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MHD Simulation of Inner 0.5 AU of FU Ori, Zhu Et Al

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MHD Simulation of Inner 0.5 AU of FU Ori, Zhu Et Al Star Formation and the Origins of Planetary Systems Lecture 6: Pre-main sequence stars MHD simulation of inner 0.5 AU of FU Ori, Zhu et al. (2020) Background reading: (Crete II) Hartmann (2008) book, Chapters: 4.1-4.2, 8.4-8.8, all of 9, all of 11 !1 Summary Lecture 5 ▪Census of high-mass YSOs in Milky Way now possible due to new observational facilities ▪Spitzer, Herschel, masers, radio ▪Earliest pre-stellar core phase still elusive ▪Two theories for massive star formation ▪Scaled-up version low-mass: turbulent core accretion ▪Competitive accretion ▪Scenario (under debate) ▪IRDC → HMPO→ hot core→UC HII ▪Long lifetime and range of morphologies UC HII regions due to combination of effects ▪No optically visible pre-main sequence phase !2 Summary Image Credit: Cormac Purcell •Hyper-compact HII regions (eg Observed as cold, dense cores Kurtz et al. 2005) •Infrared-dark clouds •Ultra-compact HII regions - well •“mm-only” cores studied (see Churchwell and co.) Q: What is wrong with this picture? A: It has all of these stages separately, whereas in reality one finds observationally a hot core next to an ultra compact H II region. SPF course progress: where are we now? Date Who Lecture 18 Feb. EvD Motivation, history, & observational facilities (Star formation) 20 Feb. EvD Pre-stellar cores, cloud collapse 25 Feb. EvD SEDs, embedded protostars Has links to core courses: 27 Feb. EvD Outflows & jets • ISM • Stellar structure & evolution 3 Mar. EvD High mass star formation 10 Mar. MM Pre-main sequence star types, stellar birthline 12 Mar. MM Circumstellar disks 17 Mar. MM Disk evolution & planet formation (Planet formation) 24 Mar. MM Planet formation: Jovian vs terrestrial planets Has links to specialist courses: 26 Mar. MM Icy bodies in outer solar system, debris disk evolution • Astrochemistry 31 Mar. EvD Condensation processes, meteorites, missions • Aromatic Universe 2 Apr. EvD Chondrules, planetary atmospheres • Exo-planet Interiors & Atmospheres 7 Apr. MM Extrasolar planets 14 Apr. MM Astrobiology (Life formation) !4 Low-mass star system formation sequence: Hogerheijde (1998) , after Shu (1987) Stellar phase definitions: "pre-stellar" "proto-stellar" "pre-main sequence" "zero-age (cloud core collapse) (object at center of (object is optically visible; main sequence: ZAMS" collapsing cloud; no H-burning) (begin H-burning) not optically visible) Starting point for Stellar Structure & Evolution course !5 Lecture structure "pre-stellar" "proto-stellar" "pre-main sequence" "zero-age main sequence: ZAMS" 1. Timescales/definitions 2. Early collapse & protostar formation What happens TO the forming star. 3. Accretion from protostars to PMS 4. Internal stellar structure & PMS evolution in HR diagram What happens IN the forming star. !6 6.1 Characteristic timescales (1/2) Free-fall, tff Accretion, tacc Thermal, tKH (KH=Kelvin-Helmholtz) Period a star would shine with current Time required for a uniform- Time required for a uniform- luminosity, if only power source were density core to collapse under density core to accrete (not fall!) conversion of gravitational energy to gravity to its center, if it suddenly onto a central point source, heat. lost all pressure support. assuming a fixed dM/dt. Hartmann, p. 60-61 Time it takes a heat wave to propagate through optically thick stellar core. 2 3π Rcore Mcore |W| GM* tff = ∼ tacc = · tKH = ∼ 32Gρ cs Macc L R*L* For M* ~1 Msun, then tff ≪ tKH and tff < tacc. !7 Characteristic timescales (2/2) Protostellar phase Pre-main sequence phase tacc < tKH tKH < tacc Rapid accretion onto star; accreted material cannot adjust Inefficient accretion, accreted material now has time to thermally, so dissipates kinetic energy into heat at accretion thermally adjust. Protostellar core evolves towards MS shock interface. on thermal timescale (tKH). Luminosity generated by accretion shock. Luminosity generated through slow, radial contraction. !8 Categories of pre-main sequence stars, by mass. Brown dwarfs Classical Intermediate-mass Herbig AeBe Stars T Tauri Stars T Tauri Stars 1.5-15 Msun, M< 0.08 Msun, M< 1Msun, 1<M< 1.5Msun, F6-B0 SpT SpT L, T - M5 SpT M5-K0 SpT G9-F7 (end state) !9 Lecture progress "pre-stellar" "proto-stellar" "pre-main sequence" "zero-age main sequence: ZAMS" 1. Timescale definitions 2. Early collapse & protostar formation 3. Accretion from protostars to PMS 4. Internal stellar structure & PMS evolution in HR diagram !10 6.2 Collapse of cloud core to initial protostar • Numerical protostellar collapse models (∆� ~20 orders of magnitude, ∆r ~7 orders). Seminal work by Larson (1969). • Consider gas (H2, H, H+, He, He+, He++) & dust with information on turbulent viscosity & opacity (κνabs, κνsca) • Solve structure equations: set of 10 partial differential equations for mass conservation, energy balance and momentum