Faraday Rotation Structure on Kiloparsec scales in the giant lobes of ...

ira.inaf.it

Faraday Rotation Structure on Kiloparsec scales in the giant lobes of ...

ong>Faradayong> ong>Rotationong> of Radio Galaxies Behind

the Lobes of Centaurus A

Jean-Pierre Macquart

Ilana Feain, Ron Ekers, Bryan Gaensler, Ray Norris, Tim Cornwell,

Melanie Johnston-Hollit, Jürgen Ott, Enno Middelberg


Outline

• Why Centaurus A?

• The observations

• Basic RM statistics

• RM structure functions

• Implications for the lobe magnetic field structure


Ilana’s composite

Morganti et al. 1999

10’

Burns et al.

image courtesy Norbert Junkes (MPIfR)


Ilana’s composite

Morganti et al. 1999

10’

Burns et al.

image courtesy Norbert Junkes (MPIfR)


Ilana’s composite

Morganti et al. 1999

10’

Burns et al.

image courtesy Norbert Junkes (MPIfR)


Ilana’s composite

Morganti et al. 1999


Burns et al.

image courtesy Norbert Junkes (MPIfR)


Why Centaurus A?

• The closest radio galaxy at only 3.8 Mpc distance

– The closest AGN

– The closest SMBH (VLBI resolution 0.01pc, 100RS)

• 1 deg equivalent to 66 kpc (1” 18 pc)

• The brightest source in the Southern Hemisphere

• Large enough to use background radio sources as

probes of the lobe structure

– Measure the physical conditions inside the

magnetized radio lobes inflated by a relativistic jet


Why Centaurus A?

• Only upper limits exist on the thermal matter density

inside radio lobes

• Controversy: conflicting evidence on the presence

of ong>Faradayong> rotating thin skin (sheath) around lobes

caused by entrainment of intergalactic plasma

– For Cyg A, Dreher et al. 1987 attribute the observed

RMs (~thousands rad/m 2 ) to the foreground

intracluster medium

– Bicknell et al. (1990) use the same data to show this

RM could arise from a thin skin around the radio

lobes (Kelvin-Helmholtz instabilities mix lobe plasma

with ICM)


The Observations:

ATCA mosaic

• 1.4 GHz continuum with 8MHz

channels, IFs centred on 1344 &

1432 MHz

• 4 x 750m array configuration

• 406 pointings, hexagonal grid

(>600h observing)

• FOV 45 deg 2

• θ~45”

• σ~0.15 mJy/beam

600kpc


Source map

• 1005 extragalactic compact radio

sources down to 3 mJy/beam

(20σ)

• 28% of these are high S/N in

linear polarization and suitable

for RM studies (281 sources at

>7σ in LP)

• First time background sources

used for such a study

– analysis not subject to depth

and beam depolarization effects

Masked, spatially filtered total intensity radio continuum image of the

Centuarus A field used to find and catalog the compact radio sources. The

contours correspond to a Parkes 1.4 GHz image at 14’ resolution (courtesy

Mark Calabretta) with levels 1.5, 2, 2.5, 3, 4, 5, 6, 10, 100 Jy beam −1 .


he lobes of Centaurus A on scales much smaller tha

ian angular scale size of the background sources themse

is ∼10 ′′ for a 10 mJy source at 1.4 GHz (Windhorst

4). Polarisation The mean fractional fraction polarization of the 121 polari

rces• Is behind there depolarisation the lobes on (quoted scales smaller with than the the standard err

mean) beam is size? 7.6% ± 0.5% compared to the mean fract

rization • Mean for source thepolarisation sources outside inside lobes the7.6±0.5%,

lobes of 7.3% ± 0

ng the outside Burn lobes (1966) it is 7.3±0.4% law for depolarization,

• If depolarisation then

f d = e −2σ 2 RM λ4 ,

• Conservatively, fd > 0.7, so there is < 10 rad m -2 RM

variance on scales 180pc.

ote that we analyze those polarized sources with a S/N 7 only; th

olarized sources below this S/N cutoff but we do not consider them

.


RM field

• 281 sources at >7σ,

93 behind Cen A, and

188 outside

• RM= -57 rad m -2

σ=30 rad m -2


FEAIN ET AL. Vol. 707

RM field

100% 10%

• 281 sources at >7σ,

1%

93 behind Cen A, and

188 outside

• RM= -57 rad m -2

0.1%

σ=30 rad m -2 RMinside= -61.3 rad m -2 , σ=29.8 rad m -2

polarized flux density plane for the 281

debiased polarized intensities correspond to

ustification of this threshold. The dashed, dionstant

fractional polarization (from top left to

.1%).

robust for all contour values that we

h were between 1 and 2 Jy beam −1 ).

Figure 6. Top panel: RM distribution of the 281 sources in Table 3. The mean

RM is −57 rad m −2 and the standard deviation is 30 rad m −2 . Middle panel:

RMoutside=

distribution of the-52.9 121 sources

rad mbehind -2 , σ=29.2

the lobes

rad

(mean

m−61.3 -2 rad m −2

and standard deviation 29.8 rad m −2 ). Bottom panel: RM distribution of the

160 sources outside the lobe (mean −52.9 rad m −2 and standard deviation

29.2 rad m −2 ). The bin size is 20 rad m −2 in all panels.

(A color version of this figure is available in the online journal.)

1. Our derived total intensity source counts are consistent,


Milky Way

contamination

Preliminary HIPASS continuum image, courtesy Mark Calabretta (CSIRO ATNF)


Milky Way

contamination

Preliminary HIPASS continuum image, courtesy Mark Calabretta (CSIRO ATNF)


Removing the MW

component

• Want to separate the MW

and Cen A RM

components, at least in a

statistical sense

• Use the 160 RMs not

located behind lobes to fit

for a foreground MW

component

• This surface (gradient ~ 6

rad m -2 deg -1 ) was

subtracted from all 281

RMs

• RMinside= -4.5±2.8 rad m -2

σ=30.4 rad m -2

• RMoutside= -1.6±2.1 rad m -2

σ=26.6 rad m -2


RM difference inside and outside lobes

• This small difference implies a limit on the thermal

electron density of

( ) −1 B √

〈n e 〉 < 4 × 10 −5 N cm

−3

1 µG

where the equipartition field is B=1.3 µG (Hardcastle et al.

2009), we assume a path length of 200kpc through the

lobes, and the magnetic field undergoes N reversals

along the line of sight

This is 2-3 times smaller than previous limits.


edges of the lobes) to a “control group” of RMs loc

sightlines outside the lobes using an approach based on

RM ong>Structureong> functions

cture function,

• What is the structure function

D RM (θ) = 〈[RM(θ + θ ′ ) − RM(θ ′ )] 2 〉,

• Why are we using it here?

– Irregular source grid means that the RM grid is not

suited to a direct Fourier spectral analysis

(horrendous windowing function)

– Offers a robust way to measure the RM power

spectrum:

D RM (θ) = 2[C RM (0) − C RM (θ)]

C RM (θ) = 〈[RM(θ + θ ′ ) −

¯ RM][RM(θ ′ ) −

¯ RM]〉

P RM (q) = 1

(2π) 2 ∫

d 2 θ exp[iθ · q]C RM (θ)


Interpretation of ong>Structureong> Functions:

A simple example

q −β exp

Power spectrum

[

− q

q in

]

saturates at outer

scale

q out

r 2 r β−2 r out ∼ q −1

q in

may oscillate if there is

a sharp feature in the

power spectrum

ong>Structureong> Function

changes slope at

inner scale

r in ∼ q −1

in

out


122

RM field spatial structure: DRM inside

5000

lobes

2000

D RM

(rad 2 m -4 )

1000

500

2 -4

200

100

This point determined using double-lobed

sources. All other sources have white noise

offset due to intrinsic/internal RM variation.

0.01 0.05 0.10 0.50 1.00

θ (degrees)

(a)


FEAIN ET AL.

RM field spatial structure: DRM outside

lobes

5000

2

2000

1

D RM

(rad 2 m -4 )

1000

500

∆D RM

(rad 2 m -4 )

200

1

100

0.01 0.05 0.10 0.50 1.00

θ (degrees)

2


RM field spatial structure - lobes only:

DRM inside-outside lobes

2000

Vol. 707

1000

Here be Dragons

∆D RM

(rad 2 m -4 )

0

1000

2000

0.05 0.10 0.50 1.00

θ (degrees)

Errors increase as scale

approaches size of

survey region (fewer

independent

measurements of

stochastic process)


SF errors

Var[ ˆD(τ)] =

∫ T


0

where u = |τ| and T ′ = T − u and

[ T

4Γ(r, u) 2 ′ ]

− |r|

T ′ 2

dr

(Jenkins & Watts 1969; Rickett, Coles & Markkanen 2000)

In the region τ ∼ < τ 0 , where τ 0 is the value at which the SF reaches half its

saturation value, we have

ˆD rms (τ) ≈ 2D ∞


τ0

T

For us D ∞ < 1500 rad 2 m −4 and τ 0 ∼ 1 ◦ .

Γ(r, u) = 0.5[D(r − u) − D(r + u) − 2D(τ)].

100

τ 2

τ 2 0 + τ 2

ˆD rms (τ)

10

This estimate based on

approximation of a 1-D field.

1

These errors comparable to

Poisson errors only at >2 deg.

0.1

0.02 0.05 0.10 0.20 0.50 1.00 2.00

τ


(a)

8. RM structure functions of (a) the 121 polarised sources

nes outside the radio lobes of Centaurus A. (c) The difference

The signal comes primarily from the

southern lobe

or version of this figure is available in the online journal.)

2000

1000

SF of all sources in the south

minus SF of all sources in

the north

2000

1000

∆D RM

(rad 2 m -4 )

0

∆D RM

(rad 2 m -4 )

0

1000

1000

2000

0.05 0.10 0.50 1.00

θ (degrees)

2000


Implications I

• A significant excess RM inside the

lobes on scales between 0.1 and

0.5 deg, with an amplitude 640 rad 2

m -4 in the structure function

• This implies the S. lobe contributes

an excess fluctuating RM

component with an rms σ≈17 rad

m -2 on scales ~0.3 deg (20 kpc)

• Excess RM could arise either due to

turbulent medium inside the lobe, or

a thin sheath

– We favour the latter

Likely source of RM excess


Implications II

• Model this contribution as follows:

thermal density nth skin , coherent magnetic field Bt, angle of

orientation θr which changes direction on a scale l~20kpc,

D~180kpc is path length through lobe

– Expected RM dispersion is then

σ RM = 467

( n

skin

th

1 cm −3 ) (

Bt

1 µG

) ( D

1 kpc

) 1/2 ( ) 1/2 l

rad m −2

1 kpc

• For our values of l and D and using the Bouchard et al. (2007)

intragroup medium density near Cen A (ne≈10 -3 cm -3 (similar to

X-ray measurements of Cen A’s ISM)) we find Bt ≈ 0.8 n1 -1 µG

where nth skin = n1 10 -3 cm -3


Conclusions

• First systematic probe of magnetic properties of

lobes using background radio sources

• Limit on excess mean rotation measure of Cen A’s

lobes places a limit of ne~5 x 10 -5 cm -3

• Detection of excess spatial structure in the

Southern lobe relative to the MW probably

associated with the lobe sheath

– estimate B~1 µG in this region


The “Standard” Model for structure

in the Ionized ISM

The ionized Interstellar Medium of

our Galaxy follows a power law on

scales 10 6 m up to 10 14 -10 18 m

The slope of the spectrum is surprisingly

close to the value expected for

Kolmogorov turbulence, β=11/3.

Armstrong, Rickett & Spangler 1995


The First Ever Speckle Image of a

scattered source in the ISM

20

1300

500

S/N

10

100

20

offset mas

0

-10

5

-20

-30

10 mas=4.12 AU

20 10 0 -10 -20 -30

RA offset (mas)

Brisken, Macquart et al.

ApJ, 2010


The First Ever Speckle Image of a

scattered source in the ISM

25

20

322.5 MHz

Relative Declination (mas)

15

10

5

0

−5

−10

−15

−20

−25

10 mas=4.12 AU

ong>Structureong> resolved

down to 0.05 AU

Scattering screen is

420pc from Earth

(64.7±0.5% of the

Earth-pulsar distance)

The velocity of the

scattering plasma is 16

±10 km s -1 and parallel

to the axis of the linear

feature

−30

30

20 10 0 −10

Relative Right Ascension (mas)

−20

Brisken, Macquart et al.

ApJ, 2010


Speckle Imaging of the ISM

Scattering Geometry revealed by Secondary Spectra




f i

2 j

2

f t i j ).v scint


Position of structure on the secondary

spectrum

delay (conjugate to

frequency axis)

Doppler shift

(conjugate to

time axis)

τ = D s

2cβ

• Secondary Spectrum shape determined by

speckle distribution

• Main parabola: set θj=0 and consider delay vs

Doppler shift

• Inverted parabolae: now set θj≠0

• Speckle image reconstruction generally not

possible unless v is known.

(

θ

2

i − θ 2 j

)


φ i

2πν + φ j

2πν

this term usually unimportant

ω = 1

λβ (θ i − θ j ) · v ⊥


Extreme Scattering towards PSR B0834+06 3

The “symmetric”

part of the phase

Figure 1. The amplitude (left on a logarithmic scale) and symmetric component of the phase (right) of the visibility secondary spectrum


How do we make this image?

In the regime of strong scattering the wavefield seen by an observer

can be approximated by the sum of a number of speckles, each with

a magnification µ and phase Φ:

u(r) =

N∑ √

µj exp(iΦ j ),

j

where the phase term contains a screen term φ(x) and a geometric

phase delay term:

(x − βr)2

Φ = φ(x) +

2rF

2 .

Here β = 1 − (distance to screen/distance to pulsar) and r is the

transverse position on the observing plane.


How do we make this image?

The visibility that we measure is just

V (b) = u(−b/2)u ∗ (b/2).

If we substitute in our formula for u(r) and Fourier transform, we find

Ṽ (b) = ∑ √

µj µ k exp {i [Φ j (−b/2) − Φ k (b/2)]} δ(f D − f D,jk )δ(τ − τ jk ).

j,k

Amplitude Phase Term

Location of point on

secondary spectrum

I.e. a double sum over all pairs of stationary phase points.

f D,jk = 1 λ (θ j − θ k ) · V eff

τ jk = D s

2cβ (θ2 j − θ 2 k) +

[

φj

2πν − φ ]

k

2πν

These are our

familiar

expressions for

the location


How do we make this image?

All the astrometric information is encoded in the phase term:

antisymmetric – 9 –

Φ j − Φ k = φ j − φ k + kD [

s

θj 2 − θk 2 + βb ]

· (θ j + θ k ) .


D s

symmetric

When we compare the τ > 0 part of the secondary spectrum to its τ < 0

counterpart and add the phases of each together, we get

ψ jk (b) = 2π λ b · (θ j + θ k ).

2

This is just the astrometric phase!

1.8

12

11.5

2

1.8

150

1.6

11

1.6

100

Differential Delay ! (ms)

1.4

10.5

1.2

10

1

The symmetric part (astrometric) of

9.5

0.8

9

the phase on 0.6 the Arecibo-GBT

baseline

0.4

8.5

0.2

8

Differential Delay ! (ms)

1.4

1.2

1

0.8

0.6

0.4

0.2

50

0

!50

!100

!150

0

!60 !40 !20 0 20 40 60

Differential Doppler frequency f D

(mHz)

7.5

0

!60 !40 !20 0 20 40 60

Differential Doppler frequency f (mHz) D


Excess RM variation in S lobe


Intrinsic PA distribution


RM distribution after background

removal


RM distribution after background

removal

More magazines by this user
Similar magazines