arXiv:1103.3269v3 [astro-ph.CO] 19 Jul 2011 Draft version September 27, 2011 Preprint typeset using L A T E X style emulateapj v. 11/10/09 CIGALEMC: GALAXY PARAMETER ESTIMATION USING A MARKOV CHAIN MONTE CARLO APPROACH WITH CIGALE Paolo Serra 1 , Alexandre Amblard 1 , Pasquale Temi 1 , Denis Burgarella 2 , Elodie Giovannoli 2 , Veronique Buat 2 , Stefan Noll 3 , Stephen Im 1 Draft version September 27, 2011 ABSTRACT We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code CIGALE (Code Investigating GALaxy emission). The original CIGALE builds a grid of theoretical Spectral Energy Distribution (SED) models and fits to photometric fluxes from Ultraviolet (UV) to Infrared (IR) to put contraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. Markov Chain Monte Carlo methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well known and studied SINGS sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time. Subject headings: galaxies: fundamental parameters - methods: data analysis 1. INTRODUCTION The spectral energy distribution (SED) of galaxies de- pends on many physical processes related to the emis- sion from different stellar populations, absorption and re-emission from dust and gas and possible presence of Active Galactic Nuclei (AGN). Each process has been studied by many authors; libraries of stellar population models (Fioc & Rocca-Volmerange (1997), Bruzual & Charlot (2003), Maraston (2005)), fitting curves for dust emission (Calzetti et al. (1994, 2000), Witt & Gordon (2000)), studies of emission of dust grains (Chary & El- baz (2001), Dale & Helou (2002), Lagache et al. (2003, 2004), and Siebenmorgen & Kr¨ ugel (2007), Silva et al. (1998), Dopita et al. (2005), da Cunha et al. (2008)) are the basis of sophisticated fitting codes which derive physical parameters such as stellar mass, star formation rate, dust luminosity and so on. Many parameters are usually necessary to describe these processes and model theoretical SEDs of galaxies. A grid of theoretical SED models is usually built and fitted to the data and statistical properties are derived for the pa- rameters of interest. A big drawback of any grid-based method is that, for any fitting process, the time to build models grows linearly with the number of models and then about exponentially with the number of parame- ters involved: such approaches are difficult to implement for complex models involving a sufficiently large num- ber of parameters or when a fine sampling of the pa- 1 Astrophysics Branch, NASA/Ames Research Center, MS 245-6, Moffett Field, CA 94035. 2 Observatoire Astronomique de Marseille-Provence, 38 rue Frederic Joliot-Curie, 13388 Marseille Cedex 13, France. 3 Institut f¨ ur Astro- und Teilchenphysik, Universit¨ at Inns- bruck, Technikerstr.25/8, 6020 Innsbruck, Austria rameter space is necessary in order to retrieve statis- tically robust results. In the past few years, Markov Chains Monte Carlo (MCMC) techniques have started being widely used in physics. In cosmology, parameter estimation from cosmic microwave background data with MCMC methods has been introduced in Christensen et al. (2001) and has been implemented in the pub- licly available code cosmomc (Cosmological Monte Carlo, Lewis & Bridle (2002)) 4 ; in astrophysics, an MCMC ap- proach to the stellar population syntesis modeling has been introduced in Conroy et al. (2009). Here we use cosmomc as a generic sampler and we inter- face it to the publicly available code CIGALE 5 (Code Investigation GALaxy Emission, Noll et al. (2009)) in order to allow a fast and accurate evaluation of the mul- tidimensional parameter space probed by this code 6 . The main advantage of this method is that the comput- ing time to fit the data scales approximately linearly with the number of parameters involved, allowing the user to consider complex models with many parameters for only small additional computational time. MCMC techniques allow to probe also the shape of the probability distribu- tion, giving far more information than just best fit and marginalized values for the parameters. The paper is organized as follows; in the next section we briefly describe CIGALE, introducing the main parame- ters used in the subsequent sections. We then explain the MCMC technique implemented in the modified version of CIGALE, which we call CIGALEMC. We test our code 4 http://cosmologist.info/cosmomc/ 5 http://www.oamp.fr/cigale/ 6 During the completion of this work we noticed that Acquaviva et al. (2011) have performed a similar work in the context of the code GALAXEV developed by Bruzual & Charlot (2003).