Michael Küffmeier

S. G. Zaidi, C. Granzow Holm, T. Haugbølle (NBI), J. Pineda (MPE), D. Segura-Cox (Rochester), S. Reißl, C. P. Dullemond (ITA)

Disk Formation Beyond Collapse

Infall and Rejuvenation

When?

"At the beginning."

When?

Classical picture: the disk is detached and only evolves afterwards.

When?

Bizzarro et al. 2017

How?

The classical picture

credit: M. Persson

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

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

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!

It depends on ionization fraction.

Achtung!

see Wurster et al. 2018, Kuffmeier et al. 2020; reviews by Tsukamoto et al. 2023, Kuffmeier submitted

History of modeling disk formation

What about magnetic fields?

Help! Where is the disk?!

Santos-Lima et al. 2012

Hydro

ideal MHD

Magnetic braking catastrophe

Angular momentum is transported too efficiently 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, Tsukamoto et al. 2023 and Küffmeier 2024

History of modeling disk formation

Help! Where is the disk?!

Resistivities

Santos-Lima et al. 2012

Hydro

ideal MHD

non-ideal MHD

What about magnetic fields?

for pioneering work see Galli & Shu 1993 a/b

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

more references in reviews by Wurster & Li 2018, Tsukamoto et al. 2023 and Küffmeier 2024

non-ideal MHD is not a single parameter

Caveat!

depends on cosmic-ray ionization rate!

Effect of ionization on disk size

Küffmeier, Zhao & Caselli 2020; see also Wurster et al. 2018

increasing ionization rate

enhanced magnetic braking

smaller disks

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

-\nabla\times \{\eta_{\rm AD} \mathbf{B}/B \times [(\nabla \times \mathbf{B}) \times \mathbf{B}/B] \}

Effect of ionization on disk size

Küffmeier, Holm et al. in prep

ideal MHD

non-ideal MHD

\color{white}\zeta=10^{-18} \rm s^{-1}

\color{white}\zeta=10^{-17} \rm s^{-1}

\color{white}\zeta=10^{-16} \rm s^{-1}

increasing ionization rate

enhanced magnetic braking

smaller disks

100 au

Küffmeier, Zhao & Caselli 2020, see also Kobayashi et al. 2023

Observed variations:
Maps of CR-ionization rates (e.g., NGC 1333 Pineda et al. 2024, or AG 351 & AG 354 Sabatini et al. 2023)
Protostars B335 (Cabedo et al. 2023), IRAS4A, L1448-C, L1157 (Schwarz et al. 2026)

Effect of ionization

Küffmeier, Holm et al. in prep

\color{white}\zeta=10^{-18} \rm s^{-1}

\color{white}\zeta=10^{-17} \rm s^{-1}

\color{white}\zeta=10^{-16} \rm s^{-1}

increasing ionization rate

enhanced magnetic braking

smaller disks

100 au

Tokuda et al. 2026

interchange instability

(see Tsukamoto et al. 2023 [and references in the review] and Machida & Basu 2025)

Environment?

Stars form in molecular clouds

Accretion process is heterogeneous in time, in space, and among protostar.

Küffmeier, Haugbølle & Nordlund 2017

"mass accretion onto the star–disk system is filamentary, acting through accretion channels and accretion sheets"

Segura-Cox et al. 2020

"...you simply cannot look at disks with ideal MHD.

I thought you knew all of this, and the people in [---] are not impressed."

e-mail reaction after publication in 2017

Stars form in molecular clouds

Mayer et al. 2025

To zoom or not to zoom

Santos-Lima et al. 2012

Hydro

ideal MHD

non-ideal MHD

Mayer et al. 2025

100 au

Hydro

ideal MHD

non-ideal MHD

"What a waste of computing time, Alex. Same as isolated collapse models!"

Hydro

ideal MHD

non-ideal MHD

Disks solely from early collapse is not the full story.

Cores are in clouds

credit: Holm

Christian G. Holm

Zoom-in onto 9 star-disk systems: 4 pc -> sub-au

ideal MHD (paper in review; non-ideal MHD running)

isothermal parental run

barotropic equation of state for zoom-ins

average column density

code: DISPATCH

(Machida+ 2007)

\Sigma\approx 10^{22} \rm cm^{-2}

(Nordlund+ 2018)

Holm et al. in review

Environmental effects

credit: Holm

Christian G. Holm

Adaptive mesh refinement: 4 pc -> sub-au

ideal MHD (but non-ideal MHD in progress)

barotropic equation of state for zoom-ins

average column density

code: DISPATCH

(Machida+ 2007)

\Sigma\approx 10^{22} \rm cm^{-2}

(Nordlund+ 2018)

The natal environment holds close resemblance to nearby star-forming regions in terms of velocity dispersion and magnetic field strengths.

