Blazar黑洞自旋能量與紅移相關(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)

CN 53-1189/P ISSN 1672-7673

Blazar黑洞自旋能量與紅移相關(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黑洞合并及吸積的信息。從文獻資料中收集了112個Blazar源，這些源包含了67個FR II射電星系(RG)，11個FR II射電噪類星體(RLQ)，27個核占優(yōu)星系(CD)。通過樣本數(shù)據(jù)研究黑洞自旋能量與紅移的相關(guān)性。研究結(jié)果表明：(1)112個Blazar的黑洞自旋能量與紅移存在相關(guān)性，尤其在愛丁頓磁場條件下(B=BEDD)，黑洞自旋能量與紅移的相關(guān)性最為明顯；(2)FR II射電星系(RG)、FR II射電噪類星體(RLQ)、核占優(yōu)星系(CD)的黑洞自旋能量在3種磁場條件下(B=BEDD，B=104G，B∝j)與紅移的相關(guān)性強弱上存在差異，但總體趨勢較為相似，均呈現(xiàn)正比關(guān)系；(3)黑洞自旋能量與紅移的強相關(guān)性表明，黑洞自旋能量在一定程度上給出黑洞并合與吸積的信息。這些研究結(jié)果與其他人用其他方法獲得的結(jié)果是一致的。

Blazar；黑洞自旋；自旋能量；紅移；相關(guān)性

黑洞自旋和質(zhì)量是Blazar的兩個基本物理量。黑洞自旋與黑洞合并和吸積有著明顯的關(guān)系[1]。文[2-7]的研究均得出相同的結(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。在并合的過程中黑洞的自旋速率會慢慢降低。文[6]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的，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[8]認為自旋及其參量與紅移一樣的功能，能對AGN黑洞的并合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(dāng)AGN吸積盤區(qū)域能觀測到X射線時，就可根據(jù)其輻射光譜的特性估算黑洞自旋[9]。又如當(dāng)一個AGN擁有較強的噴流時，其噴流的特性也可用于估算AGN黑洞的自旋大小。正如文[10]所總結(jié)的，當(dāng)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[11-12]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，與紅移之間同樣存在著相關(guān)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AGN黑洞的合并吸積特性進行精確的描繪。但目前為止自旋及自旋能量與紅移關(guān)系仍沒有統(tǒng)一定論。

文[1]討論了自旋與紅移的關(guān)系，其結(jié)果表明自旋與紅移存在著明顯的相關(guān)性。但對于黑洞自旋能量僅僅討論了黑洞吸積盤提取的自旋能量片段，沒有詳細討論黑洞自旋與黑洞質(zhì)量共同作用下的總自旋能量與紅移的相關(guān)性。本文對黑洞的自旋能量與紅移進行相關(guān)性分析。

運用文[1, 13]的黑洞樣本數(shù)據(jù)為基礎(chǔ)將數(shù)據(jù)擴大到112個Blazer源，其中包含了67個FR II射電星系(RG)、11個FR II射電噪類星體(RLQ)、27個中核星系(CD)。運用黑洞自旋的關(guān)系式計算出自旋能量，討論了不同類型的源在3種不同特性磁場下黑洞自旋能量與紅移的相關(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，這與文[1]得出的結(jié)論相同。同時也表明黑洞自旋能量同樣能在一定程度上給出黑洞合并與吸積的信息。本文給出了用模型公式估算Blazer自旋能量大小的方法，為下一步自旋能量與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[13]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)

rH為黑洞視界半徑(rH=2GM/c2)；Bp0為黑洞視界磁場強度；j≡Sc/(GM2)；M8為108M⊙為單位的黑洞質(zhì)量；B4為104G為單位的電磁場軸相分量強度。

(2)

(3)

