Science yield modeling with the Exoplanet Open-Source Imaging
Mission Simulator (EXOSIMS)
Christian Delacroix*a,b, Dmitry Savransky a,b, Daniel Garrett a, Patrick Lowrancec, Rhonda Morgand
a
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853;
b
Carl Sagan Institute, Cornell University, Ithaca, NY 14853
c
IPAC, California Institute of Technology, M/S 100-22, 1200 East California Blvd., Pasadena, CA
91125
d
Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109
ABSTRACT
We report on our ongoing development of EXOSIMS and mission simulation results for WFIRST. We present the
interface control and the modular structure of the software, along with corresponding prototypes and class definitions for
some of the software modules. More specifically, we focus on describing the main steps of our high-fidelity mission
simulator EXOSIMS, i.e., the completeness, optical system and zodiacal light modules definition, the target list module
filtering, and the creation of a planet population within our simulated universe module. For the latter, we introduce the
integration of a recent mass-radius model from the FORECASTER software. We also provide custom modules dedicated
to WFIRST using both the Hybrid Lyot Coronagraph (HLC) and the Shaped Pupil Coronagraph (SPC) for detection and
characterization, respectively. In that context, we show and discuss the results of some preliminary WFIRST simulations,
focusing on comparing different methods of integration time calculation, through ensembles (large numbers) of survey
simulations.
Keywords: high contrast imaging, exoplanets, space missions, WFIRST, coronagraphs, end-to-end simulator,
integration time, zodiacal light
1. INTRODUCTION
In addition to allowing for new detections of exoplanets and exozodiacal disks, direct imaging also enables astrometry
and photometry of these objects, and allows for better estimation of exoplanet orbital parameters (e.g., β Pictoris,1 HR
87992,3). Furthermore, high-resolution spectroscopic analysis can ultimately lead to determining the atmospheric
structure and chemical composition of exoplanets.4 Direct imaging is therefore highly desirable, but also challenging. It
requires combining technologies such as coronagraphy, wavefront sensing and control, pointing jitter control, and
software solutions leading to post-processing gains in terms of contrast. So far, only a few dozen large bright planets
have been imaged, mostly around young and nearby stars, and on fairly long-period orbits. In order to extend this
parameter space, astronomers will most likely need to send out their instrumentation on spacecraft, and observe
exoplanets directly from space. In this context, the WFIRST (Wide-Field Infrared Survey Telescope) NASA mission will
be equipped with coronagraphs5 to directly image and spectrally characterize exoplanets and exozodiacal disks around
nearby stars.
As part of the WFIRST Preparatory Science investigation, we are developing the Exoplanet Open-Source Imaging
Mission Simulator (EXOSIMS)6 designed to allow for systematic exploration of expected science yields over the course
of a specific mission. A schematic depiction of the EXOSIMS modular architecture is given in Fig. 1. This modular
structure allows users to investigate multiple missions or system designs by only modifying individual modules without
having to redefine the unaffected ones. The instantiation of all modules begins with the construction of a
MissionSimulation object, after loading the input specification from a single script file (see Fig. 1, green box). All other
module objects are then instantiated, with the arrows indicating calls to object constructors in the order shown in the flow
*[email protected]; sioslab.mae.cornell.edu
Modeling, Systems Engineering, and Project Management for Astronomy VII,
edited by George Z. Angeli, Philippe Dierickx, Proc. of SPIE Vol. 9911, 991119
© 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2233913
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Figure 1. Flow chart desscribing the insttantiation of an end-to-end sim
mulation. Each software
s
modulle is represented
d by a box,
mulation step. The
T input specification (green box) is a singlle script file loaaded by the maain module
and corresponds to a sim
MissionSiimulation. Thee code operates by successivve interactions between moddules, as indicaated by the arrrows. The
TargetLisst and SimulateedUniverse moodules (red boxxes) are being described in Sect. 2 and Sect. 3, respecttively. The
SurveySim
mulation and SurveyEnsemble
S
e modules (bluue boxes) are reesponsible for running
r
either one or a large number of
simulationns, respectivelyy.
chart. All moodule referencces are passedd to the top calling
c
modulle, such that the MissionSimulation objject has direcct
access to all other
o
moduless as its attribuutes. The last two
t constructeed modules (see Fig. 1, bluee boxes) are responsible
r
forr
performing either one (SurrveySimulatioon) or a large number (Surv
veyEnsemble)) of simulationns based on all
a of the inpuut
parameters annd models. Eaach simulation returns the mission timeline, i.e., an ordered
o
list off simulated ob
bservations of
various targetts on the targeet list along with their outcoomes.
In this paper, we give an uppdate on our ongoing
o
devellopment of EX
XOSIMS. More specificallyy, we focus on
n our upgradess
s
of the sooftware (see Fig.
F 1, red booxes) – the creeation of a tarrget list and tthe simulation
n of the wholee
to two core steps
universe, i.e.,, the planets around
a
the targget stars. In Seect. 2, we detaail some of thhe main modulles involved in
n constrainingg
the mission simulation
s
targget list, nameely the Complleteness modu
ule, the OpticaalSystem moddule, and the ZodiacalLighht
module. In Seect. 3, we intrroduce the inteegration of a recent
r
probabiilistic mass-raadius relation, made availab
ble through thee
FORECASTE
ER software.7 Finally, in Seect. 4, we shoow results of ensembles
e
of survey
s
simulaations, with a comparison
c
of
different methhods of calcullating the integration times,, that have beeen integrated to
t the OpticalSystem modu
ule.8–10
2. TARG
GET LIST FIILTERING
List module collects infformation frrom eight downstream
d
m
modules:
StaarCatalog, OpticalSystem
O
m,
The TargetL
ZodiacalLighht, PostProcesssing, BackgrroundSources,, Completeneess, PlanetPoppulation, and PlanetPhysiccalModel. Thee
target list cann contain pre--determined taarget stars whhere planets arre known to exist
e
from preevious survey
ys (e.g., radial-
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velocity surveys, transit suurveys). Alternnatively, the target
t
list can
n contain all of
o the targets ffrom a star caatalog where a
planet with sppecified param
meter ranges could
c
be obseerved. In that particular casse, the TargetL
List module first
f
copies thee
whole catalogg (e.g. SIMBA
AD) by runninng the StarCattalog module and
a removes stars
s
with any NaN attributees, to populatee
the target listt with usable attribute
a
valuees, with units defined as Py
ython Astropyy Quantities. T
Then, TargetL
List performs a
population filltering based on
o selected crriteria. For insttance, the prototype implem
mentation can do the follow
wing:
-
remoove binary staars;
-
remoove systems not
n meeting thhe single-visit completeness threshold;
-
remoove systems with
w planets ouutside of the coronagraph
c
working
w
angless;
-
remoove systems where
w
integration time is lonnger than max
ximum integraation time.
The followingg subsections illustrate the definition of some
s
of the main
m parameterrs required to constrain the target list, i.ee.
the completenness value, thhe optical sysstem throughpput, contrast, inner workingg angle (IWA
A) and outer working
w
anglee
(OWA), the zodiacal
z
light, and the integgration time.
2.1 Completteness modulle
We first calcuulate a joint probability
p
deensity functionn (PDF) of th
he planet popuulation’s appaarent separatio
on (s) togetherr
with the diffference in brigghtness between the star and
a the planeet (Δmag). Thhis photometrric restriction on exoplaneet
level for eacch target. Thee
observability is introducedd by the teleescope optics..11 Then, we evaluate a completeness
c
completenesss is the 2D inttegration of a portion (i.e., the cumulativ
ve density funnction) of a sppecific PDF su
uch as the onee
shown in Fig. 2. The integrrated portion is defined for a specific target star, and a specific imagging instrumeent, with givenn
IWA, OWA,, and a Δmaag limiting value.
v
The caalculated valu
ue corresponds to the prrobability that a particularr
observatory, while observiing a star for the first timee, will detect a planet beloonging to the assumed popu
ulation. Thesee
completenesss values are thhen updated throughout
t
thee mission, forr target stars that
t
were prevviously observed. An exacct
formulation of
o the multivaariate integral representing such a compleeteness joint probability
p
deensity function
n was recentlyy
derived in Reef. 12.
.
