Approximating RR Lyrae light curves using cubic polynomials

In this paper, we use cubic polynomials to approximate RR Lyrae light curves and apply the method to HST data of RR Lyraes in the halo of M31. We compare our method to the standard method of Fourier decomposition and find that the method of cubic polynomials eliminates virtually all ringing effects and does so with significantly fewer parameters than the Fourier technique. Further, for RRc stars the parameters in the fit are all physical. Our study also reveals a number of additional periodicites in this data not found previously: we find 23 RRc stars, 29 RRab stars and 3 multiperiodic stars.Comment: 6 pages, MNRAS accepte

Period-colour and amplitude-colour relations in classical Cepheid variables IV: The multi-phase relations

The superb phase resolution and quality of the OGLE data on LMC and 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 days. However, our multi-phase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multi-phase 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 days.Comment: 12 pages, 1 table and 13 figures, MNRAS accepte

Principal Component Analysis of RR Lyrae light curves

In this paper, we analyze the structure of RRab star light curves using Principal Component Analysis. We find this is a very efficient way to describe many aspects of RRab light curve structure: in many cases, a Principal Component fit with 9 parameters can describe a RRab light curve including bumps whereas a 17 parameter Fourier fit is needed. As a consequence we show statistically why the amplitude is also a good summary of the structure of a RR Lyrae light curve. We also use our analysis to derive an empirical relation relating absolute magnitude to light curve structure. In comparing this formula to those derived from exactly the same dataset but using Fourier parameters, we find that the Principal Component Analysis approach has disticnt advantages. These advantages are, firstly, that the errors on the coefficients in such formulae are smaller, and secondly, that the correlation between Principal Components is significantly smaller than the correlation between Fourier amplitudes. These two factors lead to reduced formal errors, in some cases estimated to be a factor of 2, on the eventual fitted value of the absolute magnitude. This technique will prove very useful in the analysis of data from existing large scale survey projects concerning variable stars.Comment: 8 pages, 10 figures, revised version, accepted for publication to MNRA

Period Color and Amplitude Color relations for MACHO project LMC RR Lyraes

In this paper, we analyze period color and amplitude color relations at minimum, mean and maximum $V$ band light for 6391 RRab stars in the Large Magellanic Cloud obtained by the MACHO project. Specifically, we find that color and amplitude are nearly independent of period at minimum light but that there exists a definite relation between period and color and amplitude and color at maximum light. These two properties are easily explained by the application of the Stefan Boltzmann law and the interaction of the photosphere and hydrogen ionization front at minimum light. When we examine the slope of the period color relation as a function of phase, we find that the slope varies significantly with phase and is small for a wide range of phases around minimum light. This suggests that another factor that needs to be considered when trying to understand RR Lyrae observed properties is their behavior at different phases during a pulsation cycle.Comment: Sumitted for publication to MNRAS Letter

Period-color and amplitude-color 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 SMC (Small Magellanic Cloud). We compare these theoretical relations with those from observations. The theoretical relations are in general 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, LMC and SMC. Our explanation relies on the hydrogen ionization front-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.Comment: 10 pages, 6 figures and 6 tables, MNRAS accepte

Period-color and amplitude-color 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 behavior is found at minimum light. The long period (P>10days) 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 days) 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 days. Our empirical 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 Cepheid PC and PL relations.Comment: 19 pages, 6 tables and 18 figures, MNRAS accepte

International poverty projections

The authors investigate the methodology used in projections of international poverty - particularly those used in many World Bank documents. The methodology, as developed by Ahluwalia, Carter, and Chenery (1979) in an influential paper, is examined critically and subjected to sensitivity analysis. It was found that their projections of poverty are not robust to reasonable changes and improvements in the methodology; in some cases, even the projections'time trend is reversed. Thus, analysts and policymakers should treat such global forecasts of poverty with caution.Economic Theory&Research,Achieving Shared Growth,Economic Conditions and Volatility,Inequality,Environmental Economics&Policies

Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations