strategy.tex

\section{LSST Strategy for Discovering Solar System Objects}
\label{sec:strategy}

We briefly describe the LSST system design and observing strategy, and discuss in more
detail image processing and moving object detection.

\subsection{A Brief Overview of LSST  Design}

LSST will be a large, wide-field ground-based optical telescope system
designed to obtain multiple images covering the sky visible
from Cerro Pach\'{o}n in Northern Chile. With an 8.4m (6.7m effective) 
primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera,
LSST will be able to image about 10,000 square
degrees of sky per night, with a fiducial dark-sky, zenith 5$\sigma$ depth
for point sources of $m_5(r)$=24.38 (AB). The system is designed to yield
high image quality (with a median delivered seeing in the $r$ band of
about $0.8\arcsec$) as well as superb astrometric  and photometric
accuracy\footnote{For detailed specifications, please see the LSST
Science Requirements Document, \url{http://ls.st/srd}}. The total survey
area will include $\sim$30,000 deg$^2$ with $\delta<+34.5^\circ$, and
will be imaged multiple times in six bands, $ugrizy$, covering the
wavelength range 320--1050 nm. The project is scheduled to  begin the
regular survey operations at the start of next decade.

LSST will be operated in a fully automated survey mode. About 90\% of the
observing time will be devoted to a deep-wide-fast survey mode which will
uniformly observe a 18,000 deg$^2$ region about 800 times (summed over
all six bands) during the anticipated 10 years of operations, and yield a coadded map
to a depth of $r\sim27.5$. These data will result in catalogs including about
$40$ billion stars and galaxies, that will serve the majority of the
primary science programs. The remaining 10\% of the observing time
will be allocated to special projects such as a very deep and fast
time domain survey\footnote{Informally known as ``Deep Drilling Fields".}.



\subsection{LSST Observing Strategy}

As designed and funded (by the U.S National Science Foundation and
the Department of Energy), LSST is primarily a science-driven mission.
The LSST is designed to achieve goals set by four main science themes:
\begin{enumerate}
\item Probing Dark Energy and Dark Matter;
\item Taking an Inventory of the Solar System;
\item Exploring the Transient Optical Sky;
\item Mapping the Milky Way.
\end{enumerate}
Each of these four themes itself encompasses a variety of analyses, with
varying sensitivity to instrumental and system parameters. These themes
fully exercise the technical capabilities of the system, such as photometric
and astrometric accuracy and image quality.

The current baseline survey strategy is designed to maximize the overall science returns, including
Solar System science, rather than just the completeness of NEO/PHAs brighter than $H=22$ (though the
two goals are highly interrelated). Discovering and linking objects in the Solar System
moving with a wide range of apparent velocities (from several degrees per day for
NEOs to a few arc seconds per day for the most distant TNOs) places strong
constraints on the cadence of observations. The baseline strategy requires closely
spaced pairs of observations, two or preferably three times per lunation. The visit
exposure time is set to 30 seconds to minimize the effects of trailing for the majority of
moving objects. The images are well sampled to enable accurate astrometry, with
anticipated absolute calibration accuracy of at least 0.1 arcsec (based on an early analysis 
of Gaia's Data Release 1, the accuracy of astrometric calibration will probably improve 
by more than an order of magnitude when using upcoming Gaia's dataset; \citealt{Gaia}).
Typical astrometric errors for LSST detections will range from about 50 mas or better
at the signal-to-noise ratio SNR=100 (dominated by systematics), to 150 mas at SNR=5
(dominated by random errors). 

LSST observations can be simulated using the LSST Operations Simulator tool
\citep[OpSim,][]{delgado14}. OpSim runs a survey simulation with user-defined
science-driven proposals, a software model of the telescope and its control
system, and models of weather and other environmental variables. The output of
the simulation is an ``observation pointing history''; a record of times,
pointings, filters, and associated environmental data and telescope
activities throughout the simulated survey.  This history can be examined using
the LSST Metrics Analysis Framework tool \citep[MAF,][]{jones14} to assess the
efficacy of the simulated survey for any particular science goal or
interest\footnote{For examples of such analysis, see \url{http://ls.st/xpr}}. These
tools -- OpSim and MAF, and the sky brightness, throughput and sensitivity modeling --
are part of the LSST simulation effort \citep{LSSTSimsOverview}, which provides high-fidelity
tools to evaluate LSST performance.


\subsubsection{LSST Baseline Survey Simulation}

As the system understanding improves, the baseline survey strategy and the telescope model
are updated, generally on a yearly schedule. The current
reference baseline simulated survey is known as {\it minion\_1016}. It includes 2.4
million visits collected over 10 years, with 85\% of the observing time spent on the
main survey and the rest on various specialized programs. The median number of visits
{\it per night} is 816, with 3,026 observing nights. The median airmass is 1.23 (the
minimum attainable altitude for the LSST telescope is 20 deg.). In the $r$ band, the median
seeing (FWHM) is 0.81 arcsec, and the median $5\sigma$ depth for point sources is 24.16
(using the best current estimate of the sky background and system throughputs and accounting
for the distribution of observing conditions in the baseline survey; dark-sky, zenith observations
match the fiducial $5\sigma$ depth of $m_5(r)$=24.38).

There are a few known problems with this simulation, including twilight sky brightness
estimates that are too bright, the moon avoidance that is not as aggressive as it could be,
and observations that are biased towards west, away from the meridian. The implied impact
of these shortcomings on NEO completeness estimates is a few percent (the performance
of this simulated cadence in the NEO context is discussed in detail in \S5). An improved simulation,
that will presumably rectify these problems, will become available by the end of 2017.


\subsection{Overview of LSST  Data Management and Image Processing}

The images acquired by the LSST Camera will be processed by LSST Data Management
software \citep{juric15} to a) detect and characterize imaged
astrophysical sources and b) detect and characterize temporal changes
in the LSST-observed universe. The results of that processing will be
reduced images, catalogs of detected objects and their measured properties, and
prompt alerts to ``events'' -- changes in astrophysical scenery discovered by differencing
incoming images against older, deeper, images of the sky in the same direction ({\em
templates}). More details about the data products produced by the LSST Data Management system are described in
LSST Document LSE-163 \citep[LSST Data Products
Definition Document,][]{LSE-163}.

LSST will use two methods to identify moving objects:
\begin{enumerate}
\item Detecting trailed motion on the sky: objects trailed by more
  than 2 PSF widths (corresponding to motion faster than about 1
  deg/day) will be easily identifiable as trailed. LSST will detect sources in 
  difference images using standard point-source detection techniques;
  these sources will then be measured by PSF photometry and by fitting a trailed
  point source model \citep[see][Footnote 41]{LSE-163}).
  Two detections, both recognized as trailed, and within 20--60 minutes in a single night
  will be sufficient to identify an object as an NEO candidate,
\item Inter-night linking of pairs of detections from the same night: the Moving Object 
Processing System (MOPS) will recover objects moving too slow to be measurably elongated in a single exposure.
\end{enumerate}

We note that sources detected in difference images \citep[\DIASources in LSST parlance, see][]{LSE-163}
will also include false detections, colloquially known as {\it false positives}.
In addition to false detections due to instrumental artifacts and software glitches,
in this context they will also include detections of true astrophysical transients
(e.g. gamma-ray burst afterglow) that will not be associated with static sources
(e.g. stars and galaxies). Estimates of expected false detection rates are derived
in \S\ref{sec:imDiff}.



\subsection{The Basic Strategy for Linking Detections into Orbits}

The LSST strategy for linking detections into orbits assumes the following main steps:
\begin{enumerate}
\item Detections in difference images (obtained during the same night), that do not
         have a nearby static object (e.g. variable stars) within a small exclusion radius
         (a fraction of an arcsecond, but possibly larger for brighter stars), are linked into tracklets. There will be of the order
         a million tracklets per observing night (see \S\ref{sec:tracklets}).
\item At least three tracklets obtained in a 15-30 day wide window are linked into
         candidate tracks, using kd-trees and pre-filtering steps based on tracklets' positions
         and motion vectors (see \S\ref{sec:tracks}). These pre-filtering steps result in
         about the same number of false tracks as true tracks on the Ecliptic (of the order
         a million), with the completeness depending on population (e.g. main-belts
         asteroids vs. NEOs) and chosen tunable pre-filtering parameters (generally well above 90\%).
\item Candidate tracks are then filtered further (pruned from false tracks) by
        performing an initial orbit determination (IOD) to assess which tracks
        correspond to Keplerian orbits.
         Due to the high astrometric accuracy of the observations (uncertainties of 0.15 arcsec for the faintest objects,
         see \S\ref{sec:astromerrors}), the number of false tracks which 
         could pass IOD-based filtering becomes negligible, as is the incompleteness induced by this 
         step. A detailed discussion of the IOD step, 
         including an analysis of the accuracy of fitted orbital parameters,  will be presented in 
         a future publication; however an independent JPL study by \citet{VeresChesley2017mops} 
          confirms that orbit determination is indeed a reliable filter. This is further discussed in \S\ref{sec:mopsVeresChesleyComparison}.
\end{enumerate}

Incorrectly linked tracks will not be
an issue when identifying real moving objects because IOD will efficiently and reliably filter 
out false tracks due to the high-accuracy
astrometry and well-understood simple Keplerian model predictions. Therefore, the
essential question is whether the number of detections, including false detections, can be 
linked into tracks, and whether the resulting number of tracks, including false tracks, 
passed to the final IOD step can be handled with available computing resources.


These are all critically dependent on the performance of image differencing codes, and the number of false positive detections they may generate. We turn to these in the next section.