The Cepheid Period-Luminosity Relation The Cepheid Period-Luminosity Relation and Astronomy Education in Rural and Astronomy Education in Rural

Upstate New YorkUpstate New York

Shashi M. KanburShashi M. Kanbur

SUNY Oswego, February 28 SUNY Oswego, February 28 2007.2007.

CollaboratorsCollaborators

Chow Choong Ngeow (University of Illinois)Chow Choong Ngeow (University of Illinois) Douglas Leonard (San Diego State Douglas Leonard (San Diego State

University), Lucas Macri (NOAO),Nial University), Lucas Macri (NOAO),Nial Tanvir (University of Hertfordshire, UK) Tanvir (University of Hertfordshire, UK) Alan Ominisky (SCC High School)Alan Ominisky (SCC High School)

Daniel Crain, Greg Feiden, Richard Daniel Crain, Greg Feiden, Richard Stevens, Christina Phelps, Sean Scott, Jim Stevens, Christina Phelps, Sean Scott, Jim Young, Dylan Wallace.Young, Dylan Wallace.

FundingFunding

American Astronomical Society Small American Astronomical Society Small Research Grant.Research Grant.

HST Legacy Project.HST Legacy Project.

American Astronomical Society American Astronomical Society ChretienChretien International Research International Research Award.Award.

SUNY Oswego.SUNY Oswego.

Basic CosmologyBasic Cosmology

Cosmological Principle (homogeneity Cosmological Principle (homogeneity and isotropy) plus general relativity and isotropy) plus general relativity implyimply

FriedmannFriedmann equations which describe equations which describe the history and evolution of the the history and evolution of the Universe.Universe.

These equations contain a number of These equations contain a number of parameters, notably Hubbleparameters, notably Hubble’’s s constant, H0.constant, H0.

Basic Cosmology IIBasic Cosmology II

H0 governs the size scale of the Universe H0 governs the size scale of the Universe and is convolved with many other and is convolved with many other parameters of the parameters of the FreidmannFreidmann equations.equations.

HubblesHubbles law: v = H0 x dlaw: v = H0 x d Measure v from Measure v from redshiftsredshifts, measure d, measure d And the gradient gives H0.And the gradient gives H0. Measurements of H0 help to narrow down Measurements of H0 help to narrow down

the particular cosmology ( a particular the particular cosmology ( a particular solution of the solution of the FriedmannFriedmann equations) that equations) that we live in. This then determines the we live in. This then determines the UniverseUniverse’’s fate: big crunch, coast, s fate: big crunch, coast, expansion etc.expansion etc.

2/27/2006 7

CepheidsCepheids and the PL relationand the PL relation

Intrinsically variable stars with regularly Intrinsically variable stars with regularly repeating light curves.repeating light curves.

Periods of the order of 2 days to 100 days.Periods of the order of 2 days to 100 days. Absolute magnitude =Absolute magnitude =MvMv = = a+blogPa+blogP Measure P, get Measure P, get MvMv, observe , observe mvmv.. mvmv--MvMv: distance modulus is related to the : distance modulus is related to the

distance in parsecs.distance in parsecs. CepheidsCepheids help to tie together local distance scale help to tie together local distance scale

measures (parallax and main sequence fitting measures (parallax and main sequence fitting with more distant measures such as SBF and with more distant measures such as SBF and Tully Fisher Tully Fisher pluplu scalibratescalibrate the the SNIaSNIa Hubble Hubble diagrams.diagrams.

HST and HST and CepheidsCepheids

19931993--2003: HST Key Project: 2003: HST Key Project: Discover Discover CepheidsCepheids in local galaxies in local galaxies and measure distances to them toand measure distances to them to

Create the Create the ““extraextra--galactic distance galactic distance ladder.ladder.””

This has measured H0 to 10% This has measured H0 to 10% accuracy.accuracy.

Assumption: The Cepheid PL relation Assumption: The Cepheid PL relation in the LMC is universal.in the LMC is universal.

HST HST CepheidsCepheids

CMB studies measure many cosmological CMB studies measure many cosmological parameters, but there is some parameters, but there is some degeneracy.degeneracy.

