The linearity of the Wesenheit function for the Large Magellanic Cloud Cepheids

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  μ₀=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  μ₀=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.     

Further empirical evidence for the non-linearity of the period–luminosity relations as seen in the Large Magellanic Cloud Cepheids

Recent studies, using OGLE data for LMC Cepheids in the optical, strongly suggest that the period–luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break or non-linearity at a period of 10 d. In this paper we apply statistical tests, the chi-squared test and the F -test, to the Cepheid data from the MACHO project to test for a non-linearity of the V - and R -band PL relations at 10 d, and extend these tests to the near-infrared ( JHK -band) PL relations with 2MASS data. We correct the extinction for these data by applying an extinction map towards the LMC. The statistical test we use, the F -test, is able to take account of small numbers of data points and the nature of that data on either side of the period cut at 10 d. With our data, the results we obtained imply that the VRJH -band PL relations are non-linear around a period of 10 d, while the K -band PL relation is (marginally) consistent with a single-line regression. The choice of a period of 10 d, around which this non-linearity occurs, is consistent with the results obtained when this 'break' period is estimated from the data. We show that robust parametric (including least-squares, least absolute deviation, robust regression) and non-parametric regression methods, which restrict the influence of outliers, produce similar results. Long-period Cepheids are supplemented from the literature to increase our sample size. The photometry of these long-period Cepheids is compared with our data and no trend with period is found. Our main results remain unchanged when we supplement our data set with these long-period Cepheids. By examining our data at maximum light, we also suggest arguments as to why errors in reddening are unlikely to be responsible for our results. The non-linearity of the mean V -band PL relation as seen in both of the OGLE and the MACHO data, using different extinction maps, suggests that this non-linearity is real.     

Period–luminosity relations for red supergiant variables – I.The calibration

We present CCD photometry of red supergiant long-period variables (LPVs) in the Per OB1 association, the Large Magellanic Cloud (LMC) and M33. The photometry was obtained in the Kron–Cousins R and I bandpasses and in a narrow bandpass ( λ ₀=8250 Å, FWHM=300 Å) chosen to avoid TiO bands in the spectral energy distribution of the LPVs. Because the strength of the TiO bands varies greatly with temperature, which varies with the phase of an LPV, avoiding TiO reduces the amplitude of the photometric variations seen in LPVs. The result is a lower dispersion and a well defined period–luminosity (PL) relation.
For the LMC sample we find an rms dispersion of 0.27 mag in the narrow-band PL relation and slightly larger dispersions for the LPVs in Per OB1 and M33. This dispersion is comparable to that of the Cepheid PL relation at similar wavelengths. Adopting a distance modulus of 18.5±0.1 mag for the LMC, we obtain distance moduli of 11.68±0.15 mag for Per OB1 and 24.85±0.13 mag for M33. These distances agree well with those based on main sequence fitting for Per OB1 and the Cepheid distance for M33. Since LPVs are ∼ 5 times more common than Cepheids and have a well defined PL relation, LPVs provide a promising method for estimating Galactic and extra galactic distances.     

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.     

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.     

On the period-luminosity-colour relation for galactic Cepheids

A period-luminosity-colour relation is derived from the data of 29 galactic Cepheids with known distances collected from the literature, and is then compared with the simpler period-luminosity relation. The insignificant reduction in the dispersion seems to argue against the introduction of the colour term. It is, however, demonstrated that this evidence may be fictitious and due to the use of Cepheids, whose membership in a star aggregate is still doubtful. The exclusion of these stars leads to a PLC relation which shows a significantly smaller dispersion than that given by the corresponding PL relation.     

Period–colour and amplitude–colour relations in classical Cepheid variables – V. The Small Magellanic Cloud Cepheid models

Period–colour (PC) and amplitude–colour (AC) relations at maximum, mean and minimum light are constructed from a large grid of full amplitude hydrodynamic models of Cepheids with a composition appropriate for the Small Magellanic Cloud (SMC). We compare these theoretical relations with those from observations. The theoretical relations are, in general, in good agreement with their observational counterparts, though there exist some discrepancy for short period  (log [ P ] < 1)  Cepheids. We outline a physical mechanism which can, in principle, be one factor to explain the observed PC/AC relations for the long and short period Cepheids in the Galaxy, Large Magellanic Cloud (LMC) and SMC. Our explanation relies on the hydrogen ionization front (HIF)–photosphere interaction and the way this interaction changes with pulsation period, pulsation phase and metallicity. Since the PC relation is connected with the period–luminosity (PL) relation, it is postulated that such a mechanism can also explain the observed properties of the PL relation in these three galaxies.     

