A&A 474, 975-981 (2007)

DOI: 10.1051/0004-6361:20078225

## The projection factor, period-radius relation, and surface-brightness colour relation in classical cepheids

**M. A. T. Groenewegen**

Instituut voor Sterrenkunde, Celestijnenlaan 200 D, 3001 Leuven, Belgium

e-mail: groen@ster.kuleuven.be

(Received 5 July 2007 / Accepted 14 August 2007)

** Abstract ***Context.*The projection factor (*p*-factor) is of crucial importance in linking
radial velocity variations to radius variations in radially variable
stars such as RR Lyrae of Cepheids. In turn, this is a crucial ingredient
in the Baade-Wesselink method in obtaining distances to these stars using
a surface-brightness (SB) colour relation.*Aims.*Our aim is to establish a relation between the *p*-factor and pulsation period
based on six cepheids with interferometrically measured angular
diameter variations and known distances. As a by-product, a
period-radius (PR) relation is derived which in turn is used to derive the
*p*-factor and distance for two stars.
In addition, the data allows calibration of the SB colour relation.*Methods.*Literature values of the *V*-band, *K*-band and radial velocity
curves are collected and fitted with Fourier series. For stars with
known distances and measured angular diameters as a function of the
pulsation phase, values for the radius and the *p*-factor can be
obtained. A PR relation is derived based on five stars. For two
cepheids, this PR relation is used to determine the radius and then
solve for the *p*-factor and the distance. From the Fourier series, the
*V* and *K* values at the times of the angular diameter measurements
are derived, and the SB colour relation can be established. Allowance
is made for the recent discovery of circumstellar material around some
cepheids which influences both the derived angular diameters and the
colours.*Results.*The PR relation derived is: log *R* = 0.686 log *P* + 1.134,
slightly shallower than recently discussed PR-relations in the
literature but in agreement with theory. Based on a total of eight
stars with periods in the range 5-35 days there is no evidence that the
*p*-factor depends on period, and the best-fitting constant value is
*p* = 1.27 0.05. The SB relation derived is
log = 0.275 (*V*-*K*)_{0} + 0.524, in excellent agreement with that
derived by Kervella et al. (2004b, A&A, 428, 587).

**Key words:**stars: distances

**--**Cepheids

**--**distance scale

**--**stars: oscillations

**©**

*ESO 2007*