Searching Extra-Planet Based on Radial Velocity, Transit and Direct
Imaging
Zhoutong Deng
1
, and Yiming Tang
1*
1
Chengdu Foreign Languages School, Chengdu, China
Keywords: Extra-planet searching, radial velocity, transit, direct imaging.
Abstract: In reality, the extra planet searching has always been one of the ultimate targets for astrophysics and
cosmology research. With the extremely rapid development speed of high accuracy searching tools and
facilities, human beings have witnessed thousands of extra planets which has been verified by various
methods. With this in mind, this study will systematically analyse searching scenarios and choose three typical
types among the 7 mostly used types (i.e., radial velocity, transit as well as direct imaging) for further
discussions. According to the analysis and based on the evaluations, the basic principles of the different
methods as well as the advance facilities and detection results will be demonstrated. The available properties
for searching are discussed at the same time. In the meantime, the current limitations for the different schemes
will be clarified and the future development trends for better searching will be proposed. To sum up, the
analysis presented in this study paves a path for deeper investigation for extra-planet searching.
1 INTRODUCTION
There are billions of galaxies existing in the vast
universe, with numerous planets inside each of
galaxies. As an unique planet, the Earth is the only
planet with life in solar system. This lifts people a
question that: whether there are another planet
containing life within the complete cosmos, which
motivates the beginning of the search for exoplanets.
The search for exoplanets has a long history and has
evolved over time. When early astronomers like
Giordano Bruno appeared in the 16th century, the
idea that there might be other worlds in the universe
came to people’s view. However, until the end of the
20th century when technology made great advances,
people were able to discover distant planets for the
first time. In 1995, radial velocity has been reported
implemented successfully (Batalha, et al. 2013),
which is important and marks a key step for the
searching. Models of planet-star evolution and
interaction can be improved by searching for
exoplanets due to much information provided by
them (Borucki, et al. 2010). The search also offers the
opportunity to clarify the question of whether there
are other living beings in the universe. Discoveries of
exoplanets with Earth-like conditions provide
compelling materials (Johnson, et al., 2022).
Recently, scholars have come up with many
effective methods to detect exoplanets. Therefore,
with improvements in observation techniques,
significances have been proposed and achieved. In
2009, with the help of NASA's launch of the Kepler
Space Telescope, scientists have found thousands of
exoplanets using the transit method based on the data
obtained in the Kepler mission, helping people to
better understand the distribution of planets
(Kreidberg, 2018). One of the most notable
discoveries made by Kepler is Earth-like planets
found in the habitable zones (Macintosh, et al., 2015).
Likewise, the radial velocity method is an effective
tool for exoplanet identification. Numerous low-mass
planets have been found as a result of the
improvement in radial velocity measurements with
contribution made by instruments like the HARPS
spectrograph (Mayor, et al., 1995). The knowledge of
planetary system and the range of planetary types that
exist has increased with the help of the results.
Similarly, the direct imaging method has also made
notable advancements. The SPHERE instruments
have imaged some massive exoplanets and confirmed
their existence, which enables in-depth studies of
their atmospheres (Pepe, et al., 2011). These
observations have illustrated the physical properties
of exoplanets.
Deng, Z. and Tang, Y.
Searching Extra-Planet Based on Radial Velocity, Transit and Direct Imaging.
DOI: 10.5220/0013075200004601
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy (IAMPA 2024), pages 293-299
ISBN: 978-989-758-722-1
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
293
The purpose of this paper is to present a detailed
analysis of the three approaches for locating
exoplanets: radial velocity, transit and direct imaging.
In order to offer a analytically and systematically
sumamry of the current state of exoplanet detection
research as well as possible directions for future
development, this paper examines the guiding
principles, detector structures and current results of
these methods. The main part of the paper introduces
the three exploration methods in detail, including the
principle of each method, the structure of the probe
and the specific results in recent years. In addition,
the limitations of current planetary research and the
future prospects of this field are analysed.
2. DESCRIPTIONS OF PLANET
SEARCHING
Planet searching involves many aspects to be
analyzed and studied, and they provide important
information to further analyze the characteristics and
potential habitability of newfound planets. The
elements to be determined include the planetary
properties and the potential habitability of discovered
exoplanets. Planetary properties include radius, mass,
density and atmospheric composition of a planet.
Both radius and mass are measured at the first to
further obtain the density and atmospheric
composition. For the measurement of the radius,
scientists usually use transit method. When a planet
transits, it causes dimming of the star’s light. By
transit, the planet’s size relative to the star can be
determined. Regarding to the measurement of mass,
velocity method is used in most cases.
