Outside the Wall: Hydrodynamics of Type I Supernovae Interacting with a Partially Swept-Up Circumstellar Medium

Explaining the observed diversity of supernovae (SNe) and the physics of explosion requires knowledge of their progenitor stars, which can be obtained by constraining the circumstellar medium (CSM). Models of the SN ejecta colliding with CSM are necessary to infer the structure of the CSM and tie it back to a progenitor model. Recent SNe I revealed CSM concentrated at a distance $r\sim10^16$ cm, for which models of SN interaction are extremely limited. In this paper, we assume the concentrated region is a "wall" representing swept-up material, and unswept material lies outside the wall. We simulate one-dimensional hydrodynamics of SNe Ia & Ib impacting 300 unique CSM configurations using RT1D, which captures the Rayleigh-Taylor instability. We find that the density ratio between the wall and ejecta -- denoted $A_0$ or "wall height" -- is key, and higher walls deviate more from self-similar evolution. Functional fits accounting for $A_0$ are presented for the forward shock radius evolution. We show that higher walls have more degeneracy between CSM properties in the deceleration parameter, slower shocks, deeper-probing reverse shocks, slower shocked ejecta, less ejecta mass than CSM in the shock, and more mixing of ejecta into the CSM at early times. We analyze observations of SN 2014C (Type Ib) and suggest that it had a moderately high wall ($10 < A_0 < 200$) and wind-like outer CSM. We also postulate an alternate interpretation for the radio data of SN 2014C, that the radio rise occurs in the wind rather than the wall. Finally, we find that hydrodynamic measurements at very late times cannot distinguish the presence of a wall, except perhaps as an anomalously wide shock region.Comment: 17 pages, 13 figures, accepted to Ap

Skill set profile clustering based on student capability vectors computed from online tutoring data

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. To address this, we introduce a capability matrix showing for each skill the proportion correct on all items tried by each student involving that skill. We apply variations of common clustering methods to this matrix and discuss conditioning on sparse subspaces. We demonstrate the feasibility and scalability of our method on several simulated datasets and illustrate the difficulties inherent in real data using a subset of online mathematics tutor data. We also comment on the interpretability and application of the results for teachers

Skill set profile clustering: the empty K-means algorithm with automatic specification of starting cluster centers

While students’ skill set profiles can be estimated with formal cognitive diagnosis models [8], their computational complexity makes simpler proxy skill estimates attractive [1, 4, 6]. These estimates can be clustered to generate groups of similar students. Often hierarchical agglomerative clustering or k-means clustering is utilized, requiring, for K skills, the specification of 2^K clusters. The number of skill set profiles/clusters can quickly become computationally intractable. Moreover, not all profiles may be present in the population. We present a flexible version of k-means that allows for empty clusters. We also specify a method to determine efficient starting centers based on the Q-matrix. Combining the two substantially improves the clustering results and allows for analysis of data sets previously thought impossible

Against the Wind: Radio Light Curves of Type Ia Supernovae Interacting with Low-Density Circumstellar Shells

For decades, a wide variety of observations spanning the radio through optical and on to the x-ray have attempted to uncover signs of type Ia supernovae (SNe Ia) interacting with a circumstellar medium (CSM). The goal of these studies is to constrain the nature of the hypothesized SN Ia mass-donor companion. A continuous CSM is typically assumed when interpreting observations of interaction. However, while such models have been successfully applied to core-collapse SNe, the assumption of continuity may not be accurate for SNe Ia, as shells of CSM could be formed by pre-supernova eruptions (novae). In this work, we model the interaction of SNe with a spherical, low density, finite-extent CSM and create a suite of synthetic radio synchrotron light curves. We find that CSM shells produce sharply peaked light curves, and identify a fiducial set of models that all obey a common evolution and can be used to generate radio light curves for interaction with an arbitrary shell. The relations obeyed by the fiducial models can be used to deduce CSM properties from radio observations; we demonstrate this by applying them to the non-detections of SN 2011fe and SN 2014J. Finally, we explore a multiple shell CSM configuration and describe its more complicated dynamics and resultant radio light curves.Comment: 15 pages, 11 figures, ApJ accepte

