } log M(t) log n(k) ne/W ne/W log k log t ne(r) δ α M(t) t− ∝ { W (r) } 1 1 1 α δ≈0.05 to 0.1 ˙ α δ α δ ˙ Z α− δ M Nef−f L − M − ¯ Z ∝ ∝ { ¯ } Kudritzki et al., 1989 α 2δ v e− vesc Puls et al., 1996, ∞ 1 α ∝ − Kudritzki & Puls, 2000 numerical calculations Kudritzki et al., 1987 Z/Z_sun = 0.1 … 1.0 ˙ Z 0.6 0.1 Z 0.15 M Z ± v Z ∝ { ¯ } ∞ ∝ { ¯ } Leitherer et al., 1992 Z/Z_sun = 0.01 … 3.0 Z 0.8 0.1 v Z 0.13 M˙ ± Z Z ∞ ∝ { ¯ } ∝ { ¯ } Vink et al., 2001 Z/Z_sun = 0.03 … 3.0 ˙ Z 0.69 0.1 M Z ± ∝ { ¯ } data from: Puls & Kudritzki, 2000 Crowther et al., 2002 Hillier et al., 2003, Repolust et al., 2004 Markova et al., 2004 Evans et al., 2004 Massey et al., 2004 Massey et al., 2005 Martins et al., 2004 Bouret et al., 2005 data from: Puls & Kudritzki, 2000 Crowther et al., 2002 Hillier et al., 2003, Trundle et al., 2003 2004 Evans et al., 2004 Massey et al., 2004 Massey et al., 2005 O-star wind momenta new: MW, LMC, SMC without wind clumping LMC observed SMC theory Vink et al., 2001 MW Mokiem, deKoter, Puls et al. 2006, A&A 441, 711 WLR: theoretical [Z] dependence calculations by calculated Vink et al., 2002 observed SMC regression calculations by Kudritzki, 2002, ApJ 577, 389 Bresolin, Kudritzki etal., 2003 Rome 2005 supergiants 6 lateB,earlyA-type Wind analysis G 0:AsprinsWLR NGC 300:Asupergiants Rome 2005 WLR: Asupergiants Bresolin, Kudritzkietal.,2001, 2003 NGC 3621 predicts shift ofWLR todotted line Æ have lower metallicity NGC 3621 andNGC300 objects Æ Æ B +Aspectraltypes Theory (Kudritzki, 2003) 2003) Theory (Kudritzki, need plotvs.M ltv M plot vs v ignores B.C. ignores bol Winds, ionizing fluxes and spectra of the first generations of very massive stars in the early universe Rolf-Peter Kudritzki Institute for Astronomy, University of Hawaii Kudritzki & Puls, 2000, ARAA 38, 613 Kudritzki et al., 2000, ApJ 536, 19 Bromm, Kudritzki, Loeb, 2001, ApJ 552, 464 Kudritzki, 2002, ApJ 577, 389 - 408 Marigo, Chiosi, Kudritzki, 2003, A&A 399, 617 Rix, Pettini, Leitherer, Bresolin, Kudritzki, Steidel, 2004, ApJ 615, 98 evolution of galaxies in early universe Introduction heavily influenced by first generations of very massive stars cosmic web@ z=3.5 Springel & Hernquist, 2003 very massive WMAP stars -3 • Z/Zsun ≤ 10 Æ star formation preferably stars with 1000 Msun > M > 100 Msun hydro-simulations: Abel et al., 2000, 2002 Bromm et al., 2000, 2002 • contribution to re-ionization @ redshift 20 > z > 6 Carr et al. 1984, Couchman & Rees 86, Haiman & Loeb 1997, Bennet et al. 2003, Spergel et al. 2003, Becker et al. 2001, Fan et al., 2001, Springel & Hernquist 2003 • progenitors of GRBs at high redshift Bromm & Loeb 2002, Ciardi & Loeb 2001, Kulkarni et al. 2000, Djorgovski et al. 2001, Lamb & Reichart 2000 • extreme Ly-α emitters at high redshift Kudritzki et al. 2001, Rhoads & Malhotra 2001 Malhotra & Rhoads 2002, Hu et al. 2003 The first stars in the universe - clues from hydrodynamic simulations • Hydrodynamic simulations by Davé, Katz, & Weinberg – Ly-α cooling radiation (green) – Light in Ly-α from forming stars (red, yellow) z=10 z=8 z=6 Stars forming at z=10! Observable with a 30m telescope! 