Takuya Akahori, Dongsu Ryu Chungnam National University

2010.08.20 SKA-KR Workshop 2010, KASI, Daejeon, Korea Akahori 1/20

Study of Faraday Rotation due to the Intergalactic Magnetic Field~Preparing the Era of the Square Kilometer Array~

Takuya Akahori, Dongsu Ryu

Chungnam National University

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Log10 |RM| [rad m-2]

-50 -25 0 25 50[h-1Mpc]


Contents

• Introduction– State-of-the-Art/Unresolved Problems

• Faraday Rotation Measure (RM) due to the Intergalactic Magnetic Field (IGMF)– Part 1. present-day local universe

• Coherence length, rms value, PDF, power spectrum

– Part 2. cosmological effects• LSS evolution, radio source distribution, X-ray emission

– Part 3. galactic foreground• Scale difference, FFT/FWT filtering analyses

• Summary• Status of SKA in Japan


Introduction

• RM & synchrotron observations– Simard-Normandin, Kronberg, Button (81), Kim+ (89; 90; 91), Clarke, Kronberg, Bo

hringer (01), Taylor, Fabian, Allen (02), Govoni+ (04), Xu+ (06), Pizzo+ (08), Taylor+ (09), Govoni+ (10)

• Cross correlation & structure function of RM– Brown, Farnsworth, Rudnick (09), Lee+ (09), Stasyszyu+ (10), Mao+ (10)

• Spectral analyses, tomography– Frick+ (01), Brentjens, Bruyn (05), Schnitzeler, Katgert, Bruyn (09)

• Modeling of magnetic field and its power spectrum– Feretti+ (95), Felton (96), Krause+ (09)– Vogt, Ensslin (03; 05), Murgia+ (04), Guidetti+ (08), Bonafede+ (10)

• Simulations and estimation of RM in the LSS– Kulsrud+ (97), Ryu , Kang, Biermann (98), Dolag+ (99; 05), Dubios. Teyssier (08),

Ryu+ (08), Dolag, Stasyszyu (09), Akahori, Ryu (10)

• Relation with metal enrichment, effects of AGN & galaxies

State-of-the-Art / Unresolved Problems


Observations of RM in Galaxy Clusters

Now) profile of RM, correlation with the X-ray morphologySKA) what’s the origin? when developed? how important?

Radial RM profilesClarke, Kronberg, Bohringer (01)Govoni+ arXiv:1007.5207

Galaxy cluster

RM~ 100 [rad mRM~ 100 [rad m-2-2]]IGMF ~1-10 [μG]IGMF ~1-10 [μG]


Estimations of RM in Galaxy Clusters

Now) constrains of IGMF structure by fitting with modelsSKA) statistical argument using large samples

n=11/3 (Kolmogorov)?n=11/3 (Kolmogorov)? (e.g. Vogt, Ensslin 05; Guidetti+08; Bonafede+10)

→ existence of Kolmogorov turbulence and turbulence amplification of the IGMF?

- Power-law Gaussian random IGMF model e.g., Murgia+ (2004)

Govoni+ arXiv:1007.5207Guidetti+ (08)


Observations of RM in the LSS

Now) RM<10 rad m-2, or it has too complicate structures to distinguish them from noise

SKA) 1 source /arcmin2 with ~1 rad m-2 error

Orion ArmRegion ALoop II

Loop I

Coma

Virgo

Perseus

North Polar Spar

Hercules supercluster

All sky RM map, Taylor, Stil, Sunstrum (09)

Xu+ (06)

RM < 10 [rad mRM < 10 [rad m-2-2] ?] ?IGMF < 1 [μG] ?IGMF < 1 [μG] ?


Estimations of RM in the LSS

• Cosmological HD/MHD simulations– MHD…still hard to treat the evolution of

turbulence and amplification of the IGMF correctly

log |B| μG

5 Mpc

Dubios, Teyssier (08)

Now) estimations of RM from HD/MHD simulationsSKA) observational appearance of RM

→ Radio source distribution in space→ Uncertainty of RM at the source, our local group, and our galaxy→ Of course, a reasonable IGMF model

Stasyszyn+ arXiv:1003.5085Akahori, Ryu (10) ApJ submitted


• Turbulence Dynamo Model① Calculate curl component of flow motion & its energy εw

② Regard εw as the turbulence energy εturb

③ Adopt the growth model εB/εturb=f(t/teddy) & B=(8πεB)1/2

Our Model for the IGMF

time [teddy]

En

erg

y d

en

sity

filaments

GCs

Ryu+ (08)

10-4μG |B| 10μG

100 h-1 Mpc

Ryu+ (08) Cho & Ryu (09)

IGMF ~0.1 [μG]IGMF ~0.1 [μG]RM~ 1 [rad mRM~ 1 [rad m-2-2]]


1 Present-day local universe: 2D map

• RM ~100 (GCs), ~10 (Groups), ~0.01-1 (filaments)• Mixture of positive and negative RM, that reflects the rand

omness and the coherence scale of IGMFs in the LSS

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(z=0, L=100 h-1 Mpc)

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1 Present-day local universe: radial profile

