The Core Collapse Supernova Rate from the SDSS-II Supernova Survey

We use the Sloan Digital Sky Survey II Supernova Survey (SDSS-II SNS) data to measure the volumetric core collapse supernova (CCSN) rate in the redshift range (0.03<z<0.09). Using a sample of 89 CCSN we find a volume-averaged rate of (1.06 +/- 0.19) x 10**(-4)/(yr Mpc**3) at a mean redshift of 0.072 +/- 0.009. We measure the CCSN luminosity function from the data and consider the implications on the star formation history.Comment: Minor corrections to references and affiliations to conform with published versio

On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

From network structure to network reorganization: implications for adult neurogenesis

Networks can be dynamical systems that undergo functional and structural reorganization. One example of such a process is adult hippocampal neurogenesis, in which new cells are continuously born and incorporate into the existing network of the dentate gyrus region of the hippocampus. Many of these introduced cells mature and become indistinguishable from established neurons, joining the existing network. Activity in the network environment is known to promote birth, survival and incorporation of new cells. However, after epileptogenic injury, changes to the connectivity structure around the neurogenic niche are known to correlate with aberrant neurogenesis. The possible role of network-level changes in the development of epilepsy is not well understood. In this paper, we use a computational model to investigate how the structural and functional outcomes of network reorganization, driven by addition of new cells during neurogenesis, depend on the original network structure. We find that there is a stable network topology that allows the network to incorporate new neurons in a manner that enhances activity of the persistently active region, but maintains global network properties. In networks having other connectivity structures, new cells can greatly alter the distribution of firing activity and destroy the initial activity patterns. We thus find that new cells are able to provide focused enhancement of network only for small-world networks with sufficient inhibition. Network-level deviations from this topology, such as those caused by epileptogenic injury, can set the network down a path that develops toward pathological dynamics and aberrant structural integration of new cells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85406/1/ph10_4_046008.pd

Cloud Atlas: Weak Color Modulations Due to Rotation in the Planetary-mass Companion GU Psc b and 11 Other Brown Dwarfs

Among the greatest challenges in understanding ultracool brown dwarf and exoplanet atmospheres is the evolution of cloud structure as a function of temperature and gravity. In this study, we present the rotational modulations of GU Psc b—a rare mid-T spectral type planetary-mass companion at the end of the L/T spectral type transition. Based on the Hubble Space Telescope/WFC3 1.1–1.67 μm time-series spectra, we observe a quasi-sinusoidal light curve with a peak-to-trough flux variation of 2.7% and a minimum period of 8 h. The rotation-modulated spectral variations are weakly wavelength-dependent, or largely gray between 1.1 and 1.67 μm. The gray modulations indicate that heterogeneous clouds are present in the photosphere of this low-gravity mid-T dwarf. We place the color and brightness variations of GU Psc b in the context of rotational modulations reported for mid-L to late-T dwarfs. Based on these observations, we report a tentative trend: mid-to-late T dwarfs become slightly redder in J − H color with increasing J-band brightness, while L dwarfs become slightly bluer with increasing brightness. If this trend is verified with more T-dwarf samples, it suggests that in addition to the mostly gray modulations, there is a second-order spectral-type dependence on the nature of rotational modulations

Cloud Atlas: High-precision HST/WFC3/IR Time-resolved Observations of Directly Imaged Exoplanet HD 106906b

HD 106906b is an ~11M_(Jup), ~15 Myr old directly imaged exoplanet orbiting at an extremely large distance from its host star. The wide separation (7 11) between HD 106906b and its host star greatly reduces the difficulty in direct-imaging observations, making it one of the most favorable directly imaged exoplanets for detailed characterization. In this paper, we present HST/WFC3/IR time-resolved observations of HD 106906b in the F127M, F139M, and F153M bands. We have achieved ~1% precision in the lightcurves in all three bands. The F127M lightcurve demonstrates marginally detectable (2.7σ significance) variability with a best-fitting period of 4 hr, while the lightcurves in the other two bands are consistent with flat lines. We construct primary-subtracted deep images and use these images to exclude additional companions to HD 106906 that are more massive than 4 M_(Jup) and locate at projected distances of more than ~500 au. We measure the astrometry of HD 106906b in two HST/WFC3 epochs and achieve precisions better than 2.5 mas. The position angle and separation measurements do not deviate from those in the 2004 HST/ACS/HRC images for more than 1σ uncertainty. We provide the HST/WFC3 astrometric results for 25 background stars that can be used as reference sources in future precision astrometry studies. Our observations also provide the first 1.4 μm water band photometric measurement for HD 106906b. HD 106906b's spectral energy distribution and the best-fitting BT-Settl model have an inconsistency in the 1.4 μm water absorption band, which highlights the challenges in modeling atmospheres of young planetary-mass objects

Cloud Atlas: Rotational Spectral Modulations and potential Sulfide Clouds in the Planetary-mass, Late T-type Companion Ross 458C

Measurements of photometric variability at different wavelengths provide insights into the vertical cloud structure of brown dwarfs and planetary-mass objects. In seven Hubble Space Telescope consecutive orbits, spanning $\sim$10 h of observing time}, we obtained time-resolved spectroscopy of the planetary-mass T8-dwarf Ross 458C using the near-infrared Wide Field Camera 3. We found spectrophotometric variability with a peak-to-peak signal of 2.62$\pm$0.02 % (in the 1.10-1.60~$\mu$m white light curve). Using three different methods, we estimated a rotational period of 6.75$\pm$1.58~h for the white light curve, and similar periods for narrow $J$- and $H$- band light curves. Sine wave fits to the narrow $J$- and $H$-band light curves suggest a tentative phase shift between the light curves with wavelength when we allow different periods between both light curves. If confirmed, this phase shift may be similar to the phase shift detected earlier for the T6.5 spectral type 2MASS J22282889-310262. We find that, in contrast with 2M2228, the variability of Ross~458C shows evidence for a {color trend} within the narrow $J$-band, but gray variations in the narrow $H$-band. The spectral time-resolved variability of Ross 458C might be potentially due to heterogeneous sulfide clouds in the atmosphere of the object. Our discovery extends the study of spectral modulations of condensate clouds to the coolest T dwarfs, planetary-mass companions.Comment: Accepted in ApJ

Cloud Atlas: High-Contrast Time-Resolved Observations of Planetary-Mass Companions

Directly-imaged planetary-mass companions offer unique opportunities in atmospheric studies of exoplanets. They share characteristics of both brown dwarfs and transiting exoplanets, therefore, are critical for connecting atmospheric characterizations for these objects. Rotational phase mapping is a powerful technique to constrain the condensate cloud properties in ultra-cool atmospheres. Applying this technique to directly-imaged planetary-mass companions will be extremely valuable for constraining cloud models in low mass and surface gravity atmospheres and for determining the rotation rate and angular momentum of substellar companions. Here, we present Hubble Space Telescope Wide Field Camera 3 near-infrared time-resolved photometry for three planetary-mass companions, AB Pic B, 2M0122B, and 2M1207b. Using two-roll differential imaging and hybrid point spread function modeling, we achieve sub-percent photometric precision for all three observations. We find tentative modulations ($<\!\!2\sigma$) for AB Pic B and 2M0122B but cannot reach conclusive results on 2M1207b due to strong systematics. The relatively low significance of the modulation measurements cannot rule out the hypothesis that these planetary-mass companions have the same vertical cloud structures as brown dwarfs. Our rotation rate measurements, combined with archival period measurements of planetary-mass companions and brown dwarfs do not support a universal mass-rotation relation. The high precision of our observations and the high occurrence rates of variable low-surface gravity objects encourage high-contrast time-resolved observations with the James Webb Space Telescope.Comment: Accepted for publication in AAS Journa

Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems

Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become phase-locked to its radiated phonon waves, hence the mobility of the chain may decrease as one increases the external force.Comment: 4 figures, to appear in Phys. Rev.

Cloud Atlas: Discovery of Rotational Spectral Modulations in a Low-mass, L-type Brown Dwarf Companion to a Star

Observations of rotational modulations of brown dwarfs and giant exoplanets allow the characterization of condensate cloud properties. As of now rotational spectral modulations have only been seen in three L-type brown dwarfs. We report here the discovery of rotational spectral modulations in LP261-75B, an L6-type intermediate surface gravity companion to an M4.5 star. As a part of the Cloud Atlas Treasury program we acquired time-resolved Wide Field Camera 3 grism spectroscopy (1.1--1.69~$\mu$m) of LP261-75B. We find gray spectral variations with the relative amplitude displaying only a weak wavelength dependence and no evidence for lower-amplitude modulations in the 1.4~$\mu$m water band than in the adjacent continuum. The likely rotational modulation period is 4.78$\pm$0.95 h, although the rotational phase is not well sampled. The minimum relative amplitude in the white light curve measured over the whole wavelength range is 2.41$\pm$0.14\%. We report an unusual light curve with seemingly three peaks approximately evenly distributed in rotational phase. The spectral modulations suggests that the upper atmosphere cloud properties in {LP261-75B} are similar to two other mid-L dwarfs of typical infrared colors, but differ from that of the extremely red L-dwarf WISE0047