Evaluation of the Effective Temperature of Sunspots Using Molecular Parameters of AlF

Abstract

The physical conditions of celestial objects can be analyzed using the spectrum of atoms or molecules present in the object. The present work focuses on the spectroscopic analysis of astrophysically significant molecule AlF. The evaluation of Franck-Condon (FC) factors and r -centroids is done by a numerical integration procedure using the suitable potential energy curves for [superscript] C 1 [/superscript] [superscript] Σ + [/superscript] - [superscript] A 1 [/superscript] [superscript] Σ + [/superscript] , [superscript] b 3 [/superscript] [superscript] Σ + [/superscript] - [superscript] a 3 [/superscript] [subscript] Π r [/subscript] , [superscript] c 3 [/superscript] Σ - [superscript] a 3 [/superscript] [subscript] Π r [/subscript] , and [superscript] f 3 [/superscript] Π - [superscript] a 3 [/superscript] [subscript] Π r [/subscript] band systems of AlF molecule. The intensity of various bands is discussed with the help of derived FC factors. The band degradation and the nature of potential energy curves are studied using r -centroid values. The vibrational temperature of sunspot is estimated to be around 1220 ± 130 K which falls in the reported temperature range of cold sunspots.

K. Balachandrakumar 1 and V. Raja 2 and B. Karthikeyan 1 and S. P. Bagare 3 and N. Rajamanickam 4

Academic Editor:Dean Hines

1, Department of Physics, Kamaraj College of Engineering and Technology, Virudhunagar 626 001, India
2, Department of Physics, RD Government Arts College, Sivagangai 630 560, India
3, Indian Institute of Astrophysics, Bangalore 560 034, India
4, Physics Research Centre, V.H.N.S.N College, Virudhunagar 626 001, India

Received 9 September 2014; Revised 4 December 2014; Accepted 15 December 2014; 29 January 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The existence of AlF molecule in various astrophysical sources has been confirmed by various researchers. For instance, Cernicharo [1] and Turner [2] identified the presence of AlF molecule in the envelope of brightest C-rich evolved object IRC + 10216. The AlF molecular species was also found in the gas or dust envelopes of asymptotic giant branch (AGB) stars [3]. With reference to HF spectroscopy of the red giant stars, the presence of AlF in IRC + 10216 indicated that large quantities of fluorine were present in the inner stellar envelope and the element was produced in helium shell flashes and not in explosive nucleosynthesis [4]. Turner [2] has predicted that the AlF molecule must have a significant presence in the region of thermochemical equilibrium occurring in the dense, hot, and innermost envelope of the stellar atmosphere. Sauval and Tatum [5] have reported that the AlF molecule may be present in the stellar and cometary spectra.

According to Joshi et al. [6], the AlF molecule is likely to be present in the sunspots umbral atmosphere. Wöhl [7] examined sunspots spectra towards the identification of various diatomic molecules and found 100 lines of AlF molecule. Bagare et al. [8] made an extensive search for AlF molecular lines in the spectra of sunspots and confirmed their presence. With the help of vibronic transition probability parameters such as Franck-Condon (FC) factors, [figure omitted; refer to PDF] -centroids, relative intensities, oscillator strength, and vibrational temperature of diatomic molecular species, the spectroscopic technique could be very useful in the identification of molecular lines and in the estimation of relative abundance of the species in astrophysical sources. A number of workers have therefore undertaken theoretical studies to provide those parameters for diatomic molecules which are of importance not only in astrophysics, but also in the fields of gas kinetics, combustion process, and so forth [9-11].

The literature on the reports of Franck-Condon factors and [figure omitted; refer to PDF] -centroids for the [figure omitted; refer to PDF] and [figure omitted; refer to PDF] band systems of AlF molecule is not made. Murty [12] reported on a partial array of FC factors and [figure omitted; refer to PDF] -centroids for [figure omitted; refer to PDF] band system. The present study focuses on the complete array of the FC factors and [figure omitted; refer to PDF] -centroids using experimental vibrational levels and vibrational temperature of the source using relative intensity of the bands.

