Trans-Neptunian Objects

Transcription

1 Fakulteta za Matematiko in Fiziko Univerza v Ljubljani Trans-Neptunian Objects Mirko Kokole Mentor: Prof. Dr. Tomaž Zwitter May 1, 2005

2 Abstract In the last decade our view of the Solar system changed dramatically. We now know our planetary system is composed not only of nine planets and an asteroid belt, but also of a large number of minor bodies beyond the orbit of Neptune up to the heliocentric distance of 50 a.u.. These objects are known as TNOs (Trans Neptunian Objects), KBOs (Kuiper Belt Object) or EKOs (Edgeworth-Kuiper Belt Objects). They offer an insight into the formation and evolution of our Solar system. Here we present an overview of our current knowledge of dynamical and physical properties of KBOs. The theory for determination of object diameter and albedo is presented in more detail.

3 Contents 0.1 Introduction Dynamical classes [12] Classical Kuiper Belt Objects Resonant Kuiper Belt Objects Scattered Kuiper Belt Objects Physical Properties of TNOs Basics of Planetary Photometry [13] Determination of the object s diameter from thermal emissions [10] Sizes and size distribution of TNOs Colors of TNOs Conclusion

4 0.1 Introduction Until recently we believed that our solar system was composed of nine planets, a large number of asteroids between the orbits of Mars and Jupiter and comets. The first two papers proposing an existence of objects beyond the orbit of Neptune appeared in 1949 by Edgeworth and in 1951 by Kuiper. They argued that short-period comets have an origin in outer regions of the solar system, similarly as the long period comets have an origin in the Oort cloud. In 1992 the first Kuiper Belt object was discovered. There are currently 998 known Kuiper Belt Objects. These objects show different dynamical properties and are classified into three different dynamical classes. Their physical characteristics also differ from asteroids in the main asteroid belt. Main Kuiper belt extends from 30 a.u. to 50 a.u.. The three dynamical families of objects are: Classical Kuiper Belt objects in circular orbits, Resonant Kuiper Belt objects in orbital resonances of Neptune, and Scattered Kuiper Belt objects that have considerably elliptic orbits and perihelia in the Neptune region. Judging from statistics there are at least objects larger than 100km in the Kuiper belt. We also have to mention the Centaurs, these are objects with orbits between Jupiter and Neptune and are probably escaped KBOs. Some of these objects, notably the 2060 Chiron, also show cometary characteristics such as a coma, and are likely a link between KBOs and comets. 0.2 Dynamical classes [12] Classical Kuiper Belt Objects Classical Kuiper belt objects or CKBOs are defined by semi-major axes smaller than 43 a.u. and perihelia larger than 39 a.u.. The archetypal CKBO is 1992 QB1, also the first KBO discovered. Two thirds of all KBOs are classical. Their orbits are stable over an age of the solar system, because their perihelia are well separated from the orbit of Neptune. CKBO s orbits have moderate eccentricities, but their inclinations can reach more than 35 degrees (see fig. 2). Distributions of eccentricities and inclinations are too wide to be explained only by planetary perturbation over the life of the planetary system. Numerical simulations that model only planetary perturbation give eccentricities of only up to 0.02 and inclinations up to 1 degree, this suggests a currently unknown excitation mechanism. One possibility is that massive planetesimals have been scattered by Neptune 2

5 Figure 1: A plot of the outer solar system. The orbits of the planets are shown in light blue and the current location of each object is marked by large darkblue symbols. Unusual high eccentricity objects are shown as cyan triangles, Centaurs as orange triangles, Plutinos as white circles, scattered objects as magenta circles and classical objects as red circles. Objects observed at only one opposition are denoted by open symbols, objects with multipleopposition orbits are denoted by filled symbols. Numbered periodic comets are shown as filled light-blue squares. Other comets are shown as unfilled light-blue squares. Source: MPC in the early days of the Solar system. These planetesimals can excite inclinations of CKBOs. Problem is that they would also depopulate Neptune s resonances, and the existence of Plutinos is evidence against this mechanism. Another possibility is excitation by a passing star. This hypothesis solves the problem with Plutinos. Since close stellar encounters are nowadays very rare, it is more likely that these encounters took place as the Solar system formed in a cluster of stars. In this case the probability of a close passage was much higher. The edge at 50 a.u. is currently believed to be real and is not an artifact of insufficient observations. The outer edge can be explained by a close stellar 3

6 encounter. For a star to truncate the disk at 50 a.u., a star must pass 150 a.u. form the Sun. In the present environment such an encounter is improbable since the main distance between stars is nearly 1pc or a.u. This mechanism is probably similar to the truncation of disk-like structures (proplyds) seen around newly forming stars. Proplyds can be only 50 a.u. to 100 A.U across, similar to the size of the Kuiper belt. Beyond the edge are scattered objects that have semi-major axes more then 1000 a.u.. But there could also be a population of objects in circular orbits, provided that they are further away than 100 a.u.. Currently the only way to detect these objects is by the occultation technique. Figure 2: A graph of inclinations (left) against semi-major axes and eccentricity (right) against semi-major axes. We can distinctly see the separation of Plutinos and Classical KBO. Positions of major outer planets and the 3:2 main motion resonance of Neptune are marked with arrows. Data taken from the table of TNOs at MPC (cfa Resonant Kuiper Belt Objects. About 1 of known trans-neptunian objects have orbits near the main motion resonances of Neptune. These objects are called Resonant Kuiper Belt 4 Objects, and can be found mostly in 3:2 mean motion resonance, which is also occupied by Pluto. Objects in 3:2 resonance are called Plutinos to mark their dynamical similarity with Pluto. Other objects are also in resonances, notably 2:1 (1996 TR66), 4:3 (1995 DA2) and 5:3(1994 JS) mean motion resonances. Apparent fraction of Plutinos is overestimated because of the observational bias. Plutinos have orbits that are closer to Earth and so appear brighter 4

7 and easier to detect. From corrected statistics we know that their true fraction so probably from 10% to 15%. And so Plutions represent a minority component of the Kuiper belt. It is not firmly established how mean motion resonances are populated. The most promising mechanism is the outward migration of Neptune caused by angular momentum exchange with planetesimals scattered from the protoplanetary disk. Simulations have shown that trapping of KBOs by outward migration of Neptune is especially efficient for the 3:2 and 2:1 mean motion resonances [16]. The relative population of resonances depends partly on the rate of migration. This means that a migration rate could be established from the study of population ratios. A problem with the resonance sweeping model is that most of the KBOs are not trapped in mean motion resonances. The CKBOs should have been completely sweeped by the 2:1 mean motion resonance at approximately 48a.u Scattered Kuiper Belt Objects The Scattered Kuiper Belt Objects or SKBOs have highly eccentric and inclined orbits with perihelia near 35a.u.. Representative object of this class is 1996 TL66. At first it was not completely clear what kind of dynamical objects they are. But now is clear that they are a dynamical class of Kuiper belt. The perihelion distance of 35 a.u. allows a weak dynamical control of SKBOs by Neptune. SKBO s orbits are changed in a billion year time scale by the perturbations from Neptune. They form a fat doughnut around the CBKOs extending to large distances. SKBOs were scattered in the early days of the solar system. Because of their dynamical involvement with Neptune the SKBOs are a potential source of short-period comets. Occasionally Neptune will perturb SKBO and deflect it into inner solar system, this will cause the sublimation of ices and the formation of a coma and so transforming a KBO to a comet. Statistically SBKOs pose a problem. They can be only detected when near perihelion, because of their highly eccentric orbits. For example 1999 CF119 would be undetectable for more than 90% of each orbit. 5

8 0.3 Physical Properties of TNOs Basics of Planetary Photometry [13] Here we will describe some of the basics of planetary photometry and the quantities involved. Special emphasis will be on the photometry of the minorplanets. Bodies in the Solar system do not emit visible light so we can only measure the reflected light. Let us examine how visible light is reflected from a body in the solar system. Suppose R sun is radius of the Sun, r heliocentric distance of the object, R object s radius and F sun flux density at the surface of the Rsun Sun. Then light flux density at the object is F o = F 2 sun, and the flux r 2 or luminosity on the surface of the object is L = F o πr 2. We now define the bond or spherical albedo by fraction of incident luminosity and reflected luminosity. A = L ref (1) L A is equal zero for a black body and between 0 and 1 for a gray body. If an observer is at the distance from the object and the reflection is isotropical, then the light flux density received by the observer is F = L ref /(4π 2 ). Since reflection is not isotropical we have to correct by a factor CΦ(α). Where α is a phase angle. So the reflected flux density received 1 by the observer is given by the following equation: F = CΦ(α)L ref = CΦ(α) 4π 2 4π 2 AR2 sun r 2 πr2 (2) Now lets define the geometric albedo as: p = C A 4 So that bond albedo can be expressed as: (3) A = p q (4) where q is the phase integral q = π 0 Φ(α) sin(α)dα The reflected flux density received by the observer at zero phase angle is: 1 At zero phase angle F = p R 2 R2 sunf sun 2 r 2 (5) 6

9 Object 3 p R 2060 Chiron TO TC Varuna Huya AW Quaoar Ixion 0.15 Table 1: Table of albedos calculated for the measured size. Data are from table 2 of [1]. As we see from equation 5 it is not possible to measure object s size directly. We can only determine the product of geometric albedo and radius. To determine object s bond albedo it is necessary to know the phase function. Phase functions are usually very difficult to determine, especially for a distant object that can only be observed at a limited range of phase angles. We must also note that geometric albedo p is wavelength dependent. Usually we use different spectral regions defined by color filters. For example p R is geometric albedo for the red color filter. For easier comparison we assign absolute magnitudes H to objects 2. If the object is observed at zero phase angle and the geocentric distance is measured in a.u., we can calculate object s magnitude with the following relation m = H + 5 log( ). We have seen that it is not always easy to measure object s physical parameters such as diameter and albedo from the observation. The geometric albedo and object radius are usually coupled and the bond albedo is even harder to determine. For the KBOs the bond albedo is impossible to determine from geometric albedo, since we can not measure the phase function. For example: observable phase angles for a object at 40a.u. are ±1.4degrees. To determine the size of the KBOs from photometry we use an assumption that their albedos are small and comparable to the albedos of cometary nuclei. The value most often used is This is reasonable since they are supposed to have common origin. But if we look at the table 1 of measured albedos for some of the KBOs, we can see that KBOs posses higher albedos than cometary nuclei, and the 2 An absolute magnitude of the object in the solar system, is the magnitude the object would have, if it was at the distance of 1 a.u. from the Sun and was observed at zero phase angle from the Sun 7

10 assumption of 0.04 as geometric albedo is not always good. Albedos also seem to differ from object to object and is therefore not good to assume a single value. This calls for independent measurements of sizes. In the next section we will see how to determine object s diameter from thermal emissions. This method is currently the best one for measuring diameters of the small objects such as KBOs Determination of the object s diameter from thermal emissions [10] Here we will describe how to measure object s diameter from the thermal emissions. Let us consider a spherical object with a surface temperature distribution T (θ, φ), where θ and φ are polar coordinates on the object such that θ is the angular distance from the subsolar point 4. The thermal emissions are assumed to have black body spectrum B ν (T ), so the flux density seen by an observer at the distance from the object at zero phase angle is: F = B ν (T (θ, φ))ɛ ν dω (6) Where ɛ ν is thermal emissivity. Now suppose that we are observing thermal emissions from the part of the Planck function where Rayleigh-Jeans limit applies, so that we have: B ν 2 k T (7) λ 2 This is a good approximation if we are observing at 800µm and the surface temperature of the body is around 100K. The peak of Planck function from Wien law is at 29µm for surface temperature of 100K. The equation 6 now becomes: F ν = 2 k T π r 2 ɛ λ 2 ν (8) 2 T is the average temperature on the visible hemisphere subtended by solid angle, it is a function of magnitude and direction of the body s spin vector and its thermal properties; Bond albedo, infrared emissivity and thermal conductivity. For a spherical, nonrotating, nonconducting body in thermal equilibrium we can compute a temperature at the angle ψ from the subsolar point from equation: F sun (1 A) cos(ψ) = ɛ R 2 IR σ T 4 (θ, φ) (9) 4 Subsolar point is the point on the object where the Sun is seen in the zenith. 8

11 Where F sun = 1360W/m 2 is solar constant, A is Bond albedo, ɛ IR infrared emissivity and R heliocentric distance. The average temperature can be expressed with subsolar T (0, 0) temperature as: T = T (0, 0) χ 1/4 (10) where [10] χ = 1.6 for nonrotating body and χ = 4 for a fast rotating body where heat is carried to the night side and the surface temperature becomes isothermal. So a ratio of mean temperatures for the extreme rotation regimes is only (4/1.6) 1/4 = This is important since rotation periods for the most objects are unknown. We can now write the object s diameter in terms of the thermal flux density. ( ) 2 1/2 ( ) Fν σ R 2 1/8 ( ) ɛir χ 1/8 D = λ (11) π k ɛ sm F sun 1 A The most important property of the equation 11 is that it is quite insensitive to the known properties ɛ IR, χ and A. For example the factor of 2 in these quantities produces a relative error of 9% in the diameter. The equation is more sensitive to the submilimeter emissivity, but in the case of the TNOs we can asume a value of 0.9. This value is derived from the measured submilimeter emissivity of Ganymede (0.85), Calisto (1.04) and Pluto (0.82). A more accurate diameter than above can be calculated if we use a conduction model for calculation of surface temperature. For this we need to solve the equation: T ρc p t = ( c T ) (12) z z with a boundary condition: F sun (1 A) cos(ψ) R 2 = ɛ σ T 4 + λ T z (13) where c is thermal conductivity, and ψ is a function of time due to rotation. These equations must be solved numerically. In figure 3 we see a result of such a conduction model calculated for 2060 Chiron. This method of diameter determination is still model dependent and we have to guess the values for physical parameters. But since the equation 11 is less sensitive to the unknown parameters it is possible to get much better constraints for the diameter. For example let us look at the results for the 2060 Chiron [10]. If we vary for example the rotation rate we get a diameter of 270km for non rotating body and 302km for fast rotating body, 9

12 Figure 3: Surface temperature form the conduction model for the 2060 Chiron [10]. With subsolar point at 90 degrees. Isotherms are drawn in steps of 5K. Coordinates are local coordinates on the object. meaning our method is quite good even when we know nothing about body s rotation. If we vary bond albedo from 0.0 to 0.5 we get 270km (A=0.0) and 294km(A=0.5). This is all due the temperature dependence of thermal emissions in the Rayleih-Jeans approximation. Currently there are 9 KBOs (see table 2) with size measured by this method [1]. These measurements have shown us that albedos ob KBOs significantly differ from the assumed values derived from cometary nuclei Sizes and size distribution of TNOs Optical surveys of TNOs are flux limited and so lead to bias toward large and closer objects. As a result size distribution must be inferred form cumulative luminosity function and a distribution model. Cumulative Luminosity Function (CLF) Σ(M R ) describes a cumulative surface density or a number of objects per square degree to the magnitude m R and is well described by a power law relation [17]: log(σ(m r )) = α(m R m 0 ) (14) where α and m o are constants. m o is a magnitude at which there is 1 object per square degree. The fits for CLF give for example [17] α = 0.64 ± 0.1 and m o = ± 0.2. But these values can differ [12] a little when different fitting methods are used. 10

13 The size distribution is well described by the differential power law [7]: n(r)dr = ΓR q dr (15) Where n(r)dr is a number of objects with radii between R and R + dr. If we assume that the size is independent of heliocentric distance, than there is a relation between q and α [7]: q = 5α + 1 (16) Parameters for the size distribution can also be calculated from Monte Carlo simulation [12] and are Γ = and q = 4. If q = 4 is assumed to be correct than a cumulative number of objects grater that R is N(> R) = Γ. 3R 3 and we get N(50km) 10 5 and N(1000km) 10 [12]. This is consistent with currently detected distribution. From the above distribution we get the total mass of Kuiper belt [12] of M 0.1M Earth. The current mass of the Kuiper Belt is too small for the KBOs to have formed in the 10 8 years prior to the formation of the Neptune. So the original mass of the Kuiper Belt must have been some 100 times larger. Table 2 shows diameters of the largest KBOs found. These objects are important since they confirm the size distribution extrapolated from cumulative luminosity function, and are also big enough for meaningful measurements of their physical properties Quauor is the only object with diameter was measured directly with Hubble Space Telescope. Other diameters were measured from thermal emissions as described above. Object Diameter [km] Pluto 2320 Charon DW 1500? Quaoar 1200 Ixion AW Varuna 900 Table 2: Table of the largest KBOs. They are similar in size or larger than the biggest main belt object Ceres. Diameter of Ceres is 946 km. Source: jewitt/kb.html 11

14 0.3.4 Colors of TNOs Most TNOs are too faint for spectroscopic studies. Broad band color photometry can be used as a low resolution spectroscopy, but with much higher signal to noise ratio. The color photometry can also be a useful tool for object classification. Figure 4 shows a classification of the main belt asteroids. For KBOs we would expect to find a single class of objects with similar Figure 4: The classification of the main belt asteroids based on the UVB photometry [13]. The color indices B-V and U-B are different for different types of asteroids. B-V index is a difference in blue and green (visual) magnitudes. Red objects are in upper right and blue in lower left. color indices. Surprisingly (see figure 5) KBOs show a wide variety of colors, ranging from neutral gray to very red. First surveys suggested a bimodality in color [12], this would mean that there are two types of objects. But later studies [2] showed that there is no bimodality. An interesting fact is that KBOs and Centaurs are not distinguishable in the color-color plots, suggesting a common origin, and strengthening the idea that Centaurs are KBOs disturbed by planetary perturbation into the orbits with smaller perihelia. However there is a problem with the colors of comets and KBOs. Their colors are unmatched, because of the extremely red colors of KBOs. This red material is not present on comets. The absence of the red material in comets is consistent with either destruction and burial of the irradiation mantle formed in the Kuiper belt. 12

15 Figure 5: Color-color plot of the TNO, Centaurs and cometary nuclei [2] There exist three simple explanation [12] for the wide color diversity of KBOs. It is possible that the KBOs possess intrinsically different compositions, and so the color diversity is truly a trace of the compositional variations. For example main belt asteroids show compositions that depend on their formation site. There is a problem with this simple explanation, since most of the KBOs formed in a very slight radial temperature gradient, as opposed to the main belt asteroids (T r 1/2 ). A second explanation comes from the possibility of collisional excavations of the buried material, and exposure of the unirradiated ices. This mechanism requires that timescales for excavation of material and irradiation damage are comparable. Thirdly some laboratory experiments, done on the bitumen samples, showed that reflected color can be dependent on the effective particle size in the scattering surface. Currently only one KBO has given useful spectroscopic results (see figure 6). The spectroscopy of Quaoar [11] showed the presence of crystalline ice. This is most intriguing since we would expect only amorphous ice. This suggests a process of heating from internal source and a process of surfacing such as cryovulcanism. Another possibility is that surface material is mixed by impacts. It is important to note that the crystalline ice is transformed to amorphous by the energetic particles in the timescale of 19 Myrs [12]. This means that crystalline ice on the surface has formed recently suggesting an active surface. 13

16 Figure 6: Reflection spectrum of Quaoar [11]. The broad mini ma at 1.5 and 2.0 microns indicate a water ice on the surface and the sharper 1.65 minimum proves that the ice is crystalline. 0.4 Conclusion We have seen that our solar system is much more varied than it was previously expected. The discovery of trans-neptunian objects showed that the Solar system is larger and more complex. From dynamical properties of KBOs we have learned that our Sun and the Solar system probably formed in the cluster of stars. There is evidence of the planetary migration. From the size distribution we know that the total mass of the Kuiper belt is about 0.1 mass of Earth, but must have been much more massive before, about 100 times more so. From the color photometry and spectroscopy we have learned that Kuiper belt objects differ from asteroids and even from comets. Since they are supposed to be the origin of the short-period comets this suggests some physical process that changes their surface material. There is still an open question what are relative population of the main motion resonances for Neptune. What is the excitation process that caused the wide velocity dispersion, and are the short-period comets really fragments of larger bodies in the Kuiper belt. We have showed how it is possible to determine object s diameter from thermal emissions and so disentangle the diameter and geometric albedo. The method explained is very insensitive to the unknown parameters and so very 14

17 useful. The discovery of a very large Kuiper belt object such as Quaoar and 2004 DW opened the question whether Pluto is a planet or a KBO. All this questions are important enough the inspire a space probe mission to study Pluto and the Kuiper Belt. The mission called The New Horizons [4] will be lunched in early The probe will encounter Pluto and Charon in 2015 and will fly trough the Kuiper belt between 2016 in The mission will bring important data about Pluto, especially its surface properties and the physical properties of some KBOs. 15

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19 [13] H. Karttunen, P. Kröger, H. Oja, M. Poutanen, and K. J. Donner. Fundamental Astronomy. Springer-Verlag Berlin Heidelberg New York, [14] J. Luu and D. Jewitt. Color Diversity Among the Centaurs and Kuiper Belt Objects. AJ, 112:2310 +, November [15] J. Luu, B. G. Marsden, D. Jewitt, C. A. Trujillo, C. W. Hergenrother, J. Chen, and W. B. Offutt. A New Dynamical Class in the Trans- Neptunian Solar System. Nature, 387: , June [16] R. Malhotra. The Origin of Pluto s Orbit: Implications for the Solar System Beyond Neptune. AJ, 110:420 +, July [17] C. A. Trujillo, D. C. Jewitt, and J. X. Luu. Properties of the Trans- Neptunian Belt: Statistics from the Canada-France-Hawaii Telescope Survey. AJ, 122: , July