TiO - VALD Documentation

TiO data - see also see TiO/LambdaDoubling

Contents

Next steps
Summary of files
Calculated TiO data from B. Plez
Observed wavenumbers
1. Observed lines in beta system
2. Observed lines in gamma prime system
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	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
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: 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 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:

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:

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: