Modeling
the chemical evolution of galaxies
Mercedes Mollá
CIEMAT
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Angeles y mis inicios en
Astronomía
Trabajando en el CSN…evaluando centrales nucleares….y
cuidando niños!
Las funciones del Consejo de Seguridad Nuclear son las de evaluación y
control de la seguridad de las instalaciones, en todas y en cada una de las
etapas en la vida de una central (diseño, construcción, pruebas, operación y
clausura). Controla y vigila los niveles de radiactividad dentro y fuera de las
instalaciones, tanto nucleares como radiactivas, y vela por la protección
radiológica de las personas y el medio ambiente.
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Galaxies Chemical Evolution Aim
Chemical elements are created and then:
 Ejected and diluted in the
interstellar medium
 Incorporated to the sucessive
generations of stars
Elemental abundances give clues about
star formation: when, how, with which
rate stars form
•Phases:
–to understand processes,
–to predict elemental abundances,
–to compare with data
GCE tries to explain how and when the elements appear
From elemental abundances we may deduce the evolutionary histories of galaxies
La Cristalera, Abril 2015
A) Tinsley 1981: El modelo simple
1)The system will have 2 types of stars

those with mass m>m1 with t 0 dying when
form

those with m< m1 and t=
¥
2) The system is closed f=0
M
Z = y ln
= y ln m -1
Mg
If
3) Metals are instantaneously mixed with the ISM
Model predictions:
1.
Abundance proportional to the total yield of one stellar generation
2.
This relation abundance-yield is independent of the star formation history or
the star formation rate
Model problems:
1.
The G-dwarf metallicity distribution is not
reproduced
2.
The relation not sufficient to obtain the
observed radial gradient of abundances
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
A) Tinsley 1981: El modelo simple
1)The system will have 2 types of stars

those with mass m>m1 with t 0 dying when
form

those with m< m1 and t=
¥
2) The system is closed f=0
M
Z = y ln
= y ln m -1
Mg
If
3) Metals are instantaneously mixed with the ISM
Model predictions:
• El modelo simple no vale
1.
Abundance proportional to the total yield of one stellar generation
2.
This relation abundance-yield is independent of the star formation history or
the star formation rate
Model problems:
1.
The G-dwarf metallicity distribution is not
reproduced
2.
The relation not sufficient to obtain the
observed radial gradient of abundances
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
A) Tinsley 1981: El modelo simple
1)The system will have 2 types of stars

