Initial Mass Function and

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Lecture 3 Initial Mass Function and Chemical
Evolution Essentials of Nuclear Structure The
Liquid Drop Model
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The Initial Mass Function and Cosmic Chemical
Evolution
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See Shapiro and Teukolsky for background reading
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just a fit
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But Figer (2005) gets ? -0.9 in a young
supercluster.
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Warning. Salpeter IMF not appropriate below about
0.5 solar masses. Actual IMF is flatter. Used
MS here.
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Since G -1.35
sensitive to choice of ML Use MS Table instead.
For Salpeter IMF
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solar neighborhood
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Upper mass limit theoretical predictions
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Upper mass limit observation
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What is the most massive star (nowadays)?
The Arches Supercluster Massive enough
and young enough to contain stars of 500
solar masses if extrapolate Salpeter
IMF Figer, Nature, 434, 192 (2005) Kim, Figer,
Kudritzki and Najarro ApJ, 653L, 113 (2006)
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Lick 3-m (1995)
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Keck 10-m (1998)
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HST (1999)
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Initial mass function
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Introductory Nuclear Physics Liquid Drop Model
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In fact, the neutron and proton are
themselves collections of smaller fundamental
quarks.
4He
p
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In addition there is a collection of bosons whose
exchange mediates the four fundamental
forces. g, W-, Z0, gluon, graviton
Only quarks experience the color force
and quarks are never found in isolation
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In the standard model . Hadrons are
collections of three quarks (baryons) or a quark
plus an anti-quark (mesons). This way they are
able to satisfy a condition of color neutrality.
Since there are three colors of quarks, the only
way to have neutrality is to have one of each
color, or one plus an antiparticle of the
same (anti-)color. The gluons also carry color
(and anti-color) and there are eight possible
combinations, hence 8 gluons. The color force
only affects quarks and gluons
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The weak interaction allows heavier quarks and
leptons to decay into lighter ones. E.g.,
For background on all this, please
read http//particleadventure.org
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intermediate stages not observable
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There are many, many more. Exchange of these
lightest mesons give rise to a force that is
complicated, but attractive. But at a shorter
range, many other mesons come into play,
notably the rho meson (776 MeV), and the nuclear
force becomes repulsive.
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There are two ways of thinking of the strong
force - as a residual color interaction or as the
exchange of mesons. Classically the latter was
used.
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The nuclear force at large distances is not just
small, it is zero.
Repulsive at short distances.
Nuclear density nearly constant.
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?The nuclear force is only felt among
hadrons. ?At typical nucleon separation (1.3 fm)
it is a very strong attractive force. ?At
much smaller separations between nucleons the
force is very powerfully repulsive, which keeps
the nucleons at a certain average
separation. ?Beyond about 1.3 fm separation, the
force exponentially dies off to zero. It is
greater than the Coulomb force until about 2.5
fm ?The NN force is nearly independent of
whether the nucleons are neutrons or protons.
This property is called charge
independence. ?The NN force depends on whether
the spins of the nucleons are parallel or
antiparallel. ?The NN force has a noncentral or
tensor component.
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Since the nucleons are fermions they obey FD
statistics
n 0.17 fm-3
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Nuclear density is a constant.
Deformation is an indication of nuclear rotation
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Nuclear binding energy is the energy required to
disperse a nucleus. It is the absolute value of
the sum of the Fermi energies (positive),
electrical energy (positive), and strong
attractive potential energy (negative)
x
15 is an empirical number
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correction
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purely quantum mechanical corrections to the
liquid drop model
Adding a nucleon increases the nuclear binding
energy of the nucleus (no direct analogue to
atomic physics). If this is nucleon is added to a
lower energy state, more binding is obtained. A
low state might be one where there is already
an unpaired nucleon.
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Pairing increases the binding energy of
nuclei with even numbers of neutrons and/or
protons
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Experiment
Liquid drop
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http//128.95.95.61/intuser/ld3.html
Given A, what is the most tightly bound Z?
N A-Z N-Z A-2Z
Only the Coulomb and pairing terms contained
Z explicitly
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