An independent estimate of H0 accurate to An independent estimate of H0 accurate to a few percent can remove these a few percent can remove these degeneraciesdegeneracies and, for example, increase and, for example, increase the accuracy on estimate of Omega the accuracy on estimate of Omega (average density of matter) by a factor of (average density of matter) by a factor of two.two.

Hence its important to further refine the Hence its important to further refine the Cepheid distance scale.Cepheid distance scale.

The Cepheid PL relationThe Cepheid PL relation

For the last 70 years, this relation For the last 70 years, this relation has been assumed to be linear.has been assumed to be linear.

Mv = a + b.log(P).Mv = a + b.log(P).

The slope of this relation is b.The slope of this relation is b.

I s it linear? Or are the data Is it linear? Or are the data consistent with two lines:consistent with two lines:

Mv = a1 + b1.log(P), P<10 daysMv = a1 + b1.log(P), P<10 days

Mv=a2 + b2.log(P), P>10 daysMv=a2 + b2.log(P), P>10 days

WHY?WHY?

Precision comsology: affects H0 to the Precision comsology: affects H0 to the level of 1-2%. level of 1-2%.

Zero Point errors are being reduced – NGC Zero Point errors are being reduced – NGC 4258.4258.

Theory of Stellar Pulsation/Evolution.Theory of Stellar Pulsation/Evolution. Constrain Mass-Luminosity relations and Constrain Mass-Luminosity relations and

Cepheid Cepheid atmospheric/pulsation/evolutionary atmospheric/pulsation/evolutionary effects.effects.

Nature of convection in stellar interiors.Nature of convection in stellar interiors.

Statistical/Physical TestsStatistical/Physical Tests

F tests, Least Absolute Deviation.F tests, Least Absolute Deviation. Testimators (estimation plus Testimators (estimation plus

smooting), Schwarz Information smooting), Schwarz Information Criteria – likelihood based methods.Criteria – likelihood based methods.

Robust Estimation, non-parametric Robust Estimation, non-parametric LOESS, least absolute deviation.LOESS, least absolute deviation.

Adding data: OGLE plus SEBO, Adding data: OGLE plus SEBO, MACHO plus SEBO, CALDWELL and MACHO plus SEBO, CALDWELL and LANEY etc.LANEY etc.

Statistical/Physical TestsStatistical/Physical Tests So far, LMC data is consistent with two So far, LMC data is consistent with two

lines of significantly differing slope with lines of significantly differing slope with the “break” at a period of 10 days.the “break” at a period of 10 days.

Break is present for U,B,V,R,I,J, marginal at Break is present for U,B,V,R,I,J, marginal at K.K.

SMC/Galactic PL relations do not show the SMC/Galactic PL relations do not show the break.break.

2 weeks of time on NOAO/SMARTS 2 weeks of time on NOAO/SMARTS facilities in Chile yielded over 100Gb of facilities in Chile yielded over 100Gb of data for SUNY Oswego undergraduates to data for SUNY Oswego undergraduates to analyze.analyze.

Period-Color and Amplitude-Color Period-Color and Amplitude-Color Relations in Cepheids.Relations in Cepheids.

Stefan Boltzmann law:Stefan Boltzmann law: logL(max) – logL(min) =4logT(max) – 4logT(min).logL(max) – logL(min) =4logT(max) – 4logT(min). Period-Color relation flat at maximum/minimum Period-Color relation flat at maximum/minimum

then Amplitude-Color relation flat at then Amplitude-Color relation flat at minimum/maximum.minimum/maximum.

Properties at mean light are really an average of Properties at mean light are really an average of properties at all phases.properties at all phases.

PC/AC relations change abruptly at a period of 10 PC/AC relations change abruptly at a period of 10 days in the LMC.days in the LMC.

PL relation changes strongly related to PC relation PL relation changes strongly related to PC relation changes due to PLC.changes due to PLC.

The Photosphere/HIF InteractionThe Photosphere/HIF Interaction

Hydrogen Ionization front (HIF): region of rapid Hydrogen Ionization front (HIF): region of rapid spatial change in temperature. Photosphere spatial change in temperature. Photosphere (optical depth 2/3) are NOT comoving as the star (optical depth 2/3) are NOT comoving as the star pulsates.pulsates.

When the photosphere is located at the base of When the photosphere is located at the base of the HIF, photospheric temperature and hence the HIF, photospheric temperature and hence color is related to the temperature at which color is related to the temperature at which hydrogen ionizes.hydrogen ionizes.

