Basic Concepts on Chemical
Evolution
Cesare Chiosi
Department of Astronomy
University of Padova, Italy
Aims
To understand the pattern of abundances in the solar system, in the solar vicinity,
in the Halo, Bulge, and Disk of the Milky Way, in external galaxies of different
morplogical type, and finally in the Universe as a whole.
An easy and difficult task at the same time!
Abundances
Standard abundances in the solar system and solar vicinity (inside 0.5 Kpc radius)
provide the richest information. Detailed compilations are available (Cameron,
Anders & Grevesse….).
Surprisingly abundances are fairly homogenous going from one site to another.
The Cosmic Soupe tastes the same in all restaurants!! With obvious differences.
Why?
Need to know the amount of mass (total and in gas and stars) in the solar vicinity.
highly controversial, say total 70 Mo /pc^2 (from dynamics), stars 25 Mo/pc^2,
gas 6 Mo/pc^2
An old compilation but still….
Abundances are the relative number of atoms, gradients in dlogX/dR (R in kpc)
Abundance ratios (neglect the lines)
a-enhancement problem
Metallicity Distribution
G-Dwarf problem
In the Disk virtually no star of low metallicity. In the Halo the opposite
Age-Metallicity relationship
In reality the relationship is
much more dispersed: at any
age a large scatter in metallicity
can be seen.
Present-day and Initial Mass Function
in the Solar Vicinity
The present day mass function is derived from the observed luminosity function
ms (log m)  LF ( M V )
m( M V ) is a mass - luminosity relation and
hz (t ) is the vertical scale hight (referred to disk)
dM V
ms (log m)  LF ( M V )
2hz (t )
d log m
Passing from PDMF to IMF
By definition
T
 (m)    (t ) (m)dt
0
where  (m) is normalized in such a way that
mu
 A(m)dm  1
ml
For stars with t
For stars with t
m
 T
(m) 
φ(m)
Ψ(T)t m
m  2M 
m
T
(m) 
φ(m)
 Ψ(T)  T
m  1M 
  T
 (T )
 (m) cannot be derived without assuming  (t)
Continuity
t1 
Popular IMFs
 ( m)  m
x
Salpeter
ms a
 (m)  m exp[ ( ) ]
m
x
x and a positive numbers
Larson, Chabrier
Other, more or less equivalent formulations
have been proposed over the years
Need an assumption for (t)
Simple exponential
Ψ(t)  exp(-t/τ )
where τ is a suitable time scale
or a more realistic one
(t) starts low, grows to a maximum and then declines
or a complicate function of the gas density (such as in
the so - called infall models). Confirmed by N - Body
TSPH simulations.
Simple Models
Assumptions:
Initial conditions
Closure of the system: infall, outflow, radial flow, galactic winds
Star formation rate (t)
Chemical Yields
Mixing
Let ST, Sg, Ss be the surface mass densities (or masses in general) of
total baryonic matter, gas, and stars respectively ………
Basic Equations
dS T
 f (t )  w(t ) where f(t) infall and w(t) outflow
dt
dS g
  (t )  E (t )  f (t )  w(t )
dt
dS s
 (1  R) (t )
dt
d ( X iS g )
  X i  (t )  Ei  X if f (t )  X i (t ) w(t )
dt
where X i the abundance by mass of the elemental species i
mu
E (t )   (m  mr ) (t   m ) (m)dm
mt
mu
Ei (t )   [( m  mr  mpim ) X i (t   m )  mpim ] (t   m ) (m)dm
mt
Instantaneous recycling
Suppose τ m << t or m1 > 1 M Θ 
E( t ) 
mu
 ( t )( m - m
r
)( m )dm  ( t )R
m1
R the return fraction (depends only stellar properties and  )
Ei ( t )  RX i ( t )( t )  Yi ( 1 - R )( 1 - X i )( t )
where
mu
 mp
 ( m )dm
im
Yi 
m1
1- R
The Yield per stellar generation
The equation for gas becomes…
dS g
dt
 (1  R) (t )  f (t )  w(t )
… and that for abundances…
dX i
Sg
 Yi (1  R)(1  X i ) (t )  ( X if  X i ) f (t )
dt
Yi is the Key Quantity to be derived from stellar nucleosynthesis theory
Particular solutions
Close-Box Model
ST
X i  Yi ln
Sg

1
S
X i  Yi S Yi P (ln T ) 2
2
Sg
ST
Z  Yz ln
Sg
for primary elements
for secondary elements
Primary versus secondary elements…………………
In many circumstances, this type of solution is not particularly satisfactory
when compared to observational data
Particular solutions
Open Model
X
P
i
ST
 Yi [ln
 1]
Sg
P
The abundances tend to the Yield
This type of model is often in better agreement with the observational data,
e.g. the G-dwarf Problem in the Solar Vicinity
Most popular model
Open
f(t)  0 w(t)  0
dS T
f (t ) 
 K exp( t /  )
dt
together w ith
 (t) 
dS g
dt
 CS g
k
Schmidt law
Predicts the right temporal dependence for (t) to explain G-Dwarf (Chiosi, 1980)
The Chemical Yields: prescription
The chemical yields are based on the state-of-the-art of stellar evolution
and stellar nucleasynthesis theory.
Important parameters and quantities to remember are MHe, Mco, Mr,
and Mej (this latter for each elemental species)
Prescription 1 (single stars)
Prescription 2 (single stars)
Prescription 3 (single stars)
Prescription 4 (binary stars)
Prescription 5 (binary stars)
Prescription 6 (binary stars)
Prescription 7 (final remarks)
Structure Diagrams
Element by element…..
Element by element
Is this theory successful ?
Yes
Results: O/Fe
Results: alpha/Fe
Results: C/Fe
Results: N/Fe
Remarks
•
•
•
•
It explains
G-Dwarf problem
Age-Metallicity
Gross chemical features of galaxies of
different morphological type
• It has been used in many different
contexts and environments