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Astron. Astrophys. 322, 679-686 (1997)

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8. Conclusion

The 1994 observations confirm the variation of the phase factor as a function of rotational phase. The statistical analysis is performed in independent parts each being a direct one with few magnitudes near the same phase P directly compared. A Fourier analysis would require that a great number of interrelated unknowns are solve for in a single solution involving all observations simultaneously, with a more uncertain interpretation as a result.

Errors in the computed rotational phases can not account for the large values 0.05 to 0.13 mag/deg of the phase factors. The largest slope is dy/dP=-1.4 mag/deg at P=0.57. The 10 period determinations from single oppositions (AN 312 p.215) gives errors [FORMULA] rev/day. In the 3 days observation interval with a phase change of 0.6 deg the max. error in [FORMULA] is thus less than [FORMULA] mag/0.6 deg = [FORMULA] 0.007 mag/deg. In sec.3 is shown that the comparison 1983-94 gives errors of order [FORMULA] 0.01 rev, corresponding to [FORMULA] 0.023 in [FORMULA]. The effect found is thus not caused by a possible "alias" error in the rotational period.

The correlation coefficient between [FORMULA] and dy/dP is r=-0.205 with f=23 degrees of freedom. This is insignificant as the 5% limit is 0.396. On the other hand the present data does not prove that there is no "alias" error, only that if present it is not the cause of the large values of the phase factor.

The "amplitude-phase relationship" (Zappala et al. 1990) implies different phase factors at maxima and minima. For reasons of continuity we should therefore expect a correlation between the magnitude, say y, and the phase factor [FORMULA]. This correlation coefficient is r =-0.050 and the 5% limit is 0.396. The present data do not indicate a connection between the slope of the phase curve and the magnitude itself. The amplitude is here 0.10 mag. which according to Zappala et al. should give a phase factor variation of order 0.100 [FORMULA] 0.015=0.0015 mag/deg which can not be observed. The present data does not contradict Zappala et al.

The separation of the lightcurve from the phase curve requires a uniform distribution of observations in both rotational and solar phase. With the ephemeris for physical observations now available it would be possible - given enough telescope time - to determine individual phase curves for the different sides of the body.

So far 51 Nemausa is the only object for which phase factor variation has been detected. The development of asteroid photometry requires that other objects must be investigated.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998