Differences between revisions 43 and 44

Contents

TiO data

TiO data

Next steps

Convert ascii TiO line lists to VALD binary format
Extract TiO line lists for use with e.g. Synth
Calculate synthetic spectra
Compare with observed spectra of M dwarfs and giants

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): 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, transition id and quantum numbers. In an update on 10 June 2009, the phi system was added (and the radiation damping constants for the delta system were changed).

Transitions:

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 wave numbers) by Ulrike (2009-02-06, 2009-06-30), see section on lambda doubling below.

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

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

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) 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:

-  ⇤ ← Revision 43 as of 2009-05-22 22:48:05 → 
  Size: 12600
  Editor: UlrikeHeiter
  Comment: Next steps added
+   ← Revision 44 as of 2010-05-04 17:58:25 → ⇥
  Size: 13020
  Editor: UlrikeHeiter
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 18:
-Original lists (Plez 2008): {{{ linelist??_all.dat.gz }}}
+Original lists (Plez 2008/2009): {{{ linelist??_all.dat.gz }}}
 Line 41:
-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, transition id and quantum numbers. In an update on 10 June 2009, the phi system was added (and the radiation damping constants for the delta system were changed).
 Line 49:
-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 wave numbers) by Ulrike (2009-02-06, 2009-06-30), see section on lambda doubling below.
 Line 54:
-The calculated lists where lambda doubling is resolved are gamma prime, delta, epsilon and E-B.
+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 60:
-||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 ||