Massive Protostars Accretion Mechanism Debate Protostellar Evolution: - Radiative stability - Deuterium shell burning - Contraction and Hydrogen Ignition Stahler & Palla (2004): Section 11.4 Accretion Mechanisms Core Accretion Competitive Accretion Stellar Collisions: now tend to be disfavored as it requires stellar densities that are much higher than observed.
Massive Star Formation Theories Core Accretion: wide range of dm*/dt ~10-5 - 10-2 M! yr -1 (e.g. Myers & Fuller 1992; Caselli & Myers 1995; McLaughlin & Pudritz 1997; Osorio+ 1999; Nakano+ 2000; Behrend & Maeder 2001) Turbulent Core Model: (McKee & Tan 2002, 2003) Stars form from cores that fragment from the clump. Competitive (Clump-fed) Accretion: (Bonnell, Clarke, Bate, Pringle 2001; Bonnell, Vine, & Bate 2004; Schmeja & Klessen 2004; Wang, Li, Abel, Nakamura 2010) Stars, especially massive stars, gain most mass by Bondi-Hoyle accretion of ambient clump gas. If in equilibrium, then self-gravity is balanced by internal pressure: B-field, turbulence, radiation pressure (thermal P is small) Cores form from this turbulent medium: at any given time there is a small mass fraction in unstable cores. These cores collapse quickly to a central disk to form individual stars or binaries. Originally based on simulations including only thermal pressure. Massive stars form on the timescale of the star cluster. Do massive protostars arise from dense cores with properties similar to those forming low-mass protostars? Starless core properties Low-mass Massive n(h 2 ) [cm -3 ] 10 4-10 5 10 5-10 6 T kin [K] ~10 10-20 M [M! ] a few hundreds Δv NT [km s -1 ] 0.1-0.3 1-2 P ext /k B [cm -3 K] 10 4-10 5 10 8-10 9
Radiative Stability Let s tentatively assume that the picture of collapse (including the accretion rate, ~10-6 - 10-5 M! yr -1 ) we have developed for low-mass clouds is applicable to all stellar masses and let the observations indicate when this hypothesis fails. [However, it now seems likely that higher accretion rates are needed for massive protostars] We need to solve the four Stellar Structure equations in the four variables r, P, T and L int : r = 1 4π r 2 ρ P = GM r 4π r 4 T 3 T = L int = ε T s t 3κL int 256π 2 σ B r 4 They must be supplemented by the equation of state and by knowledge of µ, κ, ε and 5 s as a function of ρ and T. M * cannot increase far above 1 M! before an important change occurs: the protostar s interior, which was fully convective from deuterium burning, now reverts to a radiatively stable state (because the average opacity declines and thus the interior luminosity can reach the surface more easily). If M * continues to grow, the radiative stability is maintained until it begins to fuse hydrogen. More quantitatively: To test for radiative stability, we need to compare at each M r -value L int with L crit, the critical luminosity, i.e. the maximum value that can be carried at that location by radiative diffusion. To obtain L crit, let s divide T 3 T = 3κL int 256π 2 σ B r 4 by P = GM r 4π r 4 in order to express the radiative luminosity in terms of T/ P.
At the stability limit, where the specific entropy is held fixed, we obtain: T M * R * 1 P M * 2 R * 4 L crit = 64πGM rσ B T 3 & T ) ( + 3κ ' P * κ ρt 7 / 2 (Kramer's Laws, valid @ T > 10 4 K) L crit M * 11/ 2 R * 1/ 2 The average L crit increases so sharply during protostellar accretion that it eventually surpasses the actual interior luminosity L int. At this point, the convection disappears. L crit > L int Radiative Stability s L int L D M * 0 ε D dm r M δ M * (M! ) δ = [D]/[H]X ΔE D m H L int stems mostly from deuterium fusion and its peak value is proportional to the accretion rate. The value of the transition mass is insensitive to the accretion rate and falls near 2 M!. radiative barrier L crit rises quickly with M *, whereas L int barely changes. After the first radiative barrier appears, the protostar s thermal structure quickly changes. L crit = L int for M * =2.38 M!, at the mass shell M r =1.70 M!.
Deuterium Shell Burning The radiatively stable region near 1.7 M! constitutes a barrier because it prevents freshly accreted deuterium from reaching the center through the turbulent transport associated with convection (driven by nuclear fusion!). Once the barrier is established, the residual deuterium inside is consumed rapidly and convection disappears throughout the interior volume. If infall persists, D accumulates in a thick mantle outside the barrier. The central T slowly rises with time. With the exhaustion of D, the increase of R * stops. M * /R * grows faster and the T rise accelerates. The base of the D mantle reaches 10 6 K, the fuel ignites and induces convection out to surface (fresh D from infall). 9 The onset of deuterium shell burning Luminosity as a function of interior mass for indicated values of the total protostellar mass, in solar units. The lowest profile corresponds to 2.38 M!, the protostar mass at which the radiative barrier first appears. Consequences: The injection of heat raises the specific entropy of the outer layers, and the protostar swells dramatically.
