The Astrophysical Journal Letters, 713:L79–L86, 2010 April 20 doi:10.1088/2041-8205/713/2/L79
C
2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
KEPLER MISSION DESIGN, REALIZED PHOTOMETRIC PERFORMANCE, AND EARLY SCIENCE
David G. Koch
1
, William J. Borucki
1
, Gibor Basri
2
, Natalie M. Batalha
3
, Timothy M. Brown
4
, Douglas Caldwell
5
,
Jørgen Christensen-Dalsgaard
6
, William D. Cochran
7
, Edna DeVore
5
, Edward W. Dunham
8
, Thomas N. Gautier III
9
,
John C. Geary
10
, Ronald L. Gilliland
11
, Alan Gould
12
,JonJenkins
5
, Yoji Kondo
13
, David W. Latham
10
,
Jack J. Lissauer
1
, Geoffrey Marcy
2
, David Monet
14
, Dimitar Sasselov
10
, Alan Boss
15
, Donald Brownlee
16
,
John Caldwell
17
, Andrea K. Dupree
10
, Steve B. Howell
18
, Hans Kjeldsen
6
, Søren Meibom
10
, David Morrison
1
,
Tobias Owen
19
, Harold Reitsema
20
, Jill Tarter
5
, Stephen T. Bryson
1
, Jessie L. Dotson
1
, Paul Gazis
5
, Michael R. Haas
1
,
Jeffrey Kolodziejczak
21
, Jason F. Rowe
1,23
, J effrey E. Van Cleve
5
, Christopher Allen
22
, Hema Chandrasekaran
5
,
Bruce D. Clarke
5
,JieLi
5
, Elisa V. Quintana
5
, Peter Tenenbaum
5
, J oseph D. Twicken
5
, and Hayley Wu
5
1
NASA Ames Research Center, Moffett Field, CA 94035, USA; D.Koch@NASA.gov
2
Department of Astronomy, University of California-Berkeley, Berkeley, CA 94720, USA
3
Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192, USA
4
Las Cumbres Observatory Global Telescope, Goleta, CA 93117, USA
5
SETI Institute, NASA Ames Research Center, Moffett Field, CA 94035, USA
6
Aarhus University, DK-8000, Aarhus C, Denmark
7
McDonald Observatory, University of Texas at Austin, Austin, TX 78712, USA
8
Lowell Observatory, Flagstaff, AZ 86001, USA
9
Jet Propulsion Laboratory/California Institute of Technology, Pasadena, CA 91109, USA
10
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
11
Space Telescope Science Institute, Baltimore, MD 21218, USA
12
Lawarence Hall of Science, University of California-Berkeley, Berkeley, CA 94720, USA
13
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
14
United States Naval Observatory, Flagstaff, AZ 86002, USA
15
Carneige Institution of Washington, Washington, DC 20015, USA
16
Departmant of Astronomy, University of Washington, Seattle, WA 98195, USA
17
Department of Physics and Astronomy, York University, Toronto, ON M3J 1P3, Canada
18
National Optical Astronomy Observatory, Tucson, AZ 85726, USA
19
Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, USA
20
Ball Aerospace and Technologies Corp., Boulder, CO 80306, USA
21
Space Science Office, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
22
Orbital Sciences Corp., NASA Ames Research Center, Moffett Field, CA 94035, USA
Received 2009 November 24; accepted 2010 January 26; published 2010 March 30
ABSTRACT
The Kepler Mission, launched on 2009 March 6, was designed with the explicit capability to detect Earth-
size planets in the habitable zone of solar-like stars using the transit photometry method. Results from just
43 days of data along with ground-based follow-up observations have identified five new transiting planets with
measurements of their masses, radii, and orbital periods. Many aspects of stellar astrophysics also benefit from
the unique, precise, extended, and nearly continuous data set for a large number and variety of stars. Early results
for classical variables and eclipsing stars show great promise. To fully understand the methodology, processes,
and eventually the results from the mission, we present the underlying rationale that ultimately led to the flight
and ground system designs used to achieve the exquisite photometric performance. As an example of the initial
photometric results, we present variability measurements that can be used to distinguish dwarf stars from red giants.
Key words: instrumentation: photometers – planetary systems – space vehicles: instruments – stars: statistics –
stars: variables: general – techniques: photometric
1. INTRODUCTION
The foremost purpose of the Kepler Mission is to detect Earth-
size planets in the habitable zone (Kasting et al. 1993) of solar-
like stars (F to K dwarfs), determine their frequency, and identify
their characteristics. The method of choice is transit photometry
(Pont et al. 2009), which provides the orbital period and size
of the planet relative to its star. When combined with stellar
parameters and radial velocity measurements, the mass, radius,
and density of the planet are obtained. Transit photometry
requires high photometric precision with continuous time series
data of a large number of stars over an extended period of time.
Although designed for the explicit purpose of terrestrial planet
detection, the nature of the Kepler data set is also of tremendous
23
NASA Postdoctoral Program fellow.
value for stellar astrophysics. Asteroseismology (Stello et al.
2009), gyrochronology (Barnes 2003), and astrometry, the
studies of solar-like stars (Basri et al. 2010; Chaplin et al. 2010),
eclipsing binaries (Gimenez et al. 2006), and classical variables
(Gautschy & Saio 1996) all depend on precise, extended,
continuous flux time series. Results from many of these fields
in turn tie back into the interpretation of exoplanet science.
Kepler was launched on 2009 March 6, commissioned in
67 days and began science operations on May 13. In this Letter,
we present results from the first two data sets: Q0 consisting of
9.7 days of data taken during commissioning and Q1 consisting
of 33.5 days of data taken before the first quarterly roll of the
spacecraft. The Q0 data are particularly unique and interesting,
since all spectral types and luminosity classes of stars with
V < 13.6 were included.
L79
L80 KOCH ET AL. Vol. 713
2. FUNDAMENTAL REQUIREMENTS
Borucki et al. (2008) have described the scientific goals and
objectives of the Kepler Mission. Overviews of much of the
hardware have been given elsewhere (Koch et al. 2004). This
section describes how the scientific goals formed the basis for
the design of the mission.
2.1. Mission Duration
The fundamental requirement for mission success is to
reliably detect transits of Earth-size planets. To have confidence
that the signatures are of planets, we require a sequence of
at least three transits, all with a consistent period, brightness
change, and duration. To be able to detect three transits of a
planet in the habitable zone of a solar-like star led to the first
requirement, a mission length of at least three years.
2.2. Number of Stars to Observe
Transit photometry requires that the orbital plane of the
exoplanet must be aligned along our line of sight to the
exoplanet’s parent star. Let θ be the angle between the line
of sight and the orbital plane for a planet that just grazes
the edge of its star. Then sin(θ) = R/a, where R is the sum
of the radii of the star and the planet, and a is the semimajor
axis of the orbit, taken to be nearly circular. The solid angle
integrated over the sky for all orbital pole positions where the
planet can be seen transiting is 4π sin(θ). Dividing by the total
area of the sky (4π) and substituting in for sin(θ) yields
ϕ = R/a (1)
as the geometric random probability for alignment of a transit,
with no small angle approximation even down to where a = R.
For an Earth–Sun analog, R/a
∼
=
0.5%. The second requirement
is to observe at least one hundred thousand solar-like stars with
∼5000 having V 12. Assuming each solar-like star has just
one R = 1.0 R
⊕
planet in or near the habitable zone, one would
expect 25 “Earths,” a statistically meaningful result (Borucki
et al. 2009a). A null result would also be significant.
2.3. Photometric Precision
An Earth–Sun analog transit produces a signal of 84 parts
per million (ppm), the ratio of their areas. A central transit
of an Earth–Sun analog lasts for 13 hr. The third requirement
is to reliably detect transits of 84 ppm in 6.5 hr (half of a
central transit duration for an Earth–Sun analog). There are three
distinct types of noise that determine the detection threshold:
(1) photon-counting shot noise, (2) stellar variability, and (3)
measurement noise. We define the combination of these sources
as the combined differential photometric precision (CDPP):
CDPP = (shot noise
2
+ stellar variability
2
+ measurement noise
2
)
1/2
. (2)
Equation (2) needs to be used with caution, since stellar vari-
ability and many of the measurement noise terms do not scale
simply with time. CDPP is differential, since it is the difference
in brightness from the near-term trend that is important—not
long-term variations. For an 84 ppm signal to be detected at
4σ , the CDPP must be 20 ppm. In a well-designed exper-
iment, little is gained by reducing any noise component to be
significantly smaller than the total. We have no control over
the stellar variability contribution other than selecting stars with
low variability. Analysis of data from the Sun shows that vari-
ability during solar maximum on the timescale of a transit is
typically 10 ppm (Jenkins 2002). For the shot noise from a star
to be 14 ppm in 6.5 hr, the flux from the star needs to result
in 5 × 10
9
photoelectrons. Quadratic subtraction of these two
components from 20 ppm leaves ∼10 ppm for the measurement
noise. Measurement noise includes not just detector and elec-
tronic noise, but also such things as pointing jitter, image drift,
thermal, optical, and integration-time stability, stray light, video
and optical ghosting, and sky noise.
2.4. Stability: the Key to Success
A technology demonstration was performed (Koch et al.
2000) to prove the feasibility of the Kepler Mission. Key lessons
learned from these tests were that pointing stability had to be
better than 0.003 arcsec/15 min and thermal stability of the
CCD had to be better than 0.15 K day
−1
. This led to the fourth
design requirement: photometric noise introduced by any source
must either have a mean value of zero or not vary significantly
on the timescale of a transit.
Several other aspects were also demonstrated: (1) the required
precision can be achieved without a shutter, (2) optimum
photometric apertures are necessary, (3) pixels with large full
wells allow for longer times between readouts, (4) traps in
the CCDs will remain filled if the CCDs are operated below
about −85
◦
C and the integration times are kept <8s,(5)
precision photometry works even with saturated pixels, if the
upper parallel clock voltage is properly set, and (6) data at the
individual pixel level should be preserved.
2.5. Pixel Time Series
Preserving the individual pixel time series that compose each
stellar image permits the ground analysis to (1) measure and
decorrelate the effects of image motion (Jenkins et al. 2010a),
(2) remove cosmic rays at the pixel level (Jenkins et al. 2010a),
(3) remove instrumental features and systematic noise (Caldwell
et al. 2010), (4) measure the on-orbit pixel response function
(PRF) (Bryson et al. 2010), (5) fit and remove local background
for each star (Jenkins et al. 2010a), (6) measure any centroid
shift during a transit at the sub-millipixel level (Batalha et al.
2010a), (7) perform astrometry and obtain parallaxes and hence
distances to the stars (Monet et al. 2010), and (8) reprocess the
data using improved understanding of the instrument and data.
3. MISSION DESIGN CHOICES
3.1. Observing Strategy
Three design considerations enter into the choice of how
best to observe a large number of stars for transits: size of the
field of view (FOV), aperture of the optics, and duty cycle.
Concepts considered were large FOV fish-eye optics, multiple
aperture optics, a single large aperture, and single versus
multiple pointings during each cadence. After considering
various combinations, the design that was settled upon was a
1 m class aperture with a FOV >100 deg
2
and viewing of a
single star field. Pointing to a single star field has the advantages
of (1) selecting the richest available star field; (2) minimizing
the stellar classification necessary to select the desired stars;
(3) optimizing the spacecraft design; (4) maximizing the duty
cycle; (5) simplifying operations, data processing, and data
accounting; and (6) continuous asteroseismic measurements
over long periods of time. The combination of these factors
No. 2, 2010 KEPLER DESIGN, PHOTOMETRIC PERFORMANCE, AND EARLY SCIENCE L81
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mirror (2)
FFL & BP (3)
CCD QE (4)
Combined (5)
1
2
3
4
5
Wavelength(nm)
Measured Responses
Schmidt Corrector (1)
300 400 500 600 700 800 900 1000
Figure 1. Spectral response curves. An average value is shown for the 21 FFLs
and the BP filters, which are multi-layer coatings on the back of the sapphire
FFLs. The CCD QE is the average from all 42 CCDs. The combined response
curve also includes a 4% loss for contamination
results in a photometric database with unprecedented precision,
duration, contiguity, and number and variety of stars.
For an extended mission, there are many reasons to not change
the star field. Beside the points above, additional reasons are (7)
extending the maximum orbital period for planet detection, (8)
improving the photometric precision for the already detected
planets, (9) improving the statistics for marginal candidates,
(10) decreasing the minimum detectable size of planets, (11)
providing a longer time base for transit and eclipsing binary
timing to enable detection of unseen companions, and (12)
observing stellar activity cycles that approach the timescale of a
solar cycle. Based solely on the current rate of propellant usage,
the only expendable, the mission can operate for nearly 10 years.
3.2. The Photometer
The Delta II (7925–10L) launch vehicle provided by NASA’s
Discovery program defined the combination of the size of the
optics, the sunshade and solar avoidance angle, the spacecraft
mass, and the orbit. In the final analysis, it was found that a
1 m class Schmidt telescope with a 16
◦
diameter FOV and a 55
◦
Sun avoidance angle could be launched into an Earth-trailing
heliocentric orbit (ETHO). The shot noise of 14 ppm in 6.5 hr
is met with the 0.95 m aperture for a V = 12 solar-like star. The
large FOV required a curved focal surface and the use of sapphire
field-flattening lenses (FFLs) on each CCD module. The spectral
bandpass (BP) is defined by the optics, the quantum efficiency
(QE) of the CCDs, and BP filters. To maximize the signal-to-
noise ratio (S/N) for solar-like stars, the BP filters applied to
the FFLs have a >5% response only from 423 nm to 897 nm.
This is shown in Figure 1. The blue cutoff was chosen to avoid
the UV and the Ca II H and K lines. For the Sun, 60% of the
irradiance variation is at <400 nm, but photons <400 nm only
account for 12% of the total flux (Krivova et al. 2006). The red
cutoff was selected to avoid fringing due to internal reflection of
light in the CCDs. The spectral response is somewhat broader
than a combination of V and R bands. Kepler magnitudes
(Kp) are usually within 0.1 of an R magnitude for nearly all
stars.
We shall refer to the single instrument on the Kepler Mis-
sion as the photometer. The heart of the photometer is the
95 megapixel focal plane composed of 42 science CCDs and
four fine guidance sensor CCDs (Figure 2). The science CCDs
are thinned, back-illuminated, and anti-reflection coated, four-
phase devices from e2v Technologies Plc. The CCD controller,
located directly behind the focal plane, provides the clocking
signals and digitizes the analog signals from the 84 CCD out-
puts. Data from each CCD are co-added on board for 270 read-
outs to form a long cadence (LC) of ∼30 minutes, the primary
data for planet detection. At the end of each LC, only the pixels
of interest (POIs) for each star are extracted from the image,
compressed, and stored for later downlink. In parallel, a limited
set of 512 POIs are extracted from the image every nine read-
outs, to provide short cadence (SC) one-minute data. The SC
data are used to provide improved timing of planetary transits
and to perform asteroseismology (Gilliland et al. 2010a). In ad-
dition to the POIs for measuring stellar brightnesses, significant
amounts of collateral data are also collected to enable calibration
(Caldwell et al. 2010). Full-field images (FFIs) are also recorded
once per month, calibrated, and archived. The design and test-
ing of the focal plane assembly is described by Argabright
et al. (2008). A summary of the key characteristics is given in
Table 1.
3.3. The Orbit
An ETHO is significantly more benign and stable for pre-
cision photometry than an Earth orbit. Important features of
an ETHO (nearly identical to the Spitzer ETHO; Werner et al.
2004) versus a low-Earth orbit are as follows: (1) the space-
craft is not passing in and out of the radiation belts or the
South Atlantic Anomaly, (2) the spacecraft is not passing in
and out of Earth’s shadow and heating from the Sun, (3) there
is no atmospheric drag or gravity gradient to torque the space-
craft, and (4) there is no continuously varying earthshine get-
ting into the telescope—all of these happening on the timescale
of a transit. The largest disturbing torque in an ETHO is
sunlight.
3.4. Star Field Selection
The 55
◦
Sun avoidance angle limited the choice to a star
field >55
◦
from the ecliptic plane. Two portions of the Galactic
plane are accessible. Counting stars brighter than V = 14 from
the USNO star catalog showed the Cygnus region, looking along
the Orion arm of our Galaxy, to be the richest choice. After
reviewing the confusion due to distant background giants in
the Galactic plane, the center of the FOV was placed at 13.
◦
5
above the Galactic plane at an R.A. = 19
h
22
m
40
s
and decl. =
44
◦
30
00
. For distances greater than a few kiloparsecs, stars
in the field are above the Galactic disk, thus minimizing the
number of background giant stars. The distance to a V = 12
solar-like star is ∼270 pc, with the typical distance to terrestrial
planets detected by Kepler being 200–600 pc. An important
aspect of the northern over the southern sky is that the team re-
sources needed for ground-based follow-up observing are in the
north.
The final orientation of the focal plane was chosen to
minimize the number of bright stars on the CCDs. Bright stars
bloom and cause significant loss of useable pixels. Only a dozen
stars brighter than V = 6 are on silicon, with only one, θ Cyg,
being brighter than V = 5. The spacecraft needs to be rotated
about the optical axis every one-quarter of an orbit around the
Sun to keep the Sun on the solar panels and the radiator that
cools the focal plane pointed to deep space. To keep the bright
stars in the gaps between the CCDs and blooming in the same
direction on the CCDs, the 42 CCDs were arranged with four-
fold symmetry (except for the central two CCDs) and mounted
to within ±3 pixels of co-alignment.
L82 KOCH ET AL. Vol. 713
Sunshade
55º solar avoidance
Focal Plane
Electronics:
clock drivers and
analog to digital converters
Mounting Collet
S
unshad
e
55º
s
olar
a
F
ocal
P
lane
E
lectronics:
c
lock driver
s
and
analog to digital converters
Primary Mirror
1.4 m dia, ULE
Thermal Radiator
Schmidt Corrector
with 0.95 m dia
aperture stop
Focal Plane:
42 CCDs,
>100 sq deg FOV
4 Fine Guidance Sensors
Figure 2. Cross-sectional view of the photometer and inset of the focal plane. The overall height with the sunshade is 4.3 m. The spacecraft (not shown) is a hexagonal
structure 0.8 m high that surrounds the base of the photometer.
Given the 16
◦
diameter FOV and the large varying angle
between the center of the star field and the velocity vector of the
spacecraft as it orbits the Sun, the effect of velocity aberration
on the locations of the stars on the CCDs is significant. This
effect causes the diameter of the FOV to change on an annual
basis by 6 arcsec, and is taken into account when computing the
POI used for each star.
3.5. The Kepler Input Catalog
To maximize the results, we preferentially observe solar-
like stars. Most star catalogs provide sufficient information to
approximate T
eff
, but the stellar size is generally not provided.
We chose two approaches to distinguish dwarf from giant stars:
The primary approach was to perform multi-band photometric
observations using a filter set similar to the Sloan Survey (g, r, i,
z) with the addition of a filter for the Mg b line, that is especially
sensitive to log (g), and then modeling of the observations to
derive T
eff
and log (g). This resulted in the Kepler Input Catalog
(KIC)
24
. The process of ranking and selecting stars based on
multiple parameters using the KIC is described by Batalha et al.
(2010b). The backup approach was to observe all the stars in
the FOV brighter than Kp = 15 early in the mission (the reason
for the larger star handling capacity at the start of the mission)
and, based on their measured variability, distinguish the dwarfs
from giants (this result is described below.).
24
http://archive.stsci.edu/kepler/kepler_fov/search.php
4. PERFORMANCE
4.1. Saturation and Dynamic Range
The design of the photometer called for collecting 5 × 10
9
photoelectrons in 6.5 hr for a V = 12 star. In a single 6.02 s
integration, this amounts to 1.4 × 10
6
e
−
. For the tightest PRFs,
60% of the energy can fall into 1 pixel (Bryson et al. 2010),
so stars brighter than Kp ∼ 11.5 saturate, depending on FOV
location. We have set the upper parallel clock voltage on the
CCDs so that the overflow electrons are preserved and fill the
adjacent pixels in the same column. No electron is left behind.
The photometric aperture sizes are adjusted for saturated stars,
and the photometric precision is preserved.
To illustrate that photometric precision is attained in saturated
stars, light curves for some of the brightest stars, which are
saturated by as much as a factor of 100, are presented in Figure 3.
These data also illustrate that the measurement noise must be
well under 10 ppm. Stars fainter than Kp = 15 are also useful.
Noise measurements of many of these are near shot noise limited
performance, indicating the instrument is not limiting the noise.
The dynamic range is at least from Kp = 7toKp = 17 (Gilliland
et al. 2010b).
4.2. The Commissioning Data Set
As a final step during commissioning, 9.7 days of photometric
data were taken. A special set of 52,496 stars was used. This
set had oversize apertures to compensate for the ±3pixels
prelaunch uncertainty in the focal plane geometry. The geometry
No. 2, 2010 KEPLER DESIGN, PHOTOMETRIC PERFORMANCE, AND EARLY SCIENCE L83
Tab le 1
Kepler Mission Characteristics
Component Value Comment
Optics Brashear & Tinsley Manufacturers
Schmidt corrector 0.99 m dia./0.95 m dia. stop Corning Fused silica
Primary mirror F1 1.40 m dia., silver coated Corning ULE
R
Central obscuration 23.03% Due to focal plane and spider
FFLs 2.
◦
5 square Sapphire
PRF 3.14–7.54 pixels, 95% encircled energy diameter Depends on FOV location
Sunshade 55
◦
sun avoidance From center of FOV
CCDs e2v Technologies Manufacturer
Format 1024 rows × 2200 columns Two outputs per CCD
Pixel size 27 μm square Four phases
Plate scale 3.98 arcsec pixel
−1
Full well 1.05 × 10
6
electrons, typical Set by parallel clock voltage
Dynamic range 7 Kp 17 Meets photometric precision
Operating temperature −85
◦
C 10 mK stability
Controller Ball Aerospace Design and manufacturer
Channels 84 Multiplexed into 20 ADCs on five electronic board pairs
CCD integration time 6.02 s Selectable 2.5–8 s
CCD readout time 0.52 s Fixed
LC period 1765.80 s 270 integrations + reads
SC period 58.86 s 9 integrations + reads
Maximum LC targets 170,000 Average 32 pixels/target
Maximum SC targets 512 Average 85 pixels/target
Timing accuracy 50 ms For asteroseismology and transit timing
System Ball Aerospace Design, integration, and test
Spectral response 423–897 nm 5% points
FOV 105 deg
2
<10% vignetted 115 deg
2
of non-contiguous active silicon
Pointing jitter 3 mas per 15 minutes 1σ per axis
CDPP (total noise) 20 ppm in 6.5 hr for >90% of FOV V = 12 solar-like star including 10 ppm for stellar variability
Data downlink period 31-day average <1 day observing gap
Mission length 3.5 years Baseline. May be extended
Orbital period 372 days by year 3.5 Earth-trailing heliocentric
4965 4970 4975 4980 4985 4990 4995
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time, JD-2450000
Relative Flux, ppm
KepId= 6116048; Kp=8.4; CDPP=10 ppm
KepId= 7510397; Kp=7.8; CDPP=10 ppm
KepId= 3427720; Kp=9.1; CDPP=11 ppm
KepId= 9025370; Kp=8.8; CDPP=11 ppm
KepId=12258514; Kp=8.1; CDPP=12 ppm
KepId= 7940546; Kp=7.4; CDPP=13 ppm
KepId=11255615; Kp=8.8; CDPP=15 ppm
KepId=10454113; Kp=8.6; CDPP=16 ppm
KepId=10124866; Kp=7.9; CDPP=19 ppm
KepId=10644253; Kp=9.2; CDPP=21 ppm
1 Earth-size transit
Figure 3. Flux time series for 10 of the brighter G-dwarf stars. The CDPP is calculated by applying a moving-median filter that is 48 hr wide and then computing the
rms deviation for 6.5 hr. For reference, a grazing one-Earth-size transit (84 ppm) is shown to scale.
