Dynamical evolution of comets and the problem of cometary fading

Possibilities to explain the observed 1/a-distribution are discussed in the light of improved understanding of the dynamical evolution of long-period comets. It appears that the fading problem applies both to single-injection and continuous-injection models. Although uncertainties due to nongravitational effects do not allow detailed results to be drawn from the observed 1/a-distribution at small perihelion distance q, that for q 1.5 AU shows that a constant fading probability cannot explain all the features of the observed distribution. Assuming that comets can reappear following a period of fading, values for the assumed constant fading and renewal probabilities, and the total cometary flux have been estimated for q > 1.5 AU.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

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.     

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.     

Are There Many Inactive Jupiter-Family Comets among the Near-Earth Asteroid Population?

We analyze the dynamical evolution of Jupiter-family (JF) comets and near-Earth asteroids (NEAs) with aphelion distances Q>3.5 AU, paying special attention to the problem of mixing of both populations, such that inactive comets may be disguised as NEAs. From numerical integrations for 2×10⁶ years we find that the half lifetime (where the lifetime is defined against hyperbolic ejection or collision with the Sun or the planets) of near-Earth JF comets (perihelion distances q<1.3 AU) is about 1.5×10⁵ years but that they spend only a small fraction of this time (∼ a few 10³ years) with q<1.3 AU. From numerical integrations for 5×10⁶ years we find that the half lifetime of NEAs in “cometary” orbits (defined as those with aphelion distances Q>4.5 AU, i.e., that approach or cross Jupiter's orbit) is 4.2×10⁵ years, i.e., about three times longer than that for near-Earth JF comets. We also analyze the problem of decoupling JF comets from Jupiter to produce Encke-type comets. To this end we simulate the dynamical evolution of the sample of observed JF comets with the inclusion of nongravitational forces. While decoupling occurs very seldom when a purely gravitational motion is considered, the action of nongravitational forces (as strong as or greater than those acting on Encke) can produce a few Enckes. Furthermore, a few JF comets are transferred to low-eccentricity orbits entirely within the main asteroid belt (Q<4 AU and q>2 AU). The population of NEAs in cometary orbits is found to be adequately replenished with NEAs of smaller Q's diffusing outward, from which we can set an upper limit of ∼20% for the putative component of deactivated JF comets needed to maintain such a population in steady state. From this analysis, the upper limit for the average time that a JF comet in near-Earth orbit can spend as a dormant, asteroid-looking body can be estimated to be about 40% of the time spent as an active comet. More likely, JF comets in near-Earth orbits will disintegrate once (or shortly after) they end their active phases.     

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.     

On the dynamic connection of comets with Uranus

We consider the connection with Uranus for: (1) 945 near-parabolic comets (the period P > 200 years, the perihelion distance q > 0.1 AU), (2) 1277 Kreutz comets (P > 200 years, q < 0.01 AU), and (3) 414 short-period comets (P < 200 years). It turns out that none of near-parabolic comets passed through Uranus’s activity sphere, none of the Kreutz comets approach Uranus closer than 11 AU, and only two short-period comets, C/2006 U7 and C/2006 F2, could have a close approach to Uranus during 5000 years.     

A Model for the Common Origin of Jupiter Family and Halley Type Comets

A numerical simulation of the Oort cloud is used to explain the observed orbital distributions and numbers of Jupiter-family (JF) and Halley-type (HT) short-period (SP) comets. Comets are given initial orbits with perihelion distances between 5 and 36 au, and evolve under planetary, stellar and Galactic perturbations for 4.5 Gyr. This process leads to the formation of an Oort cloud (which we define as the region of semimajor axes a > 1,000 au), and to a flux of cometary bodies from the Oort cloud returning to the planetary region at the present epoch. The results are consistent with the dynamical characteristics of SP comets and other observed cometary populations: the near-parabolic flux, Centaurs, and high-eccentricity trans-Neptunian objects. To achieve this consistency with observations, the model requires that the number of comets versus initial perihelion distance is concentrated towards the outer planetary region. Moreover, the mean physical lifetime of observable comets in the inner planetary region (q < 2.5 au) at the present epoch should be an increasing function of the comets’ initial perihelion distances. Virtually all observed HT comets and nearly half of observed JF comets come from the Oort cloud, and initially (4.5 Gyr ago) from orbits concentrated near the outer planetary region. Comets that have been in the Oort cloud also return to the Centaur (5 < q < 28 au, a < 1,000 au) and near-Neptune high-eccentricity regions. Such objects with perihelia near Neptune are hard to discover, but Centaurs with characteristics predicted by the model (e.g. large semimajor axes, above 60 au, or high inclinations, above 40°) are increasingly being found by observers. The model provides a unified picture for the origin of JF and HT comets. It predicts that the mean physical lifetime of all comets in the region q < 1.5 au is less than ～200 revolutions.     

End-states of short-period comets and their role in maintaining the zodiacal dust cloud

Physical lifetimes and end-states of short-period comets are analysed in connection with the problem of the maintainance of the zodiacal dust cloud. In particular, the problem of the comet-asteroid relationship is addressed. Recent studies of the physical properties of Apollo-Amor asteroids and short-period comets (e.g., Hartmann et al., 1987) show significant differences between them, suggesting that they are distinct classes of objects. A few percent of the active SP comets might become asteroidal-like bodies in comet-type orbits due to the buildup of dust mantles. The remainder probably disintegrate as they consume their volatile content so their debris can only be observed as fireballs when they meet the Earth. Unobservable faint SP comets — i.e., comets so small (m 10¹⁴ g) that quickly disintegrate before being detected, might be a complementary source of dust material. They might be completely sublimated even at rather large heliocentric distances (r - 3 AU). Yet the released dust grains can reach the vicinity of the Sun by Poynting-Robertson drag. The mass associated with unobservable SP comets with perihelion distances q 3 AU might be comparable to that computed for the sample of observed SP co-mets with q 1.5 AU. It is concluded that SP comets (from the large to the unobservable small ones) may supply an average of several tons/sec of meteoric matter to the zodiacal dust cloud.     

Debiased Orbital and Absolute Magnitude Distribution of the Near-Earth Objects

The orbital and absolute magnitude distribution of the near-Earth objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions that we believe provide most NEOs to the inner Solar System. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the transneptunian disk. The nearly isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions that passed into the NEO region (perihelia q<1.3 AU and aphelia Q≥0.983 AU) were tracked until they were eliminated by striking the Sun or a planet or were ejected out of the inner Solar System. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced an NEO model population that could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a best-fit NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region.Our best-fit model is consistent with 960±120 NEOs having H<18 and a<7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly isotropic comets. Nearly isotropic comets are generally restricted to a Tisserand parameter (with respect to Jupiter) of T<2, such that few are believed to have a<7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H<22, indicates that the Amor, Apollo, and Aten populations contain 32±1%, 62±1%, and 6±1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth's orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury's orbit. Overall, our model predicts that ∼61% of the NEO population comes from the inner main belt (a<2.5 AU), ∼24% comes from the central main belt (2.5<a<2.8 AU), ∼8% comes from the outer main belt (a>2.8 AU), and ∼6% comes from the Jupiter-family comet region (2<T?3). The steady-state population in each NEO source region, as well as the influx rates needed to replenish each region, were calculated as a by-product of our method. The population of extinct comets in the Jupiter-family comet region was also computed.     

Dynamical capture and physical decay of short-period comets

The brightness evolution of short-period comets is discussed in connection with their physical lifetimes. It is shown that changes in the fraction of the free-subliming area of the nuclear surface may be more important than mass decrease in determining brightness variations. The decrease in the activity of short-period comets caused by the buildup of a dust mantle may be interrupted—and partially reversed—by dust blowoffs that leave exposed areas of fresh ices. Short-period comets may thus be subject to random brightness fluctuations that make quite uncertain any derivation of their physical lifetime based on comparisons of their absolute brightness at different apparitions. As an alternate procedure, the numerical integration of the whole sample of short-period comet orbits carried out by A. Carusi, L.Kresák, E. Perozzi and G. B. Valsecchi (1984, Long-Term Evolution of Short-Period Comets. Istituto Astrofisica Spaziale Internal Report 12, Rome) is used to draw conclusions about the transfer rate of their perihelia from Jupiter's region to the region of the terrestrial planets (heliocentric distances<1.5 AU). It is found that about one short-period comet per century reaches the region of the terrestrial planets. From this result and under the assumption of a steady-state comet population, an average lifetime of the order of 6 × 10³ years (～10³ revolutions) is derived for a typical kilometer-sized short-period comet of perihelion distance q ～ 1 AU. Such a rather long comet lifetime, as compared to some previous derivations, is consistent with the survival of some periodic comets on small-q orbits of long dynamical time scales.     

Invisible comets on evolutionary track of short-period comets

We systematically surveyed the orbits of short-period (SP) comets that show a large change of perihelion distance (q) between 1–2 AU (visible comets) and 4–5 AU (invisible comets) during 4400 years. The data are taken from Cosmo-DICE (Nakamura and Yoshikawa 1991a), which is a long-term orbital evolution project for SP comets. Recognizing that q is the most critical element for observability of comets, an invisibility factor (f), defined as the ratio of unobservable time span to observable span during 4400 years, is calculated for each of the large-q-change comets. A detection limit for each comet is obtained from the heliocentric distance at discovery and/or the absolute magnitude at recent apparitions. A mean f value for 35 SP comets with 2.9 J (J is the Tisserand's invariant) is found to be 19.8. This implies that for each visible SP comet of this J-range, at every epoch of time, there exist about 20 invisible comets near the capture orbits by Jupiter, under the assumptions of steady-state flux and ergodicity for the SP-comet population.     

The distribution of short-period comet magnitudes

Short-period comets with P 15 yr represent one of the most complete comet samples. The magnitude distribution of these comets was analysed using a maximum likelihood method. The brightness (magnitude) index for the comets with H ₁₀ 11 mag was estimated together with the large sample errors and found to be 0.62 ± 0.09. It was clear that many faint comets with H ₁₀ > 11 mag remain to be discovered. Some of the faint, smaller comets have probably been removed from the distribution altogether.Observational selection was also apparent for the sample of comets with perihelia q < 1.5 AU. It was found that comets satisfying the combined criteria P 15 yr, H ₁₀ 11 mag, q < 1.5 AU probably represent the most complete set of comets available. The brightness index of this sample estimated by maximum likelihood was 0.69 ± 0.14. This translates into a mass distribution index s of 1.69 ± 0.14 indicating that most of the mass is contained in a few of the larger comets rather than spread throughout the smaller ones. This distribution, although modified by mass loss, is most likely to have been produced by a process of particle accretion.     

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 10⁹ years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 10³ to 5 × 10⁴ AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 10⁵ AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 10⁴ < a < 3 × 10⁴ AU. The orbital planes of the comets with initial $\text{a ≧ 3 × 10}{}^4\text{AU}$ acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 10⁴AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiter's orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 10¹⁰ and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.     

Transneptunian object 2003 UB 313 as a source of comets

The possibility of interrelation between long-period comets and 2003 UB 313, a recently discovered large Kuiper Belt body, is investigated. For this purpose, 78 objects crossing the plane of motion of this body at distances from 37.8 to 97.6 AU have been selected from 860 long-period comets. The overpopulation of comets with this characteristic is also considered. The plane of motion of 2003 UB 313 is compared with the orbital planes of other objects in number of comet crossings in the specified distance interval or in some parts of it. A statistically significant overpopulation of elliptic and intermediate comets with the corresponding orbital nodes has been established. Recently discovered and absolutely faint comets show the best effect in this sense. The same is also true for comets with osculating eccentricities e < 1. A similar result is also obtained for comets with “original” a ^?1 > 0.010000. It is hypothesized that the 2003 UB 313 family is present among the 78 comets. Four of them have aphelion distances from 37.8 to 97.6 AU. An ellipticity is traceable in the distribution of some of the 78 distant nodes. This may be considered as a further argument for the suggested hypothesis. Generally, the body 2003 UB 313 may be assumed to play a prominent role in injecting observable comets from the transneptunian region     

The population of faint Jupiter family comets near the Earth

We study the population of faint Jupiter family comets (JFCs) that approach the Earth (perihelion distances q<1.3 AU) by applying a debiasing technique to the observed sample. We found for the debiased cumulative luminosity function (CLF) of absolute total magnitudes H₁₀ a bimodal distribution in which brighter comets (H₁₀?9) follow a linear relation with a steep slope α=0.65±0.14, while fainter comets follow a much shallower slope α=0.25±0.06 down to H₁₀∼18. The slope can be pushed up to α=0.35±0.09 if a second break in the H₁₀ distribution to a much shallower slope is introduced at H₁₀∼16. We estimate a population of about 10³ faint JFCs with q<1.3 AU and 10<H₁₀<15 (radii ∼0.1-0.5 km). The shallowness of the CLF for faint near-Earth JFCs may be explained either as: (i) the source population (the scattered disk) has an equally very shallow distribution in the considered size range, or (ii) the distribution is flattened by the disintegration of small objects before that they have a chance of being observed. The fact that the slope of the magnitude distribution of the faint active JFCs is very similar to that found for a sample of dormant JFCs candidates suggests that for a surviving (i.e., not disintegrated) object, the probability of becoming dormant versus keeping some activity is roughly size independent.     

Comet classification with new methods for gas and dust spectroscopy

We present the results of a program of comet long-slit spectroscopy with the Kast Dual Spectrograph on the 3-m Shane Telescope at Lick Observatory. A total of 26 comets, from a variety of dynamical families, were observed on 39 different nights from 1996 to 2007. A new statistical method extracted the twilight sky from comet frames, because traditional sky subtraction techniques were inadequate. Because previously published Haser model parent and daughter scale lengths did not fit the data well, unbiased ranges of scale lengths were searched for the best-fitting pairs. Coma gas production rates for OH, CN, C₂, C₃, NH, NH₂, and OH confirmed the widely reported carbon-chain depletion for a sub-class of comets, most notably high-perihelion Jupiter-family comets observed at r_h > 1.5 AU, with different behaviors for C₂ and C₃. Our long-slit spectroscopy data was also adapted for the A(θ)fρ dust production parameter. The assumption that A(θ)fρ is constant throughout the nucleus was not upheld. High dust-to-gas ratios for comets with large perihelia were not a selection effect, and suggest that the dust was released earlier in the formation of the coma than the gas. The dust-to-gas ratio did not exhibit any evolutionary traces between different comet dynamical families. The comet survey illuminates the diversity among comets, including the unusually carbon poor Comet 96P/Machholz.     

Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation

The orbital structure of trans-neptunian objects (TNOs) in the trans-neptunian belt (Edgeworth-Kuiper belt) and scattered disk provides important clues to understand the origin and evolution of the Solar System. To better characterize these populations, we performed computer simulations of currently observed objects using long-arc orbits and several thousands of clones. Our preliminary analysis identified 622 TNOs, and 65 non-resonant objects whose orbits penetrate that of at least one of the giant planets within 1 Myr (the centaurs). In addition, we identified 196 TNOs locked in resonances with Neptune, which, sorted by distance from the Sun, are 1:1 (Neptune trojans), 5:4, 4:3, 11:8, 3:2, 18:11, 5:3, 12:7, 19:11, 7:4, 9:5, 11:6, 2:1, 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4. Kozai resonant TNOs are found inside the 3:2, 5:3, 7:4, and 2:1 resonances. We present detailed general features for the resonant populations (i.e., libration amplitude angles, libration centers, Kozai libration amplitudes, etc.). Taking together the simulations of Lykawka and Mukai [Lykawka, P.S., Mukai, T., 2007. Icarus 186, 331-341], an improved classification scheme is presented revealing five main classes: centaurs, resonant, scattered, detached and classical TNOs. Scattered and detached TNOs (non-resonant) have q (perihelion distance) <37 AU and q>40 AU, respectively. TNOs with 37 AU<q<40 AU occupy an intermediate region where both classes coexist. Thus, there are no clear boundaries between the scattered and detached regions. We also securely identified a total of 9 detached TNOs by using 4-5 Gyr orbital integrations. Classical objects are non-resonant TNOs usually divided into cold and hot populations. Their boundaries are as follows: cold classical TNOs (i?5°) are located at 37 AU<a<40 AU (q>37 AU) and 42 AU<a<47.5 AU (q>38 AU), and hot classical TNOs (i>5°) occupy orbits with 37 AU<a<47.5 AU (q>37 AU). However, a more firm classification is found with i>10° for hot classical TNOs. Lastly, we discuss some implications of our classification scheme comparing all TNOs with our model and other past models.     

Close encounters of nearly parabolic comets and planets

An overview is given of close encounters of nearly parabolic comets (NPCs; with periods of P > 200 years and perihelion distances of q > 0.1 AU; the number of the comets is N = 1041) with planets. The minimum distances Δ_min between the cometary and planetary orbits are calculated to select comets whose Δ_min are less than the radius of the planet’s sphere of influence. Close encounters of these comets with planets are identified by numerical integration of the comets’ equations of motion over an interval of ±50 years from the time of passing the perihelion. Close encounters of NPCs with Jupiter in 1663–2011 are reported for seven comets. An encounter with Saturn is reported for comet 2004 F2 (in 2001).     

Some requirements of a colliding comet source of gamma ray bursts

Colliding comets in the Solar System may be an important source of gamma ray bursts. The spherical gamma ray comet cloud required by the results of the Venera Satellites (Mazets and Golenetskii, 1987) and the BATSE detector on the Compton Satellite (Meeganet al., 1992a, b) is neither the Oort Cloud nor the Kuiper Belt. To satisfy observations ofN(>P _max) vsP _max for the maximum gamma ray fluxes,P _max > 10^–5 erg cm^–2 s^–1 (about 30 bursts yr^–1), the comet density,n, should increase asn a ¹ from about 40 to 100 AU wherea is the comet heliocentric distance. The turnover above 100 AU requiresn a ^–1/2 to 200 AU to fit the Venera results andn a ^1/4 to 400 AU to fit the BATSE data. Then the masses of comets in the 3 regions are from: 40–100 AU, about 9 earth masses,m _E; 100–200 AU about 25m _E; and 100–400 AU, about 900m _E. The flux of 10^–5 erg cm^–2 s^–1 corresponds to a luminosity at 100 AU of 3 × 10²⁶ erg s^–1. Two colliding spherical comets at a distance of 100 AU, each with nucleus of radiusR of 5 km, density of 0.5 g cm^–3 and Keplerian velocity 3 km s^–1 have a combined kinetic energy of 3 × 10²⁸ erg, a factor of about 100 greater than required by the burst maximum fluxes that last for one second. Betatron acceleration in the compressed magnetic fields between the colliding comets could accelerate electrons to energies sufficient to produce the observed high energy gamma rays. Many of the additional observed features of gamma ray bursts can be explained by the solar comet collision source.