ABSOLUTE MAGNITUDES of RR LYRAE STARS J. Fernley1, T.G

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ABSOLUTE MAGNITUDES OF RR LYRAE STARS

1 2 1 3 3

J. Fernley , T.G. Barnes , I. Skillen , S.L. Hawley , C. Hanley ,

4 1 5

D.W. Evans , E. Solano , R. Garrido

IUE Observatory,P.O. Box 50727, 28080 Madrid, Spain

McDonald Observatory, Univ. of Texas, Austin, Texas 78712, USA

Dept. Physics and Astronomy, Michigan State Univ., E. Lansing, Michigan 48824, USA

Royal Greenwich Obs., Madingley Rd, Cambridge CB3 OHA, England

Inst. Astro sica de Andalucia, Ap do 3004, 18080 Granada, Spain

1. Of the 180 stars listed as RR Lyraes in the Hip- ABSTRACT

parcos Input Catalogue we removed 36 stars, either

b ecause they were not RR Lyraes or b ecause the data

Using rstly, the Hipparcos prop er motions and the

were missing or of p o or quality.

metho d of Statistical Parallax and secondly, the Hip-

parcos parallax of RR Lyrae itself and thirdly, the

2. In order that the V magnitudes were homogeneous

Baade-Wesselink results from the literature we nd

we used the Hipparcos photometry. For each star

the zero-p oint of the RR Lyrae absolute magnitude -

the raw V magnitudes were converted to uxes

Hip

metallicity relation to b e M = 0.720.10 at [Fe/H]

and then phased using the p erio d from the GCVS

= 1:52. The small error on this zero-p oint re ects

Kholop ov et al. 1985. The p erio d was then opti-

the remarkably good agreement between the three

mised and the resulting light curve tted to a Fourier

indep endent metho ds. Taking a value of 0.180.03

Series. This analysis was done using the program

for the slop e of the relation from the literature we ob-

PULSAR Skillen 1985. The mean ux was then

tain a distance mo dulus of the LMC of 18.31. This is

converted back into a magnitude and transformed

compared to other recent determinations of the dis-

onto the Johnson system using the equations given

tance to the LMC.

by the Hipparcos pro ject. Comparing these intensity

mean magnitudes with those listed by Liu and Janes

1990a shows, for 13 stars in common, a mean di er-

ence of 0.003 mag and an rms scatter of 0.007 mag.

1. INTRODUCTION

3. Reddenings were taken from Burstein and Heiles

1982. The de-reddened stars were then used to de-

termine p erio d-colour relations which were in turn

RR Lyraes are one of the primary distance indicators,

used to estimate the reddening for the stars at low

b oth within the Galaxy and within the Lo cal Group,

galactic latitudes.

and in this article we use the recently released Hip-

parcos data to estimate their absolute magnitudes.

4. The parallaxes are from Hipparcos. Only one

In Section 3 we consider the trigonometric parallaxes

star, RR Lyrae itself, has a well-determined paral-

and in Section 4 the prop er motions and the metho d

lax, 4.380.59 mas. For the remaining stars the par-

of statistical parallax. In Section 5 we then take these

allaxes are smaller mean value = 0.8 mas and the

results and combine them with previous work to de-

standard errors larger mean value = 2.6 mas.

riveanM ,[Fe/H] calibration for RR Lyraes. Finally

in Section 6 we discuss the distance to the LMC us-

5. The prop er motions are also from Hipparcos.

ing this calibration and compare it with other recent

In Figure 1 we compare these prop er motions with

determinations of the LMC distance mo dulus. We

ground-based measurements as given in Layden et al.

b egin in Section 2 with a brief discussion of the data.

1996. It can b e seen that overall the agreementis

go o d, the main di erence is that the Hipparcos stan-

dard errors are lower than the ground-based ones,

2. THE DATA

= 2.2 mas/yr compared to 5.6 mas/yr.

6. The radial velo cities are from the literature. The

For the purp oses of the present pap er the following

radial velo cities typically have a standard error of

data were required: intensity mean V magnitudes,

3 km/s which, at the mean distance of the RR Lyraes

reddenings, parallaxes, prop er motions, radial velo c-

of 1250 p cs = 0.8 mas in parallax, translates into

ities and metallicities. These data were taken b oth

an error of 0.55 mas/yr.

from Hipparcos and previously published work and a

full listing will app ear in Fernley et al. 1997a. Here

7. The metallicities are also taken from the literature. we make only a few comments:

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3. TRIGONOMETRIC PARALLAXES 5. THE ABSOLUTE MAGNITUDE

CALIBRATION

As discussed in the previous section only one star,

If we write:

RR Lyrae itself, has a well-determined parallax,

M = [Fe=H] + 1

4.380.59 mas. With V = 7.76 and EB-V = 0.06

this gives M = 0.780.29. For the remaining stars

then we are concerned with determining the zero-

the parallaxes are to o uncertain to give any useful

p oint, , and slop e, , using the Hipparcos results

information, either individually or collectively.

given in this pap er and previously published work.