Intermediate Palomar Transient Factory: Realtime Image Subtraction Pipeline

A fast-turnaround pipeline for realtime data reduction plays an essential role in discovering and permitting follow-up observations to young supernovae and fast-evolving transients in modern time-domain surveys. In this paper, we present the realtime image subtraction pipeline in the intermediate Palomar Transient Factory. By using high-performance computing, efficient database, and machine learning algorithms, this pipeline manages to reliably deliver transient candidates within ten minutes of images being taken. Our experience in using high performance computing resources to process big data in astronomy serves as a trailblazer to dealing with data from large-scale time-domain facilities in near future.Comment: 18 pages, 6 figures, accepted for publication in PAS

Low Hubble Constant from Type Ia Supernovae by van den Bergh's Method

An interesting way to calibrate the absolute magnitudes of remote Type Ia supernovae (SNe Ia) that are well out in the Hubble flow, and thus determine the value of the Hubble constant, H_0, has been introduced by van den Bergh. His approach relies on calculations of the peak absolute magnitudes and broad--band colors for SN Ia explosion models. It does not require any corrections for extinction by interstellar dust, and no SNe Ia are excluded on grounds of peculiarity. Within the last few years distances have been determined to the parent galaxies of six SNe Ia by means of Cepheid variables. Cepheid--based distances also have become available for three other SNe Ia if one is willing to use the distance to a galaxy in the same group in lieu of the distance to the parent galaxy itself. Here we determine the value of H_0 in a way that is analogous to that of van den Bergh, but now using Cepheid--based distances instead of calculated light curves. We obtain H_0 = 55 km/s/Mpc. This value, with Lambda=0 and Omega=1, corresponds to a cosmic expansion time of 12 Gyr, which is consistent with several recent determinations of the ages of globular clusters.Comment: Latex, 4 pages, 1 table, 1 figure, Submitted to Nature March 28, 1996. PostScript version available at http://www.nhn.ou.edu/~nugent

The Host Galaxies of Sub-Chandrasekhar Mass Type Ia Supernovae

In recent years, there has been ample evidence for the existence of multiple progenitor pathways that can result in Type Ia supernova (SNe Ia), including SNe Ia of sub-Chandrasekhar mass origin best distinguished by their redder colors and higher Si II velocities near peak brightness. These SNe can contaminate the population of normal events used for cosmological analyses, creating unwanted biases in the final analyses. Given that many current and future surveys using SNe Ia as cosmological probes will not have the resources to take a spectrum of all the events, likely only getting host redshifts long after the SNe Ia have faded, we need to turn to methods that could separate these populations based purely on photometry or host properties. Here, we present a study of a sample of well observed, nearby SNe Ia and their hosts to determine if there are significant enough difference between these populations that can be discerned only from the stellar population properties of their hosts. Our results indicate that the global host properties, including star formation, stellar mass, stellar population age, and dust attenuation, of sub-Chandrasekhar mass explosions do not differ significantly from those of normal mass origin. However, we do find evidence using Na I D equivalent widths that the local environments of sub-Chandrasekhar mass explosions are more dust-affected than normal SNe Ia. Future work requires strengthening photometric probes of sub-Chandrasekhar SNe and their local environments to distinguish these events.Comment: 16 pages, 10 figures, 2 tables, submitte

The volumetric rate of calcium-rich transients in the local universe

We present a measurement of the volumetric rate of `calcium-rich' optical transients in the local universe, using a sample of three events from the Palomar Transient Factory (PTF). This measurement builds on a detailed study of the PTF transient detection efficiencies, and uses a Monte Carlo simulation of the PTF survey. We measure the volumetric rate of calcium-rich transients to be higher than previous estimates: $1.21^{+1.13}_{-0.39}\times10^{-5}$ events yr$^{-1}$ Mpc$^{-3}$. This is equivalent to 33-94% of the local volumetric type Ia supernova rate. This calcium-rich transient rate is sufficient to reproduce the observed calcium abundances in galaxy clusters, assuming an asymptotic calcium yield per calcium-rich event of ~0.05$\mathrm{M}_{\odot}$. We also study the PTF detection efficiency of these transients as a function of position within their candidate host galaxies. We confirm as a real physical effect previous results that suggest calcium-rich transients prefer large physical offsets from their host galaxies.Comment: Accepted for publication in ApJ. 9 pages, 5 figure