The PL calibration for Milky Way Cepheids and its implications for the distance scale

The rationale behind recent calibrations of the Cepheid PL relation using the Wesenheit formulation is reviewed and reanalyzed, and it is shown that recent conclusions regarding a possible change in slope of the PL relation for short-period and long-period Cepheids are tied to a pathological distribution of HST calibrators within the instability strip. A recalibration of the period-luminosity relation is obtained using Galactic Cepheids in open clusters and groups, the resulting relationship, described by log L/L _⊙=2.415(±0.035)+1.148(±0.044)log P, exhibiting only the moderate scatter expected from color spread within the instability strip. The relationship is confirmed by Cepheids with HST parallaxes, although without the need for Lutz-Kelker corrections, and in general by Cepheids with revised Hipparcos parallaxes, albeit with concerns about the cited precisions of the latter. A Wesenheit formulation of W _V =−2.259(±0.083)−4.185(±0.103)log P for Galactic Cepheids is tested successfully using Cepheids in the inner regions of the galaxy NGC 4258, confirming the independent geometrical distance established for the galaxy from OH masers. Differences between the extinction properties of interstellar and extragalactic dust may yet play an important role in the further calibration of the Cepheid PL relation and its application to the extragalactic distance scale.     

Classical Cepheids in the Galactic outer ring R1R ′2

The kinematics and distribution of classical Cepheids within ∼3 kpc from the Sun suggest the existence of the outer ring R₁R ′₂ in the Galaxy. The optimum value of the solar position angle with respect to the major axis of the bar, θ_b, providing the best agreement between the distribution of Cepheids and model particles, is θ_b = 37° ±13°. The kinematical features obtained for Cepheids with negative galactocentric radial velocity V_R are consistent with the solar location near the descending segment of the outer ring R₂. The sharp rise of extinction toward of the Galactic center can be explained by the presence of the outer ring R₁ near the Sun. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ultra long period Cepheids: a primary standard candle out to the Hubble flow

The cosmological distance ladder crucially depends on classical Cepheids (with P=3–80 days), which are primary distance indicators up to 33 Mpc. Within this volume, very few SNe Ia have been calibrated through classical Cepheids, with uncertainty related to the non-linearity and the metallicity dependence of their period–luminosity (PL) relation. Although a general consensus on these effects is still not achieved, classical Cepheids remain the most used primary distance indicators. A possible extension of these standard candles to further distances would be important. In this context, a very promising new tool is represented by the ultra-long period (ULP) Cepheids (P≳80 days), recently identified in star-forming galaxies. Only a small number of ULP Cepheids have been discovered so far. Here we present and analyse the properties of an updated sample of 37 ULP Cepheids observed in galaxies within a very large metallicity range of 12+log(O/H) from ∼7.2 to 9.2 dex. We find that their location in the colour-magnitude (V−I,V) diagram as well as their Wesenheit (V−I) index-period (WP) relation suggests that they are the counterparts at high luminosity of the shorter-period (P≲80 days) classical Cepheids. However, a complete pulsation and evolutionary theoretical scenario is needed to properly interpret the true nature of these objects. We do not confirm the flattening in the studied WP relation suggested by Bird et al. (Astrophys. J. 695:874, 2009). Using the whole sample, we find that ULP Cepheids lie around a WP relation similar to that of the LMC, although with a large spread (∼ 0.4 mag).     

The visual surface brightness method and the radii of dwarf Cepheids

In order to determine the radii of dward Cepheids by applying the visual surface brightness method, the empirical relationship betweenF _V and (b–y) was derived. Seventeen stars of spectral type A to F where both angular diameters anduvby photometric data are available were selected from the literature. A theoretical [F _V , (b–y)] relation was derived by using the Kurucz model atmospheres. It was found that the theoretical relation is strongly dependent upon metallicity and surface gravity. To demonstrate that the visual surface brightness method is an effective way to determine the radii of dwarf Cepheids, both theoretical and empirical relations were applied to seven dwarf Cepheids. The most reliable result was obtained for AD CMi where the quality of the radial velocity data is superior.     

The effective temperatures,radii and masses of Dwarf Cepheids

Using the flux values determined with the infrared flux method (IRFM) developed by Blackwell and Lynas-Gray (1993), we derived the empirical relationship between flux (F _v ) and (V — K) colour appropriate to Dwarf Cepheids. For three Dwarf Cepheids CY Aqr, YZ Boo and SZ Lyn where both VK photometry and radial velocities were available from the literature, effective temperatures were determined using the intrinsic Strömgren indices, model atmosphere grids for (V — K) and the relation between temperature and (V — K) colour. Then, by applying the infrared surface brightness method, radii and distances and hence masses and absolute magnitudes were estimated with effective temperatures determined by three different methods. It was found that the average mass of these variables is about 0.5 solar mass and this result supports the hypothesis that Dwarf Cepheids are pre-white dwarf objects. It was also confirmed that the temperatures determined with the IRFM are most successful in the application of the surface brightness method to the radius estimation of Dwarf Cepheids.     

Period-luminosities relation of classical Cepheids

A new PL-relation (10) — Figure 2 for the Cepheids in the Galaxy, the Magellanic Clouds and M31 has been constructed. On deriving this relation both the period-radius (3) and period-colour relations (7), (8) and (9) are essentially used. The PC-relation (7) determined after the colours of 88 galactic cepheids (Table I), which are obtained from the colour-spectrum relation (6) — Figure 1, common for Cepheids and non-variable supergiants, are used also for the M31 Cepheids, whereas (8) and (9) are for the Large and Small MC Cepheids, respectively, all three PC-relations having a common slope. The comparison of the relations (8) and (9) with (7) shows that the LMC and SMC Cepheids are bluer than the galactic ones with 0^m.04 and 0^m.19, respectively, probably because of their metal-poor abundance. The places of thes-Cepheids in Figure 2 show that these Cepheids possess a dissimilar PL-relation with a different slope. The reason for such a difference is that thes-Cepheids are first harmonic pulsators. The distance moduli of the three galaxies under discussion are obtained from the PL-relation (10). The colour-coefficient of period-colour-luminosity-relation is briefly discussed. The general conclusion based on a comparison of the PL-relation in the present paper with those by other authors (Table V) is that our PL-relation differs in the zero-point by less than 0^m.2; therefore, the manner of constructing the PL-relation by means of PR and PC-relations is reasonable and useful.     

Calibrating the Cepheid Period-Luminosity relation from the near-infrared surface brightness technique

We have applied the near-infrared surface-brightness method to 111 Cepheids in the Milky Way and in the Large and the Small Magellanic Clouds determining distances and luminosities for the individual stars. We find that the K-band Period-Luminosity (PL-)relations for Milky Way and Large Magellanic Cloud Cepheids are almost identical, whereas the zero point of the Wesenheit relation depends significantly on metallicity, metal poor Cepheids being fainter.     

Ba II lines as luminosity indicators: s-Cepheids and non-variable supergiants

Ba II line equivalent widths appear to be well correlated with the absolute magnitudes for yellow supergiants. Two Ba II lines 5853.6 Å and 6141.7 Å were applied for investigation of the possible relation between their equivalent widths and M_v for small-amplitude Cepheids and non-variable supergiants.     

Study of the effect of metallicity on the amplitudes of Cepheids

Results concerning the dependence of photometric and radial velocity amplitudes on metallicity are presented based on about 200 Galactic classical Cepheids pulsating in the fundamental mode. The Galactic distribution of the [Fe/H] value of Cepheids is also studied. We show that the photometric amplitude ratio A_I/A_V is independent of metallicity. The observed dependence of this ratio on the pulsation period does not correspond to the theoretical predictions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New opacities and first overtone mode Cepheids

Some results of linear adiabatic and nonlinear pulsation models of first overtone mode Cepheids are discussed. New and augmented opacities and a nonstandard mass-luminosity relation have been taken into account. The models indicate the possible importance of the resonanceP1/P4 = 2 nearP1 = 3 days. The resonance could explain the observed characteristics of the light curve shape of first overtone mode Cepheids.     

