RESEARCH ARTICLES CURRENT SCIENCE, VOL. 80, NO. 3, 10 FEBRUARY 2001 361 Cepheid distance estimation for Virgo cluster Anwesh Mazumdar* and D. Narasimha Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India A measurement of distance to the Virgo cluster and a few of its member galaxies by direct method is clearly important for a reliable determination of the Hubble constant as well as for studying the dynamics of a nearby rich galaxy cluster. Cepheid variables in a few galaxies in the Virgo cluster were observed with the Hubble Space Telescope (HST) over the last few years. This work is a reanalysis of the HST data following our study of the Galactic and Magellanic Cloud Cepheids. The log (period) vs V-magnitude relation is re-calibrated using the Galactic, LMC as well as the HST observations. The number density of Cepheid variables as a function of their period is used to determine the role of flux-limited incompleteness and a prescription is given to correct for this bias in the sample. The extinction correction is carried out using period vs mean 〈 V – I〉 0 colour and V-amplitude vs (V – I) colour at the brightest phase relations. The dis- tance and error estimation is based on L 1 minimiza- tion. The mean distance to Virgo cluster is estimated to be 20.5 ± 1.8 (random) ± 2.5 (systematic) Mpc. A natural scale length for the Universe is provided by the Hubble constant (H 0 ) and undoubtedly a reliable determi- nation of its value is one of the central problems of cosmology. Over the years, there has been a lively debate about the value of H 0 and the present estimates range from less than 50 km s –1 Mpc –1 to over 80 km s –1 Mpc –1 . The major reason for the discrepancy is primarily due to the conventional distance ladder method involving multi- ple steps. Its main drawback is that an analysis of the sys- tematic errors becomes difficult when the calibrating local sample and the observed sample at the next step of the ladder are not identical. Consequently, it is believed that an accurate measurement of the distance to a galaxy clus- ter which is located at around ~ 20–30 Mpc, without involving intermediate steps, will lead to a reliable direct estimate of the value of H 0 , provided the recession velocity of the cluster is independently known. The Virgo cluster, which is the nearest cluster of galaxies, is fairly rich in terms of galaxy population, and an average of the dis- tances to the individual galaxies by different methods should provide a good estimate to its mean distance. One of the key projects of the Hubble Space Telescope (HST) was devoted to a calibration of the extragalactic distance scale, mainly by using the Cepheid variables. The classical Cepheid variables are known to provide an important standard candle to measure distances to galaxies up to ~ 30 Mpc. The Cepheid distance scale based on the period–luminosity relation is considered to be among the most reliable methods of distance calibra- tion because the physics of Cepheid pulsation is reasona- bly well-understood and the relation between the pulsation period and luminosity of the star is a well-established observational quantity. Cepheid variables are radially pulsating giants and supergiants, having pulsation periods in the range of less than a day to upwards of 100 days. Their pulsation is very stable and the amplitude of light variation in the V (Johnson) band may be up to nearly 2 magnitudes, although most of the Cepheids have ampli- tudes between 0.6 and 1.3 magnitude. Cepheids are among the most luminous stars, having a narrow range of surface temperatures. The intrinsic scatter in their period–luminosity relation is believed to be less than 0.3 mag. However, the Cepheid distance scale cannot be directly calibrated from the observation of nearby stars and consequently, several systematic effects could undermine its effectiveness as a standard primary candle to determine extragalactic dis- tances beyond a few Mpc. A major problem concerning the calibration of the Cepheid distance scale is the follow- ing: Is a single period–luminosity relation applicable to the entire instability strip? Are the preferential pulsation modes of Cepheids period-dependent? Theoretically, it is widely accepted that at shorter peri- ods, a good fraction of the Cepheid variables should be first overtone pulsators, while at longer periods almost all of them are likely to be fundamental mode pulsators. The crucial question is: where does the transition period lie? There is no agreement between the theoreticians on this question which is extremely important while determining the slope of the period–luminosity relation. A mixture of fundamental mode and first overtone at shorter periods and pure fundamental mode at longer periods will have shallower slope compared to a sample containing only fundamental modes at all periods. Another aspect which is not taken into serious consideration is their evolutionary status: Most of the Cepheid variables are in their second or third crossing of the instability strip in the Hertzsprung– Russell diagram during the core helium burning phase. However, at periods less than around 15 days, the contri- bution to their number density could arise from stars at *For correspondence. (e-mail: anwesh@astro.tifr.res.in) RESEARCH ARTICLES