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We investigate the spectroscopic characteristics of Intermediate Luminosity Red Transients (ILRTs), a class of elusive objects with peak luminosity between that of classical novae and standard supernovae. We present the extensive optical and near-infrared (NIR) spectroscopic monitoring of four ILRTs, namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd and AT 2019udc. First we focus on the evolution of the most prominent spectral features observed in the low resolution spectra, then we discuss more in detail the high resolution spectrum collected for NGC 300 2008OT-1 with the Very Large Telescope equipped with UVES. Finally we analyse late time spectra of NGC 300 2008OT-1 and AT 2019ahd through comparisons with both synthetic and observed spectra. Balmer and Ca lines dominate the optical spectra, revealing the presence of slowly moving circumstellar medium (CSM) around the objects. The line luminosity of H$\alpha$, H$\beta$ and Ca II NIR triplet presents a double peaked evolution with time, possibly indicative of interaction between fast ejecta and the slow CSM. The high resolution spectrum of NGC 300 2008OT-1 reveals a complex circumstellar environment, with the transient being surrounded by a slow ($\sim$30 km s$^{-1}$) progenitor wind. At late epochs, optical spectra of NGC 300 2008OT-1 and AT 2019ahd show broad ($\sim$2500 km s$^{-1}$) emission features at $\sim$6170 A and $\sim$7000 A which are unprecedented for ILRTs. We find that these lines originate most likely from the blending of several narrow lines, possibly of iron-peak elements., Comment: 28 pages, 19 figures. Submitted to A&A

Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization, a fundamental interpretable data analysis model, and has applications in hyperspectral unmixing and topic modeling. To obtain identifiable solutions, a standard approach is to find minimum-volume solutions. By taking advantage of the duality/polarity concept for polytopes, we convert minimum-volume SSMF in the primal space to a maximum-volume problem in the dual space. We first prove the identifiability of this maximum-volume dual problem. Then, we use this dual formulation to provide a novel optimization approach which bridges the gap between two existing families of algorithms for SSMF, namely volume minimization and facet identification. Numerical experiments show that the proposed approach performs favorably compared to the state-of-the-art SSMF algorithms., Comment: 31 pages, 10 figures

We study the spectral properties of flipped Toeplitz matrices of the form $H_n(f)=Y_nT_n(f)$, where $T_n(f)$ is the $n\times n$ Toeplitz matrix generated by the function $f$ and $Y_n$ is the $n\times n$ exchange (or flip) matrix having $1$ on the main anti-diagonal and $0$ elsewhere. In particular, under suitable assumptions on $f$, we establish an alternating sign relationship between the eigenvalues of $H_n(f)$, the eigenvalues of $T_n(f)$, and the quasi-uniform samples of $f$. Moreover, after fine-tuning a few known theorems on Toeplitz matrices, we use them to provide localization results for the eigenvalues of $H_n(f)$. Our study is motivated by the convergence analysis of the minimal residual (MINRES) method for the solution of real non-symmetric Toeplitz linear systems of the form $T_n(f)\mathbf x=\mathbf b$ after pre-multiplication of both sides by $Y_n$, as suggested by Pestana and Wathen.

We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output channel. Our analysis is based on the Puiseux series expansion of the eigenvalue decomposition of analytic para-Hermitian matrices on the complex unit circumference. We study the case in which the rectangular matrix does not admit a full analytic singular value factorization, either due to partly multiplexed systems or to sign ambiguity. We show how to find an SVD factorization in the ring of Puiseux series where each singular value and the associated singular vectors present the same period and multiplexing structure, and we prove that it is always possible to find an analytic pseudo-circulant factorization, meaning that any arbitrary arrangements of multiplexed systems can be converted into a parallel form. In particular, one can show that the sign ambiguity can be overcome by allowing non-real holomorphic singular values.

