IAUS241: Stellar population challenge

M. Koleva$^{1,2}$ and Ph. Prugniel1

2006 December 5

$\textstyle \parbox{0.8\textwidth}{
$^{1}$\ Observatoire de Lyon, 9 av. Charles...
...ty ''St. Kliment Ohridski'',5 James Bourchier Blvd., Sofia,BG-1164, Bulgaria
}$



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Abstract:

We present the results from test3 of the IAUS241 Stellar Population Challenge. We determined SSP-equivalent ages and metallicity, as well as the instrumental & physical broadening fitting the whole spectra against population models Pegase.HR-ELODIE and Vazdekis-Miles with a simple $\chi^{2}$ parametric minimization. We did not make error estimate by Monte-Carlo simulations because the lack of time. Our experience is that the fits are quite robust with respect to the choice of the wavelength range, but are sensitive to the stellar library, and in particular to the interpolation of the spectra in these libraries. See more tests and comparisons using spectrum fitting in the Poster by Koleva et al. (this conference).

Introduction

We developed a method to reconstruct the star formation history from intermediate resolution spectra (R$>\approx 1000$). The principle is to fit an observed spectrum against a population model to obtain in the same time the broadening (by the internal kinematics, but for the challenge it includes also the instrumental broadening) and the parameters of the stellar population [1]. For this purpose we prepared the ELODIE library2, based on 1962 spectra of 1388 stars covering the T, G, [Fe/H] space [6]; [7]. For this test we used the new version of the library (E3.1) which is ready for a public release. As models we are using SSPs produced by PÉGASE.HR3 at high resolution (R=10000, or $\delta\lambda=0.55$Å) [2] and, it order to check robustness, Vazdekis-MILES4 [3],[4]. The inversion is based on a simple parametric $\chi^{2}$ minimization. Pierre Ocvirk, developed a different non-parametric methods that is presented separately in the Challenge. In this report we are briefly describing the ingredients of our method, then we give the results of the tests and some comments.

The Method

. The three ingredients are (i) the stellar library, (ii) the population synthesis and (iii) the inversion program.

ELODIE.3.1

Along the different versions, the ELODIE library has grown in size and in quality. For the present work, we are using a new version which is not yet distributed, version 3.1. Different aspects have been improved: An important, even critical, step, after the data-reduction is the generation of the grid stars used to compute the models. The key points are (i) the atmospheric parameters of the stars and (ii) the interpolation over the library to produce spectra at given T, G and [Fe/H]. These two aspects have been improved. The version of this library will be released in a near future.

Pegase.HR

The Pegase.HR code has been previously described and we are using the version which is publicly available. The isochrones are slightly different than those of Vazdekis-Miles (giants are colder by 3%) and therefore, inversion with Pegase.HR may give ages 10-20% younger than Vazdekis-Miles for intermediate and old populations.

Inversion

The inversion program is based on classical kinematical fitting program. We made an implementation based on the PPXF 5 (penalized pixel fitting) code written by M. Cappellari [8]. First, a grid of models is computed using the synthesis code and an interpolation guarantying continuous derivatives provide a model for any given age and metallicity (and eventually any other parameter, if we are not fitting SSPs). Then a $\chi^{2}$ minimization takes all the observed spectrum (ie. each pixel) and returns the parameters of the line-of-side velocity distribution (LOSVD) and those of stellar population (age and metallicity):
\begin{displaymath}
{\rm {Obs_{px}}}= P_{n}*(SSP(Age,Z) \odot LOSVD(vsys,\sigma)) \, ,
\end{displaymath} (1)

where $Obs_{px}$ is the observational spectrum; $P_{n}$ is the multiplicative polynomial of order n, $SSP(Age,Z)$ is the best fitted SSPs model convolved the parameters of LOSVD (systematic velocity and velocity distribution). An important detail here, is the free multiplicative polynomial $P_{n}$ which makes the difference with classical SED fitting: The method is insensitive to the shape of the continuum. It is not affected by the calibration uncertainties nor by any extinction. Note than when using Pegase.HR with Elodie library, it is wise to use a high degree of multiplicative polynomial in order to absorb the residual oscillations of the flux calibration linked with the reconnection of the 67 orders (each order is 30 to 50 Åwide). The program eventually allows to fit a combination of bursts (or of any model), but for this Challenge tests, we restricted to SSPs.

Results

The degree of the multiplicative polynomial can be determined experimentally, testing how the residuals change with wavelength and degree. In practice, with Elodie, a degree greater than 10 is required, and the results are very stable when the degree is above 15 (for a wavelength range of 200-250 nm). With the Miles spectra, a degree of 5 is satisfactory, but a reasonably higher degree does not hurt. For the Challenge, we used a degree of 60 for the Pegase.HR spectra (which is more than necessary, but does not introduce any artifact; such a high degree is intended to compensate some residual oscillations of the continuum due to the reconnection of the orders of the Elodie spectra). We masked center of NaD where the reliability of the libraries is lower due to the correction of the telluric extinction and we masked also the region of water vapour (in library restframe) at 630 nm. Except for spectrum4 where the SNR is given for each pixel, we was assuming a reasonable SNR which is given in Table 1. As a consequence the estimate of the errors are not accurate. The $\chi^{2}$ are not correctly scaled, but the plots of the residuals show that there is in general some template missmach left. Unfortunately we was short in time and we did not perform Monte-Carlo simulations for proper estimation of the errors. For spectrum5 (which we could not avoid to recognize as M67, because we use it for some other tests) we was using line-spread function (LSF) injection. That is, we are determining the instrumental broadening as a function of wavelength and inject it in the population models. This complication was necessary because M67 has low physical velocity dispersion and the total broadening is limited by the instrument. In Table 1 we are presenting the results for the different spectra. In the figures from 1 to 7 we are showing the fits and the residuals.
The inversions with the two population models are consistent. In general, the ages found with Pegase.HR are younger than those found with Vazdekis-Miles by 10 to 40% (for two of the spectra the age returned by Pegase.HR is older by 10%). This difference may be connected with the choice of evolutionary tracks; it has the correct direction and order of magnitude.

