Melnikov theory to all orders and Puiseux series for subharmonic solutions

We study the problem of subharmonic bifurcations for analytic systems in the plane with perturbations depending periodically on time, in the case in which we only assume that the subharmonic Melnikov function has at least one zero. If the order of zero is odd, then there is always at least one subharmonic solution, whereas if the order is even in general other conditions have to be assumed to guarantee the existence of subharmonic solutions. Even when such solutions exist, in general they are not analytic in the perturbation parameter. We show that they are analytic in a fractional power of the perturbation parameter. To obtain a fully constructive algorithm which allows us not only to prove existence but also to obtain bounds on the radius of analyticity and to approximate the solutions within any fixed accuracy, we need further assumptions. The method we use to construct the solution -- when this is possible -- is based on a combination of the Newton-Puiseux algorithm and the tree formalism. This leads to a graphical representation of the solution in terms of diagrams. Finally, if the subharmonic Melnikov function is identically zero, we show that it is possible to introduce higher order generalisations, for which the same kind of analysis can be carried out.Comment: 30 pages, 6 figure

Evidence for a Compact Wolf-Rayet Progenitor for the Type Ic Supernova PTF 10vgv

We present the discovery of PTF 10vgv, a Type Ic supernova (SN) detected by the Palomar Transient Factory, using the Palomar 48 inch telescope (P48). R-band observations of the PTF 10vgv field with P48 probe the SN emission from its very early phases (about two weeks before R-band maximum) and set limits on its flux in the week prior to the discovery. Our sensitive upper limits and early detections constrain the post-shock-breakout luminosity of this event. Via comparison to numerical (analytical) models, we derive an upper-limit of R ≾ 4.5 R_☉ (R ≾ 1 R_☉) on the radius of the progenitor star, a direct indication in favor of a compact Wolf-Rayet star. Applying a similar analysis to the historical observations of SN 1994I yields R ≾ 1/4 R_☉ for the progenitor radius of this SN

An ASKAP Search for a Radio Counterpart to the First High-significance Neutron Star-Black Hole Merger LIGO/Virgo S190814bv

We present results from a search for a radio transient associated with the LIGO/Virgo source S190814bv, a likely neutron star-black hole (NSBH) merger, with the Australian Square Kilometre Array Pathfinder. We imaged a 30 deg2 field at ΔT = 2, 9, and 33 days post-merger at a frequency of 944 MHz, comparing them to reference images from the Rapid ASKAP Continuum Survey observed 110 days prior to the event. Each epoch of our observations covers 89% of the LIGO/Virgo localization region. We conducted an untargeted search for radio transients in this field, resulting in 21 candidates. For one of these, AT2019osy, we performed multiwavelength follow-up and ultimately ruled out the association with S190814bv. All other candidates are likely unrelated variables, but we cannot conclusively rule them out. We discuss our results in the context of model predictions for radio emission from NSBH mergers and place constrains on the circum-merger density and inclination angle of the merger. This survey is simultaneously the first large-scale radio follow-up of an NSBH merger, and the most sensitive widefield radio transients search to-date

On the stellar content of the Carina dwarf spheroidal galaxy

We present U,B,V,I photometry of the Carina dwarf spheroidal galaxy, based on more than 4,000 CCD images. Special attention was given to the photometric calibration, and the precision for the B,V,I bands is better than 0.01 mag. We compared in the V,B-V and V,B-I color-magnitude diagrams (CMDs) Carina with three Globular Clusters (GCs, M53, M55, M79). We find that only the more metal-poor GCs (M55, [Fe/H]=-1.85; M53, [Fe/H]=-2.02 dex) provide a good match with the Carina giant branch. We performed a similar comparison in the V,V-I CMD with three SMC intermediate-age clusters (IACs, Kron3, NGC339, Lindsay38). We find that the color extent of the SGB of the two more metal-rich IACs (Kron3, [Fe/H]=-1.08; NGC339, [Fe/H]=-1.36 dex) is smaller than the range among Carina's intermediate-age stars. However, the ridge line of the more metal-poor IAC (Lindsay38, [Fe/H]=-1.59 dex) agrees quite well with the Carina intermediate-age stars. These findings indicate that Carina's old stellar population is metal-poor and seems to have a limited spread in metallicity (Delta [Fe/H]=0.2--0.3 dex). Carina intermediate-age stars can hardly be more metal-rich than Lindsay38 and its spread in metallicity appears modest. We also find that the synthetic CMD constructed assuming a metallicity spread of 0.5 dex for intermediate-age stars predicts evolutionary features not supported by observations. The above results are at odds with recent spectroscopic investigations suggesting that Carina stars cover a broad range in metallicity (Delta [Fe/H]~1--2 dex). We present a new method to estimate the metallicity of complex stellar systems using the difference in color between the red clump and the middle of the RR Lyrae instability strip. The observed colors of Carina's evolved stars indicate a metallicity of [Fe/H]=-1.70+-0.19 dex, which agrees quite well with spectroscopic measurements.Comment: Accepted on PASP, 12 pages, 6 figure