The four stages of deuterium burning 1. Active burning begins at the center 2. A radiative barrier appears 3. Radiative stability with interior depleted of deuterium 4. The fuel reignites in a thick shell, inducing convection in the outermost region. Mass-radius relation in a spherical protostar dm/dt = 1 10-5 M! yr -1 Onset of full convection Second initiation of central convection, as a result of hydrogen fusion Radiative barrier appearance The first rise in R * (M * ) from central deuterium burning occupies a relatively narrow mass range. Nevertheless, from the IMF we know that the majority of protostars are actually in this interval.
Contraction and Hydrogen Ignition If the protostar continues to accrete mass, both the convection and swelling gradually disappear. The L crit rise drives the convection zone toward the surface. When the star is almost fully radiatively stable, averaging over the stellar interior, <L int > L crit : # M < L int > 1 L * &! % ( $ 1 M! ' 11/2 # R * & % ( $ 1 R! ' The protostar s interior luminosity soon outstrips that produced by steady-state shell burning. For M * ~ 3 M!, <L int > ~ 200 L! and even dominates L acc. Between 5 and 6 M!, the luminosity surpasses 10 3 L!. -1/2 What accounts for this climb? the gravitational contraction of the bulk interior After the cessation of central deuterium burning, self-gravity keeps building until it becomes paramount. Even the large swelling due to shell ignition is soon reversed and the intermediate-mass protostar begins a rapid contraction. Rapid contraction The accreting star has not entered a state of dynamical collapse like that which terminates the first core. Velocities interior to the accretion shock remain subsonic, as gravity slowly squeezes the configuration against thermal pressure.
The time scale for R * to decrease significantly is much longer than t ff, and is set by the magnitude of the radiative losses, or the Kelvin-Helmoltz time: t KH GM 2 * R * L * $ M ~ 1 10 5 yr * ' & ) % 3.5 M! ( 2 $ R * ' & ) % 10 R! ( 1 $ L ' & ) % 310 L! ( The decline of R * implies a fast rise of the interior temperature. Once the central value of T c surpasses 1 10 7 K, the protostar begins to fuse ordinary hydrogen. The creation of 4 He from four H nuclei releases sufficient energy (ΔE=26.7 MeV) to halt the stellar contraction. Hydrogen burning in protostars commences when the total mass reaches about 5 M!. Initially, pairs of protons begin to combine: 1 1 H + 1 H 2 H + e + + ν The deuterium produced here almost immediately fuses with another proton to create 3 He. The conversion of 3 He to 4 He proceeds through PP chains. However, the temperature within our contracting protostar becomes so elevated that the CNO cycle takes over. Energy production rates for the PP chain and CNO cycle as a function of temperature (units of 10 6 K)
The CNO cycle of hydrogen fusion Along the way, four protons are consumed to produce one 4 He nucleus. Thus, the net reaction is: 4 1 H 4 He + 2e + + 2ν The energy output is 26.7 MeV as in the PP chains. The CNO cycle dominates once the protostar s mass is ~ 6 M! and T c ~ 2 10 7 K. Second initiation of central convection, as a result of hydrogen fusion Contraction halts At this point, the contraction begins to slow. The contribution from nuclear burning to luminosity grows at the expenses of that from gravitational contraction. The specific entropy near the center begins to rise. Soon, the entropy profile overturns and a central convection zone appears. The zone extends to M r = 1.3 M! by the time contraction halts (at M * = 8 M! ). The object is now an accreting main-sequence star. Infall gives only a minor 18 contribution to the total luminosity of 3.5 10 3 L! (but blocks V and UV photons).
Changing the accretion rate M =1 10 6 M! yr -1 The accretion luminosity is diminished; Smaller radius; M * /R * and internal temperature are higher The protostar begins main-sequence hydrogen fusion at a mass near 4 M!. This is empirically ruled out, because Herbig Ae/Be stars often have M > 4 M! but they originates from protostars that have not yet ignited hydrogen. M =1 10 4 M! yr -1 Larger radii; Lower internal temperature at every mass; Entry to the main-sequence is delayed to 15 M! BUT: 3 M a = m T 0 G implies a pre-collapse cloud temperature of 100 K!! However, larger accretion rates are ok, if we replace sound speed with a turbulent velocity dispersion (McKee & Tan 2002).