Table 1: Results of the fit. SSP-equivalent ages and metallicities returned using each population model. The column [Mg/Fe] indicate the over-abundancy with respect to the library: $-$ (slightly under-abundant), $+$ and $++$ (slight or significant over-abundant). SNR, is the signal to noise ratio used to compute the noise seen in the Figures.
 Name PegaseHR(ELODIE 3.1)      
   age [Gyr] [Fe/H] [dex] age [Gyr] [Fe/H] [dex] Mg/Fe SNR  
 spectrum1 6.9 +0.1 10.2 0.00   100  
 spectrum2 5.6 -0.20 7.0 -0.30 - 100  
 spectrum3 3.9 0.00 4.4 -0.05 + 100  
 spectrum4 5.5 -0.01 5.8 -0.04 ++    
 spectrum5 3.8 -0.12 3.2 -0.06   100  
 spectrum6 5.9 +0.09 5.2 0.10   500  
 spectrum7 10.5 +0.04 12.6 0.00   500  

Figure 1: Inversions of spectrum1. There maybe a slight defect of the wavelength calibration in the middle of the spectrum (Mgb); this region seems slightly red-shifted (this is not a global shift which would have been absorbed by the LOSVD fitting).
\includegraphics[width=\textwidth]{sp1.ps} \includegraphics[width=\textwidth]{sp1_vaz_30.ps}
Figure 2: Inversions of spectrum2. Possibly a very slight Mg under abundancy compared to the libraries (which have the pattern of Solar neighborhood)
\includegraphics[width=\textwidth]{sp2_phr_30.ps} \includegraphics[width=\textwidth]{sp2_vaz_30.ps}
Figure 3: Inversions of spectrum3. Very slight Mg over-abundancy.
\includegraphics[width=\textwidth]{sp3_phr_30.ps} \includegraphics[width=\textwidth]{sp3_vaz_30.ps}
Figure 4: Inversions of spectrum4. Significant Mg over-abundancy.
\includegraphics[width=\textwidth]{sp4.ps} \includegraphics[width=\textwidth]{sp4_vaz_30.ps}
Figure 5: Inversions of spectrum5.(M67)
\includegraphics[width=\textwidth]{m67_phr_4000_md60.ps} \includegraphics[width=\textwidth]{m67_vaz_fwl_md60.ps}
Figure 6: Inversions of spectrum6. Apparent problem of wavelength calibration. (this is not a global shift which would have been absorbed by the LOSVD fitting)
\includegraphics[width=\textwidth]{sp6_phr_30.ps} \includegraphics[width=\textwidth]{sp6_vaz_30.ps}
Figure 7: Inversions of spectrum7. Synthetic population with Vazdekis-Miles
\includegraphics[width=\textwidth]{sp7.ps} \includegraphics[width=\textwidth]{sp7_vaz_30.ps}

Comments

Notes on individual fits

Spectrum4. If we do not mask the emission lines we find an older age (the given result is after masking the emission lines). In the plot is seen that this object is overabundant in $\alpha$-elements (the Mg$_{b}$ is not fitted well) in respect of the solar neighborhoods.
Spectrum5 (M67). For this spectrum, the age and metallicity determined with Pegase.HR varies between 3.8 and 2.9 Gyrs when the degree of the multiplicative polynomial is changed from 30 to 60, while the quality of the fit remains the same (this is an unusual behaviour of our program that we are going to investigate).
Spectrum6. There is an important wavelength calibration error. See the figures, in the zoom around Mgb. LSF injection would solve the problem (it is easy to do, but we have no time; we do not know how much it affects the result).
Spectrum7. It must be a spectrum of Vazdekis-MILES convolved by dispersion of $\approx 250$ km/s. The inversion using Vazdekis model is perfect! The inversion with Pegase.HR returns a slightly younger age that we believe is compatible with the difference of evolutionary tracks.

General remarks

From our experience with simulated spectra [9], dwarf galaxies (Chilingarian, this conference), and Galactic clusters (Prugniel et al., this conference) we can stress the following points:

Bibliography

1
Ocvirk et al.,2003, SF2A conf, 309

2
Damien Le Borgne et al. 2004, A&A,425, 881

3
Vazdekis et al., 2003,MNRAS, 340,1317

4
Sánchez-Blázquez, P.,2006, MNRAS, 371, 703

5
Le Borgne, J.-F. et al.,2003,A&A,402,433

6
Ph. Prugniel and C. Soubiran, 2001,A&A,369, 1048

7
Ph. Prugniel and C. Soubiran, 2004,astro-ph,0409214

8
M. Cappellari and E. Emsellem,2004, PASP, 116, 138

9
M. Koleva et al.,2006,astro-ph 0602362


Footnotes

... library2
http://www.obs.u-bordeaux1.fr/m2a/soubiran/elodie_library.html
... P\'EGASE.HR3
http://www2.iap.fr/pegase/pegasehr/
... Vazdekis-MILES4
http://www.ucm.es/info/Astrof/users/pat/models.html
... PPXF5
http://www.strw.leidenuniv.nl/ mcappell/idl/