The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10⁶ comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1M_⊙−2M_⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.     

Injection of Oort Cloud comets: the fundamental role of stellar perturbations

We present Monte Carlo simulations of the dynamical evolution of the Oort cloud over the age of the Solar System, using an initial sample of one million test comets without any cloning. Our model includes perturbations due to the Galactic tide (radial and vertical) and passing stars. We present the first detailed analysis of the injection mechanism into observable orbits by comparing the complete model with separate models for tidal and stellar perturbations alone. We find that a fundamental role for injecting comets from the region outside the loss cone (perihelion distance q > 15 AU) into observable orbits (q < 5 AU) is played by stellar perturbations. These act in synergy with the tide such that the total injection rate is significantly larger than the sum of the two separate rates. This synergy is as important during comet showers as during quiescent periods and concerns comets with both small and large semi-major axes. We propose different dynamical mechanisms to explain the synergies in the inner and outer parts of the Oort Cloud. We find that the filling of the observable part of the loss cone under normal conditions in the present-day Solar System rises from <1% for a < 20 000 AU to about 100% for a ? 100 000 AU.     

Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort cloud comets discernable

For an Oort cloud comet to be seen as a new comet, its perihelion must be moved from a point exterior to the loss cylinder boundary to a point interior to observable limits in a single orbit. The galactic tide can do this continuously, in a non-impulsive manner. Near-parabolic comets, with specific angular momentum , will most easily be made observable. Therefore, to reduce the perihelion distance H must decrease. Since weakly perturbed comets are, in general, more numerous than strongly perturbed comets, we can anticipate that new comets made observable by a weak tidal torque will more likely be first observed when their slowly changing perihelion distances are approaching their minimum osculating values under the action of the tide, rather than receding from their minimum values. That is, defining ΔH_tide as the vector change due to the galactic tidal torque during the prior orbit, and H_obs as the observed vector, the sign S≡Sign(H_obs·ΔH_tide) will more likely be −1 than +1 if a weak galactic tidal perturbation indeed dominates in making comets observable. Using comet data of the highest quality class (1A) for new comets (a>10,000 AU), we find that 49 comets have S=−1 and 22 have S=+1. The binomial probability that as many or more would exhibit this characteristic if in fact S=?1 were equally likely is only 0.0009. This characteristic also persists in other long-period comet populations, lending support to the notion that they are dominated by comets recently arrived from the outer Oort cloud. The preponderance of S=−1 also correlates with weakly perturbed (i.e., smaller semimajor axis) new comets in a statistically significant manner. This is strong evidence that the data are of sufficiently high quality and sufficiently free of observational selection effects to detect this unique imprint of the tide.     

The key role of massive stars in Oort cloud comet dynamics

The effects of a sample of 1300 individual stellar encounters spanning a wide range of parameter values (mass, velocity and encounter distance) are investigated. Power law fits for the number of injected comets demonstrate the long range effect of massive stars, whereas light stars affect comets mainly along their tracks. Similarly, we show that the efficiency of a star to fill the phase space region of the Oort cloud where the Galactic tides are able to inject comets into the observable region - the so-called “tidally active zone” (TAZ) - is also strongly dependent on the stellar mass. Power laws similar to those for direct injection are obtained for the efficiency of stars to fill the TAZ. This filling of the tidally active zone is crucial for the long term flux of comets from the Oort cloud. Based on long-term Monte Carlo simulations using a constant Galactic tide and a constant flux of stellar encounters, but neglecting the detailed effects of planetary perturbations, we show that this flux essentially results from a two step mechanism: (i) the stellar injection of comets into the TAZ; and (ii) the tidal injection of TAZ comets into the loss cone. We find that single massive stars are able to induce “comet drizzles” - corresponding to an increase of the cometary flux of about 40% - which may last for more than 100 Myr by filling the TAZ to a higher degree than normal. It appears that the stars involved in this process are the same that cause comet showers.     

A model of the galactic tidal interaction with the oort comet cloud

We consider a model of the in situ Oort cloud which is isotropic with a random distrihution of perihelia directions and angular momenta. The energy distribution adopted has a continuous range of values appropriate for long-period (>200 yr) comets. Only the tidal torque of the Galaxy is included as a perturbation of comet orbits and it is approximated to be that due to a quasi-steady state distribution of matter with disk-like symmetry. The time evolution of all orbital elements can be analytically obtained for this case. In particular, the change in the perihelion distance per orbit and its dependence on other orbital elements is readily found. We further make the assumption that a comet whose perihelion distance was beyond 15 AU during its last passage through the Solar System would have orbit parameters that are essentially unchanged by planetary perturbations. Conversely, if the prior passage was inside 15 AU we assume that planetary perturbations would have removed the comet from the in situ energy distribution accessible by the galactic tide. Comets which had their perihelia changed from beyond 15 AU to within 5 AU in a single orbit are taken to be observable. We are able to track the evolution of 10⁶ comets as they are made observable by the galactic tidal touque. Detailed results are obtained for the predicted distribution of new (0 < 1/ < 10^–4 AU^–1) comets. Further, correlations between orbital elements can be studied. We present predictions of observed distributions and compare them with the random in situ results as well as with the actual observed distributions of class I comets. The predictions are in reasonable agreement with actual observations and, in many cases, are significantly different from random when perihelia directions are separated into galactic northern and southern hemispheres. However the well-known asymmetry in the north-south populations of perihelia remains to be explained. Such an asymmetry is consistent with the dominance of tidal torques today if a major stochastic event produced it in the past since tidal torques are unable to cause the migration of perihelia across the latitude barriers ±26°.6 in the disk model.     

Tidal gravitational forces: The infall of “new” comets and comet showers

The tidal gravitational field of the Galaxy directed into the galactic plane changes the angular momentum of comets in the Oort cloud. For comet orbits with semimajor axis greater than 2 × 10⁴ AU, the change of angular momentum in one orbit is sufficient to bring comets from the Oort cloud into the visible region, causing the infall of “new” comets. The limiting size orbit is weakly dependent on the angle between the major axis of the comet orbit and the galactic plane. The flux of comets into the inner Solar System caused by the galactic tidal field will be continuous and nearly isotropic. This effect appears to exclude any determination of the trajectories of passing stars by analysis of the angular distribution of new comets. The production of intense comet showers by the tidal field of a solar companion or of an interstellar cloud is considered. We show that the direction of a solar companion cannot be found from the present distribution of observable comets. The frequency of comet showers induced by encounters with interstellar clouds is found to be much lower than that from passing stars, and the tidal fields of interstellar clouds are not strong enough to cause comet showers of sufficient intensity to result in Earth impacts.     

Oort Cloud Comet Perihelion Asymmetries: Galactic Tide, Shower or Observational Bias?

We investigate the distribution of Oort cloud comet perihelia. The data considered includes comets having orbital elements of the two highest quality classes with original energies designated as new or young. Perihelion directions are determined in galactic, ecliptic and geocentric equatorial coordinates. Asymmetries are detected in the scatter and are studied statistically for evidence of adiabatic galactic tidal dynamics, an impulse-induced shower and observational bias. The only bias detected is the well-known deficiency of observations with perihelion distances q > 2.5 AU. There is no significant evidence of a seasonal dependence. Nor is there a substantive hemispherical bias in either ecliptic or equatorial coordinates. There is evidence for a weak stellar shower previously detected by Biermann which accounts for ≈ 10% of the total observations. Both the q bias and the Biermann star track serve to weaken the evidence for a galactic tidal imprint. Nevertheless, statistically significant asymmetries in galactic latitude and longitude of perihelia remain. A latitude asymmetry is produced by a dominant tidal component perpendicular to the galactic disk. The longitude signal implies that ≈ 20% of new comets need an additional dynamical mechanism. Known disk non-uniformities and an hypothetical bound perturber are discussed as potential explanations. We conclude that the detected dynamical signature of the galactic tide is real and is not an artifact of observational bias, impulsive showers or poor data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stellar velocity dispersion and mass estimation for galactic disks

