Sternentstehung - Star Formation Sommersemester 2009 Henrik Beuther 3.4 Today: Introduction & Overview 10.4 Karfreitag 17.4 Physical processes I 24.4 Physcial processes II 1.5 Tag der Arbeit 8.5 Collapse models I 15.5 Collapse models II 22.5 Observations of outflows and jets 29.5 No lecture 5.6 Jet theory (Christian Fendt) 12.6 Accretion disks 19.6 Protostellar evolution, stellar birthline, pre-main sequence evolution 26.6 High-mass star formation, clusters and the IMF 3.7 Extragalactic star formation (Eva Schinnerer) 10.7 Summary More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ss09.html [email protected] Topics today - The first core - The protostellar envelope structure - Protostellar evolution - Pre-main-sequence evolution Star Formation Paradigm The first core I - Contraction of core via ambipolar diffusion initially slow process. - When Σ/B reaches critical threshold, contraction speeds up, high density, core becomes opaque cooling less efficient T & P rise. - Interior still mainly molecular hydrogen important for final collapse The first core II - Temperature estimate based on viral theorem: 2T + 2U + W + M = 0 W = -2U (kinetic and magnetic energy approximated as 0) => -Gm2/R = -3mRT/µ => T = µGm/(3R R) -1 = 850K (m/0.05Msun) (R/5AU) --> significantly warmer than original core - With the addition of mass and further shrinking, it soon reaches 2000K, where collisional dissociation of H2 starts. --> Temperature increase less steep. - However, thermal energy per molecule at 2000K ~ 0.74eV compared to dissociation energy of H2 of ~ 4.48eV --> Even modest increase of dissociated H2 absorbs most of the gravitational energy from the collapse --> marginal increase in temperature and pressure - Region of atomic H spreads outward from center - Without significant T & P increase, the first core cannot keep equilibrium, hence the entire core becomes unstable, collapses and forms protostar. --> significant temperature and density increase, sufficient to collisionally ionize most hydrogen --> emerging protostar is now dynamically stable. 5 -2 -3 - A protostar of 0.1Msun has radius of several Rsun, T~10 K and ρ~10 g cm Accretion shock and Accretion luminosity - The gravitational energy released per unit accreted mass can be approximated by the gravitational. potential GM*/R* - Hence the released accretion luminosity of the protostar can be approximated by this energy multiplied by the accretion rate: Lacc = G(dM/dt)M*/R* -5 -1 = 61Lsun ((dM/dt)/10 Msun/yr) (M*/1Msun) (R*/5Rsun) - Additional luminosity contributions from contraction and early nuclear fusion are negligable compare to Lacc for low- to intermediate-mass stars. - Conventional definition of (low-mass) protostar: “Mass-gaining star deriving most of its luminosity from accretion.” (However, caution for massive stars.) Topics today - The first core - The protostellar envelope structure - Protostellar evolution - Pre-main-sequence evolution Protostellar envelope I - Outer envelope largely optically thin. - As infalling gas continues to be compressed (inside-out collapse), the protostellar radiation becomes trapped by high dust grain opacities. Relative dimensions of - This dust then reradiates the emission outer region at far-infrared wavelengths. greatly reduced in sketch. --> Dust photosphere (a few AU for typical low-mass star) is the effective radiating surface observable from outside at that evolutionary stage (not optically visible yet). - Rapid T increase in dust envelope --> dust sublimation at T~1500K. - Inside dust destruction front greatly reduced opacity, and infalling gas almost transparent to protostellar radiation --> opacity gap. - Immediately outside the accretion shock, gas gets collisonally ionized and the opacity increases again --> so-called radiative precursor Protostellar envelope II - Difference in radiation from shocked “radiative precursor” and far-infrared radiation from dust photosphere - In shock region gas approaches protostar approximately at free-fall Relative speed: 1/2mv 2 = GM m/R dimensions of ff * * outer region => vff = √2GM*/R* greatly reduced 1/2 -1/2 in sketch. = 280 km/s (M*/1Msun) (R*/5Rsun) --> Immediate postshock temperature >106K, UV and X-ray regime --> Postshock settling region opaque, quick temperature decrease --> The surface of precursor radiates as approximate blackbody in opacity gap: Stephan-Boltzmann law: 2 4 3 1/4 Lacc ~ 4πR* σBTeff Substituting Lacc => Teff ~ (GM*(dM/dt)/4πR* σB) -1 1/4 -3/4 => Teff ~ 7300K ((dM/dt)/1e-5Msunyr ) (M*/1Msun) (R*/5Rsun) Opacity gap is bathed in “optical emission” similar to main-sequence star. Very different to observable dust photosphere. Temperatures and dimensions of envelope Relative dimensions of outer region greatly reduced in sketch. - Temperature profile in optically thick dust envelope T(r) ~ r-0.8 - Temperature profile in optically thin outer envelope T(r) ~ r-0.4 - Typical dimensions for a 1Msun protostar: Outer envelope: a few 100 to a few 1000 AU Dust photosphere: ~ 10 AU Dust destruction front: ~ 1 AU Protostar: ~ 5 R* ~ 0.02 AU Effects of Rotation - Full contours: T decrease