當(dāng)黑洞噴流較強時用這種方法估算黑洞自旋比較準確[13]。這種方法是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(guān)的標準模型[14-16]。很多黑洞自旋與噴流電子束關(guān)系模型中*http://arxiv.org/abs/1307.3246，磁場強度和黑洞質(zhì)量通常被設(shè)定為常數(shù)[17-18]，它們有如下關(guān)系[19-20]：

(4)

Lj為黑洞噴流電束功率；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?。籧為光速；B為吸積盤和黑洞的電磁場軸相分量的強度[21]。由此算出黑洞自旋量j的值*http://arxiv.org/abs/1312.6698：

(5)

1.2 自旋能量

在本文中運用文[1]的計算公式求出黑洞樣本的自旋能量。用(5)計算出黑洞自旋j后，可以用其估算自旋能量ES[23]：

(6)

2 實驗結(jié)果

根據(jù)文[1]及文[15]的黑洞樣本[1,15]收集擴充了Blazar源[14]，用(5)、 (6)式計算了相關(guān)的量給出了表1。本文著重討論黑洞自旋能量與紅移的相關(guān)性。計算過程這里不再復(fù)述。數(shù)據(jù)源按紅移值由小到大排列。

在考慮黑洞質(zhì)量的情況下，由圖1、2、3可以看出ES/Mc2與紅移z分別在B=BEDD、B=104G、B∝j3種磁場情況下具有較高的相關(guān)性。說明黑洞的自旋能量和紅移z都存在聯(lián)系，紅移z與黑洞自旋能量在總體上的關(guān)聯(lián)緊密。自旋能量與紅移的關(guān)系滿足Blazar的一些基本觀測特征。

圖1 ES/Mc2與紅移z的相關(guān)性(B=BEDD)

Fig.1 The correlation between redshifts andES/Mc2(withB=BEDDassumed) of the black holes

圖2ES/Mc2與紅移z的相關(guān)性(B=104G)

Fig.2 The correlation between redshifts andES/Mc2(withB=104G assumed) of the black holes

如圖4射電星系ES/Mc2與紅移z在3種不同磁場下均存在一定相關(guān)性。在愛丁頓磁場(B=BEDD)條件下射電星系的ES/Mc2與紅移z存在強相關(guān)性。但在B=104G與B∝j兩種磁場條件下，射電星系ES/Mc2與紅移z有弱相關(guān)性。但總體上射電星系ES/Mc2與紅移z存在正比關(guān)系，說明黑洞的自旋能量隨紅移z的增大而增加。這與文[1]的研究結(jié)果相同。

如圖5射電噪類星體(RLQ)的ES/Mc2與紅移z的相關(guān)性與射電星系(RG)相比較低，但數(shù)據(jù)整體趨勢非常相似。射電噪類星體(RLQ)ES/Mc2與紅移z在3種不同磁場下均存在一定相關(guān)性。在B=BEDD磁場條件下，射電噪類星體(RLQ)Es/Mc2與紅移z存在強相關(guān)性。但在B=104G與B∝j兩種磁場條件下，射電噪類星體ES/Mc2與紅移z有弱相關(guān)性。但總體上射電星系(RG)的ES/Mc2與紅移z存在正比關(guān)系，說明黑洞的自旋能量隨紅移z的增大而增加。這與文[1]的研究結(jié)果也是相同的。

