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Back to basics... The phase angle  is the angle Sun-Target-Earth. Since the 1950's

A search for correlations between magnitude-phase curves of KBOs and their physical and orbital parameters P. Rousselot (Obs. de Besançon, France) I. Belskaya (Univ. Kharkiv, Ukraine). Back to basics... The phase angle  is the angle Sun-Target-Earth. Since the 1950's

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Back to basics... The phase angle  is the angle Sun-Target-Earth. Since the 1950's

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  1. A search for correlations between magnitude-phase curves of KBOs and their physical and orbital parametersP. Rousselot(Obs. de Besançon, France)I. Belskaya(Univ. Kharkiv, Ukraine)

  2. Back to basics... • The phase angle  is the angle Sun-Target-Earth. • Since the 1950's (asteroidal observations…) it is known that the brightness of a planetary body lineary increases when  decreases and presents a steep brightness increase when  tends to zero degree: Opposition Surge. • Due to: - shadow-hiding effects • - coherent backscatterring Target  Sun Earth (Harris et al., 1989)

  3. A phase function is difficult to measure because:  Lightcurve.  Different observing runs corresponding to different phase angles are necessary.  Absolute photometric calibration needed. Example: (29981) 1999 TD10 (SDO) (Mueller et al., 2004) (Rousselot et al., 2006) lightcurve: Phase curve:

  4. Phase function of KBOs : → The phase angle range is restricted: typically <1.5 deg for a≈40 AU and <6 deg for a≈10 AU. → The phase angle range 0.5<<1.5 deg can be obtained for nearly all the TNOs or Centaurs and permit some comparisons between the different objects.

  5. This work (work in progress): search for a good criterion to compare the different phase functions : → It is necessary to use a common phase angle range, to avoid observational biases. → The standard H-G formalism, used for asteroids, do not seem adapted for KBOs (e.g. negative G values) → The limited number of data prevents to use too sophisticated models (Hapke, 1986; Akimov, 1980 and 1988; Shevchenko, 1996 and 1997) which need too many parameters. Our choice : The linear slope  (mag/deg) in the 0.5<<1.5 deg range

  6. Data used for this work : → Slopes already published by different authors (Bagnulo et al. 2006; Bauer et al. 2003; Belskaya et al. 2006; Buie and Bus 1992; Rousselot et al. 2005; Rousselot et al. 2006; Shaefer and Rabinowitz 2002; Sheppard and Jewitt 2002) → A reanalysis of individual data already published, by many authors. → Our own data, not yet published (case of Ixion, mixed with the one of Boehnhardt et al., 2004).

  7. To get homegeneous data from different authors : www.obs-besancon.fr/bdp

  8. Results : Object Slope (mag/deg) 12 TNOs: 1998 HK151 (91133) 0.10+/-0.03 1998 WH24 (19521 Chaos) 0.06+/-0.12 1999 DE9 (26375) 0.27+/-0.08 (SDO) 1999 KR16 (40314) 0.14+/-0.02 (SDO) 1999 TD10 0.18+/-0.06 (SDO) 2000 EB173 (38628 Huya) 0.125+/-0.009 2000 GN171 (47932) 0.14+/-0.03 2000 WR106 (20000 Varuna) 0.11+/-0.03 2001 CZ31 0.13+/-0.04 2001 FZ173 (82155) 0.30+/-0.16 (SDO) 2001 KX76 (28978 Ixion) 0.20+/-0.04 2002 LM60 (50000 Quaoar) 0.16+/-0.02 4 Centaurs: 1992 AD (5145 Pholus) 0.136+/-0.037 1995 DW2 (10370 Hylonome) 0.12+/-0.16 1998 QM107 (49036 Pelion) 0.13+/-0.25 2000 EC98 (60558 Echeclus) 0.20+/-0.06

  9. Correlation with orbital parameters: i=f()

  10. Correlation with orbital parameters: e=f()

  11. Correlation with orbital parameters: a=f()

  12. Correlation with orbital parameters: q=f()

  13. Correlation with orbital parameters: Vrms=f() <Vrms>=Vk(e2+i2)1/2 (Mean excitation velocity)

  14. Correlation with physical parameters: V-I=f()

  15. Correlation with physical parameters: B-R=f() Correlation for Centaurs+Scat. not too red ??

  16. Correlation with physical parameters: H=f()

  17. Correlation with physical parameters: albedo=f() Albedo is the main physical parameter that can influence phase curve slope. - Clear correlation observed for asteroids (Belskaya and Shevchenko, 2000) - For smaller  value the coherent backscattering can influence this correlation.

  18. Correlation with physical parameters: albedo=f() From Spitzer's results (Stansberry, private communication), except Quaoar (Brown & Trujillo 2004), Pluto (Buratti et al. 2003 (qv) / Buie et al. 1997 ()) and Charon (Buie et al. 1997)

  19. Conclusions : → No clear correlation phase curve slopes / colors for TNOs or Centaurs except, may be, for B-R and Centaurs + SDOs with moderate B-R → blue objects with high albedo ? → No clear correlation phase curve slopes / orbital parameters. → Correlation phase curve slope / albedo: need for more numerous and accurate albedo measurements...

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