# GalMod tutorial

In this tutorial, we explain how to use the GalMod web interface. All the parameters and a detailed derivation of the formulation adopted are in three dedicated papers: Pasetto et al. (2016, 2018a,b).

## What does GalMod produce and how to use it?

GalMod aims to generate mock catalogs for a specified field of view of our Galaxy (the Milky Way, MW), an external galaxy as, e.g. Andromeda (M31), a dwarf galaxy, or a quasi-equilibrium stellar model. To each input set of parameters corresponds a single output. The output is not unique, being the product of stochastic simulations based on Monte Carlo integration methods. If the user runs GalMod twice (or more) on the same set of parameters, GalMod produces “statistically equivalent” results but not identical.

GalMod requires the user to fill a (basic) input form, containing the minimum requirements for the model to work (or an extended/advanced input form). The preset parameters that the user finds in the GalMod input form are random examples of the field of view based on an MW “optimal model.” The user is free to change those parameters within the indicated range (or accept the preset parameters). Once the user fills all the parameters and provides a correct email address, GalMod produces the simulation and sends an email with a password and a link to download the results (the website is mobile friendly). The timescale for the delivery of a mock catalog depends on the input parameters and the servers’ availability; a minimum time of 10 minutes is preset, times longer than 10000 mins indicate either difficult f.o.v.s or a bug in GalMod. In that case feel free to contact the support (see below).

The input form requires the user to provide a set of parameters (grouped by background color) referring to a Galactic composite stellar population (CSP). By hovering with the mouse over any box inside these sections, a brief explanation of the parameter appears with a few hints on its possible value. The allowed parameter range (if a real number) is below the input box, written in mathematical notation, e.g., $x \in \left] {a,b} \right]$ meaning $a < x \le b$, or $y = {a..d}$ for integer number limits meaning $y = a \vee y = b \vee y = c \vee y = d$. Each box must contain a single number; no arrays of numbers are allowed as input. The input form comes with preset parameters for the Galaxy to facilitate the use of the model (including a field of view as an example). Selecting a parameter outside the range of allowed values causes the box border to become red to indicate the mistake. By refreshing the web page, GalMod performs a check on the full list of parameters values. Reloading the page resets the preset parameters to their original values.

If the input is accepted, the simulation runs "as soon as possible," and when finished, GalMod sends a communication to the provided email address with a temporary password and a link to download the file from GalMod. The simulations are available for download for about a few days.

## Input form (basic)

Field of view definition

The input form is color-coded depending on the nature of the parameters. Not all the parameters are necessary to run GalMod; the recommended fields to fill are:

1. field of view of interest or simulation type,
2. photometric system.

If the user wants to study a direction in the Galaxy, an all-sky mock catalog results in a low-resolution model in the direction of interest. Hence it is strongly recommended to specify the field of view because this allows GalMod to produce a better simulation only in the direction of interest. Whole sky simulations are allowed, there is no limit on the solid angle of the field of view. GalMod informs the user on the correct amount of stars that should fill the desired field of view under the specified parameters.

To choose a photometric system is also important. A few important photometric systems are available by drop-down list menu, and the closest to the user’s interest should be set.

Other relevant parameters to set are:

• Number of stars: GalMod computes a probability distribution function (PDF) and populates it with a number of stars that is fixed in agreement with the multiple-stellar population consistency theorem (MSP-CT, Pasetto et al. 2018b). If the user knows the number of stars expected in an observation/catalog, GalMod can renormalize the PDF to the requested value. Then, if the number of stars required is lower than that predicted by MSP-CT, GalMod renormalizes the PDF with the number of stars requested, automatically adjusting the different proportion for the multiple-stellar-population to agree with the structural parameters provided. If the number of stars requested is larger than that predicted by GalMod, the user can increase the number of stars by changing the structural parameters of the Galaxy (density profiles, star formation history, cuts). Again, in this case, GalMod automatically adjusts the different proportion for the multiple-stellar-population to agree with the structural parameters provided in agreement with the MSP-CT.
• Photometric system. GalMod is so far equipped with a few photometric systems: Johnson-Cousins, HST/ACS-WFC, HST/ACS-HRC, Gaia, SDSS, 2MASS, etc. (see below for a complete list). The input form changes depending on the photometric system selected. A magnitude/color cut in the output CMD acts on the photometric systems by selecting which filter is on the y-axis of the CMD (called $1^{st}$ filter). For example, to simulate a field of view with SDSS filters with $g \in \left[ {13.5,17.5} \right]$ mag and $g - i \in \left[ { - 1.2,3.2} \right]$ mag, the $1^{st}$ filter ($1_{\rm{fltr}}^{st}$) is $g$(bluer filter first), i.e., the second SDSS filter, and the ${2^{nd}}$ filter is $i$, i.e., the fifth SDSS filter (the SDSS filters are $\left\{1^{st},2^{nd},3^{rd},4^{th},5^{th} \right\} = \left\{u,g,v,r,i \right\}$. Thus, in the online form, the $2_{\rm{fltr}}^{nd} = 5$, and then the minimum magnitude considered in the first filter is${\rm{mag}}_\min ^{1_{\rm{fltr}}^{st}} = 13.5$ mag while the maximum magnitude is ${\rm{mag}}_\max^{1_{\rm{fltr}}^{st}} = 17.5$ mag. The color is the difference between first and second magnitude, i.e., ${\rm{col = 1}}_{\rm{fltr}}^{st} - 2_{\rm{fltr}}^{nd}$ spanning values between ${\rm{co}}{\rm{l}}_\min = - 1.2$ mag and ${\rm{co}}{\rm{l}}_\max = + 3.2$ mag.
• Photometric errors. Every observation comes with errors. We suggest setting an (or accepting the preset) error function while producing your mock observations with GalMod. GalMod uses a Gaussian distribution with magnitude dispersion dependent on the $1_{\rm{fltr}}^{st}$ magnitude, with the dispersion computed from the following formula ${\sigma _m} = {\left( {\frac{\sigma _{m_\max}}{\sigma _{m_\min }}} \right)^{\frac{m - {m_\min }}{m_\max - m_\min }}}$ where $\sigma _{m_\max}$ is the error at ${\rm{mag}}_\max^{1^{st}{\rm{fltr}}}$, e.g., $\sigma _{m_\max}$ = 0.1 mag, and ${\sigma _{\rm{ma}{\rm{g}_\min }}}$is the error at the brightest magnitude limit ${\rm{mag}}_\min ^{1^{st}{\rm{fltr}}}$, e.g., ${\sigma _{\rm{ma}{\rm{g}_\min }}}$ = 0.01 mag. If ${\sigma _{\rm{ma}{\rm{g}_\min }}} = \sigma _{m_\max} = 0.0$ is set, GalMod introduces no mag errors. If ${\sigma _m} > {\rm{co}}{\rm{l}}_\max - {\rm{co}}{\rm{l}}_\min$ GalMod renormalizes the error function to ${\sigma _m} = {\rm{co}}{\rm{l}}_\max - {\rm{co}}{\rm{l}}_\min$.
• Metallicity limits. These boxes influence the CMD obtained from GalMod. While every CSP spans different metallicity ranges, the resulting CMD of the CSP is filtered by these cuts a posteriori. For example, to study the halo kinematics of the solar neighborhood, a simple cut in metallicity below a threshold limit allows to decontaminate the stars from coherent circular motions.
• Field of view (f.o.v.) definition. This box determines the direction of the GalMod mock catalog as generated from the solar location, or the kind of simulation generated (MW, M31 or semi-equilibrium models). There are six different options, of which the first four limit the sky area considered:
• By setting the four parameters $\left\{l_\min ,l_\max,b_\min ,b_\max \right\}$, i.e., the longitude and latitude min and max respectively. For example, because $l \in \left[ {0,360} \right[$, the MW central direction is examined by setting ${l_\min } = 350$ deg, ${l_\max} = 5$ deg, ${b_\min } = - 5$ deg, and ${b_\max} = 5$deg;
• By setting the four parameters $\left\{l_c,b_c,\Delta l,\Delta b \right\}$, i.e., the central longitude and latitude of the field of view and its opening angle in longitude and latitude. For example, ${l_c} = 180$, ${b_c} = 0$ , $\Delta l = 180$ $\Delta b = 180$ returns the 2nd and 3rd Galactic quadrant;
• By setting the three parameters $\left\{\alpha _c,\delta _c,OA \right\}$, i.e., the central right ascension and declination of the field of view and its opening angle. In this case, the field of view is circular and centered on the equatorial coordinates $\left\{\alpha _c,\delta _c \right\}$. All inputs are in [deg].
• By setting the four parameters $\left\{\alpha _c,\delta _c,\Delta \alpha ,\Delta \delta \right\}$ with the same meaning as above, but with the input given in [arcmin].
The last two options activate a set of parameters to model semi-equilibrium systems or a specific M31 field of view:
• Equilibrium systems (experimental). This option activates a GalMod experimental modality to realize the semi-equilibrium collisionless model of spiral galaxies. The CSPs are set coherently with the input provided by the user, but GalMod spreads the total mass of the resulting galaxy among the total number of “star-like” particles (established by the user). GalMod realizes a full sky survey without photometric limits where mass, metallicity, and phase-space are assigned to massive particles as explained in a dedicated paper (Pasetto et al. 2012). A finely tuned code to perform this initial condition generation is freely available upon request to the project P.I.
• Andromeda(M31)/dwarf galaxy field of view. This option activates a group of preset values that allow modeling M31 and its surrounding area as seen from the solar position. This option is equivalent to move the sun location outside the Galaxy and rotate the field of view accordingly. The simulation, in this case, does not model the MW foreground that the user needs to add as a result of a separate simulation. The location of M31, the inclination of the M31 plane to the line of sight, and the position angle on the celestial sphere are free parameters too, thus allowing GalMod to model virtually any collisionless stellar system as seen from the solar location.
• Field depth. This parameter determines the heliocentric distance reached by the integration of the galaxy potential. To ask for a very deep field (a ${r_{\rm{hel}}}$ as large as 50 kpc is allowed) could require a longer integration time that might not be necessary because of the adopted photometric cuts or because of the presence of external stellar systems that prevent the line of sight to be seen beyond a given limit. For example, if the solar position is outside the MW (e.g., to simulate M31 or another spiral galaxy), GalMod computes possible spiral arm resonance locations up to the nominal 50 kpc or according to the branch cut discontinuity in the complex plane implemented for a given Hypergeometric function. It is up to the user to understand whether physically meaningful results are obtained.
• Velocity space constraints. Because GalMod realizes simulations as a mock catalog in the space of observations, the limitations on the velocity space are applied directly on radial velocities and proper motions. The proper motions are either $\left\{\mu _\alpha ,\mu _\delta \right\}$ or $\left\{\mu _l,\mu _b \right\}$ depending on the adopted field of view definition.

