Constraining the cometary flux through the asteroid belt during the late heavy bombardment

In the Nice model, the late heavy bombardment (LHB) is related to an orbital instability of giant planets which causes a fast dynamical dispersion of a transneptunian cometary disk. We study effects produced by these hypothetical cometary projectiles on main-belt asteroids. In particular, we want to check whether the observed collisional families provide a lower or an upper limit for the cometary flux during the LHB. We present an updated list of observed asteroid families as identified in the space of synthetic proper elements by the hierarchical clustering method, colour data, albedo data and dynamical considerations and we estimate their physical parameters. We selected 12 families which may be related to the LHB according to their dynamical ages. We then used collisional models and N-body orbital simulations to gain insight into the long-term dynamical evolution of synthetic LHB families over 4 Gyr. We account for the mutual collisions, the physical disruptions of comets, the Yarkovsky/YORP drift, chaotic diffusion, or possible perturbations by the giant-planet migration. Assuming a "standard" size-frequency distribution of primordial comets, we predict the number of families with parent-body sizes D_PB >= 200 km which seems consistent with observations. However, more than 100 asteroid families with D_PB >= 100 km should be created at the same time which are not observed. This discrepancy can be nevertheless explained by the following processes: i) asteroid families are efficiently destroyed by comminution (via collisional cascade), ii) disruptions of comets below some critical perihelion distance (q <~ 1.5 AU) are common. Given the freedom in the cometary-disruption law, we cannot provide stringent limits on the cometary flux, but we can conclude that the observed distribution of asteroid families does not contradict with a cometary LHB.Comment: accepted in Astronomy and Astrophysic

An advanced multipole model of the (130) Elektra quadruple system

The Ch-type asteroid (130) Elektra is orbited by three moons, making it the first quadruple system in the main asteroid belt. We aim to characterise the irregular shape of Elektra and construct a complete orbital model of its unique moon system. We applied the All-Data Asteroid Modelling (ADAM) algorithm to 60 light curves of Elektra, including our new measurements, 46 adaptive-optics (AO) images obtained by the VLT/SPHERE and Keck/Nirc2 instruments, and two stellar occultation profiles. For the orbital model, we used an advanced $N$-body integrator, which includes a multipole expansion of the central body (with terms up to the order $\ell = 6$), mutual perturbations, internal tides, as well as the external tide of the Sun acting on the orbits. We fitted the astrometry measured with respect to the central body and also relatively, with respect to the moons themselves. We obtained a revised shape model of Elektra with the volume-equivalent diameter $(201\pm 2)\,{\rm km}$. Out of two pole solutions, $(\lambda, \beta) = (189; -88)\,{\rm deg}$ is preferred, because the other one leads to an incorrect orbital evolution of the moons. We also identified the true orbital period of the third moon S/2014 (130) 2 as $P_2 = (1.642112 \pm 0.000400)\,{\rm d}$, which is in between the other periods, $P_1 \simeq 1.212\,{\rm d}$, $P_3 \simeq 5.300\,{\rm d}$, of S/2014 (130) 1 and S/2003 (130) 1, respectively. The resulting mass of Elektra, $(6.606 \substack{+0.007 \\ -0.013}) \times 10^{18}\,{\rm kg}$, is precisely constrained by all three orbits. Its bulk density is then $(1.536 \pm 0.038)\,{\rm g\,cm}^{-3}$. The expansion with the assumption of homogeneous interior leads to the oblateness $J_2 = -C_{20} \simeq 0.16$. However, the best-fit precession rates indicate a slightly higher value, ${\simeq}\,0.18$.Comment: 19 pages, 23 figure

Improved model of the triple system V746 Cas that has a bipolar magnetic field associated with the tertiary

V746 Cas is known to be a triple system composed of a close binary with an alternatively reported period of either 25.4d or 27.8d and a third component in a 62000d orbit. The object was also reported to exhibit multiperiodic light variations with periods from 0.83d to 2.50d, on the basis of which it was classified as a slowly pulsating B star. Interest in further investigation of this system was raised by the detection of a variable magnetic field. Analysing spectra from four instruments, earlier published radial velocities, and several sets of photometric observations, we arrived at the following conclusions: (1) The optical spectrum is dominated by the lines of the B-type primary (Teff1~16500(100) K), contributing 70% of the light in the optical region, and a slightly cooler B tertiary (Teff3~13620(150) K). The lines of the low-mass secondary are below our detection threshold; we estimate that it could be a normal A or F star. (2) We resolved the ambiguity in the value of the inner binary period and arrived at a linear ephemeris of T_super.conj.=HJD 2443838.78(81)+25.41569(42)xE. (3) The intensity of the magnetic field undergoes a~sinusoidal variation in phase with one of the known photometric periods, namely 2.503867(19)d, which we identify with the rotational period of the tertiary. (4) The second photometric 1.0649524(40)d period is identified with the rotational period of the B-type primary, but this interpretation is much less certain and needs further verification. (5) If our interpretation of photometric periods is confirmed, the classification of the object as a slowly pulsating B star should be revised. (6) Applying an N-body model to different types of available observational data, we constrain the orbital inclination of the inner orbit to ~60 deg to 85 deg even in the absence of eclipses, and estimate the probable properties of the triple system and its components.Comment: Accepted for publication in Astronomy and Astrophysic

A unified solution for the orbit and light-time effect in the V505 Sgr system

The multiple system V505 Sagittarii is composed of at least three stars: a compact eclipsing pair and a distant component, which orbit is measured directly using speckle interferometry. In order to explain the observed orbit of the third body in V505 Sagittarii and also other observable quantities, namely the minima timings of the eclipsing binary and two different radial velocities in the spectrum, we thoroughly test a fourth-body hypothesis - a perturbation by a dim, yet-unobserved object. We use an N-body numerical integrator to simulate future and past orbital evolution of 3 or 4 components in this system. We construct a suitable chi^2 metric from all available speckle-interferometry, minima-timings and radial-velocity data and we scan a part of a parameter space to get at least some of allowed solutions. In principle, we are able to explain all observable quantities by a presence of a fourth body, but the resulting likelihood of this hypothesis is very low. We also discuss other theoretical explanations of the minima timings variations. Further observations of the minima timings during the next decade or high-resolution spectroscopic data can significantly constrain the model

Pumping Capacity of Pitched Blade Impellers in a Tall Vessel with a Draught Tube

A study was made of the pumping capacity of pitched blade impellers (two, three, four, five and six blade pitched blade impellers with pitch angles α = 35° and 45°) coaxially located in a cylindrical pilot plant vessel with cylindrical draught tube provided with a standard dished bottom. The draught tube was equipped with four equally spaced radial baffles above the impeller pumping liquid upwards towards the liquid surface. In all investigated cases the liquid aspect ratio H/T = 1.2 - 1.5, the draught tube / vessel diameter ratios DT /T = 0.2 and 0.4 and the impeller / draught tube diameter ratio D/DT = 0.875. The pumping capacity of the impeller was calculated from the radial profile of the axial component of the mean velocity in the draught tube below the impeller at such an axial distance from the impeller that the rotor does not affect the vorticity of the flow. The mean velocity was measured using a laser Doppler anemometer with forward scatter mode in a transparent draught tube and a transparent vessel of diameter T = 400 mm. Two series of experiments were performed, both of them under a turbulent regime of flow of the agitated liquid. First, the optimum height of the dished bottom was sought, and then the dependences of the dimensionless flow rate criterion and the impeller power number on the number of impeller blades were determined for both pitch angles tested under conditions of optimum ratio HT /DT. It follows from the results of the experiments that the optimum ratio HT /DT = 0.25 when the cross sectional areas of the horizontal flow around the bottom and the vertical inflow to the draught tube are the same. For all the tested pitched blade impellers the impeller power number when α = 45° exceeds the value of this quantity when pitch angle α  =   35°, while the flow rate number when α = 35° exceeds this quantity when α = 45°. On the other hand, the absolute values of the impeller power number when the draught tube was introduced correspond fairly well to the dimensionless impeller power input measured in a system without a draught tube. However, the absolute values of the flow rate number found in the former system are significantly lower than the dimensionless impeller pumping capacity determined in the latter system. The hydraulic efficiency of pitched blade impellers N3Qp/Po for the investigated geometry of the agitated systems does not depend on the number of impeller blades, but it is significantly lower than the quantity determined in an agitated system with a dished bottom but without the draught tube

Did the Hilda collisional family form during the late heavy bombardment?

We model the long-term evolution of the Hilda collisional family located in the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution evolves mostly due to the Yarkovsky/YORP effect and assuming that: (i) impact disruption was isotropic, and (ii) albedo distribution of small asteroids is the same as for large ones, we can estimate the age of the Hilda family to be $4_{-1}^{+0}\,{\rm Gyr}$. We also calculate collisional activity in the J3/2 region. Our results indicate that current collisional rates are very low for a 200\,km parent body such that the number of expected events over Gyrs is much smaller than one. The large age and the low probability of the collisional disruption lead us to the conclusion that the Hilda family might have been created during the Late Heavy Bombardment when the collisions were much more frequent. The Hilda family may thus serve as a test of orbital behavior of planets during the LHB. We tested the influence of the giant-planet migration on the distribution of the family members. The scenarios that are consistent with the observed Hilda family are those with fast migration time scales $\simeq 0.3\,{\rm Myr}$ to $3\,{\rm Myr}$, because longer time scales produce a family that is depleted and too much spread in eccentricity. Moreover, there is an indication that Jupiter and Saturn were no longer in a compact configuration (with period ratio $P_{\rm S}/P_{\rm J} > 2.09$) at the time when the Hilda family was created

V2368 Oph: An eclipsing and double-lined spectroscopic binary used as a photometric comparison star for U Oph

The A-type star HR 6412 = V2368 Oph was used by several investigators as a photometric comparison star for the known eclipsing binary U Oph but was found to be variable by three independent groups, including us. By analysing series of new spectral and photometric observations and a critical compilation of available radial velocities, we were able to find the correct period of light and radial-velocity variations and demonstrate that the object is an eclipsing and double-lined spectroscopic binary moving in a highly eccentric orbit. We derived a linear ephemeris T min.I = HJD (2454294.67 +/- 0.01) + (38.32712 +/- 0.00004)d x E and estimated preliminary basic physical properties of the binary. The dereddened UBV magnitudes and effective temperatures of the primary and secondary, based on our light- and velocity-curve solutions, led to distance estimates that agree with the Hipparcos distance within the errors. We find that the mass ratio must be close to one, but the limited number and wavelength range of our current spectra does not allow a truly precise determination of the binary masses. Nevertheless, our results show convincingly that both binary components are evolved away from the main sequence, which makes this system astrophysically very important. There are only a few similarly evolved A-type stars among known eclipsing binaries. Future systematic observations and careful analyses can provide very stringent tests for the stellar evolutionary theory.Comment: 10 pages, 7 figs, in press 2011 A&