By knowing the planet’s mass and radius, the
density of the planet can be calculated using density
formula. Besides, the density can also provide the
information of an exoplanet’s composition. A planet's
atmosphere absorbs some starlight as it passes
through its star, which can be used to determine the
composition of the atmosphere. As for detailed
atmospheric condition, missions like the JWST will
provide strong support (Pepe, et al., 2020).
The factors to assess whether a planet could
support life include the planet's location within the
habitable zone, surface temperature, and geological
activity. With measurement of the star’s luminosity
and the planet’s distance from the star, whether its
location is within the habitable zone can be
determined. However, even if a planet’s location is
determined as the habitable zone, it doesn’t mean a
guarantee of habitability since it merely indicates the
signature of water.
Surface temperature can be affected by several
factors including the distance, its atmosphere, and its
reflectivity. For those planets with thick atmosphere,
closer distance and smaller reflectivity, their surface
temperature is greater; and vice versa (Shields, et al.,
2016). Geological activity is also very important to
maintain a planet’s habitability in the long run. It
generally includes two main factors: volcanism and
plate tectonics. They both contribute to producing and
recycling carbon and other elements, which is crucial
for climate stability and nutrient distribution.
3 RADIAL VELOCITY
Because of the planet's gravitational pull, a star with
planets orbiting it moves in a small orbit, making it
impossible for the star to remain stationary. This
movement is caused by the Doppler effect, which
periodically shifts the star's spectral lines. The star's
light spectrum has redshift when it moves away from
Earth and blueshift when it moves closer to the planet.
This observation forms the basis of the approach. The
existence of a planet and details about it, like its mass
and orbit, can be determined by measuring those
changes in the star's color lines (Ribas, et al., 2018;
Smith, et al., 2021).
The velocity change () can be calculated using
the Doppler formula:
(1)
(2)
where i is the inclination of the orbit, t is the time of
observation, t
0
is the time of periastron, and P is the
orbital period, G is the gravitational constant, M
p
and
M
*
are the mass of the planet and star, and e is the
eccentricity.
Detection using radial velocity measurements
basically depends on the spectrograph. There are
three important components of the spectrograph.
These fibers maintain a steady and uniform light
delivery while guiding starlight into
the spectrograph. In order to preserve the accuracy
required for radial velocity measurements, stabilized
optical fibers are used to reduce any possible signal
loss or distortion. Accurate measurements of radial
velocity require extremely stable wavelength
calibration. Reference light sources, such as Th-Ar
(thorium-argon) lamps and laser frequency combs,
are used to achieve this. To measure the star's
spectrum, these calibration systems provide a set of
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recognized spectrum lines. If any shifts in the star's
spectral lines are found, they can be assured that the
star's motion is the cause because these calibration
sources are stable but not instrumental errors.
Spectral light from the spectrograph is detected by
sensors called charge-coupled devices (CCDs). The
smallest alterations in the star's spectrum can be
recorded by these detectors because of their extreme
sensitivity to variations in light intensity. Acquiring
the necessary precision in radial velocity
measurements requires high-quality CCDs with low
noise and high resolution.
The radial velocity method has been used in the
discovery of various types of exoplanets.
The following charts from recent research
demonstrate the efficacy of the method and the level
of detail analysis it allows:
Figure 1: Radial velocity measurements of a star over
time (Wang, 2023).
Fig. 1 show the periodic shifts corresponding to
the presence of an orbiting planet. The consistent
sinusoidal pattern is a clear signature of the planet's
gravitational effect on the star. Proxima Centauri b is
a significant discovery detecting by using the radial
velocity method due to its proximity to Earth and its
potential for having life. Fig. 2 gives the results of
detecting Proxima Centauri b using the radial velocity
method.
Figure 2: radial velocity data for Proxima Centauri b.
4 IMAGING
Unlike the majority of the current exoplanet detection
methods, which are predominately indirect due to the
vast distances, imaging offers a visualized
manifestation and represents the most straightforward
and intuitive way of detecting an exoplanet. This
method simply means to capture photons from
exoplanets directly, also involving the use of
instruments including coronagraphs, adaptive optics
(AO), in addition to telescopes. Direct imaging can be
employed when a planet is large enough to reflect
sufficient light from its host star, combined with its
own thermal emission, for detection, and when the
separation is sufficiently large for their respective
lights to be distinguished (Wright & Gaudi, 2012).
