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OBSERVING EXOPLANETS WITH HIGH DISPERSION CORONAGRAPHY.
I. THE SCIENTIFIC 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 Bj
̈
orn Benneke
3
(Received; Accepted)
to appear in ApJ
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 Disper-
sion 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
configurations, 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
starlight suppression level. Compared to the
10
−
7
planet/star contrast, HDC relaxes the starlight 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 starlight
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).
1.
INTRODUCTION
Out of the thousands of exoplanets detected to
date, the few that have been directly imaged are
excellent targets for studying orbital configura-
tions (Pueyo et al. 2015; Zurlo et al. 2015; Millar-
Blanchaer et al. 2015; Maire et al. 2015) and at-
mospheric chemical compositions (Konopacky et al.
2013; Oppenheimer et al. 2013; Bonnefoy et al. 2015;
Rajan et al. 2015). However, direct imaging and
characterization faces several technical challenges
owing to the small angular separation and high con-
trast between exoplanets and their host stars. High-
contrast imaging (HCI) systems mitigate these ef-
fects by suppressing diffracted star light, that may
otherwise overwhelm the planet signal, with an ex-
treme adaptive optics system and a coronagraph.
Current state-of-the-art high contrast imaging in-
struments, 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 better than 10
−
4
star
light suppression level at a few tenths of an arcsec,
ji.wang@caltech.edu
1
Department of Astronomy, California Institute of
Technology, MC 249-17, 1200 E. California Blv, Pasadena,
CA 91106 USA
2
Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA
3
Division of Geological and Planetary Sciences, Califor-
nia Institute of Technology, Pasadena, CA 91125, USA
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; Ri-
aud & Schneider 2007; Kawahara & Hirano 2014;
Snellen et al. 2015; Lovis et al. 2016). In this High
Dispersion Coronagraphy (HDC) scheme, the coro-
nagraphic component serves as a spatial filter to
separate the light from the star and the planet. The
HRS serves as spectral filter taking advantage of
differences in spectral features between the stellar
spectrum and the planetary spectrum, e.g., differ-
ent absorption lines and radial velocities (RV).
Using HRS as a way of spectral filtering has
been successfully demonstrated by a number of
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 validate 3D exo-
planet atmosphere models (Kempton et al. 2014).
For planets detected via RV, the spectral lines 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
arXiv:1703.00582v1 [astro-ph.EP] 2 Mar 2017
2
Wang et al. - HDC
orbital inclination (Brogi et al. 2012, 2013, 2014;
Lockwood et al. 2014). Moreover, HRS permits de-
tailed study of spectral lines arising from a planet’s
atmosphere. This approach led to the first mea-
surement of a planet’s rotational velocity (Snellen
et al. 2014). With time-series HRS, surface fea-
tures such as cloud or spot coverage may be in-
ferred via Doppler imaging, which has been demon-
strated on the closest brown dwarf system, Luhman
16 AB (Crossfield et al. 2014).
As showcased by the examples above, HRS may
be used to detect planets that are
∼
10
−
4
times
as bright as their host stars. When coupled with a
state-of-the-art HCI system capable of reaching star
light suppression levels of
∼
10
−
4
, an HDC instru-
ment is sensitive to much fainter planets. Mean-
while, relatively bright planets may be observed at
a higher signal-to-noise ratio (SNR) allowing 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 per-
formance of an HDC instrument. Although similar
calculations have been performed as part of previ-
ous studies (Sparks & Ford 2002; Riaud & Schneider
2007; Kawahara & Hirano 2014; Snellen et al. 2015;
Lovis et al. 2016), a thorough end-to-end simulation
that explores the SNR trade space between spec-
tral resolution and starlight suppression for ground-
based and space-based observations is lacking. In
this paper, we simulate a variety of HDC instru-
ments that are either under development or in the
conceptual design phase and quantify their poten-
tial for detecting new planets as well as particular
molecular species in the atmosphere of known plan-
ets (e.g. Proxima Cen b, 51 Eri b, HR 8799 e) and
hypothetical Earth-like planets around stars of dif-
ferent spectral types.
The paper is organized as follows. We outline
the procedure used to simulate the performance of
an HDC instrument for detecting and characteriz-
ing exoplanets in
§
2. The planned Keck HDC in-
strument is briefly described in
§
3. We study the
prospects of using the Keck HDC instrument to ob-
serve previously imaged exoplanets in
§
4. HDC ob-
servations of potential Earth-like planets (e.g. Prox-
ima Cen b) in the habitable zone of M dwarfs are
investigated in
§
5 for current and next-generation
extremely large telescopes. Observing Earth-like
planets around solar-type stars with future space
telescopes is considered in
§
6. A summary and dis-
cussion are provided in
§
7.
2.
HDC FUNDAMENTAL TRADE-OFF ANALYSIS
2.1.
Simulating the Observations
In this section, we describe our workflow to sim-
ulate the end-to-end performance of an HDC sys-
tem, 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 be-
tween raw star light suppression and spectral reso-
lution for various instrument configurations, target
types, and science cases. Fig. 1 shows a flow chart
to illustrate the procedure and the system-related
inputs to the simulation. The resulting data prod-
ucts, e.g., cross correlation fuction (CCF) and their
quality (e.g. SNR) will inform observation strate-
gies and system requirements, including the coron-
agraph design and the performance of the adaptive
optics (AO) system.
2.1.1.
Generating Spectra of Stars and Planets
Gas-giant planet spectra consisting of all molecu-
lar species are derived from the published BT-Settl
grids (Baraffe et al. 2015). The grids cover effec-
tive temperatures (
T
eff
) from 1200 K 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 consid-
ered here. If necessary, the planet and star fluxes
are scaled to match the observed absolute flux.
High-resolution spectra discerning the individual
contributions of the molecular absorbers H
2
O, CO,
and CH
4
are simulated using the SCARLET model
(Benneke 2015; Benneke & Seager 2013). In this
work, SCARLET first iteratively computes the line-
by-line radiative transfer and atmospheric chem-
istry to converge to a self-consistent vertical tem-
perature structure and molecular composition. To
isolate the contribution from individual molecules,
we then artificially remove all opacities in the atmo-
sphere except the opacity of the respective molecu-
lar absorber and collision-induced absorption in the
simulation of the planets’ thermal emission spec-
tra. In this way, we compute emission spectra for
each of the molecular absorbers individually. The
SCARLET model considers the molecular opaci-
ties of H
2
O, CH
4
, NH
3
, HCN, CO, and CO
2
and
TiO from the high-temperature ExoMol database
(Tennyson & Yurchenko 2012), and O
2
, O
3
, OH,
C
2
H
2
, C
2
H
4
, C
2
H
6
, H
2
O
2
, and HO
2
from the HI-
TRAN database (Rothman & Gordon 2009). Ab-
sorption by the alkali metals (Li, Na, K, Rb, and
Cs) is modeled based on the line strengths pro-
vided in the VALD database (Piskunov et al. 1995)
and H
2
-broadening prescription provided in Bur-
rows & Volobuyev (2003). Collision-induced broad-
ening from H
2
/
H
2
and H
2
/
He 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,b,
2013; Hu & Seager 2014). We first calculate the
molecular abundance as a function of altitude, con-
trolled by photochemical and disequilibrium chem-
istry processes. The details of the model are de-
scribed in Hu et al. (2012a) and the molecular abun-
dances have been validated against measurements
on Earth.
We include the effects of clouds in the resulting
4
https://phoenix.ens-lyon.fr/Grids/BT-
Settl/CIFIST2011
2015/FITS/
5
https://phoenix.ens-lyon.fr/Grids/BT-
Settl/CIFIST2011/SPECTRA/
3
Figure 1.
Flow chart of simulation of an HDC instrument. Photons from star and planet go through an HCI instrument.
Residual star light and planet light is picked up by a single-mode fiber, which feeds the light into an HRS instrument. Spectra
are simulated with detector noise and then reduced into data product, e.g., CCF (see
§
2.2). 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.
spectra by averaging two scenarios: a cloud-free sce-
nario where we assume a clear atmosphere and a
high-cloud scenario where we assume a reflective
H
2
O cloud at 9-13 km. This procedure produces
a continuum albedo of
∼
0.3 and provides a real-
istic estimate of the strength of spectral features,
similar to Des Marais et al. (2002). Eighth-order
Gaussian integration is used to calculate the con-
tribution of the whole planetary disk for both the
reflected light and thermal emission. We include the
opacities of CO
2
, O
2
, H
2
O, CH
4
, O
3
, and N
2
O and
calculate the planetary flux at a spectral resolution
of
R
=
λ/
∆
λ
= 500
,
000, high enough to resolve in-
dividual 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 con-
fusion between molecules that appear in both the
planet’s and Earth’s atmosphere, e.g., H
2
O and O
2
.
We use the Mauna Kea sky transmission
6
and emis-
sion spectra
7
, available from the Gemini observa-
tory website (Lord 1992), with wavelength cover-
age of 0.9-5.6
μ
m. A water column density of 1.6
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
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 Na-
tional Solar Observatory for wavelengths shorter
than 0.9
μ
m
8
.
2.1.3.
Simulation Procedure
An HDC instrument contains two major compo-
nents, a coronagraph and a high-resolution spec-
trograph, which are linked by a set of single-mode
fibers: a planet fiber, a star fiber, and/or a sky
fiber. One end of these fibers is located at the im-
age plane after the coronagraph and the other end of
the fibers is at the entrance slit of the spectrograph.
The star fiber and sky fiber provide calibration spec-
tra in data reduction described in
§
2.2. Following
Fig. 1, light from the star and planet go through
a coronagraph and form an image. The fiber at
the planet location leads the planet light, as well as
residual star light, into the spectrograph. The de-
tector records the planet spectrum along with con-
taminating stellar spectrum. We note that atmo-
spheric effect, i.e., absorption and emission, is only
considered for ground-based observations.
f
detector
= (f
planet
+f
star
×
C)
×
f
transmission
+f
sky
.
(1)
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 W
·
m
−
2
·
μ
m
−
1
at
a reference height (
d
ref
). We calculate the inci-
8
diglib.nso.edu/ftp.html
4
Wang et al. - HDC
dent star and planet photon flux on the detec-
tor,
f
star
and
f
planet
, with the following equation:
f
=
F
×
(
d
ref
/d
)
2
×
A
×
∆
λ
×
η
×
t
exp
/ hν
, where
F
is the flux at the reference height (
d
ref
),
d
is distance
between the star-planet system and an observer, A
is telescope receiving area, ∆
λ
is wavelength cover-
age per wavelength bin,
η
is telescope and instru-
ment end-to-end throughput, t
exp
is exposure time,
h
is Planck constant and
ν
is the frequency of a
photon.
At the image plane after a coronagraph, stellar
flux is suppressed by a factor
C
, a parameter we
denote as star light suppression factor, i.e., the frac-
tion of the total starlight that couples into the fiber.
Both stellar and planetary spectra are rotation-
ally broadened. The effect of rotation broaden-
ing is calculated by summing spectra from surface
grids evenly spaced in longitudinal and latitudinal
direction. The rotationally-broadened spectra are
then multiplied by the Earth’s atmosphere trans-
mission spectrum (
f
transmission
) for ground-based
observation. The Earth’s atmosphere transmission
spectrum is unitless and normalized to unity, with
zero meaning entirely opaque and one meaning en-
tirely transmissive. For space-based observations,
f
transmission
is set to unity.
The spectra are then broadened by instrumen-
tal line spread function (LSF). The instrumental
broadening is approximated by convolving a spec-
trum with a normalized Gaussian core with a full
width at half maximum (FWHM) of one spectral
resolution element, which is
λ
0
/R, where
λ
0
is cen-
tral wavelength and R is the spectral resolution of
a spectrograph.
The broaden spectra are then added by sky emis-
sion spectrum (
F
emission
), which is also broadened
at a given spectral resolution. The sky emission is
in the unit of photons
·
s
−
1
·
arcsec
−
2
·
m
−
2
·
μ
m
−
1
. We
calculate the incident photon flux from sky emission
on detector using the following equation:
f
emission
=
F
emission
×
t
exp
×
θ
2
×
A
×
∆
λ
, where
θ
2
is the pro-
jected area of sky to the input fiber fundamental
mode size which we assume to be (1
.
0
λ
0
/
D)
2
, where
λ
0
is central wavelength and D is telescope aperture
diameter. For space-based observation,
f
emission
is
set to zero. The simulated spectra are then resam-
pled at the pixel sampling rate per resolution ele-
ment.
