140 Siwa: light/rotation curves
Observed: Oct 2005-Feb 2006
16 Dec 2005
Revised: 17 Dec 2005
Updated and revised 2 Apr 2009
with more data and a new analysis.
Time-series are obtained for this asteroid. A period of rotation
is searched using a Monte Carlo algorithm.
Minor planet 140 Siwa orbits the Sun in 4.5 yr:
Siwa orbit according to the
Its absolute magnitude is H=8.34 mag, which suggests a diameter of
about 110 km.
It is spining with a synodic period of P=18.495 h (Le Bras et al (2001)).
However this does not seem to be well determined, as other observers have
found different values.
The observations were carried out with a 203mm f/6.3 SC telescope, a
Clear filter and a SBIG ST7E camera (KAF401E CCD). Each exposure is 1mn
Aperture photometry is performed for each image. The comparison stars
differ for each session, as the asteroid is moving. The magnitude variations
of Siwa are faint (maximum of about 0.1 mag). The choice of a Clear filter
is then rather unfortunate (a red or BB filter would have improved the
S/N). To get the most of the photometry, a stringent extra-losses software
filter (Gary (2007)) is applied for each session, with a threshold of
0.1 mag. When a few images of a time-serie are below the threshold, they
are discarded. When there are many of them below the threshold the whole
time-serie is discarded.
An example of a light curve:
Red: Siwa, Blue: the check star. The error bars are +/- the 1-sigma
and of the corresponding extra losses filter:
The points are expected to be along the blue line. The filter is the
green line: the images that give zero points below it are discarded.
A résumé of the 9 usable sessions:
|10 Oct 2005
||Ensemble photometry (6 COMP)
||UCAC2-34-394-008 = GSC-630-00771
|20 Nov 2005
||UCAC2-33-686-602 = GSC-34-00610
||UCAC2-33-686-618 = GSC-35-01006
|23 Dec 2005
||UCAC2-33-863-903 = GSC-34-00823
||UCAC2-33-863-894 = GSC-34-00762
|19 Jan 2006
||UCAC2-34-768-974 = GSC-623-00395
|22 Jan 2006
||UCAC2-34-769-081 = GSC-633-00962
||UCAC2-34-769-073 = GSC-623-00287
|25 Jan 2006
||UCAC2-34-954-388 = GSC-623-00962
||UCAC2-34-954-376 = GSC-623-01295
|31 Jan 2006
||UCAC2-35-140-616 = GSC-630-00189
||UCAC2-35-140-622 = GSC-630-00024
|1 Feb 2006
||UCAC2-35-140-661 = GSC-630-00066
|10 Feb 2006
||UCAC2-35-509-740 = GSC-634-01182
||UCAC2-35-509-738 = GSC-634-01215
The following sessions where discarded because of the extra losses filter:
23 Oct 2005
1 Nov 2005
24 Dec 2005
15 Jan 2006
20 Jan 2006
2 Feb 2006.
Futhermore, the session of 24 Jan 2006 was also discarded as the asteroid
was moving across a crowded field.
The magnitude measurements are searched for a periodicity, which would
be due to the asteroid spin.
For the first 2 sessions (10 Oct, 20 Nov 2005) the aspect of Siwa as
seen from Earth and lighted by the Sun changes substantially. So these
two sessions are not used in the period search. For the remaining 7 sessions,
Earth is moving away from the asteroid which is seen with almost always
the same aspect; see HERE diagrams of the Sun-Siwa-Earth
geometry. The time of each measurement is corrected for the light time
The variations of Siwa are faint but quite slow. The photometry measurements
may then be grouped 4 by 4 to improve the S/N. This gives 208 measurements
for the 7 sessions used in the period search.
To search for a periodicity I use a Monte Carlo algorithm the following
the magnitudes of the 6 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 dimming of the asteroid
due mostly to the increasing Earth-Siwa distance;
the period is scanned from 12 h to 24 h with an
increment of 2 s;
for each period, the phases of the observations
the observations are sorted
by increasing phases;
the last 6 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 Siwa is varying. These numbers are taken randomly between 0.2
and -0.2 mag;
the absolute values of the magnitude differences
between 2 adjacent (in phase) measurements are summed, giving the
"length" of the phase plot;
this process of shifting the magnitudes
by a set of random shifts is repeated 20,000 times;
the set of magnitude shifts that gives the shortest
phase plot length is retained;
the period that gives the shortest phase plot length
The above algorithm is re-run a 100 times. This does not lead to a unique
period solution however, but rather to a spectrum strongly peaked around
The average value of the period from the 45 values in the strong peak
P = 19.7266 h +/- 18 s (the uncertainty is the standard deviation)
and the magnitude shitfs are:
19 Jan 2006 +0.020+/-0.006
22 Jan 2006 -0.104+/-0.008
25 Jan 2006 -0.027+/-0.006
31 Jan 2006 -0.118+/-0.007
01 Feb 2006 -0.002+/-0.006
10 Feb 2006 -0.020+/-0.006
The resulting phase plot:
What about the 2 time-series that were not used to determine the period
(10 Oct, 20 Nov 2005)? Putting them on the phase plot gives:
Keeping in mind that the geometrical aspect was different of the sets
used to derive the period, they may be considered as in agreement.
If the different time-series do not match very well, because of a changing
geometry or of poor photometry, the Monte Carlo algorithm may tend to
give longer periods. (If nothing match, the period will be as long as the
A period of 18.495 h was derived by Le Bras et al (2001). When I fold
my data with this period I do not get a realistic light curve, with 2
time-series at the same phase not being parallel.
A period of 17.16 h is reported on the R.
Behrend's web site (as of March 2009). Actually I also find one solution
(i.e. 1/100) at P=17.064 h. I get realistic light curves with these periods,
but not as good looking as the one with the 19.7 h period.
The conclusion is that the period derived here is uncertain. Better
observations would have been necessary, with the use of a filter and longer
exposures, more measurements but spanning over a shorter time so as to
have a fairly constant geometry.
Gary B. (2007) Exoplanet observing for amateurs Reductionist Publications.
(May be downloaded from
Le Bras A. et al (2001) A&A 379 660.
A similar period search for asteroid 329
Telescope and camera configuration.
Computer and software configuration.