Michael Küffmeier

The flip of polarization in multi-wavelength observations

and some encouragement to compare ionization rates with disk sizes

Stefan Reißl (ITA Heidelberg), Hannah Woodward (UVA), Zhi-Yun Li (UVA), Paola Caselli (MPE), Bo Zhao (McMaster)

Why care about magnetic fields?

Mocz, Burkhart et al. 2017

hydro

MHD

Santos-Lima et al. 2012

Stars are born in large assemblies of gas

Star-disk systems form in different environments provided by Giant Molecular Clouds (Size: 10 - 100 pc)

Serpens SMM1 (Le Gouellec et al. 2019)

Zoom-in method

Küffmeier et al. 2017

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

M_{\rm box} \approx 10^5 \mathrm{M}_{\odot}

B_{\rm box, rms} = 3.5 \mu G

Zoom-in on embedded protostellar multiple

Küffmeier, Calcutt

& Kristensen 2019

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

for zoom-ins on disks see Küffmeier et al. 2017/18

Zoom-in simulations

Start from a snapshot of a young Giant Molecular Cloud (GMC)

Model stars as sink particles

Turbulence as a result of supernova feedback

l_{\rm box} = 40\, \rm pc

Adaptive mesh refinement (AMR)

ideal Magnetohydrodynamics (MHD)

Magnetic fields in simulation

Küffmeier, Reißl et al. 2020

...in bridge

Field strength in bridge:

about 1 to 2 mG

...around primary protostar

Field strength close to foot point:

>100 mG

B-field important on smaller scales <100 au

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.

Stokes vector: description of polarized light

Poincaré sphere; credit: wikipedia

Synthetic observation with POLARIS

Küffmeier, Reißl et al. 2020

Emitted radiation

at 1.3 mm: polarization traces magnetic field structure

(we display e-vectors rotated by 90°)

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?

Wavelength dependence: 1.3 mm vs 53 micron

1.3 mm: good tracer of magnetic field

53 micron: tricky tracer of magnetic field

Küffmeier, Reißl et al. 2020

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

Synthetic maps from ~pc to ~10 000 au scales

Hannah Woodward

UVA undergraduate; graduate at University Wisconsin-Madison from September 2022

Woodward, Küffmeier & Li in prep

based on MHD simulations of Haugbølle et al. 2018 (see R. Kuruwita's poster)

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

Resistivity depends on ionization rate

Küffmeier, Zhao & Caselli 2020

Question: What is the effect on disk formation when differing the ionization rate?

In fact, we use a 2D setup (r- and z-coordinate)

Parameter study

Küffmeier, Zhao & Caselli 2020

Effect of ionization on disk size

increasing ionization rate

enhanced magnetic braking

smaller disks

Küffmeier, Zhao & Caselli 2020

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

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

more references in Wurster & Li 2018 (review)

Disk size distribution

Tobin+ 2019

Are disks born small in some regions?

Is there a correlation with cosmic-ray ionization rate regions?

Cazzoletti+ 2019

Alternative to external photoevaporation:

Disk size distribution

Küffmeier, Zhao & Caselli 2020

Take-away points

Linear polarization of dust reemission at wavelength >200 micron is a good tracer of magnetic field structure on scales beyond the disk.

(Cosmic-ray) ionization might be a key parameter for setting the difference in mean disk size between star-forming regions of similar age.

At smaller wavelengths (i.e., SOFIA HAWC+) and regions of higher column densities, the signal tends to be dominated by absorption instead of emission causing a flip in orientation.