Proper Motion ofSeyfert 1 Galaxy PKS 2201+044

Hiroshi Sudou (Gifu University),
Phil Edwards (CISRO),& Japanese VLBI team2008 VERA Users MeetingUnified Scheme for radio-loud AGNsQuasar
BL Lacθ~30 － 40 deg (Ghisellini et al. 1993)

BrighterCompact jet
Jet
Radio Galaxy (FR II)(FR I )
WeakerDefuse jet
BH

Radio property is generally controlled by the jet viewing angle
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PKS 2201+044
Elliptical galaxy at z ~ 0.02
Optical property

Violent variability ∆m ～2 mag
Recent spectroscopy  Seyfert 1 Galaxy
Previous spectroscopy  BL Lac ObjectRadio property

FR I type
Apparent size ~ 50 kpc
Showing optical jet as well as radio one

Measuring the viewing angle of the radio jet Which is likely BL Lac or Seyfert (Radio Galaxy) ?
2008 VERA Users Meeting3How to measure the viewing angleProper motion of the jet βapp (β, θ) = βsinθ/(1－βcosθ)
Doppler factor δ(β, θ) = 1/{γ(1－βcosθ)}

From Synchrotron self-Compton model
Estimate from the comparison between observed
and predicted X-ray fluxFrom Compton catastrophy of Brightness temperature
Brightness temperature of > 1012[K] leads tocatastrophic inverse Compton losses and forces theradiation to have a lower value

Jet/counter-jet intensity ratio
R (β, θ) = {(1＋βcosθ)/(1－βcosθ)}3+α2008 VERA Users Meeting4Observations
DateFrequency Array
Resolution[GHz][ant. num.] [mas]24 May,2000

8.6

VLBA [10] 130 July,
2006

8.6

JVN [5]328 May,2007

8.6

JVN [8]

3JVN [5] = VERA + Kashima
JVN [8] = VERA+ Kashima+ Yamaguchi+ Usuda + Gifu
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Maps
VLBA 2000

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JVN 2006

6

Direction of the jet
ScalePosition angle[deg]

Reference50 kpc
(VLA)

280

Laurent-Muehleisen et al.
1993

1 kpc
(VLA, HST)

310

Scarpa et al. 1999 LaurentMuehleisen et al. 1993

pc
(VLBA, JVN)

315

This work

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Proper motion (βapp)
Knot identificationNormal method  Gaussion fitting of knots
The most likely positional shift of the knot
component is (⊿x, ⊿y) = (－3.8, －3.5)

Proper motion is estimated to be 5.1 [mas]for 6 yrs @position angle of 313 [deg]In this case, we adopt βapp= 1.1

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Doppler factor (δ)
Synchrotron self-Comptonδ=0.2  consistent with Ghisellini et al. 1993

Brightness temperatureδ=

TB,int
TB,obsT B, obs=0.7×1011 [K] was estimated from VLBA data
δ=0.07 － 0.7
for T B,int= 1012 and 1011[K], respectively

 consistent with the SSC results
We adopt δ=0.2
2008 VERA Users Meeting9Jet/Counter-jet intensity ratio (R)Counter-jet was not detected
Lower limit of R can be estimated to be 5 from theVLBA map
We adopt R > 5NoteCounter-jet might be absorbed by dense plasma torus(e.g., Kameno et al. 2001),
Thus intrinsic R could be lower than observed one
2008 VERA Users Meeting10Viewing angle and speed of the jet1intrinsic jet speed

Doppler factor
0.9
0.8

Proper motion

0.7

Jet/counter-jet (lower limit)

0.6
0.5
010

2030

405060viewing angle [deg]708090: (β,θ) ~ (0.95, 80)
2008 VERA Users Meeting11Possible geometry of the jet
0.95 c80 deg*Highly relativistic speed*Almost perpendicular to the line of sightIn view of the jet geometry PKS 2201+044
is similar to Radio Galaxies, not to BL Lacs.
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2008 VERA Users MeetingSummary (Science Part)
Proper motion of PKS 2201+044 isestimated to be 1.1 c
 Together with Doppler factor, the jetviewing angle is estimated to be ~80 deg This indicates that this source should be aSeyfert (radio) galaxy, rather than an BLLac Difference between optical and radioclassification should be considered2008 VERA Users Meeting13

Appendix:
Methods of Knot Identification

2つのマップがあったとする


ジェットの固有運動を計りたい

しかし、2つのマップは異なる望遠鏡で（つまり異なる分解能、感度）で得られている または、ジェットの形状が非常に複雑（e.g.,
M87 @VLBA 43GHz）

ＶＳＯＰ－２ではよりこの傾向が強まる knot同定の精度を上げるには？
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明確なknotが見えるか？

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General Methods
1.
2.

3.



Local Peak： ピークの1ピクセルのみ
Gaussian Peak： 明確なガウス型ピークを構成する複数のピクセル（通常の方法）
Correlation： ある強度レベル以上の全てのピクセル
画像情報をできるだけ多く取り込むことで、精度を向上させる
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Two Correlation Methods
A( j ) = ∫ X (i )Y (i + j )diX (i )Y (i + j )B( j ) = ∫diQ( j )Q( j ) = ∫ X (i )Y (i + j )di2

2

Ａ：通常の相関
Ｂ：自己相関による規格化
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Case of PKS 2201+044(preliminary)
・各マップ3σでカット（3σ以下の強度は0とおいた）・マップごとに重みはかけていない（より精度のいいＶＬＢＡデータに重みをかけることも今後検討）∆X [mas]∆Y [mas]

ガウスフィット(No.8参照)

4.5

4.3

相関A(j)

43

相関B(j)

47

・いくつかのパラメータ（e.g., カットオフ、重み関数）にて再検討したい
・疑似データを使ったシミュレーションでも検証してみたい2008 VERA Users Meeting18

Next Step
この手の画像処理の一般的手法は？
 多少ノイズが大きくても、精度良く固有運動を検出する最適手法を見つける（SNR等、ケースごとに異なるかもしれない）
 ＶＳＯＰ－２に向け、複雑な構造のジェットの固有運動の同定方法の検討
 ビームに埋もれた複数の成分を検出できるアルゴリズムもほしい（e.g., Doublecore）
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