Transcript Variable Stars: Pulsation, Evolution and

Variable Stars: Pulsation,
Evolution and applications
to Cosmology
Shashi M. Kanbur
SUNY Oswego, June 2007
Stellar Evolution
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Recall equations of stellar structure.
Nuclear energy generation rate ε(ρ,T) slowly changes the
composition decreasing the amount of Hydrogen and
increasing the amount of Helium on a nuclear time scale –
the characteristic time for stellar properties to change as a
result of nuclear burning: tnuc ~ 1010M/L years.
This timescale is much longer than those involved in stellar
pulsation.
So solve equations of stellar structure, get structure of star
at t=0.
Δt ~ tnuc, so X, Y, Z change due to nuclear burning.
Find X(t+Δt), Y(t+Δt), Z(t+Δt), recalculate stellar stucture
with these new values.
Now there is a new ε = ε(ρ,T); recompute changes to X, Y,
Z over the next time interval Δt.
Continue and develop a stellar evolutionary track.
Hertzsprung –Russell Diagram
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Plot of T on X axis against L on Y axis.
Or, plot of color on X axis against
magnitude on Y axis.
At each t, star has a certain surface
temperature and luminosity. Plot of
(T,L) or ((B-V),V) as a function of time is a
stellar evolutionary track on a HR
diagram.
HR diagram is the most important diagram
in Astronomy.
Aspects of the HR diagram
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Main Sequence (ms): all stars are nuclear
burning hydrogen to helium in their core.
Mass increases as you go up the ms, but stars do
not travel “too much” on the ms.
Upper ms: high mass, hot stars (why?),
convective core, radiative envelope, H burning by
CNO cycle: M > 4-8Msun
Lower ms: low mass, cooler stars (why?),
radiative core, convective envelope, H burning by
proton-proton chain: M < 4 Msun.
Sun is a lower main sequence star.
Partially understand in terms of Stefan Boltzmann
law: L ~ R2T4
Luminosity Classes and Spectral
Types
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Luminsoity Class I: Supergiants, II:
Bright giants, III: Giants, IV:
Subgiants, V: Main Sequence
Spectral Type: classifcation of stellar
spectra, essentially a temperature
sequence, OBAFGKM
Sun is a G2V, Betelgeuse is a M5V
Exercise
Low Mass Stellar Evolution
High Mass Stellar Evolution
Basics of stellar evolution
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Governed by Ideal Gas law:P~ρT
Star’s battle against gravity. The only
weapon it has are the ability of its core to
shrink and start nuclear burning of the
next element in the core or the same
element in a shell around the core.
Low mass stars do no get hot enough in
their core to burn anything heavier than
Helium
High mass stars can go until their core is
made up of Fe/Si. Then nuclear fusion
cannot proceed: Supernova – of type II.
Lifetime on MS
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High mass stars have lots of fuel but
use up their reserves quickly.
Low mass stars use their store of
nuclear fule more sparingly.
tMS ~ M/L ~ M-3, since L~M4
1 Msun star has tMS ~ 10Gy.
10 Msun star has tMS ~ 10 Million yrs
0.1Msun star has tMS ~ 10 Trillion
Years.
Clusters
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Open cluster : loose collection of few (perhaps
20), mostly young stars: in disk of galaxy –
considered to be at the same distance.
Thus a plot of apparent magnitude against color,
say B-V (a Color-Magnitude diagram) is like
plotting temperature against luminosity ( An HR
diagram).
Pleiades and Hyades clusters.
Globular clusters: tight collection of many,
10,000-100,000 stars: cant resolve stars in the
center. All stars in a GC formed at the same time
eg. M3, M15.
Cluster HR diagrams
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Subgiant branch: stars which have only just left
the main sequence, burning H to He in a thick
shell around a He core; short lived phase, only
seen in very old clusters.
Red Giant branch: stars burning H in a shell,
outer envelope expanding, core contracting.
Horizontal branch: low mass stars which are
burning He in the core after the He flash. RR
Lyraes found here.
Asymptotic giant branch: Core He exhausted, He
in a shell around the core, outer envelope
expands, cools.
White dwarfs in M4.
Main Sequence Fitting
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HR diagram for local stars whose
distances are known.
HR diagram for a cluster whose stars
are all assumed to be at the distance
– thus mv is just like MV
Distance modulus (m – M) can be
obtained by determining the offste to
the main sequence from nearby stars
whose distances are known.
Evolutionary Tracks
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Evolutionary tracks depend on input physics:
convective overhsoot etc.
These lead to different M-L relations for tracks
going through the instability strip:
LogL = a+ blogM
Constant a, b depend on stellar evolutionary
input physics.
Get, M,L so, input into a stellar pulsation code
and get theoretical light curves, compare with
observations:
Compare stellar evolution with stellar pulsation
theories.