P. Pravec, A. W. Harris, P. Kušnirák, A. Galád, K. Hornoch Ond řejov Observatory , Czech Republic

1. Absolute magnitudes of asteroids and a revision of asteroid albedo estimates from WISE thermal observations.* P. Pravec, A. W. Harris, P. Kušnirák, A. Galád, K. Hornoch Ondřejov Observatory, Czech Republic and More Data! Inc., California Asteroids, Comets, Meteors 2012 16-20 May 2012, Niigata, Japan *Report on a work for Icarus (paper revision completed, thanks to our reviewers Stephen Wolters and Amy Mainzer for constructive comments}

2. Asteroid albedos and diametersestimated from thermal models Wide-field Infrared Survey Explorer (WISE) - The recent most productive thermal IR survey. The WISE team estimated albedos and diameters for > 105 asteroids. (Mainzer et al., Astrophys. J. 741, 90, 2011, Astrophys. J. 743, 156, 2011, Masiero et al., Astrophys. J. 741, 68, 2011) • Input data: • Infrared measurements of the emitted thermal flux (four passbands 3.4 to 22 μm) • Photometric measurements of the reflected light flux (V band) • A practice of the asteroid thermal modeling is to estimate the integral optical flux from the asteroid's absolute visual magnitude Hand a model of its phase function. • The WISE team used H values from the MPCORB catalog. • Biases in the catalog H values need to be studied! (Mainzer et al., Astrophys. J. 743, 156, 2011)

3. WISE asteroid albedos Mainzer et al. (Astrophys. J. 741, 90, 2011) found a correlation of the estimated WISE albedos with diameter: Below D ~ 30 km, S type asteroids appeared to have systematically higher albedos, the mean albedo was up to ~50% greater at D < 10 km than in the range 30-200 km. Mainzer et al. suggested that it could be due to selection biases of the visual surveys against lower albedo objects among S types.

4. Checking catalog H data • [Definition: The absolute magnitude, H, of a Solar System object is defined as the apparent magnitude of the object illuminated by the solar light flux at 1 AU and observed from the distance of 1 AU and at zero phase angle.] • The catalog H data – a by-product of astrometric observations. • Catalog H values are problematic especially for smaller asteroids: Analyses of SDSS asteroid data showed an average offset of 0.2-0.4 mag (Parker et al. 2008, Jurić et al. 2002, Galád2010) for the MPCORB and AstOrbcatalogs. • Need to analyze a size- (or H-)dependence of the catalog H offset. • Control sample: • 583 asteroids observed photometrically from Ondřejov, Table Mountainand our other observatories during 1978-2011. • Absolute errors δH = 0.03-0.20 mag (one-apparition data), • the median δH = 0.10 mag. • Our observational and H estimation procedure: • Use of the Johnson-Cousins VR standard stars (Landolt 1973, 1983, 1992) • Rotation of asteroids accounted for -> mean H estimated • G estimated, or assumed according to the known taxonomy or orbital group • R data converted to V (to get H = HV) using mean (V-R) for the known • taxonomic class or orbital group • Biases in our data sample estimated to be not greater than 0.1 mag in mean H.

5. Bias in the catalog H data The maximum negative offset of the MPCORB H values is about -0.45 mag at H about 14. (Similar biases in the Pisa AstDyS and JPL Horizons catalogs.) Resulting in the WISE albedos systematically too bright by ~50% at D ~ 5 km (corresp. to H = 14 for S types).

6. Revised WISE albedos The WISE albedo estimates for 300 asteroids in our sample revised using our accurate H data with the method of Harris and Harris (Icarus 126, 450, 1997). A basic assumption of the method is that the quantity (1 - Av)D2 is invariant. This conserves the thermal flux measured from the spacecraft, and revises pVand D using updated H value. Result: No prominent change of albedo with size for S type asteroids. The trend of increasing albedo with decreasing size from ~30 downto ~5 km seen in the preliminary WISE albedos appears to be mainly due to the bias in the catalog H data they used. The null hypothesis of constant albedo is not rejected at a level greater than 3σ in the range D = 0.6-200 km for S type asteroids. The mean albedo of S types: <pV> = 0.197. Standard deviation (dispersion) of the sample is 0.051. The formal mean error of the mean albedo is ± 0.006. The mean albedo of C types: <pV> = 0.057. (Sample dispersion 0.013, formal error ± 0.002.)

7. Bias in the catalog H data – smaller effects The H offset, S vs C type dispersion A difference between S/S-like and C/C-like asteroids – the latter are systematically higher by ~0.09 mag in the (HMPCORB – H) plot. The “color dispersion” may be because the catalogs computers used a) a single default G (0.15), b) a single default V-R (0.4) for transformation of R or unfiltered magnitudes to V.

8. Bias in the catalog H data – smaller effects The H offset, an effect of rotational amplitude High-amplitude asteroids show the catalog H bias stronger by a few 0.01 to 0.1 mag. The small increase of (Hcatalog – H) with asteroid amplitude – actual reason unknown, but could be a natural consequence of the survey observations more likely to be taken around lightcurve maximum rather than minimum.

9. Conclusions Absolute magnitudes of asteroids in orbit catalogs are systematically biased. The bias is H-dependent; the negative offset (Hcatalog – H) reaches a maximum around H = 14. As a result, the preliminary albedo estimates from WISE observations were overestimated for asteroids smaller than ~30 km. We corrected the bias and found that there is no prominent trend in albedo with size for S type asteroids over the range 5 to 200 km.