2. Theory and Computational Procedure

2.1. Franck-Condon Factors and [figure omitted; refer to PDF] -Centroids

The intensity of a vibrational band within a band system of a diatomic molecule is controlled mainly by the population on the vibrational level from which the transition takes place and by the FC factor ( [figure omitted; refer to PDF] ) which is defined as the square modulus of the vibrational overlap integral that is [10] [figure omitted; refer to PDF] where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the vibrational quantum numbers and [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the vibrational wave functions for the upper and lower states, respectively.

The [figure omitted; refer to PDF] -centroids [figure omitted; refer to PDF] are seen to be the weighted average with respect to [figure omitted; refer to PDF] of the range of [figure omitted; refer to PDF] values experienced by the molecule in both states of the [figure omitted; refer to PDF] transition. The form of [figure omitted; refer to PDF] can be expressed as [10] [figure omitted; refer to PDF] Using the molecular constants [13] mentioned in Table 1, the potential energy curves for the electronic states [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] and [figure omitted; refer to PDF] of AlF molecule have been constructed first using Morse [14] and Rydberg-Klein Rees (RKR) [15] functions. The turning points of the potential energy curves are finally presented in the Tables 2-7, where the potential energy curves derived from Morse function coincide well with the RKR curves. The Morse potential can yield reliable FC factors and [figure omitted; refer to PDF] -centroids for the bands in an electronic transition involving low vibrational quantum numbers [16].

Table 1: Molecular constants taken from the compilation of Huber and Herzberg [13] for the electronic states of AlF molecule.

State	[figure omitted; refer to PDF] (cm-1 )	[figure omitted; refer to PDF] (cm-1 )	[figure omitted; refer to PDF] (cm-1 )	[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	[figure omitted; refer to PDF] (Å)
[figure omitted; refer to PDF]	938.22	5.09	-0.017	0.00480	0.58992	1.6010
[figure omitted; refer to PDF]	803.94	5.99	-0.050	0.00534	0.55640	1.6485
[figure omitted; refer to PDF]	938.90	5.90	-	0.00480	0.59355	1.5961
[figure omitted; refer to PDF]	933.66	4.81	-	0.00457	0.58861	1.6028
[figure omitted; refer to PDF]	786.37	7.64	-0.009	0.00650	0.56280	1.6391
[figure omitted; refer to PDF]	827.80	3.90	-	0.00453	0.55703	1.6476

Table 2: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	467.83	1.661	1.547	1.661	1.547
1	1395.82	1.709	1.511	1.709	1.512
2	2313.47	1.744	1.488	1.745	1.489
3	3220.69	1.775	1.469	1.777	1.471
4	4117.37	1.802	1.454	1.805	1.457
5	5003.41	1.828	1.441	1.830	1.444

Table 3: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	400.47	1.714	1.591	1.714	1.591
1	1192.26	1.767	1.553	1.768	1.553
2	1971.63	1.807	1.528	1.807	1.529
3	2738.27	1.841	1.510	1.842	1.510
4	3491.88	1.873	1.494	1.874	1.494
5	4232.15	1.902	1.481	1.903	1.481
6	4958.80	1.930	1.469	1.932	1.469
7	5671.52	1.957	1.459	1.959	1.458
8	6370.00	1.983	1.449	1.983	1.448

Table 4: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	391.27	1.706	1.581	1.706	1.581
1	1162.33	1.761	1.543	1.761	1.544
2	1981.03	1.803	1.520	1.803	1.520
3	2658.31	1.839	1.501	1.839	1.502
4	3383.13	1.873	1.487	1.873	1.487
5	4092.42	1.905	1.473	1.905	1.474
6	4786.14	1.935	1.463	1.935	1.462
7	5464.22	1.965	1.453	1.965	1.452
8	6126.62	1.995	1.444	1.994	1.443

Table 5: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	465.63	1.663	1.549	1.663	1.549
1	1389.67	1.711	1.512	1.711	1.513
2	2304.09	1.746	1.489	1.747	1.490
3	3208.89	1.776	1.470	1.777	1.472
4	4104.07	1.804	1.455	1.806	1.457

Table 6: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	467.98	1.656	1.542	1.656	1.543
1	1395.08	1.705	1.507	1.705	1.507

Table 7: Turning points for the molecular vibration in the [figure omitted; refer to PDF] -state of AlF.

