Download Lecture 1 - SUNY Oswego

Variable Stars: Pulsation,
Evolution and application to
Cosmology.
Shashi M. Kanbur
SUNY Oswego, July 2007
Contents
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Lecture I: Observation
Aspects/Theory
Lecture II: Stellar Pulsation
Lecture III: Stellar Evolution
Lecture IV: Pulsation Modeling
Lecture V: Applications: The distance
and age scales.
Lecture I: Observational Aspects
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Classical Cepheids: Cepheids and RR
Lyraes.
Very regular brightness fluctuations
ranging from hours to days.
Pulsation is due to internal
mechanism, not due to binary or
occulting effects.
Comparitively rare: 1 in a million.
Magnitudes and Black Bodies
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Luminosity: total energy radiated into space/second: Watts,
Sun’s luminosity is about 4*1026 Watts
Magnitude, M = -2.5*log L + const.
Vega defined to have zero magnitude.
Absolute and apparent magnitude
mv-MV = 5logd – 5; inverse square law,
B = L/4πd2
Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K
etc.
Stars are good examples of black bodies, Stefan Boltzmann
law:
L = 4πr2σT4
Colors: Difference of two magnitudes: eg. B-V, V-I.
Color: independent of distance, bluer or smaller values of
the color index imply hotter stars – Wien’s law.
Cepheids
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Young, population I,high metal content:
X=0.7, Z=0.02
Periods range from 2 days to about 100120 days.
M: 2-10 solar masses, L: ranges from tens
to thousands of solar luminosities – massluminosity relation (ML), Teff: 5000-6400K
Brightness fluctuations of the order of 1
magnitude, surface velocities of the order
40-60km/s.
Located in the disks of spiral galaxies.
RR Lyraes
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Old, population II, low metal content,
X=0.7, Z = 0.001 – 0.0001.
Periods range from 0.2 -0.9 hours.
0.5-0.9 solar masses, tens – hundreds of
solar luminosities, Teff: 6000 – 7000K.
Brightness fluctuations of the order of 1
magnitude and velocity fluctuations of the
order of 40-60km/s.
Located in globular clusters and in the
field.
Cepheids
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Fundamental mode, first and second overtone
oscillators – some double mode stars.
Radial Oscillators.
Many recent microlensing surveys have produced
lots of new data: exciting field.
OGLE, MACHO
SDSS, LSST
Hubble Space Telescope has observed Cepheids
in some 30 galaxies in our local group:HST
Amplitude of oscillations generally decreases as
wavelength of observation increases.
Hertzsprung Progression
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Around P=7d, bumps appear on the
descending branch.
At 10 days, bumps area at maximum
light.
Around P=12d, bumps appear on
ascending branch.
Around P=20d, bumps disappear.
Fourier Decomposition
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Need to quantify the structure of the light
curve.
V = A0 + Σk(Aksin(kωt + φk)),
ω=2π/P, P the period in days,
The summations goes from k=1 to N, the
order of the fit; typically N is about 8.
Ak,φk: Fourier amplitudes and phases
Use least squares to fit this to observed
data points.
Compute Rk1=Ak/A1, φk1=φk-kφ1 and plot
these against period.
Fourier Decomposition and the
Hertzsprung progression
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Major discontinnuity in Rk1, φk1 at a period
of 10 days, the center of the Hertzsprung
progression.
Seen in many wavelength bands.
Seen in Galaxy, LMC and SMC at about the
same period: no significant evidence of a
large change in the location at 10 days as
a function of metallicity.
Galaxy: metal rich (Z=0.02), LMC
intermediate (Z=0.008), SMC metal
poorer or at least has less metals than the
LMC (Z=0.004).
RR Lyraes
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Again fundamental, first and second
overtone pulsations: some double mode or
beat stars.
Radial oscillators but ….?
Amplitude generally decreases as
wavelength increases.
Some stars exhibit the “Blazhko effect”:
second periodicity superimposed on the
first.
Use Fourier decomposition as well to
characterize light curve structure.
RR Lyraes in M3
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Variables in M3
The Cepheid Period-Luminosity
Relation
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Empirical relation initially observed
by Henrietta Leavit.
MACHO PL relation in the LMC
The Cepheid PL relation
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MX = aX + bXlogP
How do aX bX vary from galaxy to galaxy
or with metallicity?
For a given galaxy, does bX vary with
period?
How do aX, bX vary with X, the waveband
of observations.
Interstellar reddening: astronomical
objects appear redder than they actually
are:
Other types of variable stars
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Type II Cepheids; population II
counterpart of classical Cepheids
Miras: Long period variables, periods
of the order of hundreds of days.
Semi-regular variables: variable
luminosity but no real regularity or
repetition.
Non-Radial Oscillators: eg Sun.
Lecture II: Stellar Pulsation.