A STUDY OF CEPHEIDS IN M81 WITH THE LARGE BINOCULAR TELESCOPE (EFFICIENTLY CALIBRATED WITHHUBBLE SPACE TELESCOPE)

The Cepheid period-luminosity (PL) relation is important in distance scale studies and stellar pulsation studies. This relation has been thought to be linear for a long time. However, recent work has strongly suggested that the PL relation for Large Magellanic Cloud (LMC) Cepheids is nonlinear: there are two relations, with a break at 10 days. In addition, the LMC periodcolor (PC) relation is also shown to be nonlinear. The main motivation for this dissertation is to investigate the nonlinearity of the LMC PL and PC relations and its implications for distance scale studies and for stellar structure, pulsation, and evolution. Due to the intrinsic dispersion of the PL relation and the relatively small number (∼100) of LMC Cepheids used in previous studies, the nonlinear nature of the LMC PL relation was not discovered until large numbers (∼1000) and high-quality LMC Cepheids became available from the OGLE (Optical Gravitational Lensing Experiment) and MACHO (Massive Compact Halo Objects) surveys. To test the existence of a nonlinear LMC PL relation, we apply a rigorous statistical test, the F-test, to the OGLE and MACHO data. After applying proper extinction corrections to both samples, the F-test results strongly suggested that the LMC PL relation is not linear in the VI bands (from OGLE data) and the VR bands (from MACHO data), with more than 99.5% confidence. A similar result from two totally independent samples suggested that the nonlinear LMC PL relation is real and is not due to artifacts of photometric reductions, extinction, or sample selections. The nonlinear nature of the LMC PL relation is further extended to the JH bands, but not the K band, with Two Micron All Sky Survey data. The fundamental reason that the LMC PL relation is nonlinear is that the LMC PC relation is also nonlinear. F-test results again strongly suggest that the LMC PC relation is nonlinear but that the Galactic PC relation is linear. This is because both the PL and PC relations follow the period-luminosity-color (PLC) relations for Cepheid variables; hence, understanding the nonlinear nature of the PC relation helps in understanding the nonlinear PL relation. Note that the PC relation here is actually the PC relation at mean light, which is the properties averaged over a pulsation cycle. Any “anomaly” of the color at certain phases of the pulsation (e.g., at maximum or minimum light) for some phase or period range would affect the mean-light properties of the PC relation and hence produce the observed break in the PC and PL relations. Consider that the relation , where V V ∝ log T log T T min max max min max and are the temperature at maximum and minimum light, Tmin respectively, which is directly related to the color and V min , is just the amplitude of the Cepheid. If versus period V log T max max has a flat slope for a given period range, then there is a relation between the amplitude and , hence the amplitude-color log Tmin relation, and vice versa. This flatness of the PC relation at maximum and/or minimum light could in principle influence the PC relation at mean light and produce the observed nonlinear PC (mean) relation. One mechanism that can produce a flat PC relation at maximum (and/or minimum) light is the interaction of the hydrogen ionization front (HIF) with the photosphere (defined at an optical depth of ), which halts the temperature of the photosphere 3 at some characteristic values that are independent of the global properties. Using stellar pulsation codes that include a recipe for turbulent convection, we constructed the Galactic and LMC Cepheid models to investigate this interaction. Comparing the “distance” as a function of period between the HIF and photosphere (in mass distribution) for these models, we found evidence that (1) the HIF-photosphere interaction for long-period LMC models occurs at maximum light, which is similar to the Galactic models, and (2) the same interaction for short-period LMC models occurs at minimum light, which is the opposite of Galactic models and behaves more like RR Lyrae stars. We believe that these different behaviors of the HIF-photosphere interaction between the longand short-period LMC models lead to the observed nonlinear PC (mean) and PL (mean) relations. In addition, we also constructed empirical multiphase PC relations from the LMC and Galactic Cepheids. The results show that the empirical LMC PC relations are nonlinear for most of the pulsation phases (especially near phase ∼0.8, where phase zero corresponds to maximum light), in contrast to the empirical Galactic multiphase PC relations. Cepheid distances were usually derived through a Wesenheit function (WF), a linear combination of the PL and PC relations. Although the LMC PL and PC relations are nonlinear, the WF for the LMC Cepheids is found to be linear, as the nonlinearities for both PL and PC relations cancel out when the WF is constructed. Comparisons of Cepheid distances obtained with the (correct) nonlinear PL and PC relations using the WF will only introduce a !0.07 mag (systematic) error in the distance modulus, or ∼4% in distance. However, a full understanding of the nonlinear nature of the Cepheid PL and PC relations is important in terms of stellar pulsation and evolutionary studies.

Context. Anomalous Cepheids (ACs) are pulsating variable stars, and are less studied compared to the well-known Classical Cepheids (CCs) and RR Lyrae stars. The ACs are metal poor ([Fe/H] < 1.5) and follow distinct period-luminosity (PL) and period-Wesenheit (PW) relations that can be used for distance measurements, and they can pulsate in the fundamental (F) and first overtone (1O) modes. Aims. Our goal is to evaluate the precision and accuracy of distances obtained via PL and PW relations of ACs and thus to assess if they could be used to establish a cosmic distance scale independent from CCs. To this aim, we derived new, precise PL and PW relations for the F mode, the 1O mode, and, for the first time, the combined F+1O mode ACs in the Magellanic Clouds. We investigated the wavelength dependence of these relations and applied them to calculate the distances of various stellar systems in the Local Group hosting ACs, as well as to confirm the classification of these variable stars. Methods. We analyzed near-infrared (NIR) time series photometry in the Y, J, and Ks bands for about 200 ACs in the Magellanic Clouds acquired during 2009–2018 in the context of the VISTA survey of the Magellanic Clouds system (VMC), a European Southern Observatory public survey. The VMC NIR photometry was complemented with optical data from Gaia DR3 and the Optical Gravitational Lensing Experiment IV survey, which also provided the identification, periods, and pulsation mode for the investigated ACs. Custom templates generated from our best light curves were used to derive precise intensity-averaged mean magnitudes for 118 and 75 ACs in the Large (LMC) and Small Magellanic Clouds (SMC), respectively. Results. Optical and NIR mean magnitudes were used to derive multiband PL and PW relations, which were calibrated with the geometric distance modulus to the LMC based on eclipsing binaries. We investigated the dependence of PL relations on wavelength, finding that slopes increase and dispersion decreases when going from optical to NIR bands. We calculated the LMC distance modulus through calibrated AC PW relations in the Milky Way using Gaia parallaxes, the LMC-SMC relative distance modulus, and we confirmed the AC nature of a few new pulsators in Galactic globular clusters. We derived a distance modulus for the Draco dwarf spheroidal galaxy of 19.425 ± 0.048 mag, which is in agreement with recent literature determinations, but a discrepancy of 0.1 mag with RR Lyrae-based distance hints at possible metallicity effects on the AC PL and PW relations. Future spectroscopic surveys and Gaia DR4 will refine the AC distance scale and assess metallicity effects on PLRs and PWRs.

Context. In the era of the Hubble tension, it is crucial to obtain a precise calibration of the period-luminosity (PL) relations of classical pulsators. Type II Cepheids (T2Cs; often exhibiting negligible or weak metallicity dependence on PL relations) used in combination with RR Lyraes and the tip of the red giant branch may prove useful as an alternative to classical Cepheids for the determination of extragalactic distances. Aims. We present new theoretical PL and period-Wesenheit (PW) relations for a fine grid of convective BL Her (the shortest period T2Cs) models computed using MESA-RSP in the Gaia passbands and we compare our results with the empirical relations from Gaia DR3. Our goal is to study the effect of metallicity and convection parameters on the theoretical PL and PW relations. Methods. We used the state-of-the-art 1D non-linear radial stellar pulsation tool MESA-RSP to compute models of BL Her stars over a wide range of input parameters: metallicity (−2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5 M⊙ − 0.8 M⊙), stellar luminosity (50 L⊙ − 300 L⊙), and effective temperature (across the full extent of the instability strip; in steps of 50 K). We used the Fourier decomposition technique to analyse the light curves obtained from MESA-RSP and Gaia DR3 and then compared the theoretical and empirical PL and PW relations in the Gaia passbands. Results. The BL Her stars in the All Sky region exhibit statistically different PL slopes compared to the theoretical PL slopes computed using the four sets of convection parameters. We find the empirical PL and PW slopes from BL Her stars in the Magellanic Clouds to be statistically consistent with theoretical relations computed using the different convection parameter sets in the Gaia passbands. There is a negligible effect coming from the metallicity on the PL relations in the individual Gaia passbands. However, there is a small but significant negative coefficient of metallicity in the PWZ relations for the BL Her models using the four sets of convection parameters. This could be attributed to the increased sensitivity of bolometric corrections to metallicities at wavelengths shorter than the V band. Our BL Her models also suggest a dependence of the mass-luminosity relation on metallicity. We found the observed Fourier parameter space to be covered well by our models. Higher mass models (> 0.6 M⊙) may be needed to reliably model the observed light curves of BL Her stars in the All-Sky region. We also found the theoretical light curve structures (especially the Fourier amplitude parameters) to be affected by the choice of convection parameters.

We present the first gri-band period–luminosity (PL) and period–Wesenheit (PW) relations for the fundamental mode anomalous Cepheids. These PL and PW relations were derived from a combined sample of five anomalous Cepheids in globular cluster M92 and the Large Magellanic Cloud, both of which have distance accurate to ∼1% available from literature. Our g-band PL relation is similar to the B-band PL relation as reported in previous study. We applied our PL and PW relations to anomalous Cepheids discovered in dwarf galaxy Crater II, and found a larger but consistent distance modulus than the recent measurements based on RR Lyrae. Our calibrations of gri-band PL and PW relations, even though less precise due to small number of anomalous Cepheids, will be useful for distance measurements to dwarf galaxies.

We present the first gri-band period-luminosity (PL) and period-Wesenheit (PW) relations for the fundamental mode anomalous Cepheids. These PL and PW relations were derived from a combined sample of five anomalous Cepheids in globular cluster M92 and the Large Magellanic Cloud, both of which have distance accurate to ~1% available from literature. Our g-band PL relation is similar to the B-band PL relation as reported in previous study. We applied our PL and PW relations to anomalous Cepheids discovered in dwarf galaxy Crater II, and found a larger but consistent distance modulus than the recent measurements based on RR Lyrae. Our calibrations of gri-band PL and PW relations, even though less precise due to small number of anomalous Cepheids, will be useful for distance measurements to dwarf galaxies.

view Abstract Citations (122) References (59) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Extragalactic Distance Scale Key Project. III. The Discovery of Cepheids and a New Distance to M101 Using the Hubble Space Telescope Kelson, Daniel D. ; Illingworth, Garth D. ; Freedman, Wendy F. ; Graham, John A. ; Hill, Robert ; Madore, Barry F. ; Saha, Abhijit ; Stetson, Peter B. ; Kennicutt, Robert C., Jr. ; Mould, Jeremy R. ; Hughes, Shaun M. ; Ferrarese, Laura ; Phelps, Randy ; Turner, Anne ; Cook, Kem H. ; Ford, Holland ; Hoessel, John G. ; Huchra, John Abstract We report on the discovery of 29 Cepheid variables in the galaxy M101 using the original Wide Field Camera (WFC) and the new Wide Field and Planetary Camera 2 (WFPC2) on the Hubble Space Telescope. We observed a field in M101 at 17 independent epochs in V (F555W), five epochs in I (F785LP/ F814W), and one epoch in B (F439W), with a time interval baseline of 381 days. We have found Cepheids with periods ranging from 10 to 60 days. The data have been calibrated using WFPC2 observations with zero points derived from ω Cen, Pal 4, and NGC 2419 observations. This calibration has been verified by using the Medium Deep Survey (MDS) WFC photometric zero points, and ground-based secondary standards in V and I. The V calibrations agree to +/- 0.06 mag, and the I calibrations agree to +/- 0.04 mag. We have constructed V and I period-luminosity (PL) relations and have derived apparent distance moduli based on a distance modulus for the Large Magellanic Cloud (LMC) of 18.50 mag and a reddening of E(B - V) = 0.10 mag to the LMC Cepheids. Period-residual minimization was used to minimize the effects of Malmquist bias on the period- luminosity relation fitting process. Using a Galactic extinction law and the apparent V and I distance moduli, we have found a mean reddening for the M101 sample of E(B- V) = 0.03 mag and a true distance modulus to MI01 of 29.34+/-0.17 mag, corresponding to a distance of 7.4 +/- 0.6 Mpc. The sources of error have been rigorously tracked through an error budget; systematic and random errors contribute roughly equally to the quoted error. The mean gas-phase metal abundances in the LMC and in the M101 outer field are similar so we expect metallicity effects to be minimal. These Cepheids will be used in conjunction with results from a Key Project search for Cepheids in an inner field, where the metallicity is larger by a factor of 5, to probe the effects of abundance on the Cepheid period-luminosity relation. Publication: The Astrophysical Journal Pub Date: May 1996 DOI: 10.1086/177221 Bibcode: 1996ApJ...463...26K Keywords: GALAXIES: INDIVIDUAL MESSIER NUMBER: M101 full text sources ADS | data products SIMBAD (50) NED (1) MAST (1) ESA (1) CDS (1) Related Materials (29) Part 1: 1994ApJ...427..628F Part 2: 1994ApJ...428..143H Part 4: 1997ApJ...478..430K Part 5: 1996ApJ...464..568F Part 6: 1997ApJ...475..853F Part 7: 1998ApJ...496..648H Part 8: 1996ApJ...470....1S Part 9: 1997ApJ...477..535G Part 10: 1997ApJ...490..517R Part 11: 1998ApJ...500..763P Part 12: 1998ApJ...501...32H Part 13: 1998ApJ...505..207T Part 14: 1998ApJ...507..655F Part 15: 1998ApJ...498..181K Part 16: 1999ApJ...515....1S Part 17: 1999ApJ...515...29M Part 18: 1999ApJ...512...48G Part 19: 1999ApJ...521..155M Part 20: 1999ApJ...514..614K Part 21: 1999ApJ...516..626G Part 22: 2000ApJ...528..655M Part 23: 1999ApJ...525...80P Part 24: 1999ApJ...523..540S Part 25: 2000ApJ...529..698S Part 26: 2000ApJ...529..723G Part 27: 2000ApJ...529..745F Part 28: 2000ApJ...529..768K Part 29: 2000ApJ...529..786M Part 30: 2000ApJ...545..547M

