GalMod: the Milky Way Galaxy model

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, 2017a,b for a complete description of the model.

P.I. of the project is Pasetto S. (spasetto@carnegiescience.edu). 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. Web-design and server maintenence by CLOVER-lab (www.clover-lab.com).

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 repot.

For a detailed description of the model please visit our tutorial

Input form (basic)

Set the number of stars that GalMod will attempt to realize in the the f.o.v. (see tutorial)
N ∈ {101 .. 106}
The number of stars better representing your model will be automatically determined by GalMod.
Johnson-Cousins photometric system. Set 1 for U, 2 for B, 3 for V, etc.
$1^{st}_\text{fltr}$ ∈ {1..7}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..8}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
Hubble space telescope's Wide Field Camera photometric system. Set 1 for F435W, 2 for F475W etc.
$1^{st}_\text{fltr}$ ∈ {1..11}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..12}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
Hubble space telescope's high-resolution channel photometric system. Set 1 for F220W, 2 for F250W etc.
$1^{st}_\text{fltr}$ ∈ {1..15}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..16}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
Gaia photometric system. Set 1 for Gbp, 2 for G etc.
$1^{st}_\text{fltr}$ ∈ {1..2}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..3}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
SDSS photometric system. Set 1 for u, 2 for g etc.
$1^{st}_\text{fltr}$ ∈ {1,4}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..5}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
2MASS photometric system. Set 1 for J, 2 for H etc.
$1^{st}_\text{fltr}$ ∈ {1,2}
$\text{mag}_{\min }^{1^{st}_\text{fltr}}$ ∈ ]5.0, 35.0] mag
$\text{mag}_{\max }^{1^{st}_\text{fltr}}$ ∈ ]$\text{mag}_{\min }^{1^{st}_\text{fltr}}$, 35.0] mag
$2^{nd}_\text{fltr}$ ∈ {$1^{st}_\text{fltr}$+1..3}
colmin ∈ ]-2.0, 5.0] mag
colmax ∈ ]colmin, 5.0] mag
σmag($\text{mag}_{\min }^{1^{st}_\text{fltr}}$) ∈ ]0.0, 5.0] mag
σmag($\text{mag}_{\max }^{1^{st}_\text{fltr}}$) ∈ ]σmag($\text{mag}_{\min }^{1^{st}_\text{fltr}}$), 5.00] mag
Zmin ∈ ]0.0001, 0.05] dex
Zmin ∈ ]Zmin, 0.05] dex
f.o.v. angular definition
lmin ∈ ]0,360] deg
lmax ∈ ]0,360] deg
bmin ∈ [-90.0,90.0] deg
bmax ∈ ]bmin,90.0] deg
f.o.v. depth
rhel,min ∈ [0.0,50.0] kpc
rhel,max ∈ ]rhel,min, 50.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
f.o.v. angular definition
lcen ∈ ]0.0,360.0] deg
bcen ∈ [-90,90] deg
Δl ∈ ]0.0,360.0] deg
Δb ∈ ]0.0,180.0] deg
f.o.v. depth
rhel,min ∈ [0.0,50.0] kpc
rhel,max ∈ ]rhel,min, 50.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
f.o.v. angular definition {RA/dec/O.A.}
αcen ∈ ]0,360] deg
δcen ∈ [-90,90] deg
O.A. ∈ ]0,360] deg
f.o.v. depth
rhel,min ∈ [0.0,50.0] kpc
rhel,max ∈ ]rhel,min, 50.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
f.o.v. angular definition {RA/dec,ΔRA,Δdec}
αcen ∈ [0,360] deg
δcen ∈ [-90,90] deg
Δα ∈ ]0,21600] [arcmin]
Δδ ∈ ]0,10800] [arcmin]
f.o.v. depth
rhel,min ∈ [0.0,50.0] kpc
rhel,max ∈ ]rhel,min, 50.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
f.o.v. angular definition
lmin ∈ ]0,360] deg
lmax ∈ ]0,360] deg
bmin ∈ [-90.0,90.0] deg
bmax ∈ ]bmin,90.0] deg
f.o.v. depth
rhel,min ∈ [0.0,50.0] kpc
rhel,max ∈ ]rhel,min, 50.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
f.o.v. angular definition in the M31 direction
lmin ∈ ]111,131] deg
lmax ∈ ]lmin,131] deg
bmin ∈ [-31.6,-11.6] deg
bmax ∈ ]bmin,-11.6] deg
f.o.v. depth toward M31
rhel,min ∈ [0.0,1000.0] kpc
rhel,max ∈ ]rhel,min, 1000.0] kpc
Proper motion limits
μl,min ∈ [-400,400] mas/yr
μl,max ∈ ]μl,min,400] mas/yr
μb,min ∈ [-400,400] mas/yr
μb,max ∈ ]μb,min,400] mas/yr
Radial velocity limits
vr,min ∈ [-400,400] km/s
vr,max ∈ ]vr,min,400] km/s
M31 properties
xM31 xM31 ∈ [-1.0,1.0]x103 kpc
yM31 yM31 ∈ [-1.0,1.0] kpc
zM31 zM31 ∈ [-1.0,1.0] kpc
μl,M31 μl,M31 ∈ [-10.0,10.0] mas/yr
μb,M31 μb,M31 ∈ [-10.0,10.0] mas/yr
vr,M31 vr,M31 ∈ [-150.0,150.0] km/s
PA: position angle on the celestial sphere
PAM31 ∈ ]0.0,90.0] deg
i: inclination
iM31 ∈ ]0.0,90.0] deg
Radial solar location R ∈ ]6.0,9.0] kpc
Azimuthal solar location φ ∈ ]0.0,360.0] deg
Vertical solar location z ∈ ]-0.10,0.10] kpc
Radial motion to the LSR vR,☉ ∈ [-20.0,20.0] km/s
Azimuthal motion to the LSR vφ,☉ ∈ [-20.0,20.0] km/s
Vertical motion to the LSR vz,☉ ∈ [-20.0,20.0] km/s

Input form (advanced)

Bulge
109
ρB ∈ ]1.0,10.0]x109 M kpc-3
hr,B ∈ ]0.1,2.0] kpc
ra,B ∈ ]0.1,2.0] kpc
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0]
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Bar CSP I
106
ρbar ∈ ]0.01,100]x106 M kpc-3
hR,bar ∈ ]1.0,4.0] kpc
hz,bar ∈ ]0.01,hR,bar[ kpc
hz,bar ∈ ]0.01,hR,bar[ kpc
σRR,bar ∈ ]σφφ,bar,100.0] km/s
σφφ,bar ∈ ]σzz,bar,100.0] km/s
σzz,bar ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Bar treatment for Bar CSP I
Ωp ∈ ]20.0, 40.0] km s-1 kpc-1
Φ0a ∈ ]500.0,1500.0]km2 s-2 kpc-1
hbara ∈ ]1.0,4.0]kpc
Thin disk CSP I
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Spiral arm treatment for thin disk CSP I
Ωp ∈ ]20.0, 40.0] km s-1 kpc-1
Φ0a ∈ ]500.0,1500.0] km2 s-2 kpc-1
hspa ∈ ]1.0,4.0] kpc
p ∈ ]5.0,25.0] deg
m = 2 or 4
hs ∈ ]1.0,4.0] kpc
Thin disk CSP II
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Thin disk CSP III
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Thin disk CSP IV
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Thin disk CSP V
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Thick disk CSP I
106
ρD ∈ ]0.01,100]x106 M kpc-3
hR,D ∈ ]1.0,4.0] kpc
hz,D ∈ ]0.01,hR,D[ kpc
hz,D ∈ ]0.01,hR,D[ kpc
σRR,D ∈ ]σφφ,D,100.0] km/s
σφφ,D ∈ ]σzz,D,100.0] km/s
σzz,D ∈ ]1.0,100.0] km/s
${\bar v_\phi }$ ∈ [160,200.0] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Stellar Halo CSP I
104
ρ0,H* ∈ ]1.0,9.9]x104 M
α ∈ ]-3.0,-2.0] kpc
hr,H* ∈ ]0.1,5.0] kpc
σRR,D ∈ ]σφφ,D,200.0] km/s
σφφ,D ∈ ]σzz,D,200.0] km/s
σzz,D ∈ ]50.0,200.0] km/s
${\bar v_\phi }$ ∈ [-50,50] km/s
Constant star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and max met. of the CSP, Zmax.
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Exponential in/de-creasing star formation, $\psi \propto {e^{t/{h_\tau }}}$, between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
109
τ ∈ ]-10,-1[∪]1,10]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
Linear in/de-creasing star formation between the min age of the CSP, tmin, and the max age of the CSP, tmax. Constant metallicity between the min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFRnorm(tmin), SFRnorm(tmax)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
SFRnorm ∈ ]0.0, 1.0]
SFRnorm ∈ ]0.0, 1.0]
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
$\psi \propto {(t_{max}-t)^\zeta }{e^{ - (t_{max}-t)/{h_\tau }}}$ between the min age of the CSP, tmin, and the max age of the CSP, tmax, with constant metallicity between min met. of the CSP, Zmin, and the max met. of the CSP, Zmax. SFR values are normalized to the max(SFR(t)).
109
tmin ∈ ]0.0, 13.0] Gyr
109
tmax ∈ ]tmin+0.1, 13.0] Gyr
ζ ∈ ]0.5,3.0] Gyr
109
hτ ∈ ]2.0, 8.0] Gyr
Zmin ∈ ]0.0001, 0.05] dex
Zmax ∈ ]Zmin, 0.05] dex
IMF of the form Mξ(M)dM = const. Mα
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
IMF of the form Mξ(M)dM = const. Mαi with i={1,2,3} and 2 separation masses Msep,j with j={1,2}
 
 
 
 
Log-normal IMF with a parameter, σM, below the separation mass, Msep,1, and a power-law with slope, α, above it
 
Interstellar medium
106
ρISM ∈ ]1.0,100.9]x106 M kpc-3
hR,ISM ∈ ]1.0,5.0] kpc
hz,ISM ∈ ]0.01,hR,D[ kpc
Dark matter
v0 ∈ ]100.0,200.0] km s-1
hr,DM ∈ ]4.0,10.0] kpc
q ∈ ]0.5,1.0]
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