Comet dust as a mixture of aggregates and solid particles: model consistent with ground-based and space-mission results

The most successful model of comet dust presents comet particles as aggregates of submicron grains. It qualitatively explains the spectral and angular change in the comet brightness and polarization and is consistent with the thermal infrared data and composition of the comet dust obtained {\it in situ} for comet 1P/Halley. However, it experiences some difficulties in providing a quantitative fit to the observational data. Here we present a model that considers comet dust as a mixture of aggregates and compact particles. The model is based on the Giotto and Stardust mission findings that both aggregates (made mainly of organics, silicates, and carbon) and solid silicate particles are present in the comet dust. We simulate aggregates as {\bf Ballistic Cluster-Cluster Aggregates (BCCA)} and compact particles as polydisperse spheroids with some distribution of the aspect ratio. The particles follow a power-law size distribution with the power -3 that is close to the one obtained for comet dust {\it in situ}, at studies of the Stardust returned samples, and the results of ground-based observations of comets. The model provides a good fit to the angular polarization curve. It also reproduces the positive spectral gradient of polarization, red color of the dust, and {\bf low albedo. It also has the ratio of compact to fluffy particles close to the one found {\it in situ} for comet 1P/Halley} and the mass ratio of silicate to carbonaceous materials equal to unity that is in accordance with the elemental abundances of Halley's dust found by Giotto mission.Comment: "Earth and Planetary Science" (Japan), in pres

Photometry and polarimetry of the nucleus of comet 2P/Encke

Broadband imaging photometry, and broadband and narrowband linear polarimetry was measured for the nucleus of 2P/Encke over the phase-angle range 4 - 28 deg. An analysis of the point spread function of the comet reveals only weak coma activity, corresponding to a dust production of the order of 0.05 kg/s. The nucleus displays a color independent photometric phase function of almost linear slope. The absolute R filter magnitude at zero phase angle is 15.05 +/- 0.05, and corresponds to an equivalent radius for the nucleus of 2.43 +/- 0.06 km (for an adopted albedo of 0.047). The nucleus color V - R is 0.47 +/- 0.07, suggesting a spectral slope of 11 +/- 8 %/100nm. The phase function of linear polarimetry in the V and R filters shows a widely color independent linear increase with phase angle (0.12 +/- 0.02%/deg). We find discrepancies in the photometric and polarimetric parameters between 2P/Encke and other minor bodies in the solar system, which may indicate significant differences in the surface material properties and light-scattering behavior of the bodies. The linear polarimetric phase function of 2P/Encke presented here is the first ever measured for a cometary nucleus, and its analysis encourages future studies of cometary nuclei in order to characterize the light-scattering behavior of comets on firm empirical grounds and provide suitable input to a comprehensive modeling of the light scattering by cometary surfaces.Comment: Accepted by A&

Tighter Connections between Derandomization and Circuit Lower Bounds

We tighten the connections between circuit lower bounds and derandomization for each of the following three types of derandomization: - general derandomization of promiseBPP (connected to Boolean circuits), - derandomization of Polynomial Identity Testing (PIT) over fixed finite fields (connected to arithmetic circuit lower bounds over the same field), and - derandomization of PIT over the integers (connected to arithmetic circuit lower bounds over the integers). We show how to make these connections uniform equivalences, although at the expense of using somewhat less common versions of complexity classes and for a less studied notion of inclusion. Our main results are as follows: 1. We give the first proof that a non-trivial (nondeterministic subexponential-time) algorithm for PIT over a fixed finite field yields arithmetic circuit lower bounds. 2. We get a similar result for the case of PIT over the integers, strengthening a result of Jansen and Santhanam [JS12] (by removing the need for advice). 3. We derive a Boolean circuit lower bound for NEXP intersect coNEXP from the assumption of sufficiently strong non-deterministic derandomization of promiseBPP (without advice), as well as from the assumed existence of an NP-computable non-empty property of Boolean functions useful for proving superpolynomial circuit lower bounds (in the sense of natural proofs of [RR97]); this strengthens the related results of [IKW02]. 4. Finally, we turn all of these implications into equivalences for appropriately defined promise classes and for a notion of robust inclusion/separation (inspired by [FS11]) that lies between the classical "almost everywhere" and "infinitely often" notions

