- Email: [email protected]
Cerenkov Line-like Radiation and the Origin of Broad Emission Lines in Quasars
CHINESE ASTRONOMY AND ASTROPHYSICS
ELSEVIER
ChineseAstronomy Astronomy and Astrophysics Chinese Astrophysics34 34(2010) (2010)113–120 113–120
Cerenkov Line-like Radiation and the Origin of Broad Emission Lines in Quasars† YUAN Ai-fang2 MENG Xian-ru2 LIU Dang-bo1 DANZENG Luo-bu 2 YOU Jun-han 1 1
Institute of Particle Physics and Cosmology, Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 2 Institute of Cosmic Ray, Department of Physics, College of Science, Tibet University, Lhasa, 850000
Abstract When the thermal relativistic electrons with isotropic distribution of velocities move through a dense gas region or impinge upon the surface of a cloud of dense gas, the Cerenkov effect will produce peculiar atomic or ionic emission lines, which we call the “Cerenkov line-like radiation”. This prediction has been verified by the laboratory experiments in optical waveband. In this paper, the importance of the Cerenkov line-like radiation in the exploration of broad emission lines in quasars and Syf1s is pointed out. By using this mechanism, some long standing and significant puzzles in the study of quasars could be solved. Furthermore, the magnitude orders of energy losses of various effects of a relativistic electron in cosmic gas are estimated and compared with each other to prove the effectiveness of this new mechanism in quasars. Key words: quasars: general—radiation mechanism: non-thermal—line: formation
† Supported by National Natural Science Foundation, Research Fundation for Doctoral Program of Higher Education and National Basic Research Program Received 2008–10–08; revised version 2008–12–31 A translation of Acta Astron. Sin. Vol. 50, No. 4, pp. 356–363, 2009 [email protected]
0275-1062/01/$-see front matter © 2010 Elsevier B.V. All rights reserved. c 2010 Elsevier Science B. V. All rights reserved. 0275-1062/01/$-see front matter doi:10.1016/j.chinastron.2010.04.004 PII:
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1. INTRODUCTION Early in the 1980’s, we suggested a new line emission mechanism, the Cerenkov line-like radiation (You and Cheng, 1980; You et al., 1984, 1986). We further confirmed it and improved the formulae system in recent years (You et al., 2000; Chen et al., 2005). We argue that, when the relativistic electrons with isotropic distribution of velocities move in a dense gas region or impinge upon the surface of a cloud or filament composed of dense gas, the radiation produced by the Cerenkov effect will concentrate in a narrow waveband Δλ, very near the intrinsic atomic or molecular wavelength λlu , where l and u denote the corresponding lower and upper levels of an atom or ion. Only in this narrow band the refractive index of gas is markedly larger than unity, n > 1, making it possible to satisfy the Cerenkov radiation condition n > c/v ≡ 1/β . Therefore it looks more like an atomic line (for gas consisting of atoms) or molecular line (for molecular gas)(e.g., Δλ ∼ 10 − 100 ˚ A), rather than continuum, thus the name “Cerenkov line-like radiation”, or simply “Cerenkov emission line”. Here we would like to explain the necessity of the “isotropic distribution of velocities of relativistic electrons”. Generally, for the beamed relativistic electrons, along a specific observer’s sight line, it is impossible to detect a complete Cerenkov line owing to the remarkable angular dispersion θc (λ) ∼ λ of Cerenkov radiation. However, the angular dispersion can be compensated by the isotropic motion of the relativistic electrons. Only in this case, the distant observer can receive a perfect Cerenkov line with a broad, asymmetric profile and a slight “Cerenkov line redshift”. This new line-emission mechanism has been verified by elegant laboratory experiments. By using a radioactive 90 Sr β-ray source with the fast coincidence technique adopted in the nuclear physics, Xu et al. successfully detected the peculiar emission lines in O2 , Br2 and Na vapor at the expected angular directions, wavelengths and plane of polarizations (Xu et al., 1988; Yang et al., 1989). The Cerenkov line-like radiation is potentially important in the high-energy astrophysics. The first candidate for the application of new mechanism might be quasars and other active galactic nuclei (AGNs, e.g., Syf1s). It is a consensus that there exist both the abundant relativistic electrons and the dense gas regions in AGNs, including quasars. This is just the sufficient condition for producing the peculiar Cerenkov lines. It is well known that the observed broad emission lines of quasars and Syf1s have numerous peculiar properties, e.g., the slightly different redshifts of different broad emission lines, the anomalous intensity-ratios of various lines, particularly among the hydrogen lines, etc.. Except for the well-known “steep Balmer decrement” and the “Lyα/Hβ problem” of hydrogen lines in the studies of AGNs (e.g., see Davidson and Netzer 1979), the most striking one among these puzzles is the “Lyα/Lyβ problem”. Using a sample of over 2200 quasars and Syf1s in the Sloan Digital Sky Survey (SDSS), the mean intensity-ratio Lyα/Lyβ has been obtained, Lyα/Lyβ ≈ 10.4 (Vanden Berk et al., 2001), which is much lower than the prediction of the classical recombination and collisional excitation theory. For the optically thin case, which favors the line emission, the ratio of line intensities is simply given by Lyα/Lyβ = jLyα /jLyβ = N2 A21 hνα /N3 A31 hνβ . Taking the typical temperature of the clouds in the broad line region of quasars T ∼ 104 K to determine N2 /N3 , the classical value is unexpectedly high as Lyα/Lyβ ≈ 40 . Even in the most favorable cases, Davidson and Netzer (1979) got Lyα/Lyβ > ∼ 20 . The estimated ratio is further higher if the Lyα trapping effect, existing in the real environment, is taken into account, which greatly enhances the
