Estimating the black hole masses of AGNs from emission line properties

Estimating the black hole masses of AGNs from

emission line properties

Ran Wang

Department of Astronomy, Peking University

Abstract

Empirical relations between the BLR size and continuum luminosity have been derived and widely used to calculate the BLR sizes and black hole masses of large samples of AGNs. However, optical and ultraviolet continuum may be affected significantly by jets for radio-loud AGNs. To avoid this affection, we first use the emission line luminosity instead of the continuum luminosity as the representative of ionizing luminosity. In the optical band, we find a reliable empirical relation between the BLR size and Hβ line luminosity,R(lightdays)24.05(LH/1042ergss1)0.68, with a sample of 34 AGNs. Furthermore when applying this relation to calculate the black hole mass of radio-loud AGNs, we get lower black hole masses compared to the values estimated with the R-L5100Å relation. Such a difference becomes more obvious when the radio-loudness increases, consistent with our prediction. In the ultraviolet band, we find another tight empirical relation between the BLR size and Mg II emission line luminosity, R(lightday)17.9(LmgII/1042ergss1)0.61, from 26 AGNs in the sample above with the ultraviolet spectra available. Then the two relations are applied to estimate the black hole masses of a sample of 80 AGNs in the Large Bright Quasar Survey. The black hole masses estimated from these two estimations have a best-fitting relation with a slope of 0.958, which indicates that the estimation with Mg II emission line luminosity is reliable. Therefore, we conclude that the emission line luminosity is more suitable than the continuum luminosity to be used to derive the BLR size of AGNs, and the estimation of black hole mass from the emission line luminosity is more accurate.

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1.Introduction

The idea that the active galactic nuclei (AGN) has a supermassive black hole in its centre is widely realized and accepted. So how to accurately estimate the central black hole mass correctly becomes more and more important. With a fundamental assumption that the motion of the BLR material is virialized, the black hole mass can be calculated if the radius from AGN center to the broad-line emission gas and the keplerian velocity of the gas are known. For most AGNs, the broad emission line width can be a good indicator of the keplerian velocity with a uniform coefficient (We adopt3/2 follow Kaspi(2000)). The BLR sizes of about 34 AGNs have been directly measured with the reverberation mapping technique(Kaspi et al. 2000) based on long term monitoring of these objects. With the FWHM of Hβ broad emission lines the 34 black hole masses were estimated(Kaspi et al. 2000), using M1.464105(VRBLR)(3FWHM1)2M ltdays10kmsand an empirical relation between the BLR radius and 5100Å continuum luminosity is also derived (Kaspi et al.2000). The relation can be understood theoretically with a photo ionization model which gives an index of 0.5 between the radius and photo-ionizing luminosity theoretically. And what it asks for is only the continuum luminosity at 5100Å, so the method is applied to estimate black hole masses of large samples of AGNs(Laor 2000; McLure & Dunlop 2001; Oshlack 2002).

However, there are still several problems in these studies. First of all, among radio-loud AGNs the contribution from the powerful jets to the UV/optical continuum can not be neglected. As the radiation from jets are not only in the radio band, it is very likely that the UV/optical continuum is not dominated by the radiation from the accretion disk. And considering the fact that the sample selected by Kaspi consists of 17 radio-quiet quasars and 17 Seyfert 1 galaxies nearby, using 5100Å continuum luminosity as an indicator of the photo-ionizing luminosity is not appropriate for radio-loud AGNs.

Secondly, the use of Hβ emission line and 5100Å continuum luminosity in the rest frame asks for a low red shift ranging from 0 to 0.9. New empirical relations and methods for the high redshift AGNs black-hole estimation have been discussed such as R-L3000Å with Mg II emission line(McLure & Jarvis 2002) and R-L1350Å with C IV emission line(M.Vestergaard 2002). But compared to Mg II emission line C IV may not suitable when several factors are concern. The C IV broad line emission luminosity may mix with the component from outflows, and even the motion

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of the broad-line gas are not clear. Furthermore, because of similar ionization potentials the line-emitting gas of Hβ and Mg II likely to be at the same radius, and the Mg II line is available with a redshift up to 2.5, which can instead when the Hβ line move to infrared band. Those are amply discussed by McLure & Jarvis(2002). However, the R-L relation derived by McLure & Jarvis(2002) shows an index of 0.5 both on 3000Å and 5100Å,which is different from previous relation. And in the continuum around 3000Å, the jet affection still exists.

