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Register a new userObservational calibration of the projection factor of Cepheids. II. Application to nine Cepheids with HST/FGS parallax measurements
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The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spectroscopic radial velocity measurements and angular diameter estimates to derive the distance of the star. An important application of this method is the determination of Cepheid distances, in view of the calibration of their distance scale. However, the conversion of radial to pulsational velocities in the PoP method relies on a poorly calibrated parameter, the projection factor (p-factor). We aim to measure empirically the value of the p-factors of a homogeneous sample of nine Galactic Cepheids for which trigonometric parallaxes were measured with the Hubble Space Telescope Fine Guidance Sensor. We use the SPIPS algorithm, a robust implementation of the PoP method that combines photometry, interferometry, and radial velocity measurements in a global modeling of the pulsation. We obtained new interferometric angular diameters using the PIONIER instrument at the Very Large Telescope Interferometer, completed by data from the literature. Using the known distance as an input, we derive the value of the p-factor and study its dependence with the pulsation period. We find the following p-factors: 1.20 $pm$ 0.12 for RT Aur, 1.48 $pm$ 0.18 for T Vul, 1.14 $pm$ 0.10 for FF Aql, 1.31 $pm$ 0.19 for Y Sgr, 1.39 $pm$ 0.09 for X Sgr, 1.35 $pm$ 0.13 for W Sgr, 1.36 $pm$ 0.08 for $beta$ Dor, 1.41 $pm$ 0.10 for $zeta$ Gem, and 1.23 $pm$ 0.12 for $ell$ Car. These values are consistently close to p = 1.324 $pm$ 0.024. We observe some dispersion around this average value, but the observed distribution is statistically consistent with a constant value of the p-factor as a function of the pulsation period. The error budget of our determination of the p-factor values is presently dominated by the uncertainty on the parallax, a limitation that will soon be waived by Gaia.
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The distances of pulsating stars, in particular Cepheids, are commonly measured using the parallax of pulsation technique. The differe
We focus on empirically measure the p-factor of a homogeneous sample of 29 LMC and 10 SMC Cepheids for which an accurate average LMC/SMC distance were estimated from eclipsing binary systems. We used the SPIPS algorithm, which is an implementation of the BW method. As opposed to other conventional use, SPIPS combines all observables, i.e. radial velocities, multi-band photometry and interferometry into a consistent physical modeling to estimate the parameters of the stars. The large number and their redundancy insure its robustness and improves the statistical precision. We successfully estimated the p-factor of several MC Cepheids. Combined with our previous Galactic results, we find the following P-p relation: -0.08(log P-1.18)+1.24. We find no evidence of a metallicity dependent p-factor. We also derive a new calibration of the P-R relation, logR=0.684(log P-0.517)+1.489, with an intrinsic dispersion of 0.020. We detect an IR excess for all stars at 3.6 and 4.5um, which might be the signature of circumstellar dust. We measure a mean offset of $Delta m_{3.6}=0.057$mag and $Delta m_{4.5}=0.065$mag. We provide a new P-p relation based on a multi-wavelengths fit, and can be used for the distance scale calibration from the BW method. The dispersion is due to the MCs width we took into account because individual Cepheids distances are unknown. The new P-R relation has a small intrinsic dispersion, i.e. 4.5% in radius. Such precision will allow us to accurately apply the BW method to nearby galaxies. Finally, the IR excesses we detect raise again the issue on using mid-IR wavelengths to derive P-L relation and calibrate the $H_0$. These IR excesses might be the signature of circumstellar dust, and are never taken into account when applying the BW method at those wavelengths. Our measured offsets may give an average bias of 2.8% on the distances derived through mid-IR P-L relations.
The projection factor (p-factor) is an essential component of the classical Baade-Wesselink (BW) technique, that is commonly used to determine the distances to pulsating stars. It is a multiplicative parameter used to convert radial velocities into pulsational velocities. As the BW distances are linearly proportional to the p-factor, its accurate calibration for Cepheids is of critical importance for the reliability of their distance scale. We focus on the observational determination of the p-factor of the long-period Cepheid RS Pup (P = 41.5 days). This star is particularly important as this is one of the brightest Cepheids in the Galaxy and an analog of the Cepheids used to determine extragalactic distances. An accurate distance of 1910 +/- 80 pc (+/- 4.2%) has recently been determined for RS Pup using the light echoes propagating in its circumstellar nebula. We combine this distance with new VLTI/PIONIER interferometric angular diameters, photometry and radial velocities to derive the p-factor of RS Pup using the code Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). We obtain p = 1.250 +/- 0.064 (+/-5.1%), defined for cross-correlation radial velocities. Together with measurements from the literature, the p-factor of RS Pup confirms the good agreement of a constant p = 1.293 +/- 0.039 (+/-3.0%) model with the observations. We conclude that the p-factor of Cepheids is constant or mildly variable over a broad range of periods (3.7 to 41.5 days).
In a step toward understanding the origin of the Galactic Halo, we have reexamined Type II Cepheids (T2C) in the field with new input from the second data release (DR2) of Gaia. For 45 T2C with periods from 1 to 20 days, parallaxes, proper motions, and [Fe/H] values are available for 25 stars. Only 5 show [Fe/H] < -1.5, while the remaining stars show thick disk kinematics and [Fe/H] > -0.90. We have compared the T2C stars of the field with their cousins in the globular clusters of the Halo and found that the globular clusters with T2C stars show metallicities and kinematics of a pure Halo population. The globulars may have formed during the overall collapse of the Galaxy while the individual thick disk T2C stars may have been captured from small systems that self-enriched prior to capture. The relationship of these two populations to the micro-galaxies currently recognized as surrounding the Galaxy is unclear.
We discuss the observed pulsation properties of Type II Cepheids (TIICs) in the Galaxy and Magellanic Clouds. The period (P) distributions, luminosity amplitudes and population ratios of the three different sub-groups (BL Herculis[BLH, P<5 days], W Virginis [WV, 5<P<20 days], RV Tauri [RVT, P>20 days]) are quite similar in different stellar systems, suggesting a common evolutionary channel and a mild dependence on both metallicity and environment. We present a homogeneous theoretical framework based on Horizontal Branch (HB) evolutionary models, envisaging that TIICs are mainly old (t<10 Gyr), low-mass stars. The BLHs are predicted to be post early asymptotic giant branch (PEAGB) stars (double shell burning) on the verge of reaching their AGB track (first crossing of the instability strip), while WVs are a mix of PEAGB and post-AGB stars (hydrogen shell burning) moving from cool to hot (second crossing). Thus suggesting that they are a single group of variable stars. RVTs are predicted to be a mix of post-AGB stars along their second crossing (short-period tail) and thermally pulsing AGB stars (long-period tail) evolving towards their white dwarf cooling sequence. We also present several sets of synthetic HB models by assuming a bimodal mass distribution along the HB. Theory suggests, in agreement with observations, that TIIC pulsation properties marginally depend on metallicity. Predicted period distributions and population ratios for BLHs agree quite well with observations, while those for WVs and RVTs are almost a factor of two smaller and larger than observed, respectively. Moreover, the predicted period distributions for WVs peak at periods shorter than observed, while those for RVTs display a long period tail not supported by observations. We investigate several avenues to explain these differences, but more detailed calculations are required to address them.
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