Observer position
• Solar location This parameter sets the place in the Galactic model where some of the density profiles and velocity normalization profiles are normalized. These values also define the preferred observer location. In the semi-equilibrium model case, this parameter is neglected.
• Solar motion to the Local Standard of Rest (LSR). This value sets the motion of the Sun to the local standard of rest. The value is positive for the direction pointing outside the Galaxy, in the anti-rotation direction, and toward the NGP.

Structural parameters

The “basic” parameter section influences the way in which the Galaxy “looks” in the simulation output. To modify the structural parameters changes the way in which the Galaxy “is,” independently from the possibility of evidencing it in the output catalog. This concept can be explained with a few simple examples. To modify the structure parameters of the bulge components for a small field of view of a MW model pointing toward the anticenter direction rarely results in visible changes in the mock catalog obtained (even though the changes of the bulge parameters impact to the global potential of the MW). Another less straightforward example. Modifying the metallicity/age of a thin disk CSP in the structure section implies a variation in the velocity dispersion distribution of stars because of the implemented age-velocity dispersion relation for the thin disk CSPs. However, if the user requires a model with a high-velocity-dispersion for very young thin disk CSPs, the MSP-CT predicts a small probability for this type of CSP to exist, thus reducing this CSP total mass in favor of another disk CSPs. The MSP-CT “redistributes” the mass onto other more probable CSP. Vice versa, the stellar halo, which is supposed to be old and metal-poor but whose connection with other CSPs is not obvious, is left free to be metal-poor and old as well as metal-rich and young. The GalMod user has the responsibility of the simulation inputs as well as the freedom to experiment.

GalMod generates the Galaxy potential, the number of stars in the CMDs and the kinematics of the stars depending on a set of parameters that define the stellar populations, the dark matter and the gas contents of the Galaxy. For each CSP, these parameters are:

• Density defining parameters. Each CSP is specified by a set of parameters extensively described in Pasetto et al. (2016) Sec. 4 to 6 and Pasetto et al. (2018a) Sec. 3 and Appendix A.
• Kinematics parameters. Some of the CSP components contain free parameters not directly related to the potential. These are typically second order moments of the unknown phase-space distribution function of the unperturbed component. A complete description of the implemented model is given in Sec. 7 of Pasetto et al. (2016). These parameters normalize the velocity dispersion profiles at the solar location set by the user.
• Age parameters. The age of the stars is a free parameter. GalMod uses parametric profiles of star formation rate (SFR) and $\psi \left( t \right)$, from which the stars are sampled. Four SFR profiles are available:
• Constant star formation rate. The stellar age is randomly sampled from a constant SFR profile, $\psi \left( t \right) = {\rm{const}}{\rm{.}}$ between $t_\min$ and $t_\max$. The constant is determined coherently from the density profiles and initial mass function by the MSP-CT.
• Exponential star formation rate. The stellar age is randomly sampled from an exponential SFR profile, $\psi \left( t \right) = {\rm{const}}{\rm{.}} \times {e^{\frac{t}{h_\tau }}}$ between $t_\min$ and $t_\max$. The constant is determined coherently from the density profiles and initial mass function set in agreement with the MSP-CT. ${h_\tau }$ is the timescale of the profile (it can be both a positive or a negative value).
• Linear star formation rate. The stellar age is randomly sampled from a linear SFR profile of the type $\frac{t - t_\min }t_\max - t_\min = \frac{\psi \left( t \right) - \psi \left( {t_\min } \right)}{\psi \left( {t_\max} \right) - \psi \left( {t_\min } \right)}$ between $t_\min$ and $t_\max$. In the case of $\psi \left( t_\max \right) = \psi \left( t_\min \right)$ GalMod will switch to the $\psi = {\rm{const}}{\rm{.}}$ case treated above.
• Rosin-Rammler. This SFR is taken from Chiosi et al. (1981) with the aim to offer a more realistic SFR profile over a broad temporal range between $t_\min$ and $t_\max$. The profile is bi-parametric $\psi \left( t \right) = {\rm{const}}{\rm{.}} \times {t^\zeta }{e^{ - \frac{t}{h_\tau }}}$ with both $\zeta$ and ${h_\tau }$ strictly positive. Note how the profile uses a look-back time where $t \to t_\max - t$. Depending on the galaxy the user needs to model the input accordingly.
• Metallicity range. The stellar metallicity is a free parameter sampled uniformly between ${Z_\min }$ and ${Z_\max}$. An age-metallicity relation on a single stellar population (CSP) is not implemented but can be obtained by implementing sequential metallicity ranges over the five CSPs.
The thin disk CSP-I, green background section is modeled as a spiral arm CSP and smoothly connects with the bar structure. The code will return information on whether the Galaxy component happens to have stars or is empty (e.g., this can occur if the input number of stars is too low and the density is low). The code will output the number of stars of each CSP. All the CSPs are always considered in the potential computation even if their result is empty based on the input number of stars. For example, when inputting 1000 stars in the anticenter direction, the bulge mass distribution is considered in the total potential even though probably zero bulge stars will ultimately be produced. Note that the dark matter component automatically accounts for the hot coronal gas in the outermost layer of the MW ($R > 40kpc$). For the specific case of M31 simulations, or any other spiral or S0 galaxy, the user is supposed to set the parameters of interest manually. GalMod will then provide kinematics and photometry accordingly to the input and return feedback information on the resulting galaxy potential, i.e., rotation curve, total mass, Oort constants, and so forth at the location of normalization for the density and velocity profiles (the site of a virtual-Sun on M31).