outward from 1050K in 50K steps. - Dashed contours: ρ -1 -1 - Model: M* = 0.5 Msun, dM/dt = 5e-6 Msun yr , Ω = 1.35e-14 s , ωcen = 0.4 AU outside the dust destruction front. However, most luminosity stems from accretion shock on protostar or inner disk. - Temperature structure slightly oblate within ωcen because of local density enhancement there trapping radiation and increasing temperature. - In contrast, outside ωcen T structure more prolate because of this radiation blockage in the equatorial plane. Topics today - The first core - The protostellar envelope structure - Protostellar evolution - Pre-main-sequence evolution Protostellar evolution/Stellar Structure equations - The protostellar evolution can be analyzed numerical similarly to stars. --> Stellar Structure equations - The used spatial variable is Mr, the mass within shells of radius r r 2 Mr = 0∫ 4πr ρ dr 2 => ∂r/∂Mr = 1/(4πr ρ) (1) Hydrostatic equilibrium: -1/ρ grad(P) - grad(Φg) = 0 2 => ∂P/∂r = -GρMr/r (2) Combining (1) in (2), one gets 4 => ∂P/∂Mr = -GMr/(4πr ) (3) Pressure obeys ideal gas equation: P = ρ/µ RT (4) (mean molecular weight µ depends on state of ionization and is function of T and ρ) Thermal structure of opaque interior is described by diffusion equation 3 2 4 T ∂T/∂Mr = - 3κLint/(256π σBr ) (5) (mean opacity κ is again function of T and ρ) And the spatial variation of the internal luminosity Lint can be described by the heat equation: ∂Lint/∂Mr = ε(ρ,T) - T ∂s/∂t (6) (ε(ρ,T) rate of nuclear energy release; s(ρ,T) is the entropy) For a mono-atomic gas, the entropy is: s(ρ,T) = R/µ ln(T3/2/ρ) - Using adequate boundary conditions, one can now follow numerically the protostellar evolution. Mass-radius relation - Initial size unknown, but that does not matter since it quickly converges. - Adding additional infalling mass shells, the protostar can be described by its entropy profile s(Mr), reflecting the changing conditions at the accretion shock. - Since s represents heat content of each added mass shell, an increase of s(MR) causes a swelling of the protostar. - In the absence of nuclear burning, an increasing s(Mr) arises naturally because with rising M*, the velocity of the infalling gas and hence the accretion shock and Lacc increases. --> Protostellar radius increases with time. - Suppose initial core very large, then low infall velocity --> low Lacc and s(Mr) would dip at beginning of protostellar evolution --> initial decrease of R* - Opposite effect for very small initial state. Convection I - Displace parcel outward. Pext decreases. --> parcel expands and (ρint)1 < (ρint)0 - Question: If (ρint)1 < (ρext)1 then parcel gets buoyant --> convection starts and becomes important for heat transfer. If (ρint)1 > (ρext)1 then parcel will sink back down and star remains radiatively stable. - If parcel displacement very quick, its heat loss is negligable and its specific entropy s stays the same. - In the absence of nuclear burning protostar has rising entropy profile s(Mr). --> (sint)0 = (sint)1 < (sext)1 - However, (Pint)1 = (Pext)1 and for ordinary gases (∂ρ/∂s)P < 0, i.e. --> density falls with increasing entropy at constant pressure. --> (ρint)1 > (ρext)1 for a rising entropy profile. --> ∂s/∂Mr > 0 implies radiative stability. Convection II - However, the ratio M*/R* rises fast and interior temperatures increase. 6 Nuclear reactions start at center (at ~0.3Msun deuterium burning at ~10 K). --> entropy profile overturns ∂s/∂Mr < 0, radiative stability criterium not given anymore. - Convection begins because deuterium fusion produces too much energy to be transported radiatively through opaque interior. Since ∂s/∂Mr < 0 parcels are underdense ((ρint)1 < (ρext)1) and hot. After transfering excess heat to surrounding medium, denser/cooler parcels travel downward again. --> Protostellar interior is well mixed and provides its own deuterium to center for further fusion processes. - Convection is local phenomenon, some regions can be convective whereas others remain radiatively stable. Deuterium burning Circles: onset of full convection - 2H + 1H --> 3He + ∆E with ∆E ~ 5.5 MeV, important from 106K - The degree of protostellar size increase depends partly on the accretion rate but the deuterium burning is more important. - The deuterium burning is very temperature sensitive. An increase of T causes more deuterium burning --> more heat --> increase of proto- stellar radius --> lower T again --> Deuterium burning acts as kind of thermostat keeping protostellar core at that evolutionarys stage at about 106K. - Steady supply by new Deuterium from infalling gas via convection necessary to maintain thermostat. Radiative stability again for different protostellar masses Radiative barrier - What happens for protostars gaining more than 1-2Msun of mass? - The critical luminosity Lcrit is the maximum value to be caried by radiative diffusion. - Continuum opacity from free-free emission (Kramers-law opacity) scales -7/2 κff ∝ ρT --> strong decrease with T 11/2 -1/2 - And one finds: Lcrit ∝ M* R* --> For growing protostars, Lcrit rises sharply surpassing interior luminosity.