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Can lines of C−2 be observed in carbon stars?
CHEMICAL
VoIume 73, number 3
PHYSICS
1 August IS80
LETTERS
COMMENT CAN LWES
OF C,
M.S. VARDYA Tata Znstrhrte
BE OBSERVED
and K S. KRISHNA
of Fundamental
Recerved 20 March 1980.
Resecrch,
IN CARBON SWAMY Bombay
m final lorm 5 t&y
400
tn the tntrared spectra of carbon stars. A pos~twe Identtficatron
Negative tons are tmportant sources of opacity tn cool stars of solar chemtcal composttron and of pecubar composrtton, the opactty artsmg from bound-free and free-free contmuum transrttons [f-3]. Here we discuss brrefly the contribution from bound-bound transltlons m CF. Molecular equrhbrmm cdlculatrons have shown that the CT [on should be abundant m carbon stars [2]. and may contrtbute srgmficantly to the opactty Spectral features drtsmg from CT may be detectable_ Laboratory spcctroscoptc data are not dvatlable on thus ton. but Zettz and Peyerrmhoff [4] have made a theorettcal annlysrs of the bound electronic states of the C’y _They predtct that the value of the electronic energy, T,, for the ‘TI, state of thrs ton ts 0 40 eV above the ground level 72: The transtttons between these two electronrc states should gave lutes m the wavelength range around 3 urn. The opttwl depth at the centre of the line IS given by [5] r(Ccg) = aolv(CF),
(1)
where a0 ts the absorptton cross section (in cm?) at the centre of the lute and IV IS the column number density (m cm-?) of the CT ton For a Dopplerltne at a temperature
T, ‘x0 IS gtven
00.5. Indro
1980
A ‘fl,-Y 2~i lmes of CT should bc observable laboratory spectkoptc data on thts ton
broadened
STARS?
depth
awats
IS
7 = 3 x IO-
W(C~).
(3)
Takmg the radius of a carbon star as 5 X lot2 cm [7] and approxrmatmg rt for the column length, the optrcal depth to be srgntficant requtres a number density of C, of 10’ cmw3, whrch may be reahzed m carbon rich stars [2]. The equivalent line width is given by the relatton cg1 AkV(A) = (~e2/nIe~~)hZ(E.tm)fN(CZ) = 8 x IO-‘%V(CY)
(4)
The expected number of C, III carbon rich stars could, therefore, grve nse to an observable equivalent wrdth. The spectra of stars tn the 3 m region 19-l I] contam several untdenttfied features. A poslttve lute identification of thts ton in the spectra of carbon stars wtlf requtre prectse laboratory wavelengths. The ldentrficatton of a negatrve ton could be the first of thrs kind m the annals of astrophysical spectra and this note wtll have served tts purpose rfit encourages laboratory spectroscoprc studies of CT.
by [S]
References
cko =
(dw/lll,c)fJAv(J.
au,
=
[l]
(l+yC)(x?-/M)‘;
.
where f 1s the osctilator strength of the transttron. Takmg T 2 3000 K. and / a 0 00 1 [4.6]. the optical
(2)
LM Branscomb and B E.J Pagel, Monthly Notices Roy Asuon Sot. 118 (1958) 258. [2] hI S Vardya, Mem Roy. Astron Sot 71 (1967) 249. 131 M S. Vardya, Ann. Rev. Astron. Astrophys. 8 (1970) 87.
Volume 73, number 3
CHEMICAL
[4 ] M. Zeltz and S D Peyerlmhoff, Chem Phys. Letters 64 (1979) 243 [S] L H. AUer, The atmospheres of sun and stars (The Ronald Press, New York, 1963) p. 322 [6] A Schadce, I Quant. Spectry. Racliahve Transfer 7 (1967) 169 (71 C.W Allen, Astrophysical quantities (The Athlone Press, London, 1973) p. 206.
PHYSICS
LETTERS
lAogust
[S] A. Schadee, Bull. Astron. Inst Neth. 17 (1964) 3il191 R.I. Thomson, H.W. Schnopper. RL Mitchell and RL. Johnson, Astrophys. J. 158 (1969) L 5% [lOI ST. Ridgeway, D-F. Carbon and 0-N-B. Hall. AzZro@YSJ. 225 (19’18) 138. I11 J R. Beer, R-B. Hut&son, RH. Norton and D-L. Lambert, Astrophys. J. 172 (1972) 89.
ERRATA A N. Dharamsi and J. Tulip, A CNDO/S investigation of contact CT complexes of some organic molecules with O,, Chem. Phys. Letters 71 (1980) 224. On page 226, second column, penultimate paragraph: “For example in the resting model 1 the transitions...” should read “For example m the resting model 2 the transitions...“.
G. MaIh, Spherical gaussian basis sets in relativrstic quantum chemistry, Chem. Phys. Letters 68 (1979) 529. In eqs. (5) and (6) the factor 2 in the denominator should be m the numerator. Furthermore, in eq. (6) the argument (aKKp+ crKs+ aKsQ+ tienf)-l of the first 2FI shouId be (Q + cllKq* aKeS+ a,~r)-l.
C. Malli and J. Oreg, Ab initio relativistic self-consistent-field (RSCF) wavefunctions for the diatomics LIZ and Bez, Chem. Phys. Letters 69 (1980) 3 13. On p. 314 the paragraph “It can be seen _._is fairly slgmficant” is misleading and should be replaced by “It is not possible to predict the relativistic corrections to orbital energies (E), etc. from such preliminary RSCF calculations with minimal atomic spinor basis set”.
