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A new explanation of the Balmer decrement in quasars
Volume 109A, number 8
PHYSICS LETTERS
17 June 1985
A N E W E X P L A N A T I O N OF T H E B A L M E R D E C R E M E N T IN Q U A S A R S T. K I A N G
Dunsink Observatory, Castleknock, Dublin 15, Ireland J.H. Y O U , F.Z. C H E N G and F.H. C H E N G
Center for Astrophysics, University of Science and TechnologFof China, Hefei, Anhui Province, People's Republic of China Received 31 January 1985; accepted for publication 19 April 1985
The very steep Balmer decrement, one of the most important puzzles in quasars, has been satisfactorily explained by use of a new theory of Cerenkov line emission.
The observed very steep Balmer decrement for low red shift quasars has been one o f the most important puzzles for many years. The observed intensity ratios o f the Balmer line series for QSOs are seriously in disagreement with those for ordinary nebulae. Generally the ratio I(Ha)[I(H~) is always far larger than that for nebulae and I(Ho)/I(H,r) is also larger [ 1 - 3 ] . It is very difficult to explain the above phenomena by classical radiative recombination theory. Table 1 gives the recent observations o f ten QSOs by Puetter et al. and Neugebauer et al. [4,5]. The second column shows the mean observed ratios o f the ten objects, the third column shows the median observed ratios *1, the ,1 An average between the observations of Puetter et al. and Neugebauer et al. has been done.
fourth one shows the Balmer decrement o f nebulae given according to the standard classical radiative recombination theory (it is well known to be accurately in agreement with the observations o f nebulae) [6]. Obviously the observed ratios are seriously in disagreement with those predicted by the classical theory. There have been some possible explanations [ 7 - 1 1 ], the most direct possibility is a wavelength dependent extinction caused by dust in QSOs (the absorption o f dust for visible light is much stronger for short wavelengths). This will produce larger I(Ha)/I(H#) and I(H#)/I(H.r), but the above explanation is facing a serious difficulty: if a reasonable correlation between dust extinction and the wavelength is given, none can interpret the ratios I(Ho~)/I(H#) and l(Hfj)[l(H,r) simultaneously; it has also failed in trying to explain
Table 1 Comparison between the ratios of the Balmer line series from observations, from the classical theory and from the Cerenkov line emission theory. Intensity ratios
I(Ho)[I(H#) I(H,~)]I(H#) I(Hs)/I(H #) I(He)/I(H#)
408
Observations mean
median
3.71 0.35 0.14 0.07
3.70 0.34 0.14 0.05
Values by classical theory
Values by Cerenkov line emission
2.8 0.50 0.29 0.18
(3.7) 0.36 0.15 0.07
0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 109A, number 8
the ratios by use of atomic collisional excitation [ 12], even if dust extinction was considered. Now most people suppose L~ photons in emitting clouds to be trapped by neutral hydrogen (trapping effect), which makes the number density of hydrogen atoms at 2nd energy level increased anomalously and makes the nebulae optically thick for photons of the Balmer line series. In this case, the evaluated values near the observational ratios can be obtained by adjusting a group of parameters properly [ 13,14]. But these models generally contain a number of adjustable parameters, the results are very model-dependent, even so, none could claim to have achieved more than a moderate success in matching the entire observed ratio-sequence from H a to H eIn this paper, we wish to report that the observed Balmer decrement is precisely reproduced in a theory of "Cerenkov line emission" initiated by You and Cheng [ 15]. The calculated ratios are shown in the last column of table 1. If the first intensity ratio I(Ha)/l(Ht3 ) is taken to be same as the median observed value (3.7), then the other three intensity ratios will be uniquely determined by the theory of Cerenkov line emission without introducing any other adjustable parameter. The only parameter used is the first intensity ratio I(Ha)/I(H#), which is taken to be the median observed value (3.7); there is no theoretical arbitrariness and this ratio I(Ha)/I(H#) becomes a believable and reasonable parameter. The basic calculating formula is eq. (41) in ref. [15] in the optically thick case, i.e. 1 = Y{ln(1 + X 2) - 2 [1 - arctg(X)/X] ) ,
17 June 1985
PHYSICS LETTERS
(1)
where Y = ~NeC 1/C3, X = ~ / C 2 U l i m = C3~/-C-~2Co'Y2, and CO, C 1, C 2 and'C 3 are given by eq. (36) of ref. [15]. In normal physical conditions, at least for the lowest energy levels of gaseous atoms, we always have N 1 ~, N 2 >>N 3 ... or N i >>N/, i.e. the particle numbers at lower energy level are far larger than those at higher levels, thus we have Ni/g i - N/[g/ ~ Ni/gi; ~,lN1l-5 Nll-5, i.e. only the first term of the summation is kept, where l represents the principal quantum number o f the lowest excitation level which can be ionized by photoelectric absorption. Therefore, eq. (36) in ref. [15] can be simplified to
6.72 X
lO-14~i4A]z(gj/gi)NRi,
C 1 ~ 1.46 X
lO-21X2Afi(gJgi)NRi,
C 2 ~- 1.12 ×
lO-24Xi4Aji(g//gi)NRirij,
C 3 ~ 1.04 X
IO-2~i3/NRII-5 ,
Co
(2)
where R i - Ni/N (AT is the number density of nonionized atoms), R i is the coefficient of atomic energy level distribution, i.e. N 1 : N 2 :N 3 ... = RIN:R2N: R3N .... In general conditions, R 1 ~ 1 (i.e. almost all neutral hydrogen atoms are in the ground state) and R 1 >> R 2 ~, R 3 >> .... so the emitting intensity of each Balmer line can be obtained according to eqs. (1) and (2), for instance, / ( H e) = YO{In(1 + X~) - 2 [1 -
arctg(Xa)/XO] ),
where
Y# = 7 X lO-2°NeX~lA42(g4/g2)(R2/R3), X# = 6.5 X lO-3xT/2A1]2r"42 42 ~s4/g21al/23-5/2
x vil/2(NvZx/ 2R3).
(3)
Intensities for other lines, I(Ha), I(H,r), I ( H 6) and /(He) can be calculated in the same way. But the calculation can be greatly simplified if one is only concerned with the intensity ratios of the same line series. This is due to the fact that the lines in the Balmer series have the same lower level (i.e. i = 2) and the same photoionized level (i.e. l = 3). Hence the parameters X and Y of each line can all be represented by X a and Y~ of the H~ line, the coefficients only depend on the atomic parameters (e.g. ~,/i, A/i, Fi/etc.). A calculation shows: X a = 4.60Xt3,
X~ = 0.470Xt3,
Xn = 0.289X#,
X e = 0.202X#,
Ya = 2.18Y#,
Y'r = 0.526r#,
Y~ = 0.308Yg,
}re = 0"196Ya"
The intensity ratio
(4)
l(Ha)[l(Ha) is given by
/ ( H a ) / I ( H a ) = 2.18 {In[1 + (4.60Xa)2 ] -
2 [1 -
arctg(4.6OXa)/4.6OXtj ] )
X {ln(1 + X~) - 2 [1 -
arctg(Xa)/Xal } - 1 .
Therefore, the intensity ratio
(5)
I(Ha)/l(Ha) only de. 409
Volume 109A, number 8
PHYSICS LETTERS
pends on one parameter Xa. Analogously we can write the o ther ratio s I(H~)/I(H#), I ( n 8)/I(n#) and I(He)[I(H#) which also depend only on X#. If the first intensity ratio I(H~)/I(H#) is just taken to be the median value 3.7 then we find Xt~ = 20.9 according to eq. (5). Inserting this value into the intensity ratio s I(H~)/I(H~), I ( H 8)/I(H~) and I(He)[I(Ha), the theoretical ratios o f the last column in table 1 are obtained; they are in good agreement with the observed values. Another advantage o f the Cerenkov mechanism is that only one parameter has to be fixed, i.e. the first intensity ratio I(Hc~)/I(Ha) is taken to be 3.7, orX 0 is taken to be 20.9. According to eq. (3), Xt3 is proportio nal to (N72x/R 2R 3), where N is the atomic number density, 7 is the characteristic energy o f relativistic electrons and R 1, R2 are the distribution coefficients o f atomic energy levels. Thus taking X~_.~ 20.9 is a confinement for the product ofN72x/R2R-3-3. The calculated results are in agreement with observations, which seems to be a strong support to the Cerenkov line emission mechanism, which must now be taken more seriously when considering the emission lines o f quasars. The abundant relativistic electrons in quasars not only produce continuum spectra from radio to X-ray (synchrotron radiation, inverse Compton scattering), but also produce Cerenkov emission lines. Just like those pointed out in ref. [15], these kind o f lines are very broad, asymmetrical in
410
17 June 1985
profile and different in red shifts. All these theoretical properties are in qualitative agreement with the observed characteristics o f quasar emission lines. Therefore it might open a new way to solving the quasar puzzles by adopting this new mechanism.
References [1] J.A. Baldwin, Astrophys. J. 201 (1975) 26. [2] D.W. Weedman, Ann. Rev. Astron. Astrophys. 15 (1977) 69. [3] D.E. Osterbrock, Astrophys. J. 215 (1977) 733. [4] R.C. Puetter, H.E. Smith, S.P. Wliiner and J.L. Pipher, Astrophys. J. 243 (1983) 345. [5] G. Neugebauer, J.B. Oke, E.E. Becklin and K. Mattews, Astrophys. J. 203 (1979) 79. [6] V.A. Ambartsumyan, ed., Theoretical astrophysics (Pergamon, Oxford, 1958) p. 424. [7] D.E. Osterbrock and R.A.R. Parker, Astrophys. J. 141 (1965) 892. [8] J.B. Oke and W.L.W. Sargent, Astrophys. J. 151 (1968) 807. [9] K.S. Anderson, Astrophys. J. 162 (1970) 743. [10] E.J. Wampler, Astrophys. J. 164 (1971) 1. [11] W.M. Adams and V. Petrosian, Astrophys. J. 192 (1974) 199. [12] R.A.R. Parker, Astrophys. J. 139 (1964) 208. [13] H. Netzer, Mort. Not. R. Astron. Soc. 171 (1975) 395. [14] K. Davidson and H. Netzer, Rev. Mod. Phys. 51 (1979) 715. [15] J.H. You, T. Kiang, F.H. Cheng and F.Z. Cheng, Acta Phy~ Sin. (1985), to be published.
PHYSICS LETTERS
17 June 1985
A N E W E X P L A N A T I O N OF T H E B A L M E R D E C R E M E N T IN Q U A S A R S T. K I A N G
Dunsink Observatory, Castleknock, Dublin 15, Ireland J.H. Y O U , F.Z. C H E N G and F.H. C H E N G
Center for Astrophysics, University of Science and TechnologFof China, Hefei, Anhui Province, People's Republic of China Received 31 January 1985; accepted for publication 19 April 1985
The very steep Balmer decrement, one of the most important puzzles in quasars, has been satisfactorily explained by use of a new theory of Cerenkov line emission.
The observed very steep Balmer decrement for low red shift quasars has been one o f the most important puzzles for many years. The observed intensity ratios o f the Balmer line series for QSOs are seriously in disagreement with those for ordinary nebulae. Generally the ratio I(Ha)[I(H~) is always far larger than that for nebulae and I(Ho)/I(H,r) is also larger [ 1 - 3 ] . It is very difficult to explain the above phenomena by classical radiative recombination theory. Table 1 gives the recent observations o f ten QSOs by Puetter et al. and Neugebauer et al. [4,5]. The second column shows the mean observed ratios o f the ten objects, the third column shows the median observed ratios *1, the ,1 An average between the observations of Puetter et al. and Neugebauer et al. has been done.
fourth one shows the Balmer decrement o f nebulae given according to the standard classical radiative recombination theory (it is well known to be accurately in agreement with the observations o f nebulae) [6]. Obviously the observed ratios are seriously in disagreement with those predicted by the classical theory. There have been some possible explanations [ 7 - 1 1 ], the most direct possibility is a wavelength dependent extinction caused by dust in QSOs (the absorption o f dust for visible light is much stronger for short wavelengths). This will produce larger I(Ha)/I(H#) and I(H#)/I(H.r), but the above explanation is facing a serious difficulty: if a reasonable correlation between dust extinction and the wavelength is given, none can interpret the ratios I(Ho~)/I(H#) and l(Hfj)[l(H,r) simultaneously; it has also failed in trying to explain
Table 1 Comparison between the ratios of the Balmer line series from observations, from the classical theory and from the Cerenkov line emission theory. Intensity ratios
I(Ho)[I(H#) I(H,~)]I(H#) I(Hs)/I(H #) I(He)/I(H#)
408
Observations mean
median
3.71 0.35 0.14 0.07
3.70 0.34 0.14 0.05
Values by classical theory
Values by Cerenkov line emission
2.8 0.50 0.29 0.18
(3.7) 0.36 0.15 0.07
0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 109A, number 8
the ratios by use of atomic collisional excitation [ 12], even if dust extinction was considered. Now most people suppose L~ photons in emitting clouds to be trapped by neutral hydrogen (trapping effect), which makes the number density of hydrogen atoms at 2nd energy level increased anomalously and makes the nebulae optically thick for photons of the Balmer line series. In this case, the evaluated values near the observational ratios can be obtained by adjusting a group of parameters properly [ 13,14]. But these models generally contain a number of adjustable parameters, the results are very model-dependent, even so, none could claim to have achieved more than a moderate success in matching the entire observed ratio-sequence from H a to H eIn this paper, we wish to report that the observed Balmer decrement is precisely reproduced in a theory of "Cerenkov line emission" initiated by You and Cheng [ 15]. The calculated ratios are shown in the last column of table 1. If the first intensity ratio I(Ha)/l(Ht3 ) is taken to be same as the median observed value (3.7), then the other three intensity ratios will be uniquely determined by the theory of Cerenkov line emission without introducing any other adjustable parameter. The only parameter used is the first intensity ratio I(Ha)/I(H#), which is taken to be the median observed value (3.7); there is no theoretical arbitrariness and this ratio I(Ha)/I(H#) becomes a believable and reasonable parameter. The basic calculating formula is eq. (41) in ref. [15] in the optically thick case, i.e. 1 = Y{ln(1 + X 2) - 2 [1 - arctg(X)/X] ) ,
17 June 1985
PHYSICS LETTERS
(1)
where Y = ~NeC 1/C3, X = ~ / C 2 U l i m = C3~/-C-~2Co'Y2, and CO, C 1, C 2 and'C 3 are given by eq. (36) of ref. [15]. In normal physical conditions, at least for the lowest energy levels of gaseous atoms, we always have N 1 ~, N 2 >>N 3 ... or N i >>N/, i.e. the particle numbers at lower energy level are far larger than those at higher levels, thus we have Ni/g i - N/[g/ ~ Ni/gi; ~,lN1l-5 Nll-5, i.e. only the first term of the summation is kept, where l represents the principal quantum number o f the lowest excitation level which can be ionized by photoelectric absorption. Therefore, eq. (36) in ref. [15] can be simplified to
6.72 X
lO-14~i4A]z(gj/gi)NRi,
C 1 ~ 1.46 X
lO-21X2Afi(gJgi)NRi,
C 2 ~- 1.12 ×
lO-24Xi4Aji(g//gi)NRirij,
C 3 ~ 1.04 X
IO-2~i3/NRII-5 ,
Co
(2)
where R i - Ni/N (AT is the number density of nonionized atoms), R i is the coefficient of atomic energy level distribution, i.e. N 1 : N 2 :N 3 ... = RIN:R2N: R3N .... In general conditions, R 1 ~ 1 (i.e. almost all neutral hydrogen atoms are in the ground state) and R 1 >> R 2 ~, R 3 >> .... so the emitting intensity of each Balmer line can be obtained according to eqs. (1) and (2), for instance, / ( H e) = YO{In(1 + X~) - 2 [1 -
arctg(Xa)/XO] ),
where
Y# = 7 X lO-2°NeX~lA42(g4/g2)(R2/R3), X# = 6.5 X lO-3xT/2A1]2r"42 42 ~s4/g21al/23-5/2
x vil/2(NvZx/ 2R3).
(3)
Intensities for other lines, I(Ha), I(H,r), I ( H 6) and /(He) can be calculated in the same way. But the calculation can be greatly simplified if one is only concerned with the intensity ratios of the same line series. This is due to the fact that the lines in the Balmer series have the same lower level (i.e. i = 2) and the same photoionized level (i.e. l = 3). Hence the parameters X and Y of each line can all be represented by X a and Y~ of the H~ line, the coefficients only depend on the atomic parameters (e.g. ~,/i, A/i, Fi/etc.). A calculation shows: X a = 4.60Xt3,
X~ = 0.470Xt3,
Xn = 0.289X#,
X e = 0.202X#,
Ya = 2.18Y#,
Y'r = 0.526r#,
Y~ = 0.308Yg,
}re = 0"196Ya"
The intensity ratio
(4)
l(Ha)[l(Ha) is given by
/ ( H a ) / I ( H a ) = 2.18 {In[1 + (4.60Xa)2 ] -
2 [1 -
arctg(4.6OXa)/4.6OXtj ] )
X {ln(1 + X~) - 2 [1 -
arctg(Xa)/Xal } - 1 .
Therefore, the intensity ratio
(5)
I(Ha)/l(Ha) only de. 409
Volume 109A, number 8
PHYSICS LETTERS
pends on one parameter Xa. Analogously we can write the o ther ratio s I(H~)/I(H#), I ( n 8)/I(n#) and I(He)[I(H#) which also depend only on X#. If the first intensity ratio I(H~)/I(H#) is just taken to be the median value 3.7 then we find Xt~ = 20.9 according to eq. (5). Inserting this value into the intensity ratio s I(H~)/I(H~), I ( H 8)/I(H~) and I(He)[I(Ha), the theoretical ratios o f the last column in table 1 are obtained; they are in good agreement with the observed values. Another advantage o f the Cerenkov mechanism is that only one parameter has to be fixed, i.e. the first intensity ratio I(Hc~)/I(Ha) is taken to be 3.7, orX 0 is taken to be 20.9. According to eq. (3), Xt3 is proportio nal to (N72x/R 2R 3), where N is the atomic number density, 7 is the characteristic energy o f relativistic electrons and R 1, R2 are the distribution coefficients o f atomic energy levels. Thus taking X~_.~ 20.9 is a confinement for the product ofN72x/R2R-3-3. The calculated results are in agreement with observations, which seems to be a strong support to the Cerenkov line emission mechanism, which must now be taken more seriously when considering the emission lines o f quasars. The abundant relativistic electrons in quasars not only produce continuum spectra from radio to X-ray (synchrotron radiation, inverse Compton scattering), but also produce Cerenkov emission lines. Just like those pointed out in ref. [15], these kind o f lines are very broad, asymmetrical in
410
17 June 1985
profile and different in red shifts. All these theoretical properties are in qualitative agreement with the observed characteristics o f quasar emission lines. Therefore it might open a new way to solving the quasar puzzles by adopting this new mechanism.
References [1] J.A. Baldwin, Astrophys. J. 201 (1975) 26. [2] D.W. Weedman, Ann. Rev. Astron. Astrophys. 15 (1977) 69. [3] D.E. Osterbrock, Astrophys. J. 215 (1977) 733. [4] R.C. Puetter, H.E. Smith, S.P. Wliiner and J.L. Pipher, Astrophys. J. 243 (1983) 345. [5] G. Neugebauer, J.B. Oke, E.E. Becklin and K. Mattews, Astrophys. J. 203 (1979) 79. [6] V.A. Ambartsumyan, ed., Theoretical astrophysics (Pergamon, Oxford, 1958) p. 424. [7] D.E. Osterbrock and R.A.R. Parker, Astrophys. J. 141 (1965) 892. [8] J.B. Oke and W.L.W. Sargent, Astrophys. J. 151 (1968) 807. [9] K.S. Anderson, Astrophys. J. 162 (1970) 743. [10] E.J. Wampler, Astrophys. J. 164 (1971) 1. [11] W.M. Adams and V. Petrosian, Astrophys. J. 192 (1974) 199. [12] R.A.R. Parker, Astrophys. J. 139 (1964) 208. [13] H. Netzer, Mort. Not. R. Astron. Soc. 171 (1975) 395. [14] K. Davidson and H. Netzer, Rev. Mod. Phys. 51 (1979) 715. [15] J.H. You, T. Kiang, F.H. Cheng and F.Z. Cheng, Acta Phy~ Sin. (1985), to be published.