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Executive Summary

The Transiting Exoplanet Survey Satellite ( TESS ) will perform a two-year survey of nearly the entire sky , with the main goal of detecting exoplanets smaller than Neptune around bright , nearby stars .
There do not appear to be any fundamental obstacles to continuing science operations for at least several years after the two-year Primary Mission .

Any decisions regarding use of the TESS spacecraft after the Primary Mission should be made with the broadest possible input and assistance from the astronomical community .
As has recently been made clear by the NASA K2 mission , there are many applications of precise time-series photometry of bright objects besides exoplanet detection .

Nevertheless , exoplanet detection is likely to be part of the motivation for a TESS Extended Mission .
To provide a head start to those who are planning and proposing for such a mission , this white paper presents some simulations of exoplanet detections in a third year of TESS operations .
Our goal is to provide a helpful reference for the exoplanet-related aspects of any Extended Mission , while recognizing that this will be only one part of a larger discussion of the scientific goals of such a mission .

We performed Monte Carlo simulations to try to anticipate the quantities and types of planets that would be detected in several plausible scenarios for a one-year Extended Mission following the two-year Primary Mission .
The strategies differ mainly in the schedule of pointings on the sky .
For simplicity we did not compare different choices for the cadence of photometric measurements , or for the target selection algorithm , although different choices might prove to be advantageous and should be studied in future work .

We considered six different scenarios for Year 3 of the TESS mission , illustrated in Figure 1 : 1 Six possible pointing strategies for a TESS Extended Mission , visualized in ecliptic coordinates .
None of these scenarios spend the entire year observing the ecliptic ; we concluded that such a plan is inadvisable because of interruptions by the Earth and Moon ( see Fig . 9 ) . Figure 1 Six possible pointing strategies for a TESS Extended Mission , visualized in ecliptic coordinates .
None of these scenarios spend the entire year observing the ecliptic ; we concluded that such a plan is inadvisable because of interruptions by the Earth and Moon ( see Fig . 9 ) .

1 . hemi , which re-observes one of the ecliptic hemispheres in essentially the same manner as in the Primary Mission ( i.e. , neglecting the zone within 6 ^ { \circ } of the ecliptic ) ;

2 . pole , which focuses on one of the two ecliptic poles ;

3 . hemi+ecl , which re-observes an ecliptic hemisphere , but moving all fields 6 ^ { \circ } closer in latitude to the ecliptic plane .
This scenario has a continuous viewing zone with angular diameter 12 ^ { \circ } rather than 24 ^ { \circ } ;

4 . ecl_long , which has a series of pointings with the long axis of the 24 ^ { \circ } \times 96 ^ { \circ } field-of-view along the ecliptic ( in combination with some fields near the ecliptic pole , when the Earth or Moon would prevent effective observations of the ecliptic ) ;

5 . ecl_short , which has a series of pointings with the short axis of the field-of-view along the ecliptic ( again in combination with some fields near the ecliptic pole ) ;

6 . allsky , which covers nearly the entire sky with \sim 14-day pointings ( as opposed to the 28-day pointings of the Primary Mission ) , by alternating between northern and southern hemispheres .

We numerically computed the results based on the methodology of .
Some of the most important findings are :

1 . The overall quantity of detected planets We define ‘ detected planet ’ to mean one with at least two observed transits , and a phase-folded \mathrm { SNR } > 7.3 ( Eq . 1 ) .
All statistics are quoted for R _ { p } < 4 R _ { \oplus } planets . does not depend strongly on the sky-scanning schedule .
Among the six scenarios considered here , the number of newly-detected planets with radii less than 4 R _ { \oplus } is the same to within about 30 % .

2 . The number of newly-detected sub-Neptune radius planets ( R _ { p } \lesssim 4 R _ { \oplus } ) in Year 3 is approximately the same as the number detected in either Year 1 or Year 2 .
Thus , we do not expect a sharp fall-off in the planet discovery rate in Year 3 .
This is because the Primary Mission will leave behind many short-period transiting planets with bright host stars , with a signal-to-noise ratio just below the threshold for detection .
These planets can be detected by collecting more data in Year 3 .

3 . Apart from detecting new planets , a potentially important function of an Extended Mission would be to improve our ability to predict the times of future transits and occultations of TESS -detected planets .
With data from the Primary Mission alone , the uncertainty in planetary orbital periods will inhibit follow-up observations after only a few years , as the transit ephemerides become stale .
By re-observing the same sky that was observed in the Primary Mission , hemi , hemi+ecl , and allsky address this issue .

4 . Regarding newly detected sub-Neptunes , the allsky , pole , and hemi+ecl strategies offer the greatest number ( 1350-1400 , as compared to the 1250 during each year of the Primary Mission ) .

5 . Regarding planets with orbital periods > 20 days , the allsky and pole strategies discover twice as many such planets as will be discovered in each year of the Primary Mission .
However , this assumes that two transits are sufficient for secure detection .
If instead we require three transits , then pole detects 260 new long-period planets , while the next-best scenarios , allsky , hemi , and hemi+ecl , all detect about 160 .
( The simulated Primary Mission detects 145 ; see Figs . 13 and 15 ) .

6 . Regarding new planets with very bright host stars ( I _ { c } < 10 ) , the allsky , hemi+ecl , and ecl_short strategies offer the greatest numbers ( \approx 190 , about the same as are found in each year of the Primary Mission ; see Table 2 ) .

7 . Regarding planets with near-terrestrial insolation ( 0.2 < S / S _ { \oplus } < 2 ) , all the strategies considered here offer similar numbers ( about 120 , as compared to 105 in each year of the simulated Primary Mission ) .

The rest of this report is organized as follows .
Sec . 1 discusses how we selected and compared different pointing strategies , as well as how we modeled TESS ’ sobservations .
Sec . 1.3 describes some figures of merit for comparing Extended Mission scenarios , including a discussion of some scenarios we chose not to study .
Sec . 1.7 lists the most important assumptions we made for the simulations .
Sec . 2 compares the characteristics of newly-detected planets for the six scenarios under consideration .
Sec . 3.1 discusses some considerations and implications for future years of the Extended Mission , beyond the one-year scenarios that were simulated in detail .
Sec . 3.2 raises the critical issue of the uncertainty in transit ephemerides .
Sec . 3.3 discusses the reliability and limitations of our methodology .
Sec . 4 concludes and recommends avenues for further study .

The catalogs of simulated detected planets ( for both the Primary and Extended Missions ) are available online scholar.princeton.edu/jwinn/extended-mission-simulations .
This website also contains a less formal document with some ideas and questions regarding the broader applications of a TESS Extended Mission .
We welcome any other ideas , comments , or corrections ; please send them to : luke @ astro.princeton.edu .