In addition to the spectrum described by Equa-
tion 1, we simulate more spectra for subsequent
data reduction. For ground-based observation, we
simulate sky emission and stellar spectra, assum-
ing there are two dedicated fibers for sky and star.
The stellar spectrum can be used to remove at-
mospheric transmission and/or contaminated stel-
lar lines in the planet spectrum. For example, in
the case of ground-based observations 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 ground-based observations of Proxima
Cen b, the observed spectrum is a reflection spec-
trum containing both the star and planet absorption
lines and is contaminated by the Earth’s atmosphere
lines, so it is necessary to have a separate simul-
taneous observation of the host star to remove at-
mospheric transmission and/or contaminated stellar
lines in the planet spectrum. For space-based obser-
vations, 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, and dark current based on
the performance of a Teledyne HgCdTe H2RG in-
frared detector and a e2v optical charge-coupled de-
vice (CCD). Readout noise and dark current for the
H2RG detector are 2.0 e
−
(Fowler-32 readout, per-
sonal correspondence with Roger Smith) and 0.002
e
−
/s
(Blank et al. 2012), respectively. An e2v opti-
cal CCD
9
has a readout noise of 2.0 e
−
and a dark
current of 0.02 e
−
/
hour.
δ
=
√
f + n
exp
×
RN
2
+ dark
×
t
exp
,
(2)
The total noise is calculated by Equation 2, where
δ
is the combined noise, f is the photon noise fol-
lowed by terms for readout noise (RN) and dark
current (dark), n
exp
is the number of readout within
a total observation time
t
exp
. The number of read-
outs n
exp
is determined by the linear range or de-
tector persistence limit, i.e. the signal level where
a new frame needs to be taken in order to avoid
non-linearity or persistence.
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 12000 electrons. During operations such as
sky emission removal, telluric/stellar line removal,
noises are added in quadrature.
2.2.
Spectral Analyses
Once the detected spectra are obtained, we per-
form the data processing steps required to extract
the planet signal using the cross correlation tech-
nique (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 stel-
lar removal is subtractive, stellar removal needs ad-
ditional care in the presence of significant planet
light and abundant stellar lines (Schwarz et al.
2016). Then, the detected planet spectrum is cross-
correlated with a synthetic planet template spec-
trum. For ground-based observations, the spectra
used in the cross-correlation are high-pass filtered
to remove the spectral continuum component (
<
100
cycles per micron). For space-based observations of
planets whose spectra are dominated by reflected
light, we remove the continuum by dividing the re-
flected light spectrum by the stellar spectrum. The
9
http://www.e2v.com/resources/account/download-
datasheet/1364
5
cross-correlation between the reduced spectrum and
the synthetic spectrum results in a CCF. The peak
of the CCF is compared with the fluctuation level
of the CCF (illustrated in Fig. 2). We define CCF
SNR as the ratio of CCF peak value and the RMS
of CCF fluctuation.
To calculate the RMS, we
use either the first or the fourth quarter of CCF,
whichever is further awary from the CCF peak. In
order to be qualified as a significant detection, we
require that (1) CCF SNR is higher than 3 and (2)
the RV of CCF peak is consistent with the input
planet RV within one resolution element. Any sig-
nificant detection of the CCF peak is equivalent to
detecting the planet. To detect a certain molecular
species in the planet spectrum (e.g., CO, H
2
O), we
simply 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 atmo-
sphere. This is especially the case if the molecular
species of interest is also present in the Earth’s at-
mosphere, 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 due to
its orbital motion and the Earth’s barycentric mo-
tion whereas the RV variation of telluric lines stays
within tens of m/s. To measure an RV change of
tens of km/s, the spectral resolution needs to be at
least a few thousand at moderate SNR. Therefore,
we consider only spectral resolutions higher than
R=1,000 for ground-based observations. The abil-
ity of a spectrograph to distinguish the signal from
an exoplanet and the signal from the Earth’s atmo-
sphere in RV space improves with increased spectral
resolution. For space-based observations, the spec-
tral resolution may be as low as R=25.
3.
