T{}_{\mathrm{eff}}, log g, [Fe/H] in post-AGB stars

Determination of Stellar Atmospheric Parameters for a sample of the post-AGB stars

R. E. Molina    11affiliation: Laboratorio de Investigación en Física Aplicada y Computacional, Universidad Nacional Experimental del Táchira, CP 5001, Venezuela.
Abstract

We report for the first time the stellar atmospheric parameters for a a set of post-AGB stars classified by Suárez et al. (2006). The stellar spectra were taken from optical region, with low-resolution and have different spectral ranges. We select a sample of 70 objects with A–K spectral types and luminosities I and Ie. The large majority of these objects have been scarcely studied and are located toward the galactic south pole region. We employ a set of empirical relationships that use pseudo-equivalent widths like spectral feature to estimate effective temperature, surface gravity and metallicity. The criteria chosen for selection of absorption are similar to employed by MK classification system.

\fulladdresses

R. E. Molina: Laboratorio de Investigación en Física Aplicada y Computacional, Universidad Nacional Experimental del Táchira, Venezuela, (rmolina@unet.edu.ve). \listofauthorsR. E. Molina \resumenReportamos por primera vez los parámetros atmosféricos estelares para un conjunto de estrellas clasificadas como post-AGB por Suárez et al. (2006). Los espectros estelares empleados para el estudio fueron tomados en la región óptica, con baja resolución y poseen diferentes rangos espectrales. Seleccionamos una muestra de 70 objetos con tipos espectrales que abarcan un rango entre A–K y clases de luminosidades I y Ie. La mayoría de las estrellas han sido poco estudiadas y se encuentran ubicadas hacia la región del polo sur galáctico. Se emplean un conjunto de calibraciones empíricas que utilizan los pseudo anchos equivalentes como característica espectral para estimar la temperatura efectiva, la gravedad superficial y la metalicidad. Los criterios tomados para la selección de las líneas de absorción son similares a los empleados por el sistema MK. \addkeywordStars: equivalent widths \addkeywordStars: stellar atmospheric parameters \addkeywordStars: post-AGB

1 Introduction

When performing a detailed analysis of the chemical abundances, it is essential to estimated as accuratelly as possible the relevant physical parameters that will lead the choise of the proper atmospheric models, i.e. effective temperature, surface gravity, and micro-turbulence velocity. This can be archieved from a variety of photometric (e.g. Arellano Ferro, Mendoza & Eugenio 1993; Schuster et al. 1996; Alonso et al. 1999; Mauro et al. 2013) and spectroscopic methods (e.g. Gray et al. 2001; Giridhar & Goswami 2002; Molina & Stock 2004; Soubiran et al. 2010; Wu et al. 2011, Chen et al. 2015; Teixeira et al. 2016).

Stellar atmosphere is characterized mainly by T, log , and [Fe/H], and the knowledge of these parameters is crucial in many research areas related to the stellar and galaxy physics.

The traditional spectroscopic method to initially derive the effective temperature and gravity is via the ionization equilibrium of a well represented specie, such as that of \ionFei and \ionFeii or \ionTii and \ionTiii and a set of stellar models such as ODFNEW-ATLAS9 (Castelli & Kurucz 2003) and MARCS (Gustafsson et al. 2008).

Empirical calibrations to estimate the stellar parameters employ, besides equivalent widths, other quantifiable spectroscopic features such as the central residual intensities and pseudocontinuum peaks (Rose 1984), relative depth ratios (Kovtyukh et al. 2003) and photometric bandheads (Árnadóttir et al. 2010). It is important to note that the stellar parameters derived from empirical calibrations have been one of the main sources of information for the selection and validation of the stellar model for any object under study.

The large data bases that have become available over the last decade, e.g. RAVE (Zwitter et al. 2008), APOGEE (Allende-Prieto et al. 2008), LAMOST (Zhao et al. 2012), to name a few, require automated processing methods that allow the characterization of high volumes of information (stellar spectra) in relatively short time (Graff et al. 2013; Bellinger et al. 2016; Dafonte et al. 2016; Damiani et al. 2016; Ren et al. 2016).

Recently, automatic or semiautomatic methods for determining equivalent widths and stellar parameters have been developed, such as ROBOSPECT (Waters & Hollek 2013), GALA (Mucciarelli 2013), FAMA (Magrini et al. 2013), ISpec (Blanco-Cuaresma et al. 2014) and ARES+MOOG (Sousa 2014). These methods have been calibrated for a wide range of stars in different evolutionary stages from dwarf stars to giant stars. Stellar parameters and elemental abundances estimated via these automated methods show some degree of reliability and efficiency (Teixeira et al. 2016). However, these methods have not been tested for highly evolved objects such as post-AGB stars (hereinafter PAGB) due to the peculiarities of their spectra, e.g. complex emission and absoption profiles, profiles of strong absorption distorted by emission and splitting, and metal emission features (Klochkova 2014).

This paper aims to estimate T, log  and [Fe/H] for a set of stars PAGB via empirical calibrations of equivalent widths of selected features. Such empirical calibrations to determine the stellar parameters in PAGB stars are scarces (e.g. Arellano Ferro 2010; Molina 2012) as they are sensitive to the fact that these stars may be variables and their extinction, which is commonly a combination of interstellar and circumstellar, significantly affect the estimations temperature, gravity and distance of the central star.

This paper are organized as follows: § 2 describes the selection of the sample stars and how equivalent widths were determined. § 3 shows the spectroscopic calibrations that allow us to derived the stellar atmospheric parameters. In § 4 is dedicated to discuss our results, and finally, in § 5 gives the conclusions of the paper.

Figure 1: Maximum and minimun points (red squares) that allow us to derive the equivalent widths for IRAS 08281 – 4850 (F0I) and IRAS 17332 – 2215 (K2I) using an automatic code. The location of different absorption lines selected are labeled by continuous lines.
IRAS SpT CaIIK Fe,TiII FeI blend FeI OI ref.
number 3933 4172-9 4271 4383 7771-5
(Å) (Å) (Å) (Å) (Å)
02143  5852 F7Ie 1.01 0.18 0.32 0.05 01
02528  4350 1.26 0.19 0.13
04296  3429 F7I 01
05341  0852 F5I 1.94 0.23 0.29 1.52 01
06530  0213 F0Iab 2.40 0.80 3.23 02
07134  1005 F7Ie 1.25 0.27 0.31 01
07253  2001 F2I 0.27 01
07430  1115 G5Ia 0.99 04
08005  2356 F5Ie 4.68 1.42 0.73 1.27 01
08143  4406 F8I 8.39 2.09 0.48 0.99 05
08187  1905 F6Ib/II 0.24 03
08213  3857 F2Ie 0.74 0.19 0.22 01
08281  4850 F0I 1.22 0.94 2.74 1.65 1.90 01
10215  5916 A7Ie 11.32 4.22 2.37 3.12 1.77 01
10256  5628 F5I 12.72 1.38 1.75 0.42 2.17 01
11201  6545 A3Ie 0.48 01
11387  6113 A3Ie 0.74 0.30 0.44 01
12067  4505 F6I 0.05 06
14325  6428 A8I 6.18 1.10 0.24 0.96 07
14429  4539 A1I 0.91 1.05 0.23 0.47 1.85 02
14482  5725 A2I 1.13 01
14488  5405 A0I 0.02 01
15039  4806 A5Iab 0.75 0.50 0.12 0.21 1.64 08
15310  6149 A7I 0.09 01
15482  5741 F7I 1.88 0.33 0.22 01
16283  4424 A2Ie 4.50 0.25 3.00 1.58 2.38 01
17106  3046 F5I 9.62 2.68 1.25 0.58 2.10 01
17208  3859 A2I 0.57 0.23 0.82 01
17245  3951 F6I 9.13 2.00 1.49 2.13 2.02 01
17287  3443 0.96 0.10 0.15 0.14 0.74
17310  3432 A2I 0.36 0.22 1.30 01
17376  2040 F6I 01
17436  5003 F3Ib 6.76 1.88 1.14 1.07 09
17441  2411 F4I 7.38 1.16 0.99 0.52 2.06 01
17488  1741 F7I 01
17576  2653 A7I 5.13 0.85 0.02 0.58 2.12 01
17579  3121 F4I 2.42 0.24 0.98 01
18025  3906 G1I 13.14 2.18 0.22 1.30 01
18044  1303 F7I 01
19114  0002 G5Ia 9.86 3.90 1.82 1.59 10
19207  2023 F6I 3.44 3.74 01
19386  0155 F5I 8.31 1.20 1.70 0.97 1.66 11
19422  1438 F5I 01
19500  1709 F0Ie 1.67 0.95 0.44 0.74 1.94 01
19589  4020 F5I 01
20160  2734 F3Ie 4.52 1.95 1.28 1.33 01
20259  4206 F3I 01
20572  4919 F3Ie 4.41 0.92 0.73 0.63 01
21289  5815 A2Ie 0.68 1.12 1.94 0.76 01
