Physical Properties of Kuiper Belt and Centaur Objects: Constraints from Spitzer Space Telescope To Appear in: The Solar System beyond Neptune (M.A. Barucci et al., Eds.) U. Arizona Press, 2007 John Stansberry University of Arizona Will Grundy Lowell Observatory Mike Brown California Institute of Technology Dale Cruikshank NASA Ames Research Center John Spencer Southwest Research Institute David Trilling University of Arizona Jean-Luc Margot Cornell University Detecting heat from minor planets in the outer solar system is challenging, yet it is the most efficient means for constraining the albedos and sizes of Kuiper Belt Objects (KBOs) and their progeny, the Centaur objects. These physical parameters are critical, e.g., for interpreting spectroscopic data, deriving densities from the masses of binary systems, and predicting occultation tracks. Here we summarize Spitzer Space Telescope observations of 47 KBOs and Centaurs at wavelengths near 24 and 70 µm. We interpret the measurements using a variation of the Standard Thermal Model (STM) to derive the physical properties (albedo and diameter) of the targets. We also summarize the results of other efforts to measure the albedos and sizes of KBOs and Centaurs. The three or four largest KBOs appear to constitute a distinct class in arXiv:astro-ph/0702538v2 5 Nov 2007 terms of their albedos. From our Spitzer results, we find that the geometric albedo of KBOs and Centaurs is correlated with perihelion distance (darker objects having smaller perihelia), and that the albedos of KBOs (but not Centaurs) are correlated with size (larger KBOs having higher albedos). We also find hints that albedo may be correlated with with visible color (for Centaurs). Interestingly, if the color correlation is real, redder Centaurs appear to have higher albedos. Finally, we briefly discuss the prospects for future thermal observations of these primitive outer solar system objects. 1. INTRODUCTION of material in the transneptunian region, and relating vis- ible magnitude frequency distributions to size- and mass- The physical properties of Kuiper Belt Objects (KBOs) frequency is uncertain, at best. Quantitative interpreta- remain poorly known nearly 15 years after the discovery tion of visible and infrared spectra is impossible without of (15760) 1992 QB1 (Jewitt and Luu, 1993). While KBOs knowledge of the albedo in those wavelength ranges. Size can be discovered, their orbits determined, and their visible- estimates, when coupled with masses determined for bi- light colors measured (to some extent) using modest tele- nary KBOs (see Noll et al. chapter), constrain the density, scopes, learning about fundamental properties such as size, and hence internal composition and structure, of these ob- mass, albedo, and density remains challenging. Determin- jects. All of these objectives have important implications ing these properties for a representative sample of TNOs for physical and chemical conditions in the outer proto- is important for several reasons. Estimating the total mass planetary nebula, for the accretion of solid objects in the 1 outer Solar System, and for the collisional evolution of present initial conclusions regarding the relationship be- KBOs themselves. Of course, there is a relative wealth of tween albedo and orbital and physical properties of the information about Pluto and Charon, the two longest known targets, and discuss future prospects for progress in this KBOs, and we do not address their properties further here. area. The Centaur objects, with orbits that cross those of one or more of the giant planets, are thought to be the dynam- 2. THERMAL MODELING ical progeny of KBOs (e.g. Levison and Duncan, 1997; Measurements of thermal emission can be used to con- Dones et al. chapter). The Centaurs are particularly inter- strain the sizes, and thereby albedos, of un-resolved targets. esting both because of their direct relation to KBOs, and Tedesco et al. (1992; 2002) used Infrared Astronomical also because their orbits bring them closer to the Sun and to Satellite (IRAS) thermal detections of asteroids to build a observers, where, for a given size, they are brighter at any catalog of albedos and diameters. Visible observations of wavelength than their more distant relatives. Because of the brightness of an unresolved object are inadequate to de- their planet-crossing orbits, the dynamical lifetimes of Cen- termine its size, because that brightness is proportional to taurs are relatively short, typically a few Myr (e.g. Horner the product of the visible geometric albedo, pV , and the et al., 2004). cross-sectional area of the target. Similarly, the brightness The sizes of some KBOs and Centaurs have been de- in the thermal IR is proportional to the area, and is also a termined by a variety of methods. Using HST, Brown and function of the temperature of the surface, which in turn Trujillo (2004) resolved the KBO 50000 Quaoar, placed an depends on the albedo. Thus, measurements of both the upper limit on the size of Sedna (Brown et al. 2004), and visible and thermal brightness can be combined to solve resolved 136199 Eris (Brown et al., 2006). Recently Ra- for both the size of the target and its albedo. Formally the binowitz et al. (2005) placed constraints on the size and method requires the simultaneous solution of the following albedo of 136108 (2003 EL61) based on its short rotation two equations: period (3.9 hr) and an analysis of the stability of a rapidly rotating ellipsoid. Trilling and Bernstein (2006) performed F⊙ 2 Φ F = ,vis R p vis (1a) a similar analysis of the lightcurves of a number of small vis (r/1AU)2 V ∆2 KBOs, obtaining constraints on their sizes and albedos. Ad- 2 R Φir vances in the sensitivity of far-IR and sub-mm observato- Fir = ǫ Bλ(T (θ, φ)) sin θ dθ dφ (1b) π∆2 Z ries have recently allowed the detection of thermal emis- sion from a sample of outer solar system objects, providing where F is the measured flux density of the object at a constraints on their sizes and albedos. Jewitt et al. (2001), wavelength in the visible (“vis”) or thermal-infrared (“ir”); Lellouch et al. (2002), Margot et al. (2002, 2004), Altenhoff F⊙,vis is the visible-wavelength flux density of the Sun at et al. (2004), and Bertoldi et al. (2006) have reported 1 AU; r and ∆ are the object’s heliocentric and geocen- submillimeter–millimeter observations of thermal emission tric distances, respectively; R is the radius of the body (as- from KBOs. Sykes et al. (1991; 1999) analyze Infrared As- sumed to be spherical); pV is the geometric albedo in the tronomical Satellite (IRAS) thermal detections of 2060 Ch- visible; Φ is the phase function in each regime; Bλ is the iron and the Pluto-Charon system, determining their sizes Planck function; and ǫ is the infrared bolometric emissivity. and albedos. Far-infrared data from the Infrared Space Ob- T = T (pV q,η,ǫ,θ,φ) is the temperature, which is a func- servatory (ISO) were used to determine the albedos and di- tion of pV ; ǫ; the “beaming parameter,” η; surface planeto- ameters of KBOs 15789 (1993 SC), 15874 (1996 TL66) graphic coordinates θ and φ; and the (dimensionless) phase (Thomas et al., 2000) and 2060 Chiron (Groussin et al., integral, q (see below for discussions of η and q). 2004). Lellouch et al. (2000) studied the thermal state of In practice, the thermal flux depends sensitively on the Pluto’s surface in detail using ISO. Grundy et al. (2005) temperature distribution across the surface of the target, and provide a thorough review of most of the above, and in- uncertainties about that temperature distribution typically clude a sample of binary KBO systems with known masses, dominate the uncertainties in the derived albedos and sizes to constrain the sizes and albedos of 20 KBOs. (see Fig. 1). Given knowledge of the rotation vector, shape, Spitzer Space Telescope (Spitzer hereafter) thermal ob- and the distribution of albedo and thermal inertia, it is in servations of KBOs and Centaurs have previously been principle possible to compute the temperature distribution. reported by Stansberry et al. (2004: 29P/Schwassmann- Unsurprisingly, none of these things are known for a typi- Wachmann 1), Cruikshank et al. (2005: 555652002 AW197), cal object where we seek to use the radiometric method to Stansberry et al. (2006: 47171 1999 TC36), Cruikshank et measure the size and albedo. The usual approach is to use al. (2006), Grundy et al. (2007a: 65489 2003 FX128) and a simplified model to compute the temperature distribution Grundy et al. (in preparation: 42355 2002 CR46. Here we based on little or no information about the object’s rotation summarize results from several Spitzer programs to mea- axis or even rotation period. sure the thermal emission from 47 KBOs and Centaurs. These observations place secure constraints on the sizes 2.1. Standard Thermal Model and albedos of 42 objects, some overlapping with determi- The most commonly employed model for surface tem- nations based on other approaches mentioned above. We perature on asteroidal objects is the Standard Thermal 2 η pV (%) D (km) 100.000 STM : 5.0 534 1.10 ILM : 5.4 515 0.41 STM24 : 10.6 367 0.76 10.000 ILM24 : 0.6 1517 1.00 STM70 : 6.6 464 0.76 ILM : 2.5 752 1.00 1.000 70 0.100 Flux Density (mJy) 0.010 0.001 1 10 100 Wavelength (µm) Fig. 1.— Thermal models for KBO 38628 Huya (2000 EB173). Spitzer Space Telescope 24 and 70 µm data are shown as circles, with vertical error bars within them indicating the measurement uncertainties. Six models are fit to the data, with the resulting model albedos, diameters, and beaming parameters summarized in the legend.