At low densities, this temperature is almost At low densities, this temperature is almost independent of global stellar parameters, leading independent of global stellar parameters, leading to a rapid change in the PC and hence PL relation.to a rapid change in the PC and hence PL relation.

This interaction may affect observational This interaction may affect observational properties of other variable stars eg. RR Lyraes properties of other variable stars eg. RR Lyraes and other parts of the HR diagram.and other parts of the HR diagram.

Undergraduate InvolvementUndergraduate Involvement Need to study PC/AC relations as a Need to study PC/AC relations as a

function of phase. function of phase. Usually only studied at mean light.Usually only studied at mean light. Download data, Fourier decomposition Download data, Fourier decomposition

with simulated annealing, Principal with simulated annealing, Principal Component Analysis.Component Analysis.

Construct PC/AC relations. Perform Construct PC/AC relations. Perform statistical tests on these and PL relations statistical tests on these and PL relations as a function of phase.as a function of phase.

Unix, numerical methods, statistical Unix, numerical methods, statistical methods, stellar evolution/pulsation, methods, stellar evolution/pulsation, cosmology.cosmology.

Current Undergraduate ProjectsCurrent Undergraduate Projects Analysis of M31 RR Lyrae light curves Analysis of M31 RR Lyrae light curves

taken by HST: Dylan Wallace.taken by HST: Dylan Wallace. Analysis of SDSS RR Lyrae light curves: Analysis of SDSS RR Lyrae light curves:

Christina Phelps.Christina Phelps. Analysis of M31/M33/IC 1613 Cepheid Analysis of M31/M33/IC 1613 Cepheid

data: Dan Crain/Jim Young/Sean Scottdata: Dan Crain/Jim Young/Sean Scott Hydrodynamic modeling of Cepheids/RR Hydrodynamic modeling of Cepheids/RR

Lyraes: Greg Feiden.Lyraes: Greg Feiden. Development of generalized bootstrap Development of generalized bootstrap

methods to estimate confidence intervals methods to estimate confidence intervals for “break” period: Dan Crain, Richard for “break” period: Dan Crain, Richard Stevens.Stevens.

JHK Observations of LMC JHK Observations of LMC CepheidsCepheids

Using NOAO/SMARTS facilities and Using NOAO/SMARTS facilities and CPAPIR intsruments.CPAPIR intsruments.

100Gb of new data taken in Nov 100Gb of new data taken in Nov 2006/Jan 2007.2006/Jan 2007.

Addition to exisiting data.Addition to exisiting data. PL relations, light curve structure, PL relations, light curve structure,

modeling, data reduction methods.modeling, data reduction methods. Statistical methods.Statistical methods.

Southern Caygua School Southern Caygua School Observatory InvolvementObservatory Involvement

SCCS has a 14” GOTO telescope on a SCCS has a 14” GOTO telescope on a reasonably dark site – Alan Ominisky.reasonably dark site – Alan Ominisky.

SUNY Oswego purchased a ST9XE CCD SUNY Oswego purchased a ST9XE CCD camera from SBIG with some filters camera from SBIG with some filters (UBVRI).(UBVRI).

Galactic Cepheid data needs to be Galactic Cepheid data needs to be enhanced.enhanced.

Such Cepheids are pretty bright – about 6-Such Cepheids are pretty bright – about 6-88thth magnitude. Easily observable. magnitude. Easily observable.

Primarily educational, but could result in Primarily educational, but could result in some new publishable data points, some new publishable data points, especially for longer period Cepheids.especially for longer period Cepheids.

ReferencesReferences

Kanbur and Ngeow, MNRAS, 2004Kanbur and Ngeow, MNRAS, 2004 Ngeow and Kanbur 2005, 2006a Ngeow and Kanbur 2005, 2006a

2006b2006b Kanbur and Ngeow 2006aKanbur and Ngeow 2006a Kanbur, Ngeow, Nanthakumar and Kanbur, Ngeow, Nanthakumar and

Stevens, 2006b (submitted)Stevens, 2006b (submitted) Kanbur and Mariani 2004, MNRASKanbur and Mariani 2004, MNRAS Kanbur and Fernando 2005, MNRASKanbur and Fernando 2005, MNRAS