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Oscillator strengths for SiH and SiH+ deduced from the solar spectrum
J. Quant.
Specrrosc.
Radiaf.
Transfer.
OSCILLATOR
Vol.
11, pp. 65-67.
Pergamon
Press
1971. Printed
in Great
Britain
STRENGTHS FOR SiH AND SiH+ DEDUCED FROM THE SOLAR SPECTRUM N. GREVESSE
lnstitut d’Astrophysique, Universite de Liege, 4200~Cointe-Ougree, Belgium and A. J. SAUVAL Observatoire Royal de Belgique, 1180-Bruxelies, Belgium (Received 2 July 1970)
Abstract-Recent identifications of SiH (A’A-X?II) and SiH+ (A’D-X’C+) in the solar photospheric spectrum have enabled us to derive absolute oscillator strengths for the (0,O) bands of these transitions:&(SiH) = 0.0033 andf,,(SiH+) = 0.0005. Our result for SiH is compared with other values.
I. INTRODUCTION IT HAS recently been shown that, without any doubt, absorption lines of SiH (transition A’A-X211; SAUVAL,(~)) and SiH+ (A’II-X1x+ ; GREVE~~E and SAUVAL(‘)) are present in the solar photospheric spectrum. Up to now, little information was available as far as the transition probabilities of these transitions were concerned. In fact, the only available measurement of a lifetime was that made by SMITH(~)for the A2A state of SiH. In this paper, the transition probabilities are deduced from the equivalent widths of the solar lines.
II. SOLAR
DATA
SAWAL has found that numerous lines of the (0, O)-band of the A2A-X211 transition of SiH are present in the solar photospheric spectrum and that the distribution of their equivalent widths (IV,) over the Qicdand Qidebranches (i = 1,2) shows a maximum near J = 14.5 of about W, = 2mA. Following the recent laboratory analysis of SiH+ by DOUGLAS and LUTZ,(~) GREVESYE and SAUVAL~‘) firmly established the presence of lines of the (0,O) and (0,l) bands of the A’ll-X1x+ transition in the solar photospheric spectrum. Maximum equivalent widths for the Q branch (which occur at J = 15), are of the order of 2.5 rnA for the (0,O) band and 1.3 A for the (0,l) band.
65
66
N. GREVESSEand
A. J. SAUVAL
III. COMPUTATION OF THE OSCILLATOR STRENGTHS With the help of programs computing line profiles on the basis of solar photospheric models, it is easy to derive values of the absolute oscillator strengths from the equivalent widths of the molecular lines in solar absorption. The total oscillator strength for a rotational line is defined as follows, (SCHADEE’~))
f&s”
&,
25” + 1 AJeJ,,
where fvr,,, is the band oscillator strength, the other quantities having their usual meaning. Ho&London factors have been taken from BENNETT.@) The computations have been made with different recent photospheric models (HOLWEGER,(‘)LAMBERT, @I GINGERICH and DE JAGER,(~)ELSTE,(loI GINGERICH~‘I) and the results depend only slightly () 25 per cent) upon the model used. We adopted the following values for the dissociation energies : 0: (SiH) = 3.06 eV (GAYDON”‘)) and 0: (SiH+) = 3.20 eV (DOUGLASand LUTZ(~)). Partition functions and dissociation constants have been computed following the method outlined by TATUM,“~) using the molecular constants of HERZBERG, LAGERQVISTand MA&ENZIE(‘~) for SiH, and of DOUGLASand LUTZ(~) for SiH+ . It has to be pointed out here that, where our values of the equilibrium constants agree with those of MORRISand WYLLER,(‘~)they are much smaller (a factor of 10) than VARDYA’S(~~) values. The solar abundance of silicon has been taken from LAMBERTand WARNER” : log N,, = 7.55 (in the usual scale where log N, = 12.OOj. With the help of the above mentioned data, we derive the following values of the absolute oscillator strengths : SiH (A’A-X’ll) SiH+ (A’ll-X1x+):
:
foe= 0.0025 ;
foe = 0.0005,
fOl= 0.0004. On the basis of the uncertainty of the physical conditions in the solar photosphere and of the possible observational errors our results could be in error by a factor of 2. IV. DISCUSSION This is the first determination of oscillator strengths for SiH+. In fact, SiH+ has only been analyzed very recently by DOUGLASand LUTZ(~) As far as SiH is concerned, SCHADEE(‘*)derived foe = 0.0024 from his measurements of the solar WA’s of SiH lines. Correcting Schadee’s value for the new values of the WA’s which are three times lower (II found foe= 0.0008. The discrepancy between than Schadee’s measurements, SAUVAL this value and our result woo = 0.0025) can be explained mainly by the use of recent photospheric models which are in better agreement with the observations of the continuous solar spectrum and by our use of more refined methods for deriving the oscillator strengths from solar Wn’s.
