Subject: LSST KBO addendum

From: Beatrice Muller

Submitted: Wed, 6 Aug 2003 21:34:38 -0700 (MST)

Message number: 158 (previous: 157, next: 159 up: Index)

Hi everyone,
 
Michael Strauss has asked me to give some input for the KBO science case
and I would like to add one point to Gary's excellent write-up (MSG 100).
 
As Gary mentions in his write-up, lightcurves of bright KBOs can be 
searched for rotational periods. This is not just important per se but can 
also be used to get a constraint on the bulk density of KBOs as an ensemble.
This has been successfully done for asteroids and is currently tried  
for cometary nuclei but the data are much too sparse for the latter.
In a plot of axial ratio of the asteroids versus rotation period,
there are no asteroids larger than 200m (with 2 exceptions) with rotation 
periods higher than 2.2hr. This indicates that a lot of these asteroids
must be rubble piles (with density larger than about 3g/cm^3). The reason
that no fast rotator exist (in the larger than 200m sizes) is that they 
would be torn apart by the centrifugal forces. (For details about the
asteroid case, ask one of the experts on your team, Al Harris).
If periods and axial ratios of a large number of KBOs will get acquired, 
meaningful constraints on the bulk density of KBOs (as an ensemble) 
could be made. This method is the only one right now to get bulk densities 
for KBOs (densities for selected individual KBOs can be obtained for 
binary KBOs).

The question is, how feasible are the LSST observations to get rotational
periods from these sparse observations. Simple simulations (by me and Nalin
Samarasinha) show promise but it will have to be investigated further.
In principle it should be doable because the rotation periods do not need
to be too accurate. If a suspected fast rotator is found, it could be 
followed up with other telescopes over a short time span with good 
temporal coverage.

Some of the problems to derive a period from a lightcurve are:
a) change in viewing geometry 
b) opposition effect (i.e. solar phase angle dependence)
c) photometric accuracy
d) recovery of rotation periods from data with large temporal gaps.

a) is not a problem because of the distance of the KBOs (might be more
   a problem for Centaurs)
b) does have to be corrected for. This depends on the scattering properties
   of the surface. It is not currently known if there is an opposition surge 
   for TNOs similar to asteroids. If there is a pronounced effect, it will be
   difficult to correct for it because there will not be enough solar phase
   angle coverage. On the other hand if there is just a linear dependence
   on solar phase angle then a range of phase coefficients can be used to
   explore the effect on the recovery of the period.
   Sheppard and Jewitt (AJ 124, 2002) measured the solar phase effect for 
   7 TNOs and found a linear dependence for those 7 inside a solar phase 
   angle of 2deg.
c) the photometric accuracy needed will depend on the amplitude of the
   lightcurve. The larger the amplitude the lower the photometric accuracy
   has to be. I do not see it as a big problem unless the majority  
   of TNOs are very spherical.
d) This will be challenging but not impossible. In principle a family of
   solutions with probable periods can be obtained with Fourier Transforms 
   and subsequent clean algorithms (using the information of the spacing of
   the data as 1-dim. psf). The advantage of a clean algorithm is that
   aliases induced by the spacing of the data and spurious periods are
   cleaned out. (The FT clean algorithms used by us are very slow 
   because they use a cross correlation to stabilize the clean algorithm 
   for noisy data. The last point should not be a problem with faster 
   computers and optimization of the codes.)
   The result of the FT and clean algorithm should be checked with other
   period search programs. 

Beatrice Mueller

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