22223  4327 F7I 8.93 2.41 1.05 1.02 01
Table 1: Equivalent widths for warm stars.
IRAS SpT FeI SrII CaI G-band FeI OI ref.
number 4063 4077 4226 4302 4383 7771-5
(Å) (Å) (Å) (Å) (Å) (Å)
01259  6823 GIab: 0.76 2.95 1.34 3.60 0.48 12
05113  1347 G5I 1.76 1.37 12
05381  1012 G2I 0.37 0.76 0.40 2.87 0.51 04
07331  0021 G5Iab 1.70 0.77 3.60 0.88 10,13
07582  4059 G5I 1.60 0.98 5.69 2.86 01
10215  5916 1.53 3.03 3.12 1.77 01
13203  5917 G2I 5.02 6.31 4.94 01
13313  5838 K5I 2.86 2.31 4.07 1.94 0.06 01
15210  6554 K2I 3.28 1.54 7.65 1.87 0.98 01
16494  3930 G2I 1.13 2.54 0.82 1.38 01
17300  3509 G2I 1.18 1.08 5.21 1.30 01
17317  2743 G4I 2.66 1.59 2.06 1.68 2.07 14
17332  2215 K2I 1.20 1.72 5.35 3.93 0.46 01
17370  3357 G3I 0.27 0.27 0.67 2.53 2.39 1.88 01
17388  2203 G0I 1.34 1.34 0.30 3.52 0.99 1.78 01
18075  0924 G2I 1.21 0.91 1.66 1.86 01
18096  3230 G3I 1.69 0.16 1.57 6.02 1.68 01
18582  0001 K2I 1.51 4.62 2.64 01
19356  0754 K2I 2.90 1.62 6.51 2.90 01
19477  2401 G0I 14
Table 2: Equivalent widths for cold stars.
IRAS SpT TT log log  [Fe/H][Fe/H] ref.
number (K) (dex)
Warm stars (6000  T 8000 K)
15039  4806 A0I 8000200 1.250.25 -0.850.10 07
14325  6428 A8I 8000125 1.000.25 -0.560.16 03
19500  1709 F0Ie 8000125 1.000.25 -0.590.10 03
08281  4850 F0I 7875125 1.250.25 -0.260.11 03
20572  4919 F3Ie 7500200 2.000.50 -0.010.10 13
15482  5741 F7I 7400150 1.400.20 -0.470.16 08
06530  0213 F0Iab: 7375125 1.250.25 -0.320.11 03
08005  2356 F5Ie 7300250 06
07134  1005 F7Ie 7250200 0.500.30 -1.000.20 04
08143  4406 F8I 7150100 1.350.15 -0.390.12 15
17436  5003 F3Ib 7065125 0.910.15 -0.090.10 09
04296  3429 F7I 7000250 1.000.50 -0.690.20 02
19386  0155 F5I 6800100 1.400.20 -1.100.15 12
19114  0002 G5Ia 6750200 0.500.25 -0.450.20 11
05341  0852 F5I 6500200 1.000.50 -0.720.12 04
22223  4327 F7I 6500125 1.000.25 -0.300.11 03
08187  1905 F6Ib 6250200 0.500.20 -0.590.15 01
18025  3906 G1I 6250100 0.250.25 -0.450.16 10
20259  4206 F3I 6100200 2.200.25 -0.100.15 10
12067  4508 F6I 6000250 1.500.50 -2.000.12 16
07430  1115 G5Ia 6000125 1.000.25 -0.330.15 03
Cool stars (4500  T 5500 K)
05113 + 1347 G5I 5500125 0.500.25 -0.540.17 03
05381 + 1012 G2I 5200100 1.000.50 -0.800.17 05
01259 + 6823 GIab: 5000200 1.500.25 -0.600.12 01
13313  5838 K5I 4540150 2.200.30 -0.090.05 14
07331 + 0021 K3/K5I 4500200 1.000.25 -0.160.16 01
Table 3: Atmospheric parameters used as calibrators taken from literature.

2 Stellar sample

The sample used in this work was selected from the Suárez et al. (2006)’s PAGB list. The full sample contains a total of 103 PAGB stars with spectral types ranging from B to M.

Figure 2: Correlation between the equivalent widths measured with the automatic code with those taken from IRAF code. Three objects IRAS 01919 + 0373, IRAS 08281 - 4850, IRAS 22223 + 4327 with spectral types A0, F0 and G0 has been used to compare their results.