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population N2 . As for the optically thick case, occurring in a dense gas, the situation is more difficult because the absorption for Lyβ line is much higher than Lyα. All the anomalies imply that some new line emission mechanisms could be in operation in the broad line regions (BLRs) in quasars. We argue that the puzzle can be solved if the Cerenkov line-like radiation is taken into account. The intensity ratios predicted by this new mechanism are markedly different from those given by the classical recombination-cascade and/or collisional excitation. The former are closer to the observed ratios. Moreover, our estimate shows that, for the relativistic electrons with typical Lorentz factors γ ∼ 102 − 103 , the new line emission mechanism can be very efficient if the density of gas is so high as NH ∼ 1016 − 1018 cm−3 (see Table 1). On the contrary, in the dense gas the traditional line emission from the spontaneous transitions is seriously suppressed owing to the inevitable line absorption. Calculation shows that the strongest Cerenkov hydrogen lines are Lyα, Lyβ, Hα and Hβ . The high density NH ∼ 1016 − 1018 cm−3 , required by an efficient Cerenkov radiation, is obviously inconsistent with that given in the standard model of the BLRs of quasars. We thus make a moderate modification for the standard BLRs model: Except for the clouds with densities NH ∼ 1010 − 1012 cm−3 as normally required, we assume that there also exist plenty of dense clouds with densities NH ∼ 1016 − 1018 cm−3 in BLRs, accompanied with abundant relativistic electrons in the vicinities of the dense clouds. Coexistence of both the normal and the dense cloudlets in the BLR ensures the operations of two different lineemission mechanisms: the Cerenkov line-like radiation and the normal line emission from the spontaneous transitions. The observed line should be a blend of these two emissions. (However, the Cerenkov mechanism is unable to produce the high ionization lines, e.g., CIII, NV, etc., which only arise from the classical spontaneous transitions, as explained in Chen et al., 2005.) The anomalous ratios of line intensities imply that the Cerenkov line could be a significant component in the observed line, even a dominant one. In the subsequent work, by using the Cerenkov mechanism, we plan to complete a model calculation of the ratios of line intensities for all broad hydrogen lines to fit the observation data given in SDSS. (Certainly, in processing the data, we must carefully exclude all narrow components from the blend lines.) Before accomplishing this task, we have to settle a quarrel of the effectiveness of the Cerenkov mechanism in quasars. For a long time, people have always believed that the Cerenkov radiation is too weak to explain the broad lines in quasars. It is well-known that most part of the kinetic energy of a relativistic electron is exhausted in the ionization/excitation of atoms/ions as well as the bremsstrahlung process, rather than in the Cerenkov radiation. Almost all of the lost energy is ultimately released from gas in the form of radiation (in a dense gas region, the dominant component is continuum). Therefore, if the broad lines of a quasar are mainly produced by the Cerenkov emission, this sets a lower limit to the total luminosity of relativistic electrons. Obviously, if the lower limit is so high as to exceed the observed continuum luminosity, the model of Cerenkov line-like radiation for quasars is no longer acceptable. We argue that such an underestimate of the Cerenkov effect arises from the experimental examinations in laboratories, where the adopted medium is usually composed of heavy elements with atomic numbers Z 1 (e. g., water). However, for the astronomical plasma, the dominant component is hydrogen, the lightest element with atomic number Z = 1. In
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this case, the effects of ionization/excitation and bremsstrahlung are greatly weakened and the relative efficiency of Cerenkov radiation markedly increases as shown below, thus the above worry becomes unnecessary.
2. COMPARISON OF VARIOUS ENERGY-LOSSES OF A RELATIVISTIC ELECTRON In order to illustrate the effectiveness of Cerenkov mechanism in the study of the broad lines of quasars and other AGNs, in this section we estimate the magnitudes of energy losses of various effects of a relativistic electron in gas and compare them with each other. If the calculated fraction of energy loss of the Cerenkov line-like radiation in the total losses is not very small, then by making the expected luminosity of relativistic electrons to be lower than the observed continuum luminosity, the Cerenkov origin of the broad lines of quasars and Syf1s should be acceptable and practicable. 2.1 Power of Energy-loss from the Ionization/Excitation of Atoms/Ions pion The power of energy-loss of a fast electron in the ionization/excitation of atoms/ions in a medium is (Bethe, 1930; Rholf, 1994) pion =
4πα2f (¯ hc)2 m0 cβ 2
2m0 c2 γ 2 β 2 ZNZ ln − β 2 ergs · sec−1 , I
(1)