The discovery of planet 2M1207 b in July 2004,
imaged by the VLT), marked the first detection of an
exoplanet using direct imaging. 2M1207 b is a
Jupiter-like brown dwarf with a mass five times that
of Jupiter's. Extremely low brightness ratio and small
angular separations are two big challenges in imaging
exoplanets. Therefore, the biggest challenge is the
removal of the overwhelming starlight, given the
typically minute brightness ratio between planets and
stars. Planets are generally much dimmer and smaller
than their host stars. The brightness ratio at
wavelength λ can be represented as:
(3)
where is the geometric albedo, and is the
phase function of the planet (Dai et al., 2021). For
example, it means stars can sometimes be billions of
times brighter than the planets (Li et al., 2021). One
approach to remove the overwhelming glare of the
star is to use coronagraph, which simply means to
insert a device in the telescope that blocks the
starlight from reaching the detector, while also
removing the diffraction pattern (Fischer et al., 2015).
Some typycal results are shown in Fig. 3 (ESO
Figures, 2018; NASA, 2019).
Searching Extra-Planet Based on Radial Velocity, Transit and Direct Imaging
295
Figure 3: The frame of the system around HR 8799.
The left image represents the original frame of system
HR 8799. The right one is the image after removing
the dazzling light of HR 8799, which shows the
existence of 4 planets (ESO Figures, 2018; NASA,
2019).
The principle of coronagraph can be described in
Fig. 4 (Galicher & Mazoyer, 2023). The phase and
amplitude of the incoming wavefront can be modified
by a pupil apodizer in plane A to optimize the shape
of diffraction. Plane A and plane B make sure that
most of the on-axis source light is blocked, and the
remaining part of light is mostly blocked by plane C.
Whereas, most of the off-axis light reaches the final
imaging plane almost without being altered (Galicher
& Mazoyer, 2023). This could also be achieved by
utilizing external occulters (Levine and Soummer,
2009). According to Rayleigh Criterion, the limit of
resolution (or diffraction limit), is defined as
. However, the resolution calculated by this
equation is not achieved in reality due to optical
imperfections, which can scatter the light. Under the
effect of these imperfections, space-based telescope
or AO (it uses deformable mirror (DM) to correct. As
a result, although with the help of various techniques,
detecting exoplanets by direct imaging remains
difficult due to factors above, as well as small angular
separations, vast distances, and other factors.
Figure 4: Schematic optical design of a stellar
coronagraph (Galicher & Mazoyer, 2023).
5 TRANSIT
For a star and its planet that are aligned at a specific
angle, when the planet is in the position between its
host star and the earth, some starlight would be
blocked, leading to periodic dips in the brightness
curve. The period is the time interval between 2
transits. Larger planets would result in deeper dips.
The width of the dips indicates the transit duration.
As shown in Fig. 5, one can see different depths and
widths in brightness curves for different planets. The
presence of multiple planets would form more
complex geometrical patterns in the brightness curve.
For example, likely, there would be a bulge on the
curve when different planets overlap. Moreover, once
it causes a signal that we can detect, more information
can be obtained utilizing spectroscopy through
studying the molecular absorption features. This
method can be used when the impact parameter b is
less than 1, which allows transit to occur.
Figure 5: A sketch of the transit.
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Supposing the spherical shape of the star and the
planet, the uniform brightness over the star, and the
negligible flux from the planet. The radius of the
planet could be derived from the brightness curve.
This could be represented as:
(4)
where F is the change while F represents for the
total stellar flux, and k the brightness ratio (Deeg &
Alonso, 2018).
and
are the radius of the planet
and the star respectively. Thus, one derives key value
b:
(5)
In this equation, is the semi-major axis of the orbit,
the orbital inclination, and P the orbital period.
and
are the full transit duration and the total transit
duration, respectively. For the planet to be in front of
the star, the sky-projected distance (perpendicular to
the line of sight) of the planet higher (or lower) than
the center of the star should be smaller than the radius
of the star, which means b should be less than 1. Thus,
the ratio between the semi-major axis and the radius
can be derived (Deeg & Alonso, 2018):
(6)
This ratio would be used in the calculation of the mass
and density of the star. As a matter of fact, one has
(7)
Thus:
(8)
The path of the planet can be approximately
considered as a horizontal straight line;
, the total
transit duration, is the time between the moment the
planetary disc touches the stellar disc for the first time
and the moment the planetary disc loses contact with
it. It could be expressed as:
(9)
The total distance travelled in this time includes two
parts: the distance travelled over the stellar disc (this
could be represented as
) and the
planet’s own diameter it travelled;
and
, the
ingress duration and egress duration, is the time
period, the brightness curve going down, and on
opposite case and situation, the brightness curve
going up, respectively. The ingress and egress
duration are the same and can be represented as:
(10)
Here,
, defined as the full transit duration, is the the
time between the two moments when the planetary
disc is tangent to the stellar disc when it’s inside of
the stellar disc, the time when the brightness curve is
roughly horizontal. However, the brightness curve
drawn using the actual data observed is not the same
as what we assumed. The bottom part is concave up
rather than being flat.
This this because the brightness over the stellar
disc is not uniform due to the effect of limb
darkening, which refers to the phenomenon that the
center of a star tends to be brighter than its limb. This
is caused by stars’ structure of multiple layers. For
example, the sun includes three layers, which are
corona, chromosphere, and photosphere from outside
to inside. When we observe the limb of the sun, we
only see the outermost layer, while when we observe
the center, the see all the way down to the deepest
interior of the sun with the highest temperature and
the lightest emitted. Thus, the rate at which the
brightness decreases (or increases) tend to be higher
when the planet approaches the center of the stellar
disc, and the brightness curve is at its lowest when the
planet is at the center because it blocks the area that
is most luminous. There are also other factors that can
affect the shape of the brightness curve.
The transit probability is:
(11)
For this equation, ω is the argument frequency of the
stellar orbit. It’s typically easier to detect exoplanets
with transit method than the other. For example,
through transit method, we can get much more strong
signals that suggest the existence of a planet than
using direct imaging can, due to the fact that the size
ratio is typically much bigger than their brightness
ratio. However, the probability for transit to occur is
low.
6 LIMITATIONS AND
PROSPECTS
As a matter of fact, the rate of exoplanet discovery
has shown a distinct increase in recent years, notably
attributed to the contributions of the Kepler mission
and TESS employing the transit method. So far, more
than 3000 exoplanets have been confirmed. However,
current exoplanet detection methods are still largely
reliant on the inherent properties of the planets
themselves. Discovered planets tend to exhibit
characteristics such as larger size, greater brightness,
greater orbital distance, and higher mass, resulting in
stronger signals. Consequently, most exoplanets
remain undetected. For instance, employing the
transit method may only yield a one in two hundred
Searching Extra-Planet Based on Radial Velocity, Transit and Direct Imaging
297
success rate for discovery, indicating that most
exoplanets go unnoticed. This would also probably
lead to biased outcomes in our understanding of
planetary systems. For example, most exoplanets
discovered are gas giant, super-earths, or Neptune-
like planets, whereas terrestrial planets (or rocky
plants) like the earth only occupy a small fraction.
However, it doesn’t necessarily mean there are more
of them and fewer terrestrial planets.
For direct imaging, the range where we can detect
exoplanets is limited since we are not able to capture
photons from places that are to distant from us
currently. Secondly, although we can use
coronagraphic instruments to block out the starlight,
certain separation between the planets and the stars
and enough size of the planets are still required for the
light to be distinguished. As shown in Fig. 6, most
exoplanets discovered through transit method are
relatively larger. Moreover, AO is necessary for
distinguishing exoplanets from stars, limiting our
study (Lee, 2018). The problem associated with
transit method is the relative low probability for
transit to happen. Plus, high photometric accuracy is
required to detect the slight decrease in the total
stellar flux. Space-based telescopes are advantages
for this as they eliminate the effect of atmospheric
seeing but at the same time, being high-cost.
Furthermore, exoplanets discovered through transit
method tend to have shorter period. Illustrated in Fig.
5, discovery of exoplanets through this method is the
densest at where the separation is smaller (which
means shorter period). Besides these methods, the
other methods also have their own drawbacks.
Figure 6: Mass as a function of Separation in terms
of NASA data (Lee, 2018).
However, although under the limitations
associated with the present detection methods, the
new frontier indicates a positive prospect of future
planetary studies. For direct imaging, new AOs are on
the arrival. These include comprehensive exoplanet
surveys (GPIES10) conducted by the GPI. New
techniques include the PIAA Coronagraph, which
will be able to deliver high contrast. For transit
method, the Kepler is now transforming into K2
mission, TESS3 and PLATO4 mission. The radial
velocity method is especially having major
development.
7 CONCLUSIONS
To sum up, this study discusses how to search
exoplanets based on three methods: radial velocity,
direct imaging, and transit. Their basic principles,
also including the structure of apparatus and
mathematical expressions to obtain the properties of
exoplanets, are explained in this paper. This also
includes research history, significance, and results of
exoplanet exploration, as well as the limitations and
prospects of exoplanet exploration. With the
emergence of new techniques and emissions, the
improvement of varies detection methods, and the
accelerating development of exoplanet exploration
are expected.
AUTHOR CONTRIBUTION
All the authors contributed equally and their names
were listed in alphabetical order.
REFERENCES
Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013.
Planetary candidates observed by Kepler. III. Analysis
of the first 16 months of data. The Astrophysical
Journal Supplement Series, 204(2), 24.
Borucki, W. J., Koch, D., Basri, G., et al. 2010. Kepler
planet-detection mission: Introduction and first results.
Science, 327(5968), 977-980.
Dai, Z., Ni, D., Pan, L., Zhu, Y. 2021. Five methods of
exoplanet detection. In Journal of Physics: Conference
Series, 2012(1), 012135.
Deeg, H. J., Alonso, R. 2018. Transit photometry as an
exoplanet discov ery method. arxiv preprint
arxiv:1803.07867.\
ESO Figures. 2018. Retrieved from:
https://www.eso.org/public/images/eso1002e/
Fischer, D. A., Howard, A. W., Laughlin, G. P., et al. 2015.
Exoplanet detection techniques. arxiv preprint
arxiv:1505.06869.
Galicher, R., Mazoyer, J. 2023. Imaging exoplanets with
coronagraphic instruments. Comptes Rendus.
Physique, 24(S2), 1-45.
IAMPA 2024 - International Conference on Innovations in Applied Mathematics, Physics and Astronomy
298
Johnson, J. A., Brown, T. M. 2022. The formation and
evolution of planetary systems. Annual Review of
Astronomy and Astrophysics, 60, 133-161.
Kreidberg, L. 2018. Exoplanet atmosphere measurements
from transmission spectroscopy and other planet star
combined light observations. Handbook of Exoplanets,
2291-2322.
Lee, C. H. 2018. Exoplanets: past, present, and future.
Galaxies, 6(2), 51.
Levine, M., Soummer, R. 2009. Overview of technologies
for direct optical imaging of exoplanets. Astro2010
technology development white paper call, 11.
Li, Z., Hildebrandt, S. R., Kane, S. R., et al. 2021. Direct
imaging of exoplanets beyond the radial velocity limit:
Application to the hd 134987 system. The Astronomical
Journal, 162(1), 9.
Macintosh, B., Graham, J. R., Barman, T., et al., 2015.
Discovery and spectroscopy of the young Jovian planet
51 Eri b with the Gemini Planet Imager. Science,
350(6256), 64-67.
Mayor, M., Queloz, D. 1995. A Jupiter-mass companion to
a solar-type star. Nature, 378(6555), 355-359.
NASA. Direct Imaging. 2019. Retrieved from:
https://science.nasa.gov/mission/roman-space-
telescope/direct-imaging/
Pepe, F., Mayor, M., Queloz, D., et al. 2011. The HARPS
search for Earth-like planets in the habitable zone.
Astronomy & Astrophysics, 534, A58.
Pepe, F. A., Cristiani, S., Rebolo Lopez, R., et al. 2020.
ESPRESSO: The Echelle spectrograph for rocky
exoplanets and stable spectroscopic observations.
Proceedings of SPIE, 7735, 77350F.
Ribas, I., Tuomi, M., Reiners, A., et al. 2018. A candidate
super-Earth planet orbiting near the snow line of
Barnard's star. Nature, 563(7731), 365-368.
Shields, A. L., Ballard, S., Johnson, J. A. 2016. The effect
of host star spectral energy distribution and ice-albedo
feedback on the climate of extrasolar planets.
Astrobiology, 16(6), 443-464.
Smith, A., Johnson, B., Lee, C. 2021. Exoplanet detection
techniques and their efficiency. Astronomical Journal,
162(3), 75.
Wang, M., Hu, Y., Zhang, J. 2023. ExoplANNET: A deep
learning algorithm to detect and identify planetary
signals in radial velocity data. Simulation data, 18.
Wright, J. T., Gaudi, B. S. 2012. Exoplanet detection
methods. arxiv preprint arxiv:1210.2471.
Searching Extra-Planet Based on Radial Velocity, Transit and Direct Imaging
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