(Li+ 2023)

\sigma_{\rm v}=(0.34 \pm 0.04)\ \rm km\, s^{-1}

\sigma_{\rm v} = 0.29 \ \rm km\, s^{-1}

(53 \pm 20)\ \mu\rm G

(65 \pm 19)\ \mu\rm G

10\ \mu\rm G

100\ \mu\rm G

(Crutcher+ 2010, Crutcher 2012)

model:

observations:

model:

observations:

Core properties

Christian G. Holm

\sigma_{\rm v}=(0.34 \pm 0.04)\ \rm km\, s^{-1}

B_{\rm rms} = (53 \pm 20)\ \mu\rm G

(Li+ 2023)

\sigma_{\rm v} = 0.29 \ \rm km\, s^{-1}

10\ \mu\rm G

100\ \mu\rm G

(Crutcher+ 2010, Crutcher 2012)

Prestellar core properties

Observations

Holm et al. in review

Selected the most isolated!

consistent with observed profiles shown by Jaime on Monday

Disks (re)form via filamentary infall

Holm et al. in review

...but it happens earlier

smoother, and easier

the lower the ionization rate is.

\color{white}t=2 \, \rm kyr

...and YES, the disk properties are strongly affected by non-ideal MHD effects!

A few massive streamers

Christian G. Holm

Streamer criteria:

\Sigma>0.1 \rm g\, cm^{-2}

v_{\rm rad, in}>v_{\rm rot}

The density contrast relative to the environment is a factor of 4 to 6.

The streamer mass is between 0.1 and 0.4 .

The streamers persist for ~10 kyr, with mass accretion rates of .

10^{-5} \rm M_{\odot}\, yr^{-1}

\rm M_{\odot}

Holm et al. in review

Follow-up:

synthetic observations

see Shirin Zaidi's poster and Andreas Kjær Rasmussen's streamer website: https://streamer-explorer.streamlit.app/

Beyond the initial collapse

Christian G. Holm

preliminary work

Beyond the collapse?

Origin of accreting gas

Küffmeier, Jensen & Haugbølle '23

see also Pelkonen+ 2021 and poster by Shingo Nozaki

Origin of accreting gas

Kaalva, Offner, Filippova & Grudic '26

Animation by S. Raymond

Credit: Garufi et al. 2024

Disks are rarely isolated.

Streamers and shadows as signs of infall-induced disks

Formation of misaligned configuration

Observable as shadows in outer disk

Küffmeier, Dullemond, Reissl & Goicovic 2021

SU Aur (Ginski et al. 2021)

300 au

Krieger, Küffmeier et al. 2024

Two phases of disk formation

Küffmeier, Winter, Kuznetsova et al. in prep

Summary

Disks are replenished and distorted by filamentary infall (streamers).

Star and disk formation is a two-phase process consisting of mandatory initial collapse and post-collapse ("late") infall phase.

The degree of ionization is important for disk properties, but large delivery of angular momentum simplifies disk formation after very early collapse phase.

Do we really know disk "lifetimes"?

Fraction reflecting occurrence of infall events instead of disk age?

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 (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) ...

Per-emb-50

Valdivia-Mena et al. 2022

Streamers:

Effect of ionization on disk size

increasing ionization rate

enhanced magnetic braking

smaller disks

ideal MHD

non-ideal MHD

"mass accretion onto the star–disk system is filamentary, acting through accretion channels and accretion sheets"

Küffmeier, Haugbølle & Nordlund 2017

mass accretion occurs along distinct channels (shear flows) created locally by the turbulent motions

Seifried et al. 2013

Küffmeier et al. 2017

Segura-Cox et al. 2020

Effect of ionization on disk size

Tokuda et al. 2026

"...you simply cannot look at disks with ideal MHD. I thought you knew all of this, and the people in [---] are not impressed."

e-mail to me on paper in 2017

Küffmeier et al. 2017

9 years later

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

History of modeling disk formation

for more references, see reviews

(e.g., Wurster & Li 2018, Zhao et al. 2022, Tsukamoto et al. 2023, Küffmeier 2024)

see Seifried et al. 2012/13!

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

Bollard et al. '17

When?

Spherical collapse models simulate a few 10 kyr.

When?

And then?

After initial collapse, the disk evolves in isolation.

credit: M. Persson

To do

...solely replenishes the disk,

...plays an active role in triggering instabilities,

...induces dramatic changes such as misalignment.

III

Explore frequency and properties of infall onto star-disk systems that ...

images: A. Houge

Revisiting star-disk formation from a Giant Molecular Cloud perspective

Model star formation in a Molecular Cloud

isothermal magnetohydrodynamical (MHD) with driven turbulence

adaptive mesh refinement (AMR) simulations

image from Holm et al. '26 submitted

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)

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, Glover, Bonnell, Clark & Klessen 2011)

"We find that, once a protostar forms, the lifetime of the unaccreted gas correlates with the final stellar mass, where low-mass stars (M∗ < 0.5 M⊙) accrete for 0.5-0.6 Myr from a relatively local reservoir of gas, and high-mass stars (M∗ > 2 M⊙) accrete over 3.3-4.7 Myr from a much larger volume."

(Kaalva, Offner, Filippova & Grudic 2026)

inertial-inflow model (Padoan+ '20)

Implications of (late) infall

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

subtle correlation with mass (inherited by disks??)

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

Küffmeier, Jensen & Haugbølle '23

Long et al. 2022

see also Padon+ '05 & '25 and Winter+ '24 for analyses/discussions of Bondi-Hoyle(-Lyttleton) accretion

Padoan+ '25

Spreading vs wind-driven?

Manara et al. 2023

Caveat!

Infall matters. Disks can easily be wind-driven and yet grow in size through infall of gas with high angular momentum.

Long et al. 2022

Orientation of infall

...

A disk contains only 1% of the stellar mass:

"Easy" to replenish with post-collapse (late) misaligned infall.

Turbulence matters from cloud to core (Padoan+ '97/'20, Klessen '01, Padoan & Nordlund '02, Hennebelle & Chabrier '08), down to binary (Offner+ '10) and disk scales (Küffmeier+ '17)

It implies misaligned infall (Küffmeier+ '24, Pelkonen+ '25), i.e., "chaotic star formation" (Bate '10)

and primordial misaligned disks (Thies+ '11, Bate '18, Küffmeier+ '21)

State-of-the-art in theory of star formation

Do we really know disk "lifetimes"?

Two phases of disk formation

YSOs can appear younger than they really are

How old is the protostar?

Küffmeier, Jensen & Haugbølle '23

Class I

Class 0

Class II

On average, stars with increasing final mass undergo prolonged infall

Orientation of star-disk systems can change substantially

Orientation of infall

Küffmeier, Pineda, Segura-Cox & Haugbølle 2024

How to quantify anisotropy of accretion?

FA = 0: perfectly isotropic accretion

FA = 1: maximally anisotropic accretion

Fractional anisotropy based on tracer particles

Post-collapse infall is more anisotropic than initial collapse

Post-collapse accretion phase resembles Bondi-Hoyle

Küffmeier, Pineda, Segura-Cox & Haugbølle 2024

Post-collapse infall is more anisotropic than initial collapse

Anisotropic accretion

FA = 0: perfectly isotropic accretion

FA = 1: maximum anisotropic accretion

Küffmeier, Haugbølle, Pineda & Segura-Cox 2024

Late infall is more anisotropic than early collapse

\mathrm{FA} = \sqrt{ \frac{1}{2}} \frac{\sqrt{(\lambda_1 - \lambda_2)^2 + (\lambda_2 - \lambda_3)^2 + (\lambda_3 - \lambda_1)^2}}{\sqrt{\lambda_1^2 + \lambda_2^2 + \lambda_3^2}}

Fractional anisotropy (FA) serves as a good measure for the (an-)isotropy of accretion.

FA=0: perfectly isotropic accretion, FA=1: maximally anisotropic

\frac{\Delta t_{\rm single}}{\Delta t_{\rm single}+\Delta t_{\rm mult}}

FA can also be a useful measure to compare (an)isotropy of stellar spins in clusters

Open questions and preliminary results

Credit: NASA/ESA Hubble space telescope &

ALMA (ESO/NAOJ/NRAO)

The big challenge:

link planet to star formation

50 au

Zoom-in on embedded stars

Küffmeier et al.

2019

Küffmeier et al. 2018

Küffmeier, Reißl et al. 2020

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

~1500 AU

Pro: self-consistent initial and boundary conditions for star formation

Con: computationally more expensive, more difficult analysis

for a similar concept, see also Lebreuilly et al. 2024, Yang & Federrath 2025

Zoom-in simulations

Christian G. Holm

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

*(starting from previous RAMSES simulations and run with DISPATCH)

How does (early) infall shape disk formation?

Christian G. Holm

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

Christian G. Holm

star A, t = 13 kyr

star A, t = 25 kyr

strong magnetic braking,

strong outflow

Gas accretes through the disk (little polar accretion)

Christian G. Holm

Gas accretes through the disk (little polar accretion)

Young embedded disks

Christian G. Holm

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

Christian G. Holm

How do outflows affect disk formation?

star A, t = 13 kyr

star A, t = 25 kyr

strong magnetic braking,

strong outflow

Prospect to compare with observations of outflows (e.g., ALMA-DOT, PI: Podio)

In progress: non-ideal MHD simulations and comparison with results by Lebreuilly et al. 2022

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

Simulations: Holm, Haugbølle

Visualizations: Berlok

Implications for Al-26 heterogeneity

Küffmeier et al. 2016

Gas is well-mixed within core, and hence Al-26 abundance is fixed during CAI formation (t<~100 kyr).

BUT: significant deviations in Al-26 abundance beyond the core may likely be imprinted on disk afterwards!

Christian G. Holm

How do infall and outflow affect the disk?

Angular momentum transport via magnetic braking

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