We present multi-band Period-Luminosity (PL) relations for first-overtone mode Cepheids in the Small Magellanic Cloud (SMC). We derive optical band PL relations and the Wesenheit function using $VI$ mean magnitudes from the Optical Gravitational Lensing Experiment (OGLE-III) survey. We cross-match OGLE-III first-overtone mode Cepheids to the 2MASS and SAGE-SMC catalogs to derive PL relations at near-infrared ($JHK_s$) and mid-infrared ($3.6~\&~4.5\mu\mathrm{m}$) wavelengths. We test for possible non-linearities in these PL relations using robust statistical tests and find a significant break only in the optical-band PL relations at 2.5 days for first-overtone mode Cepheids. We do not find statistical evidence for a non-linearity in these PL relations at 1 day. The multi-band PL relations for fundamental-mode Cepheids in the SMC also exhibit a break at 2.5 days. We suggest that the period break around 2.5 days is related to sharp changes in the light curve parameters for SMC Cepheids. We also derive new optical and mid-infrared band PL relations for first-overtone mode Cepheids in the Large Magellanic Cloud (LMC). We compare multi-band PL relations for first-overtone mode Cepheids in the Magellanic Clouds and find a significant difference in the slope of the $V$-band PL relations but not for $I$-band PL relations. The slope of PL relations are found to be consistent in most of the infrared bands. A relative distance modulus of $\Delta\mu=0.49\pm0.02$~mag between the two clouds is estimated using multi-band PL relations for the first-overtone mode Cepheids in the SMC and LMC.

