The document summarizes a study that measured the mass of the exoplanet Kepler-78b using radial velocity measurements from the HARPS-N spectrograph. The study found Kepler-78b has a mass of 1.86 Earth masses and a density of 5.57 grams per cubic centimeter, similar to Earth. This makes Kepler-78b the smallest exoplanet with accurately measured mass and radius, and the most similar to Earth in terms of its mass, radius, and density.

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An Earth-sized planet with an Earth-like density
Akinsanmi A. Babatunde
Department of Astronomy
University of Porto
Paper by Pepe et al (2014)
AST 4007, November 2015

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Outline
1 INTRODUCTION
2 MOTIVATION
3 METHODS
4 DATA AND ANALYSIS
5 RESULTS
6 DISCUSSION
7 CONCLUSION
8 REFERENCES

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Introduction
The Star Kepler-78 was identified in 2013 to be harbouring a
transiting planet of 1.16 times the size of the Earth with an
orbital period of only 8.5 hours.
While the exquisite Kepler photometry was able to determine
its radius and period, the mass of the planet (and thus its
mean density) remained unknown in the absence of precise
radial-velocity measurements
Here we present an accurate mass measurement of Kepler-78b
using the HARPS-N spectrograph, installed on the Telescopio
Nazionale Galileo (INAF) at the Roque de los Muchachos
Observatory, La Palma, Spain

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Earth-likeness
coutesy: hires-www.cfa.harvard.edu

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Motivation
A direct measurement of the mass of Kepler-78b would permit
an evaluation of its mean density and, by inference, its
composition.
Are Earth-sized planets indeed similar to the Earth in bulk
composition?

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Methods
Kepler Spacecraft, determines the size or radius of a planet by
the amount of starlight blocked when it passes (transits) in
front of its host star
To determine the planet’s mass, we employ the radial velocity
method to measure how much the gravitational tug of an
orbiting planet causes its star to wobble.

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Planet transit
Every 8.5 hours the star Kepler 78 presents to earth a shallow eclipse
consistent with the passage of an orbiting planet of radius 1.16 earth
radius.
Light curve recorded by Kepler spacecraft reveals the secondary
eclipse of the planet behind the star as well as the variations in
the light received from the planet as it orbits the star and presents
different hemispheres to the observer

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Radial Velocity

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Radial Velocity
As the planet orbits, its gravitational pull causes the parent
star to move back and forth. This tiny radial motion shifts the
observed spectrum of the star by a correspondingly small
amount because of the Doppler shift.
The shifts can be measured and used to infer details of a
planets mass and orbit
HARP-N instrument was used for this measurement

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Media
courtesy ESO/L. Calada

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Parameters
Acquiring HARPS-N spectra of 30-min exposure time and an
average signal-to-noise ratio of 45 per extracted pixel at
550nm. we estimated the stellar parameters of Kepler-78

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Parameters
The radial velocities show a scatter of 4.08ms−1and a
peak-to-trough variation of 22ms−1

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Parameters
Radial velocities (1.96ms−1) after removal of the stellar
components, plotted along with the best-fit Keplerian at the
planetary orbital period

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Signal
To separate this signal from that caused by the planet, we
proceeded to estimate the rotation period of the star from the
de-trended light curve from Kepler (Fig 3a). We obtain period
of 12.6 days.
The power spectral density (fig 3b) of the de-trended light
curve also shows strong harmonics at respective periods of 6.3
and 4.2 d.
We note that these timescales are much longer than the
orbital period of the planet.

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Light Curve

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Markov Chain Monte Carlo (MCMC) analysis

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Results
These new data yield a mass of 1.86 Earth masses. The
resulting mean density of the planet is 5.57 grams per cubic
centimetre, which is similar to that of the Earth and implies a
composition of iron and rock.
Kepler-78b, orbits a Sun-like star called Kepler 78 located in
the Cygnus constellation at a distance of about 400 light years
from us, is now the smallest exoplanet for which both the
mass and radius are known accurately.

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Results
In terms of mass, radius and mean density, Kepler-78b is the
most similar to the Earth among the exoplanets for which
these quantities have been determined. We plot the
mass-radius diagram

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Discussion
With a semi-major axis of 0.0089AU, how did this planet
come to be and what is its fate?

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conclusion
The observations of Kepler-78 have shown the potential of the
much anticipated HARPS-N spectrograph. It will have a
crucial role in the characterization of the many Kepler planet
candidates with radii similar to that of the Earth
By acquiring and analysing a large number of precise
radial-velocity measurements, we can learn whether
Earth-sized planets (typically) have Earth-like densities (and,
by inference, Earthlike compositions), or whether even small
planets have a wide range of compositions

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Reference
Sanchis-Ojeda, R. et al. Transits and occultations of an
Earth-sized planet in an 8.5-hour orbit. Astrophys. J. 774,
5462 (2013).
Zeng, L.Sasselov, D.A detailedmodel grid for solid planets
from0.1 through 100 Earth masses. Publ. Astron. Soc. Pacif.
125, 227239 (2013).
Lissauer, J. J. et al. All six planets known to orbit Kepler-11
have low densities. Astrophys. J. 770, 131145 (2013).

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