those with mass m>m1 with t 0 dying when
form

those with
m< solutions:
m1 and t=
Posible
¥
2) The system is closed f=0
M
Z = y ln
= y ln m -1
Mg
If
1.
Infall of enriched (or not) gas
2.
Metallicity dependent yields
3.
Radial flows which dilute or enrich the gas of the region
4.
Star formation law which varies with the radial disc
3) Metals are instantaneously mixed with the ISM
Model predictions:
• El modelo simple no vale
1.
Abundance proportional to the total yield of one stellar generation
2.
This relation abundance-yield is independent of the star formation history or
the star formation rate
Model problems:
1.
The G-dwarf metallicity distribution is not
reproduced
2.
The relation not sufficient to obtain the
observed radial gradient of abundances
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
A) Tinsley 1981
B) Modelo de evolución química de Angeles y Mónica
1) Díaz & Tosi, 1984
2) Tosi & Díaz, 1985
3) Díaz & Tosi, 1986
4) Tosi & Díaz, 1990
•
•
El modelo simple no vale
Las abundancias relativas de elementos nos sirven de
“reloj”
The meanlifetimes of different stars explain the relative abundances of elements
Cycle
pp:
low
mass
stars
m<4Mo
Cycle pp+CNO: intermediate mass stars 4Mo< m < 8Mo
Cycle CNO+ capture : massive stars m > 8Mo
•
•
•
•
Low mass stars produce He and C12
Intermediate mass stars produce C,N and O
Massive stars produce O,Ne,Mg,S..,N, and Fe
Binary Systems, SNIa Fe
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
A) Tinsley 1981
B) Modelo de evolución química de Angeles y Mónica
1) Díaz & Tosi, 1984
2) Tosi & Díaz, 1985
3) Díaz & Tosi, 1986
4) Tosi & Díaz, 1990
•
•
•
La Cristalera, Abril 2015
El modelo simple no vale
Las abundancias relativas de elementos nos sirven de
“reloj”
Los gradientes de abundancia, relación con la formación de
los discos
Stars, interstellar medium, galaxies, and the chemistry between them
A) Tinsley 1981
B) Modelo de evolución química de Angeles y Mónica
1) Díaz & Tosi, 1984
2) Tosi & Díaz, 1985
3) Díaz & Tosi, 1986
4) Tosi & Díaz, 1990
•
•
•
•
La Cristalera, Abril 2015
El modelo simple no vale
Las abundancias relativas de elementos nos sirven de
“reloj”
Los gradientes de abundancia, relación con la formación de
los discos
El H2 es realmente de donde se forman las estrellas
Stars, interstellar medium, galaxies, and the chemistry between them
La evolución temporal del gradiente de
abundancias: El gradiente se va
creando con el tiempo
Mollá et al. (1992)
Ferrini et al. (1994)
La Cristalera, Abril 2015
La evolución temporal del gradiente de
abundancias: El gradiente se va
aplanando con el tiempo
Stars, interstellar medium, galaxies, and the chemistry between them
La
temporal
del gradiente
de
Enevolución
el modelo
D&T,
el disco
abundancias: El gradiente se va
está
creandoformado
con el tiempodesde el t=0
y el infall de Z=0 solo
diluye lo que se crea en el
disco
Mollá et al. (1992)
Ferrini et al. (1994)
La Cristalera, Abril 2015
En el caso de Ferrini et al,
La evolución temporal del gradiente de
el
infall forma el disco a
abundancias: El gradiente se va
medidad
cae de
aplanando conque
el tiempo
manera que el material del
que han de formarse las
estrellas va apareciendo
poco a poco
Stars, interstellar medium, galaxies, and the chemistry between them
DATA IN THE MWG
In the MWG we had some data from objects of
different age to compare the radial gradients at other
times:
• Planetary Nebulae from different mass stars
• Open Clusters of different ages
• Globular Clusters of old ages
Large uncertainties in the determination of mass, or
age
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
THE TIME EVOLUTION OF THE RADIAL GRADIENT IN OTHER SPIRAL GALAXIES
This variation of the radial gradient also occurs
in other spiral galaxies. The rate of flattening
depends on the type or size of the galaxy:
• A bright-early-massive spiral galaxy shows
a flat gradient which evolved very rapidly;
• A low mass-late galaxy maintains a steep
gradient for a longer time
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
THE GRID OF MODELS FROM MOLLÁ & DÍAZ (2005)
•Mollá & Díaz (2005): a grid of chemical evolution models depending on the galaxy
total mass and on the efficiency of star formation rate
•Radial distributions of mass calculated from the Universal Rotation Curve from
Persic, Salucci & Steel (1996)
•Efficiencies to form molecular gas and stars changed simultaneously: each N
defined a set (m, H)
•A by-parametric grid of 44 radial mass distributions, defined by the rotation
velocity, (Vrot 30 to 300 km/s) and 10 values of N (m, H in the range [0,1]), were
calculated, with the corresponding radial distributions of abundances, stars and gas
densities and star formation rates.
•Results (radial distributions of gas, abundances, star formation...), and the time
evolution of each radial region, were given as a function of the total mass of the
galaxy for different values of efficiencies to form molecular cloud and stars
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Ingredients of the multiphase chemical evolution model:
the scenario
The total mass M of each modeled galaxy and its radial distribution M(R)
have been computed from the universal rotation curve V(R) from Persic,
Salucci & Steel (1996)
(Mollá & Díaz 2005)
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Ingredients : The infall rate
tcol a M -1/2
tcol=tcol,0 exp(R/l)
•The gas collapses onto the equatorial plane and forms out the disc
• Infall rate 1/tcol
• col = f(Mgal) ---calibration with the MWG
•Since mass =f(R ),
(R )
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Inputs of the multiphase chemical evolution model:
The star formation law
2
YD (t ) = ( H1 + H 2 )cD (t ) + (a1 + a2 )S2,D (t )cD (t )
Star formation
in the halo:
SFR K g 1.5
Stars form
through cloud-cloud
collisions:
s Hc 2
In the disc
molecular clouds
form from
Stars also form
the diffuse gas
from the interaction
c mg 1.5
between massive stars
and molecular clouds:
s a c s 2
La Cristalera, Abril 2015
 Every parameter changes
along the galactocentric
radius:
 K = K (G/V)1/2
 m = m (G/Vd)1/2
 H = H cte /Vd
 a = a (G rc )1/2/ <ms2>
 The efficiency a is a local
parameter
 The efficiency K is assumed as
constant for all halos
 Efficiencies m y H are
variable for each galaxy
Stars, interstellar medium, galaxies, and the chemistry between them
Vrot
1
30
2
40
3
48
1
2
3
4
0.95
0.8
0
0.75
BCD &
HII Gal.
5
6
7
8
Low mass galaxies
9
10
DDO
154
…
10
71
…
18
Normal
spirals
99
…
--28
200
MWG
…
39
291
…
M33
M31
Starbursts
Low surface
brightness Galaxies
43
44
387
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Calibration: the model against the Solar Vicinity data
Gavilán et al. 2005, 2006
•
•
The age-metallicity relation and the star formation history for the solar region
The metallicity distribution does not show the G-dwarf problem
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Calibration: the model for MWG (Gavilán et al. 2005, 2006)
The model: Vrot=200 km/s and N=4 against the Galactic disk data and model
 We can obtain
separately the
radial distributions
of diffuse and
molecular gas
 The radial
gradients flattens
in the inner disk in
agreement with
data (Smartt et al.
2001)
 The star formation
rate surface
density is
underestimated in
the inner radii
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
The evolution of the abundance radial distributions along z
Flat radial
gradients for low
evolved galaxies,
and for the most
evolved galaxies
The inner radial
distributions
flatten compared
with the discs
Our models show a maximum oxygen abundance 12+log(O/H)~8.9- 9.0 (Pilyugin et al)
There is also a minimum abundance
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
The time evolution of the radial
gradient of oxygen abundances
Mollá 2014
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Vrot
1
30
2
40
3
48
1
2
3
4
0.95
0.8
0
0.75
BCD &
HII Gal.
5
6
7
8
Low mass galaxies
9
10
DDO
154
…
10
71
…
18
Normal
spirals
99
…
--28
200
MWG
…
39
291
…
M33
M31
Starbursts
Low surface
brightness Galaxies
43
44
387
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
EVOLUTIONARY SYNTHESIS MODELS
From the evolutionary histories and using evolutionary synthesis models, we
obtained the spectral energy distributions, magnitudes and colors, brightness
profiles and spectral absorption lines along the galactocentric radius for every
SSP
galaxy model.
Fl (t) =
ò Y(t')Fl
(t - t')dt'
t
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
SEDs and colors for our galaxy models:
Buzzoni (2005)
Boselli(2003)
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
SUMMARY OF MODELS GRID





We have used the universal rotation curve from Persic, Salucci &
Steel (1996) to calculate radial mass distribucions M (R)
We have computed the collapse time scale for each distribution
from the relation tcol,gal / tcol,MWG = (M MWG/Mgal )0.5
We have found analytical expressions for m (T) y h (T)
We compute models for 44 radial mass distributions, and 10
different values of eficiencies (m , H) between 0 and 1, as it
corresponds to their probability meaning, for each one = 440
different models
The results of this bi-parametric grid can be applied to any spiral or
irregular galaxy of given rotation velocity or total mass in order to
estimate its evolution
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
HOWEVER
•Although the radial gradient of abundances is well reproduced in
the models, our results depend on the fitting of gas stars and star
formation profiles…
•..and the molecular gas and the star formation rate show radial
distributions decreasing in the inner disk, at variance of observed.
They are not well tuned compared with observations
•It. seems that we need a slower evolution…
WE NEED BETTER MODELS
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Calibration: the model for MWG (Gavilán et al. 2005, 2006)
The model: Vrot=200 km/s and N=4 against the Galactic disk data and model
 We can obtain
separately the
radial distributions
of diffuse and
molecular gas
 The radial
gradients flattens
in the inner disk in
agreement with
data (Smartt et al.
2001)
 The star formation
rate surface
density is
underestimated in
the inner radii
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
New grid of models: updating the inputs and assumptions
•Radial distributions computed following equations from Salucci et al. (2007)
defined in terms of Mvir and arriving to longer distances along the
galactocentric radius
•Collapse time-scale t modified to follow the prescriptions from Shankar et al.
(2006) about the observed ratio Mdisk/Mhalo
•New grid of models: 75 radial mass distributions,
–Mvir ∈[5 1010 -1013] Msun
–Mdisk ∈ [1.25 108 -5.3 1011] Msun
–Vrot ∈ [42-320] km/s
•Radial dependence t(R) smoother than the old one.
•Efficiencies M and H selected independently: 10 values in the range [0--1]
•Revision of new set of stellar yields and different IMFs
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Ingredients of the multiphase chemical evolution model: the scenario
The total mass M of each modeled galaxy and its radial distribution M(R)
have been computed from the universal rotation curve V(R) from Salucci
(2007)
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Ingredients : The infall rate
tcol M-/2
•The gas collapses onto the equatorial plane and forms out the disc
• Infall rate  1/tcol
tcol = f(Mgal) ---calibration with the MWG
•Since mass =f(R ), tt(R ), following Shankar et al.
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
THE INFALL RATE HISTORY IN MOLLA + 2015
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Calibration of the MWG
The MWG model:
•Ndis=68, Mdyn=1012 M0 Mdisk=6.51010 M0 Ropt=12 kpc
La Cristalera, Abril 2015
•N(M)=4, N(H)=5
Stars, interstellar medium, galaxies, and the chemistry between them
The evolution
of the SF
efficiency
measured as
SFR/MH2
along the
redshift
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
THE GRID OF MODELS FROM MOLLÁ ET AL (2015)
The evolution of the radial gradient
is smoother than in MD05
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Molla & Díaz 2005
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Molla & Díaz 2005
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
The radial gradients for the same M
and H and different Mvir models,
when measured with normalized
distances, are equivalent
By observing different radial gradients
with a normalized radial scale we may
distinguish different efficiencies to
form molecular clouds or stars in
galaxies
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
• APRENDI CON ANGELES MUCHA ASTRONOMIA….Y
MUCHAS OTRAS COSAS
• TRABAJAR CON ANGELES HA SIDO UN PLACER…Y
ESPERO QUE LO MANTENGAMOS EN EL FUTURO
• GRACIAS A SU CONFIANZA EN MI, MI VIDA DIÓ UN
VUELCO Y ES LO QUE ES AHORA…
MIL GRACIAS, Y
MUCHAS FELICIDADES,
ÁNGELES!!!
La Cristalera, Abril 2015
Stars, interstellar medium, galaxies, and the chemistry between them
Production of nuclei in stars: Stellar yields
Burbidge, Burbidge & Hoyle 1957
 Cycle pp: low mass stars m<4Mo
 Cycle pp+CNO: intermediate mass stars 4Mo< m < 8Mo
 Cycle CNO+ capture : massive stars m > 8Mo
•
•
•
•
Low mass stars produce He and C12
Intermediate mass stars produce C,N and O
Massive stars produce O,Ne,Mg,S..,N, and Fe
Binary Systems, SNIa Fe
The basic equations
dM
= f
dt
dMs
=Y-E
dt
dMg
= -Y + E + f
dt
M = Ms + Mg
•
•