No Lutz-Kelker correction Lutz & Kelker 1973, Han-

Zero-Point : the Baade-Wesselink work on RR

son 1979 was applied to the derived absolute magni-

Lyraes Fernley 1994 and references therein gives

tude of RR Lyrae since the selection criterion was not

values for b oth the slop e and zero-p oint. The slop e

the parallax there are 13 other RR Lyraes for which

is still the sub ject of debate and so to derive a zero-

Hipparcos gives a parallax greater than it but the

p oint in the least controversial way we have rstly,

standard error on the parallax RR Lyrae has =

up dated the metallicityvalues in Fernley 1994 and

0.59 mas whereas the remaining stars all have

then we have simply taken the mean values of the

0.90 mas. It should b e noted that the correction is in

metallicity and magnitude for the 15 stars listed by

any case small, from Hanson 1979 we estimate the

Fernley that have 1:0 [Fe=H] 2:0 for reasons

correction is 0.07 mag in the sense that the derived

discussed in that pap er we have excluded SS Leo.

magnitude would b e brighter.

This gives M = 0.66 0.08 at [Fe/H] = 1:50.

The Baade-Wesselink work is sub ject to systematic

errors from several sources and these are estimated

as 0:12 mag Fernley et al. 1989, to give a nal

error on the Baade-Wesselink zero-p ointof0:14.

4. STATISTICAL PARALLAX

Combining the results from the Baade-Wesselink

work with those from the Trigonometric Parallax of

RR Lyrae M =0:780.29 at [Fe/H] = 1:39 and

the Statistical Parallax solution for the pure halo

Using the program describ ed in Hawley et al. 1986

sample M = 0:77 0:17 at a mean metallicity

and the data describ ed in Section 2 we obtained the

of [Fe/H] = 1:66 and inversely weighting by the

solutions shown in Table 1. It is imp ortant in the

square of the error we obtain M = 0:72 0:10 at

Statistical Parallax metho d to isolate a dynamically

[Fe/H] = 1:52. The small error on M re ects the

homogeneous sample of stars. In the present context

remarkably go o d agreementbetween the three inde-

this means separating the Halo and Old Disk com-

p endent metho ds used to determine the zero-p oint.

p onents and we have done this by making a cut in

metallicity. Based on previous work e.g. Layden et

Slop e : this is a sub ject of some controversy and

al. 1996, Figure 4 it is clear that b elow[Fe/H] = 1:3

has most recently b een discussed by Fernley et al.

the stars are almost entirely Halo and ab ove[Fe/H]

1997b. Based on b oth the Baade-Wesselink results

= 0:8 they are almost entirely Old Disk. Unfortu-

referred to previously and the observations by Fusi

nately there are insucient stars with [Fe/H]0:8

Pecci et al. 1996 of globular clusters in M31, they

to obtain a useful solution and so we have run in-

estimate a slop e of 0.180.03. Adopting this value

stead a metal-rich solution which contains all stars

we obtain:

with [Fe/H] 1:3. This sample is therefore not dy-

namically homogeneous in that it contains b oth Halo

M =0:18 0:03[Fe=H]+1:52 + 0:72 0:04 2

and Old Disk stars as of course do es the solution for

all stars.

6. DISTANCE TO THE LMC

Table 1. Absolute magnitudes from statistical paral laxes.

There are observations of RR Lyraes in 5 LMC Clus-

ters Walker 1992, Reid & Freedman 1994 and com-

Sample No Stars [Fe/H] M

bining the data from the clusters gives a mean dered-

dened magnitude m of 18.98 and a mean [Fe/H] of

All RR Lyraes 144 -1.32 0.76 0.13

Halo RR Lyraes 84 -1.66 0.77 0.17

1:8. From Equation 2 we obtain a distance mo du-

Metal-Rich RR Lyraes 60 -0.85 0.69 0.21

lus m M of 18.31 and in Table 2 we compare this

with other recent determinations.

It can b e seen that the distance mo dulus derived from

the RR Lyraes, which as noted earlier is based on

three indep endent metho ds of calibration, is 0.37

These results are very similar to those from previ-

less than the distance mo dulus derived from the

ous studies Hawley et al. 1986, Strugnell et al. 1986,

Cepheids, which in turn is based on two indep endent

Layden et al. 1996 which used ground-based prop er

metho ds of deriving the zero-p oint of the P-L rela-

motions. However, as noted in the previous section,

tion Gieren et al. use Baade-Wesselink metho ds and

the Hipparcos and ground-based prop er motions for

Feast & Catchp ole use the recently published Hip-

RR Lyraes are in go o d agreement, the main improve-

parcos trigonometric parallaxes. The uncertaintyin

ment with Hipparcos is the lower error.

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ACKNOWLEDGEMENTS

Table 2. LMC DistanceModuli.

Metho d m M

Our thanks to Drs Neill Reid and Norb ert Schartel

for helpful discussions.

RR Lyraes this pap er 18.31

SN1987A Ring - Gould1995 18.37

SN1987A Ring - Panagia et al. 1997 18.58

Cepheids - Gieren et al. 1993 18.65

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Figure 1. A comparison between the Hipparcos and ground-based proper motions 98 stars. The upper panel is for

declination, the lower panel for right ascensions. In both cases the solid line has slope unity.