Extinction model

The interstellar medium (ISM) component is considered in the total Galaxy density to obtain the total potential and to determine the extinction that will affect the simulated CMDs. The ISM distribution follows the spiral arm parameters adopted for the first stellar population distribution (i.e., thin disk CSP-I) but it perturbs the density profile of the ISM and is dimmed by the “reducing-factor” (see Pasetto et al. 2016). In the case of M31 simulations, the extinction of the star is computed from the solar location excluding the MW extinction that the user must account for in a separate simulation. The ray-tracing technique is a spin-off of the Ray-tracing 3D dust radiative transfer code DART-Ray by Natale et al. (2017).

## Results: galactic potential and stellar catalog

If the generation of the model is successful, the user receives a second email containing a password and a link to download the catalog of data containing the results of the simulation. The file contains an initial section that recaps the chosen input parameters, including the version of GalMod used and references to the sections of Pasetto et al. (2016, 2018a,b).

The first section of the output file looks like the following:

GalMod rel. XX.XX

GalMod is presented in Pasetto et al. (2016a, 2018a,b), and ref. therein.

The section numbers here quoted refer to the sections in those papers.

Please, see and quote that documents if you use GalMod.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Some infos about the GalMod simulation you realized are here summarized:

Total number of stars requested is automatically fixed

Squared field of view in Galactic coords

{lmin,lmax,bmin,bmax} [deg,deg,deg,deg]: {88.00, 92.00, -2.00, 2.00}

{rhelmin,rhelmax} [kpc,kpc]: {.00, 5.00}

{Vrhelmin,Vrhelmax} [km/s,km/s]: {-300.00, 300.00}

{mu_1 min,mu_1 max} [mas/yr,mas/yr]: {-300.00, 300.00}

{mu_2 min,mu_2 max} [mas/yr,mas/yr]: {-300.00, 300.00}

{R,phi,z}@Sun [kpc,deg,kpc]: {8.00, .00, .02}

{VR,Vphi,Vz}@Sun-->LSR [km/s,km/s,km/s]: {-10.90, -5.20, 7.20}

Mag{min,max}, Col{min,max} [mag,mag,mag,mag]: {10.00, 30.00,-1.00, 4.00}

ErrMag{min,max} [mag,mag]: {.01, .05}

Z{min,max} [dex,dex]: {.00040, .03000}

Bulge CSPs parameters (P18b Sec. 3.3.3) + tilted bar (P18b, Sec. 3.3.2.)

Etc…

If ${r_ \odot } < 50$ kpc, these first lines are followed by a set of parameters obtained as a solution of the Poisson equation with the input density parameters. For example:

Some structural values from the density profiles:

• the rotation curve at the solar position: ${V_\rm{rot}}\left( R_ \odot \right)\left[ {km\;{s^{ - 1}}} \right] = 222.9$;
• the rotation curve profile: ${V_\rm{rot}}\left( {R = \left\{1.0,2.0,3.0,5.0,8.0,13.0 \right\}} \right)\left[ km\;{s^{ - 1}} \right] = \left\{163.6,184.2,202.3,216.9,220.9,220.3 \right\}$;
• normalized vertical force on the plane $\frac{F_z(R_\odot,\phi_\odot,{1.1,2.0}) [kpc]}{2\pi G} = \left\{ - 67.7, - 86.3 \right\}$;
• the slope of the rotation curve (Oort constants): $\{O^+,O^-,O^\times,O^\div \}_ \odot \left[ {km\;{s^{ - 1}}\;kp{c^{ - 1}}} \right] = \left\{13.7, - 14.1, -2.1, -2.2 \right\}$;
• the radial epicyclic frequency: ${\kappa _R}\left( R_ \odot \right)\left[ {km\;{s^{ - 1}}\;kp{c^{ - 1}}} \right] = 39.7$;
• the angular frequency: ${\Omega _R}\left( R_ \odot \right)\left[ {km\;{s^{ - 1}}\;kp{c^{ - 1}}} \right] = 27.9$;
• the resulting proportionality factor to the slope of the velocity ellipsoid: $\lambda \left( R_ \odot \right) = 0.64$;
• the total mass of the stellar population obtained from the input SFH and ISM: total stellar pop mass $M_\rm{tot},r < 100\rm{kpc}\left[ M_ \odot \right] = 0.43 \times 10^{11}$;
• the resonance location computed for the spiral arm component: etc.