GAIA and the Extragalactic Distance Scale

The local expansion field (v ₂₂₀ <1200 km s^-1) and the cosmic expansion field out to 30 000 km s^-1 are characterized by H ₀ = 58 [km s^-1 Mpc^-1]. While the random error of this determination is small (± 2 units), it may still be affected by systematic errors as large as ±10%>. The local expansion is outlined by Cepheids and by Cepheid-calibrated TF distances of a complete sample of field galaxies and by nearby groups and clusters; the cosmic expansion is defined by Cepheid-calibrated SNe Ia. The main source of systematic errors are therefore the shape and the zero point of the P-L relation of Cepheids and its possible dependence on metallicity. GAIA will essentially eliminate these systematic error sources. Another source of systematic error is due to the homogenization of SNe Ia as to decline rate Δm ₁₅ and color (B-V). GAIA will discover most of the 1100 SNe Ia within 10 000 km s^-1, which will occur during its four-year lifetime. If their photometric parameters can be determined from the ground, they will fix the dependence of the SNe Ia luminosity on Δ m ₁₅ and (B-V) with high accuracy. At the same time they will yield exquisite distances to an equal number of field galaxies. – GAIA will also revolutionize the very local distance scale by determining fundamental distances of the companion galaxies of the Milky Way and even of some spirals in- and possibly outside the Local Group from their rotation curves seen in radial velocities and proper motions. Moreover, GAIA will obtain trigonometric parallaxes of RR Lyrae stars, of red giants defining the TRGB, of stars on the ZAMS, of White Dwarf defining their cooling sequence, and of globular clusters, and determine the metallicity dependence of these distance indicators. It will thus establish a self-controlling network of distance indicators within the Local Group and beyond. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Correlation between the Magnetic and Velocity Fields on the Full Solar Disk

A possible correlation between the magnetic and velocity fields has been analyzed based on the SOHO/MDI magnetograms and Dopplergrams. It is found that the observed large-scale weak magnetic field (weaker than 50 G (gauss)) is correlated with the velocity statistically. The curves of u⋅b with latitude, where u and b are the velocity and magnetic fields in a rectangular region (±15^○ in longitude, ±45^○ in latitude) on the Sun, show the same patterns in the years 2000, 2004, and 2007. The patterns indicate that u and b are positively correlated near the equator but are anti-correlated at the middle latitudes. For a strong magnetic field between 50 G and 3000 G, the curves of u⋅b with latitude show the same tendencies at the middle latitudes. Near the equator, however, the slope of the curve is positive in 2000 and is negative in 2004 and 2007. In addition, we give an estimation for the amplitude of the cross helicity h _χ (h_c=[`(u·b)]h_{\chi}=\overline{\mathbf{u}\cdot\mathbf{b}}) inferred from the MDI data, which is of the order of 10³ G m s⁻¹ near the center of the solar disk.     

A comparison of theoretical and experimental estimates of the solar proton diffusion coefficient during three flare events

The propagation time for solar protons observed during the events of January 24, February 25 and March 17, 1969 are compared with those estimated from numerical solutions of the Fokker-Planck transport equation, using values of the diffusion coefficient of the form K _r = K ₀ r ^b where r is radial distance from the Sun, K ₀ is obtained from the plasma-field parameters near the Earth and b varies from - 3 to + 1. K ₀ is derived either by assuming that all the magnetic fluctuation power is in small amplitude transverse waves or alternatively in discontinuous changes in ¦B¦ along the flux tube of propagation. In the first case it is found that the K ₀ values calculated require either b -3, implying a very rapid wave growth with r, or the Fokker-Planck equation reduces to the situation of purely convective transport which is at variance with the experimental observations. More reasonable results are found in the second case although even here K ₀ is probably underestimated. Alternative ways of deducing K ₀ empirically from particle anisotropy measurements are put forward and these seem to favour the discontinuity model.     

Kinematic parameters of young subsystems and the galactic rotation curve

We analyze the space velocities of blue supergiants, long-period Cepheids, and young open star clusters (OSCs), as well as the H I and H II radial-velocity fields by the maximum-likelihood method. The distance scales of the objects are matched both by comparing the first derivatives of the angular velocity Ω′ determined separately from radial velocities and proper motions and by the statistical-parallax method. The former method yields a short distance scale (for R₀=7.5 kpc, the assumed distances should be increased by 4%), whereas the latter method yields a long distance scale (for R₀=8.5 kpc, the assumed distances should be increased by 16%). We cannot choose between these two methods. Similarly, the distance scale of blue supergiants should be shortened by 9% and lengthened by 3%, respectively. The H II distance scale is matched with the distance scale of Cepheids and OSCs by comparing the derivatives Ω′ determined for H II from radial velocities and for Cepheids and OSCs from space velocities. As a result, the distances to H II regions should be increased by 5% in the short distance scale. We constructed the Galactic rotation curve in the Galactocentric distance range 2–14 kpc from the radial velocities of all objects with allowance for the difference between the residual-velocity distributions. The axial ratio of the Cepheid+OSC velocity ellipsoid is well described by the Lindblad relation, while σ_u≈σ_v for gas. The following rotation-curve parameters were obtained: Ω₀=(27.5±1.4) km s^?1 kpc^?1 and A=(17.1±0.5) km s^?1 kpc^?1 for the short distance scale (R₀=7.5 kpc); and Ω₀=(26.6±1.4) km s^?1 kpc^?1 and A=(15.4±0.5) km s^?1 kpc^?1 for the long distance scale (R₀=8.5 kpc). We propose a new method for determining the angular velocity Ω₀ from stellar radial velocities alone by using the Lindblad relation. Good agreement between the inferred Ω₀ and our calculations based on space velocities suggests that the Lindblad relation holds throughout the entire sample volume. Our analysis of the heliocentric velocities for samples of young objects reveals noticeable streaming motions (with a velocity lag of ～7 km s^?1 relative to the LSR), whereas a direct computation of the perturbation amplitudes in terms of the linear density-wave theory yields a small amplitude for the tangential perturbations.     

Period–colour and amplitude–colour relations in classical Cepheid variables – IV. The multiphase relations

The superb phase resolution and quality of the Optical Gravitational Lensing Experiment (OGLE) data on the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) Cepheids, together with existing data on Galactic Cepheids, are combined to study the period–colour (PC) and amplitude–colour (AC) relations as a function of pulsation phase. Our results confirm earlier work that the LMC PC relation (at mean light) is more consistent with two lines of differing slopes, separated at a period of 10 d. However, our multiphase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multiphase PC relations provide insight into why the Galactic PC relation is linear but the LMC PC relation is non-linear. This is because the LMC PC relation is shallower for short  (log  P < 1)  and steeper for long  (log  P > 1)  period Cepheids than the corresponding Galactic PC relation. Both of the short- and long-period Cepheids in all three galaxies exhibit the steepest and shallowest slopes at phases around 0.75–0.85, respectively. A consequence is that the PC relation at phase ∼ 0.8 is highly non-linear. Further, the Galactic and LMC Cepheids with  log  P > 1  display a flat slope in the PC plane at phases close to the maximum light. When the LMC period–luminosity (PL) relation is studied as a function of phase, we confirm that it changes with the PC relation. The LMC PL relation in V and I band near the phase of 0.8 provides compelling evidence that this relation is also consistent with two lines of differing slopes joined at a period close to 10 d.     

The expansion field: the value of <Emphasis Type="Italic">H</Emphasis><Subscript>0</Subscript>

Any calibration of the present value of the Hubble constant (H ₀) requires recession velocities and distances of galaxies. While the conversion of observed velocities into true recession velocities has only a small effect on the result, the derivation of unbiased distances which rest on a solid zero point and cover a useful range of about 4–30 Mpc is crucial. A list of 279 such galaxy distances within v < 2,000 km s⁻¹ is given which are derived from the tip of the red-giant branch (TRGB), from Cepheids, and/or from supernovae of type Ia (SNe Ia). Their random errors are not more than 0.15 mag as shown by intercomparison. They trace a linear expansion field within narrow margins, supported also by external evidence, from v = 250 to at least 2,000 km s⁻¹. Additional 62 distant SNe Ia confirm the linearity to at least 20,000 km s⁻¹. The dispersion about the Hubble line is dominated by random peculiar velocities, amounting locally to <100 km s⁻¹ but increasing outwards. Due to the linearity of the expansion field the Hubble constant H ₀ can be found at any distance >4.5 Mpc. RR Lyr star-calibrated TRGB distances of 78 galaxies above this limit give H ₀ = 63.0 ± 1.6 at an effective distance of 6 Mpc. They compensate the effect of peculiar motions by their large number. Support for this result comes from 28 independently calibrated Cepheids that give H ₀ = 63.4 ± 1.7 at 15 Mpc. This agrees also with the large-scale value of H ₀ = 61.2 ± 0.5 from the distant, Cepheid-calibrated SNe Ia. A mean value of H ₀ = 62.3 ± 1.3 is adopted. Because the value depends on two independent zero points of the distance scale its systematic error is estimated to be 6%. Other determinations of H ₀ are discussed. They either conform with the quoted value (e.g. line width data of spirals or the D _n −σ method of E galaxies) or are judged to be inconclusive. Typical errors of H ₀ come from the use of a universal, yet unjustified P–L relation of Cepheids, the neglect of selection bias in magnitude-limited samples, or they are inherent to the adopted models.     

