Extrasolar planets

Exoplanets
Monday, March 31, 2014

• Review Planet Formation Theory
• How are exoplanets discovered
• What has been learned about exoplanets

• Review Planet Formation Theory
• Snowline
• Core Accretion
• Migration

Water
Rock IronMethane

10 Marcy, Butler, Fischer, Vogt, Wright, Tinney and Jones
Fig. 6. The occurrence of exoplanets vs iron abundance [Fe/H] of the host star measured spectro-
scopically.21)
The occurrence of observed giant planets increases strongly with stellar metal-
licity. The solid line is a power law ﬁt for the probability that a star has a detected planet:
P(planet) = 0.03 × 102.0×[Fe/H]

• Review Planet Formation Theory:
• Snowline: Easier to form giants in outer solar system. Outer planets mostly
water, inner planets mostly rock & iron.
• Core Accretion
• Migration

2 Mordasini et al.
Figure 1. Time evolution of the mass of accreted planetesimals (solid line),
the mass of accreted gas (dotted line) and total mass of the planet (dashed
line), for initial conditions equivalent to the preferred model for the formation
of Jupiter in Pollack et al. (1996) (from Alibert et al. 2005a).

Fig. 4.—Time evolution of core mass (105, 106, and 107 yr), shown by sold lines, in the case of (a) fd ¼ 1 and (b) fd ¼ 10. Core mass is truncated by Mc;iso (top
panels) or by Mc;no iso (bottom panels), which are shown by the dashed lines. The jumps at 2.7 AU are caused by increase in solid materials due to ice condensation.
IDA & LIN396 Vol. 604

appropriate upper limit for masses of gas giants (Bryden et al.
1999).
weakened by the growth through giant impacts after the disk
depletion. The truncation conditions of the cores and gas do
Fig. 9.—Theoretically predicted distribution based on the core accretion model for gas giant planets (for the range of parameters we used, see text). Cores are
truncated by Mc;iso. Gas accretion is truncated by (a) Mg;iso, (b and c) Mg;th, and (d) Mg;vis. We adopt Áag ¼ 2rH in (a), the critical Hill radius rH;c being h and 1.5h in
(b) and (c), respectively, and ¼ 10À3
in (d). The green ﬁlled circles and the blue crosses represent rocky and icy planets with gaseous envelopes less massive than
their cores. The green and blue open circles represent gas-rich rocky and icy planets with gaseous envelopes that are 1–10 times more massive than their cores. The
red ﬁlled circles represent gas giants with envelopes more massive than 10 times their cores. For comparison, we also plot observational data of extrasolar planets in
(d). The dashed ascending lines correspond to radial velocity amplitude of 100 (upper line), 10 (middle line), and 1 m sÀ1 (lower line), assuming that the host star
mass is 1 M.
IDA LIN404 Vol. 604
• Core Accretion

water, inner planets mostly rock iron.
• Core Accretion: solid parts of planets glom quickly. If core gets large enough,
can start to attract gas. If enough gas is attracted, planet mass can run away.
• Migration

over a greater radial extent and the inward migration accelerates
with time. In all ﬁgures, we indicate the evolution of R with
asymptotic semimajor axis that is greater than 0.9 times that of
their initial semimajor axis a . Since planets that form with
Fig. 11.—Planetary migration obtained by integrating ˙ap with eqs. (65) and (68), shown by solid lines. Inside the thick dashed lines, ﬁnal semimajor axes reach
0.04 AU. They are greater than 0.9 times their original locations, outside the thick solid lines. Dashed lines express Rm. Time is scaled by mig at 1 AU (mig;1).
IDA LIN408 Vol. 604

• Migration: if disk is massive and long-lived, planets will exchange energy and
angular momentum with disk and move inwards.

• RadialVelocity
• Transits
• Microlensing

Newton’s Third Law
• For every force, there is an equal and opposite force
• If I push on you, you push on me
• If the Sun pulls on Jupiter, then Jupiter pulls on the
Sun

The wobble of stars can be used to
measure the mass of their planets
• We used the motion of Jupiter to measure the force
that the Sun exerts on Jupiter to measure the mass
of the Sun.
• We can use the (much smaller) motion of the Sun
to measure the force that Jupiter exerts on the Sun
to measure the mass of Jupiter.

Doppler Shift

Data from binary star,
not a planet, just to
illustrate the effect.
The wobble from a
planet is much smaller.

• RadialVelocity: Incredibly precise spectrograph on very apparently bright
(e.g., nearby) stars measures the mass and orbital parameters of planets. Mass
depends on (unknown) inclination.
• Transits
• Microlensing

(e.g., nearby) stars measures the mass and orbital parameters of planets.
• Transits
• Microlensing

Transit ofVenus

is capable of detecting a change in a star’s brightness equal to 20 ppm for stars that are more than
spots and other variations in the brightness of a star do not repeat consistently, especially over
Actual H-alpha image of the sun on the left, with a Jupiter transit superimposed to scale, as if viewed
from outside our solar system. The image of the sun on the right shows an Earth transit to scale.
is capable of detecting a change in a star’s brightness equal to 20 ppm for stars that are more than
spots and other variations in the brightness of a star do not repeat consistently, especially over
Actual H-alpha image of the sun on the left, with a Jupiter transit superimposed to scale, as if viewed
from outside our solar system. The image of the sun on the right shows an Earth transit to scale.
Its easier to ﬁnd big planets than small planets with transits

Transits can only ﬁnd close-in planets

Transits can only ﬁnd close-in planets or
edge on systems

FIG. 2.ÈTime series of the corrected intensity shown separately for
each of the four transits observed by HST , with successive transits o†set by
[0.006 for clarity. Note that, because the transit duration is almost two
HST orbits, complete temporal coverage was not obtained for any one
transit.
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it
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isMonday, March 31, 2014

-0.4 -0.2 0.0 0.2 0.4
Phase
0.99
1.00
1.01
1.08
1.10
nt
HAO UT 2012-02-20

Science data storage: about 2 months
Focal Plane Radiator
Sunshade
55º solar avoidance
Primary Mirror
1.4 m dia, ULE
Mounting Collet
Focal Plane:
42 CCDs,
100 sq deq FOV
4 Fine Guidance Sensors
Local Detector
Electronics:
clock drivers and
analog to digital converters
Schmidt Corrector
with 0.95 m dia
aperture stop
(Fused Silica)
Graphite Metering Structure
-Upper Housing
-Lower Housing
-Aft Bulkhead
Optical Axis

guidance CCDs in the corners.

faint for Kepler to observe the transits needed to detect Earth-size planets.
The Kepler Field of View

interiors of these planets, inflating their radii, and possibly pertur
ing other aspects of their interior structure, in ways that we do n
understand. One possibility that is currently the subject of debate
Transit
Gravitational tug of unseen
planets alters transit times
See thermal radiation from
planet disappear and reappear
Measure size of transiting
planet, see radiation from
star transmitted through the
planet’s atmosphere
Eclipse
Figure 2 | Geometry and science yield from transiting planets. During
transit, the fraction of stellar light blocked by the planet (shown black),
together with the detailed shape of the transit curve, yields the radius of boMonday, March 31, 2014

and heated
olecules H2,
CO and/or
ost spectro-
d to be the
here. Some
cm2 g–1
cm2 g–1
35 cm2 g–1
20 30
0.97
0.98
0.99
1.00
1.01
Relativeflux
–0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6
Orbital phase
0.999
1.000
1.001
1.002
1.003
Relativeflux
a
b

• Transits: Incredibly precise photometry measures the size and period.
• Microlensing

DISCUSSION
LENS-L1KE OF A STAR BY THE
DEVIATION OF LIGHT IN THE
GRAVITATIONAL FIELD
SOMEtime ago, R. W. Mandl paid me a visit and
asked me to publish the results of a little calculation,
which I had made at his request. This note complies
with his wish.
The light coming from a star A traverses the gravi-
tational field of another star B, whose radius is R,.
~~t there be an observer at a distance D from B and
at a distance z, small with D, from the ex-
tended central line =. According to the general
theory of relativity, let a, be the deviation of the light
ray passing the star B at a distance R, from its center.
-the sake let us assume that AB
is large, with the distance the
not decrease like 1/D, but like 1 / ~ 5 ,as the distance
D increases.
Of course, there is no hope of observing this phe-
nomenon directly. First, we shall scarcely ever ap-
proach closely enough to such a central line. Second,
the angle 6 will defy the resolving power of our
instruments. For, a, being of the order of magnitude
of One second of arc, the angle Bo/D, under which the
deviating star B is seen, is much smaller. Therefore,
the light coming from the luminous circle can not be
distinguished by an observer as geometrically different
from that coming from the star B, but simply will
manifest itself as increased apparent brightness of B.
The same will happen, if the observer is situated*
a small distance x from the extended central line AB.
But then the observer will see A as two point-like
light-sources, which are deviated from the true gee-
from the deviating star Be We also neglect the ecli~se metrical position of A by the angle @, approximately.
(geometrical obscuration) by the star B, which indeed
is negligible in all practically important cases. To
permit this, has to be Very large the
radius Ro of the deviating star.
It follows from the law of deviation that an observer
situated exactly on the extension of the central line
-AB will perceive, instead of a point-like star A, a
luminius circle of the angular radius @ around the
center of B, where
It should be noted that this angular diameter 6 does
The apparent brightness of A will be increased by
the lcns-like of the gravitational field of B in
the ,,tio q. This Will be considerably larger than
unity only if x is so small that the observed positions
of A and coincide, within the resolving power our
instruments. geometric lead
to the expression
x2
1-!-
I
q=-.- 21
where
ALBERT EINSTEIN
INSTITUTE FOR ADVANCED STUDY
PRINCETON, N.J.
Science, 1936

DISCUSSION
LENS-L1KE OF A STAR BY THE
DEVIATION OF LIGHT IN THE
GRAVITATIONAL FIELD
SOMEtime ago, R. W. Mandl paid me a visit and
asked me to publish the results of a little calculation,
which I had made at his request. This note complies
with his wish.
The light coming from a star A traverses the gravi-
tational field of another star B, whose radius is R,.
~~t there be an observer at a distance D from B and
at a distance z, small with D, from the ex-
tended central line =. According to the general
theory of relativity, let a, be the deviation of the light
ray passing the star B at a distance R, from its center.
-the sake let us assume that AB
is large, with the distance the
not decrease like 1/D, but like 1 / ~ 5 ,as the distance
D increases.
Of course, there is no hope of observing this phe-
nomenon directly. First, we shall scarcely ever ap-
proach closely enough to such a central line. Second,
the angle 6 will defy the resolving power of our
instruments. For, a, being of the order of magnitude
of One second of arc, the angle Bo/D, under which the
deviating star B is seen, is much smaller. Therefore,
the light coming from the luminous circle can not be
distinguished by an observer as geometrically different
from that coming from the star B, but simply will
manifest itself as increased apparent brightness of B.
The same will happen, if the observer is situated*
a small distance x from the extended central line AB.
But then the observer will see A as two point-like
light-sources, which are deviated from the true gee-
from the deviating star Be We also neglect the ecli~se metrical position of A by the angle @, approximately.
(geometrical obscuration) by the star B, which indeed
is negligible in all practically important cases. To
permit this, has to be Very large the
radius Ro of the deviating star.
It follows from the law of deviation that an observer
situated exactly on the extension of the central line
-AB will perceive, instead of a point-like star A, a
luminius circle of the angular radius @ around the
center of B, where
It should be noted that this angular diameter 6 does
The apparent brightness of A will be increased by
the lcns-like of the gravitational field of B in
the ,,tio q. This Will be considerably larger than
unity only if x is so small that the observed positions
of A and coincide, within the resolving power our
instruments. geometric lead
to the expression
x2
1-!-
I
q=-.- 21
where
Of course, there is no hope of observing
this phenomenon directly.
ALBERT EINSTEIN
INSTITUTE FOR ADVANCED STUDY
PRINCETON, N.J.
Science, 1936

Scott Gaudi, OSU

3440 3460 3480 3500
20
19
18
17
16
15
HJD - 2450000
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2005),
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only be
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caused
are hig
ﬁrst peMonday, March 31, 2014

Jennie McCormick
Housewife
Amateur Astronomer
Co-discoverer of over 20 planets

Meade LX200 ACF 14”f/10

tE , 2 days, the ten observed events are well above the model predic-
tions. The power-law and log-normal models predict 1.5 and 2.5
events with tE , 2 days, respectively, and the corresponding Poisson
probabilities for the ten observed events are 43 1026
and 3 3 1024
.
stars and brown dwarfs24
, and found that the resultant planetary-mass
function parameters are consistent with the above values (see the
Supplementary Information).
Thelensesfortheseshorteventscouldbeeitherfree-floatingplanetsor
4,290
3,900 4,000 4,100 4,200 4,300
MOA
OGLE
4,400
MOA–ip–3
tE = 1.88
u0 = 0.911
4,292 4,294
JD – 2,450,000
4,296 4,298 4,300
–0.1
0
ΔA
0.1
1
Magnification
1.4
1.2
1
Magnification
1.4
1.2
3,931
4,000 4,100 4,200
MOA
4,300 4,400
MOA–ip–10
tE = 1.19
u0 = 0.032
3,932
3,900
3,933 3,934
JD – 2,450,000
–0.2
0.2
ΔA
30
20
MagnificationMagnification
0
0
10
0
10
20
30
a b
Figure 1 | Light curves of event MOA-ip-3 and event MOA-ip-10. These
have the highest signal-to-noise ratio of the ten microlensing events with
tE , 2 days (see Supplementary Fig. 1 for the others). MOA data are in black
and OGLE data are in red, with error bars indicating the s.e.m. a, MOA-ip-3
light curve; b, MOA-ip-10 light curve. The green lines represent the best-fit
microlensing model light curves. For each event, the upper panel shows the full
two-year light curve, the middle panel is a close-up of the light-curve peak, and
the bottom panel shows the residuals from the best-fit model in units of the
magnification, DA. u0 indicates the source–lens impact parameter in units of
the Einstein radius. The second phase of MOA, MOA-II, carried out a very-
high-cadence photometric survey of 50 million stars in 22 bulge fields (of
2.2deg2
each) with a 1.8-m telescope at Mt John Observatory in New Zealand.
MOA detects 500–600 microlensing events during eight months observation
every year. In 2006–2007, MOA observed two central bulge fields every 10 min,
and other bulge fields with a 50 min cadence, which resulted in about 8,250 and
1,660–2,980 images, respectively. This strategy enabled MOA to detect very
short events with tE , 2 days. Since 2002, the OGLE-III survey has monitored
the bulge with the 1.3-m Warsaw telescope at Las Campanas Observatory,
Chile, with a smaller field-of-view but better astronomical seeing than MOA.
The OGLE-III observing cadence was 1–2 observations per night, but the
OGLE photometry is usually more precise and fills gaps in the MOA light
curves owing to the difference in longitude.
RESEARCH LETTER

• Transits: Incredibly precise photometry measures the size and period.
• Microlensing:Able to ﬁnd planets we can’t see around very distant stars,
especially at the Einstein Radius.

1990 1995 2000 2005 2010
10
3
100
10
First Publication Date
DistancetoStar[Parsecs]
exoplanets.org | 3/27/2014

1990 1995 2000 2005 2010
10
4
10
3
100
10
1
0.1
0.01
First Publication Date
PlanetMass[EarthMass]

NASA eyes app

Rep. Prog. Phys. 73 (2010) 016901
Figure 9. Planetary radii at 4.5 Gyr as a function of mass, from
0.1M⊕ to 20MJup. Models with solar metallicity (Z = 2%) and with
different amounts of heavy material (water, rock or iron) are shown
(Models from [19, 78]). The ‘rock’ composition here is olivine or
dunite, i.e. Mg SiO . Solid lines are for non-irradiated models.
the behavior of the mass–radius rel
Jupiter-like planets. The essential ph
shape of the relation was described in
Two competitive effects yield the
the M–R relationship around a few
regime, down to Earth masses, th
contribution from the classical ion
M+1/3
, characteristic of incompress
density increase, the effects of part
start to dominate over Coulomb effe
the M–R relation. Consequently,
at a critical mass which depends o
Reference [62] found a critical mass
to a maximum radius of ∼1RJup, f
under the assumption of zero-tem
recent calculations, based on impro
section 4.1, yield a critical mass ∼3
Figure 9 also illustrates the incr
on the planetary radius as mass decr
a substantial atmosphere (see secti
20M⊕ planet with 50% H2O is enhan
by a Sun at 0.045 AU [19]. For terr
radius relationship, derived from d
the same complex composition as
Rep. Prog. Phys. 73 (2010) 016901
Figure 9. Planetary radii at 4.5 Gyr as a function of mass, from
0.1M⊕ to 20MJup. Models with solar metallicity (Z = 2%) and with
different amounts of heavy material (water, rock or iron) are shown
(Models from [19, 78]). The ‘rock’ composition here is olivine or
dunite, i.e. Mg2SiO4. Solid lines are for non-irradiated models.
Dash–dotted curves correspond to irradiated models at 0.045 AU
from a Sun. The long-dashed curve, between 0.1M⊕ and 10M⊕, is
the mass–radius relationship for terrestrial planets, with detailed
structures and compositions characteristic of the Earth, after [76].
The positions of Mars, the Earth, Uranus, Neptune, Saturn and
Jupiter are indicated by solid points. Note that pure heavy material
planets (water, rock, iron) with masses 100M⊕ are unrealistic and
are only shown for illustrative purposes.
of models, covering a wide range of masses, including
the
Jupi
shap
Two
the
regi
con
M+1
den
star
the
at a
Ref
to a
und
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on t
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by a
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of wMonday, March 31, 2014

