星形成と銀河構造における磁場の役割 WS 2017 12/20-22

原始星形成における磁場の観測的可視化
Effect of interferometer observation on observed polarization map

Kazuya Saigo (NAOJ Chile Observatory)

Intro.

Polarization in protostellar system

Orion BISTRO´ L >~2000AU
Magnetic field structure of a cloud/filament/coreèInitial condition/environment of star formation´ L <~2000AU ç obs. by interferometer
Pattle et al. 2017
Magnetic field structure of a protostellar disk/envelopeè kinematics
SMA

Rao et al. 2014

Hourglass Shape=> Infall

Intro.
Ser-emb 8Turbulent
weak fieldOutflow
ConsistentHull et al. 2017
HL TauNumerical Simulation
Turbulent Weak Magnetized Cloud

Analysis of the direction and fraction ofpolarization give us information about dust
property, magnetic filed, etc.

Kataoka et al. 2017

Intro.2 Personal Motivation

BHB11 Class I Protostar
ALMA Cycle 2 Data
500AU scale SpiralMgas~0.17M8
12CO(2-1) outflow
1.3mm cont.

v-vsys~ -4km/s

Kep. Disk
M*~1.5M8300AU

Bleu lobe

Alves et al. 2017 (ALMA Cycle2)

v-vsys~ +4km/s

Intro.2 Personal Motivation
ALMA pol. result
Pol – I + E vector

BHB 11 Protostar
Mstar = 1.45M8
vsys = 3.7 km/s

Spiral E-vector
Polarization fraction ~ 6%
Is this correct?
We should check!

Saigo et al, In prep.

+P.A.=54.deg
i = 35deg
Rdisk~ 90AU

P.A.= 69.deg
i = 70deg
Rdisk= 400AU

Problem

Problems of interferometer observation
Observation by interferometer can not reproduce the extendedemission.
resolved out

In the case of polarization observation, it may change polarization
structure and polarization fraction.

?
Does the interferometer observation reproduce the actual
polarization structure? How to check?

How does ALMA observe polarization?
Antenna１Antenna 2

X-Pol、 Y-Pol

X-Pol、 Y-Pol
VX1 x VX2correlator V x VY1
Y2

X -Y Corr. ⇄ Stokes Parameters

Uncertainty of leak between theorthogonal polarizations (called D-term)

VX1 x VY2VY1 x VX2

Determine D-term using variation ofParallactic angle ψ by long observation.

Accuracy of D-term after calibration is ~1% for each antenna
è ~0.1% for integrated data (どんなにSNが⾼くてもこれが検出限界）

Method

CASA Interferometer Simulator´ We can check effect of interferometer observation with theCASA interferometer simulator.
´ 4 steps of CASA interferometer simulation
1. Full Stokes Model Images (FITS file)è XX, YY, XY, YX images

2. Virtual observation by “simobserve” task

Output is “Measurement Sets” (“ms” ) format same as real ALMA observation

3. Imaging by the “clean” task or “simanalyze” task.
4. XX,YY,XY,YX è Full Stokes images (I,Q,U,V)

Ex. 1 Disk Model

1. Disk Model
Polarization Vectors´ Disk with Radius = 2 arcsec⇔ R = 280AU at d = 140pc´ Polarization is ConcentricCircles* Magnetic Field => RadialDirection´ Uniform Polarization fraction =2.5%

Ex. 1 Disk Model

Stokes Model images
IQ

QUVUV
Spatial distribution
and spatial scale isdifferent in each
Stokes map.

Ex. 1 Disk Model

Convert to orthogonal polarization map
XXXY

YY

YX

At transit (ψ=0)

XX = I + Q
YY = I − Q
XY = U + 𝑖V
YX = U − 𝑖V
Assuming Stokes V = 0

Ex. 1. Disk Model

１. Virtual observation by CASA Simulator

XXYY

ALMA Cycle4 C40-4
Bad 7 (345GHz)XYYX

Ex. 1. Disk Model

Results: Stokes I and polarized flux (Pol-I)
Pol-I

Stokes I

Maximum Recoverable Scale> Disk radius (280AU)
It reproduces the flux of model.

1
𝑃 = (𝑄 + 𝑈 + 𝑉 )-1
𝑈
direction 𝑋 = atan
2
𝑄

Central Hole due to Beam Dilution

Ex. 1. Disk Model

Extended Configuration
Pol-I

Stokes I

Maximum Recoverable Scale > R
Significant missing Flux1
𝑃 = (𝑄 + 𝑈 + 𝑉 )-1
𝑈
direction 𝑋 = atan
2
𝑄

Beam Dilutionの⽳+ Non-axisymmetric structure+ slightly distortion

Ex. 1. Disk Model

Influence of interferometer observation
C40-4 C40-3

C40-2 C40-1

Stokes I
R=280AU
C40-5

Pol. fraction = Pol I / Stokes
10 x Pol I
2.5%

Maximum Recoverable Scale(see ALMA Proposers Guide)

Ex. 1. Disk Model

偏波率の空間分布
C40-1

C40-4

C40-2

C40-5

C40-3

Ex. 2 Hourglass

2. Hourglass Model´ Gaussian Core
FWHM = 400AU (5.7 arcsec)
at d = 140pc´ Hourglass Polarization* これはE vectorです。Hourglassとしては90度間違えました。ので、磁場と解釈するとHourglassではないですが、空間スケールの議論なので結果はあまり変わらないと思います。

´ Uniform Polarization Degree =3%

Ex. 2 Hourglass

2. Hourglass Model
FWHM < MRS

Stokes I

Pol I

Stokes I

Pol I

Compact
C40-2

FWHM > MRS
ExtendC40-3

Ex. 2 Hourglass

2. Hourglass ModelXXYYXYYX

Size scale of polarized flux
~ 1/4 of Stokes IEx. 2 Hourglass

2. Hourglass Model
C40-2 C40-1
C40-3

Pol I / Stokes I

Stokes I

C40-4
C40-5

10 x Pol I
HWHM

3%

FWHM

l Plateau size > MRS : Interferometer can not reproduce Stokes I
Special care is needed for observation of embedded protostellar objects.
l In the case of uniform magnetic field, Stokes I and Pol I decreases same rate.
è Polarization fraction ~ constantEx. 2 Hourglass

Hourglass 偏波ベクトル構造
Effect of Antenna Configuration- Model- Compact Conf.
- Medium Conf.
- Extended Conf.

Slightly distorted, influence is small in this caseEx. 3 Wave

Ex.3 Wave Structure in an uniform density cloud´ Stokes I = constant´ Polarization: Wave

Wave length 4 arcsec,
Amplitude: 1 arcsec

振幅´ Polarization fraction 3%波⻑Ex. 3 Wave

Wave Model XX,YY,YX,XY images
XXYYXYYXEx. 3 Wave

Ex.3 Wave Structure
Model

C40-4 (MRS ~ wave length)
Simulator
Amplitude 〜 2arcsec

In this case, amplitude of wave become lager with decreasing MRSSummary of Simulation Tests
To examine the effect of spatial sampling of interferometer observation
on observation results, I made virtual observations for simple models
using CASA simulator.
´ In Disk model, polarization fraction suddenly increases when theMRS size becomes smaller than the disk radius. Direction ofpolarization does not change.
´ In Gaussian (or Plateau + envelope) core model, polarization fraction
increases gradually. Direction of polarization change slightly in thenon-straight line polarization case (ex. Hourglass).
´ In uniform Stokes I case, polarization structure changes largely withMRS.
Package: scripts for polarization simulation of CASA + Disk and Hourglass Model

http://alma-intweb.mtk.nao.ac.jp/~saigo/Resources/

Finally

ALMA Cycle 6 Capability´ Single pointing observation by 12m array (Only 1/3 of the center of FoV).
´ Band 3,4,5,6,and 7 continuum (TDM), spectral(FDM)´ Detectable polarization fraction•Compact Source: 0.1% in TDM, 1% in FDM•

Extended Source: 0.3% in TDM, 3% in FDM＋´ In Cycle 6 (proposal deadline ~ next April), observation mode ofcircularly polarization will open!! Continuum observation,
spectral line observation? * Detectable polarization fraction >1~2% (may be,,)Do you have any requests about future plan?
Mosaic observation? ACP observation?

27

以下、参考参考 MRS
参考資料

TableA.1 in PG

Ex. 2 Hourglass

2. Hourglass Model Stokes map
IQUV