Accretion and outflow

SU Aur

synthetic image

Credit: Christian Granzow Holm

Michael Küffmeier

Carlsberg Reintegration Fellow at Niels Bohr Institute

Stars accrete

Manara et al. 2023

What is essential for accretion?

Angular momentum transport!

The classical picture

credit: M. Persson

star formation

planet formation

Viscous accretion disk model

Spreading of a disk ring

Pringle 1981

\tau = 12\nu \frac{t}{r_0^2}
x = r/r_0

.

.

Image: G. Lesur

recall Joanna Drążkowska's lecture

Viscous accretion disk model

Molecular viscosity

\nu_{\rm m} \approx \lambda c_{\rm s} = \frac{1}{n \sigma_{\rm m}} c_{\rm s} = 5 \times 10^4 \mathrm{cm}^2 \mathrm{s}^{-1} = 2.5 \times 10^7 \mathrm{cm}^2 \mathrm{s}^{-1}
t_{\nu} = \frac{r^2}{\nu} \approx 3 \times 10^{13} \mathrm{yr}

>10 million times too long compared to disk lifetime!

.

Polnitzky et al. 2025 in prep

Viscous accretion disk model

\nu_{\rm t} = \alpha c_{\rm s} H

turbulent transport

sound speed

scale height

magnetorotational instability (MRI)

.

Polnitzky et al. 2025 in prep

t_{\nu} = \frac{r^2}{\nu} = \left( \frac{h}{r} \right) ^{-2} \frac{1}{\alpha \Omega}
t_{\nu}(50\, \rm au) = 1\,\rm to\ 10\, \rm Myr
\alpha = 10^{-3} \ \rm to \ 10^{-2}

Velikhov '59, Balbus & Hawley '91

Shakura & Sunyaev '73; Lynden-Bell & Pringle '74

Viscous accretion disk model

\nu_{\rm t} = \alpha c_{\rm s} H

turbulent transport

sound speed

scale height

magnetorotational instability (MRI)

.

t_{\nu} = \frac{r^2}{\nu} = \left( \frac{h}{r} \right) ^{-2} \frac{1}{\alpha \Omega}
t_{\nu}(50\, \rm au) = 1\,\rm to\ 10\, \rm Myr
\alpha = 10^{-3} \ \rm to \ 10^{-2}

Are disks MRI active?

Thie et al. '18

\rm Am \equiv \frac{v_{\rm A}^2}{\eta_{\rm A} \Omega}<100

MRI is (mostly) suppressed

Perez-Becker & Chiang '11

Other instabilities possible, but do observations match     values?

\alpha

Observations: 

\alpha \sim 10^{-4} \ \rm to \ 10^{-3}

Pinte et al. '23 (and references therein)

Challenging.

Viscous accretion disk model

\nu_{\rm t} = \alpha c_{\rm s} H

turbulent transport

sound speed

scale height

.

t_{\nu} = \frac{r^2}{\nu} = \left( \frac{h}{r} \right) ^{-2} \frac{1}{\alpha \Omega}
t_{\nu}(50\, \rm au) = 1\,\rm to\ 10\, \rm Myr
\alpha = 10^{-3} \ \rm to \ 10^{-2}

Other instabilities possible, but do observations match     values?

\alpha

Observations: 

\alpha \sim 10^{-4} \ \rm to \ 10^{-3}

Pinte et al. '23 (and references therein)

Challenging.

Flaherty et al. '15

Disk

Are we missing anything?

are

Material can be ejected through winds

Option 1: Photoevaporative wind (              )

r_{\rm crit} \sim 0.1\ \rm to\ 0.2 \frac{GM}{c_{\rm s}^2}
c_{\rm s} \sim 11\, \rm km\, s^{-1}
T = 10^4 \rm K
c_{\rm s} \sim 4\ \rm to\ 7\ \rm km\, s^{-1}
T = 3000\ \rm to\ 8000\, \rm K
c_{\rm s} \sim 3\ \rm km\, s^{-1}
T = 2500\, \rm K

fully ionized gas

neutral gas

molecular gas

c_{\rm s} > v_{\rm esc}

Outflows!

outflows

see posters Aru and Gkimisi; review Pascucci et al. '23

Disk outflows

Are we missing anything?

are

Material can be ejected through winds

Option 2: Magnetically driven jet/wind (               )

v_{\rm A} > v_{\rm esc}

are

Outflows!

Machida et al. 2016

image: Armitage '18

Are we missing anything?

are

Outflows!

Machida et al. 2016

Disk outflows

image: Armitage '18

Are we missing anything?

are

Outflows!

Bjerkeli et al. 2016

Machida et al. 2016

Disk outflows

Magnetocentrifugal wind

Credit: Kimmig et al. '20

for a thorough explanation of magnetocentrifugal wind see Spruit '96

Blandford & Payne '82

Magnetocentrifugal wind

for a thorough explanation of magnetocentrifugal wind see Spruit '96

Blandford & Payne '82

\dot{J}_{\rm w} = \dot{M}_{\rm w} \Omega r_{\rm A}^2
\dot{J}_{\rm a} = \dot{M}_{\rm a} \Omega r_{\rm F}^2
\frac{\dot{M}_{\rm w}}{\dot{M}_{\rm a}} = \frac{1}{2} \left(\frac{r_{\rm F}}{r_{\rm A}}\right)^2

efficient possibility of transporting angular momentum if

r_{\rm F} < r_A

accretion

wind

Alfvén

e.g.

r_{\rm A} = 3\, r_{\rm F}

(accounting for bipolar outflow)

\dot{M}_{\rm out} \approx 2\, M_{\rm w}\approx 0.1\, \dot{M}_{\rm a}

Credit: Kimmig et al. '20

Magnetothermal wind

Gressel et al. '15

Combination of magnetic and thermal wind appears most realistic

Bai '17, Béthune et al. '17, Wang et al. '19, Gressel et. '20, Rodenkirch et al. '20, Lesur et al. '23 (PPVII)

Magnetised outflows

Credit: Christian Granzow Holm

Credit: Kimmig et al. '20

Dust polarization to measure magnetic fields

Polarization depends on degree of grain alignment and elongation

Credit: B. G. Anderson

Measuring linear polarization of dust grains allows to determine magnetic field orientation ...

... if you know the origin of polarization.

unfortunately polarization in disks is often dominated by scattered light (see Guidi's lecture on Friday).

Dust polarization to measure magnetic fields

Credit: Kwon et al. 2019

Polarization traces magnetic field

Küffmeier, Reißl et al. 2020

Emitted radiation

synthetic observations

(we display e-vectors rotated by 90°)

Polarization traces magnetic field

Küffmeier, Reißl et al. 2020

Emitted radiation

synthetic observations

(we display e-vectors rotated by 90°)

B

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

alignment efficiency higher than efficiency produced by standard RAT alignment

(also Le Goeullec+20)

IRAS 16293-2422 highly magnetized?

Reason for wavelength dependence

Küffmeier, Reißl et al. 2020

Dichroic extinction

Take-away for scales beyond the disk

< 200 micron: dichroic extinction; challenging to trace B reliably

> 200 micron: thermal emission; linear polarization traces B

(see also Valdivia et al. 2022)

see also Reissl et al. 2014, 2016 for more discussion of the flip

Credit: Tsukamoto et al. 2021

"Ash-fall" scenario aka conveyor belt

Possibility of lifting CAIs and/or chondrules from inner disk to outer disk

Credit: Connelley et al. 2012

Viscous vs wind-driven disk

wind-driven disk

Images: G. Lesur

viscous accretion disk

  • purely radial transport of angular momentum
  • disk turbulence leads to enhanced transport in disk
  • "Classical" disk model
    Shakura & Sunyaev '73; Lynden-Bell & Pringle '74
\nu_{\rm t} = \alpha c_{\rm s} H

turbulent transport

sound speed

thickness of half disk

  • vertical transport of angular momentum
  • magnetic fields exert torque which allows accretion
  • large-scale magnetic field model
    Blandford & Payne '82

efforts in formulating analytic prescription for wind scenario (Tabone et al. 2022)

Viscous vs wind-driven disk

Manara et al. 2023

Spreading vs wind-driven?

Manara et al. 2023

Interpreting disk sizes as outcome of either viscous spreading or MHD wind

Long et al. 2022

?

magnetohydrodynamics

Disk size can shrink in viscous model when accounting for external photoevaporation

e.g. Haworth & Winter 2023

Rosotti et al. '19, Somigliana et al. '23, Tabone et al. '22, Trapman et al. '22, Zagaria et al. '22

Evolved steady disk overview

Credit: Armitage 2018

poster by Fullana-García

Preliminary take-aways

  • Accretion requires angular momentum transport
  • Angular momentum can be transported radially through turbulent viscosity (   -parameter) or through magnetically driven winds
  • Ongoing paradigm shift in interpreting accretion disks as predominantly outflow-driven rather than viscous accretion disks (see PPVII reviews by Lesur et al., Pascucci et al.)
\alpha

Outflows are ubiquitous

...but wait a second!

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 '18, Tsukamoto et al. '23, Küffmeier '24

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

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

Küffmeier, Zhao & Caselli 2020

rotation

infall

from light to dark colors: high to low ionization rates

see also Wurster et al. 2018

Effect of ionization on disk size

increasing ionization rate

enhanced magnetic braking

smaller disks

Maps of CR-ionization rates (e.g., NGC 1333 Pineda et al. 2024, or AG 351 & AG 354 Sabatini et al. 2023)

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, Tsukamoto et al. 2023, Küffmeier 2024)

Modeling disk formation

Credit: Christian Granzow Holm

Is this the full picture?

