The Cepheid Period-Luminosity Relation
and Astronomy Education in Rural
Upstate New York
Shashi M. Kanbur
SUNY Oswego, February 28
2007.
Collaborators
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Chow Choong Ngeow (University of
Illinois)
Douglas Leonard (San Diego State
University), Lucas Macri (NOAO),Nial
Tanvir (University of Hertfordshire, UK)
Alan Ominisky (SCC High School)
Daniel Crain, Greg Feiden, Richard
Stevens, Christina Phelps, Sean Scott, Jim
Young, Dylan Wallace.
Funding
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American Astronomical Society Small
Research Grant.
HST Legacy Project.
American Astronomical Society
Chretien International Research
Award.
SUNY Oswego.
Basic Cosmology
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Cosmological Principle (homogeneity
and isotropy) plus general relativity
imply
Friedmann equations which describe
the history and evolution of the
Universe.
These equations contain a number of
parameters, notably Hubble’s
constant, H0.
Basic Cosmology II
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H0 governs the size scale of the Universe
and is convolved with many other
parameters of the Freidmann equations.
Hubbles law: v = H0 x d
Measure v from redshifts, measure d
And the gradient gives H0.
Measurements of H0 help to narrow down
the particular cosmology ( a particular
solution of the Friedmann equations) that
we live in. This then determines the
Universe’s fate: big crunch, coast,
expansion etc.
2/27/2006
7
Cepheids and the PL relation
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Intrinsically variable stars with regularly
repeating light curves.
Periods of the order of 2 days to 100 days.
Absolute magnitude =Mv = a+blogP
Measure P, get Mv, observe mv.
mv-Mv: distance modulus is related to the
distance in parsecs.
Cepheids help to tie together local distance scale
measures (parallax and main sequence fitting
with more distant measures such as SBF and
Tully Fisher plu scalibrate the SNIa Hubble
diagrams.
HST and Cepheids
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1993-2003: HST Key Project:
Discover Cepheids in local galaxies
and measure distances to them to
Create the “extra-galactic distance
ladder.”
This has measured H0 to 10%
accuracy.
Assumption: The Cepheid PL relation
in the LMC is universal.
HST Cepheids
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CMB studies measure many cosmological
parameters, but there is some
degeneracy.
An independent estimate of H0 accurate to
a few percent can remove these
degeneracies and, for example, increase
the accuracy on estimate of Omega
(average density of matter) by a factor of
two.
Hence its important to further refine the
Cepheid distance scale.
The Cepheid PL relation
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For the last 70 years, this relation
has been assumed to be linear.
Mv = a + b.log(P).
The slope of this relation is b.
Is it linear? Or are the data
consistent with two lines:
Mv = a1 + b1.log(P), P<10 days
Mv=a2 + b2.log(P), P>10 days
WHY?
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Precision comsology: affects H0 to the
level of 1-2%.
Zero Point errors are being reduced – NGC
4258.
Theory of Stellar Pulsation/Evolution.
Constrain Mass-Luminosity relations and
Cepheid
atmospheric/pulsation/evolutionary
effects.
Nature of convection in stellar interiors.
Statistical/Physical Tests
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F tests, Least Absolute Deviation.
Testimators (estimation plus
smooting), Schwarz Information
Criteria – likelihood based methods.
Robust Estimation, non-parametric
LOESS, least absolute deviation.
Adding data: OGLE plus SEBO,
MACHO plus SEBO, CALDWELL and
LANEY etc.
Statistical/Physical Tests
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So far, LMC data is consistent with two
lines of significantly differing slope with
the “break” at a period of 10 days.
Break is present for U,B,V,R,I,J, marginal
at K.
SMC/Galactic PL relations do not show the
break.
2 weeks of time on NOAO/SMARTS
facilities in Chile yielded over 100Gb of
data for SUNY Oswego undergraduates to
analyze.
Period-Color and Amplitude-Color
Relations in Cepheids.
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Stefan Boltzmann law:
logL(max) – logL(min) =4logT(max) –
4logT(min).
Period-Color relation flat at maximum/minimum
then Amplitude-Color relation flat at
minimum/maximum.
Properties at mean light are really an average of
properties at all phases.
PC/AC relations change abruptly at a period of 10
days in the LMC.
PL relation changes strongly related to PC
relation changes due to PLC.
The Photosphere/HIF Interaction
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Hydrogen Ionization front (HIF): region of rapid
spatial change in temperature. Photosphere
(optical depth 2/3) are NOT comoving as the star
pulsates.
When the photosphere is located at the base of
the HIF, photospheric temperature and hence
color is related to the temperature at which
hydrogen ionizes.
At low densities, this temperature is almost
independent of global stellar parameters, leading
to a rapid change in the PC and hence PL
relation.
This interaction may affect observational
properties of other variable stars eg. RR Lyraes
and other parts of the HR diagram.
Undergraduate Involvement
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Need to study PC/AC relations as a
function of phase.
Usually only studied at mean light.
Download data, Fourier decomposition
with simulated annealing, Principal
Component Analysis.
Construct PC/AC relations. Perform
statistical tests on these and PL relations
as a function of phase.
Unix, numerical methods, statistical
methods, stellar evolution/pulsation,
cosmology.
Current Undergraduate Projects
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Analysis of M31 RR Lyrae light curves
taken by HST: Dylan Wallace.
Analysis of SDSS RR Lyrae light curves:
Christina Phelps.
Analysis of M31/M33/IC 1613 Cepheid
data: Dan Crain/Jim Young/Sean Scott
Hydrodynamic modeling of Cepheids/RR
Lyraes: Greg Feiden.
Development of generalized bootstrap
methods to estimate confidence intervals
for “break” period: Dan Crain, Richard
Stevens.
JHK Observations of LMC
Cepheids
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Using NOAO/SMARTS facilities and
CPAPIR intsruments.
100Gb of new data taken in Nov
2006/Jan 2007.
Addition to exisiting data.
PL relations, light curve structure,
modeling, data reduction methods.
Statistical methods.
Southern Caygua School
Observatory Involvement
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SCCS has a 14” GOTO telescope on a
reasonably dark site – Alan Ominisky.
SUNY Oswego purchased a ST9XE CCD
camera from SBIG with some filters
(UBVRI).
Galactic Cepheid data needs to be
enhanced.
Such Cepheids are pretty bright – about
6-8th magnitude. Easily observable.
Primarily educational, but could result in
some new publishable data points,
especially for longer period Cepheids.
References
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Kanbur and Ngeow, MNRAS, 2004
Ngeow and Kanbur 2005, 2006a
2006b
Kanbur and Ngeow 2006a
Kanbur, Ngeow, Nanthakumar and
Stevens, 2006b (submitted)
Kanbur and Mariani 2004, MNRAS
Kanbur and Fernando 2005, MNRAS