Alan has sent me the detrended data obtained by Marek Kozubal and Ron
Dantowitz. 2008 TC3 was definitely a tumbler. There is seen strong
signal in two frequencies correspoding to periods 0.0269409 and
0.0136205 h, and in linear combinations of the two frequencies. I
cannot tell which of the frequencies is a rotation rate and which is
precession.
The data fitted with full 2-dimmensional Fourier series of the 4th order:
http://www.asu.cas.cz/~ppravec/2008tc3.png
The rms residual is 0.058 mag and residuals show a nearly Gaussian
distribution, so they are probably due to a photometric noise (rather
than, e.g., another possible lightcurve component].

I'm running more analyses of the complex case, so I may write an
update later.

Whichever of the two periods is a rotation, the asteroid was one of
the fastest rotators among asteroids known so far. Two others fastest
rotators compiled in the Warner&Harris LCDB:
2000 DO8, P = 0.0217 h, D~4 m
2000 WH10, P = 0.0222 h, D~10 m
(Whiteley 2002).
It is good to have another one in the sample, and especially to know
that it is a tumbler. Among superfast rotators, tumblers appear on
any spin rate, suggesting a higher mu*Q (consistent with higher
rigidity expected for coherent bodies) or younger age than larger,
cohesionless asteroids (predominating in size range D > 0.2 km). See
Pravec et al., Icarus 173, 108-131, 2005; Pravec et al., Proceedings
of the IAU Symposium 236 (Eds.: Milani A., Valsecchi, G.B.,
Vokrouhlicky, D.) Cambridge Univ. Press, pp. 167-176, 2007.

Cheers,

Petr Pravec

--- In mpml@yahoogroups.com, Alan W Harris <awharris@...> wrote:
>
> We have received a set of photometric data taken by Marek Kozubal and
> Ronald Dantowitz at the Clay Center Observatory, Dexter School, MA,
> spanning about 2 hours. In addition to a dramatic trend of about 2.5
> magnitudes brightening, the data show a very clear periodicity of
about 0.9
> magnitude amplitude and a simple period of 49 seconds, or a double
period
> of 98 seconds. Thus Richard's analysis is just about right, within his
> stated error estimate. After de-trending the data and examining a
longer
> time series, it appears that the variation is not simply periodic, but
> instead the object appears to be in a non-principal axis spin state, or
> "tumbling". There are a few other tumbling super-fast rotators, so
this is
> not a unique case. It will take a bit more time for a careful
analysis,
> since aspect is changing as fast as the brightness, so there may
need to be
> a "de-trending" of the time series applied as well.
>
> Alan Harris and Brian Warner
>
>
> At 05:26 PM 10/7/2008, RICHARD MILES wrote:
> >Gustavo,
> >
> >A most excellent animation.
> >
> >Folk might want to watch the object flashing brighter and fainter.
> >It appears to do this 26 times in a periodic fashion.
> >
> > From the field shown, I estimate the sequence lasts some 1380 seconds.
> >If the variations are due to rotational modulation of the light,
the object
> >must therefore rotate every 106 +/-8 seconds or so.
> >That would make it the 4th fastest rotator that we know of amongst the
> >asteroid community!
>
> *******************************************************************
> Alan W. Harris
> Senior Research Scientist
> Space Science Institute
> 4603 Orange Knoll Ave. Phone: 818-790-8291
> La Canada, CA 91011-3364 email: awharris@...
> *******************************************************************
>