小行星的自旋週期極限在探測小行星內部結構時扮演了關鍵角色。直徑大於一公里的小行星，它們的自轉週期不會小於2.2小時，這被稱為「自旋屏障（spin barrier）」，其存在被解釋為小行星是重力束縛的瓦礫堆結構，因此有此自旋週期極限，否則過大的離心力將使小行星崩解。因為不同類型的小行星有不同的體積密度，它們的自旋週期可能不同。我們利用PTF的小行星週期數據庫（Chang et al. 2015, Waszczak et al. 2015）和NEOWISE任務的反照率資料庫（Masiero et al. 2011），來探討X型小行星的自旋屏障，從這個角度來研究小行星的內部結構，其中我們特別關注組成物質為鐵、鎳的M型小行星。我們找到三個各屬於不同化學成份和光譜類型的、自轉速率快的小行星，包括：P型小行星(10305) Grignard、M型小行星(34946) 2286 T-1、E型小行星(10359) 1993 TU36，並假設它們的轉動週期都接近離心力不穩定性條件，以此計算出小行星的體積密度和孔隙度，藉由分析小行星的孔隙度，我們發現E型小行星1993 TU36的內部結構可能發生過重大斷裂事件，P型小行星10305 Grignard和M型小行星 2286 T-1可能為瓦礫堆結構。

The spin-rate limit of asteroids plays a key role in probing the interior structure of asteroids. The 2.2-hour spin-barrier has been interpreted as a result of the “rubble-pile” structure of asteroids (i.e., gravitationally bounded aggregations). Because asteroids of different types should have different bulk densities, their spin-rate limits could be different. We use the asteroid rotation periods of the PTF project (Chang et al. 2015, Waszczak et al. 2015) and the NEOWISE albedos (Masiero et al.2011; Mainzer et al. 2011) to study the spin-rate limits of X-type asteroids. In this way, we can study their bulk densities, which in turn probes asteroid interior structure. We are particularly interested in the M-type asteroid, which is mainly made of nickel-iron. We found three fast rotating asteroids classified to different chemical compositions and spectrum types: P-type asteroid, (10305) Grignard；M-type asteroid, (34946) 2286 T-1；E-type asteroid, (10359) 1993 TU36. If their gravitational force and centrifugal force were in balance, we found that E-type asteroid, (10359) 1993 TU36, was probably heavily fractured; P-type asteroid, (10305) Grignard and M-type asteroid, (34946) 2286 T-1, were probably rubble-pile structure.

[1] Britt, D. T., et al., “Asteroid density, porosity, and structure”, Asteroids III, pp.485-500, 2002.
[2] Britt, D. T., Consolmagno, S. J., “Stony meteorite porosities and densities: a review of the data through 2001”, Meteoritics & Planetary Science 38, Nr. 8, pp.1161-1180, 2003.
[3] Bus, S. J., et al., “Visible-wavelength spectroscopy of asteroids”, Asteroids III, pp.169-182, 2002.
[4] Bus, S. J., Binzel, R. P., “Phase II of the small main-belt asteroid spectroscopic survey: a feature-based taxonomy”, Icarus 158, pp.146-177, 2002.
[5] Chang, C.-K., Ip, W.-H., Lin, H.-W., et al. “Asteroid spin-rate study using the Intermediate Palomar Transinet Factory”, ApJ Supp. Ser., 219:27, 2015.
[6] Fornasier, S., et al., “Spectroscopic survey of M-type asteroids”, Icarus 210, pp.655-673, 2010.
[7] Fornasier, S., et al., “Spectroscopic survey of X-type asteroids”, Icarus 214, pp.131-146, 2011.
[8] Harris, A. W., “The rotation rates of very small asteroids: evidence for ‘rubble pile’ structure”, 27th Lunar and Planetary Science Conference, abstract no.1247,1996.
[9] Hiroi, T., et al., “What are the P-type asteroids made of”, 35th Lunar and Planetary Science Conference, abstract no.1616, League City, Texas, March 15-19, 2004.
[10] Krot, A. N., et al., “Classification of Meteorites”, pp.83-128, Meteorites, Comets and Planets, Vol.1, A. M. Davis (eds), Treatise on Geochemistry, H. D. Holland and K. K. Turekian (eds), Elaevier-Pergamon, Oxford, 2005.
[11] Lipschutz, M. E., et al., “Meteoritic parent bedies: Nature, number, size and relation to present-day asteroids”, Asteroid II, pp.740-777, 1989.
[12] Mainzer, A., et al., “NEOWISE studies of spectrophotometrically classified asteroids: Preliminary results”, ApJ, 741:90, 2011.
[13] Masiero, J. R., et al., “Main belt asteroids with WISE/NEOWISE I: Preliminary albedos and diameters”, ApJ, Vol. 741, No. 2, 2011.
[14] Pater, I. D., Lissauer, J. J., Planetary Sciences, Edit. 5th, Cambridge University Press, New York, 2007.
[15] Pravec, P., Harris , A. W., “Fast and slow rotation of asteroids”, Icarus 148, pp.12-20, 2000.
[16] Tholen, D. J., “Asteroid taxonomy from cluster analysis of photometry”, Ph. D. dissertation, University of Arizona, 1984.
[17] Tholen, D. J., Barucci, M. A., “Asteroid taxonomy”, Asteroids II, pp.299-315, 1989.
[18] Waszczak, A., et al., “Asteroid light curves from the Palomar Transient Factory survey: Rotation periods and phase functions from sparse photometry”, AJ, 150:75, 2015.
[19] Weisberg, M. K., McCoy, T. J., Krot, A. M., Meteorites and the Early Solar System II, University of Arizona Press, Tucson, pp.19-52, 2006.
[20] Asteroid Lightcurve Photometry Database
http://alcdef.org/
[21] Asteroid spectrum classification using Bus-DeMeo taxonomy
http://smass.mit.edu/busdemeoclass.html
[22] ColorBox
https://www.colourbox.com/image/rock-rubble-and-pebbles-in-a-small-pile-isolated-on-a-white-background-image-3963254
[23] Meteorite: density & specific gravity
http://meteorites.wustl.edu/id/density.htm
[24] IAU Minor Planet Center: Plot of the Inner Solar System
http://www.minorplanetcenter.net/iau/lists/InnerPlot.html
[25] IAU Minor Planet Center: Plot of the Outer Solar System
http://www.minorplanetcenter.net/iau/lists/OuterPlot.html
[26] Pics about Space
https://pics-about-space.com/asteroid-belt-and-meteorites?p=2
[27] SDSS database
https://sbn.psi.edu/pds/asteroid/EAR_A_I0035_5_SDSSTAX_V1_1/