A McDonald Observatory Study of Comet 19P/Borrelly: Placing the Deep Space 1 Observations into a Broader Context

We present imaging and spectroscopic data on Comet 19P/Borrelly that were obtained around the time of the Deep Space 1 encounter and in subsequent months. In the four months after perihelion, the comet showed a strong primary (sunward) jet that is aligned with the nucleus' spin axis. A weaker secondary jet on the opposite hemisphere appeared to become active around the end of 2001, when the primary jet was shutting down. We investigated the gas and dust distributions in the coma, which exhibited strong asymmetries in the sunward/antisunward direction. A comparison of the CN and C₂ distributions from 2001 and 1994 (during times when the viewing geometry was almost identical) shows that each species is remarkably similar, indicating that the comet's activity is essentially repeatable from one apparition to the next. We also measured the dust reflectivities as a function of wavelength and position in the coma, and though the dust was very red overall, we again found variations with respect to the solar direction. We used the primary jet's appearance on several dates to determine the orientation of the rotation pole to be α=214°, δ=−5°. We compared this result to published images from 1994 to conclude that the nucleus is near a state of simple rotation. However, data from the 1911, 1918, and 1925 apparitions indicate that the pole might have shifted by 5-10° since the comet was discovered. Using our pole position and the published nongravitational acceleration terms, we computed a mass of the nucleus of 3.3×10¹⁶ g and a bulk density of 0.49 g cm⁻³ (with a range of 0.29<ρ<0.83 g cm⁻³). This result is the least model-dependent comet density known to date.     

Rotational Properties of Cometary Nuclei

We review several techniques used to retrieve rotational parameters from observations. The spin period of a dozen of comets retrieved with these techniques are summarized. We describe how the spin period of comet Hale-Bopp (C/1995 O1) has been calculated with a high accuracy (11.30–11.34 h). Although several authors converged to a spin axis orientation at (α,δ) = (275 ± 15°, -55 ± 5°), detailed studies indicate that the dust jets morphology in 1996–1997 may be incompatible with this orientation. Comet 19P/Borrelly has been recently observed by the Deep Space 1 spacecraft. At the same time, its spin axis orientation and period have been determined by several authors to be respectively (α,δ) = (225 ± 15°, -10 ± 10°)and 26h. These two comets are likely to be in (or close to) a principal axis spin state. We discuss new modeling of the spin state of comet 46P/Wirtanen, the target of the Rosetta mission. The model involves a three-dimensional shape and thermal model, from which the torque of the non gravitational force is calculated at each time step. The moments of inertia are computed for each irregular shape. The results from numerical integrations show that this comet can remain in a principal axis spin state during more than 10 orbits if the spin period does not get above～6 h. If the spin period increases, its nucleus gets rapidly into excited spin states. It shows that even small and very active short-period comets are not necessarily in non principal axis spin states. In the last section, the consequences of recent observations and modeling of the rotational parameters of comet nuclei are discussed, and unsolved problems are presented.     

The chromospherically active binary star EI Eridani: I. Absolute dimensions

We present a detailed determination of the astrophysical parameters of the chromospherically active binary star EI Eridani. Our new radial velocities allow to improve the set of orbital elements and reveal long‐term variations of the barycentric velocity. A possible third‐body orbit with a period of ≈19 years is presented. Absolute parameters are determined in combination with the Hipparcos parallax. EI Eri's inclination angle of the rotational axis is confined to 56°.0 ± 4°.5, ist luminosity class IV is confirmed by its radius of 2.37 ± 0.12 R_⊙. A comparison to theoretical stellar evolutionary tracks suggests a mass of 1.09 ± 0.05 M_⊙ and an age of ≈ 6.15 Gyr. The present investigation is the basis of our long‐term Doppler imaging study of its stellar surface (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photometric observations and modelling of the asteroid 85 Io in conjunction with data from an occultation event during the 1995–96 apparition

The asteroid 85 Io has been observed using CCD and photoelectric photometry on 18 nights during its 1995–96 and 1997 apparitions. We present the observed lightcurves, determined colour indices and modelling of the asteroid spin vector and shape. The colour indices (U-B = 0.35±0.02, B-V = 0.66±0.02, V-R = 0.34±0.02, R-I = 0.36±0.02) are as expected for a C-type asteroid. The allowed spin vector solutions have the pole co-ordinates λ₀ = 285±4°, β₀ = −52±9° or λ₀ = 108±10°, β₀ = −46±10° and λ₀ = 290±10°, β₀ = −16±10° with a retrograde sense of rotation and a sidereal period P_sid = 0^d.286463±0^d.000001. During the 1995–96 apparition the International Occultation Time Association (IOTA) observed an occultation event by 85 Io. The observations and modelling presented here were analysed together with the occultation data to develop improved constraints on the size of the asteroid. The derived value of 164 km is about 5% larger than the IRAS diameter. © 1999 Elsevier Science Ltd. All rights reserved.     

Asteroid spin‐axis longitudes from the Lowell Observatory database

By analyzing brightness variation with ecliptic longitude and using the Lowell Observatory photometric database, we estimate spin‐axis longitudes for more than 350,000 asteroids. Hitherto, spin‐axis longitude estimates have been made for fewer than 200 asteroids. We investigate longitude distributions in different dynamical groups and asteroid families. We show that asteroid spin‐axis longitudes are not isotropically distributed as previously considered. We find that the spin‐axis longitude distribution for Main Belt asteroids is clearly nonrandom, with an excess of longitudes from the interval 30°–110° and a paucity between 120° and 180°. The explanation of the nonisotropic distribution is unknown at this point. Further studies have to be conducted to determine if the shape of the distribution can be explained by observational bias, selection effects, a real physical process, or other mechanism.     

Pole orientation of asteroid 44 Nysa via photometric astrometry,including a discussion of the method's application and its limitations

The results of photometric astrometry, a method of determining the orientation of a rotation axis, as applied to asteroid 44 Nysa are presented. The pole orientation of Nysa was found to be λ₀ = 100°, β₀ = +60° with an uncertainty of 10°. The sidereal period is 0^d.26755902 ± 0.00000006, and the rotation prograde. Refinements to, and limitations of, the application of the method of photometric astrometry are discussed. In light of the results presented herein, we believe that all photometric astrometry pole determinations of the past should be redone.     

Photoelectric lightcurves of the asteroid 1862 Apollo

Photoelectric lightcurves of the asteroid 1862 Apollo were obtained in November–December 1980 and in April–May 1982. The period of rotation is unambiguously determined to be 3.0655 ± 0.0008 hr. The 1980 observations span a range of solar phase angle from 30° to 90°, and the 1982 observations, 0.°2 to 90°. The Lumme-Bowell-Harris phase relation can be fit to the absolute magnitudes at maximum light with an RMS scatter of 0.06 magnitude over the entire range of phase angle. The constants of the solution are absolute V magnitude at zero phase angle and at maximum light, 16.23 ± 0.02; slope parameter, 0.23 ± 0.01. These constant corresponds to values in the linear phase coefficient system of V(1, 0) = 16.50 ± 0.02 and a phase coefficient of β_v = 0.0305 ± 0.0012 mag/degree in the phase range 10°–20°. The slope of the phase curve is typical for a moderate albedo asteroid. The absolute magnitudes observed in 1980 and 1982 fall along a common phase curve. That is, Apollo was not intrinsically brighter at one apparition than the other. This is not surprising, since the two apparitions were almost exactly opposite one another in the sky. A pole position was calculated from the observed deviation of the lightcurve from constant periodicity (synodic-sidereal difference) during both apparitions. The computed 1950 ecliptic coordinates of the pole are: longitude = 56°, latitude = −26°. This is the “north” pole with respect to right-handed (counter-clockwise) rotation. The formal uncertainty of the solution for the pole position is less than 10°, but realistically may be several times that, or even completely wrong. The sidereal period of rotation asscociated with this pole solution is 3.065436 ± 0.000012 hr.     

Radar observations of Comet 2P/Encke during the 2003 apparition

The nucleus of Comet 2P/Encke was detected with the Arecibo radar during the close approach of November, 2003, making this the first comet to yield radar detections at two different apparitions. Although the measured radar cross section of 1.0 km² was close to that obtained in 1980, the Doppler bandwidth was nearly four times larger. Most of this bandwidth difference can simply be attributed to a different observing aspect relative to the spin axis proposed by Sekanina [1988, Astron. J. 95, 911] and Festou and Barale [2000, Astron. J. 119, 3119]. Comparison of the 2003 Doppler bandwidth with infrared-based size estimates supports an 11-h dominant rotation period and excludes slower 15- and 22-h periods that have also been suggested. If one assumes a short-axis-mode rotation with an 11-h period, then the Doppler bandwidth indicates that the nucleus is an oblong object with a long-axis dimension of 9 km. The estimated radar albedo of 0.05 is similar to that measured for C/IRAS-Araki-Alcock, providing further evidence that comet nuclei have relatively low surface densities of ∼0.5-1.0 g cm⁻³. No broadband echo component was detected from large coma grains despite predictions, based on optical/infrared models, that such a component might be detectable.     