Available velocity dispersion estimates for the old stellar population of galactic disks at galactocentric distances r?2L (where L is the photometric radial scale length of the disk) are used to determine the threshold local surface density of disks that are stable against gravitational perturbations. The mass of the disk M_d calculated under the assumption of its marginal stability is compared with the total mass M_t and luminosity L _B of the galaxy within r=4L. We corroborate the conclusion that a substantial fraction of the mass in galaxies is probably located in their dark halos. The ratio of the radial velocity dispersion to the circular velocity increases along the sequence of galactic color indices and decreases from the early to late morphological types. For most of the galaxies with large color indices (B–V)₀>0.75, which mainly belong to the S0 type, the velocity dispersion exceeds significantly the threshold value required for the disk to be stable. The reverse situation is true for spiral galaxies: the ratios M_d/L_B for these agree well with those expected for evolving stellar systems with the observed color indices. This suggests that the disks of spiral galaxies underwent no significant dynamical heating after they reached a quasi-equilibrium stable state.     

Algorithms for Stellar Perturbation Computations on Oort Cloud Comets

We investigate different approximate methods of computing the perturbations on the orbits of Oort cloud comets caused by passing stars, by checking them against an accurate numerical integration using Everhart’s RA15 code. The scenario under study is the one relevant for long-term simulations of the cloud’s response to a predefined set of stellar passages. Our sample of stellar encounters simulates those experienced by the Solar System currently, but extrapolated over a time of 10¹⁰ years. We measure the errors of perihelion distance perturbations for high-eccentricity orbits introduced by several estimators – including the classical impulse approximation and Dybczyński’s (1994, Celest. Mech. Dynam. Astron. 58, 1330–1338) method – and we study how they depend on the encounter parameters (approach distance and relative velocity). We introduce a sequential variant of Dybczyński’s approach, cutting the encounter into several steps whereby the heliocentric motion of the comet is taken into account. For the scenario at hand this is found to offer an efficient means to obtain accurate results for practically any domain of the parameter space.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Application of neural networks to the study of stellar model solutions

Artificial neural networks (ANN) have different applications in Astronomy, including data reduction and data mining. In this work we propose the use ANNs in the identification of stellar model solutions. We illustrate this method, by applying an ANN to the 0.8M_⊙ star CG Cyg B. Our ANN was trained using 60,000 different 0.8M_⊙ stellar models. With this approach we identify the models which reproduce CG Cyg B’s position in the HR diagram. We observe a correlation between the model’s initial metal and helium abundance which, in most cases, does not agree with a helium to metal enrichment ratio ΔY/ΔZ = 2. Moreover, we identify a correlation between the model’s initial helium/metal abundance and both its age and mixing-length parameter. Additionally, every model found has a mixing-length parameter below 1.3. This means that CG Cyg B’s mixing-length parameter is clearly smaller than the solar one. From this study we conclude that ANNs are well suited to deal with the degeneracy of model solutions of solar type stars.     

A Fundamental Plane of Black Hole Activity: Pushing Forward the Unification Scheme

We examine the disc-jet connection in stellar mass and supermassive black holes by investigating the properties of their compact emission in the hard X-ray and radio bands. We compile a sample of ∼100 active galactic nuclei with measured mass, 5 GHz core emission, and 2–10 keV luminosity, together with eight galactic black holes with a total of ∼50 simultaneous observations in the radio and X-ray bands. Using this sample, we study the correlations between the radio (L_R) and the X-ray (L_X) luminosity and the black hole mass (M). We find that the radio luminosity is correlated with both M and L_X, at a highly significant level. We show how this result can be used to extend the standard unification by orientation scheme to encompass unification by mass and accretion rate.     

Ocean tidal perturbations on the orbit of the satellite “STARLETTE”

A continuous 300-day, world-wide laser-ranging data of the satellite STARLETTE between October 1976 and July 1977 was used to analyse the perturbation of the orbit by ocean tide. The long-period (longer than 20d) perturbations in the orbital inclination by the four main tide components K₁, P₁, K₂, S₂ were clearly identifiable in the maximum entropy power spectrum and periodogram. By comparing orbits including and excluding the tidal terms, the effect of the tide on the position of the satellite over 5 days was found to be of the order of one meter.     

Near-parabolic cometary flux in the outer solar system

The flux of near-parabolic comets in the outer-planetary region is estimated on the presumption that the major planets and the galactic tide control the dynamics of comets. It is found that the flux of the Oort cloud comets (semi-major axis > 20000 AU) is similar to the case of a strong comet shower derived on the presumption that the galactic tidal force were not operative. On the other hand, the flux of comets with semi-major axes <- 20000 AU is found to be an increasing function of q (perihelion distance) until q reaches 20 AU, while for a 45000 AU it is a rapidly increasing function for q 12 AU. In other words, for comets of the inner extension of the Oort cloud the planetary perturbation acts as a strong barrier for them to penetrate into the inner planetary region.     

Probing the physics of interacting galaxies

The morphological and velocity structures in the gaseous (HI and CO) and stellar components of two interacting systems are examined. Both Arp 140 and Arp 104 reveal extended tidal tails in the HI. The Hα and FIR fluxes of Arp 140 yield similar SFR of ∼ 0.8 M_⊙ yr^-1. In contrast the Hα flux of Arp 104 yields a SFR of ∼ 0.05 M_⊙ yr^-1, ∼ 20 times smaller than that obtained from the FIR flux. Spectra were used to examine the changing velocity of atomic and molecular gas in NGC 5218 (Arp 104). The atomic and molecular gas were found to be dynamically similar with comparable velocities and velocity widths across the galaxy; consistent with the two phases responding similarly to the interaction, or enhanced HI to CO conversion in the centre of the galaxy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Sedna and the Oort Cloud around a migrating Sun

Recent numerical simulations have demonstrated that the Sun’s dynamical history within the Milky Way may be much more complex than that suggested by its current low peculiar velocity (Sellwood, J.A., Binney, J.J. [2002]. Mon. Not. R. Astron. Soc. 336, 785-796; Roškar, R., Debattista, V.P., Quinn, T.R., Stinson, G.S., Wadsley, J. [2008]. Astrophys. J. 684, L79-L82). In particular, the Sun may have radially migrated through the galactic disk by up to 5-6 kpc (Roškar, R., Debattista, V.P., Quinn, T.R., Stinson, G.S., Wadsley, J. [2008]. Astrophys. J. 684, L79-L82). This has important ramifications for the structure of the Oort Cloud, as it means that the Solar System may have experienced tidal and stellar perturbations that were significantly different from its current local galactic environment. To characterize the effects of solar migration within the Milky Way, we use direct numerical simulations to model the formation of an Oort Cloud around stars that end up on solar-type orbits in a galactic-scale simulation of a Milky Way-like disk formation. Surprisingly, our simulations indicate that Sedna’s orbit may belong to the classical Oort Cloud. Contrary to previous understanding, we show that field star encounters play a pivotal role in setting the Oort Cloud’s extreme inner edge, and due to their stochastic nature this inner edge sometimes extends to Sedna’s orbit. The Sun’s galactic migration heightens the chance of powerful stellar passages, and Sedna production occurs around ∼20-30% of the solar-like stars we study. Considering the entire Oort Cloud, we find its median distance depends on the minimum galactocentric distance attained during the Sun’s orbital history. The inner edge also shows a similar dependence but with increased scatter due to the effects of powerful stellar encounters. Both of these Oort Cloud parameters can vary by an order of magnitude and are usually overestimated by an Oort Cloud formation model that assumes a fixed galactic environment. In addition, the amount of material trapped in outer Oort Cloud orbits (a > 20,000 AU) can be extremely low and may present difficulties for traditional models of Oort Cloud formation and long-period comet production.     

Stellar Mass—Halo Mass Relation and Star Formation Efficiency in High-Mass Halos

We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M_*,BCG ∝ M ₅₀₀ ^αBCG with the best fit slope of α_BCG ≈ 0.4 ± 0.1. We measure scatter of M_*,BCG at a fixed M₅₀₀ of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ～2?4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M_*?M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M₅₀₀ with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M₅₀₀ with scatter of ≈0.1 dex and best fit slope of α_sat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3?5 lower than the peak stellar fraction reached in M ≈ 10¹²M_⊙ halos. The difference is only a factor of ～1.5?3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L_* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M_*?M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.     

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of hot Jupiters

In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t _ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P _obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P _obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P _orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters.