arXiv subjects

Luca Rizzi

Publications and source records attributed to Luca Rizzi.

At least 91 records · Page 5Linked to original sources

arXiv2015

Curvature: a variational approach

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.

math.DG↗

arXiv2015

Two Planes of Satellites in the Centaurus A Group

Tip of the red giant branch measurements based on Hubble Space Telescope and ground-based imaging have resulted in accurate distances to 29 galaxies in the nearby Centaurus A Group. All but two of the 29 galaxies lie in either of two thin planes roughly parallel with the supergalactic equator. The planes are only slightly tilted from the line-of-sight, leaving little ambiguity regarding the morphology of the structure. The planes have characteristic r.m.s. long axis dimensions of ~300 kpc and short axis dimensions of ~60 kpc, hence axial ratios ~0.2, and are separated in the short axis direction by 303 kpc.

astro-ph.GA↗

arXiv2015

Carbon in Red Giants in Globular Clusters and Dwarf Spheroidal Galaxies

We present carbon abundances of red giants in Milky Way globular clusters and dwarf spheroidal galaxies (dSphs). Our sample includes measurements of carbon abundances for 154 giants in the clusters NGC 2419, M68, and M15 and 398 giants in the dSphs Sculptor, Fornax, Ursa Minor, and Draco. This sample doubles the number of dSph stars with measurements of [C/Fe]. The [C/Fe] ratio in the clusters decreases with increasing luminosity above log(L/L_sun) ~= 1.6, which can be explained by deep mixing in evolved giants. The same decrease is observed in dSphs, but the initial [C/Fe] of the dSph giants is not uniform. Stars in dSphs at lower metallicities have larger [C/Fe] ratios. We hypothesize that [C/Fe] (corrected to the initial carbon abundance) declines with increasing [Fe/H] due to the metallicity dependence of the carbon yield of asymptotic giant branch stars and due to the increasing importance of Type Ia supernovae at higher metallicities. We also identified 11 very carbon-rich giants (8 previously known) in three dSphs. However, our selection biases preclude a detailed comparison to the carbon-enhanced fraction of the Milky Way stellar halo. Nonetheless, the stars with [C/Fe] < +1 in dSphs follow a different [C/Fe] track with [Fe/H] than the halo stars. Specifically, [C/Fe] in dSphs begins to decline at lower [Fe/H] than in the halo. The difference in the metallicity of the [C/Fe] "knee" adds to the evidence from [alpha/Fe] distributions that the progenitors of the halo had a shorter timescale for chemical enrichment than the surviving dSphs.

astro-ph.GA↗

arXiv2014

On conjugate times of LQ optimal control problems

Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.

math.OC↗

arXiv2014

Infrared Tip of the Red Giant Branch and Distances to the Maffei/IC 342 Group

In this paper, we extend the use of the tip of the red giant branch (TRGB) method to near-infrared wavelengths from previously-used $I$-band, using the \textit{Hubble Space Telescope (HST)} Wide Field Camera 3 (WFC3). Upon calibration of a color dependency of the TRGB magnitude, the IR TRGB yields a random uncertainty of $\sim 5%$ in relative distance. The IR TRGB methodology has an advantage over the previously-used ACS $F606W$ and $F814W$ filter set for galaxies that suffer from severe extinction. Using the IR TRGB methodology, we obtain distances toward three principal galaxies in the Maffei/IC 342 complex, which are located at low Galactic latitudes. New distance estimates using the TRGB method are 3.45$^{+0.13}_{-0.13}$ Mpc for IC 342, 3.37$^{+0.32}_{-0.23}$ Mpc for Maffei 1 and 3.52$^{+0.32}_{-0.30}$ Mpc for Maffei 2. The uncertainties are dominated by uncertain extinction, especially for Maffei 1 and Maffei 2. Our IR calibration demonstrates the viability of the TRGB methodology for observations with the \textit{James Webb Space Telescope (JWST)}.

