Investigations of the Non-Linear LMC Cepheid Period-Luminosity Relation with Testimator and Schwarz Information Criterion Methods

In this paper, we investigate the linearity versus non-linearity of the Large Magellanic Cloud (LMC) Cepheid period-luminosity (P-L) relation using two statistical approaches not previously applied to this problem: the testimator method and the Schwarz Information Criterion (SIC). The testimator method is extended to multiple stages for the first time, shown to be unbiased and the variance of the estimated slope can be proved to be smaller than the standard slope estimated from linear regression theory. The Schwarz Information Criterion (also known as the Bayesian Information Criterion) is more conservative than the Akaike Information Criterion and tends to choose lower order models. By using simulated data sets, we verify that these statistical techniques can be used to detect intrinsically linear and/or non-linear P-L relations. These methods are then applied to independent LMC Cepheid data sets from the OGLE project and the MACHO project, respectively. Our results imply that there is a change of slope in longer period ranges for all of the data sets. This strongly supports previous results, obtained from independent statistical tests, that the observed LMC P-L relation is non-linear with a break period at/around 10 days.Comment: 9 pages, 5 figures and 3 tables, PASP accepte

Determination of Cepheid parameters by light-curve template-fitting

We describe techniques to characterise the light-curves of regular variable stars by applying principal component analysis (PCA) to a training set of high quality data, and to fit the resulting light-curve templates to sparse and noisy photometry to obtain parameters such as periods, mean magnitudes etc. The PCA approach allows us to efficiently represent the multi-band light-curve shapes of each variable, and hence quantitatively describe the average behaviour of the sample as a smoothly varying function of period, and also the range of variation around this average. In this paper we focus particularly on the utility of such methods for analysing HST Cepheid photometry, and present simulations which illustrate the advantages of our PCA template-fitting approach. These are: accurate parameter determination, including light-curve shape information; simultaneous fitting to multiple passbands; quantitative error analysis; objective rejection of variables with non Cepheid-like light-curves or those with potential period aliases. We also use PCA to confirm that Cepheid light-curve shapes are systematically different (at the same period) between the Milky Way (MW) and the Large and Small Magellanic Clouds (LMC, SMC), and consider whether light-curve shape might therefore be used to estimate the mean metallicities of Cepheid samples, thus allowing metallicity corrections to be applied to derived distance estimates.Comment: MNRAS in press: revised in light of referees comment

The Period-Luminosity Relation for the Large Magellanic Cloud Cepheids Derived from Spitzer Archival Data

Using Spitzer archival data from the SAGE (Surveying the Agents of a Galaxy's Evolution) program, we derive the Cepheid period-luminosity (P-L) relation at 3.6, 4.5, 5.8 and 8.0 microns for Large Magellanic Cloud (LMC) Cepheids. These P-L relations can be used, for example, in future extragalactic distance scale studies carried out with the James Webb Space Telescope. We also derive Cepheid period-color (P-C) relations in these bands and find that the slopes of the P-C relations are relatively flat. We test the nonlinearity of these P-L relations with the F statistical test, and find that the 3.6 micron, 4.5 micron and 5.8 micron P-L relations are consistent with linearity. However the 8.0 micron P-L relation presents possible but inconclusive evidence of nonlinearity.Comment: 10 pages, 11 figures and 6 tables, ApJ accepte

The extra-galactic Cepheid distance scale from LMC and Galactic period-luminosity relations

In this paper, we recalibrate the Cepheid distance to some nearby galaxies observed by the HST Key Project and the Sandage-Tammann-Saha group. We use much of the Key Project methodology in our analysis but apply new techniques, based on Fourier methods to estimate the mean of a sparsely sampled Cepheid light curve, to published extra-galactic Cepheid data. We also apply different calibrating PL relations to estimate Cepheid distances, and investigate the sensitivity of the distance moduli to the adopted calibrating PL relation. We re-determine the OGLELMC PL relations using a more conservative approach and also study the effect of using Galactic PL relations on the distance scale. For the Key Project galaxies after accounting for charge transfer effects, we find good agreement with an average discrepancy of -0.002 and 0.075 mag when using the LMC and Galaxy, respectively, as a calibrating PL relation. For NGC 4258 which has a geometric distance of 29.28 mag, we find a distance modulus of 29. 44 ± 0.06(random) mag, after correcting for metallicity. In addition we have calculated the Cepheid distance to 8 galaxies observed by the Sandage-Tammann-Saha group and find shorter distance moduli by -0.178 mag (mainly due to the use of different LMC PL relations) and -0.108 mag on average again when using the LMC and Galaxy, respectively, as a calibrating PL relation. However care must be taken to extrapolate these changed distances to changes in the resulting values of the Hubble constant because STS also use distances to NGC 3368 and 4414 and because STS calibration of SN la is often decoupled from the distance to the host galaxy through their use of differential extinction arguments. We also calculate the distance to all these galaxies using PL relations at maximum light and find very good agreement with mean light PL distances. However, after correcting for metallicity effects, the difference between the distance moduli obtained using the two sets of calibrating PL relations becomes negligible. This suggests that Cepheids in the LMC and Galaxy do follow different PL relations and constrains the sign for the coefficient of the metallicity correction, γ, to be negative, at least at the median period log(P) approximately equals 1.4, of the target galaxies