•
•
•
f= flux of inflow gas (iy may be 0 )
M= total mass of the system
YSFR (star formation rate
E= mass ejection rate by the stars
Ms=stellar mass
Mg= gas mass
Each star loss mass after its stellar lifetime tm, after this there is a remnant
tehrefore the total ejection by all stars created in a region is:
wm, and
¥
E (t ) = ò (m - w m )Y (t - t m )F(m)dm
mt
Ejected mass by a star of mass m
Initial mass function or number
of stars in the range dm
Mass of stars created in the time (t-tm)
which are now dying and ejecting mass after
a time tm
¥
pz,m is the metal
fraction ejected by a
star of mass m
The total yield of a stellar
generation
1
y=
mpz ,m F(m)dm
ò
1- R m
The abundance of metals may be
obtained fron this equation,
which implies:
d (ZMg )
= -ZY + Z f f + -Z w w + Ez
dt
1)ZY metals which dissapear from the gas when stars form
2)Zf f mass of metals which going in to the region when the gas infall
3) Zw w is the mass of metals which dissapears with the outflow of gas
4) Ez quantity of metals ejected by stars
¥
EZ = ò mp z ,m Y (t - t m )F (m)dm +
mt
¥
ò (m - w
mt
m
- mp z ,m ) Z (t - t m )Y (t - t m )F(m)dm
The first part is the yield or
metals newly created
The second one correspond
to the metals which were
before, in the original gas
with which the star form
2
1
0
-1
ln em
-2
-3
-4
-5
-6
-7
-20
0
20
40
T
2
60
80
100
120
Data of molecular and diffuse gas
mass from Young et al (1996), show
that efficiencies to form molecular
clouds and stars depend on
morphological type of galaxies
Metal Enrichment from
Hydrodynamical Simulations.El
Escorial. 2010 Sept.
IMF & stellar yields:
no effect on the radial
gradient of
abundances, only
variations on the
absolute values of
abundances
La Cristalera, Abril 2015