張 旭，張 雄

(云南師范大學(xué)物理與電子信息學(xué)院，云南 昆明 650500)

射電類星體黑洞自旋與射電噪相關(guān)性研究*

張 旭，張 雄

(云南師范大學(xué)物理與電子信息學(xué)院，云南 昆明 650500)

黑洞自旋及其參量能提供射電類星體射電噪度的信息。從文獻(xiàn)資料中收集了69個(gè)射電類星體源。這些源包含了37個(gè)陡譜射電類星體(SSRQs)，32個(gè)平譜射電類星體(FSRQs)。通過(guò)樣本數(shù)據(jù)研究黑洞自旋能量與射電類星體射電噪的相關(guān)性。研究結(jié)果表明：(1)37個(gè)陡譜射電類星體與射電噪存在明顯的相關(guān)性。這種相關(guān)性在3種磁場(chǎng)條件下都存在(B=BEDD，B=104G，B∝j)；(2)陡譜射電類星體與射電噪之間的相關(guān)性不受相對(duì)論聚束效應(yīng)的影響；(3)32個(gè)平譜射電類星體與射電噪之間不存在相關(guān)性，這說(shuō)明黑洞自旋與射電噪的相關(guān)性與射電類星體的類型有很大關(guān)系；(4)陡譜射電類星體黑洞自旋與射電噪的強(qiáng)相關(guān)性表明，黑洞自旋能量在一定程度上給出陡譜射電類星體射電噪度的信息。這些研究結(jié)果與其他人提出的理論是一致的。

射電類星體；黑洞自旋；射電噪；相關(guān)性

眾所周知黑洞質(zhì)量及寄主星系光度能反映射電類星體的射電噪度信息。近來(lái)Alexander*http://arxiv.org/abs/ 0810.1055對(duì)黑洞自旋進(jìn)行了關(guān)于類星體射電噪與射電寧?kù)o的特征分歧是否由于其中心黑洞自旋的差異而產(chǎn)生的研究。要證明此理論需要討論黑洞自旋與射電噪度是否存在必然的聯(lián)系。

黑洞自旋和質(zhì)量是類星體的兩個(gè)基本物理量。黑洞自旋與射電類星體黑洞合并和吸積有著明顯的關(guān)系，如文[1-6]均得出相同的結(jié)論。文[2]認(rèn)為黑洞自旋和質(zhì)量的變化在二元合并時(shí)是同時(shí)發(fā)生的。在合并的過(guò)程中黑洞的自旋速率會(huì)慢慢降低。文[4]認(rèn)為大質(zhì)量黑洞的吸積可能是由一系列連續(xù)隨機(jī)的吸積事件組成，正是由于這些吸積事件使大質(zhì)量黑洞具有中等的自旋。文[7]認(rèn)為自旋及其參量與紅移一樣的功能，能對(duì)活動(dòng)星系核(Active Galactic Nuclei, AGN)黑洞的合并與吸積特征進(jìn)行精確的描繪。

大質(zhì)量黑洞自旋的研究為大質(zhì)量黑洞合并與吸積提供了全新的視角?，F(xiàn)在有很多可行的方法估算大質(zhì)量黑洞的自旋。例如當(dāng)活動(dòng)星系核吸積盤(pán)區(qū)域能觀測(cè)到X射線時(shí)，可根據(jù)其輻射光譜的特性估算黑洞自旋[8]。又如當(dāng)一個(gè)活動(dòng)星系核擁有較強(qiáng)的噴流時(shí)，其噴流的特性也可用于估算活動(dòng)星系核黑洞的自旋大小。正如文[9]總結(jié)的，當(dāng)黑洞樣本中有X射線輻射源或較強(qiáng)的噴流時(shí)能提供一個(gè)憑借經(jīng)驗(yàn)估算黑洞自旋的途徑。

在文[10-11]的模型中黑洞自旋能量與自旋在不同磁場(chǎng)下均存在緊密的聯(lián)系。研究顯示，黑洞自旋能量作為黑洞自旋的重要參量，其與紅移之間同樣存在相關(guān)性。文[5]認(rèn)為，對(duì)自旋及其自旋能量的研究同紅移一樣，可以對(duì)黑洞的合并吸積特性進(jìn)行精確的描繪。

