Cosmic rays as a regulator of disk size

Michael Küffmeier

Marie Skłodowska-Curie global fellow

Wow!

Credit: ALMA (ESO/NAOJ/NRAO)

Credit:

DSHARP team

10 au

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

something

something else with Bs

something else with more Bs

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

for more references see Wurster & Li 2018 (review)

something

something else with Bs

something else with more Bs

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!

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

Küffmeier, Zhao & Caselli 2020

mass-to-flux ratio

initial strength of rotation

Disk size distribution

Disk size distribution

Tobin+ 2019

Are disks already born small in some (all?) regions?

 Does cosmic-ray ionization play a crucial role?

see A. Maury's talk

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

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), ...

The connection to the larger scales

Küffmeier, Haugbølle & Nordlund 2017

Accretion is heterogeneous

Küffmeier, Haugbølle & Nordlund 2017

Observational indication: luminosity bursts

Revised picture

Pineda ... Küffmeier 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

Late infall happens more often than assumed

For solar mass stars ~50 % of final mass from beyond prestellar core! (Pelkonen et al. 2021)

Can disks be rejuvenated?

Küffmeier et al. 2022 in prep

Possibility of replenishing and refreshing the mass and chemical budget

It's fun to work on cosmic rays,

instead of catching Covid waves.

 Does cosmic-ray ionization play a crucial role in disk formation?

The big uncertainty

Current state-of-the-art in MHD models:

constant rate independent of densities

Figure from Padovani+'22 showing observations by Shaw+'08, Indriolo & McCall '12, Neufeld & Wolfire '17, Caselli+'98, Bialy+'22, Maret & Bergin '07, Fuente+'16, Sabatini+'20, de Boisanger+'16, van der Tak+'00, Hezareh+'08, Morales Ortiz+'14, Ceccarelli+'04, Barger & Garrod'20 (in addition: results by Cabedo+'22 [blue line]) 

External vs. internal

Competition between external and internal cosmic rays 

talks by Offner, Owen, Grassi, Gaches

We need

Are cosmic ray rates environment dependent or independent?

(Cabedo, Maury+'22)

(Küffmeier, Zhao & Caselli+'20)

 a better handle on CR propagation

measurements/maps of CR rates

talks by Redaelli (L1544), Pineda (NGC1333), Cabedo & Maury (B335), Sanna (G035.02+0.35), Sabatini

Self-regulation during disk formation?

(Offner, Gaches & Holdship'19)

Do externally or internally produced cosmic rays dominate disk formation process?

Summary

Cosmic ray ionization during disk formation depends on density, space and time. 

but disk formation depends on many parameters!

increasing ionization rate

enhanced magnetic braking

smaller disks

under otherwise identical initial conditions:

to (self-consistently) account for cosmic-ray variations in multi-scale non-ideal MHD models.

The ultimate modeling challenge is

Zoom-in method

Küffmeier et al. 2017

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

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 et al. 2017 / 2022 in prep.

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

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

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

Küffmeier 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

Küffmeier et al. 2021

Inner disk orientation

M_{\rm i, disk}=4 \ M_{\rm cloudlet}
M_{\rm cloudlet} = 1.87 \times 10^{-4} \ \mathrm{M}_{\odot}
M_{\rm i,disk} = 24 M_{\rm cloudlet}
M_{\rm i,disk}=4 \ M_{\rm cloudlet}
M_{\rm i,disk} = 0.4 \ M_{\rm cloudlet}

Küffmeier et al. 2021