of 23
Observing Exoplanets with High Dispersion Coronagraphy. I. The Scienti
fi
c Potential of
Current and Next-generation Large Ground and Space Telescopes
Ji Wang
1
, Dimitri Mawet
1
, Garreth Ruane
1
, Renyu Hu
2
,
3
, and Björn Benneke
3
1
Department of Astronomy, California Institute of Technology, MC 249-17, 1200 E. California Boulevard, Pasadena, CA 91106, USA;
ji.wang@caltech.edu
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
3
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA
Received 2016 October 24; revised 2017 February 15; accepted 2017 February 16; published 2017 March 30
Abstract
Direct imaging of exoplanets presents a formidable technical challenge owing to the small angular separation and
high contrast between exoplanets and their host stars. High Dispersion Coronagraphy
(
HDC
)
is a pathway to
achieve unprecedented sensitivity to Earth-like planets in the habitable zone. Here, we present a framework to
simulate HDC observations and data analyses. The goal of these simulations is to perform a detailed analysis of the
trade-off between raw star light suppression and spectral resolution for various instrument con
fi
gurations, target
types, and science cases. We predict the performance of an HDC instrument at Keck observatory for characterizing
directly imaged gas-giant planets in near-infrared bands. We also simulate HDC observations of an Earth-like
planet using next-generation ground-based
(
TMT
)
and spaced-base telescopes
(
HabEx and LUVOIR
)
.We
conclude that ground-based ELTs are more suitable for HDC observations of an Earth-like planet than future
space-based missions owing to the considerable difference in collecting area. For ground-based telescopes, HDC
observations can detect an Earth-like planet in the habitable zone around an M-dwarf star at 10
4
star light
suppression level. Compared to the 10
7
planet
/
star contrast, HDC relaxes the star light suppression requirement
by a factor of 10
3
. For space-based telescopes, detector noise will be a major limitation at spectral resolutions
higher than 10
4
. Considering detector noise and speckle chromatic noise,
R
=
400
(
1600
)
is the optimal spectral
resolutions for HabEx
(
LUVOIR
)
. The corresponding star light suppression requirement to detect a planet with
planet
/
star contrast
=
́
-
6.1 10
11
is relaxed by a factor of 10
(
100
)
for HabEx
(
LUVOIR
)
.
Key words:
brown dwarfs
instrumentation: spectrographs
planetary systems
techniques: high angular resolution
techniques: spectroscopic
1. Introduction
Out of the thousands of exoplanets detected to date, the few
that have been directly imaged are excellent targets for
studying orbital con
fi
gurations
(
Millar-Blanchaer et al.
2015
;
Maire et al.
2015
; Pueyo et al.
2015
; Zurlo et al.
2016
)
and
atmospheric chemical compositions
(
Konopacky et al.
2013
;
Oppenheimer et al.
2013
; Bonnefoy et al.
2016
; Rajan
et al.
2015
)
. However, direct imaging and characterization
faces several technical challenges owing to the small angular
separation and high contrast between exoplanets and their host
stars. High-contrast imaging
(
HCI
)
systems mitigate these
effects by suppressing diffracted star light that may otherwise
overwhelm the planet signal with an extreme adaptive optics
(
AOs
)
system and a coronagraph. Current state-of-the-art HCI
instruments, such as the Gemini Planet Imager at the Gemini
South telescope
(
Macintosh et al.
2014
)
and SPHERE at the
Very Large Telescope
(
Beuzit et al.
2008
)
, are able to achieve a
suppression level at a few tenths of an arcsecond of better than
10
4
, which allows for the detection of gas-giant planets and
brown dwarfs orbiting nearby young stars
(
e.g., Macintosh
et al.
2015
; Wagner et al.
2016
)
.
Star light suppression can be further improved by coupling a
high-resolution spectrograph
(
HRS
)
with a coronagraphic
system
(
Sparks & Ford
2002
; Riaud & Schneider
2007
;
Kawahara & Hirano
2014
; Snellen et al.
2015
; Lovis
et al.
2017
)
. In this High Dispersion Coronagraphy
(
HDC
)
scheme, the coronagraphic component serves as a spatial
fi
lter
to separate the light from the star and the planet. The HRS
serves as spectral
fi
lter by taking advantage of differences in
spectral features between the stellar spectrum and the planetary
spectrum, e.g., different absorption lines and radial veloci-
ties
(
RVs
)
.
That HRS can be used as a way of spectral
fi
ltering has been
successfully demonstrated by several teams. For example,
high-resolution transmission spectroscopy has been used to
detect molecular gas in the atmospheres of transiting
planets
(
Snellen et al.