Let $\{\Lambda_n=\{\lambda_{1,n},\ldots,\lambda_{d_n,n}\}\}_n$ be a sequence of finite multisets of real numbers such that $d_n\to\infty$ as $n\to\infty$, and let $f:\Omega\subset\mathbb R^d\to\mathbb R$ be a Lebesgue measurable function defined on a domain $\Omega$ with $0<\mu_d(\Omega)<\infty$, where $\mu_d$ is the Lebesgue measure in $\mathbb R^d$. We say that $\{\Lambda_n\}_n$ has an asymptotic distribution described by $f$, and we write $\{\Lambda_n\}_n\sim f$, if \[ \lim_{n\to\infty}\frac1{d_n}\sum_{i=1}^{d_n}F(\lambda_{i,n})=\frac1{\mu_d(\Omega)}\int_\Omega F(f({\boldsymbol x})){\rm d}{\boldsymbol x}\qquad\qquad(*) \] for every continuous function $F$ with bounded support. If $\Lambda_n$ is the spectrum of a matrix $A_n$, we say that $\{A_n\}_n$ has an asymptotic spectral distribution described by $f$ and we write $\{A_n\}_n\sim_\lambda f$. In the case where $d=1$, $\Omega$~is a bounded interval, $\Lambda_n\subseteq f(\Omega)$ for all $n$, and $f$ satisfies suitable conditions, Bogoya, B\"ottcher, Grudsky, and Maximenko proved that the asymptotic distribution (*) implies the uniform convergence to $0$ of the difference between the properly sorted vector $[\lambda_{1,n},\ldots,\lambda_{d_n,n}]$ and the vector of samples $[f(x_{1,n}),\ldots,f(x_{d_n,n})]$, i.e., \[ \lim_{n\to\infty}\,\max_{i=1,\ldots,d_n}|f(x_{i,n})-\lambda_{\tau_n(i),n}|=0, \qquad\qquad(**) \] where $x_{1,n},\ldots,x_{d_n,n}$ is a uniform grid in $\Omega$ and $\tau_n$ is the sorting permutation. We extend this result to the case where $d\ge1$ and $\Omega$ is a Peano--Jordan measurable set (i.e., a bounded set with $\mu_d(\partial\Omega)=0$). See the rest of the abstract in the manuscript.

We analyse the convergence of the ergodic formula for Toeplitz matrix-sequences generated by a symbol and we produce explicit bounds depending on the size of the matrix, the regularity of the symbol and the regularity of the test function.

Eruptive mass loss of massive stars prior to supernova (SN) explosion is key to understanding their evolution and end fate. An observational signature of pre-SN mass loss is the detection of an early, short-lived peak prior to the radioactive-powered peak in the lightcurve of the SN. This is usually attributed to the SN shock passing through an extended envelope or circumstellar medium (CSM). Such an early peak is common for double-peaked Type IIb SNe with an extended Hydrogen envelope but is uncommon for normal Type Ibc SNe with very compact progenitors. In this paper, we systematically study a sample of 14 double-peaked Type Ibc SNe out of 475 Type Ibc SNe detected by the Zwicky Transient Facility. The rate of these events is ~ 3-9 % of Type Ibc SNe. A strong correlation is seen between the peak brightness of the first and the second peak. We perform a holistic analysis of this sample's photometric and spectroscopic properties. We find that six SNe have ejecta mass less than 1.5 Msun. Based on the nebular spectra and lightcurve properties, we estimate that the progenitor masses for these are less than ~ 12 Msun. The rest have an ejecta mass > 2.4 Msun and a higher progenitor mass. This sample suggests that the SNe with low progenitor masses undergo late-time binary mass transfer. Meanwhile, the SNe with higher progenitor masses are consistent with wave-driven mass loss or pulsation-pair instability-driven mass loss simulations., Comment: Accepted for publication in ApJ

We study the eigendecompositions of para-Hermitian matrices $H(z)$, that is, matrix-valued functions that are analytic and Hermitian on the unit circle $S^1 \subset \mathbb C$. In particular, we fill existing gaps in the literature and prove the existence of a decomposition $H(z)=U(z)D(z)U(z)^P$ where, for all $z \in S^1$, $U(z)$ is unitary, $U(z)^P=U(z)^*$ is its conjugate transpose, and $D(z)$ is real diagonal; moreover, $U(z)$ and $D(z)$ are analytic functions of $w=z^{1/N}$ for some positive integer $N$, and $U(z)^P$ is the so-called para-Hermitian conjugate of $U(z)$. This generalizes the celebrated theorem of Rellich for matrix-valued functions that are analytic and Hermitian on the real line. We also show that there also exists a decomposition $H(z)=V(z)C(z)V(z)^P$ where $C(z)$ is pseudo-circulant, $V(z)$ is unitary and both are analytic in $z$. We argue that, in fact, a version of Rellich's theorem can be stated for matrix-valued function that are analytic and Hermitian on any line or any circle on the complex plane. Moreover, we extend these results to para-Hermitian matrices whose entries are Puiseux series (that is, on the unit circle they are analytic in $w$ but possibly not in $z$). Finally, we discuss the implications of our results on the singular value decomposition of a matrix whose entries are $S^1$-analytic functions of $w$, and on the sign characteristics associated with unimodular eigenvalues of $*$-palindromic matrix polynomials.

If high-mass stars (>20-25 Msun) are the progenitors of stripped-envelope (SE) supernovae (SNe), their massive ejecta should lead to broad, long-duration lightcurves (LCs). Instead, literature samples of SE~SNe have reported relatively narrow LCs with ejecta masses between 1-4 Msun that favor progenitors <20-25 Msun. Working with the untargeted sample of (i)PTF SNe to better constrain their rates, we search for SE~SNe with broad LCs. Using a simple LC stretch compared to a template to measure broadness, we identified eight significantly broader Type~Ibc SNe after applying quantitative sample selection criteria. The LCs, colors, and spectra of these SNe are found to evolve more slowly relative to typical Type~Ibc SNe, proportional with the stretch. Bolometric LC modeling and their nebular spectra indicate high ejecta and nickel masses, assuming radioactive decay powering. Additionally, these objects are preferentially located in low-metallicity host galaxies with high star-formation rates, which may account for their massive progenitors, as well as their relative absence from the literature. Our study thus supports the link between broad LCs (as measured by stretch) and high-mass progenitor stars in SE~SNe with independent evidence from bolometric LC modeling, nebular spectra, host environment properties, and photometric evolution. In the first systematic search of its kind using an untargeted sample, we use the stretch distribution to identify a higher than previously appreciated fraction of SE~SNe with broad LCs (~13%). Correcting for Malmquist and LC duration observational biases, we conservatively estimate that a minimum of ~6% of SE~SNe are consistent with high-mass progenitors. This result has implications for the progenitor channels of SE~SNe, late stages of massive stellar evolution, oxygen fraction in the universe, and formation channels for stellar-mass black holes.(Abridged), Comment: 38 pages, 24 figures, 12 tables. Submitted to A&A

The fate of stars in the zero-age main-sequence (ZAMS) range $\approx 8-12$ Msun is unclear. They could evolve to form white dwarfs or explode as electron-capture supernovae (SNe) or iron core-collapse SNe (CCSNe). Even though the initial mass function indicates that this mass range should account for over 40% of all CCSNe progenitors, few have been observationally confirmed, likely owing to the faintness and rapid evolution of these transients. In this paper, we present a sample of nine Ca-rich/O-poor Type IIb SNe detected by the Zwicky Transient Facility with progenitors likely in this mass range. We perform a holistic analysis of the spectroscopic and photometric properties of the sample. These sources have a flux ratio of [Ca II] $\lambda \lambda$7291, 7324 to [O I] $\lambda \lambda$6300, 6364 of $\gtrsim$ 2 in their nebular spectra. Comparing the measured [O I] luminosity ($\lesssim 10^{39} \mathrm{erg\ s^{-1}}$) and derived oxygen mass ($\lesssim 0.1$ Msun) with theoretical models, we infer that the progenitor ZAMS mass for these explosions is less than 12 Msun. These correspond to He-stars with core masses less than around 3 Msun. We find that the ejecta properties (Mej $\lesssim 1$ Msun) are also consistent with those expected for such low mass He-stars. The low ejecta mass of these sources indicates a class of strongly-stripped SNe that is a transition between the regular stripped-envelope SNe and ultra-stripped SNe. The progenitor could be stripped by a main sequence companion and result in the formation of a neutron star $-$ main sequence binary. Such binaries have been suggested to be progenitors of neutron star $-$ white dwarf systems that could merge within a Hubble time, and be detectable with LISA., Comment: Accepted for publication in ApJ

We present photometric and spectroscopic observations of the Type IIn supernova SN 2019zrk (also known as ZTF20aacbyec). The SN shows a $\gtrsim$ 100 day precursor, with a slow rise, followed by a rapid rise to M $\sim -19.2$ in the $r$ and $g$ bands. The post-peak light-curve decline is well fit with an exponential decay with a timescale of $\sim 39$ days, but it shows prominent undulations, with an amplitude of $\sim 1$ mag. Both the light curve and spectra are dominated by an interaction with a dense circumstellar medium (CSM), probably from previous mass ejections. The spectra evolve from a scattering-dominated Type IIn spectrum to a spectrum with strong P-Cygni absorptions. The expansion velocity is high, $\sim 16,000$ km s$^{-1}$, even in the last spectra. The last spectrum $\sim 110$ days after the main eruption reveals no evidence for advanced nucleosynthesis. From analysis of the spectra and light curves, we estimate the mass-loss rate to be $\sim 4 \times 10^{-2}$ M$_\odot$ yr$^{-1}$ for a CSM velocity of 100 km s$^{-1}$, and a CSM mass of $\gtrsim 1$ M$_\odot$. We find strong similarities for both the precursor, general light curve, and spectral evolution with SN 2009ip and similar SNe, although SN 2019zrk displays a brighter peak magnitude. Different scenarios for the nature of the 09ip-class of SNe, based on pulsational pair instability eruptions, wave heating, and mergers, are discussed. }, Comment: 18 pages, 12 figures. Astronomy & Astrophysics, in press

In a series of recent papers the spectral behavior of the matrix sequence $\{Y_nT_n(f)\}$ is studied in the sense of the spectral distribution, where $Y_n$ is the main antidiagonal (or flip matrix) and $T_n(f)$ is the Toeplitz matrix generated by the function $f$, with $f$ being Lebesgue integrable and with real Fourier coefficients. This kind of study is also motivated by computational purposes for the solution of the related large linear systems using the (preconditioned) MINRES algorithm. Here we complement the spectral study with more results holding both asymptotically and for a fixed dimension $n$, and with regard to eigenvalues, singular values, and eigenvectors of $T_n(f), Y_nT_n(f)$ and to several relationships among them: beside fast linear solvers, a further target is the design of ad hoc procedures for the computation of the related spectra via matrix-less algorithms, with a cost being linear in the number of computed eigenvalues. We emphasize that the challenge of the case of non-monotone generating functions is considered in the current work, for which the previous matrix-less algorithms fail. Numerical experiments are reported and commented, with the aim of showing in a visual way the theoretical analysis.

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of square matrices $A_n$ arising from the discretization of differential problems. Indeed, as the mesh fineness parameter $n$ increases to $\infty$, the sequence $\{A_n\}_n$ often turns out to be a GLT sequence. In this paper, motivated by recent applications, we further enhance the GLT apparatus by developing a full theory of rectangular GLT sequences as an extension of the theory of classical square GLT sequences. We also detail an example of application as an illustration of the potential impact of the theory presented herein.

Time-dependent energy spectra of galactic cosmic rays (GCRs) carry fundamental information regarding their origin and propagation. When observed at the Earth, these spectra are significantly affected by the solar wind and the embedded solar magnetic field that permeates the heliosphere, changing significantly over an 11-year solar cycle. Energy spectra of GCRs measured during different epochs of solar activity provide crucial information for a thorough understanding of solar and heliospheric phenomena. The PAMELA experiment had collected data for almost ten years (15th June 2006 - 23rd January 2016), including the minimum phase of solar cycle 23 and the maximum phase of solar cycle 24. In this paper, we present new spectra for helium nuclei measured by the PAMELA instrument from January 2010 to September 2014 over a three Carrington rotation time basis. These data are compared to the PAMELA spectra measured during the previous solar minimum providing a picture of the time dependence of the helium nuclei fluxes over a nearly full solar cycle. Time and rigidity dependencies are observed in the proton-to-helium flux ratios. The force-field approximation of the solar modulation was used to relate these dependencies to the shapes of the local interstellar proton and helium-nuclei spectra., Comment: 9 pages, 5 figures

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost everywhere continuous function defined on a bounded set $\Omega$ with negligible boundary. Under additional assumptions on $f$ and $\Omega$, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm., Comment: In Press

The final explosive fate of massive stars, and the nature of the compact remnants they leave behind (black holes and neutron stars), are major open questions in astrophysics. Many massive stars are stripped of their outer hydrogen envelopes as they evolve. Such Wolf-Rayet (W-R) stars emit strong and rapidly expanding (v_wind>1000 km/s) winds indicating a high escape velocity from the stellar surface. A fraction of this population is also helium depleted, with spectra dominated by highly-ionized emission lines of carbon and oxygen (Types WC/WO). Evidence indicates that the most commonly-observed supernova (SN) explosions that lack hydrogen and helium (Types Ib/Ic) cannot result from massive WC/WO stars, leading some to suggest that most such stars collapse directly into black holes without a visible supernova explosions. Here, we present observations of supernova SN 2019hgp, discovered about a day after explosion. The short rise time and rapid decline place it among an emerging population of rapidly-evolving transients (RETs). Spectroscopy reveals a rich set of emission lines indicating that the explosion occurred within a nebula composed of carbon, oxygen, and neon. Narrow absorption features show that this material is expanding at relatively high velocities (>1500 km/s) requiring a compact progenitor. Our observations are consistent with an explosion of a massive WC/WO star, and suggest that massive W-R stars may be the progenitors of some rapidly evolving transients., Comment: Unedited author version, Nature in press

The origins of the high-energy cosmic neutrino flux remain largely unknown. Recently, one high-energy neutrino was associated with a tidal disruption event (TDE). Here we present AT2019fdr, an exceptionally luminous TDE candidate, coincident with another high-energy neutrino. Our observations, including a bright dust echo and soft late-time X-ray emission, further support a TDE origin of this flare. The probability of finding two such bright events by chance is just 0.034%. We evaluate several models for neutrino production and show that AT2019fdr is capable of producing the observed high-energy neutrino, reinforcing the case for TDEs as neutrino sources., Comment: 20 pages, 6 figures, 6 tables

Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode Decomposition technique and the Iterative Filtering method. When a signal contains mono-components that have rapid varying instantaneous frequencies, we can think, for instance, to chirps or whistles, it becomes particularly hard for most techniques to properly factor out these components. The Adaptive Local Iterative Filtering technique has recently gained interest in many applied fields of research for being able to deal with non-stationary signals presenting amplitude and frequency modulation. In this work, we address the open question of how to guarantee a priori convergence of this technique, and propose two new algorithms. The first method, called Stable Adaptive Local Iterative Filtering, is a stabilized version of the Adaptive Local Iterative Filtering that we prove to be always convergent. The stability, however, comes at the cost of higher complexity in the calculations. The second technique, called Resampled Iterative Filtering, is a new generalization of the Iterative Filtering method. We prove that Resampled Iterative Filtering is guaranteed to converge a priori for any kind of signal. Furthermore, in the discrete setting, by leveraging on the mathematical properties of the matrices involved, we show that its calculations can be accelerated drastically. Finally, we present some artificial and real-life examples to show the powerfulness and performance of the proposed methods.

We analyse the recovery of different roles in a network modelled by a directed graph, based on the so-called Neighbourhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that when assuming the graph is generated as a particular Stochastic Block Model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles. We also comment on the connections with the literature on Stochastic Block Models, including the case of probabilities of order log(n)/n where n is the graph size. We provide numerical experiments to assess the effectiveness of the method when applied to practical networks of finite size.

We present a study of the solar-cycle variations of >80 MeV proton flux intensities in the lower edge of the inner radiation belt, based on the measurements of the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) mission. The analyzed data sample covers an ~8 year interval from 2006 July to 2014 September, thus spanning from the decaying phase of the 23rd solar cycle to the maximum of the 24th cycle. We explored the intensity temporal variations as a function of drift shell and proton energy, also providing an explicit investigation of the solar-modulation effects at different equatorial pitch angles. PAMELA observations offer new important constraints for the modeling of low-altitude particle radiation environment at the highest trapping energies., Comment: accepted for publication in the Astrophysical Journal Letters

We present SN 2020jfo, a Type IIP supernova in the nearby galaxy M61. Optical light curves from the Zwicky Transient Facility, complemented with data from Swift and near-IR photometry are presented. The 350-day duration bolometric light curve exhibits a relatively short (~ 65 days) plateau. This implies a moderate ejecta mass (~ 5 Msun). A series of spectroscopy is presented, including spectropolarimetric observations. The nebular spectra are dominated by Halpha but also reveal emission lines from oxygen and calcium. Comparisons to synthetic nebular spectra indicate an initial progenitor mass of about 12 Msun. Stable nickel is present in the nebular spectrum, with a super-solar Ni/Fe ratio. Several years of pre-discovery data are examined, but no signs of pre-cursor activity is found. Pre-explosion Hubble Space Telescope imaging reveals a probable progenitor star, detected only in the reddest band and is fainter than expected for stars in the 10 - 15 Msun range, in tension with the analysis of the LC and the nebular spectral modeling. We present two additional core-collapse SNe monitored by the ZTF, which also have nebular Halpha-dominated spectra. This illustrates how the absence or presence of interaction with circumstellar material affect both the LCs and in particular the nebular spectra. Type II SN 2020amv has a LC powered by CSM interaction, in particular after about 40 days when the LC is bumpy and slowly evolving. The late-time spectra show strong Halpha emission with a structure suggesting emission from a thin, dense shell. The evolution of the complex three-horn line profile is reminiscent of that observed for SN 1998S. SN 2020jfv has a poorly constrained early-time LC, but shows a transition from a hydrogen-poor Type IIb to a Type IIn, where the nebular spectrum after the light-curve rebrightening is dominated by Halpha, although with an intermediate line width., Comment: Paper on SN 2020jfo in M61, and on SNe 2020amv and 2020jfv. This is the version resubmitted to A&A after responding to first referee comments. 27 pages, 12 figures. Somewhat shortened abstract

We study the empirical spectral distribution (ESD) for complex n x n matrix polynomials of degree k. We obtain exact formulae for the almost sure limit of the ESD in two distinct scenarios: (1) n -> \infty with k constant and (2) k -> \infty with n bounded by O(k^P) for some P>0. The main tools used are the logarithmic potential of some measure related to the matrix polynomial, and some classical estimates on the singular values of full random matrices with i.i.d. entries., Comment: arXiv admin note: text overlap with arXiv:2005.07501

With the observation of the gravitational wave event of August 17th 2017 the multi-messenger astronomy era has definitely begun. With the opening of this new panorama, it is necessary to have new instruments and a perfect coordination of the existing observatories. Crystal Eye is a detector aimed at the exploration of the electromagnetic counterpart of the gravitational waves. Such events generated by neutron stars' mergers are associated with gamma-ray bursts (GRB). At present, there are few instruments in orbit able to detect photons in the energy range going from tens of keV up to few MeV. These instruments belong to two different old observation concepts: the all sky monitors (ASM) and the telescopes. The detector we propose is a crossover technology, the Crystal Eye: a wide field of view observatory in the energy range from 10 keV to 10 MeV with a pixelated structure. A pathfinder will be launched with Space RIDER in 2022. We here present the preliminary results of the characterization of the first pixel., Comment: submitted to SPIE Astronomical Telescopes + Instrumentations

Interaction-powered supernovae (SNe) explode within an optically-thick circumstellar medium (CSM) that could be ejected during eruptive events. To identify and characterize such pre-explosion outbursts we produce forced-photometry light curves for 196 interacting SNe, mostly of Type IIn, detected by the Zwicky Transient Facility between early 2018 and June 2020. Extensive tests demonstrate that we only expect a few false detections among the 70,000 analyzed pre-explosion images after applying quality cuts and bias corrections. We detect precursor eruptions prior to 18 Type IIn SNe and prior to the Type Ibn SN2019uo. Precursors become brighter and more frequent in the last months before the SN and month-long outbursts brighter than magnitude -13 occur prior to 25% (5 - 69%, 95% confidence range) of all Type IIn SNe within the final three months before the explosion. With radiative energies of up to $10^{49}\,\text{erg}$, precursors could eject $\sim1\,\text{M}_\odot$ of material. Nevertheless, SNe with detected precursors are not significantly more luminous than other SNe IIn and the characteristic narrow hydrogen lines in their spectra typically originate from earlier, undetected mass-loss events. The long precursor durations require ongoing energy injection and they could, for example, be powered by interaction or by a continuum-driven wind. Instabilities during the neon and oxygen burning phases are predicted to launch precursors in the final years to months before the explosion; however, the brightest precursor is 100 times more energetic than anticipated.

