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

(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

Tohline (1982), Bate (1998) !18 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse.

Isothermal collapse

Tohline (1982), Bate (1998) !19 Exercise: Identify (& motivate) critical steps in diagram of T vs � during collapse.

Optically thick transition

RJ 1st core

Isothermal collapse

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. -8 Calvet et al. (2000) Also restructures terrestrial planet-forming region.

4 5 6 7 log (Age) [yr] Hartmann & Kenyon (1996) !29 Observational evidence for episodic accretion

Fluxes of some stars (FU Orionis-types) increase by orders of magnitude, in addition to small scale variability. • Luminosities increase by factors of 100 (6 mags). • FUors stay in high state for ~10-100 years.

Miller et al. (2011)

Hartmann & Kenyon (1996) Credit: Caltech/T. Pyle (IPAC)

Kenyon Crete II, Chapter 9 of Hartmann (2008) !30 Observational signatures of how FU Ori outbursts are triggered.

Hartmann & Kenyon (1996) water absorption

silicate emission

Zhu et al. (2008) • Optical spectra (inner disk) contain broad, atomic FU Ori absorption, typically blue-shifted by ~100 km/s. • Near-IR spectra (inner disk) contain strong water absorption bands. Mid- IR spectra (outer disk) contain silicate emission bands. • !31 Thermal instabilities trigger outburst events.

Hot, ionized midplane: high dM/dt (Typical FU Ori star)

Cool, neutral midplane: low dM/dt (Typical T Tauri star)

Armitage (2011), Fig. 10, Section 6. INSTABILITIES AND OUTBURSTS Armitage, Livio, & Pringle (2010) Each PMS star experiences ~10-100 such outbursts. !32 Weaker/shorter outburst events continue through PMS phase.

EXors: another class of outbursting stars. • Flare by 1-5 mag every few years, stay bright for several months • Named after prototype EX Lupi, which ﬂared again in 2008

Kospal et al. (2011) • New eruptive stars being discovered

So how does this thermally unstable material get onto the star?

(In constrast with the magnetospheric accretion paradigm...) !33 Magnetospheric accretion paradigm (non-outbursting times)

Infall from protostellar envelope

accretion shock

Hartmann et al. (2016), AR&A review Hartman (2008), Chapter 8.4 !34 Observational evidence for magnetospheric accretion.

emission lines from accretion columns

Hartmann et al. (2016)

Brickhouse et al. (2010) • UV continuum & Balmer jump • "Veiling" of photospheric absorption lines • Strong, broad optical emission lines • P-cygni wind proﬁles in some emission lines !35 Observational evidence for magnetospheric accretion (cont'd)

accreting T Tauri stars Classical T Tauri stars

non-accreting T Tauri star

-5 10 M☉/yr McClure et al. (2013a) 10-6 M☉/yr

10-7 M☉/yr non-accreting

Weak-lined T Tauri stars

Barentsen et al. (2013)

4000 6000 8000 wavelength (Angstroms) !36 PMS stellar classiﬁcation: exemplars of magnetospheric accretion.

Classical T Tauri Star (CTTS): M< 1Msun, SpT M5-K0

"Solar precursors" • Will evolve to produce mid-G type main-sequence stars • Ages <108 yr (strong Li λ6707 Å absorption) • Strong Hα emission & X-ray emission (high accretion) • Kinematic association with molecular cloud complexes • Tend to have near- & mid-IR excesses (disks!)

Weak-lined T Tauri Star (WTTS)

Like CTTS, but with: • Weaker Hα emission, stronger X-ray emission (little accretion) • Tend to lack near-/mid-IR excesses (evolved disks) Hartmann (2008), Chapter 8.4-8.7 !37 Unclear whether magnetospheric accretion operates here.

Herbig AeBe Star: 1.5-15 Msun, F6-B0 SpT • Ages: 0.1 - few Myr • Located in or near dark clouds • Have reﬂection nebulae • Have near- & mid-IR excesses (disks!) • Weak magnetic ﬁelds • generally higher dM/dt

Missing non-accreting Herbigs. Field stars?

Hartmann (2008), Chapter 8.8 !38 3D Simulations of accretion columns during stable vs bursting accretion.

Stable accretion Unstable accretion Orderly, along B-ﬁeld lines to poles. Along midplane, through B-ﬁeld lines to Romanova et al. (2008) stellar mid-equatorial regions. !39 Outcomes at the end of accretion. Protostar PMS star

Infalling -4 FU Ori outbursts Envelope ] -1 yr ☉ EXor outburst

[M -6 Ṁ ) log (

Disk accretion -8 Calvet et al. (2000)

4 5 6 7 log (Age) [yr] Hueso & Guillot (2005)

M<3 Msun: low-mass stars stop accreting and contract toward main sequence on Kelvin-Helmholtz timescale. M>3 Msun: massive protostars arrive on main sequence while accretion is still going on (‘cocoon’ stars)

!40 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

!41 6.4: Internal stellar structure & PMS evolution in Hertzsprung-Russell diagram

Goals • Understand how L , R, M, and T depend on M(t). • Understand how to estimate ages for PMS stars (and the caveats on these estimates).