astro-ph.GA↗

arXiv2013

Cosmicflows-2: The Data

Cosmicflows-2 is a compilation of distances and peculiar velocities for over 8000 galaxies. Numerically the largest contributions come from the luminosity-linewidth correlation for spirals, the TFR, and the related Fundamental Plane relation for E/S0 systems, but over 1000 distances are contributed by methods that provide more accurate individual distances: Cepheid, Tip of the Red Giant Branch, Surface Brightness Fluctuation, SNIa, and several miscellaneous but accurate procedures. Our collaboration is making important contributions to two of these inputs: Tip of the Red Giant Branch and TFR. A large body of new distance material is presented. In addition, an effort is made to assure that all the contributions, our own and those from the literature, are on the same scale. Overall, the distances are found to be compatible with a Hubble Constant H_0 = 74.4 +-3.0 km/s/Mpc. The great interest going forward with this data set will be with velocity field studies. Cosmicflows-2 is characterized by a great density and high accuracy of distance measures locally, falling to sparse and coarse sampling extending to z=0.1.

astro-ph.CO↗

arXiv2013

A formula for Popp's volume in sub-Riemannian geometry

For an equiregular sub-Riemannian manifold M, Popp's volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp's volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub-Laplacian, namely the one associated with Popp's volume. Finally, we discuss sub-Riemannian isometries, and we prove that they preserve Popp's volume. We also show that, under some hypotheses on the action of the isometry group of M, Popp's volume is essentially the unique volume with such a property.

math.DG↗

arXiv2010

The Star Formation History of Isolated Dwarf UGC4879

Recent observations of UGC4879 with the Advanced Camera for Surveys on the Hubble Space Telescope confirm that it is a nearby isolated dwarf irregular galaxy. We measure a distance of 1.36+/-0.03 Mpc using the Tip of the Red Giant Branch method. This distance puts UGC4879 beyond the radius of first turnaround of the Local Group and ~700 kpc from its nearest neighbor Leo A. This isolation makes this galaxy an ideal laboratory for studying pristine star formation uncomplicated by interactions with other galaxies. We present the star formation history of UGC4879 derived from simulated color-magnitude diagrams.

astro-ph.CO↗

arXiv2010

Dark matter effects in vacuum spacetime

We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime.

gr-qc↗

arXiv2010

The Step-Harmonic Potential

We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit.

quant-ph↗

arXiv2009

Extensive optical and near-infrared observations of the nearby, narrow-lined type Ic SN 2007gr: days 5 to 415

We present photometric and spectroscopic observations at optical and near-infrared wavelengths of the nearby type Ic SN 2007gr. These represent the most extensive data-set to date of any supernova of this sub-type, with frequent coverage from shortly after discovery to more than one year post-explosion. We deduce a rise time to B-band maximum of 11.5 \pm 2.7 days. We find a peak B-band magnitude of M_B=-16.8, and light curves which are remarkably similar to the so-called 'hypernova' SN 2002ap. In contrast, the spectra of SNe 2007gr and 2002ap show marked differences, not least in their respective expansion velocities. We attribute these differences primarily to the density profiles of their progenitor stars at the time of explosion i.e. a more compact star for SN 2007gr compared to SN 2002ap. From the quasi-bolometric light curve of SN 2007gr, we estimate that 0.076 $\pm$ 0.010 Msun of 56Ni was produced in the explosion. Our near-infrared (IR) spectra clearly show the onset and disappearance of the first overtone of carbon monoxide (CO) between ~70 to 175 days relative to B-band maximum. The detection of the CO molecule implies that ionised He was not microscopically mixed within the carbon/oxygen layers. From the optical spectra, near-IR light curves, and colour evolution, we find no evidence for dust condensation in the ejecta out to about 400 days. Given the combination of unprecedented temporal coverage, and high signal-to-noise data, we suggest that SN 2007gr could be used as a template object for supernovae of this sub-class.