表1 黑洞紅移質(zhì)量自旋及自旋能量

續(xù) 表

Source(1)Type(2)z(3)L44a(4)M8b(5)JM(B=BEDD)(6)Es(B=BEDD)Mc2(7)JM(B=104)(8)Es(B=104)Mc2(9)JM(B∝j)(10)Es(B∝j)Mc2(11)3C340RG0775465110400210940720079681051003559 3C352RG080683160370017902057004563 045002711 3C2631RG082413019043002459506005131704600284243C1751RG092110120490032601085012627705500420953C356RG107925028050034074055004209504400258343C252RG1105170200470029777063005750504800311693C368RG113224028048003116905400404 04400258343C267RG1144190240470029777055004209504400258343C324RG121150370340015006033001410403400150063C266RG127222023050034074062005538304700297773C13RG1351260400410022226039001999603800189334C1366RG14526016066006424709902446630600513173C682RG1575210350410022226041002222603800189333C241RG161737037051003559 05003407404300245953C470RG165329028053003875106005131704700297773C322RG1681510320660064247068006908304900326013C294RG17864402906400596880710076907051003559 3C239RG179480370600513170580047473045002711 3C334RLQ055562500190004564015000283302300067253C254RLQ07346320030011582039001999603700179023C1751RLQ076813079021000559 014000246502200061443C336RLQ092710016041004563 063021161404700493683C245RLQ1029160250410022226049005750504200297773C212RLQ1049190160560022226084003260105500233933C186RLQ106321032041004383804401217670400420953C208RLQ1109230250490022226059002583404600210943C204RLQ111217032038003260104004936803800284244C1649RLQ129622063030018933023002109402900189333C681RLQ1238410790380018933025000797 0300115823C181RLQ138233040047001158204400067250400108023C2684RLQ1483063060051317045002711 0400210943C191RLQ1952360050056002978 048002711 04100210943C9RLQ201294063063004383804700312 0410022226M87CD00042006860014000001 002800001 010001254CentaurusCD00110074860015000003 003100001 010001254HCG62CD00140039570014000003 0034000012 0110001254A262CD00160097860018000002 003500001450110001518PerseusCD001815170049000004 00700001530160001518PKS1404-267CD00220257003100003 007600006130160003226A2199CD00327200061000012 00800007230170003226A2052CD0035151700490000466007000080201600036462A0335+096CD003502414002200003 003300006130110003226MKW3SCD00454186012000005 02300001360290001518A4059CD00480962900310001808003300067250110010802HydraACD0055431101000012 01800001360250001518

續(xù) 表

Source(1)Type(2)z(3)L44a(4)M8b(5)JM(B=BEDD)(6)Es(B=BEDD)Mc2(7)JM(B=104)(8)Es(B=104)Mc2(9)JM(B∝j)(10)Es(B∝j)Mc2(11)A85CD00550372900190001254002100040920086000797 CygnusACD005613290110000005012000006 0210000927Sersic159/03CD005878170110001518016000180804000559 A133CD00662200093000151801200032260210021094A1795CD006316230044000108400540001808014000559 A2029CD00770876000200002420015000036500730002465A478CD00811260033000005 003800000030120000667A2597CD008506786004700001360093000018101800018083C388CD009221700570000276008100010840170004092PKS0745-191CD01031731012000040701300008220210003646HerculesACD015431200066000180800860002124017000559 Zw2701CD0214601703100005450440000927040003646MS07356+7421CD021669200310012393041002583403800210944C5516CD02424214009001239301400222260220018933A1835CD02531854010001015007600024650160006144Zw3146CD0291587401500012540100007230190003226

注：表中 (1) 源; (2) 類型; (3) 紅移; (4) 噴流中電子束功率; (5) 黑洞質(zhì)量部分來源于文[13]及文[14]，其余均源于NED 網(wǎng)絡(luò)數(shù)據(jù)庫; (6) 愛丁頓磁場條件下的自旋; (7) 愛丁頓磁場條件下的自旋能量; (8) 靜磁場條件下的自旋; (9) 靜磁場條件下的自旋能量; (10) 與自旋有關(guān)的磁場條件下的自旋; (11) 與自旋有關(guān)的磁場條件下的自旋能量 (運用(6)式計算得出)

Notes: The meanings of the columns are as follows. Column (1): Source name. Column (2): AGN type. Column (3): Redshift value. Column (4): Power of the electron beam in the jet. Column (5): Mass value of the black hole. Column (6): Spin of the black hole withB=BEDDassumed. Column (7): Spin energy of the black hole withB=BEDDassumed. Column (8): Spin of the black hole withB=104G assumed. Column (9): Spin energy of the black hole withB=104G assumed. Column (10): Spin of the black hole withB∝jMassumed. Column (11): Spin energy of the black hole withB∝jMassumed.

圖3 ES/Mc2與紅移z的相關(guān)性(B∝j)

Fig.3 The correlation between redshifts andES/Mc2(withB∝jMassumed) of the black holes

圖4 RG類黑洞ES/Mc2與紅移z的相關(guān)性

Fig.4 The correlation between redshifts andES/Mc2of the black holes in RG-type AGN

如圖6，核占優(yōu)星系(CD)的ES/Mc2與紅移z在3種不同磁場的相關(guān)性均存在相關(guān)性。在B=BEDD，B=104G，B∝j3種磁場條件下，核占優(yōu)星系(CD)的ES/Mc2與紅移z均存在較明顯的相關(guān)性。說明核占優(yōu)星系(CD)的黑洞自旋能量在3種磁場條件下均與紅移z存在較為直接的關(guān)聯(lián)。

圖5 RLQ類黑洞ES/Mc2與紅移z的相關(guān)性

Fig.5 The correlation between redshifts andES/Mc2of the black holes in RLQ-type AGN

圖6 cD類黑洞ES/Mc2與紅移z的相關(guān)性

Fig.6 The correlation between redshifts andES/Mc2of the black holes in cD-type AGN

不同條件下黑洞自旋能量與紅移的相關(guān)性的詳細分析數(shù)據(jù)如表2?？傮w上ES/Mc2均與紅移z存在相關(guān)性。自旋能量隨紅移z的增大而增加，與文[1]的研究結(jié)論相同。

表2 不同條件下黑洞自旋能量與紅移的相關(guān)性數(shù)據(jù)

Table 2 Results of the correlations between spin energies and redshifts of the black holes in different types of AGN under different assumptions ofB

XYNRValueProb>FValue(Intercept)Value(Slope)Error(Slope) B類型ZES/Mc211208020-00014 0023 00017B=BEDD—ZES/Mc211208270000020025 00028B=104G—ZES/Mc211208270000420013 00018B∝j—ZES/Mc267084 000022-0027 -00003 B=BEDDRGZES/Mc26701420259004290016 00139B=104GRGZES/Mc26702430051002210005 00027B∝jRGZES/Mc21107120003-00048 0023 00064B=BEDDRLQZES/Mc2110293029 001070012 00112B=104GRLQZES/Mc211039601440010200073200047B∝jRLQZES/Mc227060100020000100040700012B=BEDDCDZES/Mc227052900090000300048700017B=104GCDZES/Mc22704920017000210010540004 B∝jCD

注：表中類型“—”表示本文中RG, RLQ, cD 3種類型均考慮的總體情況

Notes: The sign‘—’means the results are for all AGN types (RG, RLQ, and cD) combined

3 結(jié) 論

由于射電噪類星體(RLQ)及核占優(yōu)星系(CD)的樣本數(shù)量較少，可能對黑洞自旋能量與紅移的相關(guān)性分析產(chǎn)生一定的誤差。要進一步詳細探討黑洞自旋能量與紅移的相關(guān)性以及測定自旋能量與紅移的關(guān)系公式，就需要更多的觀測數(shù)據(jù)來驗證本文的研究結(jié)果。

本文依據(jù)文[14]與文[1]的黑洞質(zhì)量、中子束功率及磁場強度等運用(1)式(Blandford & Znajek[13]Blandford[28]；Meier[12]；Narayan[21])依次計算出3種磁場條件下的自旋j，后運用(3)式計算出對應(yīng)的ES/Mc2(其中自旋、黑洞、磁場測量值均獨立于紅移)，并依據(jù)文[2]和文[6]的模型，對黑洞自旋能量進行估算。最后對黑洞自旋能量與紅移進行相關(guān)性分析。

