arXiv subjects

Luca Rizzi

Publications and source records attributed to Luca Rizzi.

At least 55 records · Page 3Linked to original sources

arXiv2020

KKH 22, the first dwarf spheroidal satellite of IC 342

We present observations with the Advanced Camera for Surveys on the Hubble Space Telescope of the nearby dwarf spheroidal galaxy KKH 22 = LEDA 2807114 in the vicinity of the massive spiral galaxy IC 342. We derived its distance of 3.12+-0.19 Mpc using the tip of red giant branch (TRGB) method. We also used the 6 m BTA spectroscopy to measure a heliocentric radial velocity of the globular cluster in KKH22 to be +30+-10 km/s. The dSph galaxy KKH 22 has the V-band absolute magnitude of -12.19 mag and the central surface brightness mu_v,0 = 24.1 mag/sq.arcsec. Both the velocity and the distance of KKH 22 are consistent with the dSph galaxy being gravitationally bound to IC 342. Another nearby dIr galaxy, KKH 34, with a low heliocentric velocity of +106 km/s has the TRGB distance of 7.28+-0.36 Mpc residing in the background with respect to the IC 342 group. KKH 34 has a surprisingly high negative peculiar velocity of -236+-26 km/s.

astro-ph.GA↗

arXiv2020

Bakry-Émery curvature and model spaces in sub-Riemannian geometry

We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry-Émery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound.

math.DG↗

arXiv2019

Peculiar Velocities of Galaxies Just Beyond the Local Group

The Milky Way lies in a thin plane, the Local Sheet, a part of a wall bounding the Local Void lying toward the north supergalactic pole. Galaxies with accurate distances both above and below this supergalactic equatorial plane have systematically negative peculiar velocities. The interpretation of this situation is that the Local Void is expanding, giving members of the Local Sheet deviant velocities toward the south supergalactic pole. The few galaxies within the void are evacuating the void. Galaxies in a filament in the supergalactic south are not feeling the expansion so their apparent motion toward us is mainly a reflex of our motion. The model of the local velocity field was uncertain because the apex of our motion away from the Local Void lies in obscurity near the Galactic plane. Here, results of Hubble Space Telescope infrared observations are reported that find tip of the red giant branch distances to four obscured galaxies. All the distances are $\sim7$ Mpc, revealing that these galaxies are part of a continuous filamentary structure passing between the north and south Galactic hemispheres and sharing the same kinematic signature of peculiar velocities toward us. A fifth galaxy nearby in projection, GALFA-DW4, has an ambiguous distance. If nearby at $\sim 3$ Mpc, this galaxy has an anomalous velocity away from us of +348 km/s. Alternatively, perhaps the resolved stars are on the asymptotic giant branch and the galaxy is beyond 6 Mpc whence the observed velocity would not be unusual.

astro-ph.GA↗

arXiv2019

Multi-Filament Inflows Fueling Young Star Forming Galaxies

Theory suggests that there are two primary modes of accretion through which dark matter halos acquire the gas to form and fuel galaxies, hot and cold mode accretion. In cold mode accretion, gas streams along cosmic web filaments to the center of the halo, allowing for the efficient delivery of star-forming fuel. Recently, two QSO-illuminated HI Lyman alpha (Lyα) emitting objects were reported to have properties of cold, rotating structures (Martin et al. 2015, Martin et al. 2016). However, the spatial and spectral resolution available was insufficient to constrain radial flows associated with connecting filaments. With the Keck Cosmic Web Imager (KCWI) we now have eight times the spatial resolution, permitting the detection of these in-spiraling flows. In order to detect these inflows, we introduce a suite of models which incorporate zonal radial flows, demonstrate their performance on a numerical simulation that exhibits coldflow accretion, and show that they are an excellent match to KCWI velocity maps of two Lyα emitters observed around high-redshift quasars. These Multi-Filament Inflow models kinematically isolate zones of radial inflow that correspond to extended filamentary emission. The derived gas flux and inflow path is sufficient to fuel the inferred central galaxy star formation rate and angular momentum. Thus, our kinematic emission maps provide strong evidence for the inflow of gas from the cosmic web building galaxies at the peak of star formation.