where αf = 1/137 is the fine structure constant; I is the effective ionization potential of atom, including the excitation, thus slightly lower than the true atomic ionization potential; Z and NZ are the atomic number and the density of atoms in gas, respectively; γ ≡ 1/ 1 − β 2 and β ≡ v/c are, respectively, the Lorentz factor and the velocity of electron; m0 is electron mass; ¯h and c are the Planck constant and velocity of light, respectively. For the relativistic electron and the cosmic gas, γ 1, β ≈ 1, and Z = 1, so Eq. (1) becomes γ2 ion −20 p = 2.45 × 10 NH 12.8 + ln ergs · sec−1 I (eV) γ2 −14 = 1.53 × 10 NH 12.8 + ln (2) MeV · sec−1 . I (eV) 2.2 Power of Energy-loss from the Bremsstrahlung Process of a Relativistic Electron pbrem The power of the bremsstrahlung radiation for a relativistic electron is (Heitler, 1954; Tucker, 1976) pbrem = 4αf r02 m0 c3 Z 2 NZ γΞ ergs · sec−1 , (3) where r0 is the classical radius of electrons, Ξ is the screen factor. ⎧
1 ⎨ ln 2pi − 1 , when r 137Z − 3 (for case without screen) m0 c 3
Ξ= ⎩ ln 183Z − 13 + 2 , when r 137Z − 13 (for case of complete screen) 9
(4)
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where pi = γm0 c is the momentum of the relativistic electron. For the cosmic plasma, Z = 1, and taking γ ≈ 102 − 103 , in both cases we get Ξ ≈ 5. Therefore, Eq. (3) becomes pbrem = 2.85 × 10−22 γNH ergs · sec−1 = 1.78 × 10−16 γNH MeV · sec−1 . (5) Eqs. (1) and (3) show that both pion and pbrem are strongly dependent on the atomic number Z of the medium. However, below we show that the power of each individual Cerenkov line is Z-independent (see Eq. (7) below). This property explains why in laboratories (Z 1), the Cerenkov radiation is so weak comparing with the coexistent ionization and bremsstrahlung effects. However, for the cosmic plasma mainly composed of hydrogen with Z = 1, the fraction of Cerenkov line-like radiation in the total energy-loss is obviously increasing, as the following calculation shows. 2.3 Power of Energy-loss from the Cerenkov Line-like Radiation pCer λlu The power pCer λlu of a specific Cerenkov atomic line at λ ≈ λlu can be obtained from the well-known formula of Cerenkov spectral power of a relativistic electron (Jelly, 1958; Sokolov, 1940) 2 2 β 1 pCer dλ = 4π e c 1 − dλ , (6) λ λ3 n2λ β 2 where nλ represents the refractive index of gas at wavelength λ, β ≡ v/c and e is the electron charge. For the gaseous medium, Cerenkov radiation concentrates in a narrow band (0, Δλclim ) near the intrinsic wavelength λlu , where an approximate analytical expression for the refractive index nλ of gas has been obtained (see, You et al., 1985). Inserting nλ into Eq. (6), we finally get (for details see You et al., 1985, 2000; Chen et al., 2005): 2 ylim −1 e Nl −1 2 pCer y − ylim dy = A g λ ul u λlu lu 4π gl 10−6 ylim −1 Nl −1 = 1.84 × 10−20 λ2lu Aul gu y − ylim dy , (7) gl 10−6 where pCer λlu is in units of ergs/sec. We particularly mention that the wavelength λlu in Eq. (7) is in units of cm to favor the universality of the formula in various wavebands (infrared, optical, X-ray, etc.), rather than Angstrom or nm as usually adopted in optics. Aul is the spontaneous transition probability of u → l; gu and gl are the degeneracies of levels u and l, respectively; Nu and Nl are respectively the populations at levels u and l; and y ≡ Δλ/λlu is the fractional wavelength-shift, which is a dimensionless small quantity, y 1, very useful in theoretical formulation. ylim ≡ Δλclim /λlu is the fractional width of the Cerenkov line (You et al., 1985, 2000), 1 Nu Nl Nl 4 2 −14 4 λ ylim = A g − ≈ 6.72 × 10 λ A g (8) γ γ2 . ul u lu ul u 16π 3 c lu gl gu gl
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2.4 Power of Energy-loss from the Inverse Compton Scattering pICS The total power of the inverse Compton scattering for a relativistic electron is given by (see, e. g., Rybicki & Lightman, 1979; Tucker, 1976) pICS =
32 2 πr0 cUph γ 2 = 2.6 × 10−14 Uph γ 2 (ergs · sec−1 ) = 1.6 × 10−8 Uph γ 2 MeV · sec−1 , (9) 9
where Uph is the energy density of photons (in units of ergs · cm−3 ) in the ambient radiation field, γ is the Lorentz factor of the relativistic electron. Taking the typical temperature T ∼ 104 K for the cloudlets in the BLRs of quasars (see, e. g., Davidson & Netzer, 1979), we get Uph ≈ 75 ergs · cm−3 . Therefore, Eq. (9) becomes pICS ≈ 1.97 × 10−12 γ 2 (ergs · sec−1 ) = 1.23 × 10−6 γ 2 MeV · sec−1 for T ∼ 104 K . (10) 2.5 Power of Energy-loss from the Synchrotron Radiation psyn The power of the synchrotron radiation for a relativistic electron is described by (Rybicki & Lightman 1985; Tucker 1976) psyn =
4 2 2 2 r cγ B = 2.6 × 10−14 UB γ 2 (ergs · sec−1 ) = 1.66 × 10−8 UB γ 2 MeV · sec−1 ,(11) 9 0
where UB = B 2 /8π is the energy density of magnetic field. If the dense clouds with NH ∼ 1016 − 1018 cm−3 in BLRs are confined by the pressure of the random magnetic field, then from the pressure-balance B 2 /8π ≈ NH kT and taking T ∼ 104 K, we can estimate the order of magnetic strength B ∼ 102 − 103 Gauss, which is much higher than the normal values in the standard BLR models. Therefore Eq. (11) becomes for B ∼ 103 Gauss . (12) psyn ≈ 10−9 γ 2 (ergs · sec−1 ) = 10−3 γ 2 MeV · sec−1 2.6 Total Power of All Energy-losses of a Relativistic Electron pstop The total power pstop of all energy losses of a relativistic electron can be written as: syn pCer + pICS ≈ pion + pbrem , (13) pstop = pion + pbrem + λlu + p λlu
where pstop is also called as “stopping power” in literatures (see, Rohlf, 1994). The last ICS + psyn pion + pbrem , as approximation in Eq. (13) is due to the fact of λlu pCer λlu + p shown in Table 1 below.
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Table 1 Comparison of various powers of energy losses of a relativistic electron in dense gas NH0 (cm−3 ) N2 ≈ 0.1NH0 pion (MeV/s) pbrem (MeV/s) pCer λlu 4
(MeV/s)
pCer Lyα pCer Lyβ pCer Hα pCer Hβ
pCer (MeV/s) i
1016 1015 3.0 × 103 1.8 × 102 1.3 × 102 14 30 3.5
γ = 102 1017 1016 3.0 × 104 1.8 × 103 2.0 × 103 2.6 × 102 4.1 × 102 56
1018 1017 3.0 × 105 1.8 × 104 2.6 × 104 3.9 × 103 5.3 × 103 7.7 × 102
1016 1015 3.7 × 103 1.8 × 103 2.6 × 102 39 53 7.7
γ = 103 1017 1016 3.7 × 104 1.8 × 104 3.3 × 103 5.1 × 102 6.4 × 102 98
1018 1017 3.7 × 105 1.8 × 105 3.9 × 104 6.4 × 103 7.5 × 103 1.2 × 103
1.8 × 102
2.7 × 103
3.6 × 104
3.6 × 102
4.5 × 103
5.4 × 104
i=1 pICS
(MeV/s) (for T ∼ 104 K) psyn (MeV/s) (for B ∼ 103 G) pstop (MeV/s) 4
pCer /pstop i i=1 pstop /pCer Hβ
0.012
1.2 1.7 × 103
16.6 3.3 ×
103
5.3% 9.6 ×
102
3.4 ×
104
7.8% 6.2 ×
102
3.5 ×
105
10.3% 4.6 ×
102
7.5 ×
103
6.1 × 104
6.0 × 105
7.4%
9.0%
4.8% 9.7 ×
102
6.2 ×
102
5.1 × 102
By using Eqs. (2), (5), (7), (8), (10), (12) and (13), we accomplish calculations of the energy losses of various effects of a relativistic electron in a dense gas region, and compare them to each other. In the model calculations, we take γ = 102 and 103 ; NH = 1016 , 1017 and 1018 cm−3 , respectively. For density of hydrogen in the level 2, which is needed for the calculations of Cerenkov Hα and Hβ lines, we take N2 = 0.1NH from the estimate of Lyα trapping effect, which greatly enhances the population N2 , and renders N2 to be much higher than the Boltzmann values for gas in thermal equilibrium at T ∼ 104 K. All calculated results are listed in Table 1. For shortness, we only give the line-powers for the strongest Cerenkov lines Lyα, Lyβ, Hα and Hβ in Table 1. Note that, the calculated ratios Cer Cer of line-powers. e. g., pCer Lyα : pHα : pLyβ · · · · · · are markedly different from the observed Cer Cer Cer · · · · · ·. This is understandable because for the ratios of line-intensities ILyα : IHα : ILyβ dense clouds, except for the line emission, the absorption has to be taken into account too. The line-intensity, emergent from the surface of a dense cloud, is determined by both the emissivity (power) and the absorption (see You et al., 1985, 2000; Chen et al., 2005).
3. CONCLUSIONS AND DISCUSSION From Table 1 we see that, for a relativistic electron moving in the dense gas, the dominant energy losses are due to the ionization and bremsstrahlung processes, while the losses due to all other effects, e. g., the Cerenkov line-like radiation, inverse Compton scattering and synchrotron, are small (if T ∼ 104 eV and B ∼ 103 gauss). In normal cases, among the small quantities, the Cerenkov line-like radiation is the largest one. However, the contribution of the Cerenkov line-like radiation to the line-emission can 4 /pstop ≈ 10% not be ignored, because its fraction in the total losses is so large as i=1 pCer i (see Table 1). If there really exist abundant relativistic electrons and dense gas regions in quasars, the occurrence of the Cerenkov line-like radiation will be inevitable. By using
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this new line emission mechanism, we thus provide a new way to solve the puzzles in the study of the broad lines in quasars which have perplexed astronomers for many years. If our suggestion is further confirmed in future, the conventional understanding for the environment around the central supermassive black holes of AGNs will be significantly changed. The power pCer λlu of a Cerenkov line markedly depends on the density of gas, as shown in Eq. (7) or in Table 1. This is why we must assume the existence of dense clouds in the modified BLR model to favor an efficient operation of the Cerenkov mechanism in quasars. 3 4 Table 1 gives a moderately high ratio pstop /pCer Hβ ≈ 10 − 10 in a wide (γ, NH ) range. It means that, if the broad Hβ line of quasars mainly arises from the Cerenkov mechanism, then the expected continuum luminosity Lc of relativistic electrons should be 3 or 4 magnitude
stop 3 4 orders higher than the luminosity of Hβ line Lc /LCer /pCer Hβ ≈ p Hβ ≈ 10 − 10 . Such an estimate is compatible with observations. For quasars and Syf1s, the observed typical 40 41 luminosity of Hβ line is Lobs ergs/sec, while the observed continuum luminosity Hβ ≈ 10 −10 44 48 ≈ 10 − 10 ergs/sec (including infrared). The typical value is Lobs ≈ 1045 − 1046 is Lobs c c obs obs 4 ergs/sec. Therefore we infer that the observed ratio is Lc /LHβ = 10 − 105 , about one order higher than the expectation inferred from Table 1. This indicates the feasibility of the Cerenkov mechanism for the exploration of origin of broad lines in quasars and other AGNs. ACKNOWLEDGEMENT We are sincerely grateful to Professor Ostriker for his useful discussions and suggestions when he visited Shanghai Jiao Tong University. He suggested us to calculate the energy losses of various effects of a relativistic electron, and compare them to each other. This has markedly improved our work. References Bethe H. A. Ann. Phys., 1930, 5, 325 Chen L., You J. H., Liu D. B. ApJ, 2005, 627, 177 Davidson K., Netzer H. Rev. Mod. Phys., 1979, 51, 715 Heitler W. The Quantum Theory of Radiation. London: Oxford Univ. Press, 1984, 242-256 Jelley J. V. Cerenkov Radiation and Its Application. New York: Pergamon Press, 1958, 105-112 Liu D. B., JIN G. X., SHI J. R., et al. Acta. Astron., 1997, 40, 382 Rohlf J. W. Modern Physics from α to Z. New York: Wiley, 1994, 326-333 Rybicki G. B., Lightman A. P. Radiation Processes in Astrophysics. Berlin: Wiley-VCH, 1985:, 195220 Tucker W. Radiation Processes in Astrophysics. Cambridge: MIT Press, 1975, 162-175 Vanden Berk D. E., Richards G. T., Bauer A., et al. AJ, 2001, 122, 549 Xu K. Z., Yang B. X., Xi F. Y., et al. PhRvA, 1988, 37, 2912 Yang B. X., Xu K. Z., Hao L. Y., et al. PhRvA, 1989, 40, 5411 You J. H., Cheng F. H. Acta Physica Sinica, 1980, 29, 927 You J. H., Cheng F. H., Cheng F. Z., et al. PhRvA, 1986, 34, 3015 You J. H., Kiang T., Cheng F. Z., et al. MNRAS, 1984, 211, 667 You J. H., Xu Y. D., Liu D. B., et al. A&A, 2000, 362, 762
ELSEVIER
ChineseAstronomy Astronomy and Astrophysics Chinese Astrophysics34 34(2010) (2010)113–120 113–120
Cerenkov Line-like Radiation and the Origin of Broad Emission Lines in Quasars† YUAN Ai-fang2 MENG Xian-ru2 LIU Dang-bo1 DANZENG Luo-bu 2 YOU Jun-han 1 1
Institute of Particle Physics and Cosmology, Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 2 Institute of Cosmic Ray, Department of Physics, College of Science, Tibet University, Lhasa, 850000
Abstract When the thermal relativistic electrons with isotropic distribution of velocities move through a dense gas region or impinge upon the surface of a cloud of dense gas, the Cerenkov effect will produce peculiar atomic or ionic emission lines, which we call the “Cerenkov line-like radiation”. This prediction has been verified by the laboratory experiments in optical waveband. In this paper, the importance of the Cerenkov line-like radiation in the exploration of broad emission lines in quasars and Syf1s is pointed out. By using this mechanism, some long standing and significant puzzles in the study of quasars could be solved. Furthermore, the magnitude orders of energy losses of various effects of a relativistic electron in cosmic gas are estimated and compared with each other to prove the effectiveness of this new mechanism in quasars. Key words: quasars: general—radiation mechanism: non-thermal—line: formation
† Supported by National Natural Science Foundation, Research Fundation for Doctoral Program of Higher Education and National Basic Research Program Received 2008–10–08; revised version 2008–12–31 A translation of Acta Astron. Sin. Vol. 50, No. 4, pp. 356–363, 2009 [email protected]
0275-1062/01/$-see front matter © 2010 Elsevier B.V. All rights reserved. c 2010 Elsevier Science B. V. All rights reserved. 0275-1062/01/$-see front matter doi:10.1016/j.chinastron.2010.04.004 PII:
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LIU Dang-bo et al. / Chinese Astronomy and Astrophysics 34 (2010) 113–120
1. INTRODUCTION Early in the 1980’s, we suggested a new line emission mechanism, the Cerenkov line-like radiation (You and Cheng, 1980; You et al., 1984, 1986). We further confirmed it and improved the formulae system in recent years (You et al., 2000; Chen et al., 2005). We argue that, when the relativistic electrons with isotropic distribution of velocities move in a dense gas region or impinge upon the surface of a cloud or filament composed of dense gas, the radiation produced by the Cerenkov effect will concentrate in a narrow waveband Δλ, very near the intrinsic atomic or molecular wavelength λlu , where l and u denote the corresponding lower and upper levels of an atom or ion. Only in this narrow band the refractive index of gas is markedly larger than unity, n > 1, making it possible to satisfy the Cerenkov radiation condition n > c/v ≡ 1/β . Therefore it looks more like an atomic line (for gas consisting of atoms) or molecular line (for molecular gas)(e.g., Δλ ∼ 10 − 100 ˚ A), rather than continuum, thus the name “Cerenkov line-like radiation”, or simply “Cerenkov emission line”. Here we would like to explain the necessity of the “isotropic distribution of velocities of relativistic electrons”. Generally, for the beamed relativistic electrons, along a specific observer’s sight line, it is impossible to detect a complete Cerenkov line owing to the remarkable angular dispersion θc (λ) ∼ λ of Cerenkov radiation. However, the angular dispersion can be compensated by the isotropic motion of the relativistic electrons. Only in this case, the distant observer can receive a perfect Cerenkov line with a broad, asymmetric profile and a slight “Cerenkov line redshift”. This new line-emission mechanism has been verified by elegant laboratory experiments. By using a radioactive 90 Sr β-ray source with the fast coincidence technique adopted in the nuclear physics, Xu et al. successfully detected the peculiar emission lines in O2 , Br2 and Na vapor at the expected angular directions, wavelengths and plane of polarizations (Xu et al., 1988; Yang et al., 1989). The Cerenkov line-like radiation is potentially important in the high-energy astrophysics. The first candidate for the application of new mechanism might be quasars and other active galactic nuclei (AGNs, e.g., Syf1s). It is a consensus that there exist both the abundant relativistic electrons and the dense gas regions in AGNs, including quasars. This is just the sufficient condition for producing the peculiar Cerenkov lines. It is well known that the observed broad emission lines of quasars and Syf1s have numerous peculiar properties, e.g., the slightly different redshifts of different broad emission lines, the anomalous intensity-ratios of various lines, particularly among the hydrogen lines, etc.. Except for the well-known “steep Balmer decrement” and the “Lyα/Hβ problem” of hydrogen lines in the studies of AGNs (e.g., see Davidson and Netzer 1979), the most striking one among these puzzles is the “Lyα/Lyβ problem”. Using a sample of over 2200 quasars and Syf1s in the Sloan Digital Sky Survey (SDSS), the mean intensity-ratio Lyα/Lyβ has been obtained, Lyα/Lyβ ≈ 10.4 (Vanden Berk et al., 2001), which is much lower than the prediction of the classical recombination and collisional excitation theory. For the optically thin case, which favors the line emission, the ratio of line intensities is simply given by Lyα/Lyβ = jLyα /jLyβ = N2 A21 hνα /N3 A31 hνβ . Taking the typical temperature of the clouds in the broad line region of quasars T ∼ 104 K to determine N2 /N3 , the classical value is unexpectedly high as Lyα/Lyβ ≈ 40 . Even in the most favorable cases, Davidson and Netzer (1979) got Lyα/Lyβ > ∼ 20 . The estimated ratio is further higher if the Lyα trapping effect, existing in the real environment, is taken into account, which greatly enhances the
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population N2 . As for the optically thick case, occurring in a dense gas, the situation is more difficult because the absorption for Lyβ line is much higher than Lyα. All the anomalies imply that some new line emission mechanisms could be in operation in the broad line regions (BLRs) in quasars. We argue that the puzzle can be solved if the Cerenkov line-like radiation is taken into account. The intensity ratios predicted by this new mechanism are markedly different from those given by the classical recombination-cascade and/or collisional excitation. The former are closer to the observed ratios. Moreover, our estimate shows that, for the relativistic electrons with typical Lorentz factors γ ∼ 102 − 103 , the new line emission mechanism can be very efficient if the density of gas is so high as NH ∼ 1016 − 1018 cm−3 (see Table 1). On the contrary, in the dense gas the traditional line emission from the spontaneous transitions is seriously suppressed owing to the inevitable line absorption. Calculation shows that the strongest Cerenkov hydrogen lines are Lyα, Lyβ, Hα and Hβ . The high density NH ∼ 1016 − 1018 cm−3 , required by an efficient Cerenkov radiation, is obviously inconsistent with that given in the standard model of the BLRs of quasars. We thus make a moderate modification for the standard BLRs model: Except for the clouds with densities NH ∼ 1010 − 1012 cm−3 as normally required, we assume that there also exist plenty of dense clouds with densities NH ∼ 1016 − 1018 cm−3 in BLRs, accompanied with abundant relativistic electrons in the vicinities of the dense clouds. Coexistence of both the normal and the dense cloudlets in the BLR ensures the operations of two different lineemission mechanisms: the Cerenkov line-like radiation and the normal line emission from the spontaneous transitions. The observed line should be a blend of these two emissions. (However, the Cerenkov mechanism is unable to produce the high ionization lines, e.g., CIII, NV, etc., which only arise from the classical spontaneous transitions, as explained in Chen et al., 2005.) The anomalous ratios of line intensities imply that the Cerenkov line could be a significant component in the observed line, even a dominant one. In the subsequent work, by using the Cerenkov mechanism, we plan to complete a model calculation of the ratios of line intensities for all broad hydrogen lines to fit the observation data given in SDSS. (Certainly, in processing the data, we must carefully exclude all narrow components from the blend lines.) Before accomplishing this task, we have to settle a quarrel of the effectiveness of the Cerenkov mechanism in quasars. For a long time, people have always believed that the Cerenkov radiation is too weak to explain the broad lines in quasars. It is well-known that most part of the kinetic energy of a relativistic electron is exhausted in the ionization/excitation of atoms/ions as well as the bremsstrahlung process, rather than in the Cerenkov radiation. Almost all of the lost energy is ultimately released from gas in the form of radiation (in a dense gas region, the dominant component is continuum). Therefore, if the broad lines of a quasar are mainly produced by the Cerenkov emission, this sets a lower limit to the total luminosity of relativistic electrons. Obviously, if the lower limit is so high as to exceed the observed continuum luminosity, the model of Cerenkov line-like radiation for quasars is no longer acceptable. We argue that such an underestimate of the Cerenkov effect arises from the experimental examinations in laboratories, where the adopted medium is usually composed of heavy elements with atomic numbers Z 1 (e. g., water). However, for the astronomical plasma, the dominant component is hydrogen, the lightest element with atomic number Z = 1. In
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this case, the effects of ionization/excitation and bremsstrahlung are greatly weakened and the relative efficiency of Cerenkov radiation markedly increases as shown below, thus the above worry becomes unnecessary.
2. COMPARISON OF VARIOUS ENERGY-LOSSES OF A RELATIVISTIC ELECTRON In order to illustrate the effectiveness of Cerenkov mechanism in the study of the broad lines of quasars and other AGNs, in this section we estimate the magnitudes of energy losses of various effects of a relativistic electron in gas and compare them with each other. If the calculated fraction of energy loss of the Cerenkov line-like radiation in the total losses is not very small, then by making the expected luminosity of relativistic electrons to be lower than the observed continuum luminosity, the Cerenkov origin of the broad lines of quasars and Syf1s should be acceptable and practicable. 2.1 Power of Energy-loss from the Ionization/Excitation of Atoms/Ions pion The power of energy-loss of a fast electron in the ionization/excitation of atoms/ions in a medium is (Bethe, 1930; Rholf, 1994) pion =
4πα2f (¯ hc)2 m0 cβ 2
2m0 c2 γ 2 β 2 ZNZ ln − β 2 ergs · sec−1 , I
(1)
where αf = 1/137 is the fine structure constant; I is the effective ionization potential of atom, including the excitation, thus slightly lower than the true atomic ionization potential; Z and NZ are the atomic number and the density of atoms in gas, respectively; γ ≡ 1/ 1 − β 2 and β ≡ v/c are, respectively, the Lorentz factor and the velocity of electron; m0 is electron mass; ¯h and c are the Planck constant and velocity of light, respectively. For the relativistic electron and the cosmic gas, γ 1, β ≈ 1, and Z = 1, so Eq. (1) becomes γ2 ion −20 p = 2.45 × 10 NH 12.8 + ln ergs · sec−1 I (eV) γ2 −14 = 1.53 × 10 NH 12.8 + ln (2) MeV · sec−1 . I (eV) 2.2 Power of Energy-loss from the Bremsstrahlung Process of a Relativistic Electron pbrem The power of the bremsstrahlung radiation for a relativistic electron is (Heitler, 1954; Tucker, 1976) pbrem = 4αf r02 m0 c3 Z 2 NZ γΞ ergs · sec−1 , (3) where r0 is the classical radius of electrons, Ξ is the screen factor. ⎧
1 ⎨ ln 2pi − 1 , when r 137Z − 3 (for case without screen) m0 c 3
Ξ= ⎩ ln 183Z − 13 + 2 , when r 137Z − 13 (for case of complete screen) 9
(4)
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where pi = γm0 c is the momentum of the relativistic electron. For the cosmic plasma, Z = 1, and taking γ ≈ 102 − 103 , in both cases we get Ξ ≈ 5. Therefore, Eq. (3) becomes pbrem = 2.85 × 10−22 γNH ergs · sec−1 = 1.78 × 10−16 γNH MeV · sec−1 . (5) Eqs. (1) and (3) show that both pion and pbrem are strongly dependent on the atomic number Z of the medium. However, below we show that the power of each individual Cerenkov line is Z-independent (see Eq. (7) below). This property explains why in laboratories (Z 1), the Cerenkov radiation is so weak comparing with the coexistent ionization and bremsstrahlung effects. However, for the cosmic plasma mainly composed of hydrogen with Z = 1, the fraction of Cerenkov line-like radiation in the total energy-loss is obviously increasing, as the following calculation shows. 2.3 Power of Energy-loss from the Cerenkov Line-like Radiation pCer λlu The power pCer λlu of a specific Cerenkov atomic line at λ ≈ λlu can be obtained from the well-known formula of Cerenkov spectral power of a relativistic electron (Jelly, 1958; Sokolov, 1940) 2 2 β 1 pCer dλ = 4π e c 1 − dλ , (6) λ λ3 n2λ β 2 where nλ represents the refractive index of gas at wavelength λ, β ≡ v/c and e is the electron charge. For the gaseous medium, Cerenkov radiation concentrates in a narrow band (0, Δλclim ) near the intrinsic wavelength λlu , where an approximate analytical expression for the refractive index nλ of gas has been obtained (see, You et al., 1985). Inserting nλ into Eq. (6), we finally get (for details see You et al., 1985, 2000; Chen et al., 2005): 2 ylim −1 e Nl −1 2 pCer y − ylim dy = A g λ ul u λlu lu 4π gl 10−6 ylim −1 Nl −1 = 1.84 × 10−20 λ2lu Aul gu y − ylim dy , (7) gl 10−6 where pCer λlu is in units of ergs/sec. We particularly mention that the wavelength λlu in Eq. (7) is in units of cm to favor the universality of the formula in various wavebands (infrared, optical, X-ray, etc.), rather than Angstrom or nm as usually adopted in optics. Aul is the spontaneous transition probability of u → l; gu and gl are the degeneracies of levels u and l, respectively; Nu and Nl are respectively the populations at levels u and l; and y ≡ Δλ/λlu is the fractional wavelength-shift, which is a dimensionless small quantity, y 1, very useful in theoretical formulation. ylim ≡ Δλclim /λlu is the fractional width of the Cerenkov line (You et al., 1985, 2000), 1 Nu Nl Nl 4 2 −14 4 λ ylim = A g − ≈ 6.72 × 10 λ A g (8) γ γ2 . ul u lu ul u 16π 3 c lu gl gu gl
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2.4 Power of Energy-loss from the Inverse Compton Scattering pICS The total power of the inverse Compton scattering for a relativistic electron is given by (see, e. g., Rybicki & Lightman, 1979; Tucker, 1976) pICS =
32 2 πr0 cUph γ 2 = 2.6 × 10−14 Uph γ 2 (ergs · sec−1 ) = 1.6 × 10−8 Uph γ 2 MeV · sec−1 , (9) 9
where Uph is the energy density of photons (in units of ergs · cm−3 ) in the ambient radiation field, γ is the Lorentz factor of the relativistic electron. Taking the typical temperature T ∼ 104 K for the cloudlets in the BLRs of quasars (see, e. g., Davidson & Netzer, 1979), we get Uph ≈ 75 ergs · cm−3 . Therefore, Eq. (9) becomes pICS ≈ 1.97 × 10−12 γ 2 (ergs · sec−1 ) = 1.23 × 10−6 γ 2 MeV · sec−1 for T ∼ 104 K . (10) 2.5 Power of Energy-loss from the Synchrotron Radiation psyn The power of the synchrotron radiation for a relativistic electron is described by (Rybicki & Lightman 1985; Tucker 1976) psyn =
4 2 2 2 r cγ B = 2.6 × 10−14 UB γ 2 (ergs · sec−1 ) = 1.66 × 10−8 UB γ 2 MeV · sec−1 ,(11) 9 0
where UB = B 2 /8π is the energy density of magnetic field. If the dense clouds with NH ∼ 1016 − 1018 cm−3 in BLRs are confined by the pressure of the random magnetic field, then from the pressure-balance B 2 /8π ≈ NH kT and taking T ∼ 104 K, we can estimate the order of magnetic strength B ∼ 102 − 103 Gauss, which is much higher than the normal values in the standard BLR models. Therefore Eq. (11) becomes for B ∼ 103 Gauss . (12) psyn ≈ 10−9 γ 2 (ergs · sec−1 ) = 10−3 γ 2 MeV · sec−1 2.6 Total Power of All Energy-losses of a Relativistic Electron pstop The total power pstop of all energy losses of a relativistic electron can be written as: syn pCer + pICS ≈ pion + pbrem , (13) pstop = pion + pbrem + λlu + p λlu
where pstop is also called as “stopping power” in literatures (see, Rohlf, 1994). The last ICS + psyn pion + pbrem , as approximation in Eq. (13) is due to the fact of λlu pCer λlu + p shown in Table 1 below.