Preliminary results on the determination of the theoretical nonadiabatic observable phase lag (ψT) using VIRGO color photometry

The helioseismic instruments aboard the SOHO satellite make it possible to measure solar oscillations as variations of the irradiance (VIRGO) or as variations of the photospheric velocity (GOLF). Theoretically, phase differences between different photometric bands are expected to be around 0 degrees over the p‐mode frequency range. By using VIRGO (red) and VIRGO (blue) data, we find a mean phase shift of 8.05 ± 1.81°, whereas by using VIRGO (green) and VIRGO (blue) data, we got a mean value of –1.04 ± 0.19°. Hence, when the analysis includes the VIRGO infrared range, the Sun's atmosphere does not follow an exact adiabatic behavior. In this study, we use the phase shifts obtained by VIRGO (green) and VIRGO (blue) to determine the non‐adiabatic parameter phase lag (ψ_T) as a function of frequency. To this aim, we applied the non radial linearized formula put in the complex form by Garrido: we found a mean value of ψ_T = 179.95°. The lowest value being ψ_T = 179.90°, the departure from theoretical predictions is less then a tenth of a degree over the entire p mode frequency range. We can state that the solar atmosphere has a behavior close to the adiabatic case, when the phase shifts and amplitude ratios are computed using VIRGO (green) and VIRGO (blue) data. Nevertheless this small deviation is significant. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of the nucleus shape on the maximum size of grains ejected from a comet by gentle sublimation and jet‐like features

This paper deals with obtaining the maximum size of cometary grains ejected from nuclei of different shapes. Two mechanisms in terms of grain ejection from comets are taken into consideration. The first one is dragging of particles by outflowing gas molecules released by gentle sublimation from the comets. The second one is related with gas jets from the cavities in a nucleus by cometary jet‐like phenomena. We focused on ellipsoidal shapes of cometary nuclei but with different flattening. Calculations have been carried out for a large range of cometary parameters. It has been shown that for fixed mass of the nucleus the maximum size of grains is an increasing function of the nucleus flattening. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Study of Non-Gravitational Effects of Comet C/1995 O1 HALE–BOPP

The role of non-gravitational forces in the evolution of orbitalmotion of C/1995 O1 (Hale–Bopp) has been investigated. Inorbital calculations the observational material covering theperiod from April 1993 up to August 2001 was used. To model thenon-gravitational acceleration, observed and theoretical profilesof the H₂O production rates were employed. A set of forcedprecession models of a rotating cometary nucleus consistent withthe observed spin axis orientation was fitted to positionalobservations. The non-gravitational models allowed us to constrainthe mass and radius of the comet. The orbitalevolution of Comet Hale–Bopp was investigated over ±400 k yusing two sets of randomly varied orbital elements wellrepresenting all positional observations in the pure gravitationalcase, as well as in the non-gravitational case. The calculationsshowed that the comet's motion is predictable only over an interval ofa few orbital periods. The statistical conclusions changesignificantly when non-gravitational effects are included in the analysis.     

Worldwide photometry and lightcurve observations of 16 Psyche during the 1975–1976 apparition

We present 26 lightcurves of 16 Psyche from 1975 and 1976. The synodic period during this apparition was 4^h.1958. Combining photometric data from this opposition with those from previous apparitions allowed us to derive a mean phase coefficient in V of 0.026 ± 0.002 mag/deg and to establish that Psyche's absolute V₀ magnitude and rotational amplitude vary with aspect; at 90° aspect, V₀(1, 0) = 6.27 ± 0.05 and the lightcurve amplitude is 0.30 mag, while at 0° or 180° aspect, V₀(1, 0) = 6.02 ± 0.02 and the amplitude is ?0.03 mag. This behavior is accounted for if, to first order, Psyche's shape is that of a triaxial ellipsoid with axial ratios near 5:4:3. Colors at zero phase are U-B = 0.26 ± 0.01 and B-V = 0.71 ± 0.01. Color phase coefficients are <0.001 mag/deg in U-B and 0.0010 ± 0.0004 mag/deg in B-V.     

Thermal destruction of cometary materials – application to activity of comets

Destruction mechanisms connected with thermodynamical behaviour of cometary material are reviewed with a special consideration of their effects on activity of comets. Consequences of thermal stresses which occur in the interior of a comet are discussed with reference to changes in the cometary brightness. Moreover, thermal destruction of grains placed in the head of the comet as well as on the surface of the nucleus is considered. It has been shown that the destruction of the cometary material can lead to an essential increase in the activity of the comet. Calculations have been carried out for a large assumed range of cometary parameters. The obtained simulated changes in the brightness of comets are consistent with the ones observed during the real variations and outbursts of brightness. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

短周期彗星表面水冰升华分布研究

彗星是太阳系遗留的原始星子,研究彗星彗核的演化对理解太阳系其他天体的形成和演化历史具有重要意义.在太阳的辐射作用下,彗星携带的挥发性成分会发生升华,并带动尘埃运动,造成彗核物质的损失.因此,彗核的升华活动对其表面形貌甚至整体形状演化都会产生影响.从IAU (International Astronomical Union) MPC (Minor Planet Center)获取轨道数据,并考虑了彗核的自转以及进动,利用MONET (Mass lossdriven shape evolution model)形状演化模型对短周期彗星做数值模拟,计算得到了短周期彗星1P/Halley、9P/Tempel 1、 19P/Borrelly、 67P/C-G (Churyumov-Gerasimenko)、 81P/Wild 2和103P/Hartley 2在一个轨道周期内的太阳辐射能量以及表面侵蚀深度的分布,结合其动力学参数讨论了自转、进动和公转等特性对其表面水冰升华分布的影响以及造成南北侵蚀差异的可能性.     

Orbital linkages of Comet 6P/d'Arrest based on its asymmetric light curve

We present an investigation of different models of the nongravitational acceleration on Comet 6P/d'Arrest, as used in orbital linkages spanning 150 years from the discovery of the comet in 1851 until the recent observations made in 2001. Some of our models use the time-shifted g-like function to represent the variation of outgassing rate, but the main thrust is on models using instead a production curve that is fitted to recent light curve observations—mainly those in 1976. We pay special attention to the proper scaling of such a production curve, when applied to other apparitions with a different perihelion distance q, and we find a best fit with a q^−1.6 power-law. Generally, the best fit is found with models, in which the acceleration components are expressed in terms of the angular parameters of the rotating nucleus. We thus find the orientation of the spin axis, and using the orbital evolution we are able to predict a variable time shift of the outgassing curve. The very best results are found when applying this time shift to the light-curve based, angular models. The totality of the 1851-2001 observations can then be linked with a mean residual of less than 4″. This may be brought down to ∼^2″ by solving for individual ‘activity parameters’ of all apparitions, which are multiplicative factors applied to the acceleration amplitudes. These turn out to be within 10% of unity for the best fit. We have also performed a linkage to the observations of Comet 1678 (La Hire) using our models. We find an indication of a secular increase of the amount of asymmetry of the outgassing with respect to perihelion, part of which is due to the variable time shift caused by the orbital evolution.     

Model of the Magnetic Field of HD 187474

A model is constructed for the magnetic field of the star HD 187474, which has a very long axial rotation period P = 2345^d. It turns out that the structure of the magnetic field is best described by a model of a displaced (Δα = 0.1) dipole inclined to the axis of rotation by an angle β = 24°. The star is inclined to the line of sight by an angle i = 86°. Because of the displaced dipole the magnitude of the magnetic field differs at the poles: Bp = +6300 and 11600 G. A Mercator map of the distribution of the magnetic field over the surface is obtained. The 7 slowly rotating CP stars studied thus far have an average angle β = 62°, which equals the average value for a random orientation of dipoles. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 575–583 (November 2005).     

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small,inner main-belt binaries

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3–8 km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.     

Oblateness,radius, and mean stratospheric temperature of Neptune from the 1985 August 20 occultation

The occultation of a bright (K∼6) infrared star by Neptune revealed a central flash at two stations and provided accurate measurements of the limb position at these and several additional stations. We have fitted this data ensemble with a general model of an oblate atmosphere to deduce the oblateness e and equatorial radius a₀ of Neptune at the 1-μbar pressure level, and the position angle p_n of the projected spin axis. The results are e=0.0209±0.0014, a₀=25269±10 km, p_n=20.1°±1°. Parameters derived from fitting to the limb data alone are in excellent agreement with parameters derived from fitting to central flash data alone (E. Lellouch, W.B. Hubbard, B. Sicardy, F. Vilas, and P. Bouchet, 1986, Nature 324, 227–231), and the principal remaining source of uncertainty appears to be the Neptune-centered declination of the Earth at the time of occultation. As an alternative to the methane absorption model proposed by Lellouch et al., we explain an observed reduction in the central flash intensity by a decrease in temperature from 150 to 135°K as the pressure rises from 1 to 400 μbar. Implications of the oblateness results for Neptune interior models are briefly discussed.     

Pole coordinates of the asteroids 9 metis, 22 kalliope,and 44 Nysa

By means of new photoelectric observations made in 1974 an attempt to determine the poles of asteroids 9 and 44 was made. Following a method based upon the magnitude-aspect and amplitude-aspect relations, the coordinates of the poles for 9 and 44 were found to be, respectively, λ₀ = 191° ± 5°, β₀ = 56° ± 6° and λ₀ = 100° ± 10°, β₀ = 50° ± 10°. The previously published pole for asteroid 22, λ₀ = 215° ± 10°, β₀ = 45° ± 15°, was confirmed. From its phase relation we determined the phase coefficient of 44 Nysa, a very high albedo object (p_v = 0.377). The very low phase coefficient obtained (β_v = 0.018 mag/deg) agrees very well with an inverse relation between geometrical albedo and phase coefficient. The results are summarized in a table.     

Stardust-NExT,Deep Impact,and the accelerating spin of 9P/Tempel 1

The evolution of the spin rate of Comet 9P/Tempel 1 through two perihelion passages (in 2000 and 2005) is determined from 1922 Earth-based observations taken over a period of 13 year as part of a World-Wide observing campaign and from 2888 observations taken over a period of 50 days from the Deep Impact spacecraft. We determine the following sidereal spin rates (periods): 209.023 ± 0.025°/dy (41.335 ± 0.005 h) prior to the 2000 perihelion passage, 210.448 ± 0.016°/dy (41.055 ± 0.003 h) for the interval between the 2000 and 2005 perihelion passages, 211.856 ± 0.030°/dy (40.783 ± 0.006 h) from Deep Impact photometry just prior to the 2005 perihelion passage, and 211.625 ± 0.012°/dy (40.827 ± 0.002 h) in the interval 2006–2010 following the 2005 perihelion passage. The period decreased by 16.8 ± 0.3 min during the 2000 passage and by 13.7 ± 0.2 min during the 2005 passage suggesting a secular decrease in the net torque. The change in spin rate is asymmetric with respect to perihelion with the maximum net torque being applied on approach to perihelion. The Deep Impact data alone show that the spin rate was increasing at a rate of 0.024 ± 0.003°/dy/dy at JD2453530.60510 (i.e., 25.134 dy before impact), which provides independent confirmation of the change seen in the Earth-based observations.The rotational phase of the nucleus at times before and after each perihelion and at the Deep Impact encounter is estimated based on the Thomas et al. (Thomas et al. [2007]. Icarus 187, 4–15) pole and longitude system. The possibility of a 180° error in the rotational phase is assessed and found to be significant. Analytical and physical modeling of the behavior of the spin rate through of each perihelion is presented and used as a basis to predict the rotational state of the nucleus at the time of the nominal (i.e., prior to February 2010) Stardust-NExT encounter on 2011 February 14 at 20:42.We find that a net torque in the range of 0.3–2.5 × 10⁷ kg m² s^?2 acts on the nucleus during perihelion passage. The spin rate initially slows down on approach to perihelion and then passes through a minimum. It then accelerates rapidly as it passes through perihelion eventually reaching a maximum post-perihelion. It then decreases to a stable value as the nucleus moves away from the Sun. We find that the pole direction is unlikely to precess by more than ～1° per perihelion passage. The trend of the period with time and the fact that the modeled peak torque occurs before perihelion are in agreement with published accounts of trends in water production rate and suggests that widespread H₂O out-gassing from the surface is largely responsible for the observed spin-up.