射電類星體黑洞自旋與射電噪相關性研究*

張 旭，張 雄

(云南師范大學物理與電子信息學院，云南 昆明 650500)

射電類星體黑洞自旋與射電噪相關性研究*

張 旭，張 雄

(云南師范大學物理與電子信息學院，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。從文獻資料中收集了69個射電類星體源。這些源包含了37個陡譜射電類星體(SSRQs)，32個平譜射電類星體(FSRQs)。通過樣本數(shù)據(jù)研究黑洞自旋能量與射電類星體射電噪的相關性。研究結(jié)果表明：(1)37個陡譜射電類星體與射電噪存在明顯的相關性。這種相關性在3種磁場條件下都存在(B=BEDD，B=104G，B∝j)；(2)陡譜射電類星體與射電噪之間的相關性不受相對論聚束效應的影響；(3)32個平譜射電類星體與射電噪之間不存在相關性，這說明黑洞自旋與射電噪的相關性與射電類星體的類型有很大關系；(4)陡譜射電類星體黑洞自旋與射電噪的強相關性表明，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Alexander*http://arxiv.org/abs/ 0810.1055對黑洞自旋進行了關于類星體射電噪與射電寧靜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系，如文[1-6]均得出相同的結(jié)論。文[2]認為黑洞自旋和質(zhì)量的變化在二元合并時是同時發(fā)生的。在合并的過程中黑洞的自旋速率會慢慢降低。文[4]認為大質(zhì)量黑洞的吸積可能是由一系列連續(xù)隨機的吸積事件組成，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]認為自旋及其參量與紅移一樣的功能，能對活動星系核(Active Galactic Nuclei, AGN)黑洞的合并與吸積特征進行精確的描繪。

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。例如當活動星系核吸積盤區(qū)域能觀測到X射線時，可根據(jù)其輻射光譜的特性估算黑洞自旋[8]。又如當一個活動星系核擁有較強的噴流時，其噴流的特性也可用于估算活動星系核黑洞的自旋大小。正如文[9]總結(jié)的，當黑洞樣本中有X射線輻射源或較強的噴流時能提供一個憑借經(jīng)驗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性。文[5]認為，對自旋及其自旋能量的研究同紅移一樣，可以對黑洞的合并吸積特性進行精確的描繪。

本文運用BZ模型中黑洞自旋的關系式計算收集樣本的自旋[6]的黑洞，其中包含了37個陡譜射電類星體(SSRQs)，32個平譜射電類星體(FSRQs)。運用黑洞自旋的關系式計算自旋能量，討論了不同類型的源在3種不同特性磁場下黑洞自旋與射電噪的相關特性。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算

1.1 黑洞自旋

計算黑洞自旋數(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的關系：

(1)

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

在BZ模型中黑洞自旋與黑洞磁場強度的乘積可通過經(jīng)驗公式運用電子束功率Lj及黑洞愛丁頓光度近似表達：

(2)

.

(3)

當黑洞噴流較強時用這種方法估算黑洞自旋比較準確[12]。這種方法基于噴流較強時其自旋能量與旋轉(zhuǎn)的黑洞周圍區(qū)域的吸積物質(zhì)有關的標準模型[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強度對其關系的影響。黑洞自旋與噴流電子束關系模型中，磁場強度和黑洞質(zhì)量通常被設定為常數(shù)[16-17]。它們有如下關系[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為黑洞自旋的角動量大小；c為光速；B為吸積盤和黑洞的電磁場軸向分量的強度。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種不同的磁場條件，即愛丁頓磁場、靜磁場和與自旋有關的磁場，這3種磁場分別與黑洞的參數(shù)有聯(lián)系。能量密度與愛丁頓極限下的磁場定義為愛丁頓磁場，愛丁頓磁場以104G為單位，BEDD≌6M8-1/2[21,24]，這種磁場是基于在愛丁頓光度下的輻射源檢測出的，文[25]認為很多活動星系核的輻射均在此光度下。為了鑒定愛丁頓磁場特性的影響，引入靜磁場，磁場強度以104G為單位，B4=1[18,23,25]。作為對比引入自旋磁場，如果黑洞的自旋能量是連續(xù)的，射電星系的磁場強度與自旋成比例關系以104G為單位，B4≌2.78j[21,26-27]。在Meier的hybrid模型及Allen的經(jīng)驗推論中均表明磁場強度與自旋存在某種聯(lián)系(B∝j)[28-30]，與自旋有關的磁場計算出的黑洞自旋能作為黑洞自旋與射電噪的相關性研究良好的參考項。

2 實驗結(jié)果

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

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、消除相對論聚束效應影響的射電噪R*。射電類星體的射電噪測定很大程度上受無線電及光學波段的相對論聚束效應的影響，這對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定射電類星體射電噪。運用這種方法所得的射電噪數(shù)據(jù)，將其定義為消除相對論聚束效應影響的射電噪R*。

運用(5)式分別計算了在3種不同的磁場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下的流量密度來源于河外星系網(wǎng)絡數(shù)據(jù)庫; (5)黑洞質(zhì)量; (6)愛丁頓磁場條件下的自旋; (7)靜磁場條件下的自旋; (8)B∝j條件下的自旋Refs文獻: 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種不同的磁場條件下與陡譜射電類星體射電噪R具有較高的相關性。說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)系在多種磁場條件下都成立。同時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消除相對論聚束效應影響后的射電噪度R*同樣與不同磁場條件下的黑洞自旋有著幾乎同樣高的相關性。說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種不同的磁場條件下與平譜射電類星體射電噪幾乎不具有相關性。說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。同時也表明黑洞自旋與射電類星體射電噪度的相關性與射電類星體的類型有關。

圖7 平譜射電類星體黑洞自旋j與logR的相關性(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，可能對黑洞自旋與射電噪的相關性分析產(chǎn)生一定的誤差。要進一步詳細探討黑洞自旋與陡譜射電類星體射電噪的相關性以及測定自旋與射電噪的關系公式，就需要更多的觀測數(shù)據(jù)驗證本文的研究結(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性，這種相關性在3種不同的磁場條件下均成立，而且實驗的相關性結(jié)果并不受消除相對論聚束效應影響。但平譜射電類星體的樣本中卻沒有顯現(xiàn)明顯的相關性，這可能表明黑洞自旋與射電類星體射電噪度的相關性與射電類星體的類型有關。

表2 不同條件下黑洞自旋與射電噪度的相關性數(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射電噪類星體的射電噪度進行一定的描繪。

[1] Hughes A H, Blandford R D. Black hole mass and spin coevolution by mergers [J]. The Astrophysical Journal Letters, 2003, 585(2): L101-L104.

[2] Volonteri M, Rees M J. Rapid growth of high-redshift black holes [J]. The Astrophysical Journal, 2005, 633(2): 624-629.

[3] King A R, Pringle J E. Fuelling active galactic nuclei[J]. Monthly Notices of the Royal Astronomical Society, 2007, 385(3): 1621-1627.

[4] Volonteri M, Sikora M, Lasota J P. Black hole spin and galactic morphology[J]. The Astrophysical Journal, 2007, 667(2): 704-713.

[5] Berti E, Volonteri M. Cosmological black hole spin evolution by mergers and accretion[J]. The Astrophysical Journal, 2008, 684(2): 822-828.

[6] Zhang S N, Cui W, Chen W, et al. Black hole spin in X-ray binaries: observational consequences[J]. The Astrophysical Journal, 1997, 482(2): L155-L158.

[7] McClintock J E, Narayan R, Steiner J F. Black hole spin via continuum fitting and the role of spin in powering transient jets[J]. Space Science Reviews, 2013(1): 256-258.

[8] Steiner J F, McClintock J E. Measuring black-hole spin and modeling the jet dynamics in microquasar XTE J1550-564[J]. Monthly Notices of the Royal Astronomical Society, 2011, 416 (1): 941-946.

[9] Meier D L. Simulations of relativistic jet formation[J]. The Astrophysical Journal, 1999, 35(5): 522-753.

[10]Blandford R D. Spectrum of a radio pulse from an exploding black hole[J]. Monthly Notices of the Royal Astronomical Society, 1977, 181(2): 489-498.

[11] Schmoll S, Miller J M, Volonteri M, et al. Constraining the spin of the black hole in Fairall 9 with Suzaku[J]. The Astrophysical Journal, 2009, 703(2): 2171-2176.

[12] Daly R A. Estimates of black hole spin properties of 55 sources[J]. Monthly Notices of the Royal Astronomical Society, 2011, 414(2): 1253-1262.

[13]Reynolds C S, Garofalo D, Begelman M C, et al. Trapping of magnetic flux by the plunge region of a black hole accretion disk[J]. The Astrophysical Journal, 2006, 651(2): 651-1023.

[14]Tatum M M, Turner T J, Miller L, et al. The global implications of the hard X-ray excess in type 1 AGN[J]. The Astrophysical Journal, 2012, 762(2): 80.

[15]Tchekhovskoy A, Narayan R, McKinney J, et al. Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole[J]. Monthly Notices of the Royal Astronomical Society, 2011, 418(1): L79-L83.

[16]Thorne R M, Shprits Y Y, Meredith N P, et al. Refilling of the slot region between the inner and outer electron radiation belts during geomagnetic storms [J]. Journal of Geophysical Research: Space Physics, 2007, 112(A6): 1-11.

[17]Nardini E, Fabian A C, Walton D J, et al. Investigating the reflection contribution to the X-ray emission of Ton S180[J]. Monthly Notices of the Royal Astronomical Society, 2012, 423(4): 3299-3307.

[18]Zoghbi A, Fabian A C, Uttley P, et al. Broad iron L line and X-ray reverberation in 1H0707-495 [J]. Monthly Notices of the Royal Astronomical Society, 2010, 401(1): 2419-2432.

[19]Fender R P, Belloni T M, Gallo E, et al. Towards a unified model for black hole X-ray binary jets[J]. Monthly Notices of the Royal Astronomical Society, 2004, 355(4): 1105-1118.

[20]Daly R A. Bounds on black hole spins[J]. The Astrophysical Journal Letter, 2009, 696(1): 691-L72.

[21]Narayan R, McClintock J E. Observational evidence for a correlation between jet power and black hole spin [J]. Monthly Notices of the Royal Astronomical Society, 2011, 419(1): L69-L73.

[22]Komossa S. Observational evidence for supermassive black hole binaries[C]// AIP Conference Proceedings. 2013.

[23]Dermer C D, Finke J D, Menon G, et al. Black-hole engine kinematics, flares from PKS 2155-304, and multiwavelength blazar analysis[J]. The Astrophysical Journal, 2008, 10(1): 810-1055.

[24]Rees M J. Black hole models for active galactic nuclei[J]. Annual Review of Astronomy and Astrophysics, 1984, 22(1): 471-506.

[25]King A R. Black hole outflows[J]. Monthly Notices of the Royal Astronomical Society, 2010, 402(1): 1516-1522.

[26]Emmering R T, Blandford R D, Shlosman I, et al. Magnetic acceleration of broad emission-line clouds in active galactic nuclei[J]. The Astrophysical Journal, 1992, 385: 460-477.

[27]Punsly B, Coroniti F V. Relativistic winds from pulsar and black hole magnetospheres[J]. The Astrophysical Journal, 1990, 350(2): 518-535.

[28]Daly R A, Guerra E J. High-redshift radio galaxies as a cosmological tool exploration of a key assumption and comparison with supernova results[C]// AIP Conference Proceedings. 2002.

[29]Allen S W, Dunn R J H, Fabian A C, et al. The relation between accretion rate and jet power in X-ray luminous elliptical galaxies[J]. Monthly Notices of the Royal Astronomical Society, 2006, 372(1): 21-30.

[30]Merloni A, Heinz S. Measuring the kinetic power of active galactic nuclei in the radio mode[J]. Monthly Notices of the Royal Astronomical Society, 2007, 381(2): 589-601.

[31]Brotherton M S, Wills B J, Steidel C C, et al. Statistics of QSO broad emission-line profiles. 2: the C IV wavelength 1549, C III) wavelength 1909, and MG II wavelength 2798 lines[J]. The Astrophysical Journal, 1994, 423: 131-142.

[32]Brotherton M S. The profiles of H beta and [O iii] lambda 5007 in radio-loud quasars[J]. The Astrophysical Journal Supplement Series, 1996, 102(1): 1-27.

[33]Corbin M R. The emission-line properties of steep radio spectrum quasars [J]. The Astrophysical Journal, 1991, 375(2): 503-516.

[34]Corbin M R. The emission-line properties of low-redshift quasi-stellar objects. II. the relation to radio type [J]. The Astrophysical Journal Supplement Series, 1997, 113(2): 245-267.

[35]Gu M F, Cao X W, Jiang D R, et al. On the masses of black holes in radio-loud quasars[J]. Monthly Notices of the Royal Astronomical Society, 2001, 327(4): 1111-1115.

[36]Gu Q S, Huang J H, de Diego J A, et al. The nuclear starburst activity in the Seyfert 2 galaxy NGC 7679[J]. Astronomy and Astrophysics, 2001, 374(3): 932-935.

[37]Garrington S T, Conway R G, Leahy J P, et al. Asymmetric depolarization in double radio sources with one-sided jets[J]. Monthly Notices of the Royal Astronomical Society, 1991, 250(1): 171-197.

[38]Afanas’ev V L, Dodonov S N, Moiseev A V, et al. Radio and optical spectra of objects from three complete samples of radio sources[J]. Astronomy Reports, 2006, 50(4): 255-272.

[39]Marziani P, Sulentic J W, Dultzin H D, et al. Comparative analysis of the high-and low-ionization lines in the broad-line region of active galactic nuclei[J]. Monthly Notices of the Royal Astronomical Society, 1996, 104(1): 37-70.

[40]McIntosh D H, Rix H W, Rieke M J, et al. Redshifted and blueshifted broad lines in luminous quasars[J]. The Astrophysical Journal Letters, 1999, 517(2): L73-L76.

[41]Wills B J, Browne IWA. Relativistic beaming and quasar emission lines[J]. The Astrophysical Journal, 1986, 302(1): 56-63.

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

國家自然科學基金 (U1231203, 11063004)；云南省自然科學基金 (2010CD046) 資助.

2014-12-02；修定日期：2014-12-28

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

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

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1672-7673(2015)04-0394-09

CN 53-1189/P ISSN 1672-7673