Preliminary take-aways

  • Accretion requires angular momentum transport
  • Angular momentum can be transported radially through turbulent viscosity (   -parameter) or through magnetically driven winds
  • Ongoing paradigm shift in interpreting accretion disks from viscous accretion disks to predominantly outflow-driven accretion disks (see PPVII reviews by Lesur et al., Pascucci et al.)
\alpha
  • Magnetic fields are important regulators of disk accretion and probably the source of massive early outflows/jets

Michael Küffmeier

Carlsberg Reintegration Fellow at Niels Bohr Institute

Accretion and infall

SU Aur

SU Aur

synthetic image

Ginski et al. 2021

Krieger et al. 2021

Overview and history of star-disk formation

~1 to 10 Myr

~1 to 100 pc

slide credit: G. Perotti

slide credit: G. Perotti

slide credit: G. Perotti

slide credit: G. Perotti

slide credit: G. Perotti

Revisiting star-disk formation from a Giant Molecular Cloud perspective

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+ '20), GM Aur (Huang+ '21), IRS 63 (Segura-Cox in prep.), AB Aur (Grady+ '99 / Fukagawa+ '04, Speedie+ '24), M512 (Grant+ '21, Gupta+ '24, Cacciapuoti+ '24) ...

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? 

Streamers:

A. Garufi's lectures

Adaptive mesh refinement

Adaptive mesh refinement

Model star formation in a Molecular Cloud

isothermal magnetohydrodynamical (MHD) with driven turbulence

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

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 Smith+ 2011, Pelkonen+ 2021)

Küffmeier, Jensen & Haugbølle '23

Origin of accreting gas

"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)

Implications of (late) infall

Late infall causes accretion bursts

Intriguing explanation of luminosity bursts

 

 

 

 

 

infall may also trigger smaller scale variations by causing more subtle disk instabilities

data from Clarke+ '05

YSOs can appear younger than they really are

How old is the protostar?

Küffmeier, Jensen & Haugbølle '23

Class I

Class 0

Class II

A poor analogy to a spring school

Session start

Coffee break!

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

?

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 et al. 2024

On average, stars with increasing final mass undergo prolonged infall

Orientation of star-disk systems can change substantially

Orientation of infall

Küffmeier, Haugbølle, Pineda & Segura-Cox 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

Streamers (and shadows) as signs of infall

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

Open questions and preliminary results

Do we really know disk "lifetimes"?

Polnitzky et al. 2025 in prep

Fraction reflecting occurrence of infall events instead of disk age?

Are "Peter Pan" disks around >10 Myr old stars in fact "Dorian Gray" disks?

Trails of gas: signs of Bondi-Hoyle-Lyttleton accretion or photoevaporative wind?

Haworth et al. '25

Bondi-Hoyle(-Lyttleton) accretion (poster Ashtari-Jolehkaran; Padoan+ '24, Winter+ '24, Küffmeier '24)

for external photoevaporation see posters by Aru and Gkimisi

Winter+ '24

Aru+ '24

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

Zoom-in method

Küffmeier et al. 2017

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

Zoom-in method

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

Christian G. Holm

Granzow Holm, Lambrechts, Kuffmeier et al. in prep

Zoom-in simulations

Christian G. Holm

How does (early) infall shape disk formation?

Christian G. Holm

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

*(run with DISPATCH: used only 1 instead of 24 nodes, yet faster than RAMSES)

Young embedded disks

Christian G. Holm

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

*(run with DISPATCH: used only 1 instead of 24 nodes, yet faster than RAMSES)

Christian G. Holm

Gas accretes through the disk (little polar accretion)

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

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)

Simulation: Granzow Holm

Visualizations: Berlok

Zooming in on late phase

Küffmeier & Granzow Holm in prep

Trails of gas: signs of Bondi-Hoyle-Lyttleton accretion or photoevaporative wind?

Haworth et al. '25

Küffmeier & Granzow Holm in prep

Bondi-Hoyle(-Lyttleton) accretion (poster Ashtari-Jolehkaran; Padoan+ '24, Winter+ '24, Küffmeier '24)

for external photoevaporation see posters by Aru and Gkimisi

 Sequence of star, disk & planet formation

Pineda et al. 2023

.

 

 

 

.

Star & disk are replenished by infall of initially unbound material

  • Is the disk solely replenished with fresh material?
  • Does infall frequently lead to the formation of a new misaligned outer disk (and if yes, for how long)? (see also Bate '18)
  • Is (late) infall catastrophic? Does a completely new disk form?

Key questions to be addressed in the future

  • Does infall trigger substructures that are precursors of planet formation? 

(Bae+ '15, Lesur+ '15, Küffmeier+ '18, Kuznetsova + '22)

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!

 Sequence of star, disk & planet formation

Pineda et al. 2023

.

 

 

 

.

Summary

Disks are replenished, distorted or even destroyed by misaligned infall

Protostellar environment matters 

Star formation is a two-phase process consisting of mandatory initial collapse and post-collapse infall phase

Küffmeier 2024

Credit:

M. Lützen

EAS meeting Cork 2025, June 23-27

 

Symposium

Setting the stage for planet formation:

the importance of the environment for the evolution of protoplanetary discs

 

Special session

The chemistry of planet formation