The distance to NGC 5128, the central galaxy of the Centaurus group and the nearest giant elliptical to us, has been determined using two independent distance indicators: the Mira period-luminosity (PL) relation and the luminosity of the tip of the red giant branch (RGB). The data were taken at two different locations in the halo of NGC 5128 with the ISAAC near-IR array on ESO VLT. From more than 20 hours of observations with ISAAC a very deep K s -band luminosity function was constructed. The tip of the RGB is detected at K s = 21.24 ± 0.05 mag. Using an empirical calibration of the K-band RGB tip magnitude, and assuming a mean metallicity of [M/H] = -0.4 dex and reddening of E(B - V) = 0.11, a distance modulus of NGC 5128 of (m - M) 0 = 27.87 ± 0.16 was derived. The comparison of the H-band RGB tip magnitude in NGC 5128 and the Galactic Bulge implies a distance modulus of NGC 5128 of (m - M) 0 = 27.9 ± 0.2 in good agreement with the K-band RGB tip measurement. The inner halo field has larger photometric errors, brighter completeness limits and a larger number of blends. Thus the RGB tip feature is not as sharp as in the outer halo field. The population of stars above the tip of the RGB amounts to 2176 stars in in the outer halo field (Field 1) and 6072 stars in the inner halo field (Field 2). The large majority of these sources belong to the asymptotic giant branch (AGB) population in NGC 5128 with numerous long period variables. Mira variables were used to determine the distance of NGC 5128 from a period-luminosity relation calibrated using the Hipparcos parallaxes and LMC Mira period-luminosity relation in the K-band. This is the first Mira period-luminosity relation outside the Local Group. A distance modulus of 27.96 ± 0.1 was derived, adopting the LMC distance modulus of 18.50 ± 0.04. The mean of the two methods yields a distance modulus to NGC 5128 of 27.92 ± 0.19 corresponding to D = 3.84 ± 0.35 Mpc.

There is strong evidence that the period-luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break at a period around 10 d. Because the LMC PL relation is extensively used in distance scale studies, the non-linearity of the LMC PL relation may affect the results based on this LMC calibrated relation. In this paper we show that this problem can be remedied by using the Wesenheit function in obtaining Cepheid distances. This is because the Wesenheit function is linear, although recent data suggest that the PL and the period-colour (PC) relations that make up the Wesenheit function are not. We test the linearity of the Wesenheit function and find strong evidence that the LMC Wesenheit function is indeed linear. This is because the non-linearity of the PL and PC relations cancel out when the Wesenheit function is constructed. We discuss this result in the context of distance scale applications. We also compare the distance moduli obtained from μ 0 = μ V - R(μ V - μ I ) (equivalent to Wesenheit functions) constructed with the linear and the broken LMC PL relations, and we find that the typical difference in distance moduli is ∼ +0.03 mag. Hence, the broken LMC PL relation does not seriously affect current distance scale applications. We also discuss the random error calculated with equation μ 0 = μ V - R(μ V - μ I ), and show that there is a correlation term that exists from the calculation of the random error. The calculated random error will be larger if this correlation term is ignored.

Context. The upcoming Rubin-LSST is expected to revolutionize the field of classical pulsators by offering well-sampled multi-epoch photometric data in multiple wavelengths. Type II Cepheids (T2Cs) exhibit weak or negligible metallicity dependence on period-luminosity (PL) relations. Thus, they may potentially be used as an alternative to classical Cepheids for extragalactic distance estimations, when used together with RR Lyraes and the tip of the red giant branch. It is therefore crucial to study an updated theoretical pulsation scenario of BL Herculis stars (BL Her; the shortest period T2Cs) in the corresponding Rubin-LSST photometric system. Aims. We present new theoretical light curves in the Rubin-LSST filters for a fine grid of BL Her models computed using MESA-RSP. We have also derived new theoretical PL and period-Wesenheit (PW) relations in the Rubin-LSST filters with the aim to study the effect of convection parameters and metallicity on these relations. Methods. The grid of BL Her models was computed using the non-linear radial stellar pulsation tool MESA-RSP with the input stellar parameters: metallicity (−2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5 M⊙ − 0.8 M⊙), stellar luminosity (50 L⊙ − 300 L⊙), and effective temperature (across the full extent of the instability strip; in steps of 50 K) and using four sets of convection parameters. Bolometric correction tables from MIST were used to transform the theoretical bolometric light curves of the BL Her models into the Rubin–LSST ugrizy filters. Results. The PL relations of the BL Her models exhibit steeper slopes but smaller dispersion with increasing wavelengths in the Rubin-LSST filters. The PL and PW slopes for the complete set of BL Her models computed with radiative cooling (sets B and D) are statistically similar across the grizy filters. The BL Her models exhibit weak or negligible effect of metallicity on the PL relations for wavelengths longer than the g filter for the case of the complete set of models as well as for the low-mass models. However, we find a significant effect of the metallicity on the PL relation in the u filter. Strong metallicity effects are observed in the PWZ relations involving the u filter and are found to have significant contribution from the high-metallicity BL Her models. Due to a negligible metallicity effect for relations involving the Wesenheit indices W(i, g − i), W(z, i − z), and W(y, g − y), we recommend these filter combinations for BL Her stars during observations with Rubin–LSST for use as reliable standard candles.

We use the Period-Luminosity-Color relation (PLC) for Cepheids to test for the existence of a bias in extragalactic distances derived from the classical Period-Luminosity (PL) relation. We calculate the parameters of the PLC using several galaxies observed with the Hubble Space Telescope and show that this calculation must be conducted with a PLC written in a form where the parameters are independent. The coefficients thus obtained are similar to those derived from theoretical models. Calibrating with a few unbiased galaxies, we apply this PLC to all galaxies of the Hubble Space Telescope Key Program (HSTKP) and compare the distance moduli with those published by the HSTKP team. The new distance moduli are larger (more exactly, the larger the distance the larger the difference), consistent with a bias. Further, the bias trend that is observed is the same previously obtained from two independent methods based either on the local Hubble law or on a theoretical model of the bias. The results are quite stable but when we force the PLC relation closer to the classical PL relation by using unrealistic parameters, the agreement with HSTKP distance moduli is retrieved. This also suggests that the PL relation leads to biased distance moduli. The new distance moduli reduce the scatter in the calibration of the absolute magnitude of supernovae SNIa at their maximum. This may also suggest that the relation between the amplitude at maximum and the decay of the light curve Δm 15 may not be as strong as believed.

A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.

The extragalactic distance scale builds directly on the Cepheid Period-Luminosity (PL) relation as delineated by the sample of Cepheids in the Large Magellanic Cloud (LMC). However, the LMC is a dwarf irregular galaxy, quite different from the massive spiral galaxies used for calibrating the extragalactic distance scale. Recent investigations suggest that not only the zero-point but also the slope of the Milky Way PL relation differ significantly from that of the LMC, casting doubts on the universality of the Cepheid PL relation. We want to make a differential comparison of the PL relations in the two galaxies by delineating the PL relations using the same method, the infrared surface brightness method (IRSB), and the same precepts. The IRSB method is a Baade-Wesselink type method to determine individual distances to Cepheids. We apply a newly revised calibration of the method as described in an accompanying paper (Paper I) to 36 LMC and five SMC Cepheids and delineate new PL relations in the V,I,J, & K bands as well as in the Wesenheit indices in the optical and near-IR. We present 509 new and accurate radial velocity measurements for a sample of 22 LMC Cepheids, enlarging our earlier sample of 14 stars to include 36 LMC Cepheids. The new calibration of the IRSB method is directly tied to the recent HST parallax measurements to ten Milky Way Cepheids, and we find a LMC barycenter distance modulus of 18.45+-0.04 (random error only) from the 36 individual LMC Cepheid distances. We find a significant metallicity effect on the Wvi index gamma(Wvi)=-0.23+-0.10 mag/dex as well as an effect on the slope. The K-band PL relation on the other hand is found to be an excellent extragalactic standard candle being metallicity insensitive in both slope and zero-point and at the same time being reddening insensitive and showing the least internal dispersion.

We show that the Cepheid period-luminosity (PL) relation is affected by a Malmquist-type bias, the so-called population incompleteness bias. Its calculated slope appears shallower than the true one because of the cutoff in apparent magnitude resulting from the instrumental limiting magnitude. Furthermore, the use of the PL relation, even with the correct slope, leads to an underestimation of distances that is not negligible. We confirm this finding by studying simulated PL relations, and we show that this bias may be as large as 0.2 or 0.3 mag on distance modulus. We also test the efficiency of a cutoff in log P and show that it is a good way to minimize this bias. However, a correction of this is difficult as long as the completeness of the sample is not perfectly well established.

The prevailing evidence suggests that most large-amplitude AGB variables follow the period luminosity (PL) relation that has been established for Miras in the LMC and galactic globular clusters. Hipparcos observations indicate that most Miras in the solar neighbourhood are consistent with such a relation. There are two groups of stars with luminosities that are apparently greater than the PL relation would predict: (1) in the LMC and SMC there are large amplitude variables, with long periods, P> 420 days, which are probably undergoing hot bottom burning, but which are very clearly more luminous than the PL relation (these are visually bright and are likely to be among the first stars discovered in more distant intermediate age populations); (2) in the solar neighbourhood there are short period, P<235 days, red stars which are probably more luminous than the PL relation. Similar short-period red stars, with high luminosities, have not been identified in the Magellanic Clouds.