What we know, think to know, and don't know about disk formation

Michael Küffmeier

How did it begin?

Astrophysics and planetary science department

Credit: Christian G. Holm

...

and what happened later?

Stars form in molecular clouds

NASA, ESA, CSA and STScI

2. Filaments form inside the cloud

3. Dense cores form inside the filaments

1. Giant Molecular Cloud of gas and dust

From giant molecular clouds to protostars

4a. Stars form from the collapse of dense cores

4b. Rotation in the cloud leads to the formation of a disk

5. Planets form in the disk

~1 to 10 Myr

~1 to 100 pc

The classical picture

credit: M. Persson

star formation

planet formation

t ~ 10 to 100 kyr

t = 0 kyr

t ~ 100 to 500 kyr

t ~ 1 Myr

t ~ 10 Myr

t ~ 1 to 10 Gyr

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

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

Achtung!

if you are curious to learn more about theory of MHD, talk to Martin Pessah at Niels Bohr International Academy

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

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

History of modeling disk formation

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

Credit: Tsukamoto et al. 2021

"Ash-fall" scenario aka conveyor belt

if you are curious about dust growth that leads to planet formation talk to:

Troels Haugbølle, Anders Johansen, Michiel Lambrechts, Anja Andersen or me

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

BHB1 (Alves et al. 2020), GM Aur (Huang et al. 2021), IRS 63 (Podio et al. 2024, Segura-Cox in prep.), AB Aur (Grady et al. 1999 / Fukagawa et al. 2004), M512 Grant et al. 2021, Gupta et al. 2024, Cacciapuoti et al. 2024), PPVII review by Pineda et al. 2023

Per-emb-50

Valdivia-Mena et al. 2022 (see poster!)

Streamers:

if you want to work on disk observations, reach out to Jes Jørgensen or Giulia Perotti

Zoom-in method

Küffmeier et al. 2017

ideal magnetohydrodynamics
adaptive mesh refinement

1pc ≈ 206 265 au

Text

Adaptive mesh refinement

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

How does (early) infall shape disk formation?

Christian G. Holm

Zoom-in simulation, ~1 au resolution in disk, barotropic equation of state

Simulations: Christian G. Holm, Troels Haugbølle

Visualizations: Thomas Berlok

Late infall is common for stars

On average, even solar mass stars gain ~50 % of their final mass through accretion of initially unbound material

Note that some protostars still accrete after 1.2 Myr

Küffmeier, Jensen & Haugbølle '23

(Pelkonen et al. 2021)

Two phase accretion process

Initial collapse followed by varying amount of post-collapse infall

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

Küffmeier, Jensen & Haugbølle '23

Origin of accreting gas

"In the case of the more massive stars, accretion from the environment outside the original core volume is even more important than that from the core itself. [...]

The assumption of spherical symmetry cannot be applied to the majority of collapsing cores, and is never a good description of how stars accrete gas from outside the original core radius."

(Smith et al. 2011)

YSOs can appear younger than they really are