• Inducement of RM is a random walk process with the coherence length < path length, but is dominated by the contribution from the density peak along LOS


1 Present-day local universe: statistics

・ Lognormal profile of PDF・ rms ~ 1.4 [rad m-2] for WHIM

PDF of |RM| for WHIM (105 K<Tx<107 K)Tx: emissivity weighted temperature. Black: 3×16 runs, Red: average, Blue: best-fit

・ Peaked at ~Mpc scale・ PRM(k) is close to PB||,proj

(k): RM traces B well

2D power spectra of RM and the projected IGMFBlack: 3×16 runs, Red: average

100 h-1 10 h-1 1 h-1Mpc 10 h-1 1 h-1Mpc↑ in good agreement with Cho, Ryu (09)


2 Cosmological effects: RM stacking

• |RM| increases with integrating RM along LOS

Simulation boxes are stacked up to z=5Redshift distribution of radio sources are considered

Willman+ (08)

z=0.1 0.3 0.5 1.0 3.0 5.0

Log |RM|[rad m-2]


2 Cosmological effects: statistics

• rms of RM

• PDF– lognormal

[rad m-2]

WHIM+ICM 40WHIM (theoretical) 7-10

WHIM (observational) 6-10

rms of RM integrated up to z. ICM candidates are subtracted in the integration (theoretical) or after the integration (observational) of RM

★ observational

T [K]

107

★ theoreticalTx=4keV

Tx=1.5keV

ALL

CLS

1Mpc

TM7

T57 Map Pixcels w Tx>107K

TS8 MapPixcels w Tx>107K

& Sx>10-8 e/s/cm2/sr

TS0 MapPixcels w Tx>107K

& Sx>10-10e/s/cm2/sr


2 Cosmological effects: statistics

• P(k): peak scale at ~0.2º• S2(r): characteristic scale at ~0.1-0.2º

2D power spectra P(k) integrated up to z=0.05, 0.3, 5 (thin to thick)

2nd order structure function S2(r)

1.4º 0.14º

~0.2º


All sky RM (Taylor+ 09)

• Galactic RM is a serious contamination for studying RM in filaments– galactic RM ~10-100 [rad m-2]

3 Galactic foreground: Concept of Analysis

Spectra of observed all-sky RM(Frick+ 01)

Key point: peak scales are different

10-100 degree10-100 degree0.1-1 degree0.1-1 degree

Chop! Use!


3 Galactic foreground: High-pass filters

High-pass filters have potential to subtract galactic component

Intrinsic+Noise

High-passfilter

• Fast Fourier transformation (FFT)• Fast Wavelet transformation (FWT)• Transform→ low frequency cut at kf → inverse-Transform

• Parameter: kf

Noise RM• Gaussian random fluctuation• Kolmogorov spectrum |Q(k)|2 k∝ -11/3(k>kn), k-1(k<kn)• <RM>=0, <RM>rms= σn

• Parameters: σn & kn

Intrinsic RM Filtered RM(FFT/FWT)


3 Galactic foreground: What’s the Best kf?

• A high-pass filter with kf ~ degree would effectively reduce the galactic foreground contamination

rms of RM as a function of the filter scales of FFT (left) and FWT (right)Noise model: kn= 5 (2.8º scale), <RM>rms, noise= 20 [rad m-2]


Summary

RM in filaments is discussed using a model IGMF• Present-day local universe

– rms ~ 1 [rad m-2] for WHIM, lognormal, peak at ~Mpc • Cosmological effects (stcking up to z=5)

– rms ~ several-10 [rad m-2] for WHIM, lognormal, peak at ~0.2º

• Galactic Foreground– Degree-scale high-pass filters (FFT/FWT) works well

• SKA will highlight and reveal origin and nature of the IGMF. Our estimated RM is in detection range on SKA.

• The high-pass filter is quite effective to remove galactic foreground RM, which would improve statistical analyses

– e.g., cross correlation and structure function


Status of SKA in Japan

• Japanese SKA consortium (SKA-JP)– since 2008.5, ~70 members, ~20 Institute– Science & Engineer Working Groups– Regular meeting (TV, Site) ~1/month

• International Workshops– SKA-JP WS 2004.11, 2008.11– SKA-JP Workshop 2010.11.3-4@NAOJ

• Recommendation of Science Council of Japan– LCGT, TMT, SKA, SPICA, ASTRO-H,..– Japan should bear 10% (~2-300M$?) of co

nstruction and use costs– But, “observer” so far


Status of SKA in Japan

• Science Working Group– 8 subgroups　　 Cosmic Magnetic Fields / AGN / Pulsars /

Galaxy evolution and high-z universe / Astrometry / Star and Planet Formation / Wide-Band Spectral Line Survey / Antenna

– Summary of unresolved problems 　　 To be uploaded on SKA memo http://www.skat

elescope.org/pages/page_memos.htm

• Engineer Working Group – Ultra-wide band polarized wave m

easurement on >~ 10 GHzUltra-wide feed, tapered slot antennaDigital polarized wave measurement system

• Collaboration with East-Asian countries

Documents

Takuya Akahori, Dongsu Ryu Chungnam National University