本文運(yùn)用BZ模型中黑洞自旋的關(guān)系式計(jì)算收集樣本的自旋[6]的黑洞，其中包含了37個(gè)陡譜射電類星體(SSRQs)，32個(gè)平譜射電類星體(FSRQs)。運(yùn)用黑洞自旋的關(guān)系式計(jì)算自旋能量，討論了不同類型的源在3種不同特性磁場(chǎng)下黑洞自旋與射電噪的相關(guān)特性。得出的結(jié)果表明Blazer黑洞自旋能量與紅移存在較為直接的聯(lián)系，這與Alexander得出的結(jié)論相同，表明黑洞自旋能量在一定程度上給出陡譜射電類星體射電噪度的信息。本文給出了用模型公式估算Blazer自旋能量大小的方法，為下一步自旋與射電類星體模型的研究提供了依據(jù)。

1 黑洞自旋及自旋能量的計(jì)算

1.1 黑洞自旋

計(jì)算黑洞自旋數(shù)據(jù)的方法與文[12]相同。在著名的BZ模型中電子束功率Lj的產(chǎn)生與自旋j的關(guān)系：

(1)

r為黑洞視界半徑(r=2GM/c2)；BP0為黑洞視界磁場(chǎng)強(qiáng)度；j≡Sc/(GM2)；M8是以108M⊙為單位的黑洞質(zhì)量；B4是以104G為單位的電磁場(chǎng)軸向分量強(qiáng)度。

在BZ模型中黑洞自旋與黑洞磁場(chǎng)強(qiáng)度的乘積可通過(guò)經(jīng)驗(yàn)公式運(yùn)用電子束功率Lj及黑洞愛(ài)丁頓光度近似表達(dá)：

(2)

.

(3)

當(dāng)黑洞噴流較強(qiáng)時(shí)用這種方法估算黑洞自旋比較準(zhǔn)確[12]。這種方法基于噴流較強(qiáng)時(shí)其自旋能量與旋轉(zhuǎn)的黑洞周圍區(qū)域的吸積物質(zhì)有關(guān)的標(biāo)準(zhǔn)模型[13-15]。由于噴流及自旋的數(shù)值很大，可以忽略黑洞自旋及磁場(chǎng)強(qiáng)度對(duì)其關(guān)系的影響。黑洞自旋與噴流電子束關(guān)系模型中，磁場(chǎng)強(qiáng)度和黑洞質(zhì)量通常被設(shè)定為常數(shù)[16-17]。它們有如下關(guān)系[18-21]：

Lj∝j2M2B2，

(4)

Lj為黑洞噴流電子束功率；M是黑洞質(zhì)量；j為黑洞自旋量j=a/m,a=S/(Mc),m=GM/c2；S為黑洞自旋的角動(dòng)量大?。籧為光速；B為吸積盤(pán)和黑洞的電磁場(chǎng)軸向分量的強(qiáng)度。由此算出黑洞自旋量j的值[21-22]：

j=k(L44)0.5B4-1M8-1，

(5)

本文引入了3種不同的磁場(chǎng)條件，即愛(ài)丁頓磁場(chǎng)、靜磁場(chǎng)和與自旋有關(guān)的磁場(chǎng)，這3種磁場(chǎng)分別與黑洞的參數(shù)有聯(lián)系。能量密度與愛(ài)丁頓極限下的磁場(chǎng)定義為愛(ài)丁頓磁場(chǎng)，愛(ài)丁頓磁場(chǎng)以104G為單位，BEDD≌6M8-1/2[21,24]，這種磁場(chǎng)是基于在愛(ài)丁頓光度下的輻射源檢測(cè)出的，文[25]認(rèn)為很多活動(dòng)星系核的輻射均在此光度下。為了鑒定愛(ài)丁頓磁場(chǎng)特性的影響，引入靜磁場(chǎng)，磁場(chǎng)強(qiáng)度以104G為單位，B4=1[18,23,25]。作為對(duì)比引入自旋磁場(chǎng)，如果黑洞的自旋能量是連續(xù)的，射電星系的磁場(chǎng)強(qiáng)度與自旋成比例關(guān)系以104G為單位，B4≌2.78j[21,26-27]。在Meier的hybrid模型及Allen的經(jīng)驗(yàn)推論中均表明磁場(chǎng)強(qiáng)度與自旋存在某種聯(lián)系(B∝j)[28-30]，與自旋有關(guān)的磁場(chǎng)計(jì)算出的黑洞自旋能作為黑洞自旋與射電噪的相關(guān)性研究良好的參考項(xiàng)。

2 實(shí)驗(yàn)結(jié)果

由于本文的計(jì)算方法與文[12]相同，為了保證分析結(jié)果的準(zhǔn)確性，故采用與文[12]相同的流量樣本采集方案。從文獻(xiàn)中采集了69個(gè)具有準(zhǔn)確噴流能量數(shù)據(jù)的射電類星體源，樣本計(jì)算黑洞自旋所需要的178 MHz流量密度L44(以央斯基為單位)均來(lái)源于NASA/IPAC河外星系數(shù)據(jù)庫(kù)。

采集的射電類星體樣本數(shù)據(jù)包括紅移、黑洞質(zhì)量、178 MHz流量密度、射電噪度R、消除相對(duì)論聚束效應(yīng)影響的射電噪R*。射電類星體的射電噪測(cè)定很大程度上受無(wú)線電及光學(xué)波段的相對(duì)論聚束效應(yīng)的影響，這對(duì)于平譜射電類星體尤其明顯。為了消除這種影響，引用核心射電光度替代熱光度測(cè)定射電類星體射電噪。運(yùn)用這種方法所得的射電噪數(shù)據(jù)，將其定義為消除相對(duì)論聚束效應(yīng)影響的射電噪R*。

運(yùn)用(5)式分別計(jì)算了在3種不同的磁場(chǎng)條件下黑洞自旋以及自旋能量，以上數(shù)據(jù)均列于表1中。本文著重討論黑洞自旋與射電類星體射電噪的相關(guān)性。本文數(shù)據(jù)按源IAU名稱由小到大排列。

表1 黑洞紅移質(zhì)量自旋及射電噪度

續(xù) 表

注1：表中(1)源; (2)類型; (3)紅移; (4)151 MHz下的流量密度來(lái)源于河外星系網(wǎng)絡(luò)數(shù)據(jù)庫(kù); (5)黑洞質(zhì)量; (6)愛(ài)丁頓磁場(chǎng)條件下的自旋; (7)靜磁場(chǎng)條件下的自旋; (8)B∝j條件下的自旋Refs文獻(xiàn): B94b[31]: Brotherton et al. (1994). B96[32]: Brotherton (1996). C91[33]: Corbin (1991). C97[34]: Corbin (1997). CJ01[35]: Gu & Jiang et al. (2001). G01[36]: Gu et al. (2001). H02[37]: Garrington et al. (1991). L96[38]: Lawrence et al. (1996). M96[39]: Marziani et al. (1996). M99[40]: McIntosh et al. WB86[41]: Wills & Browne (1986)

由圖1～3可以看出黑洞自旋在3種不同的磁場(chǎng)條件下與陡譜射電類星體射電噪R具有較高的相關(guān)性。說(shuō)明黑洞自旋與陡譜射電類星體射電噪之間存在聯(lián)系，且這種聯(lián)系在多種磁場(chǎng)條件下都成立。同時(shí)表明黑洞自旋在一定程度上給出陡譜射電類星體射電噪度的信息。

由圖4～6消除相對(duì)論聚束效應(yīng)影響后的射電噪度R*同樣與不同磁場(chǎng)條件下的黑洞自旋有著幾乎同樣高的相關(guān)性。說(shuō)明黑洞自旋與陡譜射電類星體射電噪之間的聯(lián)系不受寄主星系影響。再次印證了黑洞自旋在一定程度上反應(yīng)陡譜射電類星體射電噪度的信息。

圖1 陡譜射電類星體黑洞自旋j與logR的相關(guān)性(B=BEDD)Fig.1 The statistical correlation between black hole spin values and logR of SSRQs (under the assumption B=BEDD)

圖2 陡譜射電類星體黑洞自旋j與logR的相關(guān)性(B=104G)Fig.2 The statistical correlation between black hole spin values and logR of SSRQs (under the assumption B=104G)

圖3 陡譜射電類星體黑洞自旋j與logR的相關(guān)性(B∝j)Fig.3 The statistical correlation between black hole spin values and logR of SSRQs (under the assumption B∝j)

圖4 陡譜射電類星體黑洞自旋j與logR*的相關(guān)性(B=BEDD)Fig.4 The statistical correlation between black hole spin values and logR* of SSRQs (under the assumption B=BEDD)

圖5 陡譜射電類星體黑洞自旋j與logR*的相關(guān)性(B=104G)Fig.5 The statistical correlation between black hole spin values and logR* of SSRQs (under the assumption B=104G)

圖6 陡譜射電類星體黑洞自旋j與logR*的相關(guān)性(B∝j)Fig.6 The statistical correlation between black hole spin values and logR* of SSRQs (under the assumption B∝j)

由圖7～12可以看出黑洞自旋在3種不同的磁場(chǎng)條件下與平譜射電類星體射電噪幾乎不具有相關(guān)性。說(shuō)明黑洞自旋與平譜射電類星體射電噪之間并不存在類似陡譜射電類星體的聯(lián)系，且這種聯(lián)系在多種磁場(chǎng)條件下都不成立。表明黑洞自旋在一定程度上給出陡譜射電類星體射電噪度的信息。同時(shí)也表明黑洞自旋與射電類星體射電噪度的相關(guān)性與射電類星體的類型有關(guān)。

