GalSBI-SPS: Overview of the model

In this tutorial, we will give an overview of the stellar population synthesis-based galaxy population model GalSBI-SPS that is used in the galsbi package when using Tortorelli+25 in the model definition. We will explain how galaxy catalogs are generated and how the model can be customized. As in the phenomenological model, we assume that galaxies are split into two populations: star-forming (or blue) galaxies and quiescent (or red) galaxies, with a scatter that allows the two populations to overlap, reflecting the observed continuum of galaxy properties, in terms of both SEDs and global physical characteristics. More details for each component can be found in Tortorelli+25.

Galaxy stellar mass function

The first step GalSBI-SPS performs to generate a galaxy catalogue is to sample logarithmic formed stellar masses \(\log{\mathcal{M}}\) (in solar mass units \(M_{\odot}\)) and redshifts \(z\) from a redshift-evolving galaxy stellar mass function (GSMF). We model the GSMF as the sum of two Schechter functions, a low-mass component (l subscript) and a high-mass component (h subscript), with different parameter values for the populations of blue and red galaxies. The functional form is as follows:

\[\begin{split}\Phi(\log{\mathcal{M}}, z) = &\mathrm{ln}(10) e^{-10^{\log{\mathcal{M}} - \log{\mathcal{M}^*(z)}}} \\ & \times \left [ \phi_{l}^*(z) \left( 10^{\log{\mathcal{M}} - \log{\mathcal{M}^*(z)}} \right)^{\alpha_{l}+1} \right] \\ & \times \left [ \phi_{h}^*(z) \left( 10^{\log{\mathcal{M}} - \log{\mathcal{M}^*(z)}} \right)^{\alpha_{h}+1} \right].\end{split}\]

The parameters \(\alpha_{l}\) and \(\alpha_{h}\) are the low and high-mass component faint-end slopes, respectively. \(\log{\mathcal{M}^*(z)}\) is the characteristic stellar mass, assumed to be the same for the low and high-mass components. \(\phi_{\mathrm{l}}^*(z)\) and \(\phi_{\mathrm{h}}^*(z)\) represents the low and high-mass number density of galaxies at the characteristic stellar mass.

\(\alpha_{l}\) and \(\alpha_{h}\) can be modified in GalSBI-SPS with the parameters sm_fct_alpha_*_lowmass and sm_fct_alpha_*_highmass, where * can be either blue or red depending on the specific galaxy population.

In the current implementation, for \(\log{\mathcal{M}^*(z)}\) and \(\phi^*(z)\), GalSBI-SPS offers only a single parametrization:

  • sm_fct_parametrization = “logquadratic_power”:
    \[\begin{split}\log{\mathcal{M^*}}(z) &= \log{\mathcal{M^*}}_0 + \log{\mathcal{M^*}}_1 \times \log{(1+z)} + \log{\mathcal{M^*}}_2 \times \log{(1+z)}^2, \\ \phi^*_{\mathrm{l,h}}(z) &= \phi^*_{\mathrm{amp},\mathrm{l,h}} \times (1 + z)^{\phi^*_{\mathrm{exp},\mathrm{l,h}}}\end{split}\]

Each of the parameters \(\log{\mathcal{M^*}}_0\), \(\log{\mathcal{M^*}}_1\), \(\log{\mathcal{M^*}}_2\) has the same value for the low and high-mass component, but different values for the blue and the red populations. They can be defined as follows:

  • \(\log{\mathcal{M^*}}_{0}\): sm_fct_m_star_*_0_lowmass, where * can be either blue or red.

  • \(\log{\mathcal{M^*}}_{1}\): sm_fct_m_star_*_1_lowmass, where * can be either blue or red.

  • \(\log{\mathcal{M^*}}_{2}\): sm_fct_m_star_*_2_lowmass, where * can be either blue or red.

