arXiv subjects

Luca Rizzi

Publications and source records attributed to Luca Rizzi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries

We prove that, on any sub-Riemannian manifold endowed with a positive smooth measure, the Bakry-Émery inequality for the corresponding sub-Laplacian implies the existence of enough Killing vector fields on the tangent cone to force the latter to be Euclidean at each point, yielding the failure of the curvature-dimension condition in full generality. Our approach does not apply to non-strictly-positive measures. In fact, we prove that the weighted Grushin plane does not satisfy any curvature-dimension condition, but, nevertheless, does admit an a.e. pointwise version of the Bakry-Émery inequality. As recently observed by Pan and Montgomery, one half of the weighted Grushin plane satisfies the RCD(0,N) condition, yielding a counterexample to gluing theorems in the RCD setting.

math.DG↗

arXiv2022

Cosmicflows-4

With Cosmicflows-4, distances are compiled for 55,877 galaxies gathered into 38,065 groups. Eight methodologies are employed, with the largest numbers coming from the correlations between the photometric and kinematic properties of spiral galaxies (TF) and elliptical galaxies (FP). Supernovae that arise from degenerate progenitors (type Ia Sne) are an important overlapping component. Smaller contributions come from distance estimates from the surface brightness fluctuations of elliptical galaxies and the luminosities and expansion rates of core collapse supernovae (SNII). Cepheid period-luminosity relation and tip of the red giant branch observations founded on local stellar parallax measurements along with the geometric maser distance to NGC 4258 provide the absolute scaling of distances. The assembly of galaxies into groups is an important feature of the study in facilitating overlaps between methodologies. Merging between multiple contributions within a methodology and between methodologies is carried out with Bayesian Markov chain Monte Carlo procedures. The final assembly of distances is compatible with a value of the Hubble constant of $H_0=74.6$ km s$^{-1}$ Mpc$^{-1}$ with the small statistical error of $\pm 0.8$ km s$^{-1}$ Mpc$^{-1}$ but a large potential systematic error of ~3 km s$^{-1}$ Mpc$^{-1}$. Peculiar velocities can be inferred from the measured distances. The interpretation of the field of peculiar velocities is complex because of large errors on individual components and invites analyses beyond the scope of this study.

astro-ph.CO↗

arXiv2022

Global Kodaira Spencer class and Massey products

We define a new notion of supported global deformation class for a semistable family of complex varieties over a curve $f\colon X\to B$. We use this notion to study when $X$, possibly up to a finite covering, has a generically finite morphism onto a product $B\times Y$ with $Y$ of general type.

math.AG↗

arXiv2022

Massey products and Fujita decomposition over higher dimensional base

Let $f\colon X\to Y$ be a semistable fibration between smooth complex varieties of dimension $n$ and $m$. This paper contains an analysis of the local systems of de Rham closed relative one forms and top forms on the fibers. In particular the latter recovers the local system of the second Fujita decomposition of $f_*ω_{X/Y}$ over higher dimensional base. The so called theory of Massey products allows, under natural Castelnuovo-type hypothesis, to study the finiteness of the associated monodromy representations. Motivated by this result, we also make precise the close relation between Massey products and Castelnuovo-de Franchis type theorems.

math.AG↗

arXiv2022

H-type foliations

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound, we prove on those structures sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of those spaces in codimension more than 2.

math.DG↗

arXiv2022

Local Systems, Algebraic Foliations and Fibrations

Given a semistable fibration $f\colon X\to B$ we introduce a correspondence between foliations $\mathcal{F}$ on $X$ and local systems $\mathbb{L}$ on $B$. Building up on this correspondence we find conditions that give maximal rationally connected fibrations in terms of data on the foliation. We prove the Castelnuovo-de Franchis theorem in the case of $p$-forms and we apply it to show when, under some natural conditions, a line subbundle of the sheaf of $p$-forms induces the Iitaka fibration.

math.AG↗

arXiv2022

Resolving the HI in Damped Lyman-α systems that power star-formation

Reservoirs of dense atomic gas (primarily hydrogen), contain approximately 90 percent of the neutral gas at a redshift of 3, and contribute to 2-3 percent of the total baryons in the Universe. These damped Lyman-$α$ systems (so called because they absorb Lyman-$α$ photons from within and from background sources) have been studied for decades, but only through absorption lines present in the spectra of background quasars and gamma-ray bursts. Such pencil beams do not constrain the physical extent of the systems. Here, we report integral-field spectroscopy of a bright, gravitationally lensed galaxy at a redshift of 2.7 with two foreground damped Lyman-$α$ systems. These systems are $>$ 238 $kpc^2$ in extent, with column densities of neutral hydrogen varying by more than an order of magnitude on $<$ 3 kpc-scales. The mean column densities are $10^{20.46}$ - $10^{20.84} cm^{-2}$ and the total masses are $> 5.5 \times 10^{8}$ - $1.4 \times 10^{9} M_{\odot}$, showing that they contain the necessary fuel for the next generation of star formation, consistent with relatively massive, low-luminosity primeval galaxies at redshifts $>$ 2.

astro-ph.GA↗

arXiv2022

Comparing Tip of the Red Giant Branch Distance Scales: An Independent Reduction of the Carnegie-Chicago Hubble Program and the Value of the Hubble Constant

The tip of the red giant branch has been used to measure distances to 500 nearby galaxies with the Hubble Space Telescope (HST) which are available in the Color-Magnitude Diagrams and Tip of the Red Giant Branch (CMDs/TRGB) catalog on the Extragalactic Distance Database (EDD). Our established methods are employed to perform an independent reduction of the targets presented by the Carnegie-Chicago Hubble Program (CCHP) in the series of papers culminating in Freedman (2021). Our distinct methodology involves modeling the observed luminosity function of red giant branch and asymptotic giant branch stars, which differs from the edge-detection algorithms employed by the CCHP. We find excellent agreement between distances for 11 hosts with new imaging, all at D < 20 Mpc. However, we are unable to measure the TRGB for 4 of the 5 hosts that use archival data designed to measure distances with Cepheids, all at D > 23 Mpc. With two new HST observations taken in the halo of the megamaser host NGC 4258, the first with the same ACS F606W and F814W filters and the post-servicing electronics used for SN Ia hosts, we then calibrate our TRGB distance scale to the geometric megamaser distance. Using our TRGB distances, we find a value of the Hubble Constant of $H_{0}$ = 71.5 $\pm$ 1.8 km/s/Mpc when using either the Pantheon or Carnegie Supernova Project (CSP) samples of supernovae. In the future, the James Webb Space Telescope will extend measurements of the TRGB to additional hosts of SN Ia and surface brightness fluctuation measurements for separate paths to $H_{0}$.

astro-ph.CO↗

arXiv2021

The Extragalactic Distance Database: The Color-Magnitude Diagrams and Tip of the Red Giant Branch Distances Catalog

The Extragalactic Distance Database (EDD) was created as a repository for high quality, redshift-independent distances. A key component of EDD is the Color Magnitude Diagrams/Tip of the Red Giant Branch (CMDs/TRGB) catalog, which provides information on the stellar content of nearby galaxies observed with the Hubble Space Telescope (HST). Here we provide a decadal update to this catalog, which has now doubled in size to over 500 galaxies. We highlight the additions to our data reduction and analysis techniques, and provide examples of the science that has been made possible with this large data set. We find the TRGB to be a reliable measure for distance, and we aim to extend its distance coverage with HST to every galaxy within 10 Mpc. In the near-future, the combination of the James Webb Space Telescope and the Nancy Grace Roman Space Telescope will dramatically increase the number of targets within our grasp.

astro-ph.GA↗

arXiv2021

Distance and mass of the NGC 253 galaxy group

Two dwarf galaxies: WOC2017-07 and PGC 704814 located in the vicinity of the nearby luminous spiral galaxy NGC 253 were observed with the Advanced Camera for Surveys on the Hubble Space Telescope. Their distances of 3.62$\pm$0.18 Mpc and 3.66$\pm$0.18 Mpc were derived using the tip of the red giant branch method. These distances are consistent with the dwarf galaxies being members of the NGC 253 group. Based on the radial velocities and projected separations of seven assumed dwarf companions, we estimated the total mass of NGC 253 to be $(8.1\pm2.6) 10^{11} M_{\odot}$, giving a total-mass-to-$K$-luminosity ratio $M_{\rm orb}/L_K = (8.5\pm2.7) M_{\odot}/L_{\odot}$. A notable property of NGC 253 is its declined rotation curve. NGC 253 joins four other luminous spiral galaxies in the Local Volume with declined rotation curves (NGC 2683, NGC 2903, NGC 3521 and NGC 5055) that together have the low average total-mass-to-luminosity ratio, $M_{\rm orb}/L_K = (5.5\pm1.1) M_{\odot}/L_{\odot}$. This value is only $\sim$1/5 of the corresponding ratio for the Milky Way and M 31.

astro-ph.GA↗

arXiv2020

On Massey products and Rational homogeneous varieties

We study the equivalence between infinitesimal Torelli theorem for smooth hypersurfaces in rational homogeneous varieties with Picard number one and the theory of generalized Massey products. This equivalence shows that the differential of the period map vanishes on an infinitesimal deformation if and only if certain twisted differential forms are elements of the Jacobian ideal of the hypersurface. We also prove an infinitesimal Torelli theorem result for smooth hypersurfaces in log parallelizable varieties.

math.AG↗

arXiv2020

Distances to PHANGS Galaxies: New Tip of the Red Giant Branch Measurements and Adopted Distances

PHANGS-HST is an ultraviolet-optical imaging survey of 38 spiral galaxies within ~20 Mpc. Combined with the PHANGS-ALMA, PHANGS-MUSE surveys and other multiwavelength data, the dataset will provide an unprecedented look into the connections between young stars, HII regions, and cold molecular gas in these nearby star-forming galaxies. Accurate distances are needed to transform measured observables into physical parameters (e.g., brightness to luminosity, angular to physical sizes of molecular clouds, star clusters and associations). PHANGS-HST has obtained parallel ACS imaging of the galaxy halos in the F606W and F814W bands. Where possible, we use these parallel fields to derive tip of the red giant branch (TRGB) distances to these galaxies. In this paper, we present TRGB distances for 11 galaxies from ~4 to ~15 Mpc, based on the first year of PHANGS-HST observations. Five of these represent the first published TRGB distance measurements (IC 5332, NGC 2835, NGC 4298, NGC 4321, and NGC 4328), and eight of which are the best available distances to these targets. We also provide a compilation of distances for the 118 galaxies in the full PHANGS sample, which have been adopted for the first PHANGS-ALMA public data release.

astro-ph.GA↗

arXiv2020

Heat content asymptotics for sub-Riemannian manifolds

We study the small-time asymptotics of the heat content of smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a technique due to Savo, we establish the existence of the full asymptotic series: \begin{equation} Q_Ω(t) = \sum_{k=0}^{\infty} a_k t^{k/2}, \qquad \text{as } t\to 0. \end{equation} We compute explicitly the coefficients up to order $k=5$, in terms of sub-Riemannian invariants of the domain and its boundary. Furthermore, we prove that every coefficient can be obtained as the limit of the corresponding one for a suitable Riemannian extension. As a particular case we recover, using non-probabilistic techniques, the order $2$ formula due to Tyson and Wang in the first Heisenberg group [J. Tyson, J. Wang, Comm. PDE, 2018]. An intriguing byproduct of our fifth-order analysis is the evidence for new phenomena in presence of characteristic points. In particular, we prove that the higher order coefficients in the expansion can blow-up in their presence. A key tool for this last result is an exact formula for the sub-Riemannian distance from a specific surface with an isolated characteristic point in the first Heisenberg group, which is of independent interest.

math.AP↗

arXiv2020

Distance and mass of the M104 (Sombrero) group

Distances and radial velocities of galaxies in the vicinity of the luminous early-type galaxy M 104 (Sombrero) are used to derive its dark matter mass. Two dwarf galaxies: UGCA 307 and KKSG 30 situated near M 104 were observed with the Advanced Camera for Surveys on the Hubble Space Telescope. The distances $9.03^{+0.84}_{-0.51}$ Mpc (UGCA 307) and $9.72^{+0.44}_{-0.41}$ Mpc (KKSG 30) were determined using the tip of the red giant branch method. These distances are consistent with the dwarf galaxies being satellites of Sombrero. Using radial velocities and projected separations of UGCA 307, KKSG 30, and a third galaxy with an accurate distance (KKSG 29), as well as 12 other assumed companions with less accurate distances, the total mass of M 104 is estimated to be $(1.55\pm0.49) 10^{13} M_{\odot}$. At the K-band luminosity of the Sombrero galaxy of $2.4 10^{11} L_{\odot}$, its total mass-to-luminosity ratio is $M_T/L_K = (65\pm20)M_{\odot}/L_{\odot}$, which is about three times higher than that of luminous bulgeless galaxies.

astro-ph.GA↗

arXiv2020

Fujita decomposition and Massey product for fibered varieties

Let $f\colon X\to B$ be a semistable fibration where $X$ is a smooth variety of dimension $n\geq 2$ and $B$ is a smooth curve. We give the structure theorem for the local system of the relative $1$-forms and of the relative top forms. This gives a neat interpretation of the second Fujita decomposition of $f_*ω_{X/B}$. We apply our interpretation to show the existence, up to base change, of higher irrational pencils and on the finiteness of the associated monodromy representations under natural Castelnuovo-type hypothesis on local subsystems. Finally we give a criterion to have that $X$ is not of Albanese general type if $B=\mathbb{P}^1$.

math.AG↗

arXiv2020

Branching geodesics in sub-Riemannian geometry

In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment. The simplest example is obtained by gluing the three-dimensional Martinet flat structure with the Heisenberg group in a suitable way. We then use this example to construct more general types of branching.

math.DG↗

arXiv2020

Cosmicflows 4: The Calibration of Optical and Infrared Tully-Fisher Relations

This study is a part of the Cosmicflows-4 project with the aim of measuring the distances of more than ~10,000 spiral galaxies in the local universe up to ~15,000 km/s. New HI linewidth information has come primarily from the Arecibo Legacy Fast ALFA Survey. Photometry of our sample galaxies has been carried out in optical (SDSS u, g, r, i, z) and infrared (WISE W1 and W2) bands. Inclinations have been determined using an online graphical interface accessible to a collaboration of citizen scientists. Galaxy distances are measured based on the correlation between the rotation rate of spirals and their absolute luminosity, known as the Tully-Fisher Relation (TFR). In this study, we present the calibration of the TFR using a subsample of ~600 spirals located in 20 galaxy clusters. Correlations among such observables as color, surface brightness, and relative HI content are explored in an attempt to reduce the scatter about the TFR with the goal of obtaining more accurate distances. A preliminary determination of the Hubble constant from the distances and velocities of the calibrator clusters is H0=76.0+-1.1(stat.)+-2.3(sys.) km/s/Mpc.

astro-ph.GA↗

arXiv2020

Internal kinematics of giant H II regions in M101 with the Keck Cosmic Web Imager

We study the kinematics of the giant H II regions NGC 5455 and NGC 5471 located in the galaxy M101, using integral field observations that include the Hbeta and [O III] 5007 emission lines, obtained with the Keck Cosmic Web Imager. We analyse the line profiles using both single and multiple Gaussian curves, gathering evidence for the presence of several expanding shells and moving filaments. The line decomposition shows that a broad (sigma = 30-50 km/s) underlying component is ubiquitous, extending across hundreds of pc, while a large fraction of the narrow components have subsonic line widths. The supersonic turbulence inferred from the global line profiles is consistent with the velocity dispersion of the individual narrow components, i.e. the global profiles likely arise from the combined contribution of discrete gas clouds. We confirm the presence of very extended (400 - 1200 km/s) low-intensity line components in three bright star-forming cores in NGC 5471, possibly representing kinematic signatures of supernova remnants. For one of these, the known supernova remnant host NGC 5471 B, we find a significantly reduced [O III]/Hbeta line ratio relative to the surrounding photoionized gas, due to the presence of a radiative shock at low metallicity. We explore the systematic width discrepancy between H I and [O III] lines, present in both global and individual spaxel spectra. We argue that the resolution of this long-standing problem lies in the physics of the line-emitting gas rather than in the smearing effects induced by the different thermal widths.

astro-ph.GA↗