2012 Vol. 12 No. 8, 1081–1106

11institutetext:  Department of Astronomy and Key Laboratory of Modern
Astronomy and Astrophysics in Ministry of Education, Nanjing
University,Nanjing 210093, China<EMAIL_ADDRESS>
Received 2012.7.9; accepted 2012.7.17

# Forming Different Planetary Systems

Ji-Lin Zhou  Ji-Wei Xie  Hui-Gen Liu  Hui Zhang  Yi-Sui Sun

###### Abstract

With the increasing number of detected exoplanet samples, the statistical
properties of planetary systems have become much clearer. In this review, we
summarize the major statistical results that have been revealed mainly by
radial velocity and transiting observations, and try to interpret them within
the scope of the classical core-accretion scenario of planet formation,
especially in the formation of different orbital architectures for planetary
systems around main sequence stars. Based on the different possible formation
routes for different planet systems, we tentatively classify them into three
major catalogs: hot Jupiter systems, standard systems and distant giant planet
systems. The standard system can be further categorized into three sub-types
under different circumstances: solar-like systems, hot Super-Earth systems,
sub-giant planet systems. We also review the planet detection and formation in
binary systems as well as planets in star clusters.

###### keywords:

Planetary systems: dynamical evolution and stability—formation—planet-disk
interactions—stars: binary: general—clusters: general

INVITED REVIEWS

##  1 Introduction

Since the discovery of a giant planet by radial velocity measurements in 51
Peg by Mayor & Queloz (1995), as well as the planets around 47 UMa and 70 Vir
(Butler & Marcy 1996; Marcy & Butler 1996), the new era of detecting
exoplanets around main sequence stars was opened at the end of last century.
Now exoplanet detection has become one of the most rapidly developed area.
With the development of measurement techniques, the precision of radial
velocity(RV) can be better than 0.5 $ms^{-1}$ with the HARPS spectrograph at
La Silla Observatory (Mayor et al. 2003), making possible to detect Earth-
sized planets in close orbits around bright stars. The detection of transiting
signals when exoplanets pass in front of their host stars has become another
powerful method in searching for planet candidates, especially after the
successful launch of CoRoT and Kepler . The unprecedented high precision of
photometric observation ($\sim 10$ppm) and long-duration continuous
observation (up to years) achieved by space missions make transits an ideal
tool to detected near-Earth-sized planets around solar type stars.

To date, around 780 exoplanets have been detected mainly by RV measurements,
with more than 100 multiple planet systems 111http://exoplanet.eu/,and
hereafter for all RV based statistics in the paper.. The first 16 months’
observation of the Kepler mission revealed more than 2321 transit candidates,
with 48 candidates in the habitable zone of their host
stars222http://kepler.nasa.gov/,and hereafter in the paper (Borucki et al.
2011; Batalha et al. 2012; Fabrycky et al. 2012).

The study of planet formation can be traced back to the 18th century, when E.
Swedenborg, I. Kant, and P.-S. Laplace developed the nebular hypothesis for
the formation of the solar system. At that time the solar system was the only
sample of a planetary system. The architecture of the solar system implied
that it was formed in a Keplerian disk of gas and dust (for reviews, see
Wetherill 1990; Lissauer 1995; Lin & Papaloizou 1996). With the discovery of
more exoplanet systems, planet formation theory has developed dramatically.
For example, the discovery of hot Jupiters(HJs) stimulated the classical
migration theory of planets embedded in the proto-stellar disk (Lin &
Papaloizou 1986, 1996), the moderate eccentricities of exoplanet orbits remind
us the planet-planet scattering(hereafter, PPS) theory (Rasio & Ford 1996),
and the observation of some HJs in retrograde orbits extends the classical
Lidov-Kozai mechanism to eccentric cases (Kozai 1962; Lidov 1962; Naoz et al.
2011b). Through population synthesis, N-body and hydrodynamical simulations,
the planet formation processes have been well revealed but are still far from
fully understood.

In this paper, we focus on recent processes in the theory of detection and
formation of solar type stars, either around single stars (§2), binary
stars(§3), or in star clusters (§4).

##  2 Planets around single stars

###  2.1 Overview of Observations

####  2.1.1 Planet Occurrence Rate

The occurrence rate of gas-giant exoplanets around solar-type stars has been
relatively well studied. Tabachnik & Tremaine (2002) fitted 72 planets from
different Doppler surveys, and found a mass ($M$)-period ($P$) distribution
with the form of a double power law,

$dN\propto M^{\alpha}P^{\beta}dlnMdlnP,$ (1)

after accounting for selection effects. They obtained $\alpha=-0.11\pm 0.1$,
and $\beta=0.27\pm 0.06$. Recently, Cumming et al. (2008) analyzed eight years
of precise RV measurements from the Keck Planet Search, including a sample of
585 chromospherically quiet stars with spectrum types from F to M. Such a
power-law fit in equation (1) for planet masses $>0.3M_{J}$ (Jupiter Mass) and
periods $<2000$ days was re-derived with $\alpha=-0.31\pm 0.2$, and
$\beta=0.26\pm 0.1$. They concluded $10.5\%$ of solar type stars have a planet
with mass $>0.3M_{J}$ and period $2-2000$ days, with an extrapolation of
$17-20\%$ of stars having gas giant planets within 20 AU.

Based on the 8-year high precision RV survey at the La Silla Observatory with
the HARPS spectrograph, Mayor et al. (2011) concluded that 50% of solar-type
stars harbor at least one planet of any mass and with a period up to 100 days.
About 14% of solar-type stars have a planetary companion more massive than
$50M_{\oplus}$ in an orbit with a period shorter than 10 years. The mass
distribution of Super-Earths and Neptune-mass planets is strongly increasing
between 30 and $15M_{\oplus}$, indicating small mass planets are more frequent
around solar type stars.

Howard et al. (2010) calculated the occurrence rate of close planets (with
$P<50$ days), based on precise Doppler measurements of 166 Sun-like stars.
They fitted the measures as a power-law mass distribution,

$df=0.39M^{-0.48}d\log M,$ (2)

indicating an increasing planet occurrence with decreasing planet mass. It
also predicted that 23% of stars harbor a close Earth-mass planet, ranging
from 0.5 to 2.0 $M_{\oplus}$ (Earth mass).