I Baraffe et al
s a function
Figure 2. Mass–radius diagram for transiting planets. The positionsMonday, March 31, 2014

1010.10.0110
-3
10
-4
PlanetMass[JupiterMass]
1 10 100
1
0.1
Orbital Period [Days]
PlanetaryRadius[JupiterRadii]

1 10 100 10
3
10
4
100
10
1
0.1
Planet Mass [Earth Mass]
PlanetaryDensity[Grams/Centimeters
3
]

v:1302.2147v3[astro-ph.EP]21May2013
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 22 May 2013 (MN LATEX style ﬁle v2.2)
Catastrophic Evaporation of Rocky Planets
Daniel Perez-Becker1
and Eugene Chiang2
1
Department of Physics, University of California at Berkeley, 366 LeConte Hall, Berkeley CA 94720-7300, USA
2
Departments of Astronomy and of Earth and Planetary Science, University of California at Berkeley, Hearst Field Annex B-20, Berkeley CA 94720-3411, USA
Submitted: 22 May 2013
ABSTRACT
Short-period exoplanets can have dayside surface temperatures surpassing 2000 K, hot enough
to vaporize rock and drive a thermal wind. Small enough planets evaporate completely. We
construct a radiative-hydrodynamic model of atmospheric escape from strongly irradiated,
low-mass rocky planets, accounting for dust-gas energy exchange in the wind. Rocky planets
with masses 0.1M⊕ (less than twice the mass of Mercury) and surface temperatures 2000
K are found to disintegrate entirely in 10 Gyr. When our model is applied to Kepler planet
candidate KIC 12557548b — which is believed to be a rocky body evaporating at a rate of
˙M 0.1 M⊕/Gyr — our model yields a present-day planet mass of 0.02 M⊕ or less than
about twice the mass of the Moon. Mass loss rates depend so strongly on planet mass that
bodies can reside on close-in orbits for Gyrs with initial masses comparable to or less than
that of Mercury, before entering a ﬁnal short-lived phase of catastrophic mass loss (which
KIC 12557548b has entered). Because this catastrophic stage lasts only up to a few percent
of the planet’s life, we estimate that for every object like KIC 12557548b, there should be
10–100 close-in quiescent progenitors with sub-day periods whose hard-surface transits may
be detectable by Kepler — if the progenitors are as large as their maximal, Mercury-like
sizes (alternatively, the progenitors could be smaller and more numerous). According to our
calculations, KIC 12557548b may have lost ∼70% of its formation mass; today we may be
observing its naked iron core.
Key words:
hydrodynamics – planets and satellites: atmospheres – planets and satellites: composition –
planets and satellites: physical evolution – planet-star interaction

for comparison.
2.4. Thermal structure
The interior structures may fall into three categories, depending on the
stellar distance, orbital history and atmospheric composition:
migration of the melt towards the upper ocean. The amount of melt pro-
duced by the internal heating in the kind of planet described in this Note is
on the order of 1 km thick layer per Myr at the interface. This is quite small
compared to the size of the ice layer. Consequently, the temperature proﬁle
in the ice mantle follows the solid/liquid transition curve, i.e., from 1150 K
at the silicate interface to the temperature at the bottom of the ocean.
Fig. 1. From left to right: (1) calculated internal structure of a 6M⊕ Ocean-Planet. Constituents are, from the centre to the outside, 1M⊕ metals, 2M⊕ silicates,
and 3M⊕ ice. The density (g cm−3) at the centre, different interfaces and top is: 19.5, 15.6–8.2, 6.2–3.9, and 1.54; gravity (g⊕): 0, 2.1, 1.96, and 1.54; pressure
(GPa): 1580, 735, 250, and ∼ 1. The upper layer is a ∼ 100 km thick ocean. The mean planetary density is 4.34 g cm−3; (2) idem for a rocky planet with the
same total mass (2M⊕ metals, 4M⊕ silicates). Density is: 21.0, 15.5–8.1, and 4.1; gravity: 0, 2.72, and 2.24; pressure: 2200, 745, and 0. The mean planetary
density is 7.74 g cm−3; (3) for comparison, the structure of the Earth calculated with the same model is shown. It agrees fairly well with the actual one. Density
is: 13, 9.5–5.2, 3.3; gravity: 0, 1.04, 1.00; pressure: 340, 130, 0. The mean planetary density is 5.57 g cm−3.

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