Małgorzata Królikowska

Where do long‐period comets come from? 26 comets from the non‐gravitational Oort spike

Since 1950, when Oort published his hypothesis, several important new facts have been established in this field. At present, there are still questions surrounding the apparent source region (or regions) of long-period comets, the definition of dynamically new comets and the characteristics of the hypothetical Oort Cloud. Our aim in this investigation is to look for the apparent source of selected long-period comets and to refine the definition of dynamically new comets. Based on pure gravitational original orbits, all comets studied in this paper are widely called dynamically new. However, we show that the incorporation of non-gravitational forces into the orbit determination process significantly changes the situation. We have determined the precise non-gravitational orbits of all investigated comets. Then, we have followed numerically their past and future motions during one orbital period. Applying the ingenious method of Sitarski of creating swarms of virtual comets compatible with observations, we have been able to derive the uncertainties of original and future orbital elements, as well as the uncertainties of previous and next perihelion distances. We conclude that the past and future evolutions of cometary orbits under Galactic tide perturbations is the only way to find which comets are really dynamically new. In our sample, fewer than 30 per cent of comets are, in fact, dynamically new. Most of these have small previous perihelion distances. However, 60 per cent of these will be lost on hyperbolic orbits in the future. This evidence suggests that the investigation into the apparent source of long-period comets is challenging. We have also shown that a significant percentage of long-period comets can visit the zone of visibility during at least two or three consecutive perihelion passages.

Near-parabolic comets observed in 2006–2010 – II. Their past and future motion under the influence of the Galaxy field and known nearby stars

Here, we continue this research with a detailed study of their past and future motion during previous and next orbital periods under the perturbing action of our Galactic environment. At all stages of our dynamical study, we precisely propagate in time the observational uncertainties of cometary orbits. For the first time in our calculations, we fully take into account individual perturbations from all known stars or stellar systems that closely (less than 3.5 pc) approach the Sun during the cometary motion in the investigated time interval of several million years. This is done by means of a direct numerical integration of the N-body system comprising of a comet, the Sun and 90 potential stellar perturbers. We show a full review of various examples of individual stellar action on cometary motion. We conclude that perturbations from all known stars or stellar systems do not change the overall picture of the past orbit evolution of long-period comets (LPCs).The future motion of them might be seriously perturbed during the predicted close approach of Gliese 710 star but we do not observe significant energy changes. The importance of stellar perturbations is tested on the whole sample of 108 comets investigated by us so far and our previous results, obtained with only Galactic perturbations included, are fully confirmed.We present how our results can be used to discriminate between dynamically new and old near-parabolic comets and discuss the relevance of the so-called Jupiter-Saturn barrier phenomenon. Finally, we show how the Oort spike in the 1/a-distribution of near-parabolic comets is built from both dynamically new and old comets. We also point out that C/2007 W1 seems to be the first serious candidate for interstellar provenience.

Warsaw Catalogue of cometary orbits: 119 near-parabolic comets

Context. The dynamical evolution of near-parabolic comets strongly depends on the starting values of the orbital elements derived from the positional observations. In addition, when drawing conclusions about the origin of these objects, it is crucial to control the uncertainties of orbital elements at each stage of the dynamical evolution. Aims. I apply a completely homogeneous approach to determine the cometary orbits and their uncertainties. The resulting catalogue is suitable for the investigation of the origin and future of near-parabolic comets. Methods. First, osculating orbits were determined on the basis of positional data. Second, the dynamical calculations were performed backwards and forwards up to 250 au from the Sun to derive original and future barycentric orbits for each comet. In the present investigation of dynamical evolution, the numerical calculations for a given object start from the swarm of virtual comets constructed using the previously determined osculating (nominal) orbit. In this way, the uncertainties of orbital elements were derived at the end of numerical calculations. Results. Homogeneous sets of orbital elements for osculating, original and future orbits are given. The catalogue of 119 cometary orbits constitutes about 70 per cent of all the first class so-called Oort spike comets discovered during the period 1801−2010 and about 90 per cent of those discovered in 1951−2010, for which observations were completed at the end of 2013. Non-gravitational (NG) orbits are derived for 45 comets, including asymmetric NG solution for six of them. Additionally, the new method for cometary orbit-quality assessment is applied for all these objects.