For this work we select a set of 70 PAGB stars with spectral types ranging from A to early-K and luminosities classes I and Ie (where “e” means emission lines). The selected sample was divided in 50 warm (6000  T 8000 K) and 20 cold (4500  T 5500 K) PAGB stars.

Subsequently, we identified in the sample those stars that have stellar atmospheric parameters T, log  and [Fe/H] derived by spectroscopic methods. A total of 21 warm and 5 cold PAGB stars have these parameters determined in the literature with the exception of IRAS 08005 - 2356, which has only temperature estimation. In warm PAGB stars, some of them have temperature that are not consistent with their spectral types (i.e. are misclassified). Table 3 provides the stellar atmospheric parameters used as calibrators collected from the literature for the PAGBs in this study.

We choose a total of 9 absorption features which have been widely used as criteria for MK spectral classification system. The limitations of some spectra in the spectral range (at the blue and near infrared region) make impossible to measure the total equivalent widths for all objects. In warm-PAGB stars, for example a total of 7 objects do not have measures of the equivalent widths and other 8 of them only have a single measure (i.e. the \ionFei feature at 4383Å) preventing the estimation of their fundamental parameters. In cold-PAGB stars, on the other hand, only one object does not have measures of the equivalent width.

2.1 Determination of equivalent widths

The quantification of equivalent widths was done in an automatic manner. In this sense we have developed a code that replaces the true continuum by a pseudo-continuum through the interpolation of a straight line that connect the peaks on both sides of an absorption line (see Figure 1).

The equivalent width is then defined as the effective area occupied between the two maximum interpolated , where is a wavelength interval (or its dispersion). Table 1 and 2 shows the quantified measures of 9 equivalent widths of absorption lines selected in this study.

We can compare the measurements of equivalent widths from the automatic code and those done manually with the IRAF code. We use the quantifiable parameters of IRAS 01919 + 0373, IRAS 08281 - 4850, IRAS 22223 + 4327 with spectral types A0, F0 and G0 respectively. From Figure 2 we note that for weaker absorption lines (i.e. with low measures and intermediate equivalent widths) their values are in good agreement among themselves, while for stronger lines their values show slight systematic differences between them, which increase slightly its error. The outliers obtained with this method are usually due to poorly measured of the equivalent widths caused by a poor maximuum points determination.

2.2 MK criteria

Our atmospheric parameters were estimated from features used by the MK system.

In determining the effective temperature we have used the equivalent widths of the calcium line \ionCaiiK at 3933 Å (warm stars) and the G-band at 4302 Å (cool stars). The \ionCaiiK feature grows dramatically in strength of A-type toward to late types (F8), for cooler spectral types their equivalent widths remain flat. Other features as \ionCai at 4226 Å and \ionMni at 4030 Å blend are not useful to estimating the temperature in warm stars.

In the G-type stars, the G-band characteristically dominates over other features. This feature increase in strength until about K2 and then decreases in intensity. Another feature as \ionMgi at 5167-72 Å triplet shows some sensitivity to temperature for cold objects.

For the surface gravity we employ ionized lines like criteria for its determination (4172–79 Å and 4395-4400 Å blends, \ionSrii at 4077 Å and \ionMgii at 4481 Å). It is also possible to use the neutral oxygen (\ionOi triplet 7771-5 Å) located in the near IR-region. In warm stars, however, only the 4172–79 Å blend of \ionFeii and \ionTiii shows sensitivity to the gravity. While the \ionSrii at 4077 Å and \ionCai at 4226 Å lines show sensitivity to gravity in cold stars.

In order to obtain the stellar metallicity we used only absorption lines of neutral iron, i.e. \ionFei (4063 Å), \ionFei (4271 Å) blend and \ionFei (4383 Å). We discard any ionized iron lines because of their expected dependence on log . In warm stars, we use as metallicity indicator the sum of iron lines \ionFei (4271 Å blend + 4383 Å), while the \ionFei (4063 Å and 4383 Å) were employed in cool stars.

The lines of \ionNaiD at 5889-95 Å and \ionOiT at 7771-5 Å are used as probable indicators for the determination of the stellar distance. The interstellar component of \ionNaiD lines at 5889-95 Å show sensitivity to luminosity in young stars, however, in evolved stars (as PAGB stars) both lines are affected by circumstellar material and therefore does not show dependence to luminosity. The \ionOiT lines at 7771-5 Å, on the other hand, also show sensitivity to luminosity. In fact, Arellano Ferro et al.(2003) found accurate spectroscopic calibrations between visual absolute magnitudes and the \ionOiT lines for a sample of 27 calibrator stars with spectral types A to G.

Figure 3: Trend of dispersion with the spectral type. We see that dispersion shows a tendency to increase with the increase of the spectral type in both warm and cold stars.

Because of the spectral range limitation in the near infrared region, the lines of hydrogen Paschen series, the oxygen and calcium triplet lines are very rare in the total sample. The equivalent widths of all features are represented in Table 1 and  2, respectively.

2.3 Error in the equivalent widths

An accurate determination of systematic and random errors of the equivalent widths is not trivial, since these come to be a function of the magnitude, spectral type, the S/N ratio and the pseudo-continuum position. We also need common stars with the same spectral types and several measures of their stellar spectra. This sample has limitations of objects with the same spectral types and also with scarce measurements of equivalent widths, which is impossible to carry out a reliable statistics.

In this section we can estimate an approximation between the errors of the equivalent widths of the selected absorption lines and the spectral types. In this sense, the spectral types were replaced by numerical values in the following sequence: A0 = 30, F0 = 40, G0 = 50 and K0 = 60 respectively. The intermediate values are between two successive classes. In view of the difficulties presented by the observational data (mentioned in the above paragraph), we decided to correlate the equivalent widths determined through the automatic code with those obtained from the IRAF code for both samples as shown in Figure 2.

A dispersion, , is obtained for each spectral type (or an average , if the spectral type is repeated), which varies from 0.02 to 0.47 in the warm stars and from 0.15 to 0.35 in the cold stars. In Figure 3 we observe that the dispersion shows a tendency to increase with the increase of the spectral type in both warm and cold stars. This dispersion results in an error in the effective temperature, T, such that using the equation 1 leads to a variation between 5 K to 68 K and from 63 K to 122 K using equations 2 and 3 respectively.

With these arguments we can infer that the new spectroscopic calibrations in effective temperature, gravity and metallicity are not affected by the dispersion in the equivalent withs.

2.4 Sample for calibration

Table 3 shows the PAGB stars that have been studied and reported in the literature. This table contains the number IRAS, spectral type, the stellar atmospheric parameters obtained from different sources and their respective references. Their stellar parameters were obtanied by different authors using spectroscopic methods.

We can observe that there are a total of 21 stars considered as warm-PAGB stars and a very small number of only 5 objects for the cold-PAGB stars. In spite of having a small number of stars as calibrators is possible to obtain a rapid and accurate determination of fundamental parameters (effective temperature, the surface gravity and the metallicity) using only suitable spectral criteria, avoiding photometric indices which are often distorted by poor known interstellar and circumstellar reddening.

In the recent past, two papers that involve photometric calibrations (Strömgren and 2MASS photometry) and that allows to estimate the stellar parameters for a group of post-AGB and RV Tauri stars were done by Arellano Ferro et al. (2010) and Molina (2012).

IRAS T T log  log  [Fe/H]
number ( 220K) ( 91K) (0.27) (0.21) (0.19)
02143  5852 7967 0.68
02528  4350 7981 0.71
07253  2001 7826 1.39 1.28 0.81
08005  2356 1.32 1.17 0.92
08213  3857 7872 1.28 0.67
10215  5916 6461
10256  5628 6257 0.85 1.18 0.42
11201  6545 7723 1.26 0.86
11387  6113 6209 7707 0.75 1.28 0.63
13245  5036\tabnotemark1 7077 0.77
14429  4539 7981 0.95 1.23 0.63
14482  5725 7402 1.13 1.01
14488  5405 7578 7950 0.86 1.28 0.75
15310  6149 5787 7915 0.98 1.35 0.77
16206  5956\tabnotemark1 7382 0.86
16283  4424 5699 7457 0.82 0.09
17106  3046 6709 0.97 0.47
17208  3859 5734 7856 0.96 1.31 0.58
17245  3951 6781 0.91 1.08 0.22
17287  3443 8024 0.69
17310  3432 7869
17376  2040\tabnotemark2
17441  2411 5404 7037 0.95 1.21 0.52
17488  1741\tabnotemark2 5860 0.73
17576  2653 7026 7365 1.26 0.64
17579  3121 5845 7790 0.78 1.01 0.56
18044  1303\tabnotemark2
19207  2023 4785 6638 0.71 0.85
19422  1438\tabnotemark2 6383 0.72
19589  4020\tabnotemark2 5231 0.78
20160  2734 6168 7454 0.80 1.09 0.36
21289  5815 8015 1.22 0.35

Emission lines.

Not has measured EWs.

Table 4: Atmospheric parameters estimated from equivalent widths for warm stars.
IRAS T T T log  log  [Fe/H]
number ( 220K) (207K) (175K) (0.27) (0.20) (0.30)
07582  4059 5042 1.12
10215  5916 5027 4852
13203  5917 6355 1.23
15210  6554 4848 0.74 0.21
16494  3930 6227 5232 4990 1.15 0.61
17300  3509 5007 1.10 1.02 0.43
17317  2743 5432 4831 1.14 0.28
17332  2215 4786 1.03
17370  3357 4869 5236 5149 0.78\tabnotemarka
17388  2203 5267 4823 1.06 0.54
18075  0924 5517 5599 5066 1.23 0.21
18096  3230 4838 0.75 0.28
18582  0001 1.10
19356  0754 4820 1.44
19477  2401
Table 5: Atmospheric parameters estimated from equivalent widths for cold stars.

2.5 Polynomial’s fitting

The stellar atmospheric parameters can be determined by fitting a series of polinomials whose independent variables are equivalent widths. Our goal is to analyze the actual dependence of the stellar parameters with respect to one or two quantifiable features. The mathematical representation of the polynomial, in general, has the form

where is any of the three stellar parameters (T, log  and [Fe/H]), a are the coefficients to determine and and are the independent variables. When the number of independent variables is greater than one we used the method adopted by Stock & Stock (1999). This method developed a quantitative method to obtain stellar physical parameters such as absolute magnitude, intrinsic colour, and a metallicity index using the equivalent widths of absortion features in stellar spectra by means of polynomials and a consistent algorithm (Molina & Stock 2004).

In order to determine the best coefficients we employ an algorithm based on least squares. This algorithm performs an initial fitting and removes those values of residuals greater than 2-. The error of each coefficient is obtained from

where the diagonal matriz and is the mean square error.

3 Stellar atmospheric parameters

The main objective of this work is to build a set of spectroscopy calibrations to derive T, log  and [Fe/H] for PAGB stars. We employ the data contained in Tables 1, 2 and 3. In this section we will show the best fits when comparing the equivalent widths with the stellar atmospheric parameters taken from literature.

Figure 4: Relation between the stellar atmospheric parameters as a function of equivalent widths for warm stars (left panel) and cold stars (right panel). Left panel. The empty squares represent those stars that left out of the best fit.

3.1 T’s calibration

For the determination of effective temperature in warm-PAGB stars we use equivalent widths of the \ionCaiiK at 3933 Å. This line has been considered in the MK system as an indicator of temperature in warm stars (Gray & Corbally 2008). Particularly, for stars with temperature between (6000  T 8000 K), the equivalent widths show sensitivity to effective temperature. A code based on least squares that relates equivalent widths and the effective temperature taken from literature (T) leads to the following relationship

(1)

where this calibration is valid for a range in the equivalent widths between 0.76  T 13.15 Å. The standard deviation derived from the equation (1) is 91 K. Four stars are left out of the fit, i.e. IRAS 08143 – 4406, IRAS 08281 – 4850, IRAS 14325 – 6428 and IRAS 22223 + 4327 respectively. The stellar temperature estimated by De Smedt et al. (2016) for IRAS 08281 – 4850, IRAS 14325 – 6428 and IRAS 22223 + 4327 are 7875 K, 8000 K and 6500 K and Reyniers et al. (2004) for IRAS 08143 – 4406 is 7150 K, while the fit of eq. (1) leads to values of 7674 K, 7211 K, 6809 K and 6856 K respectively.

In late-PAGB stars (4500  T 5500 K), on the other hand, is possible to determine the effective temperature from the G-band at 4302 Å. In spite of only 5 stars are present in the fit, is possible therefore to determine the effective temperature applying a linear fit

(2)

The equation (2) is valid for a range in the equivalent widths between 1.76  T 4.08 Å and where the standard deviation reached is 207 K. Two objects are left out of this relationship, IRAS 01259 + 6823 (5000 K), IRAS 22223 + 4327 (4500 K) and the fit for both objects reaches the same temperature value of 4788 K.

The stellar temperature for identified cold PAGB stars can be increased by using the resonance \ionCai (4226 Å) line. This line is sensitive to temperature, since it grows gradually from the G-type to the early K-type stars being stronger in those stars with mid-K. A lineal relationship can be obtained by adjusting the temperature and the \ionCai equivalent widths for four calibrating stars, this is

(3)

where its standard deviation reaches a value of 175 K and the validation range for equivalent widths can be found between 0.40 Å and 2.31 Å and the temperature between 4550 Å and 5200 Å. The results of effective temperature estimated by equations (1), (2) and (3) are in the third and fourth column of Tables 4 and  5. In the top of Figure 4, we note the dependence of the \ionCaiiK-line and the G-band with the effective temperature (see left and right panels).

3.2 Log ’s calibration

In warm stars, we can estimate the surface gravity using the Fe,TiII blend at 4172-9 Å. This blend is constituted mainly by ionized lines of Fe and Ti and has been considered as indicator as luminosity in A-F type stars. A lineal fit leads to the following relationship

(4)

The range of validation of this calibration in surface gravity covers 0.50 log  1.40, while the equivalent widths of the ionized line vary between 0.50 \ionFeTiii  3.90 Å. The standard desviation leads to a value of =0.21. Two stars fall out of the fit of eq (4), i.e. IRAS 07134 + 1005 and IRAS 18025 – 3906. According to spectral types (or effective temperature), IRAS 07134 + 1005 and IRAS 18025 – 3906 it would be expected that their equivalent widths were slightly greater than 4 Å.

We can extend the range in the surface gravity at higher values using the \ionOi triplet lines. Due to the limitations of the spectral range to the near infrared region, the number of \ionOi triplet lines are very scarce. Even though their values are not report in Table 4, and we will only show the functional relationship

(5)

where the range on gravity vary from 1.00 to 2.20 and their equivalent widths between 0.07 to 1.95 Å respectively. The standard desviation leads a value of =0.35.

In cold stars, the surface gravity is estimated using the \ionSrii-line. This line has been considered as the principal luminosity discriminator for cool stars in MK classification. Unfortunately the functional relationship is built with only 3 stars and this has the following form

(6)

The range of validation of this calibration in surface gravity covers 1.00 log  1.50, while the equivalent widths of the ionized line vary between 0.77 \ionSrii  2.95 Å. The standard desviation leads to a value of =0.20. We can also estimate the gravity for additional cold PAGB stars 132035917, 164943930, 173172743 and 173882203 when recovering the equivalent widths of the \ionSrii line from the \ionMgii line. An error of 0.25 is introduced when making this estimation.

The results of surface gravity estimated by equations (4) and  (6) are in the fifth and sixth column of Tables 4 and  5. In the middle of Figure 4, we see the dependence of the \ionFe,Tiii blend and the \ionSrii with regard to surface gravity (see left and right panels).

3.3 [Fe/H]’s calibration

For the calibration of metallicity we used only neutral Fe lines. In warm stars, we use the sum of \ionFei (4271 Å + 4383 Å). The best fitting that recovers the metallicity is generated by a polinomial that have the form

(7)

The range of validation of this calibration on metallicity covers 0.09  [Fe/H] 1.00 dex, while the equivalent widths of Fe lines vary between 0.34 \ionFei  4.40 Å. The standard desviation for this relationship is 0.19 dex. Two outliers are present in this fitting; IRAS 19386 + 0155 to very low metallicity (1.00 dex) and IRAS 20572 + 4919 to solar metallicity (0.01 dex) respectively.

In cold stars, we employ the \ionFei lines at 4063 Å and 4383 Å. Of the 17 cold-PAGB stars only 5 objects have identified stellar parameters. For the \ionFei (4353 Å) line the five objects are available for the calibration. The best fitting that recovers the metallicity within a range of 0.09  [Fe/H] 0.80 dex, involves a lineal polynomial for \ionFei line at 4383 Å, that is

(8)

where the range of equivalent widths vary between 0.48 to 1.94 Å and the standard desviation leads a value of =0.30 dex.

On the contrary, the best fitting for \ionFei line at 4063 Å has the form

(9)

The range of equivalent widths vary between 0.48 to 2.86 Å and the standard desviation leads a value of =0.30 dex.

The results of metallicity estimated by equations (7) and  (8) are in the sixth and seventh column of Tables 4 and  5. In the bottom of Figure 4 we observe the dependence of the \ionFei lines with regard to metallicity (see left and right panels).

4 Results and discussion

The results of the stellar parameters (columns 3, 5 and 6) for the sample studied are shown in Tables 4, 5 respectively. In general, the limitation in the spectral range and the low number of objects with identified stellar parameters lead to the fact that spectroscopic calibrations can not be applied individually to the total sample studied.

For the warm-PAGB stars, we observe that the \ionCaiiK line show a strong dependence on the effective temperature (see Fig. 4). However, the equivalent widths have been measured only for 9 objects out of a total of 29 identified. In order to expand the number of objects with the new values of T, we estimate the equivalent widths of the \ionCaiiK line from Fe,Ti II (4172-9 Å) blend and \ionFei (4383 Å).