(Hartmann 2008 book, Chapter 11) !42 Input stellar structure equations (1/2)

See Stellar Structure & Evolution class.

(from Carsten Dominik's notes)

!43 Input stellar structure equations (2/2)

(from Carsten Dominik's notes)

!44 Evolution viewed through energy comparison: L(M)

Energy released by accretion

Lacc Energy radiated away at stellar surface

Lsurf Lrad LD Energy transported radiatively

Energy released by burning deuterium

Image: M. K. McClure !45 Evolution of Luminosity as a function of Mass

1) Lsurf > Lrad • Fully convective star

2) Lacc >Lrad > Lsurf • Not thermally relaxed • Non-homologous contraction • L* rises

3) Lrad >Lacc • Thermally relaxed • Homologous contraction

!46 Internal stellar heating: deuterium burning precedes H burning

• Deuterium burning plays an important role in protostellar phase ([D]/[H]≈1.5x10-5). Slows down contraction. • 106 K: 2D + 1H → 3He + γ 7 • 10 K: H burning via pp-cycle (<1.2 Msun) or CNO cycle (>1.2 Msun) • Interiors of protostars not yet hot enough to fuse H, but can burn D once star ~0.1 Msun. Convection transports heat to surface, and fresh D to center (a).

-5 -1 • Steady-state burning L≈15 Lsun for dM/dt~10 Msun yr

!47 Internal stellar heating: deuterium burning (cont'd)

Protostars < 2 MSun • Burning of deuterium acts as a thermostat, 6 keeping TC~10 K. • This causes protostar to swell to a characteristic size, determined by its mass.

Protostars 2-4 MSun • If 2.4

!48 Effects of D-burning on stellar structure: M-R relation for 8 Msun star

But what happens after D used up? • Lack of nuclear burning→ heat loss → gravitational contraction Start of • tKH slow compared with tff: contraction is D-shell burning Ignition of central H quasi-static. At any instant, hydrostatic via CN-cycle equilibrium is reached. 1/3 • TC∝ρ ∝ 1/R; increases during contraction until 107 K → H fusion! No D-shell burning • H burning heating balances contraction → Ignition of Arrival on central deuterium main sequence thermal equilibrium: main sequence.

(Classical theory: Hayashi 1961; Iben 1965)

!49 Hayashi track & forbidden zone

•Interior of stars fully convective

•Teff ≪ TC because of energy radiated away

•Hayashi temperature: any star of ﬁxed M* and R* has minimum effective temperature Teff~3500 K.

This temperature is insensitive to R*→ track is nearly vertical in H-R diagram

•Region with cooler temperatures is "Hayashi forbidden zone".

•For M<0.08 Msun, TC never high enough for H- burning → steady contraction to brown dwarf

!50 Hayashi track & forbidden zone: the return of the opacity gap...

•Vertical behavior is the result of opacity of gas in Opacity gap ]

outer region of protostar, in particular opacity gap! -1 g 2 If temperature too low (~2000 K), outer layers • [cm R optically thin → no photosphere: forbidden region κ

• From 3000-10000 K, very steep increase opacity with T→ minor change in Teff compensates for Opacity: log

large change in density of photosphere and － Ices Rocks H2 H H, He entropy (<150 K) (<1400 K) (<3000 K) ion.

Fig. from Henning & Stognienko (1996) https://www2.mpia-hd.mpg.de/home/henning/Dust_opacities/Opacities/opacities.html !51 Birthlines & isochrones

6 •D acts as thermostat, keeping TC close to 10 K. Since TC∝M*/ R*→ mass-radius relation for protostars

•Assume mass accretion stops on timescale << tKH isochrones: •M*, R*, L*, and Teff are now all known for the PMS track → tell age ﬁrst appearance in HR diagram → birthline: where stars

become optically visible. Palla & Stahler (1998) •Isochrones show age after birthline for all masses.

•But for M ≥ 8 Msun, birthline intersects ZAMS → massive stars have no optical PMS phase

!52 Birthline/age measurement problems

• Hayashi track then ends when radiative core develops: then move horizontally along a radiative track. Henyey et al. (1955)

-5 -1 • Spherical accretion at constant rate ~10 Msun yr assumed: higher dM/dt yields smaller ages!