With 12 years of RV data with long-term instrumental precision better than
$3ms^{-1}$, the Anglo-Australian Planet Search targets 254 stars, and
estimates an occupance rate of 3.3% of stars hosting Jupiter analogs, and no
more than 37% of stars hosting a giant planet between 3 and 6 AU(Wittenmyer et
al.  2011a). Their results also reveal that the planet occurrence rate
increases sharply with decreasing planetary mass. In periods shorter than 50
days, they found that 3.0% of stars host a giant ($m\sin i>100M_{\oplus}$)
planet, and that 17.4% of stars host a planet with ($m\sin i<10M_{\oplus}$)
(Wittenmyer et al.  2011b). Moreover, the lack of massive planets $(>8M_{\rm
Jup})$ beyond 4 AU was reported in Boisse et al.  (2012), although with less
than 20 RV detected candidates at the moment. Such a distribution agrees with
population synthesis (Mordasini et al. 20012) , where they showed that a
decrease in frequency of massive giant planets at large distance ($\geq$ 5AU)
is a solid prediction of the core-accretion theory.

Transit observations from the Kepler spacecraft give qualitatively similar
results. Howard & Marcy (2011) checked the distribution of planets in close
orbits. For $P<50$ days, the distribution of planet radii ($R$) is given by a
power law,

$df=k(R/R_{\oplus})^{\alpha}d\log R$ (3)

with $k=2.9^{+0.5}_{-0.4}$ and $\alpha=-1.92\pm 0.11$, and $R_{\oplus}$ is the
Earth radius. They find the occurrence of $0.130\pm 0.008$, $0.023\pm 0.003$,
and $0.013\pm 0.002$ planets per star for planets with radii $2-4$, $4-8$, and
$8-32R_{\oplus}$ respectively.

The rapid increase of planet occurrence with decreasing planet size indicates
the presence of Super-Earth and Neptune size cases are quite common. Although
this agrees with the prediction of the conventional core-accretion scenario,
it conflicts with the results predicted by the population synthesis models
that a paucity of extrasolar planets with mass in the range $10-100M_{\oplus}$
and semi-major axis less than 3 AU are expected, the so called ’planet desert’
(Ida & Lin 2004).

####  2.1.2 Stellar masses of planet hosting stars

Kepler results also revealed a correlation between the planet’s occurrence
with the effective temperature ($T_{\rm eff}$) of host stars (Howard & Marcy
2011). The occurrence rate $f$ is inversely correlated with $T_{\rm eff}$ for
small planets with $R_{p}=2-4R_{\oplus}$, i.e.,

$f=f_{0}+k(T_{\rm eff}-5100K)/1000K,$ (4)

with $f_{0}=0.165\pm 0.011$ and $k=-0.081\pm 0.011$. The relation is valid
over $T_{\rm eff}=3600-7100K$, corresponding to stellar spectral typed from M
($\leq 0.45M_{\odot}$, solar mass)to F($1.4M_{\odot}$). This implies that
stars with smaller masses tends to have small size planets.

However, the occurrence of planets with radii larger than $4R_{\oplus}$ from
Kepler does not appear to correlate with $T_{\rm eff}$ (Howard & Marcy 2011).
This is in contrast with the observation by RV measurements. In fact, a much
lower incidence of Jupiter-mass planets is found around M dwarfs (Butler et
al. 2006; Michael et al. 2006; Johnson et al. 2007), and higher mass stars are
more likely to host giant planets than lower-mass ones (e.g., Lovis & Mayor
2007; Johnson et al. 2007, 2010; Borucki et al. 2011). The result is
compatible with the prediction in the core accretion scenario for planet
formation (Laughlin et al. 2004; Ida & Lin 2005; Kennedy & Kenyon 2008).

####  2.1.3 Metallicity Dependence

It has been well-established that more metal-rich stars have a higher
probability of harboring a giant planet than their lower metallicity
counterparts (Gonzalez 1997; Santos et al. 2001, 2004; Fischer & Valenti 2005;
Udry & Santos 2007; Sozzetti et al. 2009; Sousa et al. 2011). The occurrence
rate increases dramatically with increasing metallicity. Based on the CORALIE
and HARPS samples, around 25% of the stars with twice the metal content of our
Sun are orbited by a giant planet. This number decreases to $\sim 5\%$ for
solar-metallicity cases (Sousa et al. 2011; Mayor et al. 2011). Recently,
Mortier et al. (2012) showed the frequency of giant planets is
$(f=4.48^{+4.04}_{-1.38}\%)$ around stars with $[Fe/H]>-0.7$, as compared with
$f\leq 2.36\%$ around stars with $[Fe/H]\leq-0.7$. Curiously, no such
correlation between planet host rate and stellar metallicity is observed for
the lower-mass RV planets, and the stars hosting Neptune-mass planets seem to
have a rather flat metallicity distribution (Udry et al. 2006; Sousa et al.
2008, 2011; Mayor et al. 2011).

By re-evaluating the metallicity, Johnson et al. (2009) find that M dwarfs
with planets appear to be systematically metal rich, a result that is
consistent with the metallicity distribution of FGK dwarfs with planets.
Schlaufman & Laughlin (2011) find that star hosting Kepler exoplanet
candidates are preferentially metal-rich, including the low-mass stars that
host candidates with small-radius , which confirms the correlation between the
metallicity of low-mass stars and the presence of low-mass and small-radius
exoplanets.

Figure 1: Distribution of exoplanets detected by RV measure(left,
http://exoplanet.eu/), and candidates by the Kepler mission (right,
http://kepler.nasa.gov/).

####  2.1.4 Mass and Period Distributions

Figure 1 shows the distribution of planetary orbital periods for different
mass regimes. 705 planets detected by RV measurement and 2320 candidates
revealed by the Kepler mission are included. Several features of the mass-
period distribution have been well known and widely discussed in the
literatures. However, it seems that the distribution features from RV detected
exoplanets are slightly different from those of Kepler candidates.

  * •

All kinds of RV planets show a ”pile-up” at orbital periods 2-7 days (e.g.,
Gaudi et al. 2005; Borucki et al. 2011), while Kepler results show that
Jupiter-size ($>6R_{\oplus}$) candidates are more or less flat up to orbits
with $>100$ days; Neptune-size ($2M_{\oplus}<R_{p}<6R_{\oplus}$) and super-
Earth candidates ($1.25M_{\oplus}<R_{p}<2R_{\oplus}$) peak at $10-20$days.
Both of them are more abundanct relative to Jupiter-size candidates in the
period range from one week to one month(Borucki et al. 2011). Extrapolating
the distribution by considering the $(R_{p}/a)$ probability of a transiting
exoplanet could extend these peaks to a bit more distant orbits. Earth size or
smaller candidates($<1.25M_{\oplus}$) show a peak of $\sim 3$ days .

  * •

RV planets show a paucity of massive planets ($M>1M_{J}$) in close orbits
(Udry et al. 2002, 2003; Zucker & Mazeh 2002; Zucker& Mazeh 2003), and a
deficit of planets at intermediate orbital periods of $10-100$ days (Jones et
al. 2003; Udry et al. 2003; Burkert & Ida 2007). However, this is not obvious
as Kepler results show at least several tens of candidates with the radius
lying in the $10-20R_{\oplus}$ line within 10-day orbits, and the distribution
extending to 100 days is rather flat. (Fig.1). The lack of all types of
planets with orbital periods $\sim 10-1000$ days observed by RV is clear, but
from Kepler results, the lack of planets with period $>100$ days is also
shown, possibly due to the observational bias (Fig.1). RV observations from
the Anglo-Australian Planet Search indicate that, such a lack of giant planets
($M>100M_{\oplus}$) with periods between 10 and 100 days is indeed real.
However, for planets in the mass range $10-100M_{\oplus}$, the results suggest
that the deficit of such planets may be a result of selection effects
(Wittenmyer et al.  2010).

###  2.2 Hot Jupiter Systems

The HJ class is referred to a class of extrasolar planets and has mass close
to or exceeding that of Jupiter ($M_{p}\geq 0.1M_{J}$, or radius $\geq
8R_{\oplus}$ for densities of $1.4{\rm g/cm^{3}}$, a typical value of gas
giants with small rocky cores), with orbital peroids $\leq 10$ days (or
$a<0.1$ AU) to their parent stars (Cumming et al. 2008; Howard & Marcy 2011;
Wright et al. 2012). According to this definition, the RV exoplanets have 202
HJs, while Kepler candidates have 89 HJs. HJs are notable since they are easy
to detecte either by RV or by transit measurements. For example, the first
exoplanet discovered around 51 Peg was such a close-in giant planet(Mayor &
Queloz 1995). Transiting HJs also give us information about their radii, which
is crucial for understanding their compositions(e.g., Fortney et al. 2003;
Sara & Drake 2010 ). However, with the increase of RV precision and the number
of detected exoplanets, HJs are found to be in fact rare objects (e.g.,
Cumming et al. 2008; Wright et al. 2012). More interestingly, some HJs were
observed in orbits that are retrograde with respect to the spin direction of
their host stars(e.g., Winn et al. 2010), indicating that their formation
process might have been quite different with that of our solar system.

####  2.2.1 Occurrence rate and distributions

Marcy et al. (2005a) analyzed 1330 stars from the Lick, Keck, and Anglo-
Australian Planet Searches, and the rate of HJs among FGK dwarfs surveyed by
RV was estimated to be $1.2\pm 0.1\%$. Mayor et al. (2011) used the HARPS and
CORALIE RV planet surveys and found the occurrence rate for planets with
$M\sin i>50M_{\oplus}$ and $P\leq 11$ days is $0.89\pm 0.36\%$. Recently,
Wright et al. (2012) used the California Planet Survey from the Lick and Keck
planet searches, and found the rate to be $1.2\pm 0.38\%$. These numbers are
more than double the rate reported by Howard & Marcy (2011) for Kepler stars
($0.5\pm 0.1\%$) and the rate of Gould et al. (2006) from the OGLE-III transit
search. The difference might be, as pointed out by Wright et al. (2012), that
transit surveys like OGLE and Kepler (centered at galactic latitude
$b=+13.3^{o}$) probe a lower-metallicity population, on average, than RV
surveys.

Previous RV measurements show that, there is a sharp inner cutoff in the three
day pileup of HJs. They appear to avoid the region inward of twice the Roche
radius (Ford& Rasio 2006), where the Roche radius is the distance within which
a planet would be tidally shredded. However, recent RV detected exoplanets and
Kepler candidates indicate the presence of more than 200 exoplanet and
candidates within 3-day orbits, with the inner most orbital peroid being 0.24
days for system KOI-55, corresponding to a location close to its Roche radius
(Fig.1).

Also, RV detected HJs appear to be less massive than more distant planets
(Pätzold& Rauer 2002; Zucker & Mazeh 2002). For planets discovered with the RV
method, close planets have projected masses ($M\sin i$) less than twice
Jupiter’s mass. But numerous planets farther out have $M\sin i>2M_{J}$ ( Udry
& Santos 2007).

####  2.2.2  Spin-Orbit misalignment

One of the most fascinating features for HJs is that, some HJs have orbits
that are misaligned with respect to the spin of their host stars(Winn et al.
2010; Triaud et al. 2010). The sky-projected angle between the stellar spin
and the planet’s orbital motion can be probed with the Rossiter-McLaughlin
(RM) effect (Rossiter 1924; McLaughlin 1924). To date, the RM effect has now
been measured for at least 47 transiting exoplanets (see Winn et al. 2010,
Table 1 for a list of 28 planets, and Brown et al. (2012), Table 5 for a list
of 19 additional planets, and references therein). Only 7 (HAT-P-6b,HAT-P-7b,
HATP-164b, WASP-8b,WASP-15b,WASP-17b,WASP-33) of the 47 samples have projected
angles above $90^{o}$, indicating a ratio of $\sim 15\%$ that are in
retrograde motion. It is still not clear what type of stars could host HJs in
retrograde orbits. Winn et al. 2010 showed that the stars hosting HJs with
retrograde orbits might have high effective temperatures ($>6250$ K). The
underlying physics remans further study.

####  2.2.3 Lack of close companions

Few companion planets have been found in HJ systems within several AU (Wright
et al. 2009; Hébrard etal. 2010). To date, only six RV detected planetary
system have multiple planets with the inner one being HJs (HIP14810, ups And,
HAT-P-13,HD187123, HD21707, HIP 11952 ). Compared to the total number of 89 RV
detected HJs, the ratio is less than $7\%$. Interestingly, all these planetary
companions are in orbits with periods $>140$ days. This relative deficit also
shows up in the transit samples, where most attempts at detecting transit
timing variations caused by close companions have been unsuccessful (Holman&
Murray 2005; Agol et al. 2005; Rabus etal. 2009; Csizmadia etal. 2010;
Hrudková et al. 2010; Haghighipour & Kirste  2011; Steffen et al. 2012)).
Kepler data also revealed the lack of a close companion in HJ systems. Steffen
et al. (2012) present the results of a search for planetary companions
orbiting near HJ candidates in the Kepler data. Special emphasis is given to
companions between the 2:1 interior and exterior mean-motion resonances(MMRS).
A photometric transit search excludes the existence of companions with sizes
ranging from roughly $2/3$ to 5 times the size of Earth.

###  2.3 Multiple Planet systems

Figure 2: The distribution of Kepler candidates in single and multiple planet
systems for different mass regimes. Data are from http://kepler.nasa.gov.

With the increasing number of exoplanets being detected, the number of
multiple planet systems is also steadily increasing. The first 16 months of
Kepler data show that, among the 2321 candidates, 896 ones are in multiple
planet systems, so that 20% of the stars cataloged have multiple
candidates(Borucki et al. 2011; Batalha et al. 2012). Considering the present
observation bias towards large mass planets, as well as the increasing
occurrence rate of small mass planets, we have a good reason to believe that
multiple planets are very common and might occur at a much higher rate. The
systems that have been revealed with the most numerous exoplanets are HD 10180
(Lovis et al. 2011, up to seven planets) and Kepler 11 (Lissauer et al. 2011,
with six planets). All of them are mainly composed of small mass planets
(Super Earth or Neptune mass). Several important signatures have been revealed
by the Kepler mission:

  * •

Multiple planets have on average smaller masses than single planet systems.
Fig.2 shows the paucity of giant planets at short orbital periods in multiple
planet systems, and the ratio of giant planets (with radius $>6R_{\oplus}$) in
single and multiple planet systems is roughly $5.7:1$, with orbital periods of
up to $\sim 500$ days’ orbits.

  * •

Many planet pairs are near MMRs. The presence of MMR is a type of strong
evidence for the migration history of the planet pairs (e.g., Lee & Peale
2002; Zhou et al. 2005). Wright et al. 2011 summarized the data from RV
detected planets, and found 20 planetary systems are apparently in MMRs,
indicating one-third of the well-characteried RV multiple planet systems have
planet pairs in apparent MMRs. Fabrycky et al. 2012 found the Kepler multiple
transiting planet systems show some pile-up for planets pairs near lower order
MMRs (especially 3:2 and 2:1 MMRs).

  * •

Multiple planet systems are nearly coplanar. Checking the Kepler multiple-
transiting system indicates that these planets are typically coplanar to
within a few degrees (Batalha et al. 2012). Also the comparison between the
Kepler and RV surveys shows that the mean inclination of multi-planet systems
is less than $5^{o}$ (Tremaine & Dong 2012). Figueira et al. (2012)
demonstrated that, in order to match the ratio of single planet systems to the
2-planet ones observed in HARPS and Kepler surveys, the distribution of mutual
inclinations of multi-planet systems has to be of the order of $1^{o}$.

###  2.4 Planet Formation Theory

Now it is widely accepted that planets were formed in the protoplanetary disk
during the early stage of star formation (e.g.,Wetherill 1990; Lissauer 1995;
Lin & Papaloizou 1996; Tutukov & Fedorva  2012). According to the conventional
core accretion model, planets are formed through the following processes
(e.g., Lissauer 1993; Armitage  2007):

(1) grain condensation in the mid-plane of the gas disk, forming kilometer-
sized planetesimals ($10^{18}-10^{22}$ g) on timescales on the order of
$10^{4}$ yrs, from sticking collisions of dust (Weidenschilling & Cuzzi 1993;
Weidenschilling  1997) , with gravitational fragmentation of a dense particle
sub-disk near the midplane of the protoplanetary disk (Goldreich & Ward 1973;
Youdin & Shu  2002). Further growth of planetesimals can be helped by
procedures such as the onset of streaming instability (Johansen et al.  2007)
or vortices in turbulence (Cuzzi et al.  2008), or the sweeping of dust with
the ”snowball” model (Xie et al. 2010b; Ormel & Kobayashi  2012; Windmark et
al. 2012).

(2) accretion of planetesimals into planetary embryos ($10^{26}-10^{27}$ g,
Mercury to Mars size) through a phase of ”runaway” and ”oligarchic” growth on
a timescale of $\sim 10^{4}-10^{5}$ yrs (Greenberg et al. 1978; Wetherill &
Stewart 1989; Aarseth et al. 1993; Kokubo & Ida 1996, 2000; Rafikov 2003,
2004).

(3) gas accretion onto solid embryos with mass bigger than a critical mass
($\sim 10M_{\oplus}$) after a $\sim$Myrs long quasi-equilibrium stage before
gas depletion (Mizuno 1980; Bodenheimer & Pollack 1986; Pollack et al. 1996;
Ikoma et al. 2000).

(4) giant impacts between embryos, producing full-sized $(10^{27}-10^{28}$ g)
terrestrial planets in about $10^{7}-10^{8}$ yrs (Chambers & Wetherill  1998;
Levison & Agnor  2003; Kokubo et al.  2006). Thus the presence of big solid
embryos and the lifetime of the gas disk are crucial for the presence of giant
plants, while the presence of enough heavy element determines the mass of
solid embryos and terrestrial planets.

According to the above scenario, the correlation between stars that host giant
planets and stellar metallicity can be understood. By cosmological assumption,
a high stellar metallicity implies a protoplanety disk with more heavy
elements, thus a metal-rich protoplanetary disk enable the rapid formation of
Earth-mass embryos necessary to form the cores of giant planets before the
gaseous disk is dissipated. That correlation might also indicate a lower limit
on the amount of solid material necessary to form giant planets. Johnson & Li
(2012) estimated a lower limit of the critical abundance for planet formation
of $[Fe/H]_{\rm crit}\sim-1.5+\log({\rm r}/1{\rm AU})$, where $r$ is the
distance to the star. Another key point may be the correlation between
metallicity and the lifetime of the gas disk. There is observational evidence
that the lifetime of circumstellar disks is short at lower metallicity, likely
due to the great susceptibility to photoevaporation(Yasui et al. 2009).

Although the above procedures for single planet formation are relatively
clear, there are some bottleneck questions (see previous listed reviews).
Next, we focus on the formation of orbital architectures for different planet
systems.

####  2.4.1 Formation of Hot Jupiter systems

Due to the high temperature that might hinder the accretion of gas in forming
giant planets, the HJs were assumed to be formed in distance orbits rather
than formed in situ. There are mainly three theories that were proposed to
explain the formation of HJ systems with the observed configurations.

Disk migration model. The earliest model for the formation of HJ systems is
the planet migration theory embed in protostellar disks (Lin & Papaloizou
1986; Lin et al. 1996). Giant planets formed in distant orbits, then migrated
inward under the planet-disk interactions and angular momentum
exchanges(Goldreich & Tremaine  1980; Lin & Papaloizou 1986). The so called
type II migration will be stalled at the inner disk edge truncated by the
stellar magnetic field. The maximum distance of disk truncation is estimated
to be $\sim 9$ stellar radii (Königl 1991). Considering the radius of the
protostar is generally 2-3 times larger than their counterpart in the main
sequence, the inner disk truncation would occur at $\sim 0.1$AU. This might
naturally explain the pileup of orbits with periods of $3-10$ days’ for HJs.
However, as type II migration is effective only in the plane of the disk, and
disk’s tidal forces try to dampen the inclination of planets (Goldreich &
Tremaine  1980), this procedure can not explain the formation of HJs in orbits
with high inclination, as well as the lack of planetary companions in close
orbits. Recently, Lai et al.  (2011) proposed that stellar-disk interaction
may gradually shift the stellar spin axis away from the disk plane, on a time
scale up to Gyrs.

Planetary scattering model. Another mechanism that might account for the
formation of HJ systems is the PPS model. Close-encounters among planets can
excite their orbital eccentricities ($e$). In the extreme case that $e$ is
near unity, the orbital periastron will be small enough so that star-planet
tidal interactions might be effective and circularize the orbits to become HJs
(Rasio & Ford 1996; Ford et al.  2001; Papaloizou & Terquem  2001; Ford &
Rasio 2008). The planetary scattering model can reproduce the observed
eccentricity distribution of moderately eccentric $(e\sim 0.1-0.3)$, non-HJ
extra-solar planets (Zhou at al.  2007; Chatterjee et al. 2008; Juric &
Tremaine  2008). However, the required high eccentricity and the long
timescale required for tidal damping be effective might be not easy to achieve
unless some secular effects (e.g. the Lidov-Kozai mechanism) are excited
(e.g., Nagasawa et al. 2008).

Secular models. The third class of models relate to the Lidov-Kozai effect
(Lidov 1962; Kozai 1962) in the presence of a third body. To account for the
high inclination of HJs, Wu & Murray (2003) proposed that a companion star
which is a third body in a high inclination orbit can induce Kozai
oscillations on the planet’s evolution, gradually exciting the planet’s orbit
to an eccentricity near unity so that it can reach a proximity close to the
central star, until tidal dissipation circularizes the orbit into a HJ.
Fabrycky & Tremaine (2007) found such resulting HJs should be double-peaked
with orbital inclinations of $\sim 40^{o}$ and $140^{o}$. Such an idea has
been extended to brown dwarf companion by Naoz et al. (2011a).

However, because the population studies have established that only $10\%$ of
HJs can be explained by Kozai migration due to binary companions (Wu et al.
2007; Fabrycky & Tremaine 2007), but studies show that most of the HJ systems
do not have stellar or substellar companions. Whether this mechanism can
account for the formation of most HJs is not known. Another question is that,
in the stellar companion case ($m_{c}$, a star or a brown dwarf), the orbital
angular momentum (AM) of $m_{c}$ dominates that of the system and determines
an invariant plane, thus the $z-$component of AM (perpendicular to the
invariant plane) of the planet ($m_{p}$) is conserved when $m_{c}$ is in a
distant orbit. Thus $m_{p}$ can be in an apparent retrograde orbit relative to
the spin axis of the main star only when $m_{c}$ has a relatively large
inclination with respect to the equator of the main star(Wu et al.  2007;
Fabrycky & Tremaine 2007), and this retrograde motion is not with respect to
the invariant plane determined by the total AM.

To avoid relying on the effects of stars or brown dwarf companions, and also
to find the occurrence of retrograde motion relative to the invariant plane,
one resorts to the conditions under which the Lidov-Kozai mechanism works for
planet mass companions ($m_{c}$). Naoz et al. (2011b) study the mechanism with
a general three-body model. Denote $a,a_{c}$ as the semimajor axes of inner
planet ($m_{p}$) and companion, respectively, with $e_{c}$ being the
eccentricity of $m_{c}$; they find that as long as
$(a/a_{c})e_{c}/(1-e_{c}^{2})$ is not negligible, the octuple-level of the
three-body Hamiltonian would be effective, so that the z-component of $m_{p}$
in AM is no longer conserved, allowing the occurrence of retrograde motion
relative to the invariant plane. Thus , to make a retrograde HJ, a companion
in a close and eccentric orbit is required, but the mass of the companion is
not important.

However, newly-born planets are assumed to be in near circular and coplanar
orbits. To generate the required eccentricity, Nagasawa et al. 2008, 2011
introduced planet scattering into the above pictures. Starting from a
relatively compact system ($\sim 3.6R_{H}$, Hill’s radius) with three Jupiter-
mass planets, the planets scatter one another on a timescale of $\sim 10^{3}$
years. They found $\sim 30\%$ of the simulations can result in a planet with
eccentricity high enough, that Kozai excitations from outer planets can become
effective, so that it can be either in a close orbit with non-negligible
eccentricity, or in a highly inclined (even a retrograde orbit) with
relatively small eccentricity over a timescale of $10^{9}$ years. However, it
is unclear whether the initial condition of a compact and highly unstable
planetary system can exist, as required by this theory (Matsumura et al.
2010). Also the scatted planets can be observed to test the theory.

Another route to generate eccentricities other than through violent PPS is the
diffusive chaos arising from a multiple planet system after it forms. The
generation of eccentricity in a multiple planet system is a slow, random walk
diffusion in the velocity dispersion space, and the timescale increases with
the logarithm of the initial orbital separations (Zhou at al.  2007).
Recently, Wu & Lithwick 2011 proposed that secular chaos may be excited in an
orderly space system, and it may lead to natural excitation of the
eccentricity and inclination of the inner system, resulting in observed HJ
systems. They inferred that such a theory can also explain the eccentricities
and inclinations for distant giant planets. However, to what extent such a
mechanism could be effective within the age of planetary systems remains for
further study.

To summarize, the Lidov-Kozai mechanism seems to be the most promising
mechanism for the formation of HJs. Provided that initial eccentricities of
the planet’s companion can reach high enough value, inter planetary Kozai
oscillations can bring the inner planets into HJ orbits with sufficiently high
inclinations.

####  2.4.2 Formation of multiple planet architectures and a system of
classification

What should a ’standard’ planet system be like? Before answering this
question, let us first check the possible outcome of a planet system after the
formation of individuals by the procedure listed at the beginning of section
2.4.

According to the core accretion scenario, by depleting all the heavy elements
in a nearby region (called the feeding zone, roughly 10 Hill radii), an embryo
without any migration will be stalled from growing, which is a case called an
isolation mass(Ida & Lin 2004). In a disk with metallicity $f_{d}$ times the
minimum mass solar nebula(MNSN) (Hayashi 1981), the isolation mass can be
estimated as (Ida & Lin 2004, Eq.19)

$M_{\rm iso}\approx 0.16\eta_{\rm ice}^{3/2}f_{d}^{3/2}(\frac{a}{\rm
1AU})^{3/4}(\frac{M_{*}}{M_{\odot}})^{-1/2}M_{\oplus},$ (5)

where $\eta_{\rm ice}$ is the enhancement factor, with a value of $1$ and
$\approx 4.2$ respectively inside and outside the snow line ( location with
temperature 170K beyond which water is in the form of ice, $\sim 2.7$ AU in
the solar system). The time required for the core to accrete nearby materials
and become isolated is on the order of (Ida & Lin 2004. Eq.18)

$\tau\approx 1.2\times 10^{5}\eta_{\rm
ice}^{-1}f_{d}^{-1}f_{g}^{-2/5}(\frac{a}{1\rm AU})^{27/10}(\frac{M_{\rm
iso}}{M_{\oplus}})^{1/3}(\frac{M_{*}}{M_{\odot}})^{-1/6}~{}{\rm yr},$ (6)

where $f_{g}$ is the enhancement factor of gas disk over MMSN. So for a
typical disk with 2 times the MNSN ($f_{d}=f_{g}=2)$, isolation embryos inside
the snow line are small ($<1M_{\oplus}$), and they can not develop. Embryos
beyond the snow line can grow to $\sim 10M_{\oplus}$ so that they can accrete
gas to form gas giants. However, the growth time of embryos with mass
$10M_{\oplus}$ in distant orbits ($>20AU$) is long ($\sim 10Myr$ at 10AU and
$\sim 70Myr$ at 20 AU). Within a disk with a moderate lifetime of $\sim 3$ Myr
for classical T-Tauri stars (Haisch et al. 2001) , embryos in distant orbits
do not have enough time to accrete gas, thus they will stall their growth at
the mass of a sub-giant mass, like Uranus and Neptune in the solar system.

As the gas disk is depleted, the induced secular resonance sweeps through the
inner region of the planetary systems, causing further mergers of cores
(Nagasawa et al. 2003). Terrestrial planet formed after the gas disk was
depleted at $\sim 200$Myrs(Chambers 2001) . After depletion of the gas disk ,
a debris disk with leftover cores interacted with giant plants, causing small
scale migration, such as in the Nice model(Gomes et al. 2005; Morbidelli et
al. 2005; Tsiganis et al. 2005). Thus, assuming no giant migrations occurred,
the solar system is the basic ”standard” multiple planet system. As all
planetary embryos were formed in near mid-plane of the gas disk, without
perturbations in the vertical direction, such a standard planet system is
nearly coplanar, like many multiple planet systems observed by the Kepler
mission.

However, several procedures make the above picture more complicated. One of
the most difficult task is to understand the migration of embryos or planets
embedded in the gas disk before depletion. For a sub-Earth protoplanet , the
exchanges of angular momentum between it and the nearby gas disk will cause a
net momentum lose on it, which results in a so-called type I migration over a
timescale on the order of $<0.1Myr$ (Goldreich & Tremaine 1979; Ward 1986,
1997; Tanaka et al. 2002). If the protoplanet can avoid such disastrous inward
migration, and successfully grow massive enough to accrete gas and become a
gas giant, the viscous evolution of the disk may cause the giant planet to
undergo a type II migration, with a timescale of Myrs(Lin & Papaloizou 1986).
Recent studies infer that, under more realistic conditions, the migration
speeds of both types can be reduced or even with their direction-being
reversed, leading to an even rarer outcome Kley & Nelson 2012).

The evidence for planet migration is the observed systems in MMR. Since 2:1
MMR has the widest resonance width, especially for planetesimals in nearly
circular orbits (Murray & Dermott 1999), many planet pair are expected to show
2:1 MMRs if they had a history of convergent migration (e.g. Rivera et al.
2010; Zhou et al. 2010; Wang et al.  2012; Gerlach & Haghighipour  2012).
However, Kepler planets give many planets conditions near but not in MMR. This
can be understood by the phenomenon that later stage planetesimal and planet
interactions may cause further migrations but with smaller extensions, causing
strict commensurability to be lost (Terquem & Papaloizou,  2007). Giant
planets in MMR might be strong enough and survive under such perturbations,
like the GJ 876 system(Lee & Peale  2002; Rivera et al.  2010; Gerlach &
Haghighipour  2012). Hydrodynamical simulations show that different disk
geometries might lead the planet pair to either convergent migration (thus
possibly the trap of different MMRs), or sometimes to divergent
migrations(Zhang & Zhou  2010a, b). However planet pairs may not necessarily
lead to MMRs configurations for some dynamical configurations (Batygin &
Morbidelli  2012), e.g. the resonant repulsion of planet pairs is discussed by
Lithwick & Wu  (2011).

The orbital configurations of multiple planet systems incorporating planetary
migration have been studied extensively by population syntheses (e.g., Ida &
Lin 2008, 2010,Mordasini et al. 2009a, b) and N-body simulations(e.g.,Thommes
et al.  2008, Liu et al. 2011). Thommes et al.  (2008) found that for giant
planet formation, two timescales are crucial: the lifetime of the gas disk
$\tau_{\rm disk}$ and the time to form the first gas giant $\tau_{\rm giant}$.
In cases with $\tau_{\rm giant}>\tau_{\rm disk}$, the gas is removed before
any gas giant has a chance to form, leaving behind systems consisting solely
of rocky-icy bodies. In cases with $\tau_{\rm giant}<\tau_{\rm disk}$, such
systems generally produced a number of gas giants that migrated inward a
considerable distance. Liu et al. (2011) also showed that $\tau_{\rm disk}$ is
crucial for forming planet systems, as large $\tau_{disk}$ tends to form more
giant planets in close and nearly circular orbits, while small $\tau_{\rm
disk}$ favors forming planets with small masses in distant and eccentric
orbits.

According to the above theories as well as the currently available
observations, the planet systems around solar type stars can be roughly
classified into the following categories. A detailed classification will be
presented later( Zhou et al. , in preparation).

  * •

Class I: Hot Jupiter systems. These might be formed through some secular
mechanisms such as Lidov-Kozai cycling , as discussed previously. Typical
example: 51 Peg b.

  * •

Class II: Standard systems . They are formed either through processes similar
to our solar system, or by undergoing some large scale migrations, as
mentioned perviously. According to scenarios, they undergo migration, due to
the deficit of heavy elements in the gas disk, or due to the short lifetime of
disk, They can further be classified as,

    * –

Subclass II-1: Solar-like systems. These have planetary configurations similar
to the solar system: terrestrial planets in the inner part, 2-3 gas giant
planets in middle orbits, and Neptune-size sub-giants in outer orbits, due to
insufficient gas accretion. Typical example: Mu Ara, ups And, and HD125612
systems.

    * –

Subclass II-2: Hot super-Earth systems. With the migration of giant planets,
the sweeping of inward MMRs or secular resonances will trap the isolated
masses ($0.1-1M_{\oplus}$), and excite their eccentricities , causing further
mergers, which result in the formation of hot super Earth, like GJ 876d (Zhou
et al. 2005; Raymond et al. 2006, 2008). Other formation scenarios, see a
review (Haghighipour  2011). Typical example: GJ 876, and Kepler 9 systems.

    * –

Subclass II-3: Sub-giant planet systems. Due to the low disk mass or low
metallicity, planet embryos around some stars (especially M dwarf) might not
grow massive enough to accrete sufficient gas to become a gas giant, thus
planets in these systems are generally sub-giants, like most of the systems
discovered in Mayor et al. (2011). Typical example: the Kepler 11 system.

  * •

Class III. Distant giant systems. Through direct imaging, a type of system was
detected with many massive companions (up to several times the mass of of
Jupiter) in distant orbits, such as Fomalhaut b (Kalas et al.  2008) , the
HR8799 system(Marois et al.  2008), and beta Pic b (Lagrange et al.  2009).
Interestingly, all these stars have short ages $(\sim 100-300$ Myrs). Whether
the planets were formed in situ through gravitational instability(Boss  1997),
or formed through outward migration or scattering, is still not clear. Typical
examples: Fomalhaut, HR 8799, and beta Pic systems.

##  3 Planets in Binary Star Systems

###  3.1 Overview of Observation

Planets in binaries are of particular interest as most stars are believed to
be born not alone but in a group, e.g., binaries and multiple stellars
systems. Currently, the multiplicity rate of solar like stars is $\sim
44-46\%$, including $\sim 34-38\%$ for only binaries (Duquennoy & Mayor 1991;
Raghavan et al. 2010). Different resulting values of the multiplicity rate of
planet-bearing stars (compared to all the planet hosts) were found to be
$23\%$ (Raghavan et al. 2006) and $\sim 17\%$ (Mugrauer & Neuhäuser 2009), and
most recently $\sim 12\%$ (Roell et al. 2012). The decreasing multiplicity
rate is mainly because of the quickly increasing number of transiting planets
discovered in recent years. For example, Kepler has discovered more than 60
planets since 2010, however, followup multiplicity studies on such planet
hosts are usually postponed or even considered impracticable. In any case, the
multiplicity rate of a planet host is significantly less than the multiplicity
rate of stars. This may be because of selection biases in planet-detection
against binary systems and/or because of impacts of binarity on planet
formation and evolution (Eggenberger et al. 2011).

Depending on the orbital configuration, planets in binaries are usually
divided into two categories (Haghighipour et al. 2010; Haghighipour  2010), S
type for planets orbiting around one of the stellar binary components,
i.e.,the circumprimary case, and P type for those orbiting around both the
stellar binary components, i.e., the circumbinary case. Currently, most of
them are S type, and only a few are found in P type, including NN Ser
(Beuermann et al. 2010), HW Vir (Lee at al.  2009), DP Leo (Qian et al. 2010),
HU Aqr (Qian et al. 2010; Hinse et al. 2012), UZ For (Dai et al. 2010; Potter
et al. 2011), Kepler-16 (AB)b, Kepler-34 (AB)b, and Kepler-35 (AB)b (Doyle et
al. 2011; Welsh et al. 2012). In the following, we will focus more on the
former, and a binary system, hereafter, refers to S type unless explicitly
noted otherwise.

According to the most recent summary of observations (Roell et al. 2012),
there are 57 S type planet-bearing binary systems 333In fact, 10 of them are
triple stellar systems, but with the third star being very far away and thus
exerting less effects on the binaries with planets, which, as a subsample of
extra-solar planetary systems, may provide some significant statistics. Here
we summarize several points worth noting.

  1. 1.

_Binary separation (or orbital semimajor axis, $a_{B}$)._ Most S type systems
have a $a_{B}$ larger than 100 AU. However, there seems to be a pileup at
$a_{B}\sim 20$ AU with 4 systems: $\gamma$ Cephei (Hatzes et al. 2003), Gl 86
(Queloz et al. 2000b), HD 41004 (Zucker et al. 2004), and HD196885 (Correia et
al.  2008; Chauvin et al. 2011). Planets are slightly less frequent in
binaries with $a_{B}$ between 35 and 100 AU (Eggenberger et al. 2011). No
planet has been found in binaries with $a_{B}<10$ AU (excluding P type).

  2. 2.

_Planetary mass_. Planets in wide binaries ($a_{B}>100$ AU) has a mass range
($0.01-10M_{J}$) that is close to those in single star systems but much more
extended than those ($0.1-10M_{J}$) in close binaries ($a_{B}<100$ AU) (Roell
et al. 2012).

  3. 3.

_Planetary multiplicity_. Planets in close binaries ($a_{B}>100$ AU) are all
singleton, while those in wide binaries are diverse (Fig.3 of Roell et al.
(2012)). The occurrence rate of multiple planets in wide binaries is close to
that in single star systems (Desidera & Barbieri 2007).

  4. 4.

_Planetary orbit_. Most extremely eccentric planets are found in wider
binaries (e.g., $e=0.935$ for HD 80606 b and $e=0.925$ for HD 20782 b). The
distribution od planetary eccentricity in binaries also seems to be different
compared to those in single star systems (Kaib et al. 2012). Planetary orbital
periods are slightly smaller in close binaries as compared to those in wide
binaries and single star systems (Desidera & Barbieri 2007).

How are these planets formed with double suns? Are they behaving in a similar
way as our solar system or other single star systems? In the following, we
review some important effects on planet formation and evolution in a binary
system as compared to those in a single star system, which may provide some
clues to answer these questions.

###  3.2 Binary Effects on a Protoplanetary Disk

####  3.2.1 Disk Truncation

Planets are considered to be born in a protoplanetary disk. Such a disk, in
the solar system, could be extended to the location of the Kuiper belt, e.g.,
30-50 AU from the Sun. But in a binary system, the disk could be severely
truncated by the companion star. For the S type case, the typical radial size
of a truncated disk is about $20-40\%$ of the binary’s separation, depending
on the mass ratio and orbital eccentricity of the binary. For the P type case,
the binary truncates the circumbinary disk by opening a gap in the inner
region. The typical radial size of the gap is about 2-5 times the binary’s
separation distance. Various empirical formulas for estimating the boundary of
the truncated disk are given by Artymowicz & Lubow (1994); Holman & Wiegert
(1999); Pichardo et al. (2005)444The boundaries given by Holman & Wiegert
(1999) and Pichardo et al. (2005) are actually the boundaries of stable orbits
of a test particle. . The size range of the truncated disk puts the first
strict constraint on planet formation, determining where planets are allowed
to reside and how much material is available for their formation. The reason
why no S-type planet has been found in binaries with $a_{B}<10$ AU could be
that the truncated protoplanetary disk was too small to have enough material
for formation of a giant planet (Jang-Condell 2007).

####  3.2.2 Disk Distortion

After the violent truncation process, the left-over, truncated disk, is still
subject to strong perturbations from the companion star, and thus it is not as
dynamically quiet as disks around single stars. First, a binary in an
eccentric orbit can also cause the disk to be eccentric (Paardekooper et al.
2008; Kley & Nelson 2008; Müller & Kley 2012). Second, if the binary orbital
plane is misaligned with respect to the disk plane, then binary perturbations
can cause the disk to become warped, twisted or even disrupted (Larwood et al.
1996; Fragner & Nelson 2010). Third, the eccentric, warped disk is precessing.
All the above effects cause planet formation in binary systems to be more
complicated than that in single star systems.

####  3.2.3 Disk Lifetime

Estimating the lifetime of the protoplanetary disk is crucial as it provides a
strong constraint on the timescale of planet formation. Observations of disks
around single stars show that the typical disk life time is in the range 1-10
Myr (Haisch et al. 2001). Although disks around wide binaries show a similar
lifetime, those in close binaries ($a_{B}<40$ AU) show evidence of shorter
lifetime, i.e., $\sim 0.1-1$ Myr (Cieza et al. 2009). Such results are not
unexpected as disks in close binaries are truncated to a much smaller size and
thus have much smaller timescales of viscous evolution. In any case, such a
short disk lifetime requires that planets in close binaries (such as $\gamma$
Cephei) should form quickly, probably on a timescale less than 1 Myr.

###  3.3 Binary Effects on Planet Formation

We consider planet formation based on the core accretion scenario (Lissauer
1993; Chambers 2004) 555Gravitational instability is another candidate
scenario for planet formation in binaries (see Mayer et al. (2010) for a
review), starting from planetesimals (usually having a radius on the scale of
kilometers) embedded in a protoplanetary disk. This is the standard way that
people consider planet formation in single star systems, though planetesimal
formation itself is still unclear (Blum & Wurm 2008; Chiang & Youdin 2010).
Nevertheless, some observational indications imply that the first stages of
planet formation, i.e., dust settling and growing to planetesimals, could
proceed in binaries as well as in single star systems (Pascucci et al. 2008).

####  3.3.1 Growing Planetesimals

One straightforward way for growing planetesimals is via mutual collisions and
mergers, as long as the collisional velocity $V_{col}$ is low enough. For a
protoplanetary disk around a single star system, if the disk turbulence is
weak, e.g., in a dead zone, growth by mutual collisions could be efficient,
and it is thought that planetesimals have undergone a runaway and