conservation, plus Poisson equation for gravity + radiation energy balance. Four distinct collapse phases from cloud core to protostar. Understood mostly through hydro- dynamical simulations, as observationally difficult. Derivations given in Larson (1969); Shu (1977); Hartmann (2008) book, sections 4.1, 4.2. !11 Phase 1. Free-fall collapse (� < 10 -13 g cm-3) Derivations in lecture #3: Singular isothermal sphere (SIS) model Shu (1977) · 3 Macc = 0.975 cs G sound speed ("a" in SPF#3) -6 -1 ~ 1.6x10 Msun yr @10 K Collapse is isothermal, on free-fall timescale, with an accretion rate dependent on T. Compressional heat is radiated away by thermal dust and molecular emission. !12 Phase 2a. First core (� > 10 -13 g cm-3) Fig. 3, Machida & Matsumoto (2011) Inner layers become optically thick to IR radiation: T rises, then thermal pressure halts collapse: HSEQ. Formation of first hydrostatic core, ~3 AU in radius, M~0.004 Msun. Collapse continues adiabatically. !13 Problem! How long can 1st core maintain thermal pressure support? Opacity gap • Hydrostatic EQ maintained by high ] temperatures. -1 g 2 • High temperatures maintained by [cm R κ optical depth (opacity source) • But as T increases, grains sublimate & molecules dissociate...opacity gap! Opacity: log － Ices Rocks H2 H H, He (<150 K) (<1400 K) (<3000 K) ion. So what happens next? Fig. from Henning & Stognienko (1996) https://www2.mpia-hd.mpg.de/home/henning/Dust_opacities/Opacities/opacities.html !14 st Phase 2b. Second collapse (Tc > 2000 K, inside 1 core) Fig. 3, Machida & Matsumoto (2011) H2 dissociates into atomic H; 1st adiabatic exponent Γ= (dlog P/dlog ρ)S drops below critical value of 4/3 → Dynamical instability produces second collapse. !15 Phase 3: Opacity phase & second core Fig. 3, Machida & Matsumoto (2011) Eventually stellar densities (ρ ≈ 10-2 g cm-3) are reached. Atomic H ionizes, producing opacity such that Γ > 4/3; formation of second stellar core + first circumstellar disk. Series of additional collapse 2 phases corresponding to ionization of He and other atoms. Core grows to ~0.01 Msun in <10 yr. !16 Density vs radius during collapse & core stages. Larson (1969) !17 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse. 1st core, 2nd core, H2 dissociative collapse, isothermal collapse, optically thick transition RJ MJ T Tohline (1982), Bate (1998) !18 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse. RJ MJ Isothermal collapse T Tohline (1982), Bate (1998) !19 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse. Optically thick transition RJ 1st core T Isothermal collapse MJ Tohline (1982), Bate (1998) !20 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse. Optically thick transition RJ H2 dissoc. 1st core collapse T Isothermal collapse MJ Tohline (1982), Bate (1998) !21 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse. Optically thick transition 2nd core H2 dissoc. 1st core T collapse Isothermal MJ collapse Tohline (1982), Bate (1998) !22 Summary of protostar formation. 17 & 24 March Planet Formation by S. I. Planet Formation by C. A. Fig. 2, Inutsuka et al. (2010) !23 Lecture progress "pre-stellar" "proto-stellar" "pre-main sequence" "zero-age main sequence: ZAMS" 1. Timescale definitions 2. Early collapse & protostar formation 3. Accretion from protostars to PMS 4. Internal stellar structure & PMS evolution in HR diagram !24 6.3 Accretion (Phase 4: Accretion as a protostar) Final protostellar core is optically thick. Material still accreted from high angle. Luminosity produced by accretion shock: structure where kinetic energy of infalling material is thermalized and transformed into UV radiation, which is converted into IR radiation by surrounding material. Cooler gas settles down layer by layer to form protostar. Star rapidly becomes more massive than disk. Fig. 2, Machida & Matsumoto (2011) !25 Scale of accretion! So how long does this phase last? Fig. 2, Machida & Matsumoto (2011) !26 Estimate length of accretion-heavy phase · −6 −1 (constant dM/dt from SIS collapse models; SPF#3) M ∼ 1.6 × 10 Msun yr M 1M t = core = sun ∼ 0.6 Myr acc · −6 −1 M 1.6 × 10 Msun yr From population statistics (Dunham et al. 2015): tClass 0/I = 0.6 Myr SPF #3: But how does this dM/dt compare with rates for observed protostars...? !27 The "luminosity problem" L~1 Lsun M ~ 0.1 Msun Dunham+2013 R ~ 1 Rsun LClass 0/I = L* + Lacc · GM M ∼ * R* · −7 −1 M ∼ 10 Msun yr tClass 0/I = 10 Myr Too small! Too long! Kenyon et al. (1990), Kenyon & Hartmann (1995), Dunham et al. (2010, 2013, 2015) !28 A solution: episodic accretion Protostar PMS star Infalling FU Ori outbursts • ~10x difference in envelope-to-disk infall rate -4 Envelope vs disk-to-star mass accretion rate ] -1 • A mass pileup in the disk eventually triggers an yr ☉ EXor outburst accretion burst with rates spiking to ~104 M☉ yr-1 [M -6 ) Ṁ • Base accretion rate decays with time -8 -1 log ( to ~10 M☉ yr by PMS phase Disk accretion Way the star gets most of its mass.
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