Preliminary results for RR Lyrae stars and Classical Cepheids from the Vista Magellanic Cloud (VMC) survey

The Vista Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting K _S -band time series photometry of the system formed by the two Magellanic Clouds (MC) and the “bridge” that connects them. These data are used to build K _S -band light curves of the MC RR Lyrae stars and Classical Cepheids and determine absolute distances and the 3D geometry of the whole system using the K-band period luminosity (PLK _S ), the period–luminosity–color (PLC) and the Wesenhiet relations applicable to these types of variables. As an example of the survey potential we present results from the VMC observations of two fields centered respectively on the South Ecliptic Pole and the 30 Doradus star forming region of the Large Magellanic Cloud. The VMC K _S -band light curves of the RR Lyrae stars in these two regions have very good photometric quality with typical errors for the individual data points in the range of ∼0.02 to 0.05 mag. The Cepheids have excellent light curves (typical errors of ∼0.01 mag). The average K _S magnitudes derived for both types of variables were used to derive PLK _S relations that are in general good agreement within the errors with the literature data, and show a smaller scatter than previous studies.     

Photometric observations of Cepheids from the ASAS-3 catalog: Photoelectric <Emphasis Type="Italic">BV I</Emphasis><Subscript>c</Subscript> observations of 33 classical Cepheids

Cepheids, the principal distance indicators, point to the existence of two inner Galactic spiral arms in the immediate solar neighborhood (within 5 kpc). However, the available Cepheids are clearly insufficient for a detailed study of the structure of these arms. Fortunately, southern-sky monitoring (the ASAS project) has led to the discovery of many new variable stars, more than one thousand of which have been identified as possible Cepheids. To improve the classification and to construct reliable light curves for new Cepheids, we have begun their regular photometric observations. Here, we present the first results: 1192 photoelectricBV I _c observations were performed for 33 classical Cepheidswith the 76-cm telescope of the South-African Astronomical Observatory (SAAO, the South-African Republic) from December 2006 to January 2008. We provide tables of observations and V light and B-V and V-I _c color curves. The new observations together with ASAS-3 data have been used to improve the elements of the light variations.     

The dependence of the frequency spectra of the interplanetary magnetic-field fluctuations on the direction of the mean field

The frequency spectra of the interplanetary magnetic field fluctuations are the projection of their wavenumber spectra onto one dimension. Only the frequency spectra can be measured by spacecrafts. It is studied how their measured size depends on the direction of the mean fieldB ₀, which structures the symmetry of the fluctuations relative to the solar wind system. It is specialized for the slab model, Alfvén waves, magneto-acoustic waves and the isotropic case. For the slab model the frequency spectra are proportional to , whereq is the spectral index and the angle betweenB ₀ and the radial direction. For the diffusion coefficientK _TT the relation holds.     

Angular momenta in binary systems

The correlations angular momentaL to massesM are studied for different types of spectroscopic binaries. The functionsL=AM ^b have the coefficientb with the values expected from a Keplerian mechanics, but the valuesA(q, T), A(q, a), A(q, v), associated tob=5/3, 3/2, and 2, respectively, are given (statistically speaking) by multiples or submultiples of discrete values of: the mass ratiosq, the semi-major axesa, periodsT, and velocitiesv of the reduced mass. This indicates the existence of a discrete unit of actionL=(1/2)×potential energy xperiod. Postulates about equivalent states of angular momenta for different orbital parameters are introduced, being this coherent with the analysis of the up-to-date data. Among other examples of the application of such equivalence postulates, we haveL(M) (W-type of the WUMa systems)L(M) (main group of the Algol binaries). The quantum units of action seen here are equivalent to those seen in the solar system in one of our previous works. From comparisons with galaxies and single stars, it is evidence that there is not an unique universal functionL=AM ^b, when the fine structure of the relation is analysed: each type of object has its own coefficients,A, b. It sems to be that there are an upper and a lower limit for all the possible functions. The upper limit isL=A _gM^5/3, withA _g1 associated to periodsT Hubble time, and the lower limit isL=GM ^2/c, with 1. The existence of the upper limit can be investigated with studies of pairs of galaxies, and the lower limit can be tested with analysis of single G, K, M stars. The quantical hypothesis introduced here can be checked definitely, when available larger samples of data with low errors, with similar quality as the selected list of almost 80 eclipsing binaries (mainly detached systems) analysed here.