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Table 1 Comparison of various powers of energy losses of a relativistic electron in dense gas NH0 (cm−3 ) N2 ≈ 0.1NH0 pion (MeV/s) pbrem (MeV/s) pCer λlu 4
(MeV/s)
pCer Lyα pCer Lyβ pCer Hα pCer Hβ
pCer (MeV/s) i
1016 1015 3.0 × 103 1.8 × 102 1.3 × 102 14 30 3.5
γ = 102 1017 1016 3.0 × 104 1.8 × 103 2.0 × 103 2.6 × 102 4.1 × 102 56
1018 1017 3.0 × 105 1.8 × 104 2.6 × 104 3.9 × 103 5.3 × 103 7.7 × 102
1016 1015 3.7 × 103 1.8 × 103 2.6 × 102 39 53 7.7
γ = 103 1017 1016 3.7 × 104 1.8 × 104 3.3 × 103 5.1 × 102 6.4 × 102 98
1018 1017 3.7 × 105 1.8 × 105 3.9 × 104 6.4 × 103 7.5 × 103 1.2 × 103
1.8 × 102
2.7 × 103
3.6 × 104
3.6 × 102
4.5 × 103
5.4 × 104
i=1 pICS
(MeV/s) (for T ∼ 104 K) psyn (MeV/s) (for B ∼ 103 G) pstop (MeV/s) 4
pCer /pstop i i=1 pstop /pCer Hβ
0.012
1.2 1.7 × 103
16.6 3.3 ×
103
5.3% 9.6 ×
102
3.4 ×
104
7.8% 6.2 ×
102
3.5 ×
105
10.3% 4.6 ×
102
7.5 ×
103
6.1 × 104
6.0 × 105
7.4%
9.0%
4.8% 9.7 ×
102
6.2 ×
102
5.1 × 102
By using Eqs. (2), (5), (7), (8), (10), (12) and (13), we accomplish calculations of the energy losses of various effects of a relativistic electron in a dense gas region, and compare them to each other. In the model calculations, we take γ = 102 and 103 ; NH = 1016 , 1017 and 1018 cm−3 , respectively. For density of hydrogen in the level 2, which is needed for the calculations of Cerenkov Hα and Hβ lines, we take N2 = 0.1NH from the estimate of Lyα trapping effect, which greatly enhances the population N2 , and renders N2 to be much higher than the Boltzmann values for gas in thermal equilibrium at T ∼ 104 K. All calculated results are listed in Table 1. For shortness, we only give the line-powers for the strongest Cerenkov lines Lyα, Lyβ, Hα and Hβ in Table 1. Note that, the calculated ratios Cer Cer of line-powers. e. g., pCer Lyα : pHα : pLyβ · · · · · · are markedly different from the observed Cer Cer Cer · · · · · ·. This is understandable because for the ratios of line-intensities ILyα : IHα : ILyβ dense clouds, except for the line emission, the absorption has to be taken into account too. The line-intensity, emergent from the surface of a dense cloud, is determined by both the emissivity (power) and the absorption (see You et al., 1985, 2000; Chen et al., 2005).
3. CONCLUSIONS AND DISCUSSION From Table 1 we see that, for a relativistic electron moving in the dense gas, the dominant energy losses are due to the ionization and bremsstrahlung processes, while the losses due to all other effects, e. g., the Cerenkov line-like radiation, inverse Compton scattering and synchrotron, are small (if T ∼ 104 eV and B ∼ 103 gauss). In normal cases, among the small quantities, the Cerenkov line-like radiation is the largest one. However, the contribution of the Cerenkov line-like radiation to the line-emission can 4 /pstop ≈ 10% not be ignored, because its fraction in the total losses is so large as i=1 pCer i (see Table 1). If there really exist abundant relativistic electrons and dense gas regions in quasars, the occurrence of the Cerenkov line-like radiation will be inevitable. By using
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this new line emission mechanism, we thus provide a new way to solve the puzzles in the study of the broad lines in quasars which have perplexed astronomers for many years. If our suggestion is further confirmed in future, the conventional understanding for the environment around the central supermassive black holes of AGNs will be significantly changed. The power pCer λlu of a Cerenkov line markedly depends on the density of gas, as shown in Eq. (7) or in Table 1. This is why we must assume the existence of dense clouds in the modified BLR model to favor an efficient operation of the Cerenkov mechanism in quasars. 3 4 Table 1 gives a moderately high ratio pstop /pCer Hβ ≈ 10 − 10 in a wide (γ, NH ) range. It means that, if the broad Hβ line of quasars mainly arises from the Cerenkov mechanism, then the expected continuum luminosity Lc of relativistic electrons should be 3 or 4 magnitude
stop 3 4 orders higher than the luminosity of Hβ line Lc /LCer /pCer Hβ ≈ p Hβ ≈ 10 − 10 . Such an estimate is compatible with observations. For quasars and Syf1s, the observed typical 40 41 luminosity of Hβ line is Lobs ergs/sec, while the observed continuum luminosity Hβ ≈ 10 −10 44 48 ≈ 10 − 10 ergs/sec (including infrared). The typical value is Lobs ≈ 1045 − 1046 is Lobs c c obs obs 4 ergs/sec. Therefore we infer that the observed ratio is Lc /LHβ = 10 − 105 , about one order higher than the expectation inferred from Table 1. This indicates the feasibility of the Cerenkov mechanism for the exploration of origin of broad lines in quasars and other AGNs. ACKNOWLEDGEMENT We are sincerely grateful to Professor Ostriker for his useful discussions and suggestions when he visited Shanghai Jiao Tong University. He suggested us to calculate the energy losses of various effects of a relativistic electron, and compare them to each other. This has markedly improved our work. References Bethe H. A. Ann. Phys., 1930, 5, 325 Chen L., You J. H., Liu D. B. ApJ, 2005, 627, 177 Davidson K., Netzer H. Rev. Mod. Phys., 1979, 51, 715 Heitler W. The Quantum Theory of Radiation. London: Oxford Univ. Press, 1984, 242-256 Jelley J. V. Cerenkov Radiation and Its Application. New York: Pergamon Press, 1958, 105-112 Liu D. B., JIN G. X., SHI J. R., et al. Acta. Astron., 1997, 40, 382 Rohlf J. W. Modern Physics from α to Z. New York: Wiley, 1994, 326-333 Rybicki G. B., Lightman A. P. Radiation Processes in Astrophysics. Berlin: Wiley-VCH, 1985:, 195220 Tucker W. Radiation Processes in Astrophysics. Cambridge: MIT Press, 1975, 162-175 Vanden Berk D. E., Richards G. T., Bauer A., et al. AJ, 2001, 122, 549 Xu K. Z., Yang B. X., Xi F. Y., et al. PhRvA, 1988, 37, 2912 Yang B. X., Xu K. Z., Hao L. Y., et al. PhRvA, 1989, 40, 5411 You J. H., Cheng F. H. Acta Physica Sinica, 1980, 29, 927 You J. H., Cheng F. H., Cheng F. Z., et al. PhRvA, 1986, 34, 3015 You J. H., Kiang T., Cheng F. Z., et al. MNRAS, 1984, 211, 667 You J. H., Xu Y. D., Liu D. B., et al. A&A, 2000, 362, 762