Clearly this procedure introduces an uncertainty of 220 K to the temperature of the additional PAGB stars, i.e. 072532001, 082133857, 112016545, 113876113, 144825725, 144885405, 153106149, 172083859, 173103432, 175793121 and 192072023 respectively. A similar procedure has been applied to surface gravity and metallicity in order to add new values for those objects not studied.

Figure 5: Comparation between effective temperature and surface gravity obtained from 2MASS photometry by Molina (2012) and effective temperature and surface gravity estimated in this work (see upper and bottom panels). The solid stright line in each panel denotes perfect agreement between the sets of data.

For surface gravity the equivalent widths of the Fe,Ti II (4172-9 Å) blend is derived from the \ionMgii (4481 Å) line and 4 PAGB stars (072532001, 112016545, 144825725 and 144885405) were added with an uncertainty of 0.30. The \ionOi (7771-5 Å) triplet line can also be used to determine the surface gravity of those stars with 1.0  log  2.2 respectively. According to MK classification system the \ionOi triplet is sensitive to luminosity (or gravity).

In metallicity the neutral iron blend of \ionFei (4271 Å) is determined from \ionFei (4383 Å) line. An uncertainty of 0.31 dex is estimated for additional PAGB stars; 072532001, 080052356, 112016545, 144825725, 144885405 and 153106149 respectively.

In cold-PAGB stars, however, the G-band and the \ionFei (4383 Å) line have measures of equivalent widths for most objects, except the \ionSrii (4077 Å) and \ionCai (4226 Å) line that is present only for 12 and 17 objects. Unfortunately, the number of objects with identified stellar parameters is very scarse, which means that the calibrations made are few unreliable. The results in the metallicity that have a subindex “a” represent the values obtained from eq. 9.

We can compare our results in T and log  with a source whose values come from photometric calibrations for PAGB and RV Tauri stars (Molina 2012). The values of T and log  determined from the photometric calibrations are found in the second and fourth columns of Tables 4 and 5, respectively. In the upper and bottom panels of Figure 5 we can see the comparison between the spectroscopic and photometric calibrations.

From the Figure 5 we can observe that the T and log  obtained spectroscopically from eq. (1) and (3) (warm stars) and from eq (2) and (5) (cold stars) are slightly higher than T and log  obtained photometrically from Molina’s calibrations. PAGB stars with temperature close to 5000 K seem to be adjusted satisfactorily but at a higher temperature the dispersion increase. In surface gravity, on the other hand, the spectroscopic values seem to show agreement within their uncertainties with photometric values. These results indicate that the interstellar and circumstellar reddening significantly affects the fundamental parameters when using photometric techniques.

Finally, the equivalent widths of \ionOiT line do not show dependence to distances derived by Vickers et al.(2015).

5 Summary and conclusions

We presented a set of spectroscopic calibrations to obtain T, log , and [Fe/H] from equivalent widths of stellar spectra. The criteria choosen for selection of the absorption features are similar to employed by MK classification system. The equivalent widths for a total of 9 absorption features were measured.

We selected a total of 67 PAGB stars that include spectral types A and K, of which, 48 of them have a temperature between 6000 and 8000 K (warm stars) and 19 have temperature from 4500 to 5500 K (cold stars). For the determination of the spectroscopic calibrations we have identified the stellar parameters in the literature of 21 warm-PAGB stars and 5 cold-PAGB stars respectively.

We show the dependence of the stellar parameters with respect to the equivalent widths, although the limitations present in the spectral ranges make it difficult to determine the temperature, gravity and metallicity for all sample without previuos studies, i.e. 27 warm-and 14 cold-PAGB stars. These calibrations would be very useful to develop suitable criteria for the rapid and accurate determination of fundamental parameters for PAGB stars. The use of only spectral criteria is very important because it allows to define the parameters for such objects, while the photometric indexes are often distorted by poor known interstellar and circumstellar reddening.

As future work it is possible to expand the spectral ranges and criteria in order to involve a great number of absorption features and to improve our spectroscopic calibrations for warm-and cold-PAGB stars using high-resolution spectra.

Acknowledgments

We are grateful to Dr. Arturo Manchado for providing us the sample of low-resolution stellar spectral. We are thankful to Carolina Foundation for financial supporting to visit to Canarias Astrophysical Institute to Spain. We thank to Dr Sunetra Giridhar, Dr Armando Arellano Ferro and Dr Valentina Klochkova for numerous comments and valuable sugestions on the text. We express our gratitude to the anonymous referee for detailed comments that have improved the interpretation of the data and text.

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