Type I Error Control for Cluster Randomized Trials Under Varying Small Sample Structures

BackgroundLinear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs). Inference on parameters can be performed via Wald tests or likelihood ratio tests (LRT), but both approaches may give incorrect Type I error rates in common finite sample settings. The impact of different combinations of cluster size, number of clusters, intraclass correlation coefficient (ICC), and analysis approach on Type I error rates has not been well studied. Reviews of published CRTs find that small sample sizes are not uncommon, so the performance of different inferential approaches in these settings can guide data analysts to the best choices.MethodsUsing a random-intercept LMM stucture, we use simulations to study Type I error rates with the LRT and Wald test with different degrees of freedom (DF) choices across different combinations of cluster size, number of clusters, and ICC.ResultsOur simulations show that the LRT can be anti-conservative when the ICC is large and the number of clusters is small, with the effect most pronouced when the cluster size is relatively large. Wald tests with the between-within DF method or the Satterthwaite DF approximation maintain Type I error control at the stated level, though they are conservative when the number of clusters, the cluster size, and the ICC are small.ConclusionsDepending on the structure of the CRT, analysts should choose a hypothesis testing approach that will maintain the appropriate Type I error rate for their data. Wald tests with the Satterthwaite DF approximation work well in many circumstances, but in other cases the LRT may have Type I error rates closer to the nominal level

Precursors prior to Type IIn supernova explosions are common: precursor rates, properties, and correlations

There is a growing number of supernovae (SNe), mainly of Type IIn, which present an outburst prior to their presumably final explosion. These precursors may affect the SN display, and are likely related to some poorly charted phenomena in the final stages of stellar evolution. Here we present a sample of 16 SNe IIn for which we have Palomar Transient Factory (PTF) observations obtained prior to the SN explosion. By coadding these images taken prior to the explosion in time bins, we search for precursor events. We find five Type IIn SNe that likely have at least one possible precursor event, three of which are reported here for the first time. For each SN we calculate the control time. Based on this analysis we find that precursor events among SNe IIn are common: at the one-sided 99% confidence level, more than 50% of SNe IIn have at least one pre-explosion outburst that is brighter than absolute magnitude -14, taking place up to 1/3 yr prior to the SN explosion. The average rate of such precursor events during the year prior to the SN explosion is likely larger than one per year, and fainter precursors are possibly even more common. We also find possible correlations between the integrated luminosity of the precursor, and the SN total radiated energy, peak luminosity, and rise time. These correlations are expected if the precursors are mass-ejection events, and the early-time light curve of these SNe is powered by interaction of the SN shock and ejecta with optically thick circumstellar material.Comment: 15 pages, 20 figures, submitted to Ap

SN2010jp (PTF10aaxi): A Jet-Driven Type II Supernova

We present photometry and spectroscopy of the peculiar TypeII supernova (SN) 2010jp, also named PTF10aaxi. The light curve exhibits a linear decline with a relatively low peak absolute magnitude of only -15.9, and a low radioactive decay luminosity at late times that suggests a nickel mass below 0.003 $M_{\odot}$. Spectra of SN2010jp display an unprecedented triple-peaked H$\alpha$ line profile, showing: (1) a narrow (800 km/s) central component that suggests shock interaction with dense CSM; (2) high-velocity blue and red emission features centered at -12600 and +15400 km/s; and (3) broad wings extending from -22000 to +25000 km/s. These features persist during 100 days after explosion. We propose that this line profile indicates a bipolar jet-driven explosion, with the central component produced by normal SN ejecta and CSM interaction at mid latitudes, while the high-velocity bumps and broad line wings arise in a nonrelativistic bipolar jet. Two variations of the jet interpretation seem plausible: (1) A fast jet mixes 56Ni to high velocities in polar zones of the H-rich envelope, or (2) the reverse shock in the jet produces blue and red bumps in Balmer lines when a jet interacts with dense CSM. Jet-driven SNeII are predicted for collapsars resulting from a wide range of initial masses above 25 $M_{\odot}$ at sub-solar metallicity. This seems consistent with the SN host environment, which is either an extremely low-luminosity dwarf galaxy or very remote parts of an interacting pair of star-forming galaxies. It also seems consistent with the low 56Ni mass that may accompany black hole formation. We speculate that the jet survives to produce observable signatures because the star's H envelope was mostly stripped away by previous eruptive mass loss.Comment: 11 pages, 9 figures, submitted to MNRA

Slow-Speed Supernovae from the Palomar Transient Factory: Two Channels

Since the discovery of the unusual prototype SN 2002cx, the eponymous class of low-velocity, hydrogen-poor supernovae has grown to include at most another two dozen members identified from several heterogeneous surveys, in some cases ambiguously. Here we present the results of a systematic study of 1077 hydrogen-poor supernovae discovered by the Palomar Transient Factory, leading to nine new members of this peculiar class. Moreover we find there are two distinct subclasses based on their spectroscopic, photometric, and host galaxy properties: The "SN 2002cx-like" supernovae tend to be in later-type or more irregular hosts, have more varied and generally dimmer luminosities, have longer rise times, and lack a Ti II trough when compared to the "SN 2002es-like" supernovae. None of our objects show helium, and we counter a previous claim of two such events. We also find that these transients comprise 5.6+17-3.7% (90% confidence) of all SNe Ia, lower compared to earlier estimates. Combining our objects with the literature sample, we propose that these subclasses have two distinct physical origins.Comment: 49 pages, 36 figures, submitted to Ap

The Factory and The Beehive I. Rotation Periods For Low-Mass Stars in Praesepe

Stellar rotation periods measured from single-age populations are critical for investigating how stellar angular momentum content evolves over time, how that evolution depends on mass, and how rotation influences the stellar dynamo and the magnetically heated chromosphere and corona. We report rotation periods for 40 late-K to mid-M stars members of the nearby, rich, intermediate-age (~600 Myr) open cluster Praesepe. These rotation periods were derived from ~200 observations taken by the Palomar Transient Factory of four cluster fields from 2010 February to May. Our measurements indicate that Praesepe's mass-period relation transitions from a well-defined singular relation to a more scattered distribution of both fast and slow rotators at ~0.6 Msun. The location of this transition is broadly consistent with expectations based on observations of younger clusters and the assumption that stellar-spin down is the dominant mechanism influencing angular momentum evolution at 600 Myr. However, a comparison to data recently published for the Hyades, assumed to be coeval to Praesepe, indicates that the divergence from a singular mass-period relation occurs at different characteristic masses, strengthening the finding that Praesepe is the younger of the two clusters. We also use previously published relations describing the evolution of rotation periods as a function of color and mass to evolve the sample of Praesepe periods in time. Comparing the resulting predictions to periods measured in M35 and NGC 2516 (~150 Myr) and for kinematically selected young and old field star populations suggests that stellar spin-down may progress more slowly than described by these relations.Comment: To appear in the ApJ. 18 pages, 12 figures; version with higher resolution figures available at http://www.astro.columbia.edu/~marcel/papers/praesepe.pdf. Paper title inspired by local news; see http://tinyurl.com/redhone

Evidence for an FU Orionis-like Outburst from a Classical T Tauri Star

We present pre- and post-outburst observations of the new FU Orionis-like young stellar object PTF 10qpf (also known as LkHa 188-G4 and HBC 722). Prior to this outburst, LkHa 188-G4 was classified as a classical T Tauri star on the basis of its optical emission-line spectrum superposed on a K8-type photosphere, and its photometric variability. The mid-infrared spectral index of LkHa 188-G4 indicates a Class II-type object. LkHa 188-G4 exhibited a steady rise by ~1 mag over ~11 months starting in Aug. 2009, before a subsequent more abrupt rise of > 3 mag on a time scale of ~2 months. Observations taken during the eruption exhibit the defining characteristics of FU Orionis variables: (i) an increase in brightness by > 4 mag, (ii) a bright optical/near-infrared reflection nebula appeared, (iii) optical spectra are consistent with a G supergiant and dominated by absorption lines, the only exception being Halpha which is characterized by a P Cygni profile, (iv) near-infrared spectra resemble those of late K--M giants/supergiants with enhanced absorption seen in the molecular bands of CO and H_2O, and (v) outflow signatures in H and He are seen in the form of blueshifted absorption profiles. LkHa 188-G4 is the first member of the FU Orionis-like class with a well-sampled optical to mid-infrared spectral energy distribution in the pre-outburst phase. The association of the PTF 10qpf outburst with the previously identified classical T Tauri star LkHa 188-G4 (HBC 722) provides strong evidence that FU Orionis-like eruptions represent periods of enhanced disk accretion and outflow, likely triggered by instabilities in the disk. The early identification of PTF 10qpf as an FU Orionis-like variable will enable detailed photometric and spectroscopic observations during its post-outburst evolution for comparison with other known outbursting objects.Comment: 14 pages, 11 figures, ApJ accepte

Five new outbursting AM CVn systems discovered by the Palomar Transient Factory

We present five new outbursting AM CVn systems and one candidate discovered as part of an ongoing search for such systems using the Palomar Transient Factory (PTF). This is the first large-area, systematic search for AM CVn systems using only large-amplitude photometric variability to select candidates. Three of the confirmed systems and the candidate system were discovered as part of the PTF transient search. Two systems were found as part of a search for outbursts through the PTF photometric data base. We discuss the observed characteristics of each of these systems, including the orbital periods of two systems. We also consider the position of these systems, selected in a colour-independent survey, in colour–colour space and compare to systems selected solely by their colours. We find that the colours of our newly discovered systems do not differ significantly from those of previously known systems, but significant errors preclude a definitive answer

An Early and Comprehensive Millimetre and Centimetre Wave and X-ray Study of SN 2011dh: a Non-Equipartition Blast Wave Expanding into a Massive Stellar Wind

Only a handful of supernovae (SNe) have been studied in multiwavelengths from the radio to X-rays, starting a few days after the explosion. The early detection and classification of the nearby Type IIb SN 2011dh/PTF 11eon in M51 provides a unique opportunity to conduct such observations. We present detailed data obtained at one of the youngest phase ever of a core-collapse SN (days 3–12 after the explosion) in the radio, millimetre and X-rays; when combined with optical data, this allows us to explore the early evolution of the SN blast wave and its surroundings. Our analysis shows that the expanding SN shock wave does not exhibit equipartition (ϵe/ϵB ∼ 1000), and is expanding into circumstellar material that is consistent with a density profile falling like R−2. Within modelling uncertainties we find an average velocity of the fast parts of the ejecta of 15 000 ± 1800 km s−1, contrary to previous analysis. This velocity places SN 2011dh in an intermediate blast wave regime between the previously defined compact and extended SN Type IIb subtypes. Our results highlight the importance of early (∼1 d) high-frequency observations of future events. Moreover, we show the importance of combined radio/X-ray observations for determining the microphysics ratio ϵe/ϵB

Exploring the Optical Transient Sky with the Palomar Transient Factory

The Palomar Transient Factory (PTF) is a wide-field experiment designed to investigate the optical transient and variable sky on time scales from minutes to years. PTF uses the CFH12k mosaic camera, with a field of view of 7.9 deg^2 and a plate scale of 1 asec/pixel, mounted on the the Palomar Observatory 48-inch Samuel Oschin Telescope. The PTF operation strategy is devised to probe the existing gaps in the transient phase space and to search for theoretically predicted, but not yet detected, phenomena, such as fallback supernovae, macronovae, .Ia supernovae and the orphan afterglows of gamma-ray bursts. PTF will also discover many new members of known source classes, from cataclysmic variables in their various avatars to supernovae and active galactic nuclei, and will provide important insights into understanding galactic dynamics (through RR Lyrae stars) and the Solar system (asteroids and near-Earth objects). The lessons that can be learned from PTF will be essential for the preparation of future large synoptic sky surveys like the Large Synoptic Survey Telescope. In this paper we present the scientific motivation for PTF and describe in detail the goals and expectations for this experiment.Comment: 15 pages, 6 figures, submitted to PAS