35
tz)
c:5
d
30
,--
25
_
Figure 2. Example of jooint probability density functioon. The color iss log-scaled (baase 10) of the prrobability density in units
b
lines represent minimum
m and maximu
um values for which
w
the comppleteness joint probability
p
of AU^-1 mag^-1. The black
density fuunction is nonzeero. From Ref. 12.
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2.2 ZodiacallLight modulle
The local zoddiacal light suurface brightnness is usuallyy11,8 given by a uniform briightness of 233 mag arcsec^^-2. Howeverr,
zodiacal brigghtness changges for each observation direction,
d
and
d at each wavvelength. Thee ZodiacalLig
ght module of
EXOSIMS inntegrates a cooordinate and wavelength
w
deependence forr each target. As
A in Ref. 8, tthis dependen
nce is obtainedd
by interpolatiing Tables 177 and 19 of diiffuse night skky brightness presented in Ref. 13. Thiss interpolation
n preliminarilyy
requires coorrdinate transfoormations. In fact, the tables give zodiacal light in terms of geocentric ecliptiic coordinatess
λ–λ☉, β withh the zero poiint of λ in thhe Sun, as illuustrated in Fig
g. 3. The targget coordinatees, as copied from the starr
catalog, are defined
d
as rigght ascension (α) and declinnation (δ) in the Internatioonal Celestial Reference Sy
ystem (ICRS)),
with its originn at the barycenter of the Solar System. These
T
ICRS α,
α δ coordinatees must be traansformed into
o observatorycentered eclipptic coordinates λ, β with reespect to the spacecraft:
s
.
Then, Leinertt’s ecliptic cooordinates λ–λ☉, β can be eaasily obtained by subtractingg the longitudde of the Sun with
w respect too
the observatoory (λ☉). The latter
l
is simplyy the anti-supplementary an
ngle of the lonngitude of the observatory with
w respect too
the Sun: λ☉ = λobs + 180°.
it 13/
Figure 3. Diagram illusttrating the targeet coordinates definition,
d
S being the positionn of the sun, O tthe observatory
y, and T the
ghtness of the local zodiacall light, as seen
n from the
target. ♈ represents thee direction of the vernal equuinox. The brig
observatory, is given by Leinert’s tablee,13 for the eclipptic longitudes and
a latitudes (λλ–λ☉, β) with thhe zero point off longitude
in the dirrection of the Sun. The longgitude of the Sun
S with respeect to the obseervatory (λ☉) aand the longitu
ude of the
observatory with respect to the Sun (λobbs) are anti-suppplementary anglles.
System modu
ule
2.3 OpticalS
The Optical System
S
modulle contains alll of the necesssary information to describee the effects of the telescope and starlighht
suppression system
s
on thee target star annd planet wavvefronts. For instance, the user can speccify angular separation
s
andd
wavelength dependent
d
conntrast and throoughput definiitions, togetheer with Point Spread Functtions (PSF) fo
or on- and offfaxis sources.14,15 Because these parameeters are wavvelength depeendent, they are
a defined ass callable fun
nctions. As ann
example, Fig. 4 (left) show
ws the perform
mance curves of a coronagrraph at the speecific wavelenngth value of 550 nm. Bothh
the contrast and
a throughpuut input data arre angular sepparation-depen
ndent arrays, where
w
the arraay first colum
mn contains thee
separations inn arcsec. Theese curves alloow for the exxtraction of sp
pecific parameters includinng the instrum
ment IWA andd
OWA defineed as the minn and max anngular separattions at 50% normalized throughput,
t
aas well as thee average andd
maximum conntrast and throoughput over the IWA-OW
WA range. Fig. 4 (right) shoows the on- annd off-axis norrmalized PSFss
for the samee coronagraphh. Both horizoontal sequencces of PSFs correspond
c
too the same daata, but with two differennt
Each PSF is observed at a
colorbar scales: the upperr sequence is logarithmic, whereas the lower sequennce is linear. E
specific off-aaxis separationn, in units off λ/D, λ beingg the instrum
ment central wavelength
w
annd D the telesscope primaryy
mirror diameeter. The whitte circles on the upper seqquence corresspond to the core of the P
PSFs, with a FWHM
F
circlee
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0
1-.
1
i
1
1
eo
Contrast Throughput
2
9
0
b
b ,b
o o
oo
W
diameter. Bassed on this PS
SF sequence, one can easilyy derive the original
o
contraast and througghput curves by
b performingg
simple apertuure photometryy. As a visuall example, thee normalized throughput att a separation of ~3 λ/D (~0
0.14 arcsec) iss
about 50%, which
w
matchess the value of the
t IWA definned by the thrroughput curvee.
0.1
0.3
0:2
) ï
0.4
Sepa ratiori (arcsec)
Figure 4. Example of a starlight
s
suppreession system performance, giv
ven as input to EXOSIMS. Leeft: the throughp
put and the
contrast curves,
c
as functions of the anggular separationn, for a specific wavelength vaalue. The instruument IWA and
d OWA are
calculatedd at 50% throuughput. Right: an
a off-axis PSF
F sequence rep
presented both on a logarithm
mic and a linearr scale, for
comparisoon. Aperture phhotometry is peerformed by inntegrating the FWHM
F
white circles,
c
to reprooduce the throu
ughput and
contrast curves.
2.4 Integrattion time calcculation
As previouslyy stated, the TargetList
T
moodule filters out
o systems with
w integrationn times largerr than an inteegration cutofff
value set by the user. Byy doing so, thhe software ensures
e
that no
n observatioon will start w
with an unaccceptably longg
integration tiime, reducingg severely thhe remaining life time of the mission.. The OpticallSystem proto
otype modulee
and
as fun
calculates thee electron couunt rates for the planet siignal
a the backgground noise
nctions of thee
wavelength , based on thee spectral fluxx density electrron count ratee
where
and
Δ (1)
is the totall optical system
fficiency, is the pupil areaa, Δ is the bandwidth,
m throughputt,
is thhe quantum eff
is the spectral fllux density funnction. The laatter is obtaineed by using the following em
mpirical expreession16,17
10
.
(2)
4
which returnss ~10 photonn s^-1 cm^-2 nm^-1 at thee specific wav
velength valuee of 550 nm. The planet signal
s
electronn
count is then given by
10
. maag
mag
(3)
100
e
countt is given by
and the backgground noise electron
ENF
E
(4)
with the folloowing definitioons:
-
exceess noise factoor ENF
√2 EM-CCD orr1 CCD ;
-
supppressed starligght residuals
-
zodiiacal light (loccal + exozodi))
-
darkk current
-
clock-induced-chaarge
-
readdout noise
10
. mag
g
with
coron
n.contrast;
;
;
;
.
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The total noise budget is illustrated
i
in Fig.
F 5. Four virtual
v
planet PSFs
P
are beinng imaged at vvarious angullar separationss
from their host star, ranginng from 2 to 7 λ/D. The sequuence of imag
ges shows thatt the backgrouund noise consists primarilyy
of the residuaal diffracted starlight
s
speckkles, due to wavefront
w
erro
ors. Without any
a image poost-processing, the scatteredd
light dominattes the backgground variannce and the pllanet signals cannot be rettrieved. A 100-time post-prrocessing gainn
already reducces significanttly the specklee noise, and alllows the detection of two or
o three of the candidates.
planets
(stair cancelledI)
normaliz ed
star PS F
al zodi
)zod i
-9
;)I,.
I
2
-5
0
*
11
+ detector
+ residual
post:- processin g
noise
sipeckles
10x gain
MEIN
-11
posit-
processin
30x gain
Iiiiiiiin
-8.2
-8.3
-8.4
Figure 5.. Sequence of simulated
s
images of a target with
w four virtuaal companion planets.
p
Image a is the target normalized
n
PSF, withh a logarithmic colorbar scale. Image b assum
mes a perfect staar cancellation, and reveals cleearly the four planet
p
PSFs
at variouss angular separrations, with thhe addition of the
t diffuse sourrce of total zoddiacal light in image c. Images d and e
include thhe detector noise (dark current,, clock-inducedd charge, readou
ut) and the diffrracted starlight residual specklles. Images
f and g aree two exampless of post-processsing gain, allow
wing to retrievee two or three of the planets thaat were previou
usly hidden
by specklee noise.
3. MASS-R
RADIUS RE
ELATION USING
U
FOR
RECASTER
R
After populatting the targett list and filterring based on selected criteeria, the SimullatedUniversee module creattes a syntheticc
universe by populating
p
pllanetary systeems about som
me or all of the stars in the
t target list. Each planettary system iss
generated based on the sttatistics encodded in the PlaanetPopulatio
on module, soo that the oveerall planet occcurrence andd
r
are conssistent with the
t provided distribution functions.
f
Thee PlanetPopuulation modulee encodes thee
multiplicity rates
density functiions of all reqquired planetarry parameterss, including seemi-major axiss, eccentricityy, orbital orien
ntation, radiuss,
mass, and geoometric albedo. Certain parrameter modells may be emp
pirically derivved while otheers may come from analysess
of observatioonal surveys, and calculateed via the PlaanetPhysicalM
Model module. Most planett indirect deteections (radiaal
velocity, micrrolensing or trransit) can meeasure either the
t planet masss or its radiuss, but not bothh. Future misssions will needd
to forecast thhe missing quaantity (M or R)
R by means of
o an MR relattion, in order to predict deteectability. At the first levell,
detectability of exo-atmosphere is prooportional to
/ . Planets with known radius annd mass willl be easier too
characterize with
w follow-upp observationns such as JWST,18 which will
w not have time
t
for both measures giv
ven the limitedd
supply of cryyogen onboardd.
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In practice, trransit missions (e.g. TESS199) need the forrecast of the mass
m based uppon the radius,, while radial--velocity (RV)
missions needd the radius based
b
upon thee mass. Fig. 6 illustrates th
he whole know
wn RV planets universe gen
nerated by thee
PlanetPopulaation module. For a large majority
m
of thhese planets, only
o
the masss is available and the radiu
us needs to bee
calculated. To
T do so, we use a recent probabilistic MR relation model calledd FORECAST
TER,7 that wee integrated too
EXOSIMS inn a dedicatedd PlanetPhysiccalModel moddule. In addittion to forecaasting, the infference of thee MR relationn
enables classiification, whicch has significcant impact inn some cases, e.g., the occurrrence rate of exo-Earths ⨁ increases byy
72% when alltering their deefinition from
m
1.5 ⨁ to
ORECASTER
R leads to fourr
2.0 ⨁ .20 The classiification of FO
categories off worlds (Terraan, Neptuniann, Jovian, Stelllar) and threee transitions. The
T Neptuniann-Jovian transsition is not ass
physically inttuitive as the other
o
two. A plausible
p
physsical interprettation is that a Neptunian raadius grows raapidly as moree
7
mass is addedd, whereas a Jovian
J
mass is sufficient forr gravitational self-compresssion to start reeversing the growth.
g
102
volatille
envelo pe
I
I
Tewran
I
w<arlds
I
irogen
irning
self
compress
I
Neptuniian
world:s
1
ii .
I
.i
I
I
)
1
1
o
O
1
O
I
®,500
.i.
I
O
OP
ti
I
SteIlc
worlc
O
1
I
1
D"''-'
vO
p m0
Y
o
4 óQpoo
C? 00 r
O
RV pla nets:
unkno,wn radius
o
0W
ócw
Oo00
000e
known1
radius
10 °-
0
N -
O
0
r-I
10-1
0.0
1 0z
104
io5
_l L
Figure 6.. Radius and mass
m
values for the whole plannet population, generated from
m known radiall-velocity planeets. Only a
few of theese planets (redd dots) have booth their mass and
a radius meaasured. The largge majority (bluue dots) have their radius
value provvided by the MR
M relation from
m FORECAST
TER. Note the classification inn four worlds: Terran worlds (including
dwarf plannets), Neptuniaan worlds, Joviaan worlds (incluuding brown dw
warfs), and Stelllar worlds (K, M, and late-typ
pe G dwarf
stars). Figgure based on Ref.
R 7.
4.. SURVEY
Y ENSEMBL
LE RESULT
TS
t
TargetLisst and the SimulatedUniv
S
verse modulees, two addittional modules are calledd
After the exxecution of the
(TimeKeepinng and the Obbservatory) to predict whicch target stars are observabble at a speciffic time durin
ng the missionn
simulation annd which are unobservable
u
due to brightt objects within the field off view, such aas the sun, mo
oon, and solarr
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system planetts. The MissioonSimulation is then ready to start an ob
bserving surveey of the seleccted targets an
nd their planeet
companions. For each obsservation, an integration tim
me is calculated. The integgration time oof a specific planet, with a
specific sciennce instrumennt, involves thhe wavelengthh-dependent expressions
e
(33) and (4) intrroduced in Seect. 2.4. Thesee
and
. Differennt
equations aree used to obtaiin both the plaanet signal and the backgro
ound noise eleectron counts,
methods exist to determinee the integratioon times. Here, we focus on
n a comparisoon study of tw
wo methods, deescribed in thee
following pappers:
-
Kasddin&Braems 20069: The authors define a false alarm
m probability
probbability MD 10 . The inntegration tim
me is given by
∆
1
FA
1
MD
1
∑ PSFij
FA
3
∑ PSFij
10
0
and a misssed detectionn
(5)
d
pixel size, andd PSF is the normalized
n
PSF.
where ∆ is the dimensionless
-
Nem
mati 201410: The
T author deefines a signall-to-noise ratiio level (e.g. SNR = 5). T
The integration
n time is thenn
giveen by
SNR
(6)
SNR PP where
PP
is the exxpected gain due
d to post-prrocessing.
The results of
o our comparison study are
a illustrated in Fig. 7 and
d are obtaineed with data pproduced from
m a small buut
sufficient enssemble (N~5000) of surveyy simulations. Larger enseembles (~5000) will be ussed for final mission yieldd
evaluations. The
T baseline implementatio
i
on of the SurvveyEnsemble module is a simple
s
loopingg function thaat executes thee
desired numbber of simulatiions sequentiaally, and can be
b run in a lim
mited number of
o separate IP
Python terminaals for paralleel
computing. A specific moodule is also being
b
developped, implemen
nting a locallyy parallelizedd looping baseed on IPythonn
Parallel.21 Thhe results show
wn in Fig. 7 indicate a sim
milar yield off unique detecctions with booth methods, and a slightlyy
increased yield of total dettections with the
t Kasdin&B
Braems metho
od ( FA 3 10 and M
10 ) co
ompared to thee
MD
Nemati methood (SNR = 5). The former appears
a
to be somewhat mo
ore optimistic,, producing shhorter integrattion times.
a
C
D
0.25
I
/
/
0.20
"' L.........
cr
/
E 0.10
O
0.05
\\,
Figure 7.. Probability deensity function of unique plannet detections (lleft-hand) and total planet dettections (right-h
hand). The
plotted cuurves correspond to the Kasdinn&Braems methhod (Eq. 5, bluee curves) and Nemati
N
method ((Eq. 6, red curv
ves).
Proc. of SPIE Vol. 9911 991119-8
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5. CONCLUSIONS
We provide an update on the ongoing development of EXOSIMS. We give a detailed description of the TargetList
module filtering, based on selected criteria introduced by the user, including completeness threshold, optical system
working angles, and integration time cutoff. The completeness joint probability recently derived by our team is presented
briefly. We also show results of wavelength dependent contrast and throughput curves obtained from a sequence of onand off-axis source PSFs, using aperture photometry on the PSF core region delimited by the FWHM. The working angle
range (IWA-OWA) is then determined by the OpticalSystem module based on the calculated throughput curve. The
prototype OpticalSystem module is now also responsible for the planet signal and background noise electron count. In
that context, we study different existing methods for calculating the integration time, and we provide specific
OpticalSystem modules for each method. In addition, we explore new planet property models, and we integrate the MR
relation model from the FORCASTER software, to predict the missing property (mass or radius) of previously detected
planets (transits, radial velocities). Finally, we analyze simulation ensembles data, focusing on the comparison between
the newly implemented integration time calculation methods. Our preliminary results show consistent unique detection
yields, with slightly different mean integration times. Further analysis is ongoing. EXOSIMS will continue to be further
developed through the final release in May of 2017, and will be used to continuously refine the modeling of the WFIRST
coronagraph science.
ACKNOWLEDGEMENT
This work is supported by NASA Grant Nos. NNX14AD99G (GSFC) and NNX15AJ67G (WPS).
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