Mentari: A pipeline to model the galaxy SED using semi analytic models

The study of galaxy evolution has a long history, both theoretically and empirically. The general view of how the large-scale structure in the Universe grows includes an understanding of the virialization of dark matter and baryons, gas cooling, star formation, feedback, and mergers. Galaxy properties are driven by various possible scenarios of how such nonlinear processes occur and compete. These properties include the stellar mass, star formation history (SFH), metallicity, initial mass function (IMF), and physical state and quantity of dust and gas ([Conroy (2013), Conroy 2013]).

From the theoretical side, semi-analytic models (SAMs) have been widely used to predict the evolution of galaxies. Such models are run as a post-processing step on dark matter only N-body simulations. SAMs consist of a set of coupled differential equations, both empirically and/or physically driven, that describe each physical process believed important. Compared to a hydrodynamical simulation that solves the equations of gravity and fluid dynamics of each particle, SAMs are significantly more computationally efficient and faster at exploring the parameter space.

On the observation side, the spectral energy distribution (SED) of stars and interstellar medium in galaxies encode many of the fundamental aspects of galaxies that are key to studying their evolution. A large number of surveys using different methods have been conducted to measure the SEDs of galaxies, from wide field surveys of the local Universe such as the Sloan Digital Survey (SDSS, [York_etal00, York et al. 2000]), and the Two-degree Field Galaxy Redshift Survey (2dFGRS, [Coless et al. (2001), Coless et al. 2001]), to the deep-field survey of the high-redshift universe such as the Deep Extragalactic Evolutionary Probe (DEEP2, [Davis et al. (2003), Davis et al. 2003]).

To infer the properties of galaxies from the SED, an early approach involved trial-and-error techniques by combining stellar spectra until they matched the observations ([Spinrad & Taylor, (1971), Spinrad & Taylor 1971]). Following this, an automated fitting technique that incorporated physical constraints was developed ([Faber (1972), Faber 1972]). These methods actually matured into what has become the standard technique today, known as stellar population synthesis (SPS) modeling; it uses stellar evolution theory to constrain the range of possible stellar populations at a given age and metallicity ([Tinsley (1968), Tinsley 1968]). Currently, a number sophisticated models of galaxy spectral evolution have been developed for public use (e.g., [Bruzual & Charlot, (2003), Bruzual & Charlot 2003], [Conroy & Gunn, (2010), Conroy & Gunn 2010]).

This work combines the physically motivated star formation and metallicity histories from a SAM with the widely-applied method of stellar population synthesis. The predicted SED covers wavelengths from the far UV to infrared, will eventually include dust, gas and AGN physics, and thus will be able to tell a complete history of each galaxy and identify their fundamental properties.

The galaxy model we use is called Semi-Analytic Galaxy Evolution, or SAGE for short ([Croton et al. (2016), Croton et al. 2016], [Croton et al. (2006), Croton et al. 2006]). SAGE is a modular code written in C and available at https://github.com/darrencroton/sage. We run SAGE on the Millennium simulation of [Springel et al. (2005), Springel et al. (2005)]. This cosmological simulation follows the growth and interaction of dark matter particles in a box of length 500$h^{-1}$ Mpc. There are $2160^{3}$ particles, each with mass $8.6\times 10^{8}h^{-1}M_{\odot}$. A dark matter halo is defined to have a minimum of 20 particles. The simulation assumes the standard WMAP1 cosmological parameters ([Spergel et al. (2003), Spergel et al. 2003]).

SAGE consists of coupled equations that track the evolution of baryons inside dark matter halos, including the process of gas cooling, star formation, feedback, mergers, starbursts, and the effect of early Universe reionization. The details of the model can be found in [Croton et al. (2016), Croton et al. (2016)]. When parameterizing the model, our main objective is to reproduce the stellar mass function at redshift zero. For producing stellar mass, we use the initial mass function of [Chabrier, Chabrier (2003)]. We give an example of how changing the star formation and AGN feedback efficiency can significantly change the stellar mass function in Fig. 1. For this example, we run SAGE on the mini version of Millennium simulation, made for testing purposes. The mini version is identical to the full version but in a smaller box of side length 62.5$h^{-1}$ Mpc. We use the stellar mass function presented in [Baldry, Glazebrook & Driver (2008), Baldry, Glazebrook & Driver (2008)] as the observational benchmark in setting the model parameters.

We compute the star formation and metallicity histories of  36 thousand galaxies from $z=127$ to $z=0$ using SAGE. Fig. 2 and shows an example of the star formation and metallicity history of a Milky Way like galaxy (morphologically spiral, stellar mass $5.86\times 10^{10}M_{\odot}$, star formation rate $1.6M_{\odot}yr^{-1}$) and a typical elliptical galaxy with no current star formation rate and present stellar mass of $9.3\times 10^{10}M_{\odot}$ in the simulation. We can see the history of the spiral galaxy consists of several starbursts triggered by merger events of varying significance, and it is still undergone the star formation activity at z=0. Conversely, the elliptical galaxy had been dead since a lookback time of 8 Gyr. Using SAGE to build the star formation and metallicity histories of a large number of galaxies gives us the flexibility to customize our subject of interest. For example, it allows us to select galaxies with certain properties or history, explore the star formation activity occurring only in disk or bulge, or even look only at the intra-cluster stars around massive galaxies. The idea is to enable us to build a library of theoretical galaxies to be referenced against their observational counterparts.

Mentari is an SED generation pipeline that takes semi-analytic galaxy model data as its input. The code is python-based and although still under development, has been made publicly available at https://github.com/dptriani/mentari. It has four simple functions.

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  read_properties(redshift, firstfile, lastfile, directory, filename).

  This function reads the properties of simulated galaxies from the SAGE model output.

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  build_history(redshift, firstfile, lastfile, directory, filename). This function uses the merger tree to the correct star formation and metallicity history for each galaxy from the desired redshift. Each merger in a tree needs careful treatment because when one occurs, the old stars from the satellite galaxy will merge to the central, while the central may additionally undergo a starbursttriggered by the merger. This function will separate old stars and newly formed stars and make sure they are assigned the correct age.

• •

  generate_SED(lookbacktime, mass, metallicity). This function generates the SED from the star formation and metallicity history calculated in build_history.

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  mab(wavelength, spectra, filter_list, z). This function computes the AB magnitudes for the listed filters at the specified redshift. It will produce apparent magnitudes when the redshift is greater than zero, otherwise it assumes the user wants the absolute magnitude.

To construct the SED, mentari reads the star formation history and metallicity evolution directly from SAGE and uses the [Bruzual & Charlot, (2003), Bruzual & Charlot (2003)] stellar population synthesis library, although the pipeline will be flexible and allow other libraries. This library contains spectra per unit mass of single stellar populations at ages between $1\times 10^{5}$ and $2\times 10^{10}$ years with metallicities that range from $0.005Z_{\odot}$ to $5Z_{\odot}$. The spectra cuurently cover panchromatic wavelengths from $91\AA$ to $160\mu$m. For the stellar evolution tracks and initial mass function we use Padova 1994 ([Alongi et al. (1993), Alongi et al. 1993], [Bressan et al. (1993), Bressan et al. 1993], [Fagotto et al. (1994a), Fagotto et al. 1994a], [Fagotto et al. (1994a), Fagotto et al. 1994b], [Girardi96, Girardi et al. 1996]) and [Chabrier (2003), Chabrier (2003)], respectively.

We provide a set of filters in the pipeline to convolve the SED to AB magnitude. We can create photometric datasets of galaxies at any redshift that can then be compared with observations. Using mentari, we construct the SED and the SDSS ugriz photometry for  36 thousand galaxies from our model at z=0. We compare with the luminosity function from the GAMA survey ([Kelvin13, Kelvin et al. 2013]). This is shown in Fig. 3.

Mentari is currently still under development. The future enhancements will include additional stellar population models; more sophisticated dust modelling, especially for the IR part of the spectrum; quasar and radio mode AGN components to the composite SED; emission and absorption lines in the SED; and $H_{I}$ and $H_{2}$ gas components. The modular nature of mentari will mean that such enhancements can be included incrementally as the technical resources and scientific needs dictate.