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)

-enhancement problem

Metallicity DistributionG-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 Functionin the Solar Vicinity

)(2log

)()(log

disk) to(referredhight scale vertical theis )(

andrelation luminosity-mass a is )(

)()(log

thmd

dMMm

th

Mm

Mm

zV

VLFms

z

V

VLFms

The present day mass function is derived from the observed luminosity function

Passing from PDMF to IMF

mu

ml

T

(m)dmA

dtmtm

1

way thatasuch in normalized is (m) where

)()()(

definitionBy

0

(t) assuming without derived becannot (m)

)( tContinuity

1M m T with tstarsFor

2M m T with tstarsFor

1

m

m

T

T

TΨ(T)

φ(m)(m)

Ψ(T)t

φ(m)(m)

m

Popular IMFs

])(exp[)(

)(

asx

x

m

mmm

mm

x and a positive numbers

Salpeter

Larson, Chabrier

Other, more or less equivalent formulations

have been proposed over the years

Need an assumption for (t)Simple exponential

where τ is a suitable time scale

or a more realistic one

starts low, grows to a maximum and then declines

or a complicate function of the gas density (such

Ψ(t) exp(-t/τ )

(t)

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 T, g, s be the surface mass densities (or masses in general) of

total baryonic matter, gas, and stars respectively ………

Basic Equations

u

t

u

t

m

m

mimmiimri

m

m

mr

iifiigi

s

g

T

dmmtmptXmpmmtE

dmmtmmtE

twtXtfXEtXdt

Xd

tRdt

d

twtftEtdt

d

w(t)f(t)twtfdt

d

)()(])()[()(

)()()()(

i species elemental theof massby abundance theX where

)()()()()(

)()1(

)()()()(

outflow and infall where)()(

i

Instantaneous recycling

1

1

m 1 ΘSuppose τ << t or m > 1 M

the return fraction (depends only stellar properties and )

1 1

where

The1

u

u

m

r

m

i i i i

m

im

m

i

E( t ) ( t )( m - m ) ( m )dm ( t )R

R

E ( t ) RX ( t ) ( t ) Y ( - R )( - X ) ( t )

mp ( m )dm

Y- R

Yield per stellar generation

The equation for gas becomes…

)()()()1( twtftRdt

d g

… and that for abundances…

)()()()1)(1( tfXXtXRYdt

dXiifii

ig

Yi is the Key Quantity to be derived from stellar nucleosynthesis theory

Particular solutions

Close-Box Model

elementssecondary for )(ln2

1

elementsprimary for ln ln

2

g

TPi

Sii

g

Tz

g

Tii

YYX

YZYX

Primary versus secondary elements…………………

In many circumstances, this type of solution is not particularly satisfactory

when compared to observational data

Particular solutions

Open Model

]1[ln

g

TPi

Pi YX

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

lawSchmidt dt

d(t)

ithtogether w

)/exp(dt

d)(

0 0Open

g

T

kgC

tKtf

w(t)f(t)

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