Subject: KBO science/cadence justification

From: Gary Bernstein

Submitted: Wed, 19 Mar 2003 12:58:48 -0500

Message number: 100 (previous: 99, next: 101 up: Index)

Following is a draft of a KBO science summary and requirements for
cadence, etc, as I discussed at the SWG meeting just now. I hope that Alan
Stern & Dave Jewitt in particular will take a red pen to this, everyone
should please send me comments or revisions.

gary

LSST SWG summary of KBO science and observing methods

G. Bernstein
Initial draft 3/18/03

1. Kuiper Belt science goals for LSST

The Kuiper Belt (plus Centaurs and other distant small bodies) are
remnants of the planetesimal phase of evolution of the Solar System.
In the inner Solar System, a runaway oligarchic growth phase led
to the production of the giant planets, which subsequently ejected
most of the remaining planetesimals with perihelia interior to
Neptune. Because of the longer collisional timescales in the outer
Solar System, however, runaway growth never occured, and the Kuiper
Belt region still contains a substantial portion of the planetesimal
population. Since objects in the 10-1000 km range in extrasolar
planetary systems are likely to remain unobservable for many decades,
the KBOs represent our only chance to directly study this phase of
planetary system formation.

The Kuiper Belt is not pristine: the eccentricities and inclinations
of the known KBOs are substantial, in the sense that accretion could
not have occured in the present dynamical state. There is a drop in
the space density of ~200 km objects beyond 50 AU that is unexplained.
These and other current data indicate that the Kuiper Belt contains
clues to one or more major events in the history of the outer solar
system. The history of accretion, collisional grinding, and
perturbation by existing and vanished giant planets is written into
the joint distribution of KBOs over orbital elements and size. Colors
of KBOs are clearly diverse, but the implications of this diversity
and the coupling of these physical differences with the dynamical
distribution is also unknown. Light curves of KBOs also give
information on the shape and surface inhomogeneities of the
planetesimals, which also helps constrain the composition and
structural evolution of the system.

A high-throughput telescope such as LSST has the power to discover
millions of new KBOs, and to determine orbital elements,
colors, and time variation for many or all of these. The joint
distribution over these quantities will allow us to disentangle the
history of the outer solar system. The large number of objects is
desirable for several reasons:

(1) Structure in the dynamical (or other joint) distributions becomes
apparent only with large numbers of objects, to reduce the shot
noise in the phase-space density of KBOs.

(2) Higher object counts arise from more complete sky coverage and/or
greater depth. Since the Kuiper Belt has an outer edge, fainter
KBOs are smaller KBOs. There is likely a turnover in the KBO size
distribution in the 1-100 km region, as smaller objects have been
ground away since the collisions are currently erosive.
Understanding how the erosive turnover depends upon dynamical
variables and colors will show when the erosive transition
occurred for each dynamical family.

(3) More complete sky coverage will ensure the discovery of important
but rare objects. With $\sim1000$ KBOs known, we are still discovering
objects that force us to revise our basic scenarios (e.g. 2000
XX??, an object with highly elliptical orbit but perihelion beyond
reach of Neptune).

It should therefore be our goal to use the uniquely high throughput of
LSST to increase our knowledge of the KBO population as much as
possible.

Because KBO studies are still in the exploratory era, it is not
possible to define a single measurement that must be done and which
can be used to produce a quantitative floor on LSST specs and
cadences. Nor can we say definitively what number of KBOs with
orbits, colors, and/or light curves would be "enough." We can note
the following: with the current sample of ~600 objects, there are
critical dynamical types that are represented by only a single object
(e.g. the Neptune Trojan ....; the 5:2 (??) resonator ????; ????, which has
a scattered orbit with perihelion well beyond Neptune). Even the most
basic correlations between color or size and dynamical properties are
marginally detectable. A 100-fold increase in the cataloged population
would seem a minimum to find sufficient numbers in the known
dynamical classes to make meaningful measurements of size/color trends
within such classes. It is also clear that an extension of the
well-surveyed population to smaller sizes (= fainter limits) is
critical to understanding the accretion history. It is further likely
that there are dynamical classes that remain undiscovered in current
data.

2. The "Shallow" LSST sample

We will assume for the KBO discussion that there will be a mode of
LSST operation centered on NEA detection in which (nearly) the entire
visible hemisphere will be imaged in a series of tens of 10--20 second
exposures over the course of each year. We will refer to this as the
"shallow" survey and to KBOs that can be detected (at $5\sigma$
significance) in a single 20s exposure as "bright." Depending on the
parameters of the telescope, this will be $R\lesssim24$, which
corresponds crudely to 100~km diameter.

Current data show that the sky density of KBOs near the ecliptic plane
is (Trujillo et al 2001)

N(<R) = 10^{0.63(R-23)} {\rm deg}^{-2}

The sky distribution of known KBOs shows a half-width of
$\approx20\deg$, and the total number of "bright" KBOs is therefore
approximately $6\times10^4$. LSST would easily discover all of these
objects and determine high-quality orbits from the shallow survey,
since a good orbit will require only 4--6 detections over the
course of 2--3 years. This is a roughly 60-fold increase over the
number of presently known KBOs.

The job of detecting all the bright KBOs is in fact {\it too} easy for
LSST, in the sense that a telescope with lower etendue will be able to
sweep the sky the required 3--4 times to find all the bright KBOs.
The CFHT Legacy Survey will conduct a survey of this depth over
$\approx1000$ deg$^{2}$ centered on the ecliptic in the next six
years. Pan-STARRS or a similar project will likely have discovered all
the bright KBOs by the advent of LSST.

What does the higher throughput of LSST gain us for bright KBOs? LSST
will acquire 100 or so observations of each bright KBO over its
operative lifetime, as opposed to just a few. This would enable
important new science beyond knowing the orbital distribution of the
bright KBOs:

(a) Colors: KBOs clearly have diverse colors, but they vary by tenths
of magnitudes. Hence S/N~100 in each of two visible colors is
desirable for accurate assignment of KBO colors. This is well beyond
the S/N required for detection; the LSST will give color info for all
bright KBOs due to the many repeat visits, so the joint
color-magnitude-orbital distribution will be known for all bright
KBOs. Note that the long-term, random time sampling of the LSST
shallow survey will give magnitudes properly averaged over light
curves.

***A clear requirement is that the NEA survey be split between at
least two colors.

(b) Light curves: The 100-or-so observations of each bright KBO can be
searched for a light curve period, adding amplitude of variation as
another variable for which the bright-KBO distribution is fully
characterized. Some simulation work is required to test the
feasibility of period recovery over such long time scales.

3. A Deep KBO Survey

We propose here a different cadence for LSST observations that
unleashes the full power of LSST for KBO discovery and study by
extending the KBO sample well past the $R<24$ limit.

Longer integrations are of course necessary to discover fainter KBOs.
Near quadrature, KBO apparent motions are $\lesssim1\arcsec$ per
hour. A one-hour series of short integrations can be summed to track
all such motions, and with an imaging FWHM of 0\farcs5 or larger, the
number of required trial sums is of order 10, which remains in the
realm of computational feasibility. We will baseline, then, a survey
in which the LSST maintains a pointing for a contiguous hour.

With the effective exposure time increased from 20s to 3600s, the
detectable flux (assuming background limit) drops by a factor 13, or
2.8~mag. If the Trujillo et al luminosity function holds to R=27,
this implies a 60-fold increase in the number density of observable
KBOs. It also reduces the limiting mass for KBO detection by factor
of 50. Both the increased number density and the extension to smaller
KBO sizes will enormously increase our ability to use the KBOs to
diagnose the history of the outer solar system.

***The KBO science return will be greatly amplified by an observing
mode in which ~1-hour segments are devoted to a fixed pointing.

The requirement for useful determination of orbits is likely to be
that 3 or 4 detections must be made over a time span >=12 months. A
candidate cadence, for example, is:
1 hour at first quadrature year 0.
1 hour at second quadrature, year 0.
1 hour at second quadrature, year 1.
Simulations are needed to determine the trade of visits vs orbital
accuracy. The following points about this cadence are clear, however:

***A given 1-hour visit may be done with two or more filters, as long
as all filter give good S/N on solar-colored objects.
***Timing of the KBO visits is not critical; in most cases, delaying a
revisit of a field until the next quadrature is not fatal.
***Full sky coverage is not required (indeed not practical---see
below) but any partial sampling of the sky should be reasonably
uniform in ecliptic longitude, concentrated within 20 degrees of
the ecliptic.
***Visibility of the full ecliptic is an important criterion in the
site selection.

Each LSST field searched for faint KBOs will take a total time
investment of 3 hours, and cover 7 square degrees. Taking 170 hours
per lunation of dark/grey time, efficiency factors of 0.75, 0.75, and
0.95 for clear skies, good seeing, and uptime, respectively, there are
1200 candidate hours per calendar year of LSST operation. If we
presume that a fraction f_deep of time is devoted to the deep cadence,
then in a 10-year lifetime we can survey
28,000 f_deep deg^2
of the sky, or
2 f_deep
of the total area of sky within +-20 degrees of the ecliptic.
If f_deep is 0.1, then we can find 20% of the accessible faint KBOs,
or a total sample size of $7\times10^5$ KBOs.

Note that with these three observations in hand, one can now leverage
the accumulated NEA survey data for these fields: the orbit can be
tuned to higher precision by fitting to the 1--2 hours of 20-second
exposures that have accumulated over 10 years. Colors can be derived
for all the detected KBOs at $R\lesssim26$.

4. Required technical specifications.

Here we comment on the figures of merit for telescope engineering that
are relevant to the KBO science.

***The figure of merit for FOV, aperture, and image quality is the
usual point-source quantity (FOV*D/FWHM)^2. In fact it is the
time-averaged inverse of this quantity that is relevant---the
canonical 1-hour exposure time can be trimmed dynamically in good
conditions, if the telescope optics are good enough to take
advantage of good seeing.
***Filter choice: for the shallow survey, KBO science prefers that at
least part of the survey make use of the filter that optimizes S/N
for solar-colored point sources. However to obtain color
information, a single wide-band filter is not optimal. Some
rotation between g, r, i, and "wide-V" filters is desired.
***Filter choice: for the deep survey, a wide-V filter might provide
the best detection limit, perhaps a 1.5x gain in object counts.
But cycling between narrow filters, e.g. g and r, with i in
brighter time, will increase the scientific yield from color info,
and may provide a better match with other deep-survey goals.
***Astrometry: KBO orbits will improve usefully as astrometric
accuracy improves. A global astrometric frame with errors <<0.1"
is desirable, though not required.
***Pre-survey: a pre-survey is somewhat useful for KBOs in that it
provides a subtraction template for the shallow survey. The deep
survey would be too deep for an all-sky presurvey to serve as
subtraction template. The deep survey will have to serve as its
own subtraction template.
***Photometric accuracy: 0.02 mag is probably a requirement, better
can be used.
***Read time, slew times, overheads: for the shallow survey, the
optimization for efficiency is driven by NEO requirements. For the
deep mode, exposure times may lengthened and slewing is reduced, so
demands on overheads are substantially looser.

5. Open Questions

We need further study of the following questions:

Does the KBO surface density continue to climb to R=27? Current
surveys should answer this within the year.

Are 3 (or 4) observations at successive quadratures sufficient to
localize the orbit to desired accuracy?

What kind of tiling strategy maximizes efficiency of a subsampling of
sky while minimizing the loss of objects off the FOV over the orbital
arc?

For a deep survey, what kind of filter cadence maximizes the
scientific yield for variability studies and for the accumulation of a
valuable deep static image?

How well can light curve amplitudes and/or phases be recovered from
observations taken over a time baseline of hundreds or thousands of
periods?

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