Near-parabolic comets observed in 2006–2010. The individualized approach to 1/a-determination and the new distribution of original and future orbits

Dynamics of a complete sample of 22 small perihelion distance near-parabolic comets discovered in the years 2006 - 2010 is studied. First, osculating orbits are obtained after a careful positional data inspection and processing, including where appropriate, the method of data partitioning for determination of pre- and post-perihelion orbit for tracking then its dynamical evolution. The nongravitational acceleration in the motion is detected for 50 per cent of investigated comets, in a few cases for the first time. Different sets of nongravitational parameters are determined from pre- and post-perihelion data for some of them. The influence of the positional data structure on the possibility of the detection of nongravitational effects and the overall precision of orbit determination is widely discussed. Secondly, both original and future orbits were derived by means of numerical integration of swarms of virtual comets obtained using a Monte Carlo cloning method. This method allows to follow the uncertainties of orbital elements at each step of dynamical evolution. The complete statistics of original and future orbits that includes significantly different uncertainties of 1/a-values is presented, also in the light of our results obtained earlier. Basing on 108 comets examined by us so far, we conclude that only one of them, C/2007 W1 Boattini, seems to be a serious candidate for an interstellar comet. We also found that 53 per cent of 108 near-parabolic comets escaping in the future from the Solar system, and the number of comets leaving the Solar system as so called Oort spike comets is 14 per cent. A new method for cometary orbit quality assessment is also proposed that leads to a better diversification of orbit quality classes for contemporary comets.

Different dynamical histories for comets C/2001 Q4 and C/2002 T7?

Context. Both, C/2001 Q4 and C/2002 T7, are widely regarded in the literature as dynamically new comets that are visiting our planetary system for the first time from the Oort Cloud. Aims. We study the past dynamical evolution of these two bright comets that both have an original semimajor axis inside the so-called Oort spike (i.e. with 1/aori < 10 −4 AU −1 ). Methods. For each comet, we constructed a dedicated grid of independent, starting, osculating swarms of 5000 orbits based on different subsets of positional data and different dependences of the non-gravitational acceleration on the heliocentric distance. We then followed numerically each swarm of non-gravitational orbits one orbital revolution into the past, taking into account both planetary and Galactic perturbations and checking for all known stellar perturbers. This method allows us to obtain the orbital elements and their uncertainties at the previous perihelion passage. Results. We find that the dedicated g(r)-like function seems to be more adequate for describing the non-gravitational effects than the standard g(r)-function in the motion of both comets, but we are able to estimate only two parameters: the scale distance r0 ,a nd the exponent m. We show, however, that the greatest change in the previous perihelion value relative to that obtained in the standard approach results from the type of data subset used for non-gravitational orbit determination. The form of the dependence of nongravitational acceleration on heliocentric distance is of secondary importance for both investigated comets in this context. We find that only comet C/2002 T7 passed far beyond the planetary system during its previous perihelion passage and that C/2001 Q4 was probably well inside the Saturn orbit at a previous perihelion. Conclusions. We argue that for these comets (which have long sequences of positional data), the safest method for the previous perihelion determination is to exclude data within time intervals where some local outbursts were reported. We recommend that the non-gravitational models based on data taken at larger perihelion distance are more appropriate for estimating the distance of previous perihelion passage of C/2001 Q4 and those based on a pre-perihelion data set for previous perihelion estimation of C/2002 T7. These models suggest that C/2001 Q4 passed its previous perihelion closer than 6–7 AU from the Sun, so is dynamically old, whereas C/2002 T7 at a distance larger than 400 AU, is a dynamically new comet since it overcame the Jupiter-Saturn barrier.

New catalogue of one-apparition comets discovered in the years 1901–1950 - I. Comets from the Oort spike

Context. The orbits of one-apparition comets discovered in the early part of the last century have formerly been determined with very different numerical methods and assumptions on the model of the solar system, including the number of planets taken into account. Moreover, observations of the comet-minus-star-type sometimes led to determination of the comet position that are less precise than what we can derive today by using a more modern star catalogue. Aims. We aim to provide a new catalogue of cometary orbits that are derived using a completely homogeneous data treatment, accurate numerical integration, and a modern model of the solar system. Methods. We collected the complete sets of observations for investigated comets from the original publications. Then we recalculated the cometary positions for the comet-minus-star-type of observations using the Positions and Proper Motions Star Catalogue, and applied a uniform method for the data selection and weighting. As a final result, new osculating orbits were determined. Secondly, dynamical calculations were performed to the distance of 250 AU from the Sun to derive original and future barycentric orbits for evolution backward and forward in time. These numerical calculations for a given object start from a swarm of virtual comets constructed using our osculating (nominal) orbit. In this way, we obtained the orbital element uncertainties of original and future barycentric orbits. Results. We present homogeneous sets of orbital elements for osculating, original, and future orbits for 38 one-apparition comets. Non-gravitational orbits are derived for thirteen of them.