Calibrating the projection factor for Galactic Cepheids

The projection factor (p), which converts the radial velocity to pulsational velocity, is an important parameter in the Baade-Wesselink (BW) type analysis and distance scale work. The p-factor is either adopted as a constant or linearly depending on the logarithmic of pulsating periods. The aim of this work is to calibrate the p-factor if a Cepheid has both the BW distance and an independent distance measurement, and examine the p-factor for delta Cephei -- the prototype of classical Cepheids. We calibrated the p-factor for several Galactic Cepheids that have both the latest BW distances and independent distances either from Hipparcos parallaxes or main-sequence fitting distances to Cepheid-hosted stellar clusters. Based on 25 Cepheids, the calibrated p-factor relation is consistent with latest p-factor relation in literature. The calibrated p-factor relation also indicates that this relation may not be linear and may exhibit an intrinsic scatter. We also examined the discrepancy of empirical p-factors for delta Cephei, and found that the reasons for this discrepancy include the disagreement of angular diameters, the treatment of radial velocity data, and the phase interval adopted during the fitting procedure. Finally, we investigated the impact of the input p-factor in two BW methodologies for delta Cephei, and found that different p-factors can be adopted in these BW methodologies and yet result in the same angular diameters.Comment: 6 pages, 6 figures and 2 tables. A&A accepte

Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

Context. One challenge for measuring the Hubble constant using Classical Cepheids is the calibration of the Leavitt Law or period-luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results. Results. Our predicted geometric period-projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3 - 5%. Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in A&

Taxing the Informal Economy: The Current State of Knowledge and Agendas for Future Research

This paper reviews the literature on taxation of the informal economy, taking stock of key debates and drawing attention to recent innovations. Conventionally, the debate on whether to tax has frequently focused on the limited revenue potential, high cost of collection, and potentially adverse impact on small firms. Recent arguments have increasingly emphasised the more indirect benefits of informal taxation in relation to economic growth, broader tax compliance, and governance. More research is needed, we argue, into the relevant costs and benefits for all, including quasi-voluntary compliance, political and administrative incentives for reform, and citizen-state bargaining over taxation

Seismic Reflection Study of Upheaval Dome, Canyonlands National Park, Utah

The origin of Upheaval Dome, in Canyonlands National Park of southeastern Utah, has been a topic of controversy among geologists and planetary scientists. The structure has long been thought to have been created by salt diapirism from the underlying Paradox Formation. Recent studies have suggested that impact could have formed the dome. To test the various hypotheses, we acquired, processed, and interpreted seismic reflection data within and adjacent to the structure. Both conventionally stacked and prestack-migrated images show \u3c100 m relief in the Paradox Formation, contrary to salt diapirism hypotheses. Further, we have identified features within the images typical of impact structures, such as listric normal faults having displacements toward the center of the dome. Deformation occurs in two depth ranges, with the faulting that created the central uplift appearing only above the Hermosa Formation, in the upper 800 m of the structure. The images also suggest limited fracturing of the Hermosa and salt flow in the Paradox Formation, perhaps due to gravitational relaxation of the crater form. Our image of a nearly flat top of the Paradox salt strongly favors an impact origin for Upheaval Dome

The hybrid spatialities of transition: capitalism, legacy, and uneven urban economic restructuring

This paper conceptualises post-socialist urban economic geographies through the notion of hybrid spatialities that emerge from the mutual embeddedness of neoliberalism and socialist legacies. While the dismantling of state socialism was a massive moment towards the exacerbation of uneven development, ironically it is the socialist-era spatial legacy that has become the single major differentiating factor for the economic status of cities. This superficial overdetermination, however, masks the root causes of uneven development that must be seen in the logic of capitalism and its attendant practices which subsume legacy, recode its meaning, and recast the formerly equalitarian spaces as an uneven spatial order. The authors argue that the socialist legacy, rather than being an independent carrier of history, has been alienated from its history to become an infrastructure of neoliberalisation, conducive to capitalist process. The paper draws specifically on the experiences of Russia, although its reflections should reverberate much more broadly