Ast 777: and Formation Jonathan Williams, University of Hawaii

Accretion disks

https://www.universetoday.com/135153/first-detailed-image-accretion-disk-around-young-star/ The main phases of

https://www.americanscientist.org/sites/americanscientist.org/files/2005223144527_306.pdf Star grows by accretion through a disk

https://www.americanscientist.org/sites/americanscientist.org/files/2005223144527_306.pdf Accretion continues (at a low rate) through the CTTS phase

https://www.americanscientist.org/sites/americanscientist.org/files/2005223144527_306.pdf The of a star is, by far, the dominant parameter that determines its fate.

The question for star formation is how reach their ultimate mass. Mass infall rate

for a BE core that collapses A strikingly simple equation! in a free-fall time

isothermal sound speed

calculated for T=10K

This is very high — if sustained, a solar mass star would form in 0.25 Myr…

…but it can’t all fall into the center Conservation of

Bonnor-Ebert sphere, R ~ 0.2pc ~ 6x1017cm 11 , R ~ 3R⊙ ~ 2x10 cm

=> results in a compression of spatial scales > 6 orders of !

=> spin up!

https://figureskatingmargotzenaadeline.weebly.com/angular-momentum.html Conservation of angular momentum

Angular momentum

Moment of inertia

J is conserved

Galactic rotation provides a lower limit to core rotation (R⊙=8.2kpc, V⊙=220 km/s)

Upper limit to rotation period of the star So how do stars grow?

• Binaries (~50% of field stars are in multiples) • Lose the angular momentum through outflows • Collapse through a disk, not directly onto star

https://www.eso.org/public/news/eso1916/ Disk size

Can estimate size by balancing vs centrifugal force

Cons ang mtm

~ 100au

This is sometimes referred to as the “centrifugal radius”

Disk size

Can estimate size by balancing gravity vs centrifugal force

Cons ang mtm

~ 100au

very sensitive to initial core size and angular speed

(also ignores magnetic fields which add additional parameters that are not well measured)

Numerical simulations on core-disk scales

https://www.kuffmeier.com/movies Disk evolution over 1Myr

https://www.kuffmeier.com/movies Accretion disk physics

vKep Fg

=> radial shear, Ω ~ r-3/2

=> any will lead to , heating, and radiation Accretion disk physics

r1

r2

For each particle, the angular momentum and energy are Accretion disk physics

The sum for both particles is

If the particles move, J must remain the same (if no external torque acts on the system), but friction in the shearing disk means that E will decrease Accretion disk physics

Viscous disks naturally spread out

Pioneering paper: Lynden-Bell & Pringle 1974 Surface density evolution

Lynden-Bell & Pringle 1974 Bath & Pringle 1981 Energy dissipation means the inner particle moves inwards; it loses angular momentum and the outer particle gains (J ~ r1/2)

Ultimately, the inner particles fall, or accrete, onto the star.

(the last step is along magnetic field lines) Accretion

—> a (solar mass) protostar is bright, and readily detectable well before it begins Accretion observations

Class 0: fully embedded, can only use luminosity and kinematic measures of central mass

Class I: lines

Class II: access to a variety of UVOIR diagnostics

Recommended reading —>

2016, Annual Reviews Accretion observations

Focus on Class II for now, as it is observationally accessible, though the star has reached ~99% of its final mass

“Balmer jump”

Balmer series —> relates to #H atoms and assuming free-fall onto stellar surface gives mass accretion rate

Gas from the disk funnels along magnetic field lines, falling onto the surface in localized regions at ~ 300 km/s free-fall speed X-rays absorbed, re-radiated to produce UV-optical —> shocks —> X-rays continuum excess (—> “veiling”) and emission lines

Hartmann et al. 2016 Accretion variability (a defining characteristic of T Tauri stars)

Hartmann et al. 2016 Mass accretion rates vs

Determined from the excess continuum and/or emission lines

(with considerable scatter)

Hartmann et al. 2016 -8 Typical values ~ 10 M⊙/yr

=> M⊙/(dM/dt) ~ 100 Myr!

=> accretion rate must be ~102 x greater in the embedded (Class 0/I) phase

But accreted mass over the ~2 Myr lifetime of Class II YSOs is 0.01M⊙ = 10 MJupiter

=> Class II disks have enough mass (and time) to form planetary systems! Mass accretion rates vs time

(with considerable scatter)

Hartmann et al. 2016 Unanswered questions

- What sets the mass accretion rate? - Why does it vary as the square of the stellar mass? - Why does it decline approximately inversely with time?

Inherently hard because of variability and much of the accretion luminosity comes out in the UV A short commercial break…

~1000 (DDT) to take UV spectra of young stars + 255 hours VLT Large program + several other ancillary programs + Maunakea?

Possibilities for student involvement (but needs funding…) Accretion rates of Class I

Expected to be higher than in Class II, because they have short lifetimes (~0.5 Myr) and the star needs to gain most of its mass before the envelope is lost.

But hard to measure equivalent widths due to veiling. The warm envelope/disk adds a continuum to the stellar spectrum which decreases the line-to-continuum ratio and/or simply fills in absorption lines.

Fλ Fλ Wλ

Wλ

λ λ

=> need high s/n, high spectral resolution near-infrared observations Accretion rates of Class I protostars

standard stars Class I YSOs

Template matching to get SpT => Teff

HR diagram to get R★

Can also use NIR emission lines such as Brγ to estimate mass accretion rates

Doppmann et al. 2005 Accretion rates of Class I protostars

template + accretion observed

accretion continuum

template

But we don’t generally find substantially higher accretion rates…

Herczeg & Hillenbrand 2014 BLT diagram

Huge scatter in Lbol, and tendency for slightly higher Lbol at lower Tbol (Class 0/I), but its not as strong an effect (~102) as simple core collapse theory predicts

Dunham et al. 2014 The protostellar luminosity problem

- first identified by Kenyon et al. 1990 - proposed that stars gain their mass in short bursts of high accretion and that we generally see YSOs in their quiescent state

- alternative suggestion is that most of the low luminosity YSOs are actually proto-brown dwarfs (Offner & McKee 2011)

- (This would imply that the protostellar mass function differ from the final mass distribution [stellar IMF] and requires the formation timescale to depend on mass. However, the observational situation is unclear - an interesting project would be to measure the Class II stellar mass distribution through a complete ALMA survey of a young star-forming region…) The protostellar luminosity problem

Hartmann et al. 2016 Episodic accretion

https://sites.lsa.umich.edu/lhartm/wp-content/uploads/sites/496/2017/05/mdotseq.jpg Episodic accretion - due to MRI / GI?

Core collapse dumps material onto a disk at the centrifugal radius, but the disk cannot transfer material onto the star as fast as it acquires it - so it grows in mass until it becomes magnetically and/or gravitationally unstable

Vorobyov et al. 2013 Are disks gravitationally unstable?

Not apparent in the dust, but possibly in the gas?

https://public.nrao.edu/news/alma-captures-stirred-up-planet-factory/

Huang et al. 2020 FUor outbursts

Rarely seen, 8 since 1936 (=> greater than local SFR => stars must do this more than once) But observations are biased toward optical => late stages

Hartmann et al. 2016 Infrared outbursts

Notes: - this is not as luminous as a canonical FUor burst - 2MASS+UKIDSS comparison show outbursts are rare, once per ~104 years - ongoing JCMT monitoring project of Class 0/I sources is finding some, https://www.jpl.nasa.gov/news/news.php?feature=4518 small variability

Safron et al. 2015 Further reading / viewing

Hartmann, Herczeg, & Calvet 2016, Annual Reviews https://ui.adsabs.harvard.edu/abs/2016ARA%26A..54..135H/abstract