FIBER INJECTION UNIT, UPGRADED NIRSPEC,
AND KPIC AT KECK
While the framework described in
§
2 is a general-
purpose pipeline to simulate performance of any
HDC instruments, we will use the pipeline to study
the prospect of the Keck Planet Imager and Char-
acterizer (KPIC, Mawet et al. 2016), an HDC in-
strument that is being developed at Keck telescope.
KPIC is a four-pronged upgrade of the Keck adap-
tive optics facility. The first upgrade component
is the addition of a high performance small in-
ner working angle
L
-band vortex coronagraph to
NIRC2 (Absil et al. 2016). This operation was suc-
cessfully 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 corona-
graph focal plane mask, but also a suite of software
packages to automate the coronagraph acquisition
procedure, including automatic ultra-precise center-
ing (Huby et al. 2015), speckle nulling wavefront
control (Bottom et al. 2016), and an open source
python-based data reduction package (Gomez Gon-
zalez et al. 2016). The second upgrade component
is an infrared pyramid wavefront sensor demonstra-
tion, and potential facility for the Keck II adap-
tive optics 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 fiber injection unit (FIU).
The FIU is at the core of the KPIC instrument up-
grade, which links the Keck II telescope AO bench
to NIRSPEC, the current R
∼
25,000 workhorse in-
frared spectrograph at Keck. The FIU focuses the
light from a target of interest into single mode fibers
after the AO system with minimal losses and the
fiber outputs are reformatted to fit the slit plane of
NIRSPEC.
In 2018, the UCLA IR lab will equip NIRSPEC
with a new 5-
μ
m cutoff, 2048x2048 pixel HgCdTe
H2RG detector from Teledyne (Martin et al. 2014).
This new device offers reduced read noise and dark
current, as well as improved cosmetics, superior flat-
fielding, a modest improvement in quantum effi-
ciency in
H
and especially
K
band, and the en-
hanced stability of modern electronics. Most critical
for HRS is the H2RGs smaller pixel scale of 18
μ
m
(vs. 27
μ
m for the existing Aladdin device) which
directly improves spectral resolution with the same
grating arrangement from 25,000 to 37,500 with a
0
′′
.29 slit and 3-pixel sampling.
Simulations in
§
4 are based on the expected per-
formance 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
among the 4 known planets in HR 8799 system be-
cause of its proximity to the host star (
'
0
′′
.
4).
Following the methods detailed in
§
2, we simulate
observations with an HDC instrument (the FIU and
upgraded NIRSPEC) at Keck. Input parameters for
the planet, star, telescope, and instrument are pro-
vided in Table 1 and 2.
BT-Settl model spectra are used as the input
spectra. We use
T
eff
= 1200 K and 7400 K and
log(g) = 3.5 and 4.5 for the planet and the star, re-
spectively. The metallicity [Fe/H] is set to zero for
both planet and star.
The flux from the planet and star is adjusted such
that the model flux is consistent with the absolute
flux measured from photometry. We ensure that
the adjusted flux matches with result from Bonnefoy
et al. (2015) within uncertainties (see Fig. 3).
We consider two cases: (1) we have perfect knowl-
edge of the planet spectrum and (2) we have limited
information about the intrinsic planet spectrum. In
the first case, we use the BT-Settl model spectrum
that is used to generate observations as the tem-
plate. As a result, the input spectrum and the tem-
plate 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
the same.
6
Wang et al. - HDC
Figure 2.
A: examples of cross correlation function (see
§
4.1 for definition of different cases). CCFs are vertically and
horizontally offset for visual clarity. Peaks of CCFs are scaled to the same height to emphasize different fluctuation level outside
CCF peaks. Dashed lines indicate lower and upper boundaries for y-axis in Panel B. B: CCF fluctuation due to photon noise,
i.e., the difference between blue and green CCF in Panel A. When photon noise is small, CCF fluctuation due to photon noise
is smaller than CCF fluctuation due to intrinsic CCF structures (blue CCF in Panel A). C: close-up for CCF peaks. D: close-up
for CCF regions where we define fluctuation level of a CCF. We use the RMS of either the first quarter or the fourth quarter
to calculate CCF fluctuation level. E: close-up to show CCFs of different cases.
4.1.1.
Limiting Factors for CCF SNR
We simulate 100 observations at each star light
suppression level and for each band. The median
value of these simulations is reported in the follow-
ing discussion. We consider three scenarios in the
CCF SNR calculation (Fig. 4). In the
CCF struc-
ture limited
case, the CCF SNR is limited by the
intrinsic structure in regions where we calculate the
noise level. We use the RMS of the first quarter or
the forth quarter to calculate the noise level of CCF
(see Fig. 2 for illustration). If the CCF peak is in
the first half of CCF, then we use the forth quarter
for RMS calculation. Otherwise, we use the first
quarter for RMS calculation. The velocity span of
CCF is half of the bandwidth times the speed of
light, which is the result of Fourier transform that
is used in CCF calculation.
In theory, one can remove the intrinsic CCF struc-
ture by subtracting the noiseless CCF from the
noisy CCF. The remaining noise level is due to pho-
ton noise (see Panel B in Fig. 2), which is the
pho-
ton noise limited
case. The limiting photon noise
can be from various sources. At low level of star
light suppression, the dominating noise source is al-
ways 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, so we do not know
the noiseless CCF. Therefore, CCF SNR 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 SNR.
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
eff
= 1200 K 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 Fig. 3. This scenario yields the lowest
CCF SNR because of the spectrum mismatch.
Although this case can potentially result in a low
CCF SNR, it represents an opportunity for atmo-
sphere retrieval: a more probable molecular abun-
dance ratio, P-T profiles may be determined by
varying model parameters to maximize the CCF
peak. It highlights the importance of planet spec-
trum 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 spec-
trum, a template (likely mismatched) is used in the
cross correlation which results in a CCF peak, as-
suming 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 max-
imize the CCF peak. During this process, planet
atmospheric properties are inferred, including com-
position, abundance ratio, cloud patchiness, chem-
7
Figure 3.
Top two panels: BT-Settl spectra from HR 8799 e and 51 Eri b and comparison of absolute flux between model
(blue) and observation (red, Bonnefoy et al. 2015; Macintosh et al. 2015) in different photometric bands. Bottom three panels:
normalized spectra for individual molecular species. These spectra are used for detection of molecular species in the atmosphere
of HR 8799 e and 51 Eri b.
Figure 4.
CCF SNR vs. star light suppression level for HR 8799 e in 1-hr exposure time for three cases (see discussion in
§
4.1.1). Simulation parameters for the planet, star, telescope, and instrument are provided in Table 1 and 2.
ical equilibrium, etc. If the optimization process is
successful, the CCF SNR is limited by the CCFs in-
trinsic structure. At this stage, an auto-correlation
function is calculated from the optimized template
spectrum and subtracted from the optimized CCF
to remove intrinsic structures. After the subtrac-
tion, the data reduction and spectral retrieval can
potentially reach the photon-noise limit.
4.1.2.
Optimal Band For Planet Detection
Fig. 4 shows CCF SNRs at star light suppression
levels up to 10
−
6
. At a low level of star light sup-
pression (
>
10
−
2
), the
L
′
band outperforms other
bands because the planet/star contrast is favor-
able (see Table 2). However, the
L
′
curves level
off quickly as the star light suppression level in-
creases because sky background becomes the domi-
nant noise source. In this case, increasing star light
suppression level does not improve the CCF SNR.
However, we note that the starlight suppression at
the beginning of the plateau depends on the bright-
ness of a star. That is, deeper starlight suppression
is needed to reach the background limit for brighter
stars.
8
Wang et al. - HDC
At deeper star light suppression,
H
and
K
S
band
becomes the optimal bands that give the highest
CCF SNR. The transition of performance between
L
′
and
H
/
K
S
band takes place at star light sup-
pression levels between
∼
10
−
1
-10
−
3
depending on
different cases.
For a given angular separation, there is a trade-off
between operating wavelength and wavefront qual-
ity. For instance, the Strehl ratio is worse at shorter
wavelengths, but spatial resolution improves. Coro-
nagraph performance is usually better with more
beam widths (
λ
/D in angle) separating the star
and planet. In our simulations, we scale the nom-
inal 10% throughput with the Strehl ratio to ac-
count for better wavefront quality at longer wave-
lengths, which results both in better coronagraph
performance and fiber coupling efficiency. We do
not directly include the benefit of higher resolution
at shorter wavelengths because angular separations
(in units of
λ
/D, see Table 2) for HR 8799 e are
much larger than the spatial resolution of KPIC.
4.1.3.
Sensitivity Gain in HDC Observation
Compared to ground-based HCI observations of
HR 8799 e, HDC observations would provide a sig-
nificant gain in sensitivity. In L
′
band, the detec-
tion significance is 5-10 for HCI only on Keck tele-
scope (Currie et al. 2014). In comparison, our sim-
ulations indicate that, at a level of star light sup-
pression of 10
−
3
, CCF SNR in L
′
is between
∼
20
(mismatched spectrum case) and 200 (photon noise
limited case). This is a factor of
∼
2-40 gain in sen-
sitivity with the help of HRS. The gain is because
HRS serves as an additional filter for the planet sig-
nal. However, the gain in
L
′
band is limited by
strong sky emission.
In other bands for which the sensitivity is not lim-
ited by the sky background but by the planet/star
contrast, we expect an HDC instrument to provide
an even higher gain in sensitivity. For example, the
planet/star contrast for HR 8799 e is
∼
4
×
10
−
5
in
K
S
, which may not be seen by an HCI instrument
with star light suppression level of 10
−
3
. With an
HDC instrument, the planet can be detected with a
CCF SNR of 40-250 (Fig. 4).
4.1.4.
Molecular Detection
In addition to planet detection using the cross
correlation method, we also consider detecting in-
dividual molecular species in the atmosphere of a
planet. The template spectrum for a single molecu-
lar species is generated as described in
§
2.1.1. In to-
tal, we generate spectra for three molecular species:
CO, H
2
O and CH
4
, plotted in Fig. 3 along with
BT-Settl spectra for HR 8799 e and 51 Eri b.
While
H
,
K
S
and
L
′
bands are identified as the
optimal bands for HR 8799 e detection, we investi-
gate the potential for using all four bands in search-
ing for molecular species in the atmosphere of HR
8799 e. To do so, we cross correlate simulated ob-
served planet spectrum with a template spectrum
of an individual molecular species.
Fig. 5 shows the CCF SNR as a function of star
light suppression level for CO, H
2
O and CH
4
for
J
,
H
,
K
S
, and
L
′
band observations. The optimal
bands for CO, H
2
O and CH
4
detection are
K
S
,
H
,
and
L
′
, respectively. The differences between the
optimal bands for planet detection and molecular
species detection highlights the need for multi-band
high-resolution spectroscopy.
When comparing to previous studies, our finding
in
K
S
band is consistent with Keck OSIRIS obser-
vations of HR 8799 c. Planet c has similar effec-
tive temperature and surface temperature HR 8799
e. With a star light suppression level of
∼
10
−
2
,
Konopacky et al. (2013) detected CO and H
2
O in
HR 8799 c with Keck OSIRIS at a CCF SNR of
∼
10.
The lower CCF SNR than what is predicted in Fig.
5 can be attributed to lower spectral resolution and
higher detector noise.
The sharp drop of CCF SNR at low levels of
starlight suppression in all subplots of Fig. 5 is
due to the criteria for planet/molecular detection
in our simulation. In order to be qualified as a sig-
nificant detection, we require that (1) CCF SNR is
higher than 3 and (2) the RV of CCF peak is consis-
tent with the input planet RV within one resolution
element. Without the second criterion, there may
be interlopers from random CCF fluctuation due to
noise that may be misinterpreted as CCF peaks.
In practice, measured CCF RVs should also follow
a pattern that is consistent with the planet orbits.
Therefore, if
>
50% of the simulations result in an in-
consistent RV, we assign a zero value to CCF SNR.
The result implies that the minimum CCF SNR is
∼
10 to confirm that the absorption/emission signal
is indeed from the planet.
4.2.
51 Eri b
51 Eri b (Macintosh et al. 2015) is the only
directly-imaged planet whose inferred mass is
within the planet mass regime according to both
cold-start and hot-start models (Bowler 2016). Fur-
thermore, its brightness contrast and angular sep-
aration are representative of the practical detec-
tion limits of current ground-based high-contrast
imagers. We therefore simulate observations of 51
Eri b with an HDC instrument to provide a point
of comparison with the current state-of-the-art.
Input parameters for the planet, host star, tele-
scope, and instrument are provided in Table 1 and
3. We use input spectra with
T
eff
= 700 K and
log(g) = 3.5 for the planet and
T
eff
= 7400 K and
log(g) = 4.0 for the star. The metallicity [Fe/H] is
set to zero for both planet and star.
We adjust the planet and star flux such that
the model flux and the absolute flux measured
from photometry are consistent within uncertain-
ties (Fig. 3). We adopt values from Macintosh et al.
(2015) for the absolute flux measurement. Simi-
lar to the cross correlation calculation presented for
HR 8799 e, we use the BT-Settl spectrum as input
to simulate observations. For template spectrum
used for cross correlation, we either use the same
spectrum as the input planet spectrum, or the com-
bined molecule-by-molecule spectrum of CO, CH
4
,
and H
2
O.
9
Figure 5.
CCF SNR for molecular detection in the atmosphere of HR 8799 e assuming 1-hr exposure time. Top rows are for
the photon-noise limited case and bottom rows are for the mismatched spectrum case. Simulation parameters for the planet,
star, telescope, and instrument are provided in Table 1 and 2.
4.2.1.
Optimal Band For Planet Detection
Fig. 6 shows the CCF SNR for 51 Eri b in three
cases. We again observe a decreasing trend of CCF
SNR from the photon-noise limited case to the cases
dominated by systematics.
J
and
L
′
bands are op-
timal bands for detecting 51 Eri b.
L
′
band obser-
vation yields the highest CCF SNR for the photon-
noise limited case and the CCF structure limited
case, at low star light suppression levels (
>
10
−
3
).
However, planet cannot be detected in
L
′
band in
the mismatched spectrum case. This is possibly be-
cause of a poor knowledge of
L
′
band planet spec-
trum.
J
band is the optimal band for the photon-
noise limited case and the CCF structure limited
case if star light suppression levels is better than a
few times 10
−
4
. In addition,
J
band is also the opti-
mal band for the mismatched spectrum case. This is
largely due to the high photon flux from the planet
in
J
band.
In the photon-noise limited case and the CCF
structure limited case, we use planet template spec-
trum that is exactly the same as the planet spec-
trum used in simulating observation. This is to as-
sume that we have full knowledge of the planet’s
spectrum. While this assumption leads to a much
higher CCF SNR (see Fig. 6), we cannot practi-
cally generate a perfect planet or molecular tem-
plate spectrum.
To demonstrate this point, we use the BT-Settl
spectrum as an input to simulate the astrophysical
signal. We use the combined molecular spectrum
for CO, H
2
O, and CH
4
as the template spectrum.
As a result, CCF SNR is reduced for all bands (see
Fig. 6). Using an imperfect template in the cross
correlation operation may even lead to missed de-
tections of planets or particular molecular species.
However, as mentioned in
§
4.1.1, the mismatched
spectrum case also represents an opportunity for at-
mospheric retrieval.
4.2.2.
Molecular Detection
Fig. 7 shows the CCF SNR achieved by cross cor-
relating the reduced spectrum with template spec-
trum of individual molecular species. Depending
on the photon flux and the density and strength of
the spectral lines, the optimal band is different for
each species. H
2
O is present in all
J
,
H
,
K
S
, and
L
′
bands (see Fig. 3) and can be detected in
J
,
H
and
K
S
band. The highest CCF SNR is given in
J
band. CO has lines in
H
and
K
S
band and can
be detected in
H
band. Although abundant CH
4
lines exist in
L
′
band, CH
4
in 51 Eri b can not be
detected due to much elevated sky background and
much reduced photon flux compared to HR 8799 e.
5.
SEARCHING AND CHARACTERIZING
EARTH-LIKE PLANETS AROUND LOW-MASS
STARS WITH GROUND-BASED EXTREMELY
LARGE TELESCOPES
Searching for Earth-like planets and identifying
molecular species in their atmospheres is one of
the major science goals for ground-based extremely
large telescopes and future space-based missions.
Ground-based telescopes are generally larger than
space-based telescopes and thus have the advantage
of higher angular resolution at a given wavelength.
On the other hand, space-based telescopes can
achieve deeper star light suppression than ground-
based instruments due to their vantage point out-
side our turbulent atmosphere. These differences
in spatial resolution and achievable contrast lev-
els affect the science objectives of space-based and
ground-based missions for the study of Earth-like