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
Cosmic-Rays_Florence2022
By kuffmeier
