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TiO line lists calculated by Bertrand.

'''Transitions in BP's line list:'''

''' {{attachment:BP_transitions.png}} '''

'''Comment on "lambda doubling" (BP, 28 Jan 2009):'''

Some transitions are affected by Lambda-doubling. In that case there are 2 sublevels that give rise to transitions, and if the separation is large enough, they appear in the list as 2 lines with the same parameters except for the parity of the upper and lower level, and a slightly different wavenumber. The degeneracy of these sublevels is 2*J+1. When the Lambda-doubling is too small there are 2 lines with exactly the same data (except the parities). One way to compact the list is to merge these lines and double the gf-value 2*(2*J+1)*f.

For some transitions Lambda-doubling does not exist (if Lambda=0, i.e if one of the states is a sigma state).		 ~+'''TiO data'''+~

<<TableOfContents>>

== Next steps ==


 * Extract TiO line lists for use with e.g. Synth
 * Calculate synthetic spectra
 * Compare with observed spectra of M dwarfs and giants

Done:
 * Convert ascii TiO line lists to VALD binary format and kompress - 2011-02-15, see {{{ /vald-archive/source-lists/Molecules/TiO/Plez/tio_plez2vald.format }}}, both for calculated and observed wavelength files (with flag which has to be changed manually)

== Summary of files ==

'''Calculated line lists''':
{{{
/vald-archive/source-lists/Molecules/TiO/Plez/
}}}
Original lists (Plez 2008/2009): {{{ linelist??_all.dat.gz }}}

Lists processed for non-resolved lambda doubling (Heiter 2009):
{{{ linelist??_all_nodoubling.dat.gz }}}

Merging code: {{{ tio_plez_rm_doubling.pro }}}

'''Observed line lists''':
{{{
/vald-archive/source-lists/Molecules/TiO/Phillips/
}}}

Original list: {{{ TiO-Phillips-OBS.dat }}}

Converted list (ascii format, same format as calculated lists): {{{ linelist48-TiO-Phillips-OBS-vald.asc }}}

Conversion code: {{{ tio_phillips_to_vald_ascii.f }}}

File with O-C wavelength differences: {{{ TiO-Phillips-O-C.dat }}}

[[attachment:plot_O-C.gp.txt|Gnuplot input file to plot O-C]]

== Calculated TiO data from B. Plez ==
TiO line lists were calculated by Bertrand on 29 May 2008 with air wavelength, gf, energies for lower and upper levels, radiative damping constant, transition id and quantum numbers. In an update on 10 June 2009, the phi system was added (and the radiative damping constants for the delta system were changed).

'''Transitions:'''

{{attachment:BP_transitions.png|transitions table|width=700}}

Vibrational quantum numbers from 0 to 15, rotational quantum numbers from 1 to 200.

The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wavelengths) by Ulrike (2009-02-06, 2009-06-30), see [[TiO/LambdaDoubling|page on lambda doubling]].

In the calculated lists, parity is given by the syml and symu quantum numbers, which can be 1 or -1.
In the merged lists, syml and symu are set to 0 for the merged lines.

For gamma prime, delta, epsilon and E-B, lambda doubling is resolved (transitions involving E3-Pi, B3-Pi, and b1-Pi states), therefore there are few merged lines. For the phi transitions, lambda doubling does not exist (involves a Sigma state). For the remaining transitions (alpha, beta, gamma, a-f), lambda doubling is not resolved (therefore, all lines are merged).


'''Number of lines:'''

||Isotope ||N,,merg,,||N,,orig,,||
||46 || 8333340 ||11280189 ||
||47 || 8334680 ||11281575 ||
||48 || 8335639 ||11282895 ||
||49 || 8336542 ||11284157 ||
||50 || 8337372 ||11285088 ||
||total ||41677573 ||56413904 ||

N,,orig,, ... original lists<<BR>>
N,,merg,, ... non-resolved lambda-doubled lines merged



== Observed wavenumbers ==

A line list with observed wavenumbers from Phillips has been provided by Bertrand Plez (priv. comm. 17 Sep 2008, 14 May 2009). Reference: Davis et al. 1986, ApJ 309, 449.

It contains 35584 lines in the alpha, beta, gamma, gamma prime systems
with range:
||wavenumber(cm^-1^) ||||wavelength(Å) ||
|| || vacuum || air ||
||20997.64 ||4762.440 || 4761.109 ||
||11383.24 ||8784.845 || 8782.433 ||

Isotope: ^48^Ti (see Davis et al. 1986, IV.a p. 452)

The list has been converted to an ascii format where the observed wave numbers have been converted to air wavelengths and all other line data needed for a VALD line list have been taken from the calculated list (isotope 48, merged) by Plez (see above), by Ulrike, 2009-05-22.

The list has been sorted by wavelength after running the conversion code.

Number of lines and wavelength ranges for converted list:
|| System || N |||| Air wavelength range [Å] ||
|| A || 8761 || 4761 || 6277 ||
|| B || 826 || 5597 || 5740 ||
|| G || 21071 || 6294 || 8783 ||
|| H || 5254 || 5847 || 6891 ||
|| Total || 35912 |||| ||

Explanation for different numbers of lines in original and converted list:
 * 157 lines in systems other than gamma prime are not in the calculated list (all with J,,low,,<=4).
 * In the alpha and gamma systems, there are five "double" lines with same quantum numbers and branch names but slightly different wavenumbers. The wavenumbers for these have been averaged for the converted list. There are 18 double lines with exactly the same parameters. The duplicates have been removed for these.
 * There are 137 gamma prime P11/Q11/R11 lines, which are not in calculated list and have been discarded.
 * 290 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list.
 * There is a double entry for gamma prime 0-1 J,,low,,=7 R1D.
 * For 20 lines in the gamma prime P1,Q1,P2,Q2,R2 lists, lambda doubling is not resolved in the calculated list. The observed wavenumber differences are very small for these lines (<=0.05 cm-1, >0 only for four lines), therefore they have been averaged.
 * The double line gamma prime 0-1 J,,low,,=1 R2 is not in the calculated list.
 * P3,Q3,R3 lines in the gamma prime system are "double", because of resolved lambda doubling in the calculated list (+958 lines).
 * Totals: -630 +958


=== Observed lines in beta system ===

||v-v || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing ||
|| || || || || ||
||0-0 || P || 4 || 99 || 94 ||
||1-1 || P || 2 || 100 || 66,88,91,92,93,95 ||
||2-2 || P || 2 || 90 || 8,10,12,14,76,81,83 ||
|| || || || || ||
||0-0 || Q || 2 || 100 || 4 ||
||1-1 || Q || 1 || 100 || 2,4,96 ||
||2-2 || Q || 3 || 100 || 7,78,82,83,84,89,90,91 ||
|| || || || || ||
||0-0 || R || 2 || 100 || ||
||1-1 || R || 2 || 98 || 7 ||
||2-2 || R || 2 || 92 || 5,26,42,62,64,70,74,75,84||

=== Observed lines in gamma prime system ===

observed lines in '''gamma prime system''', '''P1,Q1,R1''' branches (C/D pairs for each v-v and J,,low,,), J,,low,, values:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing C+D || J,,low,, missing C || J,,low,, missing D ||
|| || || || || || || ||
|| 0-0 || P1 || 3 || 131 || || 3,4,5,6,13,23 || 29,104,130,131 ||
|| 1-0 || P1 || 2 || 107 || 98 || 21,77 || 15,63,103,107 ||
|| 0-1 || P1 || 2 || 145 || 89,93,109,110,120,123 || 2,10,14,28,29,63,104, 126,131,135,138,139, 140,144,145 || 23,62,68,71,72,77,84,98, 99,111,125,129,130,136 ||
|| || || || || || || ||
|| 0-0 || Q1 || 1 || 141 || 2 || 1,12,119,138,139,140,141 || 4,7,118 ||
|| 1-0 || Q1 || 1 || 120 || || 1,104,105,112,114,118 || ||
|| 0-1 || Q1 || 2 || 144 || 94,138 || 11,104,107,114,125,127, 128,129,130,132,133,143,144 || 8,77,100,102,122,124 ||
|| || || || || || || ||
|| 0-0 || R1 || 1 || 122 || 96 || 5,6,19,64,87 || 1,2,76,83,84,90,94,100, 107,>=110 ||
|| 1-0 || R1 || 1 || 135 || 126 || 28,43,78,82,95 || 116,119,121,128,131 ||
|| 0-1 || R1 || 1 || 150 || 119,122,124,148 || 22,58,78,87,100,105,106, 108,111,114,115,130, 137,>=144 || 5,38,39,53,81,103,116, 117,121,125,128,141 (7 double)||

observed lines in '''gamma prime system''', '''P1,Q1,R1''' branches, wavenumber differences between C and D lines:

{{attachment:TiO-Phillips-OBS-H-P1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R1CD-wn.png}}


observed lines in '''gamma prime system''', '''P2,Q2,R2''' branches (C/D pairs for each v-v and J,,low,,), J,,low,, values:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing C+D || J,,low,, missing C || J,,low,, missing D ||
|| || || || || || || || || ||
|| 0-0 || P2 ||11 || 106 || 16 || || 51, >=85 ||
|| 1-0 || P2 || 3 || 88 || || 3,4,6,15,34,35 || 5,16,82,88 ||
|| 0-1 || P2 || 5 || 90 || 7,9,13,16,85 || 60,67 || 69,71,74,76, >=84 ||
|| || || || || || || || || ||
|| 0-0 || Q2 || 7 || 107 || 28 || || >=84 ||
|| 1-0 || Q2 || 2 || 91 || || 90 || <=9, 35,74,91 ||
|| 0-1 || Q2 || 4 || 85 || 8,19,75,82,84 || 78 || 72,76,79,80,83,85 ||
|| || || || || || || || || ||
|| 0-0 || R2 ||11 || 106 || 19,27,32,83,96,97 || || 48,80, >=82 ||
|| 1-0 || R2 || 4 || 90 || || 18,36,81 || 4,5,6,8,22,25,37,41,50,61,75,89,90 ||
|| 0-1 || R2 || 1 || 91 || 88 || 18,20,67,76 || 44,48,82,83, >=85 ||

observed lines in '''gamma prime system''', '''P2,Q2,R2''' branches, wavenumber differences between C and D lines:


{{attachment:TiO-Phillips-OBS-H-P2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R2CD-wn.png}}

||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || wn(C)-wn(D) = delta ||
|| || || || || ||
|| 0-0 || P2 || 11 || 45 || = 0 ||
|| || || 46 || 84 || < 0 ||
|| 1-0 || P2 || 7 || 12 || |delta| < 0.07 ||
|| || || 13 || 42 || > 0 ||
|| || || 43 || 51 || |delta| < 0.07 ||
|| || || 52 || 87 || < 0 ||
|| 0-1 || P2 || 5 || 44 || = 0 (39: -0.81)||
|| || || 45 || 83 || < 0 ||
|| || || || || ||
|| 0-0 || Q2 || 7 || 44 || = 0 ||
|| || || 45 || 83 || < 0 ||
|| 1-0 || Q2 || 10 || 37 || > 0 ||
|| || || 38 || 50 || |delta| < 0.07 ||
|| || || 51 || 89 || < 0 ||
|| 0-1 || Q2 || 4 || 43 || = 0 ||
|| || || 44 || 81 || < 0 ||
|| || || || || ||
|| 0-0 || R2 || 11 || 45 || = 0 (36: +0.19)||
|| || || 46 || 81 || < 0 ||
|| 1-0 || R2 || 13 || 44 || > 0 ||
|| || || 59 || 88 || < 0 ||
|| 0-1 || R2 || 1 || 42 || = 0 ||
|| || || 43 || 84 || < 0 ||


observed lines in '''gamma prime system''', '''P3,Q3,R3''' branches:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing ||
|| || || || || ||
||0-0 || P3 || 4 || 121 || 10,14,19,31,68||
||1-0 || P3 || 7 || 95 || 63,89,93||
||0-1 || P3 || 4 || 103 || 7,19,20,52,79,82,93,97||
|| || || || || ||
||0-0 || Q3 || 11 || 130 || ||
||1-0 || Q3 || 4 || 109 || 5,10,14,17,19||
||0-1 || Q3 || 6 || 112 || 10,25,54,87,94,102,104,110||
|| || || || || ||
||0-0 || R3 || 11 || 139 || 21,25,30,65,77,118,119,123,124,134,138||
||1-0 || R3 || 5 || 124 || 99,100,103,119,122||
||0-1 || R3 || 3 || 127 || 5,14,20,70,94,95,96,98,100,113,123||

== Comparison of observed and calculated wavelengths ==

Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

O-C wavelength differences for each system:

{{attachment:O-C-all.png}}
{{attachment:O-C-A.png}}
{{attachment:O-C-B.png}}
{{attachment:O-C-G0.png}}
{{attachment:O-C-G1.png}}
{{attachment:O-C-G2.png}}
{{attachment:O-C-G3.png}}
{{attachment:O-C-G4.png}}
{{attachment:O-C-H.png}}

TiO data

Contents

  1. Next steps
  2. Summary of files
  3. Calculated TiO data from B. Plez
  4. Observed wavenumbers
    1. Observed lines in beta system
    2. Observed lines in gamma prime system
  5. Comparison of observed and calculated wavelengths

Next steps

  • Extract TiO line lists for use with e.g. Synth
  • Calculate synthetic spectra
  • Compare with observed spectra of M dwarfs and giants

Done:

  • Convert ascii TiO line lists to VALD binary format and kompress - 2011-02-15, see  /vald-archive/source-lists/Molecules/TiO/Plez/tio_plez2vald.format , both for calculated and observed wavelength files (with flag which has to be changed manually)

Summary of files

Calculated line lists: 

/vald-archive/source-lists/Molecules/TiO/Plez/

Original lists (Plez 2008/2009):  linelist??_all.dat.gz 

Lists processed for non-resolved lambda doubling (Heiter 2009):  linelist??_all_nodoubling.dat.gz 

Merging code:  tio_plez_rm_doubling.pro 

Observed line lists: 

/vald-archive/source-lists/Molecules/TiO/Phillips/

Original list:  TiO-Phillips-OBS.dat 

Converted list (ascii format, same format as calculated lists):  linelist48-TiO-Phillips-OBS-vald.asc 

Conversion code:  tio_phillips_to_vald_ascii.f 

File with O-C wavelength differences:  TiO-Phillips-O-C.dat 

Gnuplot input file to plot O-C

Calculated TiO data from B. Plez

TiO line lists were calculated by Bertrand on 29 May 2008 with air wavelength, gf, energies for lower and upper levels, radiative damping constant, transition id and quantum numbers. In an update on 10 June 2009, the phi system was added (and the radiative damping constants for the delta system were changed).

Transitions:

transitions table

Vibrational quantum numbers from 0 to 15, rotational quantum numbers from 1 to 200.

The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wavelengths) by Ulrike (2009-02-06, 2009-06-30), see page on lambda doubling.

In the calculated lists, parity is given by the syml and symu quantum numbers, which can be 1 or -1. In the merged lists, syml and symu are set to 0 for the merged lines.

For gamma prime, delta, epsilon and E-B, lambda doubling is resolved (transitions involving E3-Pi, B3-Pi, and b1-Pi states), therefore there are few merged lines. For the phi transitions, lambda doubling does not exist (involves a Sigma state). For the remaining transitions (alpha, beta, gamma, a-f), lambda doubling is not resolved (therefore, all lines are merged).

Number of lines:

Isotope

Nmerg

Norig

46

8333340

11280189

47

8334680

11281575

48

8335639

11282895

49

8336542

11284157

50

8337372

11285088

total

41677573

56413904

Norig ... original lists
Nmerg ... non-resolved lambda-doubled lines merged

Observed wavenumbers

A line list with observed wavenumbers from Phillips has been provided by Bertrand Plez (priv. comm. 17 Sep 2008, 14 May 2009). Reference: Davis et al. 1986, ApJ 309, 449.

It contains 35584 lines in the alpha, beta, gamma, gamma prime systems with range:

wavenumber(cm-1)

wavelength(Å)

vacuum

air

20997.64

4762.440

4761.109

11383.24

8784.845

8782.433

Isotope: 48Ti (see Davis et al. 1986, IV.a p. 452)

The list has been converted to an ascii format where the observed wave numbers have been converted to air wavelengths and all other line data needed for a VALD line list have been taken from the calculated list (isotope 48, merged) by Plez (see above), by Ulrike, 2009-05-22.

The list has been sorted by wavelength after running the conversion code.

Number of lines and wavelength ranges for converted list:

System

N

Air wavelength range [Å]

A

8761

4761

6277

B

826

5597

5740

G

21071

6294

8783

H

5254

5847

6891

Total

35912

Explanation for different numbers of lines in original and converted list:

  • 157 lines in systems other than gamma prime are not in the calculated list (all with Jlow<=4).

  • In the alpha and gamma systems, there are five "double" lines with same quantum numbers and branch names but slightly different wavenumbers. The wavenumbers for these have been averaged for the converted list. There are 18 double lines with exactly the same parameters. The duplicates have been removed for these.
  • There are 137 gamma prime P11/Q11/R11 lines, which are not in calculated list and have been discarded.
  • 290 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list.

  • There is a double entry for gamma prime 0-1 Jlow=7 R1D.

  • For 20 lines in the gamma prime P1,Q1,P2,Q2,R2 lists, lambda doubling is not resolved in the calculated list. The observed wavenumber differences are very small for these lines (<=0.05 cm-1, >0 only for four lines), therefore they have been averaged.

  • The double line gamma prime 0-1 Jlow=1 R2 is not in the calculated list.

  • P3,Q3,R3 lines in the gamma prime system are "double", because of resolved lambda doubling in the calculated list (+958 lines).
  • Totals: -630 +958

Observed lines in beta system

v-v

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P

4

99

94

1-1

P

2

100

66,88,91,92,93,95

2-2

P

2

90

8,10,12,14,76,81,83

0-0

Q

2

100

4

1-1

Q

1

100

2,4,96

2-2

Q

3

100

7,78,82,83,84,89,90,91

0-0

R

2

100

1-1

R

2

98

7

2-2

R

2

92

5,26,42,62,64,70,74,75,84

Observed lines in gamma prime system

observed lines in gamma prime system, P1,Q1,R1 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P1

3

131

3,4,5,6,13,23

29,104,130,131

1-0

P1

2

107

98

21,77

15,63,103,107

0-1

P1

2

145

89,93,109,110,120,123

2,10,14,28,29,63,104, 126,131,135,138,139, 140,144,145

23,62,68,71,72,77,84,98, 99,111,125,129,130,136

0-0

Q1

1

141

2

1,12,119,138,139,140,141

4,7,118

1-0

Q1

1

120

1,104,105,112,114,118

0-1

Q1

2

144

94,138

11,104,107,114,125,127, 128,129,130,132,133,143,144

8,77,100,102,122,124

0-0

R1

1

122

96

5,6,19,64,87

1,2,76,83,84,90,94,100, 107,>=110

1-0

R1

1

135

126

28,43,78,82,95

116,119,121,128,131

0-1

R1

1

150

119,122,124,148

22,58,78,87,100,105,106, 108,111,114,115,130, 137,>=144

5,38,39,53,81,103,116, 117,121,125,128,141 (7 double)

observed lines in gamma prime system, P1,Q1,R1 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

observed lines in gamma prime system, P2,Q2,R2 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P2

11

106

16

51, >=85

1-0

P2

3

88

3,4,6,15,34,35

5,16,82,88

0-1

P2

5

90

7,9,13,16,85

60,67

69,71,74,76, >=84

0-0

Q2

7

107

28

>=84

1-0

Q2

2

91

90

<=9, 35,74,91

0-1

Q2

4

85

8,19,75,82,84

78

72,76,79,80,83,85

0-0

R2

11

106

19,27,32,83,96,97

48,80, >=82

1-0

R2

4

90

18,36,81

4,5,6,8,22,25,37,41,50,61,75,89,90

0-1

R2

1

91

88

18,20,67,76

44,48,82,83, >=85

observed lines in gamma prime system, P2,Q2,R2 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

vupp-vlow

branch

Jlow,min

Jlow,max

wn(C)-wn(D) = delta

0-0

P2

11

45

= 0

46

84

< 0

1-0

P2

7

12

|delta| < 0.07

13

42

> 0

43

51

|delta| < 0.07

52

87

< 0

0-1

P2

5

44

= 0 (39: -0.81)

45

83

< 0

0-0

Q2

7

44

= 0

45

83

< 0

1-0

Q2

10

37

> 0

38

50

|delta| < 0.07

51

89

< 0

0-1

Q2

4

43

= 0

44

81

< 0

0-0

R2

11

45

= 0 (36: +0.19)

46

81

< 0

1-0

R2

13

44

> 0

59

88

< 0

0-1

R2

1

42

= 0

43

84

< 0

observed lines in gamma prime system, P3,Q3,R3 branches:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P3

4

121

10,14,19,31,68

1-0

P3

7

95

63,89,93

0-1

P3

4

103

7,19,20,52,79,82,93,97

0-0

Q3

11

130

1-0

Q3

4

109

5,10,14,17,19

0-1

Q3

6

112

10,25,54,87,94,102,104,110

0-0

R3

11

139

21,25,30,65,77,118,119,123,124,134,138

1-0

R3

5

124

99,100,103,119,122

0-1

R3

3

127

5,14,20,70,94,95,96,98,100,113,123

Comparison of observed and calculated wavelengths

Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

O-C wavelength differences for each system:

O-C-all.png O-C-A.png O-C-B.png O-C-G0.png O-C-G1.png O-C-G2.png O-C-G3.png O-C-G4.png O-C-H.png

ValdWiki: TiO (last edited 2012-05-04 17:16:40 by UlrikeHeiter)