1 Mpc (comoving) GSMT Science Working Group Report, 2003, Kudritzki et al. http://www.aura-nio.noao.edu/gsmt_swg/SWG_Report/SWG_Report_7.2.03.pdf Simulation As observed through 30-meter telescope R=3000, 105 seconds, Barton et al., 2004, ApJ 604, L1 A possible IMF diagnostic at z=10 HeII (λ1640 Å) HeII (λ1640 Å) Standard IMF Top-Heavy IMF, zero metallicity (IMF + stellar model fluxes from Bromm, Kudritzki, & Loeb 2001, ApJ 552,464) questions evolution ? spectra? winds? ionizing fluxes? recombination lines? old work ˙ 0.5 0.8 M Z/Z ··· ∝ { ¯} for 0.01 Z/Z 3 ≤ ¯ ≤ Kudritzki et al. 1987, Leitherer et al. 1992, Vink et al., 2001 lines Th grad = gradM(t) line force multiplier ν L vth 1 i νi τi M(t) = c t i L (1-e− ) P τi(r)=kit(r) line optical depth χi(r) nlower ki= fluλi line strength neσe ∝ ne vth t= neσe dv/dr optical depth parameter vth for very weak winds Æ t=neσe dv/dr << 1 τi = kit(r) < 1, for all lines -1 if t > kmax ν L vth 1 i νi τi M(t) = c t i L (1-e− ) P vth νiLνi O-stars @ Z = 1 Mmax = ki 2000 c i L ≈ (Gayley, 1995) P Z since for metal lines ki = ki¯ Z ¯ Z Mmax = 2000 Z + M H,He ¯ necessary for wind (at very low metallicity): Th g(r)-grad(r)=g(r)[1 Γ 1+M (t) ] 0 Γ = g (r)/g(r) − { } ≤ rad 1 Z 1 Γ Γmin = = 1 + 2000 + MH,He 1+M max Z − ≥ { ¯ } minimum Γ for existence of Z/Zsun Γmin line driven winds 1.0 5•10-4 0.1 5•10-3 0.01 0.05 0.001 1/3 winds only very close to 0.0001 5/6 Eddington-limit !! Winds at very low metallicities – a challenge Z 2 • saturation of M(t) at high t Z 10− ¯ ≤ kmax t ≈ 1 Æ strong curvature of M(t) log M(t) • ne/W influences curvature Æ force multipliers α, δ depth dependent ne/W ne ne ne δ(t, ) α(t, ) M(t) W t− W ∝ { W } log t new approach needed !!! M(t,Z) Teff = 50000K α(t,Z) M(t), α(t), δ(t) Z/Zsun = 1.0 0.01 0.001 δ(t,Z) Kudritzki, ApJ 577, 389, 2002 millions of lines in NLTE α (t, ne/W) Teff = 50000K -4 Z/Zsun = 10 Kudritzki, ApJ 577, 389, 2002 δ (t, ne/W) Teff = 50000K -4 Z/Zsun = 10 Kudritzki, ApJ 577, 389, 2002 line driven winds with depth dependent line force multipliers v(r) dv(r) =- 1 dPgas(r) g(r) 1+ΓM dr ρ(r) dr − { } α(t,ne/W ) δ(t,ne/W ) M=M(t− , (ne/W ) ) vth t= neσe dv/dr For details of numerical of numerical solution including singularity and regularity conditions at critical point see Kudritzki, ApJ 577, 389, 2002 wind models for evolved very massive stars at very low metallicity 4 10− Z/Z 1 ≤ ¯ ≤ 100M M 300M ¯ ≤ ≤ ¯ 40000K Teff 60000K ≤ ≤ • winds • ionizing fluxes • spectra the model grid M/Msun M/M log Mdot vs log Z sun 300 250 200 not a power law!!!! 150 120 100 analytical formula for Mdot = f(L,Z) given by Kudritzki, 2002 Kudritzki, ApJ 577, 389, 2002 M/M v∞/vesc vs log Z sun 300 250 200 150 120 100 Kudritzki, ApJ 577, 389, 2002 Z/Zsun wind momentum vs log L 1.0 0.2 0.01 0.001 0.0001 Kudritzki, ApJ 577, 389, 2002 wind energy vs log Z M/Msun 300 250 200 150 120 100 Kudritzki, ApJ 577, 389, 2002 Ionizing fluxes: Teff = 60000K, M/Msun = 250 Z = 1.0 Z = 10-4 Kudritzki, ApJ 577, 389, 2002 Ionizing fluxes: Teff = 60000K, M/Msun = 250 HeII NeII HeI H CIII OII bound-free edges for ionizing photons Kudritzki, ApJ 577, 389, 2002 Number of ionizing photons:Teff = 50000K, M/Msun = 300 Kudritzki, ApJ 577, 389, 2002 ionizing fluxes vs. metallicity, luminosity • H and He I ionizing photons unaffected • O II, Ne II, C III photons moderately affected • He II photons strongly affected 300 Msun 120 Msun 40000K 40000K 50000K 50000K 60000K 60000K Z/Z Spectra:Teff = 50000K, M/Msun = 250 sun 0.2 10-2 10-4 N V O V C IV He II Kudritzki, ApJ 577, 389, 2002 Z/Z Spectra: Teff = 60000K, M/Msun = 250 sun 0.2 10-2 10-4 N V O V C IV He II Kudritzki, ApJ 577, 389, 2002 UV line spectra -4 • line diagnostics possible down to Z/Zsun = 10 GSMT JWST -3 • wind features disappear at Z/Zsun = 10 Applications • evolution of massive Pop III stars • low metallicity starburst galaxies at high z • the first stars in the re-ionization epoch Applications • evolution of massive Pop III stars • low metallicity starburst galaxies at high z • the first stars in the re-ionization epoch Evolution of massive Pop III stars with mass-loss Marigo, Chiosi, Kudritzki 2003, A&A 399, 617 Final stages of massive Pop III stars He & CO cores at C ignition Marigo, Chiosi, Kudritzki 2003, A&A 399, 617 initial mass He enrichment of ISM He enrichment Marigo, Chiosi, Kudritzki 2003, A&A 399, 617 star formation efficiency He vs Z enrichment of ISM He enrichment Marigo, Chiosi, Kudritzki 2003, A&A 399, 617 metallicity enrichment Applications • evolution of massive Pop III stars • low metallicity starburst galaxies at high z • the first stars in the re-ionization epoch Spectral diagnostics of high-z starbursts Starburst models - fully synthetic spectra based on model atmospheres Rix, Pettini, Leitherer, Bresolin, Kudritzki, Steidel, 2004, ApJ 615, 98 Spectral diagnostics of high-z starbursts cB58 @ z=2.7 fully synthetic spectra vs. observation Rix, Pettini, Leitherer, Bresolin, Kudritzki, Steidel 2004, ApJ 615, 98 Applications • evolution of massive Pop III stars • low metallicity starburst galaxies at high z • the first stars in the re-ionization epoch Main sequence of the first stars Bromm, Kudritzki, Loeb ApJ 552, 464, 2001 Spectra and SEDs of the first stars Bromm, Kudritzki,Loeb,ApJ 552, 464, 2001 Lν / M is almost constant !!! Bromm, Kudritzki, Loeb ApJ 552, 464, 2001 SED of a cluster of 106 stars at a redshift of 10 Bromm, Kudritzki, Loeb ApJ 552, 464, 2001 First very massive stars - conclusions • generic SEDs ~ BB with T ≥ 105 K • rich H and HeII spectra • Lν/M independent of stellar mass for M ≥ 200 M_sun phot • N (H)/Mstars factor ten larger than for Salpeter IMF • (HeII) hundred • H and HeII recombination lines observable with 30m 6 • predicted continuum spectra for 10 Msun cluster at z=10 - detectable with JWST - SEDs, colors different from Salpeter IMF Bromm, Kudritzki, Loeb ApJ 552, 464, 2001 Schaerer, A&A 397, 527, 2003 Stars forming at z=10! Observable with a 30m telescope! 1 Mpc (comoving) GSMT Science Working Group Report, 2003, Kudritzki et al. http://www.aura-nio.noao.edu/gsmt_swg/SWG_Report/SWG_Report_7.2.03.pdf Simulation As observed through 30-meter telescope R=3000, 105 seconds, Barton et al., 2004, ApJ 604, L1 A possible IMF diagnostic at z=10 HeII (λ1640 Å) HeII (λ1640 Å) Standard IMF Top-Heavy IMF, zero metallicity (IMF + stellar model fluxes from Bromm, Kudritzki, & Loeb 2001, ApJ 552,464) Instabilities • a few extremely low Mdot models may suffer from de-coupling of H,He and metals (Kudritzki 2002, Krticka et al. 2003) Æ heating of winds or fallback of material • strong increase of force multiplier parameter δ Æ bi-stability of radiative line force • pulsational instabilities important for very massive stars, however see Baraffe, Heger & Woosley (2001): much weaker at low Z • rotation Æ rotationally induced mass-loss (Maeder,Meynet) • close to Γ = 1 Æ Shaviv, Owocki, Gayley porosity?? δ (t, ne/W) Kudritzki, ApJ 577, 389, 2002 Instabilities • a few extremely low Mdot models may suffer from de-coupling of H,He and metals (Kudritzki 2002, Krticka et al. 2003) Æ heating of winds or fallback of material • strong increase of force multiplier parameter δ Æ bi-stability of radiative line force • pulsational instabilities important for very massive stars, however see Baraffe, Heger & Woosley (2001): much weaker at low Z • rotation Æ rotationally induced mass-loss (Maeder,Meynet) • close to Γ = 1 Æ Shaviv, Owocki, Gayley porosity??