Oscillator strengths for SiH and SiH + deduced from the solar spectrum
67
SMITH(~) has measured the lifetime of the A2A state of SiH and he found z0 = (700 + 1OO)nsec. This corresponds to a total transition probability, A, = &A,,., z A,, = 1.43. lo6 set- ‘. As much of the intensity of this SiH transition is emitted in the (0,O) band, one can convert the total transition probability to an oscillator strength for the (0,O) band by assuming (because Franck-Condon factors or relative intensity measurements are not available) that all the intensity is emitted in the (0,O) band. This will lead to an upper limit for foO, but this result is believed to be rather near the exact value. With this assumption we obtain foO = 0.0037 +0.0006. Very recently, LAMBERT and MALLIA (19J have also deducedf,, from the solar equivalent widths of SiH lines: so0 = 0.0045. Their measurements, covering a rather small wavelength region, lead to WA’s(for the most intense lines) which are 1.67 times those found by SAUVAL.(‘) Because of the different criteria for line identifications adopted by these authors, it can be seen that Sauval’s WA’s probably represent lower limits, whilst Lambert and Mallia’s measurements could probably be considered as upper limits. By taking mean values of the equivalent widths we find j&, (L.M.) = 0.0034 and foO (this work) = 0.0033. These values, practically equal (they would be equal if the same photospheric model had been used), are in agreement with the result derived from SMITH’s(~’lifetime, foe = 0.0037. This agreement between “solar” and “laboratory” values is very encouraging. As far as molecules are concerned, the solar photosphere is an excellent laboratory source. Accurate values of band oscillator strengths can be easily deduced from the study of the molecular lines present in the solar photospheric spectrum. Acknowledgements-We would like to thank Drs. A. E. DCXJGLA~and B. L. LUTZ, 0. GINGERICH, D. L. LAMBERT and E. A. MALLIA for providing us with their results in advance of publication. Our thanks are also due to Dr. F. REMY for very helpful discussions, Note added in proof-D. ALBRUT~N and R. N. ZARE have recently computed the Franck-Condon factors for SiH. Their results show that the approximation we used to derive foe from Smith’s lifetime measurement is perfectly justified. We are most grateful to Drs. D. ALBRITTENand R. N. ZARE for their kind cooperation.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
A. J. SAUVAL, Sol. Phys. 10,319 (1969). N. GREVESSEand A. J. SAUVAL, Astron. Astrophys. (in press) W. H. SMITH, .I. Chem. Phys. 51,520 (1969). A. E. DOUGLASand B. L. LUTZ, Can. J. Phys. 48,247 (1970). A. SCHADEE,JQSRT7, 169 (1967). R. J. M. BENNETT, Mon. Not. R. astr. Sot. 147, 35 (1970). H. HOLWEGER,Z. Astrophys. 65,365 (1967). D. L. LAMBERT,Mon. Not. R. ustr. Sot. 138, 143 (1968). 0. GINGERICHand C. DE JAGER, Sol. Phys. 3,5 (1968). G. H. E. ELSTE, Sol. Phys. 3, 106 (1968). 0. GINGERICH,private communication (1969). A. G. GAYDON, Dissociation Energies and Spectra of Diatomic Molecules, Chapman J. B. TATUM, Publ. Dom. astrophys. Ohs. XIII, 1 (1966). G. HERZBERG,A. LAGERQVISTand B. J. MACKENZIE, Can. J. Phys. 47, 1889 (1969). S. MORRISand A. A. WYLLER, Astrophys. J. 150,877 (1967). M. S. VARDYA, Mon. Not. R. astr. Sot. 134, 347 (1966). D. L. LAMBERTand B. WARNER, Mon. Not. R. astr. Sot. 138,213 (1968). A. SCHADEE,BUN. astr. Inst. Neth. 17, 31 1 (1964). D. L. LAMBERTand E. A. MALLIA, Mon. Not. R. Astr. Sot. 148,3 I3 (1970).
Hall, London
(1968).
Specrrosc.
Radiaf.
Transfer.
OSCILLATOR
Vol.
11, pp. 65-67.
Pergamon
Press
1971. Printed
in Great
Britain
STRENGTHS FOR SiH AND SiH+ DEDUCED FROM THE SOLAR SPECTRUM N. GREVESSE
lnstitut d’Astrophysique, Universite de Liege, 4200~Cointe-Ougree, Belgium and A. J. SAUVAL Observatoire Royal de Belgique, 1180-Bruxelies, Belgium (Received 2 July 1970)
Abstract-Recent identifications of SiH (A’A-X?II) and SiH+ (A’D-X’C+) in the solar photospheric spectrum have enabled us to derive absolute oscillator strengths for the (0,O) bands of these transitions:&(SiH) = 0.0033 andf,,(SiH+) = 0.0005. Our result for SiH is compared with other values.
I. INTRODUCTION IT HAS recently been shown that, without any doubt, absorption lines of SiH (transition A’A-X211; SAUVAL,(~)) and SiH+ (A’II-X1x+ ; GREVE~~E and SAUVAL(‘)) are present in the solar photospheric spectrum. Up to now, little information was available as far as the transition probabilities of these transitions were concerned. In fact, the only available measurement of a lifetime was that made by SMITH(~)for the A2A state of SiH. In this paper, the transition probabilities are deduced from the equivalent widths of the solar lines.
II. SOLAR
DATA
SAWAL has found that numerous lines of the (0, O)-band of the A2A-X211 transition of SiH are present in the solar photospheric spectrum and that the distribution of their equivalent widths (IV,) over the Qicdand Qidebranches (i = 1,2) shows a maximum near J = 14.5 of about W, = 2mA. Following the recent laboratory analysis of SiH+ by DOUGLAS and LUTZ,(~) GREVESYE and SAUVAL~‘) firmly established the presence of lines of the (0,O) and (0,l) bands of the A’ll-X1x+ transition in the solar photospheric spectrum. Maximum equivalent widths for the Q branch (which occur at J = 15), are of the order of 2.5 rnA for the (0,O) band and 1.3 A for the (0,l) band.
65
66
N. GREVESSEand
A. J. SAUVAL
III. COMPUTATION OF THE OSCILLATOR STRENGTHS With the help of programs computing line profiles on the basis of solar photospheric models, it is easy to derive values of the absolute oscillator strengths from the equivalent widths of the molecular lines in solar absorption. The total oscillator strength for a rotational line is defined as follows, (SCHADEE’~))
f&s”
&,
25” + 1 AJeJ,,
where fvr,,, is the band oscillator strength, the other quantities having their usual meaning. Ho&London factors have been taken from BENNETT.@) The computations have been made with different recent photospheric models (HOLWEGER,(‘)LAMBERT, @I GINGERICH and DE JAGER,(~)ELSTE,(loI GINGERICH~‘I) and the results depend only slightly () 25 per cent) upon the model used. We adopted the following values for the dissociation energies : 0: (SiH) = 3.06 eV (GAYDON”‘)) and 0: (SiH+) = 3.20 eV (DOUGLASand LUTZ(~)). Partition functions and dissociation constants have been computed following the method outlined by TATUM,“~) using the molecular constants of HERZBERG, LAGERQVISTand MA&ENZIE(‘~) for SiH, and of DOUGLASand LUTZ(~) for SiH+ . It has to be pointed out here that, where our values of the equilibrium constants agree with those of MORRISand WYLLER,(‘~)they are much smaller (a factor of 10) than VARDYA’S(~~) values. The solar abundance of silicon has been taken from LAMBERTand WARNER” : log N,, = 7.55 (in the usual scale where log N, = 12.OOj. With the help of the above mentioned data, we derive the following values of the absolute oscillator strengths : SiH (A’A-X’ll) SiH+ (A’ll-X1x+):
:
foe= 0.0025 ;
foe = 0.0005,
fOl= 0.0004. On the basis of the uncertainty of the physical conditions in the solar photosphere and of the possible observational errors our results could be in error by a factor of 2. IV. DISCUSSION This is the first determination of oscillator strengths for SiH+. In fact, SiH+ has only been analyzed very recently by DOUGLASand LUTZ(~) As far as SiH is concerned, SCHADEE(‘*)derived foe = 0.0024 from his measurements of the solar WA’s of SiH lines. Correcting Schadee’s value for the new values of the WA’s which are three times lower (II found foe= 0.0008. The discrepancy between than Schadee’s measurements, SAUVAL this value and our result woo = 0.0025) can be explained mainly by the use of recent photospheric models which are in better agreement with the observations of the continuous solar spectrum and by our use of more refined methods for deriving the oscillator strengths from solar Wn’s.
Oscillator strengths for SiH and SiH + deduced from the solar spectrum
67
SMITH(~) has measured the lifetime of the A2A state of SiH and he found z0 = (700 + 1OO)nsec. This corresponds to a total transition probability, A, = &A,,., z A,, = 1.43. lo6 set- ‘. As much of the intensity of this SiH transition is emitted in the (0,O) band, one can convert the total transition probability to an oscillator strength for the (0,O) band by assuming (because Franck-Condon factors or relative intensity measurements are not available) that all the intensity is emitted in the (0,O) band. This will lead to an upper limit for foO, but this result is believed to be rather near the exact value. With this assumption we obtain foO = 0.0037 +0.0006. Very recently, LAMBERT and MALLIA (19J have also deducedf,, from the solar equivalent widths of SiH lines: so0 = 0.0045. Their measurements, covering a rather small wavelength region, lead to WA’s(for the most intense lines) which are 1.67 times those found by SAUVAL.(‘) Because of the different criteria for line identifications adopted by these authors, it can be seen that Sauval’s WA’s probably represent lower limits, whilst Lambert and Mallia’s measurements could probably be considered as upper limits. By taking mean values of the equivalent widths we find j&, (L.M.) = 0.0034 and foO (this work) = 0.0033. These values, practically equal (they would be equal if the same photospheric model had been used), are in agreement with the result derived from SMITH’s(~’lifetime, foe = 0.0037. This agreement between “solar” and “laboratory” values is very encouraging. As far as molecules are concerned, the solar photosphere is an excellent laboratory source. Accurate values of band oscillator strengths can be easily deduced from the study of the molecular lines present in the solar photospheric spectrum. Acknowledgements-We would like to thank Drs. A. E. DCXJGLA~and B. L. LUTZ, 0. GINGERICH, D. L. LAMBERT and E. A. MALLIA for providing us with their results in advance of publication. Our thanks are also due to Dr. F. REMY for very helpful discussions, Note added in proof-D. ALBRUT~N and R. N. ZARE have recently computed the Franck-Condon factors for SiH. Their results show that the approximation we used to derive foe from Smith’s lifetime measurement is perfectly justified. We are most grateful to Drs. D. ALBRITTENand R. N. ZARE for their kind cooperation.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
A. J. SAUVAL, Sol. Phys. 10,319 (1969). N. GREVESSEand A. J. SAUVAL, Astron. Astrophys. (in press) W. H. SMITH, .I. Chem. Phys. 51,520 (1969). A. E. DOUGLASand B. L. LUTZ, Can. J. Phys. 48,247 (1970). A. SCHADEE,JQSRT7, 169 (1967). R. J. M. BENNETT, Mon. Not. R. astr. Sot. 147, 35 (1970). H. HOLWEGER,Z. Astrophys. 65,365 (1967). D. L. LAMBERT,Mon. Not. R. ustr. Sot. 138, 143 (1968). 0. GINGERICHand C. DE JAGER, Sol. Phys. 3,5 (1968). G. H. E. ELSTE, Sol. Phys. 3, 106 (1968). 0. GINGERICH,private communication (1969). A. G. GAYDON, Dissociation Energies and Spectra of Diatomic Molecules, Chapman J. B. TATUM, Publ. Dom. astrophys. Ohs. XIII, 1 (1966). G. HERZBERG,A. LAGERQVISTand B. J. MACKENZIE, Can. J. Phys. 47, 1889 (1969). S. MORRISand A. A. WYLLER, Astrophys. J. 150,877 (1967). M. S. VARDYA, Mon. Not. R. astr. Sot. 134, 347 (1966). D. L. LAMBERTand B. WARNER, Mon. Not. R. astr. Sot. 138,213 (1968). A. SCHADEE,BUN. astr. Inst. Neth. 17, 31 1 (1964). D. L. LAMBERTand E. A. MALLIA, Mon. Not. R. Astr. Sot. 148,3 I3 (1970).
Hall, London
(1968).