圖7 平譜射電類星體黑洞自旋j與logR的相關(guān)性(B=BEDD)Fig.7 The statistical correlation between black hole spin values and logR of FSRQs (under the assumption B=BEDD)

圖8 平譜射電類星體黑洞自旋j與logR的相關(guān)性(B=104G)Fig.8 The statistical correlation between black hole spin values and logR of FSRQs (under the assumption B=104G)

圖9 平譜射電類星體黑洞自旋j與logR的相關(guān)性(B∝j)Fig.9 The statistical correlation between black hole spin values and logR of FSRQs (under the assumption B∝j)

圖10 平譜射電類星體黑洞自旋j與logR*的相關(guān)性(B=BEDD)Fig.10 The statistical correlation between black hole spin values and logR* of FSRQs (under the assumption B=BEDD)

圖11 平譜射電類星體黑洞自旋j與logR*的相關(guān)性(B=104G)Fig.11 The statistical correlation between black hole spin values and logR* of FSRQs (under the assumption B=104G)

圖12 平譜射電類星體黑洞自旋j與logR*的相關(guān)性(B∝j)Fig.12 The statistical correlation between black hole spin values and logR* of FSRQs (under the assumption B∝j)

3 結(jié) 論

由于陡譜射電類星體及平譜射電類星體的樣本數(shù)量較少，可能對(duì)黑洞自旋與射電噪的相關(guān)性分析產(chǎn)生一定的誤差。要進(jìn)一步詳細(xì)探討黑洞自旋與陡譜射電類星體射電噪的相關(guān)性以及測(cè)定自旋與射電噪的關(guān)系公式，就需要更多的觀測(cè)數(shù)據(jù)驗(yàn)證本文的研究結(jié)果。

表2為不同條件下黑洞自旋與射電噪度的相關(guān)性數(shù)據(jù)。由表2可以看出黑洞自旋與陡譜射電類星體射電噪度之間存在較高的相關(guān)性，這種相關(guān)性在3種不同的磁場(chǎng)條件下均成立，而且實(shí)驗(yàn)的相關(guān)性結(jié)果并不受消除相對(duì)論聚束效應(yīng)影響。但平譜射電類星體的樣本中卻沒(méi)有顯現(xiàn)明顯的相關(guān)性，這可能表明黑洞自旋與射電類星體射電噪度的相關(guān)性與射電類星體的類型有關(guān)。

表2 不同條件下黑洞自旋與射電噪度的相關(guān)性數(shù)據(jù)

由于黑洞自旋與陡譜射電類星體射電噪度的相關(guān)性，可推斷黑洞自旋能量能如同黑洞質(zhì)量及寄主星系的光度一樣可以對(duì)射電噪類星體的射電噪度進(jìn)行一定的描繪。

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An Analysis of Statistical Correlations between Black Hole Spin Values and Radio-Loudness Indices in Radio Loud AGN

Zhang Xu, Zhang Xiong

(School of Physics and Electronic Information Technology, Yunnan Normal University, Kunming 650500, China, Email: ynzx@yeah.net)

We have collected a sample of 69 radio-loud quasars from various

. The sample includes 37 SSRQs (withα>0.5) and 32 FSRQs (withα<0.5) with redshifts ranging from about zero to about two. We have carried out an analysis of statistical correlations between black hole spin values and radio-loudness indices for the sample. In the analysis we consider three cases of the spin values. The three cases correspond to three different assumptions about the magnetic field strengths around the black holes. Our conclusions are as follows. (1) In SSRQs their black hole spin values are strongly correlated with their radio-loudness indices; (2) The correlation in SSRQs is not caused by relativistic beaming; (3) There is no indication of a strong correlation between supermassive black hole mass values and spin values for FSRQs; (4) The correlations between black hole spin values and radio-loudness indices may be different for different types of radio-loud quasars. Our results are consistent with models of radio-loud quasars of other authors.

Radio-loud quasars; Black-hole spin; Radio loudness; Correlation

國(guó)家自然科學(xué)基金 (U1231203, 11063004)；云南省自然科學(xué)基金 (2010CD046) 資助.

2014-12-02；修定日期：2014-12-28

張 旭，男，碩士. 研究方向：黑洞，活動(dòng)星系核. Email: 2226997466@qq com

張 雄，男，教授. 研究方向：黑洞，活動(dòng)星系核. Email: ynzx@yeah net

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1672-7673(2015)04-0394-09

CN 53-1189/P ISSN 1672-7673