Progress and challenges in modeling protoplanetary disk formation

Michael Küffmeier

How did it begin?

Let's go back in time to the year 2014

Wow!

Credit: ALMA (ESO/NAOJ/NRAO)

Credit:

DSHARP team

10 au

50 au

Credit: NASA/ESA Hubble space telescope &

ALMA (ESO/NAOJ/NRAO)

The big challenge:

link planet to star formation

50 au

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

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

\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] \}

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 Wurster & Li 2018 (review)

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

Varning!

Resistivity depends on ionization rate

Küffmeier, Zhao & Caselli 2020

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

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

Disk size distribution

Küffmeier, Zhao & Caselli 2020

mass-to-flux ratio

initial strength of rotation

Disk size distribution

Tobin+ 2019

Are disks already born small in some regions?

What is the effect of local ionization rates?

Cosmic-ray ionization rate (or even Al-26)?

What about the dust?

What about magnetic fields?

Help! Where is the disk?!

Ohmic, Ambipolar, Hall

Santos-Lima et al. 2012

Hydro

ideal MHD

non-ideal MHD

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

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?

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

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), ...

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

Formation of embedded protostellar multiple

Küffmeier, Reißl et al. 2020

Magnetic field in bridge

Synthetic observation with POLARIS

Field strength in bridge:

about 1 to 2 mG

Polarization fraction in bridge:

a few %

Synthetic dust polarization maps at 1.3 mm

Küffmeier, Reißl et al. 2020

Emitted radiation

Polarization fraction in bridge:

a few %

Polarization fraction in bridge:

up to 20 %

IRAS 16293--2422

Sadavoy et al. 2018

=> IRAS 16293-2422 is strongly magnetized

Wavelength dependence: 1.3 mm vs 53 micron

Emitted radiation

1.3 mm: good tracer of magnetic field

53 micron: poor tracer of magnetic field

Küffmeier, Reißl et al. 2020

Two reasons for wavelength dependence

Küffmeier, Reißl et al. 2020

Self-scattering

Dichroic extinction

Take-away for scales beyond >100 au

< 200 micron: dichroic extinction and self-scattering; no trace of B

> 200 micron: thermal emission; linear polarization traces B

The connection to the larger scales

Küffmeier, Haugbølle & Nordlund 2017

Accretion is heterogeneous

Küffmeier, Haugbølle & Nordlund 2017

Observational indication: luminosity bursts

The connection to the larger scales

Küffmeier, Haugbølle & Nordlund 2017

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

Late infall happens more often than assumed

Pelkonen et al. 2021

Even for solar mass stars, up to 50 % of final mass from beyond the prestellar core!

Can disks be rejuvenated?

Streamers (and shadows?) as signs of infall

Formation of misaligned configuration

Observable as shadows in outer disk

Ginski et al. 2021

Küffmeier, Dullemond et al. 2021

see also Bate 2018

Revised picture

Pineda et al. 'Protostars and Planets VII'

Segura-Cox et al. in prep.

Star and planet formation are two sides of the same medal

The disk is not a static entity, but rather a buffer zone

*we haven't even touched (proto-)stellar multiplicity

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

Kuffmeier 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