Subject: Revised KBO section
From: Gary Bernstein
Submitted: 25 Aug 2003 13:32:21 -0400
Message number: 167
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Attached is a slight revision of a KBO section for the DRM document.
Numbers and some text have been updated since last writing to reflect
new results, and a few more sentences on light curves are present as per
Beatrice Muller's comments. It's now formatted using AASTeX markup.
Let me know of any comments/suggestions, particularly whether the length
and emphasis are appropriate for the DRM document. This revision has
not yet been vetted by Stern, Jewitt, Muller, etc., so don't blame them
for problems.
Regards,
Gary
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\section{LSST SWG summary of KBO science and observing methods}
Third version 8/25/03
\subsection{Kuiper Belt science goals for LSST}
The Kuiper Belt (and other distant small body populations) consists of
remnants of the early accretion and evolution of the Solar System. In
the closer Solar System, runaway and oligarchic growth of solid bodies
led to the production of the giant planets, which subsequently ejected
most of the remaining planetesimals with perihelia interior to
Neptune. In the outer Solar System, however, runaway growth was for
some reason truncated, and the Kuiper Belt region still contains a
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
study directly this phase of planetary system formation.
The Kuiper Belt is not dynamically 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 $\gtrsim 40$~ km objects beyond 50 =
AU
that is unexplained. There is a clear correlation of the size
distribution with dynamical state, with the largest bodies found
exclusively in higher-excitation orbits.
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 their shape and surface inhomogeneities; from this
one can constrain the angular momentum distribution and internal
strengths of the bodies.
A high-throughput telescope such as LSST has the power to discover
tens or hundreds of thousands of new KBOs, map their orbital distribution, =
and
determine 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 discovery of such a
large number of KB objects is desirable for several reasons:
\begin{enumerate}
\item 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 and to find niche
populations that likely provide strong clues to the origin and
evolution of the belt.
\item 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 a turnover in the KBO size
distribution below $\approx 100$~km diameter, presumably since
smaller objects are susceptible to collisional disruption and have
been ground away since the accretion epoch.
Understanding how the erosive turnover depends upon dynamical
variables and colors will show when the erosive transition
occurred for each dynamical family.
\item 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
CR105, an object with highly elliptical orbit but perihelion beyond
reach of Neptune).
\item The upper envelope of rotation rates is an indicator of the physical
strength of the bodies, since rapid rotation can cause breakup.
This is better defined with larger samples.
\end{enumerate}
It should therefore be our goal to use the uniquely high throughput of
LSST to increase our knowledge of the KBO population to the extent 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 $\sim800$ objects, there are
dynamical types that are represented by only a one or two instances
(e.g. the Neptune Trojan 2001 QR322). 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 desirable 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 (=3D fainter limits) is
critical to understanding the accretion/erosion history.=20
It is further likely that there are dynamical classes that remain
undiscovered in current data.=20
\subsection{Required Signal-to-Noise for KBO Science}
The specific requirements for different aspects of KBO science are:
\begin{itemize}
\item {\bf Detection:} $S/N>7$ is required to distinguish TNOs from
noise fluctuations, since the objects are very rare. This $S/N$ must
be acquired in a short time period (see below).
\item {\bf (P)Recovery:} $S/N>5$ is required to recover a known TNO.
The threshold for false positives is lower because we do not have to
search the entire
phase space. The discovery observation does not have to precede the
recovery observation, so any detection observation can also serve as
recovery. =20
\item {\bf Color:} KBOs clearly have diverse colors, but they vary by tenth=
s
of magnitudes. Hence $S/N \gtrsim 100$ in each of two visible colors is
desirable for accurate assignment of KBO colors. Since KBOs vary on
several-hour time scales, observations in different bands must either
be within $\ll 1$~hour of each other, or spread over many periods.
\item {\bf Light Curves:} The amplitude of known TNO lightcurves
ranges from $\approx 1$~mag to zero. A properly phased light-curve
will hence require multiple points with $S/N$ of tens to $\approx
100$, depending upon the amplitude. A cumulative $S/N$ of 25--200 is
thus required to detect the variability, depending upon amplitude.
Known light-curve periods are 0.2--1 day, so the observations must
span multiple evenings, but simulations are needed to determine how
well periods can be determined from observations spread over many
periods.=20
\end{itemize}
The power of an LSST, therefore, is not just in extending the
magnitude limit for detection of large numbers of KBOs, but a proper
observing cadence can also greatly increase the number of objects
observed with sufficient $S/N$ to obtain meaningful colors and light
curves. At present, for example, $\lesssim 10\%$ of known TNOs have
well-measured colors, and $1--2\%$ have variability characterized.