2010
; Birkby et al.
2013
; de Kok
et al.
2013
)
. At a high spectral resolution, resolved molecular
lines can be used to study day- to night-side wind
velocity
(
Snellen et al.
2010
)
and to validate 3D exoplanet
atmosphere models
(
Kempton et al.
2014
)
. For planets detected
via RV, the spectral lines that are due to the planet can
be separated from stellar lines with their drastically different
RVs
(
50 km
-
s
1
)
. Thus, the RV of the planet itself may
be measured to break the degeneracy between the true planet
mass and orbital inclination
(
Brogi et al.
2012
,
2013
,
2014
;
Lockwood et al.
2014
)
. Moreover, HRS permits the detailed
study of spectral lines arising from a planet
s atmosphere. This
approach led to the
fi
rst measurement of a planet
s rotational
velocity
(
Snellen et al.
2014
)
. With time-series HRS, surface
features such as cloud or spot coverage may be inferred via
Doppler imaging, which has been demonstrated on the closest
brown dwarf system, Luhman 16 AB
(
Cross
fi
eld et al.
2014
)
.
As showcased by the examples above, HRS may be used to
detect planets that are
10
4
timesasbrightastheirhost
stars. When coupled with a st
ate-of-the-art HCI system
capable of reaching star light suppression levels of
10
4
,
an HDC instrument is sensitive to much fainter planets.
Meanwhile, relatively bright planets may be observed at a
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153:183
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)
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//
doi.org
/
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/
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© 2017. The American Astronomical Society. All rights reserved.
1
higher signal-to-noise ratio
(
S
/
N
)
that allows for the physical
and chemical processes taking place in their atmospheres to
be studied in greater detail. Here, we develop a framework to
simulate the performance of an HDC instrument. Although
similar calculations have been performed as part of previous
studies
(
Sparks & Ford
2002
; Riaud & Schneider
2007
;
Kawahara & Hirano
2014
; Snellen et al.
2015
;Lovis
et al.
2017
)
, a thorough end-to-end simulation that explores
the S
/
N trade space between spectral resolution and star light
suppression for ground-based and space-based observations is
lacking. In this paper, we simulate a variety of HDC
instruments that are either under development or in the
conceptual design phase and quantify their potential for
detecting new planets as well as particular molecular species
in the atmosphere of known planets
(
e.g., Proxima Cen b, 51
Eri b, and HR 8799 e
)
and hypothetical Earth-like planets
around stars of different spectral types.
The paper is organized as follows. We outline the procedure
used to simulate the performance of an HDC instrument for
detecting and characterizing exoplanets in Section
2
. The
planned Keck HDC instrument is brie
fl
y described in Section
3
.
We study the prospects of using the Keck HDC instrument to
observe previously imaged exoplanets in Section
4
. HDC
observations of potential Earth-like planets
(
e.g., Proxima Cen
b
)
in the habitable zone of M dwarfs are investigated in
Section
5
for current and next-generation extremely large
telescopes. Observing Earth-like planets around solar-type stars
with future space telescopes is considered in Section
6
.A
summary and discussion are provided in Section
7
.
2. HDC Fundamental Trade-off Analysis
2.1. Simulating the Observations
In this section, we describe our work
fl
ow to simulate the
end-to-end performance of an HDC system from the intrinsic
spectrum of a planet and star to the measured spectrum and the
subsequent post-processing. The goal of these simulations is to
perform a detailed analysis of the trade-off between raw star
light suppression and spectral resolution for various instrument
con
fi
gurations, target types, and science cases. Figure
1
shows
a
fl
ow chart to illustrate the procedure and the system-related
inputs to the simulation. The resulting data products, e.g.,
cross-correlation fuction
(
CCF
)
and their quality
(
e.g., S
/
N
)
,
will inform observation strategies and system requirements,
including the coronagraph design and the performance of the
AOs system.
2.1.1. Generating Spectra of Stars and Planets
Gas-giant planet spectra consisting of all molecular species
are derived from the published BT-Settl grids
4
(
Baraffe
et al.
2015
)
. The grids cover effective temperatures
(
T
eff
)
from
1200 to 7000 K. For
T
eff
outside of this range, we use the BT-
Settl grids with Caffau et al.
(
2010
)
solar abundances
5
(
400 K
<
T
eff
<
8000 K
)
. The stellar spectra used in our
simulations are also derived from these grids, which cover
the
T
eff
and log
(
g
)
range of host stars considered here. If
necessary, the planet and star
fl
uxes are scaled to match the
observed absolute
fl
ux.
