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Revision 42 as of 2009-05-22 22:36:14
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Editor: UlrikeHeiter
Comment: link correction
Revision 65 as of 2012-05-04 15:41:22
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Editor: UlrikeHeiter
Comment:
Deletions are marked like this. Additions are marked like this.
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#acl ValdTeamGroup:read,write,delete All:read

~+'''TiO data'''+~ - see also [[TiO/LambdaDoubling]]
Line 3: Line 7:
= TiO data = == 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:
 * UH, 2012-05-04: Modified species number in Schwenke TiO VALD3 files.
 * UH, 2011-05-31: Processed Schwenke TiO line list.
 * UH, 2011-02-15, 2011-03-13, 2011-05-26, 2011-05-31, 2012-05-04: Converted ascii TiO line lists to (new) VALD3 binary format - see {{{ /vald-archive/source-lists/Molecules/TiO/ }}} for scripts, log files, format file, and binary lists; kompressed lists in CVALD3 format are in {{{ /home/vald/VALD3/VALD3/CVALD3/MOLECULES/ }}}.
Line 8: Line 21:

'''Plez''':
Line 11: Line 27:
Original lists (Plez 2008): {{{ linelist??_all.dat.gz }}} Original lists (Plez 2008/2009): {{{ linelist??_all.dat.gz }}}
Line 18: Line 34:
'''Observed line lists''': '''Schwenke''':

{{{
/vald-archive/source-lists/Molecules/TiO/Schwenke/
}}}
Original lists (Kurucz 1999): {{{ tioschwenke.bin, eschwenke.bin }}}

Lists processed for non-resolved lambda doubling and stored in ascii format (Heiter 2011):
{{{ tioschwenke??.dat.gz }}}

Merging code: {{{ rschwenk-vald.for }}}

'''Line lists with observed wavelengths''':
Line 23: Line 51:
Original list: {{{ TiO-Phillips-OBS.dat }}}

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

Converted list (ascii format, same format as calculated lists): {{{ linelist48-TiO-Phillips-OBS-vald.asc }}}
Line 33: Line 61:
== TiO electronic states ==

{{attachment:TiO_states.png|transitions table|width=400}}
Line 34: Line 66:
TiO line lists calculated by Bertrand on 29 May 2008 with air wavelength, gf, energies for lower and upper levels, transition id and quantum numbers. 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).
Line 38: Line 70:
{{attachment:BP_transitions.png}} {{attachment:BP_transitions.png|transitions table|width=600}}
Line 42: Line 74:
The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wave numbers) by Ulrike, 2009-02-06 (see below in section on lambda doubling).
The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wavelengths) by UH (2009-02-06, 2009-06-30), see [[TiO/LambdaDoubling|page on lambda doubling]].
Line 46: Line 77:

The calculated lists where lambda doubling is resolved are gamma prime, delta, epsilon and E-B.
For further information on the level data format see [[EnergyLevels]].

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).
Line 53: Line 85:
||46 || 8193347 ||11140205 ||
||47 || 8194614 ||11141521 ||
||48 || 8195512 ||11142777 ||
||49 || 8196355 ||11143980 ||
||50 || 8197133 ||11144857 ||
||total ||40976961 ||55713340 ||
||46 || 8333340 ||11280189 ||
||47 || 8334680 ||11281575 ||
||48 || 8335639 ||11282895 ||
||49 || 8336542 ||11284157 ||
||50 || 8337372 ||11285088 ||
||total ||41677573 ||56413904 ||
Line 63: Line 95:
== Lambda doubling ==

-- BertrandPlez 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).

 * lambda doubling in Plez 2008 calculated lists in '''gamma prime system'''
  * P1,Q1,R1: lambda doubling resolved for all lines
  * P2,Q2,R2: lambda doubling resolved for J,,low,,>~10
  * P3,Q3,R3: lambda doubling resolved for J,,low,,>=3
  * "resolved" here means: wavenumber difference >=0.001
 