Non-gravitational motion of the Jupiter-family comet 81P/Wild 2 - II. The active regions on the surface

Aims. The non-gravitational perturbations in the orbital motion of comet 81P/Wild 2 are investigated using a two-source model of outgassing. Methods. In the process of orbit improvement the nucleus orientation and the location of two active regions are found from numerical fitting of the non-gravitational acceleration model to positional observations of the comet. Two different approaches to the lag angle of the outgassing behind the subsolar meridian are considered, assuming this angle to be either constant or varying with heliocentric distance. Results. The derived spin axis orientation (I similar to 60 degrees, phi similar to 155 degrees) as well as the location of two active regions, the northern (beta = 84 degrees) and the southern one (beta = -42 degrees), agree with determinations based on different observations by other authors. Orbital linkages of two and three successive apparitions of 81P/Wild 2 indicate an evolution of the change in the orbital period, possible time variations of the spin axis of the comet and an increase of the source areas during the last five revolutions. The non-gravitational perturbations were also used to constrain the sizes of the two active areas as well as the mass and bulk density (similar to 400 kg m(-3)) of the comet nucleus. The modeled two-source water production curve is compared with the activity data represented by the observed water production curve and the brightness curve.

A Study of Non-Gravitational Effects of Comet C/1995 O1 Hale-Bopp

The role of non-gravitational forces in the evolution of orbital motion of C/1995 O1 (Hale-Bopp) has been investigated. In orbital calculations the observational material covering the period from April 1993 up to August 2001 was used. To model the non-gravitational acceleration, observed and theoretical profiles of the H 2 O production rates were employed. A set of forced precession models of a rotating cometary nucleus consistent with the observed spin axis orientation was fitted to positional observations. The non-gravitational models allowed us to constrain the mass and radius of the comet. The orbital evolution of Comet Hale-Bopp was investigated over ±400 k y using two sets of randomly varied orbital elements well representing all positional observations in the pure gravitational case, as well as in the non-gravitational case. The calculations showed that the comet’s motion is predictable only over an interval of a few orbital periods. The statistical conclusions change significantly when non-gravitational effects are included in the analysis.

Investigating the dynamical history of the interstellar object ’Oumuamua

Here we try to find the origin of 1I/2017 U1 ’Oumuamua, the first interstellar object recorded inside the solar system. To this aim, we searched for close encounters between ’Oumuamua and all nearby stars with known kinematic data during their past motion. We had checked over 200 thousand stars and found just a handful of candidates. If we limit our investigation to within a 60 pc sphere surrounding the Sun, then the most probable candidate for the ’Oumuamua parent stellar habitat is the star UCAC4 535-065571. However GJ 876 is also a favourable candidate. However, the origin of ’Oumuamua from a much more distant source is still an open question. Additionally, we found that the quality of the original orbit of ’Oumuamua is accurate enough for such a study and that none of the checked stars had perturbed its motion significantly. All numerical results of this research are available in the appendix.

Dynamical evolution of C/2017 K2 PANSTARRS

(Abreviated) Comet C/2017 K2 PANSTARRS drew attention to its activity already at a time of its discovery in May 2017 when it was about 16 au from the Sun. This Oort spike comet will approach its perihelion in December 2022, and the question about its dynamical past is one of the important issues to explore. To this aim it is necessary to obtain its precise osculating orbit, its original orbit, and propagate its motion backwards in time to the previous perihelion. We study a dynamical evolution of C/2017 K2 to the previous perihelion (backward calculations for about 3-4 Myr) as well as to the future (forward calculations for about 0.033 Myr). Outside the planetary system both Galactic and stellar perturbations were taken into account. We derived that C/2017 K2 is a dynamically old Oort spike comet (1/a