On the distance and reddening of the starburst galaxy IC10

We present deep and accurate optical photometry of the Local Group starburst galaxy IC10. The photometry is based on two sets of images collected with the Advanced Camera for Surveys and with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. We provide new estimates of the Red Giant Branch tip (TRGB) magnitude, m_{F814W}^{TRGB}=21.90+-0.03, and of the reddening, E(B-V)=0.78+-0.06, using field stars in the Small Magellanic Cloud (SMC) as a reference. Adopting the SMC and two globulars, Omega Centauri and 47 Tucanae, as references we estimate the distance modulus to IC10: independent calibrations give weighted average distances of mu=24.51+-0.08 (TRGB) and mu=24.56+-0.08 (RR Lyrae). We also provide a new theoretical calibration for the TRGB luminosity, and using these predictions we find a very similar distance to IC10 (mu~24.60+-0.15). These results suggest that IC10 is a likely member of the M31 subgroup.Comment: 4 pages, 4 figures, ApJ Letters accepte

A pulsational distance to Omega Centauri based on Near-Infrared Period-Luminosity relations of RR Lyrae stars

We present new Near-Infrared (J,K) magnitudes for 114 RR Lyrae stars in the globular cluster Omega Cen (NGC 5139) which we combine with data from the literature to construct a sample of 180 RR Lyrae stars with J and K mean magnitudes on a common photometric system. This is presently the largest such sample in any stellar system. We also present updated predictions for J,K-band Period-Luminosity relations for both fundamental and first-overtone RR Lyrae stars, based on synthetic horizontal branch models with metal abundance ranging from Z=0.0001 to Z=0.004. By adopting for the Omega Cen variables with measured metal abundances an alpha-element enhancement of a factor of 3 (about 0.5 dex) with respect to iron we find a true distance modulus of 13.70 (with a random error of 0.06 and a systematic error of 0.06), corresponding to a distance d=5.5 Kpc (with both random and systematic errors equal to 0.03 Kpc). Our estimate is in excellent agreement with the distance inferred for the eclipsing binary OGLEGC-17, but differ significantly from the recent distance estimates based on cluster dynamics and on high amplitude Delta Scuti stars.Comment: 24 pages, 7 figures, accepted for publication on The Astrophysical Journa

On the stellar content of the starburst galaxy IC10

We investigate the stellar content of the starburst dwarf galaxy IC10 using accurate and deep optical data collected with the Advanced Camera for Surveys and with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. The comparison between theory and observations indicates a clear change in age distribution when moving from the center toward the external regions. Moreover, empirical calibrators and evolutionary predictions suggest the presence of a spread in heavy element abundance of the order of one-half dex. The comparison between old and intermediate-age core He-burning models with a well defined overdensity in the color-magnitude diagram indicates the presence of both intermediate-age, red clump stars and of old, red horizontal branch stars.Comment: 7 pages, 4 figures, 1 table. Accepted for publication in ApJ

Light curves of hydrogen-poor Superluminous Supernovae from the Palomar Transient Factory

We investigate the light-curve properties of a sample of 26 spectroscopically confirmed hydrogen-poor superluminous supernovae (SLSNe-I) in the Palomar Transient Factory (PTF) survey. These events are brighter than SNe Ib/c and SNe Ic-BL, on average, by about 4 and 2~mag, respectively. The peak absolute magnitudes of SLSNe-I in rest-frame $g$ band span $-22\lesssim M_g \lesssim-20$~mag, and these peaks are not powered by radioactive $^{56}$Ni, unless strong asymmetries are at play. The rise timescales are longer for SLSNe than for normal SNe Ib/c, by roughly 10 days, for events with similar decay times. Thus, SLSNe-I can be considered as a separate population based on photometric properties. After peak, SLSNe-I decay with a wide range of slopes, with no obvious gap between rapidly declining and slowly declining events. The latter events show more irregularities (bumps) in the light curves at all times. At late times, the SLSN-I light curves slow down and cluster around the $^{56}$Co radioactive decay rate. Powering the late-time light curves with radioactive decay would require between 1 and 10${\rm M}_\odot$ of Ni masses. Alternatively, a simple magnetar model can reasonably fit the majority of SLSNe-I light curves, with four exceptions, and can mimic the radioactive decay of $^{56}$Co, up to $\sim400$ days from explosion. The resulting spin values do not correlate with the host-galaxy metallicities. Finally, the analysis of our sample cannot strengthen the case for using SLSNe-I for cosmology.Comment: 120 pages, 48 figures, 78 tables. ApJ in pres

Impact of Sleep and Circadian Disruption on Energy Balance and Diabetes: A Summary of Workshop Discussions

A workshop was held at the National Institute for Diabetes and Digestive and Kidney Diseases with a focus on the impact of sleep and circadian disruption on energy balance and diabetes. The workshop identified a number of key principles for research in this area and a number of specific opportunities. Studies in this area would be facilitated by active collaboration between investigators in sleep/circadian research and investigators in metabolism/diabetes. There is a need to translate the elegant findings from basic research into improving the metabolic health of the American public. There is also a need for investigators studying the impact of sleep/circadian disruption in humans to move beyond measurements of insulin and glucose and conduct more in-depth phenotyping. There is also a need for the assessments of sleep and circadian rhythms as well as assessments for sleep-disordered breathing to be incorporated into all ongoing cohort studies related to diabetes risk. Studies in humans need to complement the elegant short-term laboratory-based human studies of simulated short sleep and shift work etc. with studies in subjects in the general population with these disorders. It is conceivable that chronic adaptations occur, and if so, the mechanisms by which they occur needs to be identified and understood. Particular areas of opportunity that are ready for translation are studies to address whether CPAP treatment of patients with pre-diabetes and obstructive sleep apnea (OSA) prevents or delays the onset of diabetes and whether temporal restricted feeding has the same impact on obesity rates in humans as it does in mice