\subsection{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 150~km diameter.
Current data show that the sky density of $R<24$ KBOs near the ecliptic pla=
ne
is $\approx 3\, {\rm deg}^{-2}$, roughly equally split between the
``classical'' Kuiper Belt---a low-eccentricity, low-inclination
($i\lesssim 5\arcdeg$) population peaked near $a=3D42$~AU---and
higher-excitation populations, including Neptune-resonant and
``scattered'' orbits, with a half-width on the sky of perhaps
$\approx20\deg$. The total number of ``bright'' KBOs on the sky
is therefore $\approx2\times10^4$. =20
LSST would easily discover virtually 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 20-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: The S/N required for color is well beyond that
required for detection; the LSST will give color info for all
bright KBOs due to the many repeat visits on the full sky, 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.
{\bf 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, and to
explore favorable timing schemes. It seems
likely, however, that light curve amplitudes will be measured for many
thousands of KBOs, with periods determined for many of them.
\subsection{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. =20
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. Only a handful of objects this faint have been detected, but
estimates of the sky density suggest
this implies a 25-fold increase in the number density of observable
KBOs. It also reduces the limiting mass for KBO detection by factor
of 50. It is in this mass range that the transition to the putatively
erosion-dominated regime occurs, so the collection of large numbers of
KBOs in this range will allow comparison of the collisional history of
the various dynamical classes.
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.
{\bf 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 $\ge12$ months. A
candidate cadence, for example, is:
\begin{enumerate}
\item 1 hour at first quadrature year 0.
\item 1 hour at second quadrature, year 0.
\item 1 hour at second quadrature, year 1.
\end{enumerate}
Simulations are needed to determine the trade of visits vs orbital
accuracy. The following points about this cadence are clear, however:
\begin{itemize}
\item 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. Interlacing
filters would give high-accuracy colors for all objects $R\le25.5$
within the surveyed area.
\item Timing of the KBO visits is not critical; in most cases, delaying a
revisit of a field until the next quadrature is not fatal.
\item 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\arcdeg\ of
the ecliptic.
\item {\bf Visibility of the full ecliptic is an important criterion in the
site selection.}
\end{itemize}
Each LSST field searched for faint KBOs will take a total time
investment of 3 hours, and cover 7 deg$^2$. 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 $f_{\rm deep}$ of time is devoted to the deep
cadence, then in a 10-year lifetime we can survey
27,000 $f_{\rm deep}$ deg$^2$ of the sky, or $1.8f_{\rm deep}$
of the total area of sky within $\pm 20\arcdeg$ of the ecliptic. =20
If $f_{\rm deep}=3D0.1$, then we would expect a total of
$\approx 10^5$ detected $R<27$ KBOs. Roughly 25\% of these would have
high-precision color determinations.
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. Simulations are
required to determine the magnitude limits to which useful light-curve
data could be extracted from the combined deep/shallow database.
{\bf A modest investment in long-integration mode for LSST would yield
a five-fold increase in detected KBOs and those with useful colors,
and push into a different physical regime of KBO sizes. This mode
would likely be useful for other domains of time-variable astronomy as
well.}=20
\subsection{Required technical specifications}
Here we comment on the figures of merit for telescope engineering that
are relevant to the KBO science.
\begin{itemize}
\item The figure of merit for FOV, aperture, and image quality is the
usual point-source quantity=20
$( {\rm FOV}\times D /{\rm FWHM})^2$. 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.
\item 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.
\item 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.
\item Astrometry: KBO orbits will improve usefully as astrometric
accuracy improves. A global astrometric frame with errors $\ll
0.1\arcsec$=20
is desirable, though not required.
\item 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.
\item Photometric accuracy: 0.02 mag is probably a requirement, better
can be used.
\item 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.
\end{itemize}
\subsection{Open Questions}
We need further study of the following questions:
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?=20
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?=20
\subsection{References}
Reviews and recent publications giving an overview of the current
observed properties of KBOs and corresponding theory include:
Bernstein, G. M. et al 2003, \aj\ (submitted)
Durda, D.~D.~\& Stern, S.~A.\ 2000, Icarus, 145, 220=20
Luu, J.~X.~\& Jewitt, D.~C.\ 2002, \araa, 40, 63=20
Malhotra, R., Duncan, M. J., \& Levison, H. F.\ 2000, Protostars and
Planets IV, 1231 =20
Farinella, P., Davis, D.~R., \& Stern, S.~A.\ 2000, Protostars and
Planets IV, 1255 =20
Tegler, S. C. \& Romanishin, W. 2003, Icarus, 161, 181
\end{document}
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