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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, - PowerPoint PPT Presentation
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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