\(\phi^*_{\mathrm{amp}}\) and \(\phi^*_{\mathrm{exp}}\) have different values for the low and high-mass components and for the blue and red populations. They can be defined using the following parameters:

  • \(\phi^*_{\mathrm{amp},\mathrm{l}}\): sm_fct_phi_star_*_amp_lowmass, where * can be either blue or red.

  • \(\phi^*_{\mathrm{amp},\mathrm{h}}\): sm_fct_phi_star_*_amp_highmass, where * can be either blue or red.

  • \(\phi^*_{\mathrm{exp},\mathrm{l}}\): sm_fct_phi_star_*_exp_lowmass, where * can be either blue or red.

  • \(\phi^*_{\mathrm{exp},\mathrm{h}}\): sm_fct_phi_star_*_exp_highmass, where * can be either blue or red.

Sampling galaxies from the GSMF creates a catalogue of galaxies with redshifts and formed stellar masses. Changing the parameters of the GSMF therefore changes the number of galaxies, the redshift distribution and the formed stellar mass distribution. The impact of the different parameters on the GSMF is illustrated in the interactive figure below.

This interactive figure shows the GSMF for blue and red galaxies color-coded by redshifts. The sliders allow you to change the parameters of the GSMF and evaluate their impact on the number density of galaxies as function of formed stellar mass.

Galaxy star formation history

GalSBI-SPS models galaxy star formation histories (SFH) in units of \(M_{\odot}/yr\) using a truncated skewed Normal distribution (Robotham+20). The functional form is as follows:

\[SFR(t) = SFR(t)_{\mathrm{norm}} \times \left [ 1 - \frac{1}{2} \left[ 1 + \mathrm{erf}\left( \frac{t - \mu}{\sigma \sqrt{2}} \right) \right] \right]\]

where

\[\begin{split}\mu &= \mathrm{mpeak} \times \frac{|(\mathrm{magemax - mpeak})|}{\mathrm{mtrunc}} \\ \sigma &= \frac{|(\mathrm{magemax - mpeak})|}{2 \times \mathrm{mtrunc}} \\ SFR(t)_{\mathrm{norm}} &= \mathrm{mSFR} \times e^{\frac{X(t)^2}{2}} \\ X(t) &= \left ( \frac{t - \mathrm{mpeak}}{\mathrm{mperiod}} \right) \left( e^{\mathrm{mskew}} \right)^{\mathrm{asinh}\left( \frac{t - \mathrm{mpeak}}{\mathrm{mperiod}} \right)}\end{split}\]

\(\mathrm{magemax}\) represents the maximum age of star formation, corresponding to when the earliest galaxies are observed to exist, and can be modified in GalSBI-SPS with the parameter magemax_z0. \(\mathrm{mtrunc}\) sets the sharpness of the early-time truncation and can be modified in GalSBI-SPS with the parameter mtrunc. \(\mathrm{mSFR}\) represents the peak SFR in units of \(M_{\odot}/\mathrm{yr}\). \(\mathrm{mpeak}\) is the age in \(\mathrm{Gyr}\) at which the peak SFR occurs. \(\mathrm{mperiod}\) is the width of the star formation period in \(\mathrm{Gyr}\), while \(\mathrm{mskew}\) is the skewness controlling the asymmetry of the SFH.

The impact of the different parameters on the SFH and the resulting galaxy spectra is illustrated in the interactive figure below.

The sliders allow you to change the parameters of the truncated skewed Normal distribution and evaluate their impact on the predicted star formation history and spectrum of the galaxy. The spectra have been normalized to the median flux in the [5500, 5550] Å range of the \(\mathrm{mSFR}=50\), \(\mathrm{mpeak}=13\), \(\mathrm{mperiod}=1\), and \(\mathrm{mskew}=0\) galaxy.

The SFH is shown for a galaxy at \(z=0\) on an observer-frame look-back time grid that is the same we adopt to describe the SFHs in GalSBI-SPS. This grid goes from \(t=0\) to the age of the Universe at \(z=0\) in the adopted cosmology. Since the original SFHs in ProSpect are defined in galaxy-frame look-back time, in order to correctly compute the stellar mass formed, we set the SFH to 0 beyond \(\mathrm{magemax}' = 13.4 − t_{lb,z}\) Gyr, i.e. beyond the age of the Universe at the galaxy redshift. The age of the peak star formation \(\mathrm{mpeak}\) thus becomes \(\mathrm{mpeak}'=(\mathrm{magemax}'-\mathrm{mpeak})/ \mathrm{magemax}'\).

We separate the sampling process of the SFH parameters between those that define the SFH shape (mpeak, mperiod and mskew) and the SFH normalisation (mSFR). We parametrise \(\log{\mathrm{mpeak}'}\) for blue and red galaxies as

\[\begin{split}\begin{split} \log{(\mathrm{mpeak}')} =& \log{(\mathrm{mpeak}')}_{\mathrm{mass,evo,intcpt}} + \\ &\log{(\mathrm{mpeak}')}_{\mathrm{mass,evo,slope}} \times \log{\mathcal{M}} \end{split}\end{split}\]

with slope and intercept linearly evolving with redshift as

\[\begin{split}\log{(\mathrm{mpeak}')}_{\mathrm{mass,evo,intcpt}} =& \ \mathrm{a}_{\mathrm{mass,evo,intcpt}} + \\ & \mathrm{b}_{\mathrm{mass,evo,intcpt}} \times \log{(1+z)} \ , \\ \log{(\mathrm{mpeak}')}_{\mathrm{mass,evo,slope}} =& \ \mathrm{a}_{\mathrm{mass,evo,slope}} + \\ & \mathrm{b}_{\mathrm{mass,evo,slope}} \times \log{(1+z)} \ .\end{split}\]

\(\mathrm{a}_{\mathrm{mass,evo,intcpt}}\), \(\mathrm{b}_{\mathrm{mass,evo,intcpt}}\), \(\mathrm{a}_{\mathrm{mass,evo,slope}}\), and \(\mathrm{b}_{\mathrm{mass,evo,slope}}\) have different values for the blue and red populations. They can be defined using the following parameters:

  • \(\mathrm{a}_{\mathrm{mass,evo,intcpt}}\): logmpeak_massevo_intcpt_zevo_intcpt_*, where * can be either blue or red.

  • \(\mathrm{b}_{\mathrm{mass,evo,intcpt}}\): logmpeak_massevo_intcpt_zevo_slope_*, where * can be either blue or red.

  • \(\mathrm{a}_{\mathrm{mass,evo,slope}}\): logmpeak_massevo_slope_zevo_intcpt_*, where * can be either blue or red.

  • \(\mathrm{b}_{\mathrm{mass,evo,slope}}\): logmpeak_massevo_slope_zevo_slope_*, where * can be either blue or red.

\(\mathrm{mperiod}\) and \(\mathrm{mskew}\) are instead parametrised as function of stellar mass as

\[\begin{split}\log{(\mathrm{mperiod})} =& \log{(\mathrm{mperiod})}_{\mathrm{mass,evo,intcpt}} + \\ & \log{(\mathrm{mperiod})}_{\mathrm{mass,evo,slope}} \times \log{\mathcal{M}} \ , \\ \mathrm{mskew} =& \mathrm{mskew}_{\mathrm{mass,evo,intcpt}} + \\ & \mathrm{mskew}_{\mathrm{mass,evo,slope}} \times \log{\mathcal{M}} \ .\end{split}\]

\(\log{(\mathrm{mperiod})}_{\mathrm{mass,evo,intcpt}}\), \(\log{(\mathrm{mperiod})}_{\mathrm{mass,evo,slope}}\), \(\mathrm{mskew}_{\mathrm{mass,evo,intcpt}}\), and \(\mathrm{mskew}_{\mathrm{mass,evo,slope}}\) have different values for the blue and red populations. They can be defined using the following parameters:

  • \(\log{(\mathrm{mperiod})}_{\mathrm{mass,evo,intcpt}}\): logmperiod_massevo_intcpt_*, where * can be either blue or red.

  • \(\log{(\mathrm{mperiod})}_{\mathrm{mass,evo,slope}}\): logmperiod_massevo_slope_*, where * can be either blue or red.

  • \(\mathrm{mskew}_{\mathrm{mass,evo,intcpt}}\): mskew_massevo_intcpt_*, where * can be either blue or red.

  • \(\mathrm{mskew}_{\mathrm{mass,evo,slope}}\): mskew_massevo_slope_*, where * can be either blue or red.

The sampled parameters define the SFH shape for each galaxy. To obtain the value of the normalisation \(\mathrm{mSFR}\), we impose for each galaxy that the integral of the SFH over the galaxy lifetime returns the formed stellar \(\mathcal{M}\) drawn from the GSMF..

Metallicity history

We linearly map the stellar mass evolution of each galaxy on to the shape of the gas-phase metallicity evolution. The metal enrichment is thus following a 1-to-1 relation with the mass-build, such that e.g. when half of the stellar mass of a galaxy has been assembled, half of the metal enrichment has occurred:

\[Z_{\mathrm{gas}} (t) = Z_{\mathrm{gas,init}} + (Z_{\mathrm{gas,final}} - Z_{\mathrm{gas,init}}) \frac{1}{\mathcal{M}} \int_{0}^{t'} SFR(t) \mathrm{d}t\]

\(\mathcal{M}\) is stellar mass in units of $M_{odot}$ drawn from the SMF. \(Z_{\mathrm{gas,init}}\) is the initial metallicity for the earliest phases of star-formation and can be modified with the parameter Zgas_init. We also impose a maximum metallicity given by \(Z_{\mathrm{gas,max}}\) governed by the parameter Zgas_max. \(Z_{\mathrm{gas,final}}\) is the present-day gas-phase metallicity of the object that is sampled, in terms of gas-phase oxygen abundance \(\log{(O/H)}\), from:

\[\begin{split}\left[ 12 + \log{(O/H)} \right] =& \ \alpha(t_{\mathrm{lb}}) \log{\left( \frac{SFR}{M_{\odot} yr^{-1} } \right)} + \\ &\beta(t_{\mathrm{lb}}) \log{\left(\frac{\mathcal{M}}{M_{\odot}} \right)} + \gamma(t_{\mathrm{lb}})\end{split}\]

\(\alpha(t_{\mathrm{lb}})\), \(\beta(t_{\mathrm{lb}})\), \(\gamma(t_{\mathrm{lb}})\) and the scatter around this mean relation \(\sigma_{\mathrm{FMR}}(t_{\mathrm{lb}})\) evolve quadratically with lookback time:

\[\begin{split}\alpha(t_{\mathrm{lb}}) &= \alpha_0 + \alpha_1 t_{\mathrm{lb}} + \alpha_2 t_{\mathrm{lb}}^2 \\ \beta(t_{\mathrm{lb}}) &= \beta_0 + \beta_1 t_{\mathrm{lb}} + \beta_2 t_{\mathrm{lb}}^2 \\ \gamma(t_{\mathrm{lb}}) &= \gamma_0 + \gamma_1 t_{\mathrm{lb}} + \gamma_2 t_{\mathrm{lb}}^2 \\ \sigma_{\mathrm{FMR}}(t_{\mathrm{lb}}) &= \sigma_{\mathrm{FMR},0} + \sigma_{\mathrm{FMR},1} t_{\mathrm{lb}} + \sigma_{\mathrm{FMR},2} t_{\mathrm{lb}}^2\end{split}\]

\(\alpha_i, \beta_i, \gamma_i\) can be modified in GalSBI-SPS with the parameters gas_metallicity_alphai_*, gas_metallicity_betai_*, and gas_metallicity_gammai_*, respectively, while \(\sigma_{\mathrm{FMR},i}\) with gas_metallicity_scatteri_*, where * can be either blue or red.

\(Z_{\mathrm{gas,final}}\) and \(\log{(O/H)}\) are related through:

\[Z_{\mathrm{gas,final}} = Z_{\odot} \times 10^{\left[ 12 + \log{(O/H)} \right] - \left[ 12 + \log{(O/H)} \right]_{\odot}}\]

where \(Z_{\odot}\) and \(\left[ 12 + \log{(O/H)} \right]_{\odot}\) can be varied through the parameters SOLAR_GAS_METALLICITY and SOLAR_LOG_OH_PLUS12, respectively.

Gas ionisation

We sample the gas ionisation parameter \(logU\) from a truncated Normal distribution with mean given by:

\[\log{U} = \upsilon_0 + \upsilon_1 (\log{(O/H)} + 4) + \upsilon_2 \log{n_e} + \upsilon_3 (\log{(sSFR)} + 9)\]

where \(\log{(O/H)}\) and \(\log{(sSFR)}\) are obtained from the physical properties sampled in the SMF, SFH and metallicity history. The values of \(\upsilon_i\) can be modified in GalSBI-SPS with the parameters gas_ionization_upsiloni. The same values hold for the blue and the red population. The scatter around this relation can be varied with the parameter gas_ionization_scatter. We limit the sampled gas ionisation parameter values to the range set by the parameters logUmin and logUmax.

Dust component

We model the effect of dust in GalSBI-SPS using the Charlot & Fall (2000) two-phase dust attenuation model. Older stars are solely attenuated by a dust screen, regulated by the \(\tau_{\mathrm{ISM}}\) parameter, which represents the dust in the diffuse ISM. Young stars are instead attenuated by the dust screen and by an additional birth cloud component that adds extra attenuation towards young stars, simulating their embedding in molecular clouds and HII regions. The birth cloud component is regulated by the \(\tau_{\mathrm{BC}}\) parameter.

We sample \(\log{\tau_{\mathrm{BC}}}\) from a Normal distribution with mean \(\mu_{\log{(\tau_{\mathrm{BC,\{ b,r \}}})}}\) and scatter \(\sigma_{\log{(\tau_{\mathrm{BC,\{b,r\}}})}}\) governed in GalSBI-SPS by the parameters logtaubirth_mean_* and logtaubirth_scatter_*, where * can be either blue or red. We limit the sampled \(\log{\tau_{\mathrm{BC}}}\) values to the range set by the parameters logtaubirth_min and logtaubirth_max.

We sample \(\log{(\tau_\mathrm{ISM})}\) from Normal distribution around a hyper-plane that depends on redshift, stellar mass and sSFR as:

\[\begin{split}\log{(\tau_\mathrm{ISM})} =& \tau_{\mathrm{ISM},0} + \tau_{\mathrm{ISM},1} \log{(1+z)} + \\ &\tau_{\mathrm{ISM},2} \log{\left(\frac{\mathcal{M}}{M_{\odot}} \right)} + \tau_{\mathrm{ISM},3} \log{(sSFR)}\end{split}\]

The values of \(\tau_{\mathrm{ISM},i}\) can be changed in GalSBI-SPS with the parameters logtauscreen_a0_*, while the scatter around the relation with logtauscreen_scatter_*, where * can be either blue or red. We limit the sampled \(\log{\tau_{\mathrm{ISM}}}\) values to the range set by the parameters logtauscreen_min and logtauscreen_max.

Velocity dispersion

We model the velocity dispersion \(\sigma_{\mathrm{disp}}\) following the stellar mass-velocity dispersion relation:

\[\begin{split}\sigma_{\mathrm{disp}}(\mathcal{M}) &= \sigma_b \left ( \frac{\mathcal{M}}{M_b} \right)^{s_1} \ \mathrm{for} \ \mathcal{M} \le M_b \\ \sigma_{\mathrm{disp}}(\mathcal{M}) &= \sigma_b \left ( \frac{\mathcal{M}}{M_b} \right)^{s_2} \ \mathrm{for} \ \mathcal{M} > M_b\end{split}\]

where \(\mathcal{M}\) is the stellar mass drawn from the SMF. The values for \(\log{\sigma_b}\), \(\log{M_b}\), \(s_1\), \(s_2\), and the scatter around the relation can be varied in GalSBI-SPS through the parameters vel_disp_logsigma_b, vel_disp_logM_b, vel_disp_s_1, vel_disp_s_2 and vel_disp_std, respectively. The same values hold for the blue and the red population.

Active galactic nuclei

In GalSBI-SPS, the probability of a galaxy hosting an AGN as function of redshift and stellar mass is given by the ration between the redshift-evolving GSMFs of blue and red galaxies and the AGN host galaxy mass function (HGMF) derived in Bongiorno+16. Following López-López+24, we statistically assign an AGN to a host galaxy with a Bernoulli trial proportional to the computed probability. To assign the AGN spectral contribution, we use the Temple+21 templates, which cover u-band to W2-band wavelengths. These parametric templates are governed by a single parameter, namely the AGN bolometric luminosity. In GalSBI-SPS, the AGN luminosity is expressed as a fraction \(f_{\mathrm{AGN}}\) of the galaxy bolometric luminosity, \(f_{\mathrm{AGN}} = L_{\mathrm{bol,AGN}} / L_{\mathrm{bol,galaxy}}\).

We model \(\log{f_{\mathrm{AGN}}}\) as a two component mixture of Normal distributions We then assign AGN flux contributions to all galaxies, regardless of whether they are classified as AGN hosts. However, \(\log{f_{\mathrm{AGN}}}\) is sampled from different distributions depending on the AGN classification. Galaxies hosting AGNs draw from the high \(\log{f_{\mathrm{AGN}}}\) distribution, while non-AGN galaxies draw from the low \(\log{f_{\mathrm{AGN}}}\) one. We adopt a threshold of \(\log{f_{\mathrm{AGN}}} = -1\) to separate these two regimes.

The parameters of the two component mixture of Normal distributions are:

  • \(\mu_{f_{\mathrm{AGN,1}}}\): logfagn_mu1_*, where * can be either blue or red.

  • \(\sigma_{f_{\mathrm{AGN,1}}}\): logfagn_sigma1_*, where * can be either blue or red.

  • \(\mu_{f_{\mathrm{AGN,2}}}\): logfagn_mu2_*, where * can be either blue or red.

  • \(\sigma_{f_{\mathrm{AGN,2}}}\): logfagn_sigma2_*, where * can be either blue or red.

The user should set the parameter add_agn_component to True in the model definition to enable the spectral contribution of AGNs and define the absolute path to the folder containing the Temple+21 model with the parameter abs_path_temple2021.

Galaxy Morphology

The last step in generating a galaxy catalogue is to assign a morphological parameters to each galaxy. In GalSBI-SPS, we assume that the galaxy light profile is described by a single Sersic component. Therefore, the morphological parameters we sample are those used to describe the Sersic profile, meaning the effective radius, proxy of the galaxy size, the ellipticity and the Sersic index.

Size

In GalSBI-SPS, we sample the effective radius \(r_{50}\) (containing 50% of the total light from the model) from a lognormal distribution whose mean depends on the stellar mass \(\mathcal{M}\) of the galaxy. The size-stellar mass relation follows two different functional forms for blue and red galaxies. For blue galaxies, we model the dependence as a single power-law:

\[r_{50} = A \left( \frac{\mathcal{M}}{5 \times 10^{10} M_{\odot}} \right)^B\]

where \(\log{A}\) and \(B\) are assumed to evolve linearly with redshift:

\[\begin{split}\log{A} &= \log{A}_{\mathrm{intcpt}} + \log{A}_{\mathrm{slope}} \times z \ , \\ B &= B_{\mathrm{intcpt}} + B_{\mathrm{slope}} \times z\end{split}\]

\(\log{A}_{\mathrm{intcpt}}\), \(\log{A}_{\mathrm{slope}}\), \(B_{\mathrm{intcpt}}\), and \(B_{\mathrm{slope}}\) are controlled in GalSBI-SPS by the parameters r50_stellar_mass_logA_blue_intcpt, r50_stellar_mass_logA_blue_slope, r50_stellar_mass_B_blue_intcpt, and r50_stellar_mass_B_blue_slope, respectively. The scatter around the log-normal distribution for blue galaxy sizes is instead controlled by the parameter logr50_stellar_mass_std_blue.

For red galaxies, we model the dependence as a double power-law:

\[r_{50} = \zeta (\mathcal{M})^{\eta} \left( 1 + \frac{\mathcal{M}}{10^{\delta}} \right)^{\theta - \eta}\]

where \(\eta\) and \(\theta\) are the slope at the low and high mass end, \(\zeta\) is the normalisation, while \(10^{\delta}\) is the stellar mass at which the second derivative of the function is at a maximum. All these parameters also evolve linearly with redshift:

\[\begin{split}\eta &= \eta_{\mathrm{intcpt}} + \eta_{\mathrm{slope}} \times z \ , \\ \theta &= \theta_{\mathrm{intcpt}} + \theta_{\mathrm{slope}} \times z \ , \\ \log{\zeta} &= \log{\zeta}_{\mathrm{intcpt}} + \log{\zeta}_{\mathrm{slope}} \times z \ , \\ \delta & = \delta_{\mathrm{intcpt}} + \delta_{\mathrm{slope}} \times z \ .\end{split}\]

\(\eta_{\mathrm{intcpt}},\eta_{\mathrm{slope}},\theta_{\mathrm{intcpt}},\theta_{\mathrm{slope}},\log{\zeta}_{\mathrm{intcpt}},\log{\zeta}_{\mathrm{slope}},\delta_{\mathrm{intcpt}},\delta_{\mathrm{slope}}\) are controlled in GalSBI-SPS by the parameters r50_stellar_mass_eta_red_intcpt, r50_stellar_mass_eta_red_slope, r50_stellar_mass_theta_red_intcpt, r50_stellar_mass_theta_red_slope, r50_stellar_mass_logzeta_red_intcpt, r50_stellar_mass_logzeta_red_slope, r50_stellar_mass_delta_red_intcpt, and r50_stellar_mass_delta_red_slope. The scatter around the log-normal distribution for red galaxy sizes is instead controlled by the parameter logr50_stellar_mass_std_red.

Ellipticity

See phenomenological GalSBI page.

Light Profile

The light profile of galaxies is defined by the Sersic profile:

\[I(R) = I_0 \exp\left(-b_n \left(\left(\frac{R}{R_e}\right)^{1/n} - 1\right)\right),\]

where \(I_0\) is the intensity at the center, \(R_e\) is the effective radius, \(n\) is the Sersic index, and \(b_n\) is a constant that depends on \(n\).

In GalSBI-SPS, the Sersic index depends on the galaxy stellar mass \(\mathcal{M}\). The relation between the two is modelled as follows:

\[n = n_0 + n_1 \times \left( \frac{\log{\mathcal{M}}}{\log{(10^{10.5} M_{\odot})}} \right)^{n_2}\]

The values for \(n_i\) are controlled by the parameters sersic_n_i_*, where * can be either blue or red. This relation provides the mean of the truncated Normal distribution from which we sample $n$. The standard deviation is controlled by the parameter sersic_n_scatter_*. We limit the sampled \(n\) values to the range set by the parameters sersic_n_min and sersic_n_max.

Do I need to set all these configurations and parameters when using the galsbi package?

No, if a specific model is passed to the GalSBI class, all the configurations and parameter values are set automatically based on the model. For example, the following code snippet will

from galsbi import GalSBI
model = GalSBI(model="Tortorelli+25")

sets all the parametrizations and parameter values to the fiducial model of Tortorelli et al. (2025).

References

GalSBI-SPS is based on the following papers:

References used for the parametrizations are: