ベイズモデルを用いた ブレーザーの時系列偏光データの解析 (Uemura, et al., 2010, PASJ, 62, 69) 植村誠　（広島大学）、他「かなた」望遠鏡チーム ベイズモデルを用いた ブレーザーの時系列偏光データの解析 (Uemura, et al., 2010, PASJ, 62, 69)

Blazars in the optical band Fosati, et al. (1998) blazar Optical-NIR High polarization hope fact A probe of the magnetic field structure But, no universal law has been established

Polarization variations in blazars Erratic variations Random motion in the QU plane? Blinks of a number of polarization components? Systematic variations Increase of the polarization degree (PD) with flares Rotation of the polarization angle (PA) A probe of the magnetic field in jets Are there universal characteristics in blazar polarization? The main theme of this talk We want to find a kind of “rules” in apparently erratic variations. Positive correlation between the flux and PD. (Smith, et al. 1986) Apparently random motion in the QU plane (Moore, et al. 1982)

「かなた/TRISPEC」による ブレーザー多色偏光撮像モニタープロジェクト できればシンプルで普遍的な、”erratic”でない観測的特徴をとらえたい キャンペーン期間：昨年秋～2009年3月 40天体ほど？ いくつかの天体は2007年から順次モニター開始していた

「かなた」データの例 光度と偏光度が相関してる short flareもあれば、そうでないのもあり。。。 　AO 0235+164：相関してるのもあるが、多少タイムラグがあるものもあるような。一方で全く相関してないのも。(笹田、他、天文学会） 　PKS 1749+096：同じような時期、同じような振幅のフレアで相関してるのと、してないのと。

「かなた」データの例（続） BL Lacともあろうものが。。。 やはり、short flareには多少の反応がありそうだが。。。。。 というか、光度曲線に比べて偏光度がバタバタし過ぎ？？？ 光度変化はさほどでもないのに、突然偏光度があがったり。 ＯＪ４９は数か月のトレンドに偏光度が相関してない。。。。。。。

光度と偏光度の相関関係 めちゃくちゃ

“Bluer-when-brighter”: as a universal feature of blazars 32/42 blazars = well-observed objects (> 10 days) No significant correlation can be detected in 10 poorly-observed objects. 23/32 blazars = the bluer-when-brighter objects in their whole data. 2/32 blazars = from redder-when-brighter (faint state) to bluer-when-brighter (bright state) 3C 454.3 and PKS 1510-089 3 blazars = the bluer-when-brighter trends in year-by-year QSO 0454-234, PKS 1502+106, and PKS 0048-097 In total, 28/32 (=88%) blazars showing the bluer-when-brighter trend A sign of the trend can be seen even in the other 4 sources. Color-magnitude diagram of MisV1436

なぜ偏光の変動はめちゃくちゃなのか？ ３つの仮説 多様性が圧倒的に大きい　 フレアが、磁場の揃った（or amplifyされた）ところで起こることもあれば、揃ってないところで起こることもあるし、揃ってるところで起こったとしても途中で磁場の向きが変わることもあれば、あまり変わらないこともある。 色や偏光を観測しても普遍的な描像には届かない。。。 　　→せっかく観測してきたのに、この結論は避けたい。。。 無数の（ランダムな）細かいフレアの重ね合わせ １つ１つのフレアは固有の偏光成分をもつ Moore et al. (1982), Impey et al. (1988), Jones et al. (1985, 1988) 　　→まだマシだけど、「ランダム」だとたいていの観測結果は「たまたま」で説明できてしまうので。。。 フレアに付随する偏光成分とそうでない成分の2成分があって、観測値はその２つが重なって見えている 常に偏光度の大きいような天体だと明らかに重要 Long term成分の推定が問題 　　→もしこの可能性があるのなら、そのような解の推定には意味があるだろう。

Multiple polarization components? Stokes’ QU parameters of BL Lac for ~20 yr (Hagen-Thorn, et al. 2002) Stokes parameters for linear polarization Systematic variation could be hidden by the presence of another polarization component. Preferential direction of polarization for years Our model assumptions: A flare is always associated with the flare of the polarized flux. There is a long-term variation trend in polarization. (0,0)

Bayesian method to estimate a long-term trend in polarization Q U t flux Prior distribution of the long-term trend (smoother curve is preferred). Posterior distribution of the long-term trend Likelihood function, maximized when the total flux and polarized flux completely correlate. The estimation of the parameters is done with the Markov Chain Monte Carlo (MCMC) method.

Demonstration with artificial data Test 1: Case for low frequency flares pol. flux total flux The long-term trend is reproduced as assumed (0,0) U Q

Demonstration with artificial data Test 1: Case for low frequency flares pol. flux total flux corrected pol. flux The long-term trend is reproduced as assumed long-term trend U Q

Demonstration with artificial data Test 2: Case for High frequency flares pol. flux total flux The long-term trend is successfully estimated. This method can extract a long-term trend even if observed variations are apparently just erratic. U (0,0) Q

Demonstration with artificial data Test 2: Case for High frequency flares pol. flux total flux The long-term trend is successfully estimated. This method can extract a long-term trend even if observed variations are apparently just erratic. U Q

Blazar monitoring with the 1.5-m “Kanata” Telescope Since 2006 TRISPEC developed by Nagoya Univ. Simultaneous optical and near-infrared observation photo-polarimetric mode is available Monitoring of blazars since 2007 42 sources

Case 1: OJ 287 pol. flux Data: Oct. 2008 – May 2009 Observed Q,U distribute NOT around (Q,U)=(0,0) A long-term trend is expected to be present. As expected, our method shows a long-term trend, possibly oscillating in a small range of PA with a time scale of a few tens of days. Good example for our model. total flux (0,0) U Q

Case 1: OJ 287 pol. flux Data: Oct. 2008 – May 2009 Observed Q,U distribute NOT around (Q,U)=(0,0) A long-term trend is expected to be present. As expected, our method shows a long-term trend, possibly oscillating in a small range of PA with a time scale of a few tens of days. Good example for our model. total flux U Q

Case 2: S2 0109+224 total flux Data: Aug.2008 – May 2009 Our model works well, even if the observed Q,U apparently distribute around (Q,U)=(0,0). Growth and decay of long-term trends? Another trend was born in the latter period? pol. flux U (0,0) Q

Case 2: S2 0109+224 total flux Data: Aug.2008 – May 2009 Our model works well, even if the observed Q,U apparently distribute around (Q,U)=(0,0). Growth and decay of long-term trends? Another trend was born in the latter period? pol. flux U Q

Case 3: S5 0716+714 Data: Jul. 2008 – Feb. 2009 The estimated long-term trend leads to no significant improvement of the correlation between the light curve and the polarized flux. No long-term trend (defined in our model) total flux pol. flux U (0,0) Q

Case 3: S5 0716+714 Data: Jul. 2008 – Feb. 2009 The estimated long-term trend leads to no significant improvement of the correlation between the light curve and the polarized flux. No long-term trend (defined in our model) total flux pol. flux U Q

Summary: advantage and disadvantage Advantages of our Bayesian model We can extract a systematic long-term trend from the observed variation, even if it is apparently erratic. The model may be useful for the test of the presence of the long-term trend. The long-term trend is NOT always obtained. Disadvantages of our Bayesian model The model is only valid for the polarized flux, not for the polarization degree in % (, or Q/I, U/I). better definition of the likelihood function or prior distribution? The model do NOT provide evidence for the long-term trend. Confirmation is needed by another kind of observations