Jian-Yang Li, University of Maryland Marc Kuchner, NASA Goddard Space Flight Center

1. Jian-Yang Li, University of Maryland Marc Kuchner, NASA Goddard Space Flight Center Ron Allen, Space Telescope Science Institute Scott Sheppard, Carnegie Institution of Washington, DTM Measuring the Physical Properties of Outer Solar System Objects with the Space Interferometry Mission Li et al., BDEP, Shanghai, China

2. What is SIM? • Precision astrometry on stars to V=20. • Optical interferometer on a 6 m structure. • One science interferometer. • One guide interferometer (4.2 m baseline) and one precision guide telescope to stabilize the fringes. • Global astrometric accuracy: 4 µas. • At end of 5 year mission lifetime. • Narrow-field astrometric accuracy: 1 µas, in a single measurement. • Current state of the art is HST/FGS at ~500 µas. • Ground-based differential astrometry will reach ~20 µas. • Typical observations take about 1 minute; ~ 5 million observations in 5 years.

3. Discovery space RV will press on icy planets and close-in planets. Transit & microlensing will provide statistical census of rocky planets (e.g., Kepler @ 1 kpc, and microlensing @ 5 kpc. Together with some other instruments, SIM probes 1-10 MEarth(0.4 - 6.0 AU for nearby stars). It provides orbital parameters and masses for RV planets.

4. Look at our planetary system The outer solar system objects (KBOs and Centaurs) will help us understand the characteristics and formation of big planets far away from the star Li et al., BDEP, Shanghai, China

5. Beautiful backyard of our Sun Li et al., BDEP, Shanghai, China

6. Li et al., BDEP, Shanghai, China

7. D=34.3 mas D=40.4 mas Li et al., BDEP, Shanghai, China

8. Size  Escape Velocity Shape+ Period  Density T Radius Brown et al. 2006 Iapetus: Brightness variations Density+shape => internal structure Li et al., BDEP, Shanghai, China

9. SIM’s capability 109 KBOs + 26 Centaurs in total: 20 KBOs and 18 Centaurs are identified to be observable for SIM • SIM can measure the: • Size • Shape • Rotational status Li et al., BDEP, Shanghai, China

10.   B1 B1 B3 B2 B3 B2 Visibilities Size  Shape 2 Jinc(2πR) Inverse jinc function to get the size of a circular disk with uniform brightness distribution Three visibilities, solve for two axes and one angle Li et al., BDEP, Shanghai, China

11. Haumea (2003 EL61) • Rotation period 3.92 hr (Rabinowitz et al., 2006) • Jacobi ellipsoid • Axial ratio b/a=0.86, c/a=0.54 (Lacerda and Jewitt, 2007) • Density 2551 (+115, -10) km m-3 (Lacerda and Jewitt, 2007) • Mass from two satellites • Size 1960-2500 km (Rabinowitz et al., 2006) • Albedo ~0.6 • Dark red spots from photometric lightcurves (Lacerda et al., 2008) • Almost pure water ice on the surface (Trujillo et al., 2007) • Strong limb-darkening, k=0.85 Li et al., BDEP, Shanghai, China

12. Simulation – edge-on view • 1% uncertainty of visibility from SIM • Size can be determined to better than 5% uncertainty Li et al., BDEP, Shanghai, China

13. Tracking photocenter – uniform surface • SIM tracks the photocenter of the object precisely. • Rotational period • Pole orientation • Sense of rotation SIM can achieve ~10 µas in visibility phase Li et al., BDEP, Shanghai, China

14. Tracking photocenter – with the Dark Red Spot • Complicated pattern for a surface with albedo features: • Not a problem for period determination • Should not be a problem for pole orientation determination • May be used to track surface features Li et al., BDEP, Shanghai, China

15. Minnaert limb-darkening model: I/F = A cosk (i) cos(k-1) (e) k=0.4 High albedo, high roughness objects SSA = 0.99, Θ=50 deg, g=0 k=0.5 Low albedo objects SSA < 0.2, Moon k=0.8 High albedo, low roughness objects Triton: SSA=0.99, Θ=14 deg, g=-0.38 Li et al., BDEP, Shanghai, China

16. Measure limb-darkening • Stellar limb-darkening from simultaneously visibility measurement at multiple λ/B (e.g. Quirrenbach et al., 1996) • Limb-darkening from k=0.5 (uniform disk) to k=1 (strongest limb-darkening) • Visibility uncertainty 1% • Simultaneously measurement of visibility at multiple wavelengths from 0.4-0.9 µm • Guide interferometer can be used to extend the λ/B range Li et al., BDEP, Shanghai, China

17. Summary • Outer solar system object help us understand planetary system formation at large distances from the star. • Fundamental properties of KBOs and Centarus, such as their sizes, shapes, and rotations, can only be measured to be good at 20% level from radiometry. • SIM can observe about 40 KBOs and Centaurs • Better than a few percent in size • Determine 3-D shape • Constrain rotational status, including pole orientation and sense of rotation • Limb-darkening can be measured by SIM through simultaneously visibility measurements at multiple λ/B. Li et al., BDEP, Shanghai, China