astro-ph.GA↗

arXiv2019

On birational trivial families and Adjoint quadrics

Let $π\colon \mathcal{X}\to B$ be a family whose general fiber $X_b$ gives a $(d_1,...,d_a)$ polarisation of a general Abelian variety where $1\leq d_i\leq 2$, $i=1,...,a$ and $a\geq 4$. We show that the fibers are in the same birational class if all the $(m,0)$ forms on $X_b$ are liftable to $(m,0)$ forms on $\mathcal{X}$ where $m=1$ and $m=a-1$. Actually we show general criteria to find families with fibers in the same birational class, which leads together with a famous theorem of Nori to some interesting applications.

math.AG↗

arXiv2019

The Distance and Motion of the Maffei Group

It has recently been suggested that the nearby galaxies Maffei 1 and 2 are further in distance than previously thought, such that they no longer are members of the same galaxy group as IC 342. We reanalyze near-infrared photometry from the Hubble Space Telescope, and find a distance to Maffei 2 of $5.73\pm0.40$ Mpc. With this distance, the Maffei Group lies 2.5 Mpc behind the IC 342 Group and has a peculiar velocity toward the Local Group of $-128\pm33$ km/s. The negative peculiar velocities of both of these distinct galaxy groups are likely the manifestation of void expansion from the direction of Perseus-Pisces.

astro-ph.GA↗

arXiv2019

Weighted Fano varieties and infinitesimal Torelli problem

We solve the infinitesimal Torelli problem for $3$-dimensional quasi-smooth ${\mathbb{Q}}$-Fano hypersurfaces with at worst terminal singularities. We also find infinite chains of double coverings of increasing dimension which alternatively distribute themselves in examples and counterexamples for the infinitesimal Torelli claim and which share the analogue, and in some cases the same, Hodge-diagram properties as the length $3$ Gushel-Mukai chain of prime smooth Fanos of coindex $3$ and degree $10$.

math.AG↗

arXiv2019

On the essential self-adjointness of singular sub-Laplacians

We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp's measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This result holds under mild regularity assumptions on the singular region, and when the latter does not contain characteristic points.

math.DG↗

arXiv2018

Sub-Riemannian interpolation inequalities

We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As a byproduct, we characterize the cut locus as the set of points where the squared sub-Riemannian distance fails to be semiconvex, answering to a question raised by Figalli and Rifford in [Geom. Funct. Anal. (2010) 20: 124]. As an application, we deduce sharp and intrinsic Borell-Brascamp-Lieb and geodesic Brunn-Minkowski inequalities in the aforementioned setting. For the case of the Heisenberg group, we recover in an intrinsic way the results recently obtained by Balogh, Kristály and Sipos in [Calc. Var. PDE (2018) 57: 61], and we extend them to the class of generalized H-type Carnot groups. Our results do not require the distribution to have constant rank, yielding for the particular case of the Grushin plane a sharp measure contraction property and a sharp Brunn-Minkowski inequality.

math.DG↗

arXiv2018

The Keck Cosmic Web Imager Integral Field Spectrograph

We report on the design and performance of the Keck Cosmic Web Imager (KCWI), a general purpose optical integral field spectrograph that has been installed at the Nasmyth port of the 10 m Keck II telescope on Mauna Kea, HI. The novel design provides blue-optimized seeing-limited imaging from 350-560 nm with configurable spectral resolution from 1000 - 20000 in a field of view up to 20"x33". Selectable volume phase holographic (VPH) gratings and high performance dielectric, multilayer silver and enhanced aluminum coatings provide end-to-end peak efficiency in excess of 45% while accommodating the future addition of a red channel that will extend wavelength coverage to 1 micron. KCWI takes full advantage of the excellent seeing and dark sky above Mauna Kea with an available nod-and-shuffle observing mode. The instrument is optimized for observations of faint, diffuse objects such as the intergalactic medium or cosmic web. In this paper, a detailed description of the instrument design is provided with measured performance results from the laboratory test program and ten nights of on-sky commissioning during the spring of 2017. The KCWI team is lead by Caltech and JPL (project management, design and implementation) in partnership with the University of California at Santa Cruz (camera optical and mechanical design) and the W. M. Keck Observatory (observatory interfaces).

astro-ph.IM↗

arXiv2018

A Robust Tip of the Red Giant Branch Distance to the Fireworks Galaxy (NGC 6946)

Archival HST data taken in F606W+F814W of two different fields in the outer regions of NGC 6946 is used to measure a tip of the red giant branch (TRGB) distance to the galaxy. We employ a Bayesian maximum-likelihood modeling method that incorporates the completeness of the photometry, and allows us to model the luminosity function of the RGB population. Our two fields provide us with distances of 7.74 $\pm$ 0.42 Mpc and 7.69 $\pm$ 0.50 Mpc, respectively. Our final distance of 7.72 $\pm$ 0.32 Mpc is higher than most values published previously in the literature. This has important implications for supernova measurements, as NGC 6946 is host to the most observed supernovae (10) of any galaxy to date. We find that the supernovae in NGC 6946 are on average $\sim$ 2.3 times more luminous than previous estimates. Our distance gives NGC 6946 a peculiar velocity of $v_{pec}$ = $-229$ $\pm$ $29$ km/s in the Local Sheet frame. This velocity is the projected component of a substantial negative SGZ motion, indicating a coherent motion along with the other members of the M101 wall toward the plane of the Local Sheet. The M101 wall, a spur off the Local Sheet into the Local Void, is experiencing the expansion of the Local Void.

astro-ph.GA↗

arXiv2018

A counterexample to gluing theorems for MCP metric measure spaces

Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq κ$ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces satisfying synthetic Ricci curvature bounds in the $\mathrm{MCP}$ sense. The counterexample is given by the Grushin half-plane, which satisfies the $\mathrm{MCP}(0,N)$ if and only if $N\geq 4$, while its double satisfies the $\mathrm{MCP}(0,N)$ if and only if $N\geq 5$.

math.MG↗

arXiv2018

The Distance to the Galaxy Coma P

If the extremely low surface brightness galaxy Coma P lies at $5.5\pm0.3$ Mpc as recently proposed then it would have an extraordinarily deviant peculiar velocity of $\sim900$ km $\mathrm{s^{-1}}$ at a location where differential velocities between galaxies are low. We have accessed the images from the HST archives used to derive the literature distance from the magnitude of the tip of the red giant branch. Our analysis gives the distance to be $10.9\pm1.0$ Mpc. At this location the galaxy lies within the infall region of the Virgo Cluster, such that its still considerable peculiar velocity of $\sim500$ km $\mathrm{s^{-1}}$ is consistent with an established model. Coma P has an unusually pronounced asymptotic giant branch relative to its red giant branch. The dominant stellar population is just a few Gyr old.

astro-ph.GA↗

arXiv2018

TRGB distances to galaxies in front of the Virgo cluster

Tip of the red giant branch distances are acquired from Hubble Space Telescope images for 16 galaxies to the foreground of the Virgo Cluster. The new distances with 5% accuracy, combined with archival measurements, tightly constrain the near side location of the onset of infall into the Virgo Cluster to be 7.3+-0.3 Mpc from the cluster, reaching within 9 Mpc of the Milky Way. The mass within this turnaround radius about the cluster is 8.3+-0.9 x 10^{14} Msun. Color-magnitude diagrams are provided for galaxies in the study and there is brief discussion of their group affiliations.