Globular clusters and the Mira period–luminosity relation

A globular cluster distance scale based on Hipparcos parallaxes of subdwarfs has been used to derive estimates of M _K for cluster Miras, including one in the Small Magellanic Cloud (SMC) globular cluster NGC 121. These lead to a zero-point of the Mira infrared period–luminosity (PL) relation, PL( K ), in good agreement with that derived from Hipparcos parallaxes of nearby field Miras. The mean of these two estimates together with data on LMC Miras yields a Large Magellanic Cloud (LMC) distance modulus of     in evident agreement with a metallicity-corrected Cepheid modulus     .
The use of luminous asymptotic giant branch (AGB) stars as extragalactic population indicators is also discussed.     

Period–luminosity relations for type II Cepheids and their application

JHK _s magnitudes corrected to mean intensity are estimated for Large Magellanic Cloud (LMC) type II Cepheids in the OGLE-III survey the third phase of the Optical Gravitational Lensing Experiment (OGLE). Period–luminosity (PL) relations are derived in JHK _s as well as in a reddening-free VI parameter. Within the uncertainties, the BL Her stars  ( P < 4 d)  and the W Vir stars (   P = 4  to 20 d) are colinear in these PL relations. The slopes of the infrared relations agree with those found previously for type II Cepheids in globular clusters within the uncertainties. Using the pulsation parallaxes of V553 Cen and SW Tau, the data lead to an LMC modulus uncorrected for any metallicity effects of  18.46 ± 0.10  mag. The type II Cepheids in the second-parameter globular cluster, NGC 6441, show a PL( VI ) relation of the same slope as that in the LMC, and this leads to a cluster distance modulus of  15.46 ± 0.11  mag, confirming the hypothesis that the RR Lyrae variables in this cluster are overluminous for their metallicity. It is suggested that the Galactic variable κ Pavonis is a member of the peculiar W Vir class found by the OGLE-III group in the LMC. Low-resolution spectra of OGLE-III type II Cepheids with   P > 20  d (RV Tau stars) show that a high proportion have TiO bands; only one has been found showing C₂. The LMC RV Tau stars, as a group, are not colinear with the shorter period type II Cepheids in the infrared PL relations in marked contrast to such stars in globular clusters. Other differences between LMC, globular cluster and Galactic field type II Cepheids are noted in period distribution and infrared colours.     

Calibration of the Classical Cepheid Period-Luminosity Relation from Hipparcos Data

The calibration of the classical Cepheid Period-Luminosity (PL) relation is a fundamental step for the determination of the cosmic distance scale. In this paper a calibration obtained from Hipparcos data is presented and used to estimate the LMC distance modulus. A value of 18.35^m ± 0.13 is obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral analysis of Swift long gamma-ray bursts with known redshift

We study the spectral and energetics properties of 47 long-duration gamma-ray bursts (GRBs) with known redshift, all of them detected by the Swift satellite. Due to the narrow energy range (15–150 keV) of the Swift -BAT detector, the spectral fitting is reliable only for fitting models with two or three parameters. As high uncertainty and correlation among the errors is expected, a careful analysis of the errors is necessary. We fit both the power law (PL, two parameters) and cut-off power law (CPL, three parameters) models to the time-integrated spectra of the 47 bursts, and we present the corresponding parameters, their uncertainties and the correlations among the uncertainties. The CPL model is reliable only for 29 bursts for which we estimate the  ν f _ν  peak energy E _pk. For these GRBs, we calculate the energy fluence and the rest-frame isotropic-equivalent radiated energy,   E _γ,iso  , as well as the propagated uncertainties and correlations among them. We explore the distribution of our homogeneous sample of GRBs on the rest-frame diagram   E '_pk  versus   E _γ,iso  . We confirm a significant correlation between these two quantities (the 'Amati' relation) and we verify that, within the uncertainty limits, no outliers are present. We also fit the spectra to a Band model with the high-energy PL index frozen to −2.3, obtaining a rather good agreement with the 'Amati' relation of non- Swift GRBs.     

Cepheid space distribution and the structure of the galaxy

On the basis of the PLC relation (1) or the PL relation by Van den Bergh (2) and the PC relation by Deanet al. (1978), the distances of 284 galactic cepheids with photoelectric observations have been derived. The space distribution of these cepheids with 111 additional ones without photoelectric observations, is studied. In spite of the strong influence of the absorption matter, which makes a great number of distant cepheids unknown (Figure 4), a conclusion is drawn that the cepheids do not trace spiral arms with only one possible exception: the Carina arm. The cepheidz-coordinate distribution confirms the finding of Fernie (1968) that the cepheid layer is inclined towards the formal galactic plane. On the basis of cepheid space density, a number of vast star complexes (Table I) are identified in which other young objects, together with cepheids fall. The existence of these complexes is explained by star formation in giant molecular clouds. The cepheid mean period increase towards the galactic centre is most probably connected with the existence of a ring between the Sun and the centre of the Galaxy, with the highest density of hydrogen and the highest rate of star formation.     

