The RR Lyrae Period-Luminosity Relation. I. Theoretical Calibration

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APreprinttypesetusingLTEXstyleemulateapjv.4/12/04

THERRLYRAEPERIOD-LUMINOSITYRELATION.

I.THEORETICALCALIBRATION

M.Catelan

Ponti ciaUniversidadCat´olicadeChile,DepartamentodeAstronom´ ayAstrof´ sica,

Av.Vicu naMackenna4860,782-0436Macul,Santiago,Chile

BartonJ.Pritzl

MacalesterCollege,1600GrandAvenue,SaintPaul,MN55105

arXiv:astro-ph/0406067v1 2 Jun 2004

and

HoraceA.Smith

Dept.ofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,MI48824

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ABSTRACT

WepresentatheoreticalcalibrationoftheRRLyraeperiod-luminosity(PL)relationintheUBVRIJHKJohnsons-Cousins-Glasssystem.Ourtheoreticalworkisbasedoncalculationsofsyn-thetichorizontalbranches(HBs)forseveraldi erentmetallicities,fullytakingintoaccountevolu-tionarye ectsbesidesthee ectofchemicalcomposition.Extensivetabulationsofourresultsareprovided,includingconvenientanalyticalformulaeforthecalculationofthecoe cientsoftheperiod-luminosityrelationinthedi erentpassbandsasafunctionofHBtype.Wealsoprovide“average”PLrelationsinIJHK,forapplicationsincaseswheretheHBtypeisnotknownapriori;aswellasanewcalibrationoftheMV [M/H]relation.Thesecanbesummarizedasfollows:

MI=0.471 1.132logP+0.205logZ,MJ= 0.141 1.773logP+0.190logZ,MH= 0.551 2.313logP+0.178logZ,MK= 0.597 2.353logP+0.175logZ,

and

…… 此处隐藏0字 ……

MV=2.288+0.882logZ+0.108(logZ)2.

Subjectheadings:stars:horizontal-branch–stars:variables:other

1.INTRODUCTION

RRLyrae(RRL)starsarethecornerstoneofthePop-ulationIIdistancescale.Yet,unlikeCepheids,whichhaveforalmostacenturybeenknowntopresentatightperiod-luminosity(PL)relation(Leavitt1912),RRLhavenotbeenknownforpresentingaparticularlynote-worthyPLrelation.Instead,mostresearchershaveuti-lizedanaveragerelationbetweenabsolutevisualmag-nitudeandmetallicity[Fe/H]whenderivingRRL-baseddistances.Thisrelationpossessesseveralpotentialpit-falls,includingastrongdependenceonevolutionaryef-fects(e.g.,Demarqueetal.2000),apossiblenon-linearityasafunctionof[Fe/H](e.g.,Castellani,Chie ,&Pulone1991),and“pathologicaloutliers”(e.g.,Pritzletal.2002).

Tobesure,RRLhavealsobeennotedtofollowaPLrelation,butonlyintheKband(Longmore,Fernley,&Jameson1986).ThisisinsharpcontrastwiththecaseoftheCepheids,whichfollowtightPLrelationsboth

Electronicaddress:mcatelan@astro.puc.clElectronicaddress:pritzl@macalester.eduElectronicaddress:smith@pa.msu.edu

inthevisualandinthenear-infrared(see,e.g.,Tanvir1999).ThereasonwhyCepheidspresentatightPLre-lationirrespectiveofbandpassisthatthesestarscoveralargerangeinluminositiesbutonlyamodestrangeintemperatures.Conversely,RRLstarsarerestrictedtothehorizontalbranch(HB)phaseoflow-massstars,andthusnecessarilycoveramuchmoremodestrangeinluminosities—somuchsothat,intheircase,therangeintemperatureoftheinstabilitystripisasimportantas,ifnotmoreimportantthan,therangeinluminositiesofRRLstars,indeterminingtheirrangeinperiods.There-fore,RRLstarsmayindeedpresentPLrelations,butonlyifthebolometriccorrectionsaresuchastoleadtoalargerangeinabsolutemagnitudeswhengoingfromthebluetotheredsidesoftheinstabilitystrip—asisindeedthecaseinK.

Thepurposeofthepresentpaper,then,istoperformthe rstsystematicanalysisofwhetherausefulRRLPLrelationmayalsobepresentinotherbandpassesbesidesK.Inparticular,weexpectthat,usingband-passesinwhichtheHBisnotquite“horizontal”attheRRLlevel,aPLrelationshouldindeedbepresent.Since