 * wavenumber (wn) difference for calculated lambda-doubled lines in '''gamma prime system'''
  * P1,P2,R1,R2 (all v-v):
   * for even J,,low,,: wn(syml=-1) > wn(syml=1),
   * for odd J,,low,, vice versa
  * Q1,Q2: reverse of P
   * for even J,,low,,: wn(syml=1) > wn(syml=-1),
   * for odd J,,low,, vice versa
  * PQR 3: reverse of PQR 1,2
  * for the actual values for PQR 1 and 2 see the plots below (the values are the same for each of the three v-v combinations 0-0, 1-0, 0-1), and compare to the plots for observed lambda-doubled lines further down

{{attachment:linelist48_all-H-PQR1-wn-0.png}}
{{attachment:linelist48_all-H-PQR1-wn-1.png}}
{{attachment:linelist48_all-H-PQR1-wn-2.png}}
{{attachment:linelist48_all-H-PQR1-wn-3.png}}
{{attachment:linelist48_all-H-PQR2-wn-0.png}}
{{attachment:linelist48_all-H-PQR2-wn-1.png}}
{{attachment:linelist48_all-H-PQR2-wn-2.png}}
{{attachment:linelist48_all-H-PQR2-wn-3.png}}
== Calculated TiO data from Schwenke (1998) ==
The TiO linelist described by [[http://adsabs.harvard.edu/abs/1998FaDi..109..321S|Schwenke (1998, Faraday Discussions 109, 321)]] and published on Kurucz CDROM No. 24 (1999) was obtained from the [[http://kurucz.harvard.edu/molecules/TiO/|Kurucz website]] in Sep 2004. It contains wavelength, gf values, energies for lower and upper levels, radiative damping constant, level id and quantum numbers, for transitions among 13 different electronic states of TiO (five different Ti isotopes).
The list for isotope 48 contains lines for 70 different electronic transitions (the nine "allowed" transitions as in the Plez list, and numerous "forbidden" transitions, see discussion in Schwenke 1998 and table below). Figure 4 in Schwenke (1998) shows the absorption as a function of frequency at 3000 K for 27 of the "forbidden" systems.

'''Transitions:'''

{{attachment:Schwenke_transitions.png|transitions table|width=600}}

Vibrational quantum numbers from 0 to 19, rotational quantum numbers from 1 to 300.

The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wavelengths) by UH (2011-05-30), see [[TiO/LambdaDoubling|page on lambda doubling]].
In the calculated lists, parity is given as 'p' or 'm'.
In the merged lists, parity is set to 0 for both upper and lower level for the merged lines.
For further information on the level data format see [[EnergyLevels]].


'''Number of lines:'''

||Isotope ||N,,merg,,||N,,orig,,||
||46 || 4713961 || 6410067||
||47 || 4738024 || 6441278||
||48 || 9052370 || 11857414||
||49 || 4782693 || 6503728||
||50 || 4804039 || 6532011||
||total ||28091087 || 37744498||

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

Line 100: Line 130:
It contains 35584 lines in the alpha, beta, gamma, gamma prime systems
with range:
It contains 35584 lines in the alpha, beta, gamma, gamma prime systems.

The same data have also been retrieved from the Kurucz website:
http://kurucz.harvard.edu/molecules/TiO/tioberkeley.dat

This file was found to contain data for eight additional vibrational bands in the alpha system (3198 lines), and these were added to the data obtained via Plez.

In total, the data cover the following wavelength range:
Line 104: Line 140:
||20997.64 ||4762.440 || 4761.109 || ||22610.30 ||4422.763 || 4421.521 ||
Line 109: Line 145:
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) by Plez (see above), by Ulrike, 2009-05-22.

The list has been sorted by wavelength after running the conversion code.
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 by Plez (isotope 48, merged, see above), by UH, 2009-05-22, 2011-05-26.

Lambda doubling is resolved in the observations only for the gamma prime system (P,Q,R 1/2 branches). "The Lambda-split components are designated by the usual subscripts c and d, which are assigned arbitrarily since the symmetry is unknown" (Phillips, 1969, ApJ 157, 449). Calculated data have been assigned to Lambda-doubled components according to wavelength order.
Line 115: Line 151:
|| A ||  8761 || 4761 || 6277 || || A || 11942 || 4421 || 6277 ||
Line 119: Line 155:
|| Total || 35912 |||| || || Total || 39093 |||| ||
Line 122: Line 158:
 * 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.
 * 173 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 19 double lines with exactly the same parameters. The duplicates have been removed for these.
Line 130: Line 166:
 * Totals: -630 +958  * Totals: -647 +958
Line 150: Line 186:

see also [[TiO/LambdaDoubling]]
Line 166: Line 204:
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}}
Line 188: Line 220:
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 ||

Line 239: Line 237:
Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

O-C wavelength differences for each system:
Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=4.0Å.

O-C wavelength differences versus observed air wavelength for each system:

TiO data - see also TiO/LambdaDoubling

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:

  • UH, 2012-05-04: Modified species number in Schwenke TiO VALD3 files.
  • UH, 2011-05-31: Processed Schwenke TiO line list.
  • UH, 2011-02-15, 2011-03-13, 2011-05-26, 2011-05-31, 2012-05-04: Converted ascii TiO line lists to (new) VALD3 binary format - see  /vald-archive/source-lists/Molecules/TiO/  for scripts, log files, format file, and binary lists; kompressed lists in CVALD3 format are in  /home/vald/VALD3/VALD3/CVALD3/MOLECULES/ .

Summary of files

Calculated line lists:

Plez:

/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 

Schwenke:

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

Original lists (Kurucz 1999):  tioschwenke.bin, eschwenke.bin 

Lists processed for non-resolved lambda doubling and stored in ascii format (Heiter 2011):  tioschwenke??.dat.gz 

Merging code:  rschwenk-vald.for 

Line lists with observed wavelengths:

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

Original list:  TiO-Phillips-OBS-Plez-Kurucz.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

TiO electronic states

transitions table

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 UH (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 further information on the level data format see EnergyLevels.

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

Calculated TiO data from Schwenke (1998)

The TiO linelist described by Schwenke (1998, Faraday Discussions 109, 321) and published on Kurucz CDROM No. 24 (1999) was obtained from the Kurucz website in Sep 2004. It contains wavelength, gf values, energies for lower and upper levels, radiative damping constant, level id and quantum numbers, for transitions among 13 different electronic states of TiO (five different Ti isotopes). The list for isotope 48 contains lines for 70 different electronic transitions (the nine "allowed" transitions as in the Plez list, and numerous "forbidden" transitions, see discussion in Schwenke 1998 and table below). Figure 4 in Schwenke (1998) shows the absorption as a function of frequency at 3000 K for 27 of the "forbidden" systems.

Transitions:

transitions table

Vibrational quantum numbers from 0 to 19, rotational quantum numbers from 1 to 300.

The original line lists have been processed to merge non-resolved lambda-doubled lines (with equal wavelengths) by UH (2011-05-30), see page on lambda doubling. In the calculated lists, parity is given as 'p' or 'm'. In the merged lists, parity is set to 0 for both upper and lower level for the merged lines. For further information on the level data format see EnergyLevels.

Number of lines:

Isotope

Nmerg

Norig

46

4713961

6410067

47

4738024

6441278

48

9052370

11857414

49

4782693

6503728

50

4804039

6532011

total

28091087

37744498

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.

The same data have also been retrieved from the Kurucz website: http://kurucz.harvard.edu/molecules/TiO/tioberkeley.dat

This file was found to contain data for eight additional vibrational bands in the alpha system (3198 lines), and these were added to the data obtained via Plez.

In total, the data cover the following wavelength range:

wavenumber(cm-1)

wavelength(Å)

vacuum

air

22610.30

4422.763

4421.521

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 by Plez (isotope 48, merged, see above), by UH, 2009-05-22, 2011-05-26.

Lambda doubling is resolved in the observations only for the gamma prime system (P,Q,R 1/2 branches). "The Lambda-split components are designated by the usual subscripts c and d, which are assigned arbitrarily since the symmetry is unknown" (Phillips, 1969, ApJ 157, 449). Calculated data have been assigned to Lambda-doubled components according to wavelength order.

Number of lines and wavelength ranges for converted list:

System

N

Air wavelength range [Å]

A

11942

4421

6277

B

826

5597

5740

G

21071

6294

8783

H

5254

5847

6891

Total

39093

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

  • 173 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 19 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: -647 +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

see also TiO/LambdaDoubling

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, 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, 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=4.0Å.

O-C wavelength differences versus observed air wavelength 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)