astro-ph.GA↗

arXiv2017

Sharp measure contraction property for generalized H-type Carnot groups

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.

math.MG↗

arXiv2017

Quantum confinement on non-complete Riemannian manifolds

We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold $M$ equipped with a smooth measure $ω$, possibly degenerate or singular near the metric boundary of $M$, and in presence of a real-valued potential $V\in L^2_{\mathrm{loc}}(M)$. The main merit of this paper is the identification of an intrinsic quantity, the effective potential $V_{\mathrm{eff}}$, which allows to formulate simple criteria for quantum confinement. Let $δ$ be the distance from the possibly non-compact metric boundary of $M$. A simplified version of the main result guarantees quantum completeness if $V\ge -cδ^2$ far from the metric boundary and \[ V_{\mathrm{eff}}+V\ge \frac3{4δ^2}-\fracκδ, \qquad \text{close to the metric boundary}. \] These criteria allow us to: (i) obtain quantum confinement results for measures with degeneracies or singularities near the metric boundary of $M$; (ii) generalize the Kalf-Walter-Schmincke-Simon Theorem for strongly singular potentials to the Riemannian setting for any dimension of the singularity; (iii) give the first, to our knowledge, curvature-based criteria for self-adjointness of the Laplace-Beltrami operator; (iv) prove, under mild regularity assumptions, that the Laplace-Beltrami operator in almost-Riemannian geometry is essentially self-adjoint, partially settling a conjecture formulated in [Boscain, Laurent - Ann. Inst. Fourier, 2013] .

math.DG↗

arXiv2017

Andromeda's Parachute: A Bright Quadruply Lensed Quasar at z=2.377

We present Keck Cosmic Web Imager spectroscopy of the four putative images of the lensed quasar candidate J014709+463037 recently discovered by Berghea et al. (2017). The data verify the source as a quadruply lensed, broad absorption-line quasar having z_S = 2.377 +/- 0.007. We detect intervening absorption in the FeII 2586, 2600, MgII 2796, 2803, and/or CIV 1548, 1550 transitions in eight foreground systems, three of which have redshifts consistent with the photometric-redshift estimate reported for the lensing galaxy (z_L ~ 0.57). By virtue of their positions on the sky, the source images probe these absorbers over transverse physical scales of ~0.3-21 kpc, permitting assessment of the variation in metal-line equivalent width W_r as a function of sight-line separation. We measure differences in W_r,2796 of <40% across all sight-line pairs subtending 7-21 kpc, suggestive of a high degree of spatial coherence for MgII-absorbing material. W_r,2600 is observed to vary by >50% over the same scales across the majority of sight-line pairs, while CIV absorption exhibits a wide range in W_r,1548 differences of ~5-80% within transverse distances less than ~3 kpc. J014709+463037 is one of only a handful of z > 2 quadruply lensed systems for which all four source images are very bright (r = 15.4-17.7 mag) and are easily separated in ground-based seeing conditions. As such, it is an ideal candidate for higher-resolution spectroscopy probing the spatial variation in the kinematic structure and physical state of intervening absorbers.

astro-ph.GA↗

arXiv2017

Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds

For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev-Zelenko-Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider the sub-Riemannian structure of $3$-Sasakian manifolds, for which we provide explicit curvature formulas. We prove that any complete $3$-Sasakian structure of dimension $4d+3$, with $d>1$, has sub-Riemannian diameter bounded by $π$. When $d=1$, a similar statement holds under additional Ricci bounds. These results are sharp for the natural sub-Riemannian structure on $\mathbb{S}^{4d+3}$ of the quaternionic Hopf fibrations: \begin{equation*} \mathbb{S}^3 \hookrightarrow \mathbb{S}^{4d+3} \to \mathbb{HP}^d, \end{equation*} whose exact sub-Riemannian diameter is $π$, for all $d \geq 1$.

math.DG↗