Agnostic Learning from Tolerant Natural Proofs

We generalize the "learning algorithms from natural properties" framework of [CIKK16] to get agnostic learning algorithms from natural properties with extra features. We show that if a natural property (in the sense of Razborov and Rudich [RR97]) is useful also against functions that are close to the class of "easy" functions, rather than just against "easy" functions, then it can be used to get an agnostic learning algorithm over the uniform distribution with membership queries. * For AC0[q], any prime q (constant-depth circuits of polynomial size, with AND, OR, NOT, and MODq gates of unbounded fanin), which happens to have a natural property with the requisite extra feature by [Raz87, Smo87, RR97], we obtain the first agnostic learning algorithm for AC0[q], for every prime q. Our algorithm runs in randomized quasi-polynomial time, uses membership queries, and outputs a circuit for a given Boolean function f that agrees with f on all but at most polylog(n)*opt fraction of inputs, where opt is the relative distance between f and the closest function h in the class AC0[q]. * For the ideal case, a natural proof of strongly exponential correlation circuit lower bounds against a circuit class C containing AC0[2] (i.e., circuits of size exp(Omega(n)) cannot compute some n-variate function even with exp(-Omega(n)) advantage over random guessing) would yield a polynomial-time query agnostic learning algorithm for C with the approximation error O(opt)

Spectropolarimetry of the Deep Impact target comet 9P/Tempel 1 with HiVIS

High resolution spectropolarimetry of the Deep Impact target, comet 9P/ Tempel 1, was performed during the impact event on July 4th, 2005 with the HiVIS Spectropolarimeter and the AEOS 3.67m telescope on Haleakala, Maui. We observed atypical polarization spectra that changed significantly in the few hours after the impact. The polarization of scattered light as a function of wavelength is very sensitive to the size and composition (complex refractive index) of the scattering particles as well as the scattering geometry. As opposed to most observations of cometary dust, which show an increase in the linear polarization with the wavelength (at least in the visible domain and for phase angles greater than about 30%, a red polarization spectrum) observations of 9P/Tempel 1 at a phase angle of 41 degrees beginning 8 minutes after impact and centered at 6:30UT showed a polarization of 4% at 650 nm falling to 3% at 950 nm. The next observation, centered an hour later showed a polarization of 7% at 650 nm falling to 2% at 950nm. This corresponds to a spectropolarimetric gradient, or slope, of -0.9% per 1000 Angstroms 40 minutes after impact, decreasing to a slope of -2.3% per 1000 Angstroms an hour and a half after impact. This is an atypical blue polarization slope, which became more blue 1 hour after impact. The polarization values of 4% and 7% at 650nm are typical for comets at this scattering angle, whereas the low polarization of 2% and 3% at 950nm is not. We compare observations of comet 9P/Tempel 1 to that of a typical comet, C/2004 Machholz, at a phase angle of 30 degrees which showed a typical red slope, rising from 2% at 650nm to 3% at 950nm in two different observations (+1.0 and +0.9% per 1000 Angstroms).Comment: Icarus Deep Impact special issue, accepted Aug 28 200

Photometry, spectroscopy, and polarimetry of distant comet C/2014 A4 (SONEAR)

Context. The study of distant comets, which are active at large heliocentric distances, is important for a better understanding of their physical properties and mechanisms of long-lasting activity. Aims. We analyzed the dust environment of the distant comet C/2014 A4 (SONEAR), with a perihelion distance near 4.1 au, using comprehensive observations obtained by different methods. Methods. We present an analysis of spectroscopy, photometry, and polarimetry of comet C/2014 A4 (SONEAR), which were performed on November 5–7, 2015, when its heliocentric distance was 4.2 au and phase angle was 4.7◦. Long-slit spectra and photometric and linear polarimetric images were obtained using the focal reducer SCORPIO-2 attached to the prime focus of the 6 m telescope BTA (SAO RAS, Russia). We simulated the behavior of color and polarization in the coma presenting the cometary dust as a set of polydisperse polyshapes rough spheroids. Results. No emission features were detected in the 3800–7200 Å wavelength range. The continuum showed a reddening effect with the normalized gradient of reflectivity 21.6 ± 0.2% per 1000 Å within the 4650–6200 Å wavelength region. The fan-like structure in the sunward hemisphere was detected. The radial profiles of surface brightness differ for r-sdss and g-sdss filters, indicating a predominance of submicron and micron-sized particles in the cometary coma. The dust color (g–r) varies from 0.75 ± 0.05m to 0.45 ± 0.06m along the tail. For an aperture radius near 20 000 km, the dust productions in various filters were estimated as Afρ = 680 ± 18 cm (r-sdss) and 887 ± 16 cm (g-sdss). The polarization map shows spatial variations in polarization over the coma from about −3% near the nucleus to −8% at a cometocentric distance of about 150 000 km. Our simulations show that the dust particles are dominated (or covered) by ice and tholin-like organics. Spatial changes in the color and polarization can be explained by particle fragmentation. © ESO 2019

Exploring the surface properties of Transneptunian Objects and Centaurs with polarimetric FORS1/VLT observations

Polarization is a powerful remote-sensing method to investigate solar system bodies. It is an especially sensitive diagnostic tool to reveal physical properties of the bodies whose observational characteristics are governed by small scatterers (dust, regolith surfaces). For these objects, at small phase angles, a negative polarization is observed, i.e., the electric vector E oscillates predominantly in the scattering plane, contrary to what is typical for rather smooth homogeneous surfaces. The behavior of negative polarization with phase angle depends on the size, composition and packing of the scatterers. These characteristics can be unveiled by modelling the light scattering by the dust or regolith in terms of the coherent backscattering mechanism. We have investigated the surface properties of TNOs and Centaurs by means of polarimetric observations with FORS1 of the ESO VLT. TNOs Ixion and Quaoar, and Centaur Chiron show a negative polarization surge. The Centaur Chiron has the deepest polarization minimum (-1.5 - 1.4%). The two TNOs show differing polarization curves: for Ixion, the negative polarization increases rapidly with phase; for Quaoar, the polarization is relatively small (~ -0.6%), and nearly constant at the observed phase angles. For all three objects, modelling results suggest that the surface contains an areal mixture of at least two components with different single-scatterer albedos and photon mean-free paths.Comment: 11 pages, 7 postscript figures, accepted by A&A; astro-ph abstract has been replaced with a more complete on

Evolution of the Dust Coma in Comet 67P/Churyumov-Gerasimenko Before 2009 Perihelion

Comet 67P/Churyumov-Gerasimenko is the main target of ESA's Rosetta mission and will be encountered in May 2014. As the spacecraft shall be in orbit the comet nucleus before and after release of the lander {\it Philae}, it is necessary necessary to know the conditions in the coma. Study the dust environment, including the dust production rate and its variations along its preperihelion orbit. The comet was observed during its approach to the Sun on four epochs between early-June 2008 and mid-January 2009, over a large range of heliocentric distances that will be covered by the mission in 2014. An anomalous enhancement of the coma dust density was measured towards the comet nucleus. The scalelength of this enhancement increased with decreasing heliocentric distance of the comet. This is interpreted as a result of an unusually slow expansion of the dust coma. Assuming a spherical symmetric coma, the average amount of dust as well as its ejection velocity have been derived. The latter increases exponentially with decreasing heliocentric distance (\rh), ranging from about 1 m/s at 3 AU to about 25-35 m/s at 1.4 AU. Based on these results we describe the dust environment at those nucleocentric distances at which the spacecraft will presumably be in orbit. Astronomy and Astrophysics, in pressComment: 5 pages, 4 figure