arXiv subjects
Publications and source records attributed to Giacomo Vianello.
Using a geometric construction, we solve Plateau's Problem in the Heisenberg group $\mathbb{H}^{1}$ for intrinsic graphs defined on a convex domain $D$, under a smallness condition either on the boundary $\partial D$ or on the Lipschitz boundary datum $φ: \partial D \to \mathbb{R}$. The proof relies on a calibration argument. We then apply these techniques to establish a new regularity result for $H$-perimeter minimizers.
Consider an $(n+1)$-dimensional circular cone with opening angle $α\in (0,π)$. Using a free-boundary adaptation of the classical calibration method, we prove that, for $n \geq 4$, there exists a threshold $\barα(n) \in (0,π)$ such that if $α\geq \barα(n)$, that is, the cone is wide enough, the intersection of the cone with an axial hyperplane is area-minimizing with respect to free-boundary variations inside the cone. This provides a counterexample to a recent Vertex-skipping Theorem proved by the author in collaboration with G.P. Leonardi, at least for $n\geq4$.
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are strongly stable. As an application, we prove a local minimality property.
Given an axially-symmetric, $(n+1)$-dimensional convex cone $Ω\subset \mathbb{R}^{n+1}$, we study the stability of the free-boundary minimal surface $Σ$ obtained by intersecting $Ω$ with a $n$-plane that contains the axis of $Ω$. In the case $n=2$, $Σ$ is always unstable, as a special case of the vertex-skipping property that we recently proved in another article. Conversely, as soon as $n \ge 3$ and $Ω$ has a sufficiently large aperture (depending on the dimension $n$), we show that $Σ$ is strictly stable. For our stability analysis, we introduce a Lipschitz flow $Σ_{t}[f]$ of deformations of $Σ$ associated with a compactly-supported, scalar deformation field $f$, which satisfies the key property $\partial Σ_{t}[f] \subset \partial Ω$ for all $t\in \mathbb{R}$. Then, we compute the lower-right second variation of the area of $Σ$ along the flow, and ultimately show that it is positive by exploiting its connection with a functional inequality studied in the context of reaction-diffusion problems.
Let $E \subset Ω$ be a local almost-minimizer of the relative perimeter in the open set $Ω\subset \mathbb{R}^{n}$. We prove a free-boundary monotonicity inequality for $E$ at a point $x\in \partialΩ$, under a geometric property called ``visibility'', that $Ω$ is required to satisfy in a neighborhood of $x$. Incidentally, the visibility property is satisfied by a considerably large class of Lipschitz and possibly non-smooth domains. Then, we prove the existence of the density of the relative perimeter of $E$ at $x$, as well as the fact that any blow-up of $E$ at $x$ is necessarily a perimeter-minimizing cone within the tangent cone to $Ω$ at $x$.
Given a convex domain $Ω\subset \mathbb{R}^{3}$ and an almost-minimizer $E$ of the relative perimeter in $Ω$, we prove that the closure of $\partial E \cap Ω$ does not contain vertices of $Ω$.
Characterizing the sub-mm Galactic emission has become increasingly critical especially in identifying and removing its polarized contribution from the one emitted by the Cosmic Microwave Background (CMB). In this work, we present a parametric foreground removal performed onto sub-patches identified in the celestial sphere by means of spectral clustering. Our approach takes into account efficiently both the geometrical affinity and the similarity induced by the measurements and the accompanying errors. The optimal partition is then used to parametrically separate the Galactic emission encoding thermal dust and synchrotron from the CMB one applied on two nominal observations of forthcoming experiments from the ground and from the space. Performing the parametric fit singularly on each of the clustering derived regions results in an overall improvement: both controlling the bias and the uncertainties in the CMB $B-$mode recovered maps. We finally apply this technique using the map of the number of clouds along the line of sight, $\mathcal{N}_c$, as estimated from HI emission data and perform parametric fitting onto patches derived by clustering on this map. We show that adopting the $\mathcal{N}_c$ map as a tracer for the patches related to the thermal dust emission, results in reducing the $B-$mode residuals post-component separation. The code is made publicly available.
The Large Area Telescope (LAT) on board the \Fermi Gamma-ray Space Telescope (\Fermi) shows long-lasting high-energy emission in many gamma-ray bursts (GRBs), similar to X-ray afterglows observed by the Neil Gehrels Swift Observatory \citep[\textit{Swift};][]{gehrels2004}. Some LAT light curves (LCs) show a late-time flattening reminiscent of X-ray plateaus. We explore the presence of plateaus in LAT temporally extended emission analyzing GRBs from the second \lat GRB Catalog \citep[2FLGC;][]{Ajello2019apj} from 2008 to May 2016 with known redshifts, and check whether they follow closure relations corresponding to 4 distinct astrophysical environments predicted by the external forward shock (ES) model. We find that three LCs can be fit by the same phenomenological model used to fit X-ray plateaus \citep{Willingale2007} and show tentative evidence for the existence of plateaus in their high-energy extended emission. The most favorable scenario is a slow cooling regime, whereas the preferred density profile for each GRBs varies from a constant density ISM to a $r^{-2}$ wind environment. We also compare the end time of the plateaus in $γ$-rays and X-rays using a statistical comparison with 222 \textit{Swift} GRBs with plateaus and known redshifts from January 2005 to August 2019. Within this comparison, the case of GRB 090510 shows an indication of chromaticity at the end time of the plateau. Finally, we update the 3-D fundamental plane relation among the rest frame end time of the plateau, its correspondent luminosity, and the peak prompt luminosity for 222 GRBs observed by \textit{Swift}. We find that these three LAT GRBs follow this relation.
In 2018, the Fermi mission celebrated its first decade of operation. In this time, the Large Area Telescope (LAT) has been very successful in detecting the high-energy emission (>100 MeV) from Gamma-Ray Bursts (GRBs). The analysis of particularly remarkable events - such as GRB 080916C, GRB 090510 and GRB 130427A - has been presented in dedicated publications. Here we present the results of a new systematic search for high-energy emission from the full sample of GRBs detected in 10 years by the Fermi Gamma-Ray Burst Monitor, as well as Swift, AGILE, Integral and IPN bursts, featuring a detection efficiency more than 50\%\ better than previous works, and returning 186 detections during 10 years of LAT observations. This milestone marks a vast improvement from the 35 events contained in the first LAT GRB catalog (covering the first 3 years of Fermi operations). We assess the characteristics of the GRB population at high energy with unprecedented sensitivity, covering aspects such as temporal properties, energetics and spectral index of the high-energy emission. Finally, we show how the LAT observations can be used to inform theory, in particular the prospects for very high-energy emission.
Galactic diffuse TeV gamma-ray emission is produced by the interaction of high-energy cosmic-ray particles with matter and radiation in our Galaxy. The measurement of Galactic diffuse TeV gamma-ray emission would provide strong constraints on the acceleration and propagation of Galactic cosmic rays. The High Altitude Water Cherenkov (HAWC) Observatory, located in central Mexico at 4100 m above sea level, is sensitive to gamma rays between a few hundreds GeV and about 100 TeV. Thanks to its large field of view of 2 steradians and excellent background estimation, HAWC has a unique capability to observe large extended sources such as Galactic diffuse emission. We present the analysis strategy to detect the Galactic diffuse emission with HAWC, including techniques to remove contaminations from localized sources.
At least a fraction of Gravitational Wave (GW) progenitors are expected to emit an electromagnetic (EM) signal in the form of a short gamma-ray burst (sGRB). Discovering such a transient EM counterpart is challenging because the \LIGO/\VIRGO localization region is much larger (several hundreds of square degrees) than the field of view of X-ray, optical and radio telescopes. The Fermi Large Area Telescope (LAT) has a wide field of view ($\sim 2.4$ sr), and detects $\sim 2-3$ sGRBs per year above 100 MeV. It can detect them not only during the short prompt phase, but also during their long-lasting high-energy afterglow phase. If other wide-field high-energy instruments such as Fermi-GBM, Swift-BAT or INTEGRAL-ISGRI cannot detect or localize with enough precision an EM counterpart during the prompt phase, the LAT can potentially pinpoint it with $\lesssim 10$ arcmin accuracy during the afterglow phase. This routinely happens with gamma-ray bursts. Moreover, the LAT will cover the entire localization region within hours of any triggers during normal operations, allowing the $γ$-ray flux of any EM counterpart to be measured or constrained. We illustrate two new ad hoc methods to search for EM counterparts with the LAT and their application to the GW candidate LVT151012.
We present the \emph{Fermi} Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) observations of the LIGO binary black hole merger (BBH) event GW170104. No candidate electromagnetic counterparts was detected by either GBM or LAT. A detailed analysis of the GBM and LAT data over timescales from seconds to days covering the LIGO localization region is presented. The resulting flux upper bound from the GBM is (5.2--9.4)$\times$10$^{-7}$ erg cm$^{-2}$ s$^{-1}$ in the 10-1000 keV range and from the LAT is (0.2--13)$\times$10$^{-9}$ erg cm$^{-2}$ s$^{-1}$ in the 0.1--1 GeV range. We also describe the improvements to our automated pipelines and analysis techniques for searching for and characterizing the potential electromagnetic counterparts for future gravitational wave events from Advanced LIGO/VIRGO.
A bright burst, followed by an X-ray tail lasting ~10 ks, was detected during an XMM-Newton observation of the magnetar 1E 1547.0-5408 carried out on 2009 February 3. The burst, also observed by SWIFT/BAT, had a spectrum well fit by the sum of two blackbodies with temperatures of ~4 keV and 10 keV and a fluence in the 0.3-150 keV energy range of ~1e-5 erg/cm2. The X-ray tail had a fluence of ~4e-8 erg/cm2. Thanks to the knowledge of the distances and relative optical depths of three dust clouds between us and 1E 1547.0-5408, we show that most of the X-rays in the tail can be explained by dust scattering of the burst emission, except for the first ~20-30 s. We point out that other X-ray tails observed after strong magnetar bursts may contain a non-negligible contribution due to dust scattering.
X-ray emission from Young Stellar Objects (YSOs) is crucial to understand star formation. A very limited amount of X-ray results is available for the protostellar (ClassI) phase. A systematic search of transient X-ray phenomena combined with a careful evaluation of the evolutionary stage offer a widely unexplored window to our understanding of YSOs X-ray properties. Within the EXTraS project, a search for transients and variability in the whole XMM-Newton archive, we discover transient X-ray emission consistent with ISO-Oph 85, a strongly embedded YSO in the rho Ophiuchi region, not detected in previous time-averaged X-ray studies. We extract an X-ray light curve for the flare and determine its spectral parameters from XMM-Newton/EPIC (European Photon Imaging Camera) data using quantile analysis. The X-ray flare ($2500\,s$), the only one detected in the XMM-Newton archive for ISO-Oph 85, has a luminosity of $LogL_X[erg/s]=31.1$ and a spectrum consistent with a highly-absorbed one-component thermal model ($N_H=1.0^{+1.2}_{-0.5}10^{23}\,cm^{-2}$, $kT=1.15^{+2.35}_{-0.65}\,keV)$. We set an upper limit of $LogL_X[erg/s]<29.5$ to the quiescent X-ray luminosity. We build a SED with IR to mm photometry drawn from literature and mid-IR Spitzer and sub-mm Herschel photometry analysed by us, and compare it with pre-computed models. The sub-mm emission peak in the Herschel data suggests that the object is a ClassI protostar. However, the Herschel/IR position offset is larger than for other YSOs in the region, leaving some doubt on the association. This is the first X-ray flare from a YSO recognised as a candidate ClassI YSO via the analysis of its complete SED. This work shows how the analysis of the whole SED is fundamental for the classification of YSOs, and how the X-ray source detection techniques we developed can open a new era in time-resolved analysis of the X-ray emission from stars.
The High Altitude Water Cherenkov (HAWC) Observatory continuously observes gamma-rays between 100 GeV to 100 TeV in an instantaneous field of view of about 2 steradians above the array. The large amount of raw data, the importance of small number statistics, the large dynamic range of gamma-ray signals in time (1 - $10^8$ sec) and angular extent (0.1 - 100 degrees), and the growing need to directly compare results from different observatories pose some special challenges for the analysis of HAWC data. To address these needs, we have designed and implemented a modular analysis framework based on the method of maximum likelihood. The framework facilitates the calculation of a binned Poisson Log-likelihood value for a given physics model (i.e., source model), data set, and detector response. The parameters of the physics model (sky position, spectrum, angular extent, etc.) can be optimized through a likelihood maximization routine to obtain a best match to the data. In a similar way, the parameters of the detector response (absolute pointing, angular resolution, etc.) can be optimized using a well-known source such as the Crab Nebula. The framework was designed concurrently with the Multi-Mission Maximum Likelihood (3ML) architecture, and allows for the definition of a general collection of sources with individually varying spectral and spatial morphologies. Compatibility with the 3ML architecture allows to easily perform powerful joint fits with other observatories. In this contribution, we overview the design and capabilities of the HAWC analysis framework, stressing the overarching design points that have applicability to other astronomical and cosmic-ray observatories.
Astrophysical sources are now observed by many different instruments at different wavelengths, from radio to high-energy gamma-rays, with an unprecedented quality. Putting all these data together to form a coherent view, however, is a very difficult task. Each instrument has its own data format, software and analysis procedure, which are difficult to combine. It is for example very challenging to perform a broadband fit of the energy spectrum of the source. The Multi-Mission Maximum Likelihood framework (3ML) aims to solve this issue, providing a common framework which allows for a coherent modeling of sources using all the available data, independent of their origin. At the same time, thanks to its architecture based on plug-ins, 3ML uses the existing official software of each instrument for the corresponding data in a way which is transparent to the user. 3ML is based on the likelihood formalism, in which a model summarizing our knowledge about a particular region of the sky is convolved with the instrument response and compared to the corresponding data. The user can choose between a frequentist analysis, and a Bayesian analysis. In the former, parameters of the model are optimized in order to obtain the best match to the data (i.e., the maximum of the likelihood). In the latter, the priors specified by the user are used to build the posterior distribution, which is then sampled with Markov Chain Monte Carlo or Multinest. Our implementation of this idea is very flexible, allowing the study of point sources as well as extended sources with arbitrary spectra. We will review the problem we aim to solve, the 3ML concepts and its innovative potential.
After seven years of science operation, the Fermi mission has brought great advances in the study of Gamma-ray Bursts (GRBs). Over 1600 GRBs have been detected by the Gamma-ray Burst Monitor, and more than 100 of these are also detected by the Large Area Telescope above 30 MeV. We will give an overview of these observations, presenting the common properties in the GRB temporal and spectral behavior at high energies. We will also highlight the unique characteristics of some individual bursts. The main physical implications of these results will be discussed, along with open questions regarding GRB modeling in their prompt and temporally-extended emission phases.
Observations of Gamma-Ray Bursts with the Fermi Large Area Telescope have prompted theoretical advances and posed big challenges in the understanding of such extreme sources, despite the fact that GRB emission above 100 MeV is a fairly rare event. The first Fermi/LAT GRB catalog, published a year ago, presented 28 detections out of ~300 bursts detected by the Fermi Gamma-Ray Burst Monitor (GBM) within the LAT field of view. Building on the results from that work and on recent development in the understanding of the systematic errors on GBM localizations, we developed a new detection algorithm which increased the number of detections by 40 %. Even more recently the development of the new event analysis for the LAT ("Pass 8") has increased the number of detections within the first 3 years of the mission to 45, up 50 % with respect to the published catalog. The second LAT GRB catalog, in preparation, will cover more than 6 years of the mission and will break the barrier of 100 detected GRBs, a more than 20-fold improvement with respect to observations before the Fermi era in the same energy range. We will review the main features of the new algorithm, as well as preliminary results from this investigation.