本文結(jié)果表明Blazar的黑洞總體自旋能量與紅移存在關(guān)系，尤其以在愛丁頓磁場條件下(B=BEDD)最為明顯。黑洞自旋能量在3種不同類型的磁場條件下(B=BEDD，B=104G，B∝j)的趨勢均較為相似，呈現(xiàn)正比關(guān)系。實驗結(jié)果與文[1]得出的結(jié)論相同。說明Blazar黑洞自旋能量與紅移存在較直接的聯(lián)系。這為依據(jù)紅移與自旋能量的關(guān)系，估算Blazar自旋能量提供了依據(jù)。黑洞自旋和質(zhì)量的變化在二元合并時是共同發(fā)生的，隨著合并的發(fā)生其自旋速度降低。由于黑洞自旋能量與AGN紅移的相關(guān)性，可推斷黑洞自旋能量能如同紅移一樣可以對AGN黑洞的合并吸積歷史進行一定的描繪。

[1] Daly R A, Sprinkle T B. Black hole spin properties of 130 AGN[J]. Monthly Notices of the Royal Astronomical Society, 2014, 438(4): 3233-3242.

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

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

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

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

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

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

[8] 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, 2(1): 256-258.

[9] 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.

[10]Richardson G A, Nishikawa K I. Simulations of relativistic jet formation[J]. The Astrophysical Journal, 1999, 35: 1333.

[11]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.

[12]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.

[13] 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.

[14]Reynolds C S, Garofalo D, Begelman M C. Trapping of magnetic flux by the plunge region of a black hole accretion disk[J]. The Astrophysical Journal, 2006, 651(2): 1023-1030.

[15]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): 80-108.

[16]Tchekhovskoy A, Narayan R, McKinney J C. 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.

[17]Thorne K S, Price R H, MacDonald D A. Book-review-black-holes-the membrane paradigm[J]. The Astrophysical Journal, 1990, 311(2): 122.

[18] Nardini E, Fabian A C, Walton D J. 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.

[19] 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.

[20]Daly R A. Bounds on black hole spins[J]. The Astrophysical Journal Letters, 2009, 696(1): L32-L33.

[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]Blandford R D, Netzer H, Woltjer L. Active galactic nuclei [M]. New York: Springer-Verlag, 1990.

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

[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]Daly R A, Mory M P, Guerra E J. High-redshift radio galaxies as a cosmological tool: exploration of a key assumption and comparison with supernova results[C]// American Institute of Physics Conference Proceedings. 2002: 87-94.

[27]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.

[28]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.

A Study of Correlations between Redshifts and SpinEnergies of Black Holes in AGN

Zhang Xu, Zhang Xiong

(College of Physics and Electronic Information Technology, Yunnan Normal University, Kunming 650500,China, Email: kmzhanghj@163.com)

We have collected a sample of 112 Blazars. Our sample includes 67 FRII Quasars, 11 FRII Radio-Loud Quasars, and 27 FRII cD galaxies. The Quasars and Radio-Loud Quasars have redshifts from about 0 to about 2. We have analyzed correlations between redshifts and spin energies of black holes for our sampled AGN. The spin energies were calculated using a set of assumptions. Our conclusions are as follows. (1) The spin energies of the sampled Blazars show appreciable correlations with redshifts; the correlations are most obvious if magnetic-field strengths (B)around the black holes are assumed to followB=BEDD; (2) The correlations are similar for different types of Blazars and for three different assumptions of magnetic-field strengths (, i.e.,B=BEDD,B=104G, andB∝jM); (3) The results suggest that spin energies statistically increase with redshifts for black holes in the redshift range of 0 to 3, which is consistent with independent studies of other authors.Key words: Blazar; Spin of a black hole; Spin energy; Redshfit; Correlation

國家自然科學(xué)基金 (U1231203)；國家自然科學(xué)基金 (11163007)；云南省自然科學(xué)基金項目 (2010CD046)；云南省高能天體物理重點實驗室資助.

2014-10-12；修定日期：2014-11-01

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: kmzhanghj@163.com

P157.2

A

1672-7673(2015)03-0253-09