[figure omitted; refer to PDF]	[figure omitted; refer to PDF] in cm-1	Morse	RKR
[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å	[figure omitted; refer to PDF] in Å
0	412.93	1.711	1.590	1.712	1.590
1	1232.93	1.762	1.551	1.763	1.552
2	2045.13	1.798	1.526	1.801	1.528
3	2849.53	1.831	1.506	1.833	1.509
4	3646.13	1.859	1.490	1.863	1.493
5	4434.93	1.886	1.476	1.890	1.480
6	5215.93	1.911	1.463	1.916	1.469
7	5989.13	1.935	1.452	1.941	1.458
8	6754.53	1.958	1.442	1.964	1.448

The computation of FC factor is made using the Bates' method of numerical integration [16] and Ureña et al.'s detailed procedure [17]. The Morse wave functions are calculated at the intervals of 0.01 Å for [figure omitted; refer to PDF] ranging from 1.42 Å to 2.01 Å, from 1.42 Å to 2.01 Å, from 1.44 Å to 1.88 Å, and from 1.49 Å to 1.82 Å, for every observed vibrational level of each state of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] of the AlF molecule. The FC factors [figure omitted; refer to PDF] and [figure omitted; refer to PDF] -centroids [figure omitted; refer to PDF] are computed numerically by integrating the integrals in (1) and (2) for the bands of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] of the AlF molecule and the results are given in the Tables 8-11 with the available wavelengths [figure omitted; refer to PDF] [18-20] for all the band systems.

Table 8: Franck-Condon factors and [figure omitted; refer to PDF] -centroids of [figure omitted; refer to PDF] band system of AlF molecule.

			[figure omitted; refer to PDF] = 0	[figure omitted; refer to PDF] = 1	[figure omitted; refer to PDF] = 2	[figure omitted; refer to PDF] = 3	[figure omitted; refer to PDF] = 4	[figure omitted; refer to PDF] = 5	[figure omitted; refer to PDF] = 6	[figure omitted; refer to PDF] = 7	[figure omitted; refer to PDF] = 8
[figure omitted; refer to PDF] = 0	(a)	(i)	0.714	0.236	0.044	0.006	0.001	[low *]	[low *]	[low *]	[low *]
(ii)	0.717	0.234	0.043	-	0.001
(b)	(i)	1.629	1.562	1.494	1.423	1.349	1.271	-	-	-
(ii)	1.628	1.560	1.483	-	1.346	1.282	-	-	-
(c)		7245.9	7686.2	8175.4	-	-	2040.0	-	-	-
[figure omitted; refer to PDF] = 1	(a)	(i)	0.243	0.303	0.322	0.107	0.022	0.004	0.001	[low *]	[low *]
(ii)	0.241	0.312	0.320	0.102	0.020	-	-	-	-
(b)	(i)	1.706	1.638	1.574	1.508	1.439	1.368	1.293	-	-
(ii)	1.705	1.640	1.573	1.499	1.394	-	-	-	-
(c)		6789.9	7174.9	7599.2	8068.8	8590.8	8461.7	-	-	-
[figure omitted; refer to PDF] = 2	(a)	(i)	0.039	0.346	0.084	0.306	0.166	0.048	0.010	0.001	[low *]
(ii)	0.038	0.343	0.096	0.310	0.159	0.043	-	-	-
(b)	(i)	1.778	1.716	1.645	1.586	1.522	1.455	1.386	1.404	1.334
(ii)	1.780	1.715	1.651	1.586	1.515	1.425	-	-	-
(c)		6392.3	6732.1	7104.2	7512.8	7963.3	8461.7	8334.5	-	-
[figure omitted; refer to PDF] = 3	(a)	(i)	0.004	0.101	0.345	0.004	0.232	0.206	0.081	0.022	0.004
(ii)	0.004	0.096	0.350	-	0.247	0.199	-	-	-
(b)	(i)	1.847	1.787	1.725	1.634	1.597	1.535	1.471	1.404	1.334
(ii)	1.857	1.789	1.725	-	1.599	1.531	-	-	-
(c)		6036.9	6345.3	6674.5	-	7426.9	7858.7	8334.5	-	-
[figure omitted; refer to PDF] = 4	(a)	(i)	[low *]	0.015	0.166	0.282	0.013	0.142	0.216	0.116	0.038
(ii)	[low *]	-	0.157	0.299	-	0.166	-	-	-
(b)	(i)	1.915	1.855	1.796	1.735	1.690	1.608	1.549	1.486	1.422
(ii)	1.938	-	1.799	1.735	-	1.611	-	-	-
(c)		-	-	6298.1	6616.8	-	7341.5	7755.2	8211.1	-
[figure omitted; refer to PDF] = 5	(a)	(i)	[low *]	0.002	0.035	0.220	0.191	0.064	0.062	0.196	0.144
(ii)	[low *]	-	-	0.210	0.222	-	-	-	-
(b)	(i)	1.981	1.922	1.863	1.805	1.744	1.692	1.618	1.562	1.502
(ii)	2.025	-	-	1.808	1.745	-	-	-	-
(c)		-	-	-	6251.4	6559.5	-	-	-	8093.6

(a) [figure omitted; refer to PDF] : (i) present study; (ii) Murty (1977) [12], (b) [figure omitted; refer to PDF] (Å), (c) [figure omitted; refer to PDF] (Å), and [low *]: [figure omitted; refer to PDF] .

Table 9: Franck-Condon factors and [figure omitted; refer to PDF] -centroids of [figure omitted; refer to PDF] band system of AlF molecule.

		[figure omitted; refer to PDF] = 0	[figure omitted; refer to PDF] = 1	[figure omitted; refer to PDF] = 2	[figure omitted; refer to PDF] = 3	[figure omitted; refer to PDF] = 4	[figure omitted; refer to PDF] = 5	[figure omitted; refer to PDF] = 6	[figure omitted; refer to PDF] = 7	[figure omitted; refer to PDF] = 8
[figure omitted; refer to PDF] = 0	(a)	0.995	0.005	[low *]	[low *]	[low *]	[low *]	[low *]	[low *]	[low *]
(b)	1.649	1.028
(c)	5681.0	-
[figure omitted; refer to PDF] = 1	(a)	0.005	0.990	[low *]	0.003	[low *]	[low *]	[low *]	[low *]	[low *]
(b)	2.242	1.660		1.521
(c)	-	5697.1		-
[figure omitted; refer to PDF] = 2	(a)	[low *]	0.004	0.990	[low *]	0.005	[low *]	[low *]	[low *]	[low *]
(b)		2.579	1.671		1.585
(c)		-	5715.1		-
[figure omitted; refer to PDF] = 3	(a)	[low *]	0.003	[low *]	0.989	[low *]	0.009	[low *]	[low *]	[low *]
(b)		1.698		1.683		1.655
(c)		-		5735.3		-
[figure omitted; refer to PDF] = 4	(a)	[low *]	[low *]	0.005	[low *]	0.974	[low *]	0.014	[low *]	[low *]
(b)			1.767		1.693		1.725
(c)			-		5758.4		-
[figure omitted; refer to PDF] = 5	(a)	[low *]	[low *]	[low *]	0.008	[low *]	0.938	0.021	0.023	[low *]
(b)				1.841		1.703	2.540	1.790
(c)				-		5782.9	-	-
[figure omitted; refer to PDF] = 6	(a)	[low *]	[low *]	[low *]	[low *]	0.011	0.036	0.871	0.046	0.034
(b)					1.930	1.234	1.711	2.334	1.847
(c)					-	-	5809.3	-	-
[figure omitted; refer to PDF] = 7	(a)	[low *]	[low *]	[low *]	[low *]	[low *]	0.010	0.083	0.768	0.078
(b)						2.056	1.401	1.716	2.225
(c)						-	-	5837.9	-
[figure omitted; refer to PDF] = 8	(a)	[low *]	[low *]	[low *]	[low *]	[low *]	0.002	0.007	0.155	0.625
(b)						1.620	2.286	1.504	1.717
(c)						-	-		5869.0

(a) [figure omitted; refer to PDF] , (b) [figure omitted; refer to PDF] (Å), (c) [figure omitted; refer to PDF] (Å), and [low *]: [figure omitted; refer to PDF] .

Table 10: Franck-Condon factors and [figure omitted; refer to PDF] -centroids of [figure omitted; refer to PDF] band system of AlF molecule.

		[figure omitted; refer to PDF] = 0	[figure omitted; refer to PDF] = 1	[figure omitted; refer to PDF] = 2	[figure omitted; refer to PDF] = 3	[figure omitted; refer to PDF] = 4
[figure omitted; refer to PDF] = 0	(a)	0.751	0.215	0.032	0.003	[low *]
(b)	1.628	1.556	1.476	1.376
(c)	3608.2	3702.4	-	-
[figure omitted; refer to PDF] = 1	(a)	0.216	0.380	0.314	0.079	0.011
(b)	1.713	1.636	1.566	1.488	1.393
(c)	3492.2	3592.1	3702.4	-	-
[figure omitted; refer to PDF] = 2	(a)	0.031	0.317	0.161	0.335	0.129
(b)	1.785	1.723	1.642	1.574	1.499
(c)	-	3480.8	-	3687.1	-
[figure omitted; refer to PDF] = 3	(a)	0.003	0.078	0.343	0.048	0.308
(b)	1.864	1.795	1.734	1.642	1.584
(c)		-	3469.6	-	3672.2
[figure omitted; refer to PDF] = 4	(a)	[low *]	0.009	0.128	0.320	0.004
(b)		1.874	1.805	1.744	1.597
(c)		-	-	3458.6	-

(a) [figure omitted; refer to PDF] , (b) [figure omitted; refer to PDF] (Å), (c) [figure omitted; refer to PDF] (Å), and [low *]: [figure omitted; refer to PDF] .

Table 11: Franck-Condon factors and [figure omitted; refer to PDF] -centroids of [figure omitted; refer to PDF] band system of AlF molecule.

		[figure omitted; refer to PDF] = 0	[figure omitted; refer to PDF] = 1	[figure omitted; refer to PDF] = 2
[figure omitted; refer to PDF] = 0	(a)	0.686	0.251	0.053
(b)	1.626	1.562	1.501
(c)	2592.2	2648.6	-
[figure omitted; refer to PDF] = 1	(a)	0.268	0.271	0.312
(b)	1.698	1.636	1.570
(c)	2531.0	2584.5	2639.6

(a) [figure omitted; refer to PDF] , (b) [figure omitted; refer to PDF] (Å), and (c) [figure omitted; refer to PDF] (Å).

2.2. Variation of Electronic Transition Moment and Band Strength

With the help of FC factors and [figure omitted; refer to PDF] -centroids, one can determine the band strength of the vibrational bands using the relation [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the variation of electronic transition moment. Mathematically the intensity ( [figure omitted; refer to PDF] ) of a molecular band for an electronic transition in emission ( [figure omitted; refer to PDF] ) is written as [9] [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is a constant partly depending on the geometry of the apparatus and [figure omitted; refer to PDF] is the population of the level [figure omitted; refer to PDF] and [figure omitted; refer to PDF] the energy quantum.

In the present study, the intensities ( [figure omitted; refer to PDF] ) of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] bands as reported by Naude and Hugo [21] are used to evaluate the electronic transition moment variation with internuclear distance for the band system [figure omitted; refer to PDF] of AlF. A plot of [figure omitted; refer to PDF] versus [figure omitted; refer to PDF] yields the variation of [figure omitted; refer to PDF] wtih [figure omitted; refer to PDF] over a progression. To place all progression on the same ordinate, the rescaling procedure of Turner and Nicholls [22] was adopted. A plot of rescaled values of [figure omitted; refer to PDF] versus [figure omitted; refer to PDF] is shown in Figure 1 for the [figure omitted; refer to PDF] band system of AlF. A least square fit yields [figure omitted; refer to PDF] with standard deviation 0.63. The form of [figure omitted; refer to PDF] represented by (5) is adopted in conjunction with (3) to calculate the band strengths using the computed [figure omitted; refer to PDF] values. The band strengths have been relatively scaled by assuming the value of most intense band [figure omitted; refer to PDF] as one. The relative band strengths are evaluated using the relation [figure omitted; refer to PDF] .

Figure 1: The variation of [figure omitted; refer to PDF] with [figure omitted; refer to PDF] for AlF ( [figure omitted; refer to PDF] ) band system.

[figure omitted; refer to PDF]

2.3. Effective Vibrational Temperature

The vibrational quanta [figure omitted; refer to PDF] are calculated from [figure omitted; refer to PDF]

Using the relative band strengths [figure omitted; refer to PDF] , (4) becomes [figure omitted; refer to PDF] Since [figure omitted; refer to PDF] , (7) becomes [23] [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the Planks constant, [figure omitted; refer to PDF] is the velocity of light, [figure omitted; refer to PDF] is the Boltzmann's constant, and [figure omitted; refer to PDF] is the effective vibrational temperature of the source.

A plot of [figure omitted; refer to PDF] versus [figure omitted; refer to PDF] in Figure 2 shows a linear dependence. By least square fitting, the slope is determined and vibrational temperature [figure omitted; refer to PDF] is evaluated and discussed in the following section.

Figure 2: Plot of [figure omitted; refer to PDF] with [figure omitted; refer to PDF] for AlF [figure omitted; refer to PDF] band system.

[figure omitted; refer to PDF]

3. Results and Discussion

In the case of [figure omitted; refer to PDF] band system the FC factors manifest that [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] bands are intense. In the case of the [figure omitted; refer to PDF] band systems of the AlF molecule, the FC factors indicate that the [figure omitted; refer to PDF] sequence bands are more intense and all other bands are relatively weak. The FC factors of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] band systems indicate that the [figure omitted; refer to PDF] sequence bands are significantly intense followed by the [figure omitted; refer to PDF] sequence bands.

The [figure omitted; refer to PDF] -centroid value increases for the [figure omitted; refer to PDF] , [figure omitted; refer to PDF] and [figure omitted; refer to PDF] band systems of AlF, since [figure omitted; refer to PDF] with the decrease in wavelength which is expected in the violet degraded band system. For the [figure omitted; refer to PDF] band system, the [figure omitted; refer to PDF] -centroids value increases with the increase in wavelength which is expected in the red degraded band system.

The sequence differences are found to be constant nearly 0.01 Å for all the four band systems of AlF molecule. For [figure omitted; refer to PDF] band system, the sequence difference is varying from 0.002 Å to 0.056 Å. This suggests that the potentials are not so wide. The [figure omitted; refer to PDF] -centroid value for the [figure omitted; refer to PDF] transition is slightly greater than [figure omitted; refer to PDF] for all the band systems of AlF molecule which implies that the potentials are not very anharmonic.

The vibrational temperature of the source of [figure omitted; refer to PDF] band system is estimated as [figure omitted; refer to PDF] K and is found in the temperature range of cold sunspots. To confirm the presence of AlF molecule in sunspots spectrum, a careful study of sunspot umbral spectra in the wavelength region of 4400-9000 Å was carried out to search for the presence of AlF molecular lines of different band systems [8]. The presence of several transitions of AlF molecule in sunspot spectra was confirmed with a total of 602 rotational lines. The rotational temperature for the [figure omitted; refer to PDF] band system was [figure omitted; refer to PDF] K. Thus it clears that the vibrational temperature evaluated in the present study coincides with the reported rotational temperature.

4. Conclusions

The present work evaluates the transition probability parameters FC factors and [figure omitted; refer to PDF] -centroids which are mainly influencing the intensity of vibrational bands. Using the derived transition probability parameters and reported wavelength of the bands, the vibrational temperature of a band system of AlF molecule is determined. Since the vibrational temperature of the AlF molecule is found to coincide well with the reported sunspot temperature, the present work acts as the additional support for the confirmation of AlF molecule in sunspots.

Acknowledgments

The authors thank the reviewer for the valuable suggestions and constructive remarks. The authors (K. Balachandrakumar and B. Karthikeyan) would also like to thank the management of Kamaraj College of Engineering and Technology for their support and encouragement in pursuing research.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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