The following section contains the total number of stars that are expected to exist in the chosen field of view if no cuts were applied and all the stars between ${M_\min}$ and ${M_\max }$ were generated. These figures can be huge (except for, e.g., the small field of view typically required for HST photometry). For example:

Expected number of stars in Thin disk pop 2 is 1239443;

Expected number of stars in Thick disk pop 1 is 985840

Expected number of stars in Halo pop 1 is 36252324

GalMod also informs about the number of thin disk CSPs that are modelled as spiral arms or bar (only one is allowed in the web page version of GalMod).

115 stars in spiral or bar CSP of type 1 CSP.

Because of the hardware limits, other models such as Besancon or Trilegal offer arbitrary cuts to the number of stars produced due to hard-limit cuts on the simulation running time or the size of the files. Vice versa GalMod, with the previous output lines, informs the user of the total number of stars expected from the Galaxy probability distribution function obtained by density profiles and star formation histories adopted for the input CSPs. In this way, each simulation has to be considered complete, and the output table of stars can be safely used to deduce the normalized probability distribution function (PDF). Then, the code proceeds to distribute the requested number of stars, e.g., 10000 stars, in the following way:

3136 stars in spiral type 1 pop.

330 stars in thin disk type 2 pop.

166 stars in thin disk type 3 pop.

Etc.

These lines indicate how GalMod distributes the number of input stars in agreement with the number of stars expected for the Galaxy (before any observational cuts or convolution of the PDF with an error function). GalMod renormalizes the Galaxy probability distribution function for the field of view to the input number of stars and writes the number of stars expected before the applied cuts in the different CSPs. After the magnitude/color/proper motion/etc. cuts are applied, the resulting number of stars within the requested range could still be smaller than the user required number of stars, i.e., if 10000 stars are asked for but the model only produces 5000 stars in that magnitude/color range, only 5000 stars will be outputted.

The final section contains the stellar parameters after the selection cuts have been applied. The format of this section can change depending on the way the input form was filled. Generally, it contains from 0% to 100% of the requested number of stars: each row is a star, each column a property of the star following this list:

$t\left[ {yr} \right]$: age of the star,

${\log _{10}}\left( {L/{L_ \odot }} \right)$: logarithm of the stellar luminosity normalized to the solar luminosity,

$\log _{10}\left( T_\rm{eff}\left[ {^\circ K} \right] \right)$: logarithm of the effective temperature,

$\log _{10}\left( {g\left[ m\;s^{ - 2} \right]} \right)$: logarithm of the stellar gravity at the stellar surface,

$M\left[ M_ \odot \right]$: current stellar mass,

$Z\left[ \% \right]$: stellar metallicity,

$Y\left[ \% \right]$: fraction of He content of the star.

The following columns change depending on the stellar photometry selected:

1. Johnson-Cousin $m_{1..8} = \left\{U, B, V, R, I, J, H, K \right\}$,
2. HST/ACS-WFC $m_{1..12} = \left\{ F_{435W},F_{475W},F_{550M},F_{555W},F_{606W},F_{625W},F_{658N},F_{660N},F_{775W},F_{814W},F_{850LP},F_{892N} \right\}$
3. HST/ACS-HRC $m_{1..16} = \left\{ F_{220W},F_{250W},F_{330W},F_{344N},F_{435W},F_{475W},F_{550M},F_{555W},F_{606W},F_{625W},F_{658N},F_{660N},F_{775W},F_{814W},F_{850LP},F_{892N} \right\}$
4. Gaia DR2 $m_{1..3} = \left\{ G_{Bp},G, G_{Rp} \right\}$
5. SDSS $m_{1..5} = \left\{ u, g, r, i, z \right\}$
6. 2MASS $m_{1..3} = \left\{J, H, K_s \right\}$
7. CFHT $m_{1..5} = \left\{u, g, r, i, z\right\}_{CFHT}$
8. DECam $m_{1..6} = \left\{u, g, r, i, z, y\right\}_{\rm{DECam}}$
9. GALEX $m_{1, 2} = \left\{F_{UV},N_{UV}\right\}$
10. JWST $m_{1, 29} = \left\{ \begin{array}{l}{F_{070W},F_{090W},F_{115W},F_{140M},F_{150W2},F_{150W},F_{162M},F_{164N},F_{182M},F_{187N},\\ F_{200W},F_{210M},F_{212N},F_{250M},F_{277W},F_{300M},F_{322W2},F_{323N},F_{335M},F_{356W}, \\ F_{360M},F_{405N},F_{410M},F_{430M},F_{444W},F_{460M},F_{466N},F_{470N},F_{480M}}\end{array}\right\}$.
11. LSST $m_{1..6} = \left\{u,g,r,i,z,y\right\}_{\rm{LSST}}$
12. Pan-STARRS $m_{1..7} = \left\{g,r,i,z,y,w,open\right\}_{\rm{Pan - STARRS}}$
13. SkyMapper $m_{1..6} = \left\{u,v,g,r,i,z\right\}_{\rm{SkyMapper}}$
14. Spitzer $m_{1..4} = \left\{F_{3.6},F_{4.5},F_{5.8},F_{8.0}\right\}_{\rm{IRAC}}$
15. Swift $m_{1..6} = \left\{UVW2,UVM2,UVW1,U,B,V\right\}_{\rm{Swift}}$
16. UKIDSS $m_{1..5} = \left\{Z,Y,J,H,K\right\}_{\rm{UKIDSS}}$
17. Washington $m_{1..4} = \left\{C,M,{T_1,T_2}\right\}$
18. Stromgren $m_{1..4} = \left\{u,v,b,y\right\}$
19. WISE $m_{1..4} = \left\{W_1,W_2,W_3,W_4\right\}$
20. Kepler $m_{1..2} = \left\{K_p,D51\right\}$
21. Hipparcos + Tyco $m_{1..3} = \left\{B,H_p,V\right\}$
22. HST-WFC3 $m_{1..57} = \left\{ \begin{array}{l}{F_{200LP},F_{218W},F_{225W},F_{275W},F_{280N},F_{300X},F_{336W},F_{343N},F_{350LP},F_{373N}, \\ F_{390M},F_{390W},F_{395N},F_{410M},F_{438W},F_{467M},F_{469N},F_{475W},F_{475X},F_{487N}, \\ F_{502N},F_{547M},F_{555W},F_{600LP},F_{606W},F_{621M},F_{625W},F_{631N},F_{645N},F_{656N}, \\ F_{657N},F_{658N},F_{665N},F_{673N},F_{680N},F_{689M},F_{763M},F_{775W},F_{814W},F_{845M}, \\ F_{850LP},F_{953N},F_{098M},F_{105W},F_{110W},F_{125W},F_{126N},F_{127M},F_{128N},F_{130N},\\ F_{132N},F_{139M},F_{140W},F_{153M},F_{160W},F_{164N},F_{167N}}\end{array}\right\}$.
23. HST-WFPC2 $m_{1..13} = \left\{ \begin{array}{l}{F_{218W},F_{255W},F_{300W},F_{336W},F_{439W},F_{450W},F_{555W},F_{606W},F_{622W},F_{675W}, \\ F_{791W},F_{814W},F_{850LP}}\end{array}\right\}$.
24. Subaru Hyper Suprime-Cam $m_{1..7} = \left\{g, r, i, z, y, NB816, NB921 \right\}$

The same number of columns is then reserved for

${m_{app}}\left[ {mag} \right]$: stellar magnitude after distance and absorption have been considered,

and

$a_{m_X}\left[ {mag} \right]$: the absorption in the photometric band ${m_X}$ for each star along the l.o.s.

The following columns contain the phase-space description of each star:

$r_{\rm{hel}}\left[ {kpc} \right]$: heliocentric distance of the star,

$\left\{\alpha ,\delta \right\}\left[ \deg \right]$ or $\left\{l,b \right\}\left[ \deg \right]$: angular coordinates of the star,

$\left\{R,z \right\}\left[ {kpc} \right]$ the cylindrical coordinates of the star,

$\left\{U,V,W \right\}\left[ {km\;{s^{ - 1}}} \right]$: heliocentric velocity of the star corrected for the motion of the star with respect to the local standard of rest,

$\left\{v_x,v_y,v_z\right\}\left[ {km\;{s^{ - 1}}} \right]$ the galactocentric velocity of the star,

${v_r}[km\;{s^{ - 1}}]$: radial velocity of the star,

$\left\{\mu _\alpha ,\mu _\delta \right\}$ or $\left\{\mu _l,\mu _b \right\}$$\left[ mas\;yr^{ - 1} \right]$: the proper motion of the star.

## Limits of the model

Kinematical corrections for binary stars have been not implemented yet, nor white-dwarf sequences have been added to the CMDs. Simulations are made at one's own risk. The authors are not responsible for wrong applications of their model. For further information, please contact Galaxy.Model@yahoo.com.

## Feedback/support/work with us

The support team can be reached at Galaxy.Model@Yahoo.com. GalMod is hosted by a cloud service; the support team does not have access to either the user’s email or to the produced simulations. If support on a simulation is needed, please contact the support email and include the first 100-lines of the file received. These contain the GalMod version and the parameters introduced in the form, and it will enable us to regenerate a simulation with the same version of GalMod.

Jun 2018 release (ver. 17.10): bug fixed on the azimuthal velocity written in the output table.

Oct 2018 release (ver. 17.20): bug fixed on the M31/dwarf-galaxies velocity field and FoV definition. New faster extinction and gravitational potential computation algorithms.

Dec 2018 release (ver. 18.01): numerous bugs evidenced by a larger GalMod community of users. Bug fixed on the M31/dwarf-galaxies FoV definition. Bug fixed on the M31/dwarf-galaxies FoV radial velocity computation. Bug fixed on the number of stars computed beyond the galactic center in the (l,b)=(0,0) direction.Bug fixed on the vertical velocity dispersion for some young stellar populations. Bug fixed on the HR diagram for masses of 0.6 Msun. Bug fixed for the random generator of the age/metallicity distribution. Minor bugs fixed on the kinematics computation. Furthermore, in the modality of semi-equilibrium model initial condition generator, GalMod does not make use any more of the Database of simulations (in this way, every time the user runs a simulation, new, different i.c. are generated). Use of co-arrays (and other Fortran 2018 features) has been implemented to speed up the computations.

Feb 2019 release (ver. 18.06): bug fixed on the position angle for the M31/dwarf-galaxies simulation mode.

Mar 2019 release (ver. 18.06): Simplified web-page with Basic and Advanced input form. Implemented encryption with SSL Certificate Management System.

Apr 2019 release (ver. 18.09): bug fixed to handle crashes gracefully.

Jul 2019 release (ver. 18.15): Introduction of parallel tempering technique to sample the posterior probability distribution functions more efficiently. Introduction of the small-FoV approximation to the solution of the star count equation to speed up the computation of very small FoV. Bug fixed in the bulge dispersion velocity computation of external galaxy models and/or MW bulge.

Aug 2019 release (ver. 18.19): Subaru Hyper Suprime-Cam photometry added to synthetic CMD generator, extinciton model, and webpage access. Bugs fixed on selection cuts.

Sep 2020 release (ver. 18.20): Speed up extinction computation. Bugs fixed.

Dec 2020 release (ver. 18.21): Bugs on the AI memory database fixed. Extinction computing bug fixed.

Nov 2021 release (ver. 18.22): New spherical frustum definitions.

Dec 2022 release (ver. 18.23): Bugs on M31-FoV generation fixed.