MBCAA Observatory

329 Svea: light/rotation curves

Observed: 16, 17, 18, 19, 21, 22 March 2009

Michel Bonnardeau
2 Apr 2009

Abstract

Time-series are obtained for this asteroid. A period of rotation of 22.53 h is derived using a Monte Carlo algorithm.

Introduction

Minor planet 349 Svea orbits the Sun in 3.9 yr:

Svea orbit according to the JPL.

Its absolute magnitude is H=9.66 mag, with a diameter of about 78 km.

On 7 Nov 2007 I observed an occultation by this asteroid.

Observations

The observations were carried out with a 203mm f/6.3 SC telescope, a Rc filter and a SBIG ST7E camera (KAF401E CCD). 357 useful images were obtained, in 6 sessions, each with a 200s exposure duration. Aperture photometry is performed for each image, with a different comparison star for each session as the asteroid is moving.

An example of a light curve:

Red: Svea, Blue: the check star shifted by 0.8 mag. The error bars are +/- the 1-sigma statistical uncertainties.

A résumé of the observing sessions:

Session Nb. obs COMP star Check star

ID Average 1-sigma SD

16 Mar 2009 64 UCAC2-30-706-725 = GSC-4970-00886 UCAC2-30-706-694 = GSC-4970-00806 0.010 0.012

17 Mar 2009 52 UCAC2-30-706-674 = GSC-4970-00077 UCAC2-30-706-690 = GSC-4970-00022 0.021 0.022

18 Mar 2009 78 UCAC2-30-863-469 = GSC-4970-00339 GSC-4970-00185 0.023 0.024

19 Mar 2009 36 UCAC2-30-863-455 = GSC-4970-00081 UCAC2-30-863-432 = GSC-4970-00353 0.016 0.020

21 Mar 2009 68 UCAC2-31-015-306 = GSC-4967-00485 UCAC2-31-015-326 = GSC-4967-00501 0.010 0.011

22 Mar 2009 59 UCAC2-31-015-296 = GSC-4967-00506 UCAC2-31-015-289 = GSC-4967-00074 0.008 0.007

Period search

The magnitude measurements are searched for a periodicity, which would be due to the asteroid spin.

To search for a periodicity I use a Monte Carlo algorithm the following way:

X X X

the magnitudes of the 5 last sessions are shifted so that their average magnitudes are the same as the one of first session. This is to take into account the variation of the asteroid luminosity due mostly to the varying Earth-Svea distance;

the period is scanned from 12h to 24h with an increment of 10s;

X
for each period, the phases of the observations are computed (the time of each measurement is corrected for the light time travel);

X
the observations are sorted by increasing phases;

X
the last 5 sessions have their magnitudes shifted by some numbers (different for each session) to take into account the fact that the comparison stars differ for each session, and that Svea is varying. These numbers are taken randomly between 0.2 and -0.2 mag;

X X
the absolute values of the magnitude differences between 2 adjacent (in phase) measurements are summed, giving the "length" of the phase plot;

X X
this process of shifting the magnitudes by a set of random shifts is repeated 10,000 times;

X X
the set of magnitude shifts that gives the shortest phase plot length is retained;

the period that gives the shortest phase plot length is retained.

The above algorithm is re-run a number of times (10 or more). This leads to a unique period solution with the following average value and standard deviation:
P=22.49 h +/- 9 mn

To improve the period determination, the algorithm is run again 10 times but with the period between 22h and 24h with an increment of 5s, and, for each period, 50,000 trials for the magnitude shifts. The result is then:
P = 22.53 h +/- 11 mn

and for the magnitude shifts:
17 March 2009  0.026+/-0.004
18 March 2009  0.163+/-0.003
19 March 2009  0.086+/-0.010
21 March 2009  0.085+/-0.009
22 March 2009  0.126+/-0.009

The resulting light curve:

Discussion

A period of 22.77 h and a light curve are reported on the R. Behrend 's web site (as of March 2009). My period and light curve look quite similar.

A period of 15.201 h is reported on the JPL web site but when I fold my data with it I do not get a realistic light curve.

My uncertainty on the period is fairly large (11 mn) because my observations span only 7 days. However a longer span would have introduced uncertainties from the changing geometry of the Sun-Svea-Earth trio.