High-resolution spectra discerning the individual contribu-
tions of the molecular absorbers
H
O
2
, CO, and CH
4
are
simulated using the SCARLET model
(
Benneke & Seager
2013
; Benneke
2015
)
. In this work, SCARLET
fi
rst iteratively
computes the line-by-line radiative transfer and atmospheric
chemistry to converge to a self-consistent vertical temperature
structure and molecular composition. To isolate the contrib-
ution from individual molecules, we then arti
fi
cially remove all
opacities in the atmosphere except for the opacity of the
respective molecular absorber and the collision-induced
absorption in the simulation of the planets
thermal emission
spectra. In this way, we compute emission spectra for each of
the molecular absorbers individually. The SCARLET model
Figure 1.
Flow chart of the simulation of an HDC instrument. Photons from star and planet go through an HCI instrument. Residual star light and planet light is pic
ked
up by a single-mode
fi
ber, which feeds the light into an HRS instrument. Spectra are simulated with detector noise and then reduced into a data product, e.g., CCF
(
see
Section
2.2
)
. The atmospheric effect is optional depending on ground-based or space-based observation. The simulation pipeline provides a way of setting system
requirements for an HDC instrument and understanding the fundamental limit of the HDC technique.
4
https:
//
phoenix.ens-lyon.fr
/
Grids
/
BT-Settl
/
CIFIST2011_2015
/
FITS
/
5
https:
//
phoenix.ens-lyon.fr
/
Grids
/
BT-Settl
/
CIFIST2011
/
SPECTRA
/
2
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)
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Wang et al.
considers the molecular opacities of
H
O
2
,CH
4
,NH
3
, HCN,
C
O
,CO
2
and
T
iO
from the high-temperature ExoMol database
(
Tennyson & Yurchenko
2012
)
, and O
2
,O
3
,
OH
,
C
H
22
,
C
H
24
,
C
H
2
6
,
H
O
22
, and HO
2
from the HITRAN database
(
Rothman
& Gordon
2009
)
. Absorption by the alkali metals
(
Li, Na, K,
Rb, and Cs
)
is modeled based on the line strengths provided in
the VALD database
(
Piskunov et al.
1995
)
and in the H
2
-
broadening prescription provided in Burrows & Volobuyev
(
2003
)
. Collision-induced broadening from
H
H
22
and
H
He
2
collisions is computed following Borysow
(
2002
)
.
The spectra of Earth-like exoplanets, on the other hand, are
generated by an atmospheric chemistry and radiative transfer
model
(
Hu et al.
2012a
,
2012b
,
2013
; Hu & Seager
2014
)
.We
fi
rst calculate the molecular abundance as a function of altitude,
controlled by photochemical and disequilibrium chemistry
processes. The details of the model are described in Hu et al.
(
2012a
)
and the molecular abundances have been validated
against measurements on Earth.
We include the effects of clouds in the resulting spectra by
averaging two scenarios: a cloud-free scenario where we assume
a clear atmosphere, and a high-cloud scenario where we assume
are
fl
ective H
2
O cloud at 9
13 km. This procedure produces a
continuum albedo of
0.3 and provides a realistic estimate of
the strength of spectral features, similar to Des Marais et al.
(
2002
)
. Eighth-order Gaussian integration is used to calculate the
contribution of the whole planetary disk for both the re
fl
ected
light and thermal emission. We include the opacities of CO
2
,O
2
,
H
2
O, CH
4
,O
3
,andN
2
O and calculate the planetary
fl
ux at a
spectral resolution of
R
=
λ
/
Δ
λ
=
500,000, which is high
enough to resolve individual spectral lines of the aforementioned
species over
λ
=
0.5
5
μ
m. The resulting spectra are then
expressed as albedo and scaled with the planet
s size within the
reasonable range for terrestrial planets.
2.1.2. Spectrum of Earth
s Atmosphere
Telluric and sky emission lines are included in the simulation
to account for additional photon loss, near-infrared background
noise, and potential confusion between molecules that appear
in both the planet
s and Earth
s atmosphere, e.g., H
2
O and O
2
.
We use the Maunakea sky transmission
6
and emission spectra,
7
available from the Gemini observatory website
(
Lord
1992
)
,
with wavelength coverage of 0.9
5.6
μ
m. A water column
density of 1.6 mm and airmass of 1.5 is assumed. Since we also
consider telluric absorption at shorter wavelengths, we also use
telluric absorption data from the National Solar Observatory for
wavelengths shorter than
8
0.9
μ
m.