Type Ic supernovae represent the explosions of the most stripped massive stars, but their progenitors and explosion mechanisms remain unclear. Larger samples of observed supernovae can help characterize the population of these transients. We present an analysis of 44 spectroscopically normal Type Ic supernovae, with focus on the light curves. The photometric data were obtained over 7 years with the Palomar Transient Factory (PTF) and its continuation, the intermediate Palomar Transient Factory (iPTF). This is the first homogeneous and large sample of SNe Ic from an untargeted survey, and we aim to estimate explosion parameters for the sample. We present K-corrected Bgriz light curves of these SNe, obtained through photometry on template-subtracted images. We performed an analysis on the shape of the $r$-band light curves and confirmed the correlation between the rise parameter Delta m_{-10} and the decline parameter Delta m_{15}. Peak r-band absolute magnitudes have an average of -17.71 +- 0.85 mag. To derive the explosion epochs, we fit the r-band lightcurves to a template derived from a well-sampled light curve. We computed the bolometric light curves using r and g band data, g-r colors and bolometric corrections. Bolometric light curves and Fe II lambda 5169 velocities at peak were used to fit to the Arnett semianalytic model in order to estimate the ejecta mass M_{ej}, the explosion energy E_{K} and the mass of radioactive nickel (M(56) Ni) for each SN. Including 41 SNe, we find average values of =4.50 +-0.79 msun, =1.79 +- 0.29 x10^{51} erg, and = 0.19 +- 0.03 msun. The explosion-parameter distributions are comparable to those available in the literature, but our large sample also includes some transients with narrow and very broad light curves leading to more extreme ejecta masses values., Comment: Submitted to A&A

This paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations (PDEs), in case the domain is a generic Peano-Jordan measurable set. It is observed that such matrix-sequences often present a spectral symbol, that is a measurable function describing the asymptotic behaviour of the eigenvalues. When the domain is a hypercube, the analysis can be conducted using the theory of generalized locally Toeplitz (GLT) sequences, but in case of generic domain, a new kind of matrix-sequences and theory has to be formalized. We thus introduce the Reduced GLT sequences and symbols, developing in full detail its theory, and presenting some application to finite differences and finite elements discretization for convection-diffusion-reaction differential equations., Comment: Bit Numer Math (2021)

We present the data and analysis of SN 2018gjx, an unusual low-luminosity transient with three distinct spectroscopic phases. Phase I shows a hot blue spectrum with signatures of ionised circumstellar material (CSM), Phase II has the appearance of broad SN features, consistent with those seen in a Type IIb supernova at maximum light, and Phase III is that of a supernova interacting with helium-rich CSM, similar to a Type Ibn supernova. This event provides an apparently rare opportunity to view the inner workings of an interacting supernova. The observed properties can be explained by the explosion of a star in an aspherical CSM. The initial light is emitted from an extended CSM (~ 4000 Rsun), which ionises the exterior unshocked material. Some days after, the SN photosphere envelops this region, leading to the appearance of a SN IIb. Over time, the photosphere recedes in velocity space, revealing interaction between the supernova ejecta and the CSM that partially obscures the supernova nebular phase. Modelling of the initial spectrum reveals a surface composition consistent with compact H-deficient Wolf-Rayet and LBV stars. Such configurations may not be unusual, with SNe IIb being known to have signs of interaction so at least some SNe IIb and SNe Ibn may be the same phenomena viewed from different angles or, possibly with differing CSM configurations., Comment: Accepted for publication in MNRAS

We present SN 2019tsf (ZTF19ackjszs) and SN 2019oys (ZTF19abucwzt). These two stripped envelope Type Ib supernovae suddenly showed a (re-)brightening in their late light curves. We investigate this in the context of circumstellar material (CSM) interaction with previously ejected material, a phenomenon that is unusual among SE SNe. We analyse observational data, consisting of optical light curves and spectra. For SN 2019oys we also have detections in radio as well as limits from UV and X-rays. Both light curves show spectacular re-brightening after about 100 days. In the case of SN 2019tsf, the re-brightening is followed by a new period of decline, and the spectra never show signs of narrow emission lines that would indicate CSM interaction. On the contrary, SN 2019oys made a spectral makeover from a Type Ib to a spectrum clearly dominated by CSM interaction at the light curve brightening phase. Deep spectra reveal a plethora of narrow high ionization lines, including coronal lines, and the radio observations show strong emission. The rather similar light curve behaviour indicate CSM interaction as the powering source. For SN 2019oys the evidence for a phase where the ejecta hit H-rich material, likely ejected from the progenitor star, is conspicuous. We observe strong narrow lines of H and He, but also a plethora of high ionization lines, including coronal lines, revealing shock interaction. Spectral simulations of SN 2019oys show two distinct density components, one with density > 1e9/cm3, dominated by somewhat broader, low ionization lines of H I, He I, Na I and Ca II, and one with narrow, high ionization lines at a density about 1e6 /cm3. The former is strongly affected by electron scattering. The evidence for CSM interaction in SN 2019oys is corroborated by detections in radio. On the contrary, for SN 2019tsf, we find little evidence in the spectra for any CSM interaction., Comment: Resubmitted to A&A after first referee report

In this paper, we discuss the outcomes of the follow-up campaign of SN 2018ijp, discovered as part of the Zwicky Transient Facility survey for optical transients. Its first spectrum shows similarities to broad-lined Type Ic supernovae around maximum light, whereas later spectra display strong signatures of interaction between rapidly expanding ejecta and a dense H-rich circumstellar medium, coinciding with a second peak in the photometric evolution of the transient. This evolution, along with the results of modeling of the first light curve peak, suggests a scenario where a stripped star exploded within a dense circumstellar medium. The two main phases in the evolution of the transient could be interpreted as a first phase dominated by radioactive decays, and an later interaction-dominated phase where the ejecta collide with a pre-existing shell. We therefore discuss SN 2018jp within the context of a massive star depleted of its outer layers exploding within a dense H-rich circumstellar medium., Comment: Accepted for publication on Astronomy and Astrophysics. 11 pages, 10 figures, 1 table. Photometric table available at the CDS

A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with the Empirical Mode Decomposition (EMD) and its more rigorous mathematical structure, which makes feasible to study its convergence compared to EMD, ALIF has really good potentiality to become a reference method in the analysis of signals containing strong nonstationary components, like chirps, multipaths and whistles, in many applications, like Physics, Engineering, Medicine and Finance, to name a few. In [11], the authors analyzed the spectral properties of the matrices produced by the ALIF method, in order to study its stability. Various results are achieved in that work through the use of Generalized Locally Toeplitz (GLT) sequences theory, a powerful tool originally designed to extract information on the asymptotic behavior of the spectra for PDE discretization matrices. In this manuscript we focus on answering some of the open questions contained in [11], and in doing so, we also develop new theory and results for the GLT sequences.

Spectroscopic detection of narrow emission lines traces the presence of circumstellar mass distributions around massive stars exploding as core-collapse supernovae. Transient emission lines disappearing shortly after the supernova explosion suggest that the spatial extent of such material is compact, and hence imply an increased mass loss shortly prior to explosion. Here, we present a systematic survey for such transient emission lines (Flash Spectroscopy) among Type II supernovae detected in the first year of the Zwicky Transient Facility (ZTF) survey. We find that at least six out of ten events for which a spectrum was obtained within two days of estimated explosion time show evidence for such transient flash lines. Our measured flash event fraction ($>30\%$ at $95\%$ confidence level) indicates that elevated mass loss is a common process occurring in massive stars that are about to explode as supernovae.

Context: Type Ibn supernovae are a rare class of stripped envelope supernovae interacting with a helium-rich CSM. The majority of the SNe Ibn reported display a surprising homogeneity in their fast lightcurves and starforming hosts. Aims: We present the discovery and study of SN 2020bqj (ZTF20aalrqbu), a SN Ibn with a long-duration peak plateau lasting 40 days and hosted by a faint low-mass galaxy. We aim to explain its peculiar properties using an extensive data set. Methods: We compare the evolution of SN 2020bqj with SNe Ibn from the literature. We fit the bolometric and multi-band lightcurves with different powering mechanism models. Results: The risetime, peak magnitude and spectral features of SN 2020bqj are consistent with those of most SNe Ibn, but the SN is a clear outlier based on its bright, long-lasting peak plateau and low host mass. We show through modeling that the lightcurve can be powered predominantly by shock heating from the interaction of the SN ejecta and a dense CSM. The peculiar Type Ibn SN 2011hw is a close analog to SN 2020bqj, suggesting a similar progenitor and CSM scenario. In this scenario a very massive progenitor star in the transitional phase between a luminous blue variable and a compact Wolf-Rayet star undergoes core-collapse, embedded in a dense helium-rich CSM with an elevated opacity compared to normal SNe Ibn, due to the presence of residual hydrogen. This scenario is consistent with the observed properties of SN 2020bqj and the modeling results. Conclusions: SN 2020bqj is a compelling example of a transitional SN Ibn/IIn based on not only its spectral features, but also its lightcurve, host galaxy properties and the inferred progenitor properties. The strong similarity with SN 2011hw suggests this subclass may be the result of a progenitor in a stellar evolution phase that is distinct from those of progenitors of regular SNe Ibn., Comment: 22 pages, 14 figures, 5 tables. Accepted for publication in Astronomy & Astrophysics. Abstract abridged for arXiv submission