directing imaging techniques of exoplanets
TRANSCRIPT
Directing Imaging Techniques of Exoplanets
Taweewat Somboonpanyakul1 and Motohide Tamura2
Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637
ABSTRACT
Several exoplanets have been discovered recently, but most of them are indi-
rectly observed using techniques such as radial velocity and transiting techniques.
However, directly observed planets give more unique characteristic of a planet
such as its spectrum to find its composition and its atmosphere. But there are
many challenges preventing the discovery of direct imaging planets. Here, we
describe two important techniques for direct imaging, namely Adaptive Optics
(AO) and Angular Differential Imaging (ADI). We also use a data for GJ 504b,
which was discovered in 2013, as a demonstration of these techniques, and we
manage to find a planet around GJ 504 at the same separation with the distance
reported in the discovery paper (Kuzuhara et al. 2013). Thus, direct imaging
with these two techniques have the potential of discovering more directly ob-
served planets and finding the second Earth.
Subject headings: direct imaging, AO, ADI, LOCI
1. Introduction
1.1. Why Direct Imaging Technique?
Direct Imaging technique is one of the most important methods to detect exoplanets
because other detecting methods such as radial velocity and transit technique only allow us
to indirectly infer the existence of planets from motions and changes of its host star. On the
other hand, direct imaging technique allows us to directly observe and confirm its existence.
1The College, University of Chicago
2Department of Astronomy, Graduate School of Science, University of Tokyo
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There are several benefits from this technique apart from actually seeing the planet.
First of all, possible targets that radial velocity and transit technique most sensitive with
are large planets with small and edge-on orbit while direct imaging technique is sensitive
with large planets with large and face-on orbit. Thus, direct imaging planets will fill the gap
of possible parameter space of allowed planets in order to study the formation and evolution
of planets. Secondly being able to see the planet itself, we can eventually take a spectrum
of these planets in order to study its temperature and its atmospheric composition to see
whether they are habitable. One disadvantage of this technique is that there are very few
numbers of planets that are suitable to be detected by this technique, implying that we need
to observe more stars in order to find one planet.
Furthermore, two main challenges of the direct imaging technique from the limit of our
current technology are a high contrast flux between star and its planets and the angular
separation when we observe it from the Earth. Seeing a planets next to its host star is
extremely difficult because the starlight will be too bright that it covers all the planet’s
light. Also, because of our diffracting limit for each telescope (θdiff ≈ λ/D where D the
primary mirror diameter), there is a minimum separation between star and its companion
that we will be able to resolve into two district objects.
1.2. Why Near-IR?
The first challenge of the direct imaging technique is a large ratio between a star and its
companion flux. For example in visible light, Jupiter is 108 times fainter than the Sun while
the Earth is 3×108 times fainter than the Sun. The reason is that these planets do not emit
light in the visible spectrum, and only reflected starlight that we can observe, implying that
the closer a planet to the star, the brighter it becomes and the contrast between the two is
smaller. However, a planet with small orbit will also have a small angular separation. And
if this angular separation is smaller than the diffracting limit of the telescope, we will not
observe any companion no matter its brightness.
Nevertheless, every planet also has its own thermal emission due to its average tem-
perature around 100K - 700K. This thermal emission is often in the near-infrared region
implying that these planets will be brighter in the near-infrared. In addition, this thermal
emission does not correspond with the separation between the host star and its planets and
the problem of small angular separation does not occur in this wavelength. Therefore, we will
use the images from near-infrared region instead of visible light for direct imaging technique
in order to find exoplanets. In addition, young brown dwarfs and planets are much brighter
and have a better contrast with its host star, compared to older ones, while stars tend to
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reach the equilibrium phase of the Main Sequence and remain stable in its brightness. Fig-
ure 1 shows the brightness of different objects in the sky as a function of time. It illustrates
that planets and brown dwarfs will eventually be much fainter as they go older while the
star’s brightness remains the same. Therefore, young planetary systems will be easier to be
discovered, compared to our solar system.
Theoretically, the easiest target that we should be able to observe is a young large size
planets with a wide separation from the host star. It cannot be too old otherwise it will have
less thermal emission. An example of a first companion we can directly observe is 2M1207b,
which is 1.5 times the size of Jupiter and 40.6 AU away from its host. The host star is a
brown dwarf making it easier to discover since the contrast with its companion is much lower
than star-planet pair. However, some people would argue that 2M1207b is not a planet since
its host star is not a normal star.
Fig. 1.— Temporal evolution of luminosity of stars (blue line), brown dwarf (green line),
and planets (red lines). Low-mass objects are much brighter when they are young. Credit:
Adam Burrows (Princeton U.).
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2. Direct Imaging Technique
Another problem for observing planets directly is the need for high resolution images of
the target in order to distinguish a planet from background noise. However, the Earth atmo-
spheric turbulence limits the resolution of visible and near-infrared images to θatm ≈ 0′′.5−2.′′
When a starlight goes through the Earth atmosphere and encounters regions of different tem-
perature, each layer deflects the incoming starlight differently due to temperature-dependent
reflective index. Therefore, the incoming starlight is distorted before it reaches the telescope.
This distorted wavefront creates speckles randomly on an image. And if we integrate the
incoming starlight for a long time, the speckles will overlap each other and create a broad
Gaussian profile, whose FWHM is the atmospheric seeing, θatm (Duchene 2008).
Fig. 2.— (Left) Effect of the atmosphere to the incoming wavefront. (Right) Resulting
short-exposure image. Each speckle has a FWHM equal to λ/D (Duchene 2008).
Figure 2 shows the process of wave distortion on the left panel and the image of speckles
as a result from this distorted wavefront on the right panel. Thus, the only way to obtain
high-resolution images of a target from the ground is to observe it with a telescope equipped
with an adaptive optic (ao) system.
2.1. Adaptive Optic
The adaptive optic system consists in analyzing in real time the incoming interrupted
wavefront using wavefront sensor (WFS) and correcting it using a deformable mirror (DM).
The system will correct the distorted wavefront and create a stable image in real time. The
principle of the AO system is shown in Figure 3.
When the distorted wavefront hits a deformable mirror, the wavefront is corrected. And
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Wavefront Sensor (WFS)
interupted wavefront
corrected wavefrontSystem
Deformable
Mirror (DM)
Control
Beamsplitter
Fig. 3.— Figure demonstrates the adaptive optic (AO) system. This image is inspired
by Duchene (2008).
before reaching high-resolution camera, the starlight encounters a beamsplitter to let through
a fraction of the incoming light and reflect the remainder to the wavefront sensor to analyze
the distorted wavefront and send that information to the control system to fix it with a
deformable mirror. The system is a close-loop that has to adjust fast enough to beat the
fast-changing atmosphere. If we apply this system, then it is possible to use long exposures
to observe very faint objects while continuously correcting for the atmospheric speckles at
the same time to maintain a high resolution diffracting limit.
3. Direct Imaging Reduction Technique
3.1. Dark Frame Reduction
Dark frame reduction method is a reduction process to minimize image noise from long
exposure time. Dark image is an dark image with the same exposure time as our target
images to obtain only the noise from the sensor. This noise is called ‘fixed-pattern noise’
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meaning that all noises is the same for all images. This fixed-pattern noises consist of a hot
pixel which has a higher dark current than usual pixel and a dead pixel that did not have
any dark current for any exposure time.
3.2. Flat Frame Correction
Flat frame correction is a reduction process to remove all artifacts from any variation
between pixel to pixel sensitivity of the sensor by compensating different ‘gain’ and ‘dark
current’ to create a uniform ‘flat’ image. Shadows from out-of-focus dust specks are the
most common correction for flat field. The pixel’s gain is how much the signal received by
the sensor as a function of how much light coming to the sensor. In this case, gain is a
ration between the output and the input of the sensor. And dark current is the amount of
signal given by the sensor when there is no incident light. We can take flat frame by taking
an evenly illuminated image either from the twilight sky without many stars or evenly
illuminated surface near the telescope.
To conclude, our corrected image will come from
Ci = (Ri −D)
(< F −D >
F −D
), (1)
where Ci is the corrected image, Ri is a raw image that we are interested in, F is a flat
frame, and D is a dark frame and < F −D > is the average pixel value of the corrected flat
field frame.
3.3. Angular Differential Imaging (ADI)
Furthermore as we increases the exposure time, the short-lived speckles converge to a
quasi-static noise pattern, preventing a large gain from increasing integration time. The
quasi-static speckles come from the imperfection of the optic and slowly evolving optical
alignments. Because quasi-static speckles are long-lived and add coherently as the expo-
sure time increases, they eventually dominates over noise that add incoherently such as sky
noise (Lafreniere et al. 2007).
For a ground-based altitude/azimuth telescopes, a technique called angular differential
imaging (ADI) is implemented to subtract a significant fraction of the quasi-static noise
to improve the current detection limit. The principle of the ADI technique is that the
orientation of the image frame is kept constant while the field orientation around the target
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star rotates as we take long-exposure time. Figure 4 illustrates this principle. An object of
interest such as a planet also rotates with the field orientation while most quasi-static noise
remains fixed with the frame.
Fig. 4.— A sketch demonstrating field rotation from the viewpoint of an observer standing
next to the telescope, looking South. Credit: C.Thalmann.
Then by taking a pixel-wise median of the image stack, only structures appearing con-
sistent though out the stack show up in the median while a planet that is rotated within the
frames shows no sign in the median. The median is then subtracted from each raw image
leaving only the planet and the uncorrected component of the quasi-static noise. Now, the
stack can be derotated into the coordinate system and median-combined into a final output
image (Marois et al. 2006). Figure 5 shows the process of ADI image combination technique
in steps. However, median combining of stack of images left out lots of information about
the images. So, Lafreniere et al. (2007) developed a new combination method to combine
these images called LOCI.
3.4. Locally Optimized Combination of Images (LOCI)
LOCI is a more sophisticated version to perform the data combination in ADI. Instead
of subtracting one median background from all images in the series, an optimized background
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Fig. 5.— Figure represents the ADI image combination technique as described in the text.
Credit: C.Thalmann.
is constructed for each individual image on the basis of the others as a linear combination.
In addition, the images are divided into a concentric ring segment, and the optimization is
calculated for each segment separately (Lafreniere et al. 2007). Figure 6 shows the subsec-
tions LOCI uses to optimize and subtract. By doing so, we construct optimized corrected
images and combine them together to improve the signal to noise ratio of a planet.
4. Sample Data
In this paper, we have raw images from Subaru Telescope which is an 8-meter telescope
located in Mauna Kea, Hawaii. These raw images are used to discover GJ 504b which is one
of the latest directly observed exoplanets. The follow-up study also has a spectrum of the
planet, so that we can characterize the composition of its atmosphere and the effective tem-
perature of the planet (Kuzuhara et al. 2013). However, this paper only consider the process
of data reduction in order to see a planet from the raw images through many technique such
as dark and flat correction, angular differential imaging and LOCI.
GJ 504 is an important object for astrophysicists to study due to two reasons. First,
GJ 504 is a star with the spectrum type G which is the same spectrum type as the Sun.
This suggests that planets we found from GJ 504 will have many characteristics similar to
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Fig. 6.— Example of subtracting (shaded in gray) and optimization (delimited by thick lines)
subsection for LOCI. (Left) The subtraction and optimization area for the 1st subtraction
annuli. (Right) The subtraction and optimization area for the 13th subtraction annuli.
(Lafreniere et al. 2007).
the planets in our solar system. Second, GJ 504 is more aged, compared to the previous
discoveries of direct observed planets, implying that the star and its planetary system is less
evolution model dependence unlike other direct imaging planets where different evolution
models have a greater impact in the characteristic of a planet such as its mass.
Figure 7 shows one of many raw images in the series to find a planet. These images are
7-second exposure with a H filter and mask 0.3. First, all stack images are destriped due to
the detector systematic noise. Then, they are corrected using dark and flat field correction to
reduce image noise from long exposure time and remove all artifacts from variation between
pixel to pixel sensitivity of the sensor respectively. These images are also centered to the
central star is at the same position. After that, we inspect each image individually to remove
’bad’ images from the stack since they will affect the clarity of the final result.
Then, we construct the radial profile for the central star and each image are subtracted
by that radial profile to remove its brightness and reveal a planet. Once we have subtracted
images for each frame, we use LOCI subtraction for each frame individually and produce
a median combine of all LOCI subtracted frames. This combined image will be our final
result. Figure 8 shows the final image with the orange circle to indicate the location of a
planet that we found. However, this final image is not suitable for looking for a planet since
a planet’s signal is really faint and hard to distinguish from other noises. So, signal to noise
map of the final image is created to help find a planet. If the signal to noise ratio of any
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Fig. 7.— Figure shows a raw data of GJ 504 from Subaru Telescope without any filter.
object in the signal to noise map is higher than 5, we should carefully look more into that
object. We can confirm the existence of a planet by looking at its radial profile or its point
spread function (PSF). A planet and a star have fairly similar redial profile because both
are a point source from the perspective of the Earth while background noise and speckles do
not have the same radial profile as a planet or a star.
4.1. Direct Physical Parameter: A Seperation
The easiest physical parameter that we can measure once we found a planet is a sep-
aration between a planet and a star. We first measure a separation between the optical
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Fig. 8.— Figure shows a final result after the reduction process of ADI and LOCI from 48
series images. Orange circle indicates the location of a planet.
center of the planet and the central star in pixel number unit. In this case, the separation
between the planet and the star is 264 ± 12 pixels.1 And since a distortion-corrected plate
scale of High-Contrast Coronographic Image for Adaptive Optics (HiCIAO) is 9.500± 0.005
mas per pixel, the measured projected separation of the planet is 2.512 ± 0.043 arcsecond.
The projected separation of the planet in the discovery paper is reported to be 2.483±0.008
arcsecond, so the reported value is within the uncertainty of our measured value (Kuzuhara
et al. 2013).
1The uncertainty of the separation ∆r = r ×√
(∆x/x)2 + (∆y/y)2 where ∆x and ∆y are 4 pixels.
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We also know the distance from Earth to the star, which is 17.56 ± 0.08 pc or (3.622 ±0.017) × 106 AU (Kuzuhara et al. 2013). Therefore, the separation between the planet and
the star is 44.1 ± 0.8 AU which is greater than the furtherest planet in the solar system,
Neptune, at 30 AU.
5. Conclusion
In this paper, we learn different techniques implemented in the direct imaging techniques
of finding exoplanets such as adaptive optics and angular differential imaging. Then, we
found a planet, GJ 504b, from a raw data of the star GJ 504 provided from the Subaru
telescope by using ADI and LOCI pipeline to reduce the noise of the data in order to see a
planet.
The next step for astrophysicists is to discover the second Earth which is a planet with
the same characteristic with the Earth. Once we found the second Earth, we will be more
confident that we will discover life or even extraterrestrial intelligence on that planet. Several
national and international projects are proposed to discover the second Earth. For ground-
based telescope, the Thirty Meter Telescope (TMT) is being built at the Mauna Kea in
Hawaii with an advance adaptive optic. It is planned to finished in 2022. Terrestrial Planet
Finder (TPF) is proposed by NASA to build as a space telescope to find exoplanets. It would
include multiple small telescopes on separated spacecraft floating in precision formation to
simulate a much larger telescope by using interferometer. Unfortunately due to the lack of
funding, the project is deferred indefinitely and later reported as canceled. Nevertheless with
our next generation of telescope and instruments, we will find the second Earth and confirm
the existence of life outside the Earth.
The author thanks Prof. Motohide Tamura for discussion about direct imaging tech-
nique. In addition, the author thanks Mr. Nobuhiko Kusakabe for providing a pipeline for
ADI and LOCI and also raw data for GJ 504. Also, the author thanks Mr. Taichi Uyama
for the discussion about the materials about direct imaging and details about the pipeline.
Furthermore, the author thank to School of Science, the Univerity of Tokyo for the UTRIP
program that allows the author to come to Tokyo and conduct this research project. Finally,
the author thanks to Friends of UTokyo, Inc. (FUTI) for financially supporting the author
to work in Tokyo.
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This preprint was prepared with the AAS LATEX macros v5.2.