Future Prospects: Deep Imaging of Galaxy Outskirts using Telescopes Large and Small

The Universe is almost totally unexplored at low surface brightness levels. In spite of great progress in the construction of large telescopes and improvements in the sensitivity of detectors, the limiting surface brightness of imaging observations has remained static for about forty years. Recent technical advances have at last begun to erode the barriers preventing progress. In this Chapter we describe the technical challenges to low surface brightness imaging, describe some solutions, and highlight some relevant observations that have been undertaken recently with both large and small telescopes. Our main focus will be on discoveries made with the Dragonfly Telephoto Array (Dragonfly), which is a new telescope concept designed to probe the Universe down to hitherto unprecedented low surface brightness levels. We conclude by arguing that these discoveries are probably only scratching the surface of interesting phenomena that are observable when the Universe is explored at low surface brightness levels.Comment: 27 pages, 10 figures, Invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.Comment: 29 pages; final version; to appear in Constructive Approximatio

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

How Many CMEs Have Flux Ropes? Deciphering the Signatures of Shocks, Flux Ropes, and Prominences in Coronagraph Observations of CMEs

We intend to provide a comprehensive answer to the question on whether all Coronal Mass Ejections (CMEs) have flux rope structure. To achieve this, we present a synthesis of the LASCO CME observations over the last sixteen years, assisted by 3D MHD simulations of the breakout model, EUV and coronagraphic observations from STEREO and SDO, and statistics from a revised LASCO CME database. We argue that the bright loop often seen as the CME leading edge is the result of pileup at the boundary of the erupting flux rope irrespective of whether a cavity or, more generally, a 3-part CME can be identified. Based on our previous work on white light shock detection and supported by the MHD simulations, we identify a new type of morphology, the `two-front' morphology. It consists of a faint front followed by diffuse emission and the bright loop-like CME leading edge. We show that the faint front is caused by density compression at a wave (or possibly shock) front driven by the CME. We also present high-detailed multi-wavelength EUV observations that clarify the relative positioning of the prominence at the bottom of a coronal cavity with clear flux rope structure. Finally, we visually check the full LASCO CME database for flux rope structures. In the process, we classify the events into two clear flux rope classes (`3-part', `Loop'), jets and outflows (no clear structure). We find that at least 40% of the observed CMEs have clear flux rope structures. We propose a new definition for flux rope CMEs (FR-CMEs) as a coherent magnetic, twist-carrying coronal structure with angular width of at least 40 deg and able to reach beyond 10 Rsun which erupts on a time scale of a few minutes to several hours. We conclude that flux ropes are a common occurrence in CMEs and pose a challenge for future studies to identify CMEs that are clearly not FR-CMEs.Comment: 26 pages, 9 figs, to be published in Solar Physics Topical Issue "Flux Rope Structure of CMEs

On the structure and evolution of a polar crown prominence/filament system

Polar crown prominences are made of chromospheric plasma partially circling the Suns poles between 60 and 70 degree latitude. We aim to diagnose the 3D dynamics of a polar crown prominence using high cadence EUV images from the Solar Dynamics Observatory (SDO)/AIA at 304 and 171A and the Ahead spacecraft of the Solar Terrestrial Relations Observatory (STEREO-A)/EUVI at 195A. Using time series across specific structures we compare flows across the disk in 195A with the prominence dynamics seen on the limb. The densest prominence material forms vertical columns which are separated by many tens of Mm and connected by dynamic bridges of plasma that are clearly visible in 304/171A two-color images. We also observe intermittent but repetitious flows with velocity 15 km/s in the prominence that appear to be associated with EUV bright points on the solar disk. The boundary between the prominence and the overlying cavity appears as a sharp edge. We discuss the structure of the coronal cavity seen both above and around the prominence. SDO/HMI and GONG magnetograms are used to infer the underlying magnetic topology. The evolution and structure of the prominence with respect to the magnetic field seems to agree with the filament linkage model.Comment: 24 pages, 14 figures, Accepted for publication in Solar Physics Journal, Movies can be found at http://www2.mps.mpg.de/data/outgoing/panesar

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous H-alpha ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the center of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ~ 110 deg within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasiseparatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four H-alpha ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.Comment: 24 pages, 10 figures, Solar Physics (accepted

Using statistical and artificial neural networks to predict the permeability of loosely packed granular materials

Well-known analytical equations for predicting permeability are generally reported to overestimate this important property of porous media. In this work, more robust models developed from statistical (multivariable regression) and Artificial Neural Network (ANN) methods utilised additional particle characteristics [‘fines ratio’ (x50/x10) and particle shape] that are not found in traditional analytical equations. Using data from experiments and literature, model performance analyses with average absolute error (AAE) showed error of ~40% for the analytical models (Kozeny–Carman and Happel–Brenner). This error reduces to 9% with ANN model. This work establishes superiority of the new models, using experiments and mathematical techniques

A Helicity-Based Method to Infer the CME Magnetic Field Magnitude in Sun and Geospace: Generalization and Extension to Sun-Like and M-Dwarf Stars and Implications for Exoplanet Habitability

Patsourakos et al. (Astrophys. J. 817, 14, 2016) and Patsourakos and Georgoulis (Astron. Astrophys. 595, A121, 2016) introduced a method to infer the axial magnetic field in flux-rope coronal mass ejections (CMEs) in the solar corona and farther away in the interplanetary medium. The method, based on the conservation principle of magnetic helicity, uses the relative magnetic helicity of the solar source region as input estimates, along with the radius and length of the corresponding CME flux rope. The method was initially applied to cylindrical force-free flux ropes, with encouraging results. We hereby extend our framework along two distinct lines. First, we generalize our formalism to several possible flux-rope configurations (linear and nonlinear force-free, non-force-free, spheromak, and torus) to investigate the dependence of the resulting CME axial magnetic field on input parameters and the employed flux-rope configuration. Second, we generalize our framework to both Sun-like and active M-dwarf stars hosting superflares. In a qualitative sense, we find that Earth may not experience severe atmosphere-eroding magnetospheric compression even for eruptive solar superflares with energies ~ 10^4 times higher than those of the largest Geostationary Operational Environmental Satellite (GOES) X-class flares currently observed. In addition, the two recently discovered exoplanets with the highest Earth-similarity index, Kepler 438b and Proxima b, seem to lie in the prohibitive zone of atmospheric erosion due to interplanetary CMEs (ICMEs), except when they possess planetary magnetic fields that are much higher than that of Earth.Comment: http://adsabs.harvard.edu/abs/2017SoPh..292...89