2.1.3. Simulation Procedure
An HDC instrument contains two main components, a
coronagraph and an HRS, which are linked by a set of single-
mode
fi
bers: a planet
fi
ber, a star
fi
ber, and
/
or a sky
fi
ber. One
end of these
fi
bers is located at the image plane after the
coronagraph, and the other end of the
fi
bers is at the entrance
slit of the spectrograph. The star
fi
ber and sky
fi
ber provide
calibration spectra in data reduction that are described in
Section
2.2
. Following Figure
1
, light from the star and planet
go through a coronagraph and form an image. The
fi
ber at the
planet location leads the planet light, as well as residual star
light, into the spectrograph. The detector records the planet
spectrum along with the contaminating stellar spectrum. We
note that atmospheric effect, i.e., absorption and emission, is
only considered for ground-based observations,
=+ ́ ́ +
()()
fffCf f
.1
detector
planet
star
transmission
sky
We simulate the signal recorded on a detector as described
in Equation
(
1
)
. Flux from a star and a planet is in the unit
of
m
--
W
mm
21
at a reference height
(
d
ref
)
. We calculate
the incident star and planet photon
fl
ux on the detector,
f
star
and
f
planet
, with the following equation:
= ́ ́
()
fF d d
ref
2
lh
n
́D ́ ́
A
th
exp
, where
F
is the
fl
ux at the reference
height
(
d
ref
)
,
d
is distance between the star
planet system and
an observer, A is telescope receiving area,
l
D
is the
wavelength coverage per wavelength bin,
η
is the telescope
and instrument end-to-end throughput,
t
exp
is the exposure
time,
h
is the Planck constant, and
ν
is the frequency of a
photon.
At the image plane after a coronagraph, stellar
fl
ux is
suppressed by a factor
C
, a parameter we denote as star light
suppression factor, i.e., the fraction of the total star light that
couples into the
fi
ber.
Both stellar and planetary spectra are rotationally broadened.
The effect of rotation broadening is calculated by summing
spectra from surface grids that are evenly spaced in long-
itudinal and latitudinal direction. The rotationally broadened
spectra are then multiplied by the Earth
s atmosphere
transmission spectrum
(
f
transmissio
n
)
for ground-based observa-
tion. The Earth
s atmosphere transmission spectrum is unitless
and normalized to unity, with zero meaning entirely opaque
and one meaning entirely transmissive. For space-based
observations,
f
transmissio
n
is set to unity.
The spectra are then broadened by the instrumental line
spread function. The instrumental broadening is approximated
by convolving a spectrum with a normalized Gaussian core
with a full width at half maximum of one spectral resolution
element, which is
l
0
/
R
, where
l
0
is the central wavelength and
R
is the spectral resolution of a spectrograph.
The broadened spectra are then added by sky emission
spectrum
(
F
emission
)
, which is also broadened at a given spectral
resolution. The sky emission is in the unit of photons
m
----
sarcsec m m
1221
. We calculate the incident photon
fl
ux
from the sky emission on the detector using the following
equation:
ql
= ́ ́ ́ ́D
fFt A
emission
emission
exp
2
, where
q
2
is the projected area of sky to the input
fi
ber fundamental mode
size, which we assume to be
l
(
)
D
1.0
0
2
, where
l
0
is the
central wavelength and
D
is the telescope aperture diameter.
For space-based observation,
f
emission
is set to zero. The
simulated spectra are then resampled at the pixel sampling rate
per resolution element.
In addition to the spectrum described by Equation
(
1
)
,we
simulate more spectra for subsequent data reduction. For
ground-based observation, we simulate sky emission and stellar
spectra, assuming there are two dedicated
fi
bers for sky and
star. The stellar spectrum can be used to remove atmospheric
transmission and
/
or contaminated stellar lines in the planet
spectrum. For example, in the case of ground-based observa-
tions of the HR 8799 system, the host star itself is a fast-
rotating early-type star and thus can be used as a telluric
standard to remove atmosphere transmission. In the case of
6
http:
//
www.gemini.edu
/
sciops
/
telescopes-and-sites
/
observing-condition-
constraints
/
ir-transmission-spectra
7
http:
//
www.gemini.edu
/
sciops
/
telescopes-and-sites
/
observing-condition-
constraints
/
ir-background-spectra
8
diglib.nso.edu
/
ftp.html
3
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Wang et al.
ground-based observations of Proxima Cen b, the observed
spectrum is a re
fl
ection spectrum containing both the star and
planet absorption lines and is contaminated by the Earth
s
atmosphere lines, so that it is necessary to have a separate
simultaneous observation of the host star to remove atmo-
spheric transmission and
/
or contaminated stellar lines in the
planet spectrum. For space-based observations, we simulate
only the stellar spectrum since the background is negligible.
2.1.4. Noise Sources
We include realistic estimates of photon noise, detector
readout noise
(
RN
)
, and dark current based on the performance
of a Teledyne HgCdTe H2RG infrared detector and a e2v
optical charge-coupled device
(
CCD
)
. RN and dark current for
the H2RG detector are 2.0
-
e
(
Fowler-32 readout, personal
correspondence with Roger Smith
)
and 0.002
--
e
s
1
(
Blank
et al.
2012
)
, respectively. An e2v optical CCD
9
has an RN of
2.0
-
e
and a dark current of 0.02
--
e
hr
1
,
d
=+ ́ + ́
()
fn
t
RN dark
.
2
exp
2
exp
The total noise is calculated by Equation
(
2
)
, where
δ
is the
combined noise,
f
is the photon noise followed by terms for RN
and dark current
(
dark
)
, and
n
exp
is the number of readout
within a total observation time
t
.
exp
The number of readouts
n
exp
is determined by the linear range or detector persistence
limit, i.e., the signal level where a new frame needs to be taken
in order to avoid nonlinearity or persistence. The exposure time
per frame or the number of readouts is usually set by the raw
level of star light suppression
(
instrumental contrast
)
or sky
background emission. We make a conservative assumption that
the persistence limit is at 12,000 electrons. During operations
such as sky emission removal and telluric or stellar line
removal, noises are added in quadrature.
2.2. Spectral Analyses
Once the detected spectra are obtained, we perform the data
processing steps required to extract the planet signal using the
cross-correlation technique
(
Konopacky et al.
2013
; Schwarz
et al.
2016
)
. First, the sky emission spectrum is subtracted from
the planet spectrum and the planet spectrum is corrected for
telluric absorption and stellar lines, which results in a so-called
reduced spectrum. We note that since telluric removal is
divisive and stellar removal is subtractive, stellar removal
needs additional care in the presence of signi
fi
cant planet light
and abundant stellar lines
(
Schwarz et al.
2016
)
. Then, the
detected planet spectrum is cross-correlated with a synthetic
planet template spectrum. For ground-based observations, the
spectra used in the cross-correlation are high-pass
fi
ltered to
remove the spectral continuum component
(
<
100 cycles per
micron
)
. For space-based observations of planets whose spectra
are dominated by re
fl
ected light, we remove the continuum by
dividing the re
fl
ected light spectrum by the stellar spectrum.
The cross-correlation between the reduced spectrum and the
synthetic spectrum results in a CCF. The peak of the CCF is
compared with the
fl
uctuation level of the CCF
(
illustrated in
Figure
2
)
.Wede
fi
ne the CCF S
/
N as the ratio of the CCF peak
value and the rms of the CCF
fl
uctuation. To calculate the rms,
we use either the
fi
rst or the fourth quarter of CCF, whichever
is farther awary from the CCF peak. In order to be quali
fi
ed as a
signi
fi
cant detection, we require that
(
1
)
the CCF S
/
N is higher
than 3 and
(
2
)
the RV of CCF peak is consistent with the input
planet RV within one resolution element. Any signi
fi
cant
detection of the CCF peak is equivalent to detecting the planet.
To detect a certain molecular species in the planet spectrum
(
e.g., CO or H
2
O
)
, we repeat the same process using a synthetic
planet template spectrum consisting of only lines from that
single molecular species.
For ground-based observations, the detection of the CCF
peak is hampered by the Earth
s atmosphere. This is especially
the case if the molecular species of interest is also present in the
Earth
s atmosphere, e.g., O
2
,H
2
O, and CO
2
. In such cases, the
CCF peak could be caused by residuals from the removal of
telluric absorption lines. To distinguish the origin of the CCF
peak, we use the fact that the RV of an exoplanet changes by
tens of km s
1
due to its orbital motion and the Earth
s
barycentric motion, whereas the RV variation of telluric lines
stays within tens of m s
1
. To measure an RV change of tens of
km s
1
, the spectral resolution needs to be at least a few
thousand at moderate S
/
N. Therefore we consider only spectral
resolutions higher than
R
=
1000 for ground-based observa-
tions. The ability of a spectrograph to distinguish the signal
from an exoplanet and the signal from the Earth
s atmosphere
in RV space improves with increased spectral resolution. For
space-based observations, the spectral resolution may be as low
as
R
=
25.
3. Fiber Injection Unit
(
FIU
)
, Upgraded NIRSPEC, and the
Keck Planet Imager and Characterizer
(
KPIC
)
at Keck
While the framework described in Section
2
is a general-
purpose pipeline to simulate the performance of any HDC
instruments, we will use the pipeline to study the prospect of
the KPIC
(
Mawet et al.
2016
)
, an HDC instrument that is being
developed at Keck telescope.
The KPIC is a four-pronged upgrade of the Keck AOs
facility. The
fi
rst upgrade component is the addition of a high-
performance small inner working angle
(
IWA
)
L
-band vortex
coronagraph to NIRC2
(
Absil et al.
2016
)
. This operation
was successfully carried out in 2015 and is now available to
the Keck community in shared-risk mode. The upgrade not
only came with a brand-new coronagraph focal plane mask,
but also a suite of software packages to automate the
coronagraph acquisition procedure, including automatic ultra-
precise centering
(
Huby et al.
2015
)
, speckle nulling wavefront
control
(
Bottom et al.
2016
)
, and an open-source python-based
data reduction package
(
Gomez Gonzalez et al.
2016
)
. The
second upgrade component is an infrared pyramid wavefront
sensor demonstration, and a potential facility for the Keck II
AOs system. The third upgrade component is a higher-order
deformable mirror paired with the infrared pyramid sensor,
followed by a new single-stage coronagraph. Finally, the fourth
component of the KPIC is the FIU.
The FIU is at the core of the KPIC instrument upgrade that
links the Keck II telescope AO bench to NIRSPEC, the current
R
25,000 workhorse infrared spectrograph at Keck. The FIU
focuses the light from a target of interest into single-mode
fi
bers after the AO system with minimal losses, and the
fi
ber
outputs are reformatted to
fi
t the slit plane of NIRSPEC.
In 2018, the UCLA IR laboratory will equip NIRSPEC with
a new 5
μ
m cutoff, 2048
×
2048 pixel HgCdTe H2RG detector
from Teledyne
(
Martin et al.
2014
)
. This new device offers
reduced read noise and dark current, as well as improved
9
http:
//
www.e2v.com
/
resources
/
account
/
download-datasheet
/
1364
4
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153:183
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)
, 2017 April
Wang et al.
cosmetics, superior
fl
at-
fi
elding, a modest improvement in
quantum ef
fi
ciency in
H
and especially
K
band, and the
enhanced stability of modern electronics. Most critical for HRS
is the H2RGs smaller pixel scale of 18
μ
m
(
versus 27
μ
m for
the existing Aladdin device
)
, which directly improves the
spectral resolution with the same grating arrangement from
25,000 to 37,500 with a 0
29 slit and 3-pixel sampling.
The simulations in Section
4
are based on the expected
performance of KPIC at various stages of development.
4. Ground-based Observations of
Directly Imaged Planets with HDC
4.1. HR 8799 e
Planet e is the most challenging planet to observe of the 4
known planets in the HR 8799 system because of its proximity
to the host star
(
0. 4
)
. Following the methods detailed in
Section
2
, we simulate observations with an HDC instrument
(
the FIU and upgraded NIRSPEC
)
at Keck. The input
parameters for the planet, star, telescope, and instrument are
provided in Tables
1
and
2
.
BT-Settl model spectra are used as the input spectra. We use
=
T
1200
eff
and 7400 K and log
(
g
)
=
3.5 and 4.5 for the planet
and the star, respectively. The metallicity
[
Fe
/
H
]
is set to zero
for both planet and star.
The
fl
ux from the planet and star is adjusted such that the
model
fl
ux is consistent with the absolute
fl
ux measured from
photometry. We ensure that the adjusted
fl
ux matches the result
from Bonnefoy et al.
(
2016
)
within the uncertainties
(
see
Figure
3
)
.
We consider two cases:
(
1
)
we have perfect knowledge of
the planet spectrum, and
(
2
)
we have limited information
about the intrinsic planet spectrum. In the
fi
rst case, we use the
BT-Settl model spectrum that is used to generate observations
as the template. As a result, the input spectrum and the template
spectrum are the same. In the second case, a combined
molecule-by-molecule spectrum of CO, CH
4
, and H
2
O is used
as the template. As a result, the input spectrum and the template
spectrum are independently generated and may not necessarily
be the same.
4.1.1. Limiting Factors for the CCF S
/
N
We simulate 100 observations at each star light suppression
level and for each band. The median value of these simulations
is reported in the following discussion. We consider three
Figure 2.
(
A
)
Examples of the cross-correlation function
(
see Section
4.1
for the de
fi
nition of different cases
)
. The CCFs are vertically and horizontally offset for
visual clarity. The peaks of the CCFs are scaled to the same height to emphasize the different
fl
uctuation level outside the CCF peaks. Dashed lines indicate lower and
upper boundaries for the
y
-axis in panel
(
B
)
.
(
B
)
CCF
fl
uctuation due to photon noise, i.e., the difference between the blue and the green CCF in panel
(
A
)
. When the
photon noise is small, the CCF
fl
uctuation due to photon noise is smaller than the CCF
fl
uctuation that is due to intrinsic CCF structures
(
blue CCF in panel
(
A
))
.
(
C
)
Close-up for CCF peaks.
(
D
)
Close-up for CCF regions where we de
fi
ne the
fl
uctuation level of a CCF. We use the rms of either the
fi
rst or the fourth quarter to
calculate the CCF
fl
uctuation level.
(
E
)
Close-up to show CCFs of different cases.
Table 1
Telescope and Instrument Parameters for Simulated
Observations of HR 8799 e and 51 Eri b
Parameter
Value
Unit
Telescope aperture
10.0
m
Spectral resolution
37500
L
J
-band spectral range
1.143
1.375
μ
m
H
-band spectral range
1.413
1.808
μ
m
K
-band spectral range
1.996
2.382
μ
m
¢
L
-band spectral range
3.420
4.120
μ
m
Exposure time
3600
second
Fiber angular diameter
1.0
λ
/
D
Wavefront correction residual
a
260
nm
Telescope
+
instrument throughput
b
10%
L
Readout noise
3.0
-
e
Dark current
0.01
-
e
s
1
Notes.
a
Private communication with Peter Wizinowich.
b
This throughput is for
K
band. Throughputs for other bands are scaled with
the Strehl ratio.
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Wang et al.
scenarios in the CCF S
/
N calculation
(
Figure
4
)
. In the CCF
structure-limited case, the CCF S
/
N is limited by the intrinsic
structure in regions where we calculate the noise level. We use
the rms of the
fi
rst quarter or the forth quarter to calculate the
noise level of the CCF
(
see Figure
2
for illustration
)
. If the CCF
peak is in the
fi
rst half of the CCF, then we use the forth quarter
for the rms calculation. Otherwise, we use the
fi
rst quarter for
the rms calculation. The velocity span of the CCF is half of the
bandwidth times the speed of light, which is the result of the
Fourier transform that is used in the CCF calculation.
In theory, the intrinsic CCF structure can be removed by
subtracting the noiseless CCF from the noisy CCF. The
remaining noise level is due to photon noise
(
see Panel
(
B
)
in
Figure
2
)
, which is the photon-noise-limited case. The limiting
photon noise can originate from various sources. At a low level
of star light suppression, the dominating noise source is always
the photon noise from the star. At deeper star light suppression,
the limiting photon noise can be sky background emission
(
e.g.,
¢
L
band
)
or the planet itself
(
e.g.,
J
,
H
,
K
S
band
)
. The
photon-noise-limited case is the most optimistic case in which
we have perfect knowledge of the planet and the star.
In practice, however, we do not know the noiseless planet
and star spectra a priori, and acoordingly, we do not know the
noiseless CCF. Therefore, CCF S
/
N is almost certainly limited
by systematics. In addition to the CCF structure-limited case,
we also consider one case in which systematics dominates
the CCF S
/
N. In the mismatched-spectrum case, we consider
a mismatch between the observed and the template planet
spectrum. For the observed planet spectrum, we use a BT-Settl
spectrum with
=
T
1200 K
eff
and log
(
g
)
=
3.5. For the
template planet spectrum, we use the combined spectrum of
CO, CH
4
, and H
2
O as shown in Figure
3
. This scenario yields
the lowest CCF S
/
N because of the spectrum mismatch.
Although this case can potentially result in a low CCF S
/
N,
it represents an opportunity for atmosphere retrieval: a more
probable molecular abundance ratio,
P
T
pro
fi
les may be
determined by varying the model parameters to maximize the
CCF peak. It highlights the importance of planet spectrum
modeling and a good understanding of the systematics
associated with the cross-correlation method.
The three limiting cases represent the different stages of
spectral retrieval. From a reduced spectrum, a template
(
most
likely mismatched
)
is used in the cross-correlation, which
results in a CCF peak, assuming the template resembles the
planet spectrum in the reduced spectrum. The result of this
stage is equivalent to the mismatched-spectrum case. Then, the
template spectrum is optimized in order to maximize the CCF
peak. During this process, planet atmospheric properties are
inferred, including composition, abundance ratio, cloud
patchiness, chemical equilibrium, etc. If the optimization
process is successful, the CCF S
/
N is limited by the intrinsic
structure of the CCF. At this stage, an autocorrelation function
is calculated from the optimized template spectrum and
subtracted from the optimized CCF to remove intrinsic
structures. After the subtraction, the data reduction and spectral
retrieval can potentially reach the photon-noise limit.
4.1.2. Optimal Band for Planet Detection
Figure
4
shows CCF S
/
Ns at star light suppression levels up
to 10
6
. At a low level of star light suppression
(
>
-
10
2
)
, the
¢
L
band outperforms other bands because the planet
/
star contrast
is favorable
(
see Table
2
)
. However, the
¢
L
curves level off
quickly as the star light suppression level increases because sky
background becomes the dominant noise source. In this case,
increasing star light suppression level does not improve the
CCF S
/
N. However, we note that the star light suppression at
the beginning of the plateau depends on the brightness of a star.
That is, deeper star light suppression is needed to reach the
background limit for brighter stars.
At deeper star light suppression,
H
and
K
S
band become the
optimal bands that give the highest CCF S
/
N. The transition of
performance between
¢
L
and
H
/
K
S
band takes place at star light
suppression levels between
10
1
and 10
3
depending on
different cases.
For a given angular separation, there is a trade-off between
operating wavelength and wavefront quality. For instance, the
Strehl ratio is worse at shorter wavelengths, but spatial
resolution improves. Coronagraph performance is usually
better with more beam widths
(
λ
/
D
in angle
)
separating the
star and planet. In our simulations, we scale the nominal 10%
throughput with the Strehl ratio to account for better wavefront
quality at longer wavelengths, which results in a better
coronagraph performance and
fi
ber coupling ef
fi
ciency. We
Table 2
HR 8799 and Planet e
Parameter
Value
Unit
References
Star
Effective temper-
ature
(
T
eff
)
7193
K
Baines et al.
(
2012
)
Surface gravity
(
g
log
)
4.03
cgs
Baines et al.
(
2012
)
Distance
39.40
pc
van Leeuwen
(
2007
)
Vi
sin
37.5
km s
1
Kaye & Strassmeier
(
1998
)
Inclination
(
i
)
a
>~
40
degree Wright et al.
(
2011
)
Radial velocity
11.5
km s
1
Gontcharov
(
2006
)
Planet
Effective temper-
ature
(
T
eff
)
1100
1650 K
Bonnefoy et al.
(
2016
)
Surface gravity
(
g
log
)
3.5
4.1
cgs
Bonnefoy et al.
(
2016
)
Metallicity
(
[
M
/
H
]
)
0.0
0.5
dex
Bonnefoy et al.
(
2016
)
Vi
sin
b
<
40.0
km s
1
Konopacky
et al.
(
2013
)
Inclination
(
i
)
28
degree Soummer et al.
(
2011
)
Semimajor axis
(
a
)
14.94
20.44 au
Zurlo et al.
(
2016
)
Radial velocity
c
11.5
km s
1
Gontcharov
(
2006
)
Angular separation
0.38
0.52
arcsec Zurlo et al.
(
2016
)
Angular separation in
J
14.6
20.2
λ
/
D
Zurlo et al.
(
2016
)
Angular separation in
H
11.4
15.7
λ
/
D
Zurlo et al.
(
2016
)
Angular separation
in
K
S
8.4-11.5
λ
/
D
Zurlo et al.
(
2016
)
Angular separation
in
¢
L
4.7
6.9
λ
/
D
Zurlo et al.
(
2016
)
Planet
/
star contrast in
J
́
-
2
.0 10
6
LL
Planet
/
star contrast
in
H
́
-
1
.0 10
5
LL
Planet
/
star contrast
in
K
S
́
-
3
.8 10
5
LL
Planet
/
star contrast
in
¢
L
́
-
2
.1 10
4
LL
Notes.
a
We adopt 40
°
in simulations.
b
We assume a rotational velocity of 15 km s
1
.
c
Assumed to be the same as HR 8799.
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The Astronomical Journal,
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23pp
)
, 2017 April
Wang et al.