Michael Küffmeier (Marie Skłodowska-Curie global fellow)

Z.-Y. Li (UVA), P. Caselli (MPE), J. Pineda (MPE), S. Jensen (MPE), T. Haugbølle (NBI)

Modeling constraints on the mass reservoirs of forming disks

Let's go back in time to the year 2014

Credit: ALMA (ESO/NAOJ/NRAO)

50 au

Wow!

Credit: ALMA (ESO/NAOJ/NRAO)

Credit:

DSHARP team

10 au

50 au

Credit:

B. Saxton / I. Cleeves

The classical picture

Greene 2001

star formation

planet formation

History of modeling disk formation

spherical core collapse:

rotation

magnetization (mass-to-flux ratio)

non-ideal MHD effects

dust evolution

turbulence

useful for parameter studies

\rho(r) = \frac{\rho_{\rm c} R_{\rm c}^2}{R_{\rm c}^2 + r^2}

Bonnor-Ebert sphere

or uniform density

\rho(r) = \rho_{0}

History of modeling disk formation

What about magnetic fields?

Help! Where is the disk?!

Santos-Lima et al. 2012

Hydro

ideal MHD

L_{\rm mag} = \int_{t_{\rm c}}^{t}\int^V r (\mathbf{J} \times \mathbf{B})_\phi \mathrm{d}V\mathrm{d}t

Magnetic braking catastrophe

Angular momentum is transported too efficiently away from the disk

magnetohydrodynamics

\frac{\partial \mathbf{B}}{\partial t} = \nabla\times (\mathbf{v}\times\mathbf{B})

ideal MHD

\color{red}-\nabla\times[\eta_{\rm O} (\nabla \times \mathbf{B})]
\color{purple}-\nabla\times \{\eta_{\rm H} [(\nabla \times \mathbf{B}) \times \mathbf{B}/B] \}
\color{blue}-\nabla\times \{\eta_{\rm AD} \mathbf{B}/B \times [(\nabla \times \mathbf{B}) \times \mathbf{B}/B] \}

Ohmic dissipation

Hall

ambipolar diffusion

Non-ideal

Non-ideal MHD

Masson et al. 2016

resistivities quench pile-up of magnetic field 

avoids magnetic braking catastrophe

see Hennebelle et al. 2016 or Lee et al. 2021 for analytical studies

more references in reviews by Wurster & Li 2018 and Tsukamoto et al. 2023

History of modeling disk formation

What about magnetic fields?

Help! Where is the disk?!

Ohmic, Ambipolar, Hall 

Santos-Lima et al. 2012

Hydro

ideal MHD

non-ideal MHD

non-ideal MHD is not a single parameter that is turned on or off

Achtung!

Effect of ionization on disk size

increasing ionization rate

enhanced magnetic braking

smaller disks

Küffmeier, Zhao & Caselli 2020

rotation

infall

from light to dark colors: high to low ionization rates

see also Wurster et al. 2018

Streamers!*

What about magnetic fields?

Help! Where is the disk?!

Ohmic, Ambipolar, Hall 

Turbulence

Santos-Lima et al. 2012

Hydro

ideal MHD

non-ideal MHD

turbulence + MHD

Other effect: dust

dust growth weakens magnetic braking => larger disks

Zhao et al. 2018, Marchand et al. 2020

dust-rich disks from collapse

"ash-fall" scenario

Tsukamoto et al. 2021

 Lebreuilly et al. 2020

dust accumulates

*talk to Stefan Heigl!

What fraction of the gas and dust returns to the disk after being ejected by an outflow?

Key question

Credit: Tsukamoto et al. 2021

"Ash-fall" scenario aka conveyor belt

Increase in dust-to-gas ratio because dust can grow in disk and return

Tsukamoto et al. 2021

Is this the full picture?

Credit: ALMA (ESO/NAOJ/NRAO)

Ginski et al. 2021

Yen et al. 2019

Garufi et al. 2021

Pineda et al. 2020

50 au

see also:

BHB1 (Alves et al. 2020), GM Aur (Huang et al. 2021), IRS 63 (Segura-Cox in prep.), AB Aur (Grady et al. 1999 / Fukagawa et al. 2004), ...

Per-emb-50

Valdivia-Mena et al. 2022

Science question:

Can we get better (statistical) constraints on the relevance and importance of (late) infall from existing simulation data? 

Model star formation in a Molecular Cloud

isothermal magnetohydrodynamical (MHD)

adaptive mesh refinement (AMR) simulations with RAMSES

maximum resolution: ≈25 au (level of refinement: 15), root grid about ≈1600 au (level 9)

Total mass: 3000 solar masses

periodic boundary conditions

altogether 321 sink particles at last snapshot (2 Myr after the formation of the first star)

simulation setup including detailed description of sink recipe presented in Haugbølle+2018

Küffmeier, Jensen & Haugbølle '23

Late infall is common for stars*

 *unless they remain tiny

On average, stars with final masses of more than 1 solar mass accrete more than 50 % of their mass after 500 kyr

Note that some protostars still accrete a lot of mass after 1.2 Myr

Küffmeier, Jensen & Haugbølle '23

Origin of accreting gas

The accretion reservoir can extend beyond the core

(see also Smith+ 2011, Kuznetsova et al. 2020, Pelkonen+ 2021)

Two phase process:

Initial collapse followed by varying amount of post-collapse infall

Results:

Possibility of replenishing and refreshing the mass and chemical budget

Küffmeier, Jensen & Haugbølle '23

Angular momentum budget

  • Large scatter of ang. mom.
  • Increasing specific angular momentum for increasing final stellar mass

Specific angular momentum computed from all accreting tracer particles at the first snapshot after star formation

R_{\rm c}=\frac{J^2}{GM}
  • High centrifugal radii show importance of ang. mom. transport
  • subtle correlation with mass (inherited by disks??)

"We find marginal relationships between disk sizes and M*." (Long+ 2022)

Küffmeier, Jensen & Haugbølle '23

Late infall has high ang. momentum

Küffmeier, Jensen & Haugbølle '23

Key question:
Where does infalling material land?

YSOs can appear younger than they really are

How old is the protostar?

Küffmeier, Jensen & Haugbølle '23

A poor analogy to a conference

Session start

Coffee break!

Streamers (and shadows?) as signs of infall

Formation of misaligned configuration

Observable as shadows in outer disk

Küffmeier, Dullemond, Reissl & Goicovic 2021

Ginski et al. 2021

300 au

Zoom-in method

Küffmeier et al. 2017

  • adaptive mesh refinement
  • ideal magnetohydrodynamics
  • turbulence driven by supernovae
  • stars modelled as sink particles

Zoom-in on embedded protostars

Küffmeier, Calcutt & Kristensen 2019

bridge structure similar to IRAS 16293--2422 (e.g. Sadavoy+ 2018, van der Wiel+ 2019, Maureira+ 2020)

Küffmeier, Reißl et al. 2020

~1500 AU

Küffmeier et al. 2018

The connection to the larger scales

Küffmeier, Haugbølle & Nordlund 2017

Summary

Pineda ... Küffmeier et al. 'Protostars and Planets VII'

.

 

 

 

.

Segura-Cox et al. in prep.

Star & disk can be replenished by infall of initially unbound material

Post-collapse infall provides plenty of angular momentum

YSOs can be rejuvenated

Accretion of a binary system

You are missing

non-ideal MHD

radiative transfer

resolution

dust

...

1000 au

zoom-in with maximum resolution of 3 AU; polytropic equation of state; ideal MHD

Accretion of a binary system

zoom-in with maximum resolution of 3 AU; polytropic equation of state; ideal MHD

1000 au

Accretion of a binary system

Caveat: zoom-in with only maximum resolution of 3 AU; polytropic equation of state; ideal MHD; no radiative transfer (more to be done, but intriguing)

about 30 % of accreting mass goes through the star's own disk

almost 10 % of accreting mass of companion goes through the primary star's disk

Questions for discussion

  • What are observational tracers?
    Can streamers, misalignment/warping help?
     
  • How do outflows change the picture? Do they drastically reduce the probability of late infall?
     
  • To what extent is the excess of high angular momentum inherited by the disk?
     
  • Where does the infalling material land? Is angular momentum efficiently removed that it lands on the disk (see e.g. results by MK+18 or Lee+21) or does it land at large (initial) radii?
  • What about dust and dust traps/rings?

The connection to the larger scales

Küffmeier et al. 2017 / 2022 subm.

Gas from beyond the prestellar core can fall onto the star-disk system

Simulate cloudlet infall onto disk

AREPO, pure hydrodynamical

R_{\rm i,d}=50\, \rm au
\Sigma(r) = 170 \left(\frac{\rm g}{\rm cm}\right)^{2} \left( \frac{r}{1 \rm au} \right)^{-3/2}
M_{\rm cloudlet}(R_{\rm cloudlet}) = 0.01 {\rm M}_{\odot} \left( \frac{R_{\rm cloudlet}}{5000 \rm au}\right)^{2.3}
R_{\rm cloudlet} = 887\, \rm au

isothermal gas

vary infalling angle

\alpha = 0^{\circ} (35^{\circ}, 60^{\circ}, 90^{\circ})
b = 1774\, \rm au

vary rotation (prograde, retrograde)

Küffmeier, Dullemond, Reißl, Goicovic et al. 2021

M_{*}=2.5\, \mathrm{M}_{\odot}

Outer disk forms around inner disk

Küffmeier et al. 2021

Prograde vs. retrograde infall

Retrograde infall causes:

  • counter-rotating inner and outer disk 
  • shrinking of inner disk
  • enhanced accretion
  • larger and deeper gap between disks

see also Vorobyov+ 2016

Küffmeier et al. 2021

Inner disk orientation

M_{\rm i, disk}=4 \ M_{\rm cloudlet}
M_{\rm cloudlet} = 1.87 \times 10^{-4} \ \mathrm{M}_{\odot}
M_{\rm i,disk} = 24 M_{\rm cloudlet}
M_{\rm i,disk}=4 \ M_{\rm cloudlet}
M_{\rm i,disk} = 0.4 \ M_{\rm cloudlet}

Küffmeier et al. 2021

Resistivity depends on ionization rate

Küffmeier, Zhao & Caselli 2020

Question: What is the effect on disk formation when differing the ionization rate?

Küffmeier, Zhao & Caselli 2020

mass-to-flux ratio

initial strength of rotation

Disk size distribution

Disk size distribution

Tobin+ 2019

Are disks already born small in some (all?) regions?

 Does cosmic-ray ionization play a crucial role?

see A. Maury's talk

The big uncertainty

Current state-of-the-art in MHD models:

constant rate independent of densities

Figure from Padovani+'22 showing observations by Shaw+'08, Indriolo & McCall '12, Neufeld & Wolfire '17, Caselli+'98, Bialy+'22, Maret & Bergin '07, Fuente+'16, Sabatini+'20, de Boisanger+'16, van der Tak+'00, Hezareh+'08, Morales Ortiz+'14, Ceccarelli+'04, Barger & Garrod'20 (in addition: results by Cabedo+'22 [blue line]) 

External vs. internal

Competition between external and internal cosmic rays 

talks by Offner, Owen, Grassi, Gaches

We need

Are cosmic ray rates environment dependent or independent?

(Cabedo, Maury+'22)

(Küffmeier, Zhao & Caselli+'20)

 a better handle on CR propagation

measurements/maps of CR rates

talks by Redaelli (L1544), Pineda (NGC1333), Cabedo & Maury (B335), Sanna (G035.02+0.35), Sabatini

Self-regulation during disk formation?

(Offner, Gaches & Holdship'19)

Do externally or internally produced cosmic rays dominate disk formation process?