• No rotation, no magnetic ﬁelds included • Accretion disk modeled as photospheric boundary condition; assumes no disks in PMS phase Palla & Stahler (1993) • When and why does accretion stops? Role of outﬂows?

!53 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

!54 Example review suggestions

• Construct tables listing properties (e.g. ages, sizes, temperatures, luminosity generating mechanisms, convective/radiative interiors) for the different types of PMS stars discussed. • Take a star of a given mass and run through the HR diagram to understand why it moves as it does. • Take sample T Tauri/cloud properties (given in SPF #3), and calculate what various timescales should be, compare with expectations? • For more depth: reading indicated section of the Hartmann (2008) book.

!55 !56 !57 !58 Stellar phases:

Zero-age Proto-stellar Pre-main sequence main Optically visible? No Yes sequenceYes H-burning? No Deuterium only Yes Accretion Rapid, high Ineﬃcient, low None Luminosity Dissipation of kinetic energy into heat through Slow stellar contraction towards main H-burning source? accretion shock at stellar surface. sequence. Stellar core evolutionary Accretion: �acc < �KH Thermal: �KH < �acc timescale

Have them ﬁll this out themselves.

!59 Context: masters curriculum ladder 4. Masters Research Projects

... et cetera.

3. Specialist astronomy Aromatic Universe & Instrumentation courses Exo-planet Interiors & Atmospheres Astrochemistry ... et cetera.

Computational Astrophysics Galaxy Dynamics & Evolution

Star & Planet Formation Stellar Structure 2. General astronomy courses & Evolution

Interstellar medium

Large scale-structure & Galaxy Formation 1. Core astronomy courses

Origin & Evolution Photo by Simon Matzinger from Pexels of the Universe !60 Date Who Lecture Course connections 18 Feb. EvD Motivation, history, & observational facilities [Instrumentation courses] 20 Feb. EvD Pre-stellar cores, cloud collapse ISM, astrochemistry 25 Feb. EvD SEDs, embedded protostars 27 Feb. EvD Outﬂows & jets [Galaxy dynamics & evolution] 3 Mar. EvD High mass star formation [Galaxy dynamics & evolution] 10 Mar. MM Pre-main sequence star types, stellar birthline Stellar structure & evolution 12 Mar. MM Circumstellar disks 17 Mar. MM Disk evolution & planet formation [Galaxy dynamics & evolution] 24 Mar. MM Planet formation: Jovian vs terrestrial planets Exo-planet Interiors & Atmospheres 26 Mar. MM Icy bodies in outer solar system, debris disk evolution 31 Mar. EvD Condensation processes, meteorites, missions Astrochemistry 2 Apr. EvD Chondrules, planetary atmospheres Exo-planet Interiors & Atmospheres 7 Apr. MM Extrasolar planets Exo-planet Interiors & Atmospheres 14 Apr. MM Astrobiology Star formation [ ] = similar methods Planet formation New directions !61 Context: Tree of (astronomy) knowledge

Photo by Simon Matzinger from Pexels !62 Masters curriculum ladder 4. Masters Research Projects

... et cetera.

3. Specialist astronomy & Instrumentation courses Aromatic Universe Exo-planet Interiors & Atmospheres Astrochemistry ... et cetera.

Computational Astrophysics Galaxy Dynamics & Evolution

Star & Planet Formation Stellar Structure 2. General astronomy courses & Evolution

Interstellar medium

Large scale-structure & Galaxy Formation 1. Core astronomy courses Origin & Evolution Photo by Simon Matzinger from Pexels of the Universe !63 Collapse of cloud core to initial protostar Example core initial conditions:

M = 1Msun ρ = 10−19 g cm−3 ∼ n = 105 cm−3 T = 10 K

!64 Lecture outline

• Introduction to each stellar phase, emphasis on physical mechanisms & timescales

• Comparison tables between stellar phases

• Application to stars of different masses

!65 · 3 3/2 Macc = 0.975 cs G ∝ T

5 −1 G ∼ 1.90809 × 10 Rsun Msun (km/s)

G ∼ 6.674 × 10−8cm3 g−1 s−2 kb ∼ 1.380649 × 10−16ergK−1

1g cm2 s−2

!66 1. Timescales 2. Early growth and collapse 3. Dust envelope 4. Stellar structure I. Mass-radius relation II. Deuterium burning III. Lithiumdestruction IV. Hydrogen ignition 5. Magnetospheric accretion I. Theory II. Observations 6. Evolution in the HR diagram I. Birthline II. Hayashi tracks 7. PMS classiﬁcation I. T Tauri stars II. Weak line T Tauri stars III. FUOrionisstars IV. Herbig AeBe stars

!67