On the intrinsic colours of cepheids

Some consequences from new data on the photometrically obtained intrinsic colours are considered. It is shown that the small amplitude and almost sinusoidal light-curve cepheids (Cs-subtype) increase their pulsation amplitude towards the red instability strip edge, differing from the other galactic cepheids. This feature is discussed in connection with Efremov's (1968) hypothesis that the Cs-cepheids first cross the instability strip from left to right. The galactic cepheid period-colour relation obtained by Dean, Warren and Cousins (1978) satisfies rather well the LMC cepheid observations and, consequently, considerations for the period-luminosity relations are made. The residuals from the PL relation proposed by us (AA line instead of Gascoigne's BB line in Figure 3) correlate with the colour residuals from the DWC period-colour relation V/(B–V) being equal to 2.7 (Figure 4). The luminosity effect as a possible cause of the descrepancy between the spectroscopic cepheid colours and the photometric colours is briefly discussed.     

依巴谷星表中的经典造父变星及其距离尺度

依巴谷星表给出了223颗经典造父变星的天体测量和光度观测资料。根据近年来的光谱和光度观测成果,从不同渠道收集了有关视向速度和光度等资料。基于Feast和Catchpole建立的PL关系,给出造父变星的距离估计。     

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).     

PL whistlers

Simultaneous ground and satellite VLF observations together with raytracing studies clearly establishes the existence of ground observed PL whistlers. The dynamic spectrum $\text{(?-ν-t}\text{shape}\text{)}$ of observed PL whistlers may be reproduced exactly by raytracing in TLG magnetospheric models consistent with lower ionosphere, topside ionosphere and equatorial density measurements. The Transition Level Gradient (TLG) model is based on the observation that the transition level altitude increases towards the plasmapause (Titheridge, 1976). PL ground whistlers (i) are observed downgoing over large latitudinal ranges, for up to 2000 km of satellite travel, by ISIS II at 1400 km altitude, (ii) have almost the same dynamic spectrum over the entire latitudinal range observed by ISIS II, (iii) are indistinguishable from ducted whistlers over the observed frequency range (i.e. linear Q for ? < 10 kHz), (iv) have nose frequencies > 16 kHz, (v) at 1400 km altitude have a lower latitudinal cutoff at L ～ 2 and a higher latitudinal cutoff between L ～ 3 and L ～ 4 and (vi) probably only occur at night-time during or immediately following disturbed magnetic activity.     

Period–colour and amplitude–colour relations in classical Cepheid variables – III. The Large Magellanic Cloud Cepheid models

Period–colour (PC) and amplitude–colour (AC) relations are studied for the Large Magellanic Cloud (LMC) Cepheids under the theoretical framework of the hydrogen ionization front (HIF)–photosphere interaction. LMC models are constructed with pulsation codes that include turbulent convection, and the properties of these models are studied at maximum, mean and minimum light. As with Galactic models, at maximum light the photosphere is located next to the HIF for the LMC models. However, very different behaviour is found at minimum light. The long-period  ( P > 10 d)  LMC models imply that the photosphere is disengaged from the HIF at minimum light, similar to the Galactic models, but there are some indications that the photosphere is located near the HIF for the short-period  ( P < 10 d)  LMC models. We also use the updated LMC data to derive empirical PC and AC relations at these phases. Our numerical models are broadly consistent with our theory and the observed data, though we discuss some caveats in the paper. We apply the idea of the HIF–photosphere interaction to explain recent suggestions that the LMC period–luminosity (PL) and PC relations are non-linear with a break at a period close to 10 d. Our empirical LMC PC and PL relations are also found to be non-linear with the F -test. Our explanation relies on the properties of the Saha ionization equation, the HIF–photosphere interaction and the way this interaction changes with the phase of pulsation and metallicity to produce the observed changes in the LMC PC and PL relations.     

Solar Microwave Bursts from Electron Populations with a 'Broken’ Energy Spectrum

Usually the gyrosynchrotron emission of microwave bursts from electron populations with a power-law (PL) energy distribution has been considered under the assumption that the spectral index of the distribution is constant over a wide range of energies. Meanwhile, there is strong evidence, in particular from hard X-ray and -ray, but also from cm/mm wavelength radio observations, that in many solar flare events the spectrum of the emitting electrons is characterized by a significant hardening at energies above 100–500 keV. We present some examples of calculated microwave burst spectra at cm/mm wavelengths taking into account the above evidence. It is shown that a break in the energy spectrum of the PL electrons can indeed result in a spectral hardening sometimes observed in microwave bursts at frequencies above 10–30 GHz.