In this paper we first use the emission line luminosity of Hβ and Mg II to fit the R-L empirical relation, intending to avoid the jets affection. In section 2 and 3, we give the R-LHβ relation and the R-LMgII relation respectively. Finally, the new relations are applied and the estimation of the black hole masses are compared and discussed.

2. The relation between BLR size and Hβ emission line luminosity

We collect the available data of 16 PG quasars and 17 Seyfert 1 galaxies in the sample of 34 AGNs Kaspi have selected, adding Mrk 279 with its known Hβ luminosity and BLR size. All the date have been corrected for galactic extinction. In order to compare our result with the relation Kaspi(2000) derived previously, we adopted the cosmological parameters q0=0.5, H0=75 kms-1Mpc-1 through the calculation. In addition we use the ordinary least square(OLS) bisector method as a fitting technique throughout this paper. The empirical relation between the BLR size and Hβ luminosity we obtained is as follows:

LogR(lightdays)(1.3810.080)(0.6840.106)Log(LH/1042ergss1). (1)

Compared with the relation provided by Kaspi,

2.04410.7000.033 (2) RBLR(lightdays)(32.91.9)[L5100/10ergss]the emission line luminosity show a lower index of 0.684. So the slope

derived from 5100Å continuum is slightly steeper.

We will check the relation with both radio-loud and radio-quiet quasars in section 4.

3. The empirical relation estimating with the UV spectra

As the 34 BLR sizes we mention above were directly measured, the UV luminosity data are chosen among this sample too. We get 14 AGNs data, including 5 PG quasars and 9 Seyfert 1 galaxies, from the available International Ultraviolet Explorer(IUE) spectra, 4 PG quasars Mg II line emission data from Corbin et al.(1996) with the continuum data published by Neugebaure et al.(1987). The data of another 7 sources are obtained from Hubble Space Telescope(HST) sample(Kuraszkiewicz et al.2002), and

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the NGC3783 data is directly used from Reichert et al.(1994). Totally, the data of 26 sources have been corrected for galactic extinction, and K-correction if needed. Here we adopted Ωm=0.3, Λ=0.7, H0=70 kms-1Mpc-1 according to McLure & Jarvis(2002) in order to make a comparison with the R-L3000A relation they provided.

3.1 The relation between BLR size and Mg II luminosity

With the available data, the tight empirical relation between BLR size and Mg II(2798Å) emission line luminosity is obtained. The fitting of the data is shown in Figure 1.

Fig. 1.—The relation of BLR size and Mg II(2798Å) luminosity for 26 AGNs,

with a correlation coefficient of 0.64 adopted Ωm=0.3, Λ=0.7, H0=70

-1-1

kmsMpc .

The R-LmgII relation is

logR(lightdays)(0.6090.143)logLmgII(ergss1)(24.3256.142). (3)

3.2 The relation between BLR size and 3000Å continuum luminosity

We refit the R-L3000Å relation adding the data we measured with IUE spectra. And a steeper slope of 0.589 is found comparing to the value of 0.5 fitted by McLure & Jarvis(2002).

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Fig.2.—The relation of BLR size and 3000Å continuum luminosity of 26 AGNs,

-1-1

with a correlation coefficient of 0.81 adopted Ωm=0.3, Λ=0.7, H0=70 kmsMpc .

The new relation is as follows:

logR(lightdays)(0.5890.096)logLmgII(ergss1)(24.4614.302). (4) Obviously the continuum relation has a slightly flatter slope than that derived from MgII emission line, which is just opposite to the result we find in the optical band.