VoIume 73, number 3
PHYSICS
1 August IS80
LETTERS
COMMENT CAN LWES
OF C,
M.S. VARDYA Tata Znstrhrte
BE OBSERVED
and K S. KRISHNA
of Fundamental
Recerved 20 March 1980.
Resecrch,
IN CARBON SWAMY Bombay
m final lorm 5 t&y
400
tn the tntrared spectra of carbon stars. A pos~twe Identtficatron
Negative tons are tmportant sources of opacity tn cool stars of solar chemtcal composttron and of pecubar composrtton, the opactty artsmg from bound-free and free-free contmuum transrttons [f-3]. Here we discuss brrefly the contribution from bound-bound transltlons m CF. Molecular equrhbrmm cdlculatrons have shown that the CT [on should be abundant m carbon stars [2]. and may contrtbute srgmficantly to the opactty Spectral features drtsmg from CT may be detectable_ Laboratory spcctroscoptc data are not dvatlable on thus ton. but Zettz and Peyerrmhoff [4] have made a theorettcal annlysrs of the bound electronic states of the C’y _They predtct that the value of the electronic energy, T,, for the ‘TI, state of thrs ton ts 0 40 eV above the ground level 72: The transtttons between these two electronrc states should gave lutes m the wavelength range around 3 urn. The opttwl depth at the centre of the line IS given by [5] r(Ccg) = aolv(CF),
(1)
where a0 ts the absorptton cross section (in cm?) at the centre of the lute and IV IS the column number density (m cm-?) of the CT ton For a Dopplerltne at a temperature
T, ‘x0 IS gtven
00.5. Indro
1980
A ‘fl,-Y 2~i lmes of CT should bc observable laboratory spectkoptc data on thts ton
broadened
STARS?
depth
awats
IS
7 = 3 x IO-
W(C~).
(3)
Takmg the radius of a carbon star as 5 X lot2 cm [7] and approxrmatmg rt for the column length, the optrcal depth to be srgntficant requtres a number density of C, of 10’ cmw3, whrch may be reahzed m carbon rich stars [2]. The equivalent line width is given by the relatton cg1 AkV(A) = (~e2/nIe~~)hZ(E.tm)fN(CZ) = 8 x IO-‘%V(CY)
(4)
The expected number of C, III carbon rich stars could, therefore, grve nse to an observable equivalent wrdth. The spectra of stars tn the 3 m region 19-l I] contam several untdenttfied features. A poslttve lute identification of thts ton in the spectra of carbon stars wtlf requtre prectse laboratory wavelengths. The ldentrficatton of a negatrve ton could be the first of thrs kind m the annals of astrophysical spectra and this note wtll have served tts purpose rfit encourages laboratory spectroscoprc studies of CT.
by [S]
References
cko =
(dw/lll,c)fJAv(J.
au,
=
[l]
(l+yC)(x?-/M)‘;
.
where f 1s the osctilator strength of the transttron. Takmg T 2 3000 K. and / a 0 00 1 [4.6]. the optical
(2)
LM Branscomb and B E.J Pagel, Monthly Notices Roy Asuon Sot. 118 (1958) 258. [2] hI S Vardya, Mem Roy. Astron Sot 71 (1967) 249. 131 M S. Vardya, Ann. Rev. Astron. Astrophys. 8 (1970) 87.
Volume 73, number 3
CHEMICAL
[4 ] M. Zeltz and S D Peyerlmhoff, Chem Phys. Letters 64 (1979) 243 [S] L H. AUer, The atmospheres of sun and stars (The Ronald Press, New York, 1963) p. 322 [6] A Schadce, I Quant. Spectry. Racliahve Transfer 7 (1967) 169 (71 C.W Allen, Astrophysical quantities (The Athlone Press, London, 1973) p. 206.
PHYSICS
LETTERS
lAogust
[S] A. Schadee, Bull. Astron. Inst Neth. 17 (1964) 3il191 R.I. Thomson, H.W. Schnopper. RL Mitchell and RL. Johnson, Astrophys. J. 158 (1969) L 5% [lOI ST. Ridgeway, D-F. Carbon and 0-N-B. Hall. AzZro@YSJ. 225 (19’18) 138. I11 J R. Beer, R-B. Hut&son, RH. Norton and D-L. Lambert, Astrophys. J. 172 (1972) 89.
ERRATA A N. Dharamsi and J. Tulip, A CNDO/S investigation of contact CT complexes of some organic molecules with O,, Chem. Phys. Letters 71 (1980) 224. On page 226, second column, penultimate paragraph: “For example in the resting model 1 the transitions...” should read “For example m the resting model 2 the transitions...“.
G. MaIh, Spherical gaussian basis sets in relativrstic quantum chemistry, Chem. Phys. Letters 68 (1979) 529. In eqs. (5) and (6) the factor 2 in the denominator should be m the numerator. Furthermore, in eq. (6) the argument (aKKp+ crKs+ aKsQ+ tienf)-l of the first 2FI shouId be (Q + cllKq* aKeS+ a,~r)-l.
C. Malli and J. Oreg, Ab initio relativistic self-consistent-field (RSCF) wavefunctions for the diatomics LIZ and Bez, Chem. Phys. Letters 69 (1980) 3 13. On p. 314 the paragraph “It can be seen _._is fairly slgmficant” is misleading and should be replaced by “It is not possible to predict the relativistic corrections to orbital energies (E), etc. from such preliminary RSCF calculations with minimal atomic spinor basis set”.