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Richard Miles

Publications and source records attributed to Richard Miles.

17 recordsLinked to original sources
arXiv2021

Physical Characterization of Main-Belt Comet (248370) 2005 QN173

We report results from new and archival observations of the newly discovered active asteroid (248370) 2005 QN_137, which has been determined to be a likely main-belt comet based on a subsequent discovery that it is recurrently active near perihelion. From archival data analysis, we estimate g'-, r'-, i'-, and z'-band absolute magnitudes for the nucleus of H_g=16.62+/-0.13, H_r=16.12+/-0.10, H_i=16.05+/-0.11, and H_z=15.93+/-0.08, corresponding to nucleus colors of g'-r'=0.50+/-0.16, r'-i'=0.07+/-0.15, and i'-z'=0.12+/-0.14, an equivalent V-band absolute magnitude of H_V=16.32+/-0.08, and a nucleus radius of r_n=1.6+/-0.2 km (using a V-band albedo of p_V=0.054+/-0.012). Meanwhile, we find mean near-nucleus coma colors when 248370 was active of g'-r'=0.47+/-0.03, r'-i'=0.10+/-0.04, and i'-z'=0.05+/-0.05, and similar mean dust tail colors, suggesting that no significant gas coma is present. We find approximate ratios between the scattering cross-sections of near-nucleus dust (within 5000 km of the nucleus) and the nucleus of A_d/A_n=0.7+/-0.3 on 2016 July 22, and 1.8<A_d/A_n<2.9 in 2021 July and August. During the 2021 observation period, the coma declined in intrinsic brightness by ~0.35 mag (or ~25%) in 37 days, while the surface brightness of the dust tail remained effectively constant over the same period. Constraints derived from the sunward extent of the coma suggest that terminal velocities of ejected dust grains are extremely slow (~1 m/s for 1 micron particles), indicating that the observed dust emission may have been aided by rapid rotation of the nucleus lowering the effective escape velocity.

astro-ph.EP↗
arXiv2019

Physical Characterization of the December 2017 Outburst of the Centaur 174P/Echeclus

The Centaurs are the small solar system bodies intermediate between the active inner solar system Jupiter Family Comets and their inactive progenitors in the trans-Neptunian region. Among the fraction of Centaurs which show comet-like activity, 174P/Echeclus is best known for its massive 2005 outburst in which a large apparently active fragment was ejected above the escape velocity from the primary nucleus. We present visible imaging and near-infrared spectroscopy of Echeclus during the first week after its December 2017 outburst taken at the Faulkes North & South Telescopes and the NASA IRTF, the largest outburst since 2005. The coma was seen to be highly asymmetric. A secondary peak was seen in the near-infrared 2D spectra, which is strongly hinted at in the visible images, moving hyperbolically with respect to the nucleus. The retrieved reflectance spectrum of Echelcus is consistent with the unobscured nucleus but becomes bluer when a wider extraction aperture is used. We find that Echeclus's coma is best explained as dominated by large blue dust grains, which agrees with previous work. We also conducted a high-resolution orbital integration of Echeclus's recent evolution and found no large orbital changes that could drive its modern evolution. We interpret the second peak in the visible and near-infrared datasets as a large cloud of larger-than-dust debris ejected at the time of outburst. If Echeclus is typical of the Centaurs, there may be several debris ejection or fragmentation events per year on other Centaurs that are going unnoticed.

astro-ph.EP↗
arXiv2015

A dynamical zeta function for group actions

This article introduces and investigates the basic features of a dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single transformation. A product formula for the dynamical zeta function is established that highlights a crucial link between this function and the zeta function of the acting group. A variety of examples are explored, with a particular focus on full shifts and closely related variants. Amongst the examples, it is shown that there are infinitely many non-isomorphic virtually cyclic groups for which the full shift has a rational zeta function. In contrast, it is shown that when the acting group has Hirsch length at least 2, a dynamical zeta function with a natural boundary is more typical. The relevance of the dynamical zeta function in questions of orbit growth is also considered.

math.DS↗
arXiv2015

The dynamical zeta function for commuting automorphisms of zero-dimensional groups

For a $\mathbb{Z}^d$-action $α$ by commuting homeomorphisms of a compact metric space, Lind introduced a dynamical zeta function that generalizes the dynamical zeta function of a single transformation. In this article, we investigate this function when $α$ is generated by continuous automorphisms of a compact abelian zero-dimensional group. We address Lind's conjecture concerning the existence of a natural boundary for the zeta function and prove this for two significant classes of actions, including both zero entropy and positive entropy examples. The finer structure of the periodic point counting function is also examined and, in the zero entropy case, we show how this may be severely restricted for subgroups of prime index in $\mathbb{Z}^d$. We also consider a related open problem concerning the appearance of a natural boundary for the dynamical zeta function of a single automorphism, giving further weight to the Polya-Carlson dichotomy proposed by Bell and the authors.

math.DS↗
arXiv2014

Directional uniformities, periodic points, and entropy

Dynamical systems generated by $d\ge2$ commuting homeomorphisms (topological $\mathbb{Z}^d$-actions) contain within them structures on many scales, and in particular contain many actions of $\mathbb{Z}^k$ for $1\le k\le d$. Familiar dynamical invariants for homeomorphisms, like entropy and periodic point data, become more complex and permit multiple definitions. We briefly survey some of these and other related invariants in the setting of algebraic $\mathbb{Z}^d$-actions, showing how, even in settings where the natural entropy as a $\mathbb{Z}^d$-action vanishes, a powerful theory of directional entropy and periodic points can be built. An underlying theme is uniformity in dynamical invariants as the direction changes, and the connection between this theory and problems in number theory; we explore this for several invariants. We also highlight Fried's notion of average entropy and its connection to uniformities in growth properties, and prove a new relationship between this entropy and periodic point growth in this setting.

math.DS↗
arXiv2013

Dynamical invariants for group automorphisms

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the problem of determining the range of certain invariants of topological conjugacy is discussed. Several new results and old and new open problems are described.

math.DS↗
arXiv2010

A method for determining the V magnitude of asteroids from CCD images

We describe a method of determining the V magnitude of an asteroid using differential photometry, with the magnitudes of comparison stars derived from Carlsberg Meridian Catalogue 14 (CMC14) data. The availability of a large number of suitable CMC14 stars enables a reasonably accurate magnitude (\pm0.05 mag) to be found without having to resort to more complicated absolute or all-sky photometry. An improvement in accuracy to \pm0.03 mag is possible if an ensemble of several CMC14 stars is used. This method is expected to be less accurate for stars located within \pm10deg of the galactic equator owing to excessive interstellar reddening and stellar crowding.

astro-ph.EP↗
arXiv2010

Sloan-r' photometry of Comet 17P/Holmes beyond 3.8 AU: An observing methodology for short-period comets far from perihelion

A photometric method is described for accurately quantifying the brightness of short-period comets far from perihelion. The method utilizes the Sloan Digital Sky Survey Catalog (Data Release 7) as a homogeneous source of reference star magnitudes. Results are based on SDSS-r' filtered images taken using 2.0-m aperture telescopes for which the exposure time was adjusted to achieve a constant motion-blur of 2.0 pixels (0.56 arcsec) on the CCD chip. Aperture photometry using circular and tilted elliptical apertures was performed on images, which were stacked to increase signal to noise. Magnitude dependence on 'seeing' was determined, and this calibration was used to normalize photometry to constant seeing thereby maximizing photometric accuracy. From observations of comet 17P/Holmes between 2008 October and 2009 March, a very significant outburst of 17P was found to have occurred on 2009 Jan 4.7 (\pm0.5 day). Night-to-night measurements of the brightness of the inner coma (3000-km radius) exhibited a scatter of only 0.015-0.019 mag. No short time-scale (<36 hr) periodicity was found in the fading lightcurve. From literature data, it was estimated that reflected light from the nucleus contributed 7-11% of the signal within the inner coma and it is concluded that either the nucleus of 17P must be relatively spherical (projected axial ratio of <1.25), or, if its shape is more typical of other comet nuclei, it has a rotational period in excess of 10 days (assuming the observations were not made with the nucleus 'pole-on' to the Earth). Evidence from intermittent activity displayed by the nucleus is indicative of a possible 44-day rotation period.

astro-ph.EP↗
arXiv2009

A dichotomy in orbit-growth for commuting automorphisms

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those for which there is no excess of periodic orbits.

math.DS↗
arXiv2007

A novel mechanism for outbursts of Comet 17P/Holmes and other short-period comets

A mechanism is proposed to explain the outburst of comet 17P/Holmes based on; (a) oxidation of water within the porous surface of the comet nucleus to form hydrogen peroxide (H2O2) through exposure to UV radiation, to energetic solar-wind particles and to cosmic radiation, (b) concentration of the H2O2 component through solid-, liquid- and gas-phase processes involving sublimation, evaporation, fractional crystallization, diffusion, supercooling, capillary wetting and migration in voids within the nucleus, and (c) rapid exothermic decomposition of aqueous H2O2 liberating oxygen gas via a surface catalytic reaction through interaction with finely-dispersed transition metals, metal compounds and minerals, in particular those containing Fe, localised within a differentiated multi-component comet nucleus. An accelerated release of gaseous oxygen, concomitant self-heating and volatilisation of hydrocarbons within the nucleus results in its explosive disruption. This mechanism may also explain the observation of a repeat outburst of this comet in 1893. Laboratory studies to investigate H2O2 formation in simulated cometary environments and to evaluate H2O2 decomposition on meteoritic samples are recommended.

astro-ph↗
arXiv2007

Orbit-counting for nilpotent group shifts

We study the asymptotic behaviour of the orbit-counting function and a dynamical Mertens' theorem for the full $G$-shift for a finitely-generated torsion-free nilpotent group $G$. Using bounds for the M{ö}bius function on the lattice of subgroups of finite index and known subgroup growth estimates, we find a single asymptotic of the shape \[ \sum_{|τ|\le N}\frac{1}{e^{h|τ|}}\sim CN^α(\log N)^β \] where $|τ|$ is the cardinality of the finite orbit $τ$. For the usual orbit-counting function we find upper and lower bounds together with numerical evidence to suggest that for actions of non-cyclic groups there is no single asymptotic in terms of elementary functions.

math.DS↗
arXiv2006

Periodic Point Data Detects Subdynamics in Entropy Rank One

A framework for understanding the geometry of continuous actions of Z^d was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z^d-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the expansive subdynamics. Moreover, the finer structure of the non-expansive set is visible in the topological and smooth structure of a set of functions associated to the periodic point data.

math.DS↗
arXiv2005

Expansive algebraic actions of countable abelian groups

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic $\mathbb{Z}^d$-actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains.

math.DS↗
arXiv2005

Mixing actions of the rationals

We study mixing properties of algebraic actions of $\mathbb Q^d$, showing in particular that prime mixing $\mathbb Q^d$ actions on connected groups are mixing of all orders, as is the case for $\mathbb Z^d$-actions. This is shown using a uniform result on the solution of $S$-unit equations in characteristic zero fields due to Evertse, Schlickewei and Schmidt. In contrast, algebraic actions of the much larger group $\mathbb Q^*$ are shown to behave quite differently, with finite order of mixing possible on connected groups.

math.DS↗
arXiv2001

Expansive subdynamics for algebraic $Z^d$-actions

A general framework for investigating topological actions of $Z^d$ on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of $R^d$. Here we completely describe this expansive behavior for the class of algebraic $Z^d$-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an algebraic variety together with a directional version of Noetherian modules over the ring of Laurent polynomials in several commuting variables. We introduce two notions of rank for topological $Z^d$-actions, and for algebraic $Z^d$-actions describe how they are related to each other and to Krull dimension. For a linear subspace of $R^d$ we define the group of points homoclinic to zero along the subspace, and prove that this group is constant within an expansive component.

math.DS↗