3.3 Black hole mass calculation and comparison

To test whether the estimation of BLR size is reliable, we calculate the black hole masses with the two relations and MgII emission line FWHM, and compare them to the directly calculated masses obtained by the reverberation mapping technique(Kaspi et al. 2000). Both of the two comparisons have a slope close to 1.0, as expected. Obviously, both of the two methods are reliable for radio-quiet AGNs.

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Fig.3.-Black hole mass estimation by reverberation mapping with the measured

RBLR and rms Hβ FWHM is plotted against the mass calculated by R-LmgII relation(Eqn 3) and MgII FWHM. The solid line is fitted using the OLS bisector method, and has a slope of 0.969±0.144. The correlation coefficient is 0.62.

Fig.4.-Black hole mass estimation by reverberation mapping with the measured

RBLR and rms Hβ FWHM is plotted against the mass calculated by R-L3000Å relation(Eqn 4) and MgII FWHM.The solid line is fitted using the OLS bisector method, and has a slope of 0.971±0.077. The correlation coefficient is 0.63.

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4. Black hole mass estimation of large samples of AGNs

To discuss the contribution of jet radiation in optical continuum among radio-loud AGNs, we estimated the black hole masses of three samples. One consist of 87 PG quasars most of which are radio-quiet sources. The second contains 59 radio-loud AGNs, which are selected from Brotherton(1996)(B96),and the radio-loudness of 55 sources are known. Another sample consists of 27 radio-loud AGNs in Oshlack et al.(2002),with the radio-loudness more than 102. We use both the R-LHβ and R-L5100Å relations and the Hβ broad line emission FWHM to calculate the central black hole masses, then plot the two column of value together to discuss the difference.

The B96 sample and Oshlack’s sample together show a departure from the ‘y=x’solid line(Fig.5). This disparity can be well understood when plotted against radio-loudness(Fig.6). When the radio-loudness turns larger, which indicates the jet affection is greater, the ratio between the two mass estimations gets smaller. The largest ratio can get to 0.1. However the PG sample shows a good agreement of the two results as we have expected(Fig 7).

Fig.5.—Radio-loud AGNs black hole mass estimation of B96 sample and Oshlack’s

sample.

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The X-values are the results using R-L5100A relation(Eqn 2), while the Y-values are using R-LHβ relation(Eqn 1). The circle symbol stands for B96 sample, and triangle symbol stands for Oshlack’s sample.

Fig.6.—The ratio between mass estimation by R-LHβ relation(Eqn 1) and R-L5100A

relation(Eqn 2) plotted with radio-loudness. Symbols as above.

Fig.7.—PG quasars black hole mass estimation. Similar to Fig.5, the X-values

are the results using R-L5100A relation(Eqn 2), while the Y-values are using R-LHβ relation(Eqn 1).

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To give a further test of the Mg II emission line and BLR size relation, we choose a sample of 80 AGNs from the Large Bright Quasar Survey(LBQS). The black hole masses calculated from Hβ data and Mg II data are presented, and we obtain a fitting slope of (0.958±0.068), which confirms the black hole mass estimation with Mg II emission line luminosity. This method also avoids the possible affection by jet on UV continuum.

Fig.8.—The black hole mass value calculated by R-LHβ relation against that by the R-LMGII relation. The solid line shows a slope of 0.958±0.068.

5. Discussions

Throughout this paper, we confirm the use of emission line in calculating black hole masses. Though the comparison between the UV results and the optical ones suffer from slightly scattering, which may because of the difference between Mg II and Hβ FWHMs, the advantages of emission line estimation are overweighted. Without the contamination of jet, the black hole masses of larger numbers of AGNs with a red shift up to 2.5 can be obtained using only two observed parameters, emission line flux and the FWHM(Mg II or Hβ, according to the redshift).

However, though we have got desirable results for the BLR size estimation among both radio-loud and radio-quiet AGNs, the estimated values of black hole masses still have some uncertainties.

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Above all, an orientation angle is needed for an exact measurement of the keplerian velocity as the AGNs disks have a distribution in space. A uniform coefficient may not represent all of them. When the angle becomes smaller, the difference gets more distinct.

