GalModWeb App

GalMod

The “Galaxy Model” (GalMod) is a theoretical population synthesis model able to simulate synthetic surveys of the Milky Way, M31, and able to generate initial conditions for quasi-equilibrium collisionless models. Please refer to Pasetto et al. 2016, 2018a,b for a complete description of the model.

P.I. of the project is Pasetto S.. People involved (directly or indirectly) in the realization of this project are: Brogliato C.; Busso, G.; Cassarà, L.; Chiosi, C.; Crnojevic, D.; Fuchs, B.; Grebel, E.; Hunt, J. A. S.; Just, A.; Kawata, D.; Kollmeier, J.; Natale, G.; Piovan, L.; Tantalo, R.; Zeidler P. The realization of this project would not have been possible without the major work carried out over more than three decades by Bertelli, G.; Nasi, Vallenari A.; E.; Bressan, A.; Girardi, L.; Marigo, P. and many others.

Introduction

GalMod assumes the Galaxy to be a discrete superposition of several composite stellar populations (CSPs) representing a few nominal significant stellar populations: the thin disk, the thick disk, the stellar halo and the bulge. GalMod immerses these CSPs in a single dark matter (DM) halo component and a hot coronal gas component (HCG). A parametric model for the modeled galaxy gravitational potential is computed to secure consistency with the density profiles by solving the Poisson equation. These density profiles are used to generate synthetic Hertzsprung-Russell and color-magnitude diagrams (CMDs) in several photometric bands. Finally, the gravitational potential is used to realize the stellar kinematics.

A global model for the Milky Way's gravitational potential is built up to secure consistency with the density profiles by solving the Poisson equation. In turn, these density profiles are used to generate synthetic probability distribution functions (PDFs) for the allocation of stars in the color-magnitude diagrams (CMDs). Finally, the gravitational potential is used to constrain the stellar kinematics using the moment method on phase-space distribution functions.

GalMod contains non-axisymmetric Galactic components such as the spiral arms, bar, and photometric extinction. The realization of the f.o.v has no size limit, even full-sky synthetic surveys are possible.

Usage and tutorial

Please feel free to contact Galaxy.Model@yahoo.com for support, comments or bug report.

For a detailed description of the model please visit our tutorial

Input form

How to operate GalMod virtual telescope

choose a photometric system,
choose two bands (with magnitude and color limits),
choose a field of view (FoV) type (with direction, proper motions, and radial velocity limits),
Insert your email.
Submit.

Read tutorial for the parameters explanation, assumption and advanced form.

N, number of stars

Set the number of stars that GalMod will attempt to realize in the the FoV (see tutorial)

N ∈ {10¹ .. 10⁶}

The number of stars better representing your model will be automatically determined by GalMod.

Photometric systems

Photometric errors

σ_mag($\text{mag}_{\min }^{1^{st}_\text{fltr}}$) ∈ ]0, 5] mag

σ_mag($\text{mag}_{\max }^{1^{st}_\text{fltr}}$) ∈ ]σ_mag($\text{mag}_{\min }^{1^{st}_\text{fltr}}$), 5.00] mag

Metallicity limits

Z_min ∈ ]0.00001, 0.05] dex

Z_max ∈ ]Z_min, 0.05] dex

Simulation type: Milky Way FoV, M31/ext-galaxy FoV, or i.c. generator

FoV angular definition

l_min ∈ [0,360[ deg

l_max ∈ [0,360[ deg

b_min ∈ [-90,90] deg

b_max ∈ ]b_min,90] deg

FoV depth

r_hel,min ∈ [0.01,50[ kpc

r_hel,max ∈ ]r_hel,min, 50] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

FoV angular definition

l_cen ∈ [0,360[ deg

b_cen ∈ [-90,90] deg

Δl ∈ ]0,360] deg

Δb ∈ ]0,180] deg

FoV depth

r_hel,min ∈ [0.01,50[ kpc

r_hel,max ∈ ]r_hel,min, 50] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

FoV angular definition {RA/dec/O.A.}

α_cen ∈ [0,360[ deg

δ_cen ∈ [-90,90] deg

O.A. ∈ ]0,360] deg

FoV depth

r_hel,min ∈ [0.01,50[ kpc

r_hel,max ∈ ]r_hel,min, 50] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

FoV angular definition {RA/dec,ΔRA,Δdec}

α_cen ∈ [0,360[ deg

δ_cen ∈ [-90,90] deg

Δα ∈ ]0,21600] [arcmin]

Δδ ∈ ]0,10800] [arcmin]

FoV depth

r_hel,min ∈ [0,50[ kpc

r_hel,max ∈ ]r_hel,min, 50] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

FoV angular definition

l_min ∈ ]0,360] deg

l_max ∈ ]0,360] deg

b_min ∈ [-90,90] deg

b_max ∈ ]b_min,90] deg

FoV depth

r_hel,min ∈ [0,50] kpc

r_hel,max ∈ ]r_hel,min, 50] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

FoV angular definition in the galaxy direction

l_min ∈ [0,360[ deg

l_max ∈ ]l_min,360] deg

b_min ∈ [-90,+90] deg

b_max ∈ ]b_min,90] deg

FoV depth toward the galaxy

r_hel,min ∈ [0.01,1000.0[ kpc

r_hel,max ∈ ]r_hel,min, 1000] kpc

Proper motion limits

μ_l,min ∈ [-800,800[ mas/yr

μ_l,max ∈ ]μ_l,min,800] mas/yr

μ_b,min ∈ [-800,800[ mas/yr

μ_b,max ∈ ]μ_b,min,800] mas/yr

Radial velocity limits

v_r,min ∈ [-800,800[ km/s

v_r,max ∈ ]v_r,min,800] km/s

Galaxy phase-space position

x_gal x_gal ∈ [-900,900]x10³ kpc

y_gal y_gal ∈ [-900,900] kpc

z_gal z_gal ∈ [-900,900] kpc

μ_l,gal μ_l,gal ∈ [-800,800] mas/yr

μ_b,gal μ_b,gal ∈ [-800,800] mas/yr

v_r,gal v_r,gal ∈ [-800,800] km/s

PA: position angle on the celestial sphere

PA_gal ∈ ]-90,90] deg

i: inclination

i_gal ∈ ]0,180] deg

Email Form

Email Address

Please provide your email address. We will use it only for sending important notifications.

After you press submit, please wait for the checks to be completed. You will be forwarded to info-pages (success/download or queued).

Observer position

Solar location

Radial solar location R_☉ ∈ ]6,9] kpc

Azimuthal solar location φ_☉ ∈ [0,360] deg

Vertical solar location z_☉ ∈ [-0.2,0.2] kpc

Solar motion to the Local Standard of Rest (LSR)

Radial motion to the LSR v_R,☉ ∈ [-20,20] km/s

Azimuthal motion to the LSR v_φ,☉ ∈ [-20,20] km/s

Vertical motion to the LSR v_z,☉ ∈ [-20,20] km/s

The Solar location is the position where the density and the velocity profile normalization constants are fixed. The simulated FoVs origin at the observer position.

Bulge CSP-I

ρ_0,B: central bulge density

10⁹

ρ_B ∈ ]0,10]x10⁹ M_☉ kpc^-3

h_r,B: scale length

h_r,B ∈ ]0.1,2] kpc

r_a,B: anisotropy radius

r_a,B ∈ ]0.1,2] kpc

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and the max CSP met., Z_max. SFR values are normalized to the max(SFR_norm(t_min), SFR_norm(t_max)).

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Linear in/de-creasing star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and the max CSP met., Z_max. SFR values are normalized to the max(SFR_norm(t_min), SFR_norm(t_max)).

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, t_min, and the max age of the CSP, t_max, with constant metallicity between min met. of the CSP, Z_min, and the max met. of the CSP, Z_max. SFR values are normalized to the max(SFR(t)).

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Spiral Arms CSP-I

ρ_D: disk density normalization factor

10⁶

ρ_D ∈ ]0.0,100]x10⁶ M_☉ kpc^-3

h_R,D: scale length h_R,D ∈ ]1,4] kpc

Vertical density profile

$ {\rho _z} \propto e^{ - z/h_{z,D}} $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

$ {\rho _z} \propto \text{sech}^2(z/h_{z,D}) $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

σ_RR,D: radial velocity dispersion σ_RR,D ∈ ]σ_φφ,D,100] km/s

σ_φφ,D: azimuthal velocity dispersion σ_φφ,D ∈ ]σ_zz,D,100] km/s

σ_zz,D: vertical velocity dispersion σ_zz,D ∈ ]1,100] km/s

Ω_p: angular speed of the spiral pattern Ω_p ∈ ]20, 40] km s^-1 kpc^-1

Φ₀^a amplitude spiral arm potential Φ₀^a ∈ ]500,1500] km² s^-2 kpc^-1

h_sp^a: spiral arm potential amplitude scale h_sp^a ∈ ]1,4] kpc

p: pitch-angle p ∈ ]5,25] deg

m: number of spiral arms m = 2 or 4

h_sh: shape function scale length h_s ∈ ]1,4] kpc

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Bar CSP-I specific parameters

Bar and Spiral arms are a single dynamically connected structure. Setting the spiral arms at observer position determines the bar structure.

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Select Number of Thin Disk CSP:

Thin Disk CSP-I

ρ_D: disk density normalization factor

10⁶

ρ_D ∈ ]0.0,100]x10⁶ M_☉ kpc^-3

h_R,D: scale length h_R,D ∈ ]1,4] kpc

Vertical density profile

$ {\rho _z} \propto e^{ - z/h_{z,D}} $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

$ {\rho _z} \propto \text{sech}^2(z/h_{z,D}) $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

σ_RR,D: radial velocity dispersion σ_RR,D ∈ ]σ_φφ,D,100] km/s

σ_φφ,D: azimuthal velocity dispersion σ_φφ,D ∈ ]σ_zz,D,100] km/s

σ_zz,D: vertical velocity dispersion σ_zz,D ∈ ]1,100] km/s

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Thick Disk CSP-I

ρ_D: disk density normalization factor

10⁶

ρ_D ∈ ]0.0,100]x10⁶ M_☉ kpc^-3

h_R,D: scale length h_R,D ∈ ]1,4] kpc

Vertical density profile

$ {\rho _z} \propto e^{ - z/h_{z,D}} $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

$ {\rho _z} \propto \text{sech}^2(z/h_{z,D}) $ with h_z,D scale height h_z,D ∈ ]0.01,h_R,D[ kpc

σ_RR,D: radial velocity dispersion σ_RR,D ∈ ]σ_φφ,D,100] km/s

σ_φφ,D: azimuthal velocity dispersion σ_φφ,D ∈ ]σ_zz,D,100] km/s

σ_zz,D: vertical velocity dispersion σ_zz,D ∈ ]1,100] km/s

${\bar v_\phi }$: mean circular velocity ${\bar v_\phi }$ ∈ [150,200] km/s

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Halo CSP-I

ρ_0,H* M_☉ kpc^-3

10⁴

ρ_0,H* ∈ ]0,9.9]x10⁴ M_☉ kpc^-3

α density profile slope α ∈ ]-3,-2] kpc

h_r,H* kpc scale radius h_r,H* ∈ ]0.1,5] kpc

σ_RR,D: radial velocity dispersion σ_RR,D ∈ ]σ_φφ,D,200] km/s

σ_φφ,D: azimuthal velocity dispersion σ_φφ,D ∈ ]σ_zz,D,200] km/s

σ_zz,D: vertical velocity dispersion σ_zz,D ∈ ]50,200] km/s

${\bar v_\phi }$: mean circular velocity ${\bar v_\phi }$ ∈ [-50,50] km/s

Star Formation Rate (SFR)

Constant star formation between the min CSP age, t_min, and the max CSP age, t_max. Constant metallicity between the min CSP met., Z_min, and max CSP met., Z_max.

t_min: min CSP age t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age t_max ∈ ]t_min+0.1, 13] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 12.9] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

h_τ: timescale parameter

10⁹

τ ∈ ]-10, -1[ ∪ ]1, 10] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

SFR_norm(t_min) SFR_norm ∈ ]0, 1]

SFR_norm(t_max) SFR_norm ∈ ]0, 1]

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

t_min: min CSP age

10⁹

t_min ∈ ]0, 13] Gyr

t_max: max CSP age

10⁹

t_max ∈ ]t_min+0.1, 13] Gyr

ζ: power law exponent ζ ∈ ]0.5,3]

h_τ: timescale parameter h_τ ∈ ]2, 8] Gyr

Z_min: min CSP met. Z_min ∈ ]0.0001, 0.05] dex

Z_max: max CSP met. Z_max ∈ ]Z_min, 0.05] dex

Initial Mass Function (IMF)

IMF of the form Mξ(M)dM = const. M^α

α: IMF slope

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

IMF of the form Mξ(M)dM = const. M^α_i with i={1,2,3} and 2 separation masses M_sep,j with j={1,2}

α₁: 1^st IMF slope

α₂: 2^nd IMF slope

α₃: 3^rd IMF slope

M_sep,1 [M_☉]

M_sep,2 [M_☉]

Log-normal IMF with a parameter, σ_M, below the separation mass, M_sep,1, and a power-law with slope, α, above it

σ_M: mass dispersion factor

α: power law slope above M_sep,1

Log₁₀(M_sep,1[M_☉])

Interstellar medium

ρ_ISM: density scale factor

10⁶

ρ_ISM ∈ ]0,100]x10⁶ M_☉ kpc^-3

h_R,ISM: scale length h_R,ISM ∈ ]1,5] kpc

h_z,ISM: scale height h_z,ISM ∈ ]0.01,h_R,ISM[ kpc

Dark matter

v₀: circular speed scale factor v₀ ∈ ]10,400] km s^-1

h_r,DM: kpc scale radius h_r,DM ∈ ]1,10] kpc

q: flattening q ∈ ]0.5,1]