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
How and when?
Why does the disk matter?
The disk provides the initial condition for planet formation.
Animation by S. Raymond
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?!
Ohmic, Ambipolar, Hall
Santos-Lima et al. 2012
Hydro
ideal MHD
non-ideal MHD
non-ideal MHD is not a single parameter
Caveat!
What about magnetic fields?
depends on cosmic-ray ionization rate!
for pioneering work see Galli & Shu 1993 a/b
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
increasing ionization rate
enhanced magnetic braking
smaller disks
Observational motivation:
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)
Küffmeier, Zhao & Caselli 2020; see also Kobayashi et al. 2023
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
When?
"At the beginning."
Bollard et al. '17
When?
Spherical collapse models simulate a few 10 kyr.
When?
When?
Classical picture: the disk is detached and only evolves afterwards.
When?
Bizzarro et al. 2017
And then?
After initial collapse, the disk evolves in isolation.
credit: M. Persson
Animation by S. Raymond
Credit: Garufi et al. 2024
Problem: disks are rarely isolated.
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:
Upcoming work for DSTREAM
...solely replenishes the disk,
I
...plays an active role in triggering instabilities,
II
...induces dramatic changes such as misalignment.
III
DSTREAM will 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
Two phase process:
Initial collapse followed by varying amount of post-collapse infall
(see also Pelkonen+ 2021)
Küffmeier, Jensen & Haugbølle '23
Origin of accreting gas
Kaalva, Offner, Filippova & Grudic '26
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)
Disks solely from early collapse is not the full story.
Implications of (late) infall
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
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"?
Do we really know disk "lifetimes"?
Fraction reflecting occurrence of infall events instead of disk age?
Fraction reflecting occurrence of infall events instead of disk age?
Summary
Disks are replenished and distorted by infall
Star formation is a two-phase process consisting of mandatory initial collapse and post-collapse ("late") infall phase
Küffmeier 2024
Credit:
M. Lützen
Duration of episodic post-collapse infall phase scales on average with final stellar mass
The evolution from Class 0 to Class II is not monotonic
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}}
1
0
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
StarPlan retreat 2026
By kuffmeier
