ExoplANNET: A deep learning algorithm to detect and identify planetary signals in radial velocity data

The detection of exoplanets with the radial velocity method consists in detecting variations of the stellar velocity caused by an unseen sub-stellar companion. Instrumental errors, irregular time sampling, and different noise sources originating in the intrinsic variability of the star can hinder the interpretation of the data, and even lead to spurious detections. In recent times, work began to emerge in the field of extrasolar planets that use Machine Learning algorithms, some with results that exceed those obtained with the traditional techniques in the field. We seek to explore the scope of the neural networks in the radial velocity method, in particular for exoplanet detection in the presence of correlated noise of stellar origin. In this work, a neural network is proposed to replace the computation of the significance of the signal detected with the radial velocity method and to classify it as of planetary origin or not. The algorithm is trained using synthetic data of systems with and without planetary companions. We injected realistic correlated noise in the simulations, based on previous studies of the behaviour of stellar activity. The performance of the network is compared to the traditional method based on null hypothesis significance testing. The network achieves 28 % fewer false positives. The improvement is observed mainly in the detection of small-amplitude signals associated with low-mass planets. In addition, its execution time is five orders of magnitude faster than the traditional method. The superior performance exhibited by the algorithm has only been tested on simulated radial velocity data so far. Although in principle it should be straightforward to adapt it for use in real time series, its performance has to be tested thoroughly. Future work should permit evaluating its potential for adoption as a valuable tool for exoplanet detection.Comment: Accepted for publication; Corrected typos; Added section 6.1 with a robustness analysis of the method; Added section 6.2 with tests on a real time series; Added section 6.3 with a more detailed analysis of the caution of the network around activity periods; Added other tested models to the appendi

General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera

Towards an Ashtekar formalism in eight dimensions

We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M-theory via matroid theory.Comment: 15 pages, Latex, minor changes, to appear in Class. Quantum Gra

A photometric and kinematic study of the stars and interstellar medium in the central two kpc of NGC 3379

HST images of NGC 3379 show that the V and I luminosity profiles in the inner 13 arcsec of this E1 galaxy are represented by two different components: a stellar bulge following a Sersic Law with exponent n = 2.36, and a central core (r < 0.7 arcsec) with a characteristic "cuspy" profile. Subtraction of the underlying stellar component represented by the fitted Sersic profile revealed the presence of a small (r ~ 105 pc) dust disk of about 150 solar masses, oriented at PA = 125 degrees and inclined ~ 77 degrees with respect to the line of sight. The same absorption structure is detected in the color-index (V-I) image. The stellar rotation in the inner 20 arcsec is well represented by a parametric planar disk model, inclined ~ 26 degrees relative to the plane of the sky, and apparent major axis along PA ~ 67 degrees. The gas velocity curves in the inner 5 arcsec show a steep gradient, indicating that the gas rotates much faster than the stars, although in the same direction. The velocity field of the gaseous system, however, is not consistent with the simple model of Keplerian rotation sustained by the large (7 x 10E9 solar masses within a radius of ~ 90 pc) central mass implied by the maximum velocity observed, but the available data precludes a more detailed analysis.Comment: 23 pages, LaTeX(aaspp4.sty), 9 figures included. Figs. 1 and 5 are colour plates. Accepted for publication in The Astrophysical Journal (part 1

Very Large Telescope Observations of the peculiar globular cluster NGC6712. Discovery of a UV, H-alpha excess star in the core

We present results from multi-band observations in the central region of the cluster NGC6712 with the ESO-Very Large Telescope. Using high resolution images we have identified three UV-excess stars. In particular two of them are within the cluster core, a few arcsec apart: the first object is star "S" which previous studies identified as the best candidate to the optical counterpart to the luminous X-ray source detected in this cluster. The other UV object shows clearcut H-alpha emission and, for this reason, is an additional promising interacting binary candidate (a quiescent LMXB or a CV). The presence of two unrelated interacting binary systems a few arcsec apart in the core of this low-density cluster is somewhat surprising and supports the hypothesis that the (internal) dynamical history of the cluster and/or the (external) interaction with the Galaxy might play a fundamental role in the formation of these peculiar objects.Comment: 15 pages, 3 figures. ApJL in pres

Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems

In this paper, we show that the destruction of the main KAM islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands ('islets') for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps

Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering

In the context of nonhyperbolic chaotic scattering, it has been shown that the evolution of the KAM islands exhibits four abrupt metamorphoses that strongly affect the predictability of Hamiltonian systems. It has been suggested that these metamorphoses are related to significant changes in the structure of the KAM islands. However, previous research has not provided an explanation of the mechanisms underlying the metamorphoses. Here, we show that they occur due to the formation of a homoclinic or heteroclinic tangle that breaks the internal structure of the main KAM island. We obtain similar qualitative results in a two-dimensional Hamiltonian system and a two-dimensional area-preserving map. The equivalence of the results obtained in both systems suggests that the same four metamorphoses play an important role in conservative systems

Evidence for a 3 x 10^8 solar mass black hole in NGC 7052 from HST observations of the nuclear gas disk

We present an HST study of the nuclear region of the E4 radio galaxy NGC 7052, which has a nuclear disk of dust and gas. The WFPC2 was used to obtain B, V and I broad-band images and an H_alpha+[NII] narrow-band image. The FOS was used to obtain H_alpha+[NII] spectra along the major axis, using a 0.26 arcsec diameter circular aperture. The observed rotation velocity of the ionized gas is V = 155 +/- 17 km/s at r = 0.2 arcsec from the nucleus. The Gaussian dispersion of the emission lines increases from sigma = 70 km/s at r=1 arcsec, to sigma = 400 km/s on the nucleus. To interpret the gas kinematics we construct axisymmetric models in which the gas and dust reside in a disk in the equatorial plane of the stellar body. It is assumed that the gas moves on circular orbits, with an intrinsic velocity dispersion due to turbulence. The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole (BH). Models without a BH predict a rotation curve that is shallower than observed (V_pred = 92 km/s at r = 0.2 arcsec), and are ruled out at > 99% confidence. Models with a BH of 3.3^{+2.3}_{-1.3} x 10^8 solar masses provide an acceptable fit. NGC 7052 can be added to the list of active galaxies for which HST spectra of a nuclear gas disk provide evidence for the presence of a central BH. The BH masses inferred for M87, M84, NGC 6251, NGC 4261 and NGC 7052 span a range of a factor 10, with NGC 7052 falling on the low end. By contrast, the luminosities of these galaxies are identical to within 25%. Any relation between BH mass and luminosity, as suggested by independent arguments, must therefore have a scatter of at least a factor 10.Comment: 39 pages, LaTeX, with 16 PostScript figures. Submitted to the Astronomical Journal. Postscript version with higher resolution figures available from http://sol.stsci.edu/~marel/abstracts/abs_R22.htm

Self-dual gravity and self-dual Yang-Mills in the context of Macdowell-Mansouri formalism

In this work we propose an action which unifies self-dual gravity and self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We claim that such an action may be used to find the S-dual action for both self-dual gravity and self-dual Yang-Mills.Comment: 8 pages, Revtex, no figures, submitted to Phys. Rev.