astro-ph.SR↗

arXiv2008

Luminosity-Metallicity Relation for dIrr Galaxies in the Near-Infrared

(abridged) The present work is a first step to collect homogeneous abundances and near-infrared (NIR) luminosities for a sample of dwarf irregular (dIrr) galaxies, located in nearby groups. The use of NIR luminosities is intended to provide a better proxy to mass than the blue luminosities commonly used in the literature; in addition, selecting group members reduces the impact of uncertain distances. Accurate abundances are derived to assess the galaxy metallicity. Optical spectra are collected for Hii regions in the dIrrs, allowing the determination of oxygen abundances by means of the temperature-sensitive method. For each dIrr galaxy H-band imaging is performed and the total magnitudes are measured via surface photometry. This high-quality database allows us to build a well-defined luminosity-metallicity relation in the range -13 >= M(H) >= -20. The scatter around its linear fit is reduced to 0.11 dex, the lowest of all relations currently available. There might exist a difference between the relation for dIrrs and the relation for giant galaxies, although a firm conclusion should await direct abundance determinations for a significant sample of massive galaxies. This new dataset provides an improved luminosity-metallicity relation, based on a standard NIR band, for dwarf star-forming galaxies. The relation can now be compared with some confidence to the predictions of models of galaxy evolution. Exciting follow-ups of this work are (a) exploring groups with higher densities, (b) exploring nearby galaxy clusters to probe environmental effects on the luminosity-metallicity relation, and (c) deriving direct oxygen abundances in the central regions of star-forming giant galaxies, to settle the question of a possible dichotomy between the chemical evolution of dwarfs and that of massive galaxies.

astro-ph↗

arXiv2008

Variable stars in the Fornax dSph Galaxy. II. Pulsating stars below the horizontal branch

We have carried out an intensive survey of the northern region of the Fornax dwarf spheroidal galaxy with the aim of detecting the galaxy's short--period pulsating stars (P<0.25 days). Observations collected over three consecutive nights with the Wide Field Imager of the 2.2m MPI telescope at ESO allowed us to detect 85 high-amplitude (0.20-1.00 mag in B-light) variable stars with periods in the range from 0.046 to 0.126 days, similar to SX Phoenicis stars in Galactic metal-poor stellar populations. The plots of the observed periods vs. the B and V magnitudes show a dispersion largely exceeding the observational errors. To disentangle the matter, we separated the first-overtone from the fundamental-mode pulsators and tentatively identified a group of subluminous variables, about 0.35 mag fainter than the others. Their nature as either metal-poor intermediate-age stars or stars formed by the merging of close binary systems is discussed. The rich sample of the Fornax variables also led us to reconstruct the Period-Luminosity relation for short-period pulsating stars. An excellent linear fit, M(V)=-1.83(+/-0.08)-3.65(+/-0.07) log P(fund), was obtained using 153 Delta Scuti and SX Phoenicis stars in a number of different stellar systems.

astro-ph↗

arXiv2008

The Araucaria Project. The Distance of the Large Magellanic Cloud from Near-Infrared Photometry of RR Lyrae Variables

We have obtained deep infrared $J$ and $K$ band observations of five fields located in the Large Magellanic Cloud (LMC) bar with the ESO New Technology Telescope equipped with the SOFI infrared camera. In our fields, 65 RR Lyrae stars catalogued by the OGLE collaboration were identified. Using different theoretical and empirical calibrations of the period-luminosity-metallicity relation, we find consistent LMC distance moduli values. Since the observed fields are situated very close to the center of the LMC, the correction for the tilt of the LMC bar with respect to the line of sight is negligible. Our adopted best true distance modulus to the LMC of $18.58 \pm 0.03$ (statistical) $\pm$ 0.11 (systematic) mag agrees very well with most independent determinations to this galaxy.

astro-ph↗

arXiv2007

Our Peculiar Motion Away from the Local Void

The peculiar velocity of the Local Group of galaxies manifested in the Cosmic Microwave Background dipole is found to decompose into three dominant components. The three components are clearly separated because they arise on distinct spatial scales and are fortuitously almost orthogonal in their influences. The nearest, which is distinguished by a velocity discontinuity at ~7 Mpc, arises from the evacuation of the Local Void. We lie in the Local Sheet that bounds the void. Random motions within the Local Sheet are small. Our Galaxy participates in the bulk motion of the Local Sheet away from the Local Void. The component of our motion on an intermediate scale is attributed to the Virgo Cluster and its surroundings, 17 Mpc away. The third and largest component is an attraction on scales larger than 3000 km/s and centered near the direction of the Centaurus Cluster. The amplitudes of the three components are 259, 185, and 455 km/s, respectively, adding collectively to 631 km/s in the reference frame of the Local Sheet. Taking the nearby influences into account causes the residual attributed to large scales to align with observed concentrations of distant galaxies and reduces somewhat the amplitude of motion attributed to their pull. On small scales, in addition to the motion of our Local Sheet away from the Local Void, the nearest adjacent filament, the Leo Spur, is seen to be moving in a direction that will lead to convergence with our filament. Finally, a good distance to an isolated galaxy within the Local Void reveals that this dwarf system has a motion of at least 230 km/s away from the void center. Given the velocities expected from gravitational instability theory in the standard cosmological paradigm, the distance to the center of the Local Void must be at least 23 Mpc from our position. The Local Void is large!

astro-ph↗

arXiv2007

Tip of the Red Giant Branch Distances. II. Zero-Point Calibration

The luminosity of the Tip of the Red Giant Branch (TRGB) provides an excellent measure of galaxy distances and is easily determined in the resolved images of nearby galaxies observed with Hubble Space Telescope. There is now a large amount of archival data relevant to the TRGB methodology and which offers comparisons with other distance estimators. Zero-point issues related to the TRGB distance scale are reviewed in this paper. Consideration is given to the metallicity dependence of the TRGB, the transformations between HST flight systems and Johnson-Cousins photometry, the absolute magnitude scale based on Horizontal Branch measurements, and the effects of reddening. The zero-point of the TRGB is established with a statistical accuracy of 1%, modulo the uncertainty in the magnitude of the Horizontal Branch, with a typical rms uncertainty of 3% in individual galaxy distances at high Galactic latitude. The zero-point is consistent with the Cepheids period-luminosity relation scale but invites reconsideration of the claimed metallicity dependence with that method. The maser distance to NGC 4258 is consistent with TRGB but presently has lower accuracy.

astro-ph↗

arXiv2006

Tip of the Red Giant Branch Distances. I. Optimization of a Maximum Likelihood Algorithm

Accurate distances to galaxies can be determined from the luminosities of stars at the Tip of the Red Giant Branch (TRGB). We use a Maximum Likelihood algorithm to locate the TRGB in galaxy color-magnitude diagrams. The algorithm is optimized by introducing reliable photometric errors and a completeness characterization determined with artificial star experiments. The program is extensively tested using Monte-Carlo simulations, artificial galaxies, and a sample of nearby dwarf galaxies observed with HST/WFPC2 and ACS. Our procedure is shown to be reliable, to have good accuracy, and to not introduce any systematic errors. The methodology is especially useful in cases where the TRGB approaches the photometric limit and/or the RGB is poorly populated.

astro-ph↗

arXiv2005

The Araucaria Project: The Distance to NGC 300 from the Red Giant Branch Tip using HST/ACS imaging

We have used the Advanced Camera for Surveys on board the Hubble Space Telescope to obtain deep photometry of the NGC 300 spiral galaxy in the Sculptor group. The results have been used to derive an accurate distance determination based on the Tip of the Red Giant Branch distance estimator. Both edge-detection and maximum likelihood methods have been applied, to derive a distance modulus (m-M)_0=26.30 +/- 0.03 +/- 0.12 for edge-detection, and (m-M)_0=26.36 +/- 0.02 +/- 0.12 for maximum likelihood. These results are fully consistent with the recent distance estimate derived from near-IR photometry of Cepheids variable stars in the context of the Araucaria project, (m-M)_0= 26.37 +/- 0.05 +/- 0.03.

astro-ph↗