Moreover, some low luminosity AGNs may not share the same photo ionization model with the high luminosity ones. The presented plots of R-L relations are scattered on the low luminosity region both in the previous work of Kaspi (2000) and McLure & Jarvis (2002) and that of this paper. A sample of more sources is expected and a research concentrate on low luminosity AGNs is necessary.

Thirdly we get a steeper slope than McLure & Jarvis in the UV R-L relation with only 26 sources. To prove that the empirical relation in this paper is more reliable, larger data are still needed. Also a further research of the affection of UV jet emission needs to be done by comparing the R-LMgII relation measured result to the R-L3000A result, which we will do next.

6. Acknowledgment

Firstly, I should appreciate my advisor, Prof Xuebing Wu for his two-year direction. I have learnt a lot from his help, not only about the AGN field, but also how to be a standard researcher. Also I need give my thanks to Mingzhi Kong for the help of plenty of spectra data calculation. She taught me use some essential astronomy software, such as IRAF, and offered me some of the calculated IUE data. Moreover, thank to teacher Fukun Liu for his helpful advice and discussions about my work.

Finally, I thank to the Jun Zheng Fundation of Peking University for giving me the chance and support to do research as an undergraduate student.

References

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Corbin, M.R.,Boroson, T.A.,1996, ApJS, 107, 69

Forster, K.,Green, P.J.,Aldcroft, T.L., Vestergaard, M., Foltz, G.B., Hewett, P.C., 2001, ApJS, 134, 35

Kaspi, S., Smith, P.S., Netzer, H., Maoz, D.,Jannuzi, B.T.,& Giveon.U.,2000, ApJ, 533, 631

Kuraszkiewicz, J.K., Green, P.I., Forster, K., Aldcroft, T.L., Evans, I.N., Koratkar,A., 2002, ApJS, 143, 257 Laor, A. ApJ, 543, L111

McLure, R.J., Jarvis, M.J.2002, MINRAS, 331, 109

Neugebauer, G., Green, R.F., Mattheus, K., Schmidt, M., Soifer, B.T., & Bennett, J., 1987, ApJS, 63, 615

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Reichert, G.A.et al. 1994,ApJ, 425, 582 Vestergaard, M. 2002, ApJ, 571, 733

作者简介：

王然，女，1981年5月出生于吉林省长春市， 2000年从东北师范大学附属中学考入北京大学天文学系，在校期间获得学习优秀奖，校三好学生等奖励，在社团活动中曾担任校青年天文学会观测部长。大二下学期获得“君政基金”资助，在吴学兵教授的指导下从事活动星系核方面的研究，历时两年，拟完成两篇论文，第一篇已经投出，第二篇文章正在后期的整理中。

感谢与寄语：

从2002年5月开始，我很荣幸在吴学兵老师的指导下开始进行活动星系核黑洞质量的研究。最初由于基础知识不足，我进行了大量相关背景文献的阅读学习，然后结合课题本身内容在理解不断加深的基础上开始进行研究。在这一年半的时间里，我不仅在自己感兴趣的天文学领域中迈出了研究探索的第一步，而且对科学研究本身有了深刻的体会。如何在现有的理论和现象中发现问题，如何以科学的态度去考虑问题，这些关乎科学本身的规则虽然隐身于具体的数据图表中，却往往是得到重要理论的关键。

最后，仍然要感谢李政道先生和秦惠君女士，以及北京大学“君政基金”。正是这一项目是我可以在本科阶段提前接触科学研究，拥有了一段宝贵的科研经历。

指导教师简介：

吴学兵，男，北京大学天文学系教授、系主任助理，北京大学物理学院教学委员会委员。1996年于中科院北京天文台获得理学博士学位，1998年在中科院理论物理所博士后出站，先后在香港大学，德国Max-Planck学会地外物理所、天体物理所，美国Alabama大学Huntsville分校物理系进行留学访问。主要研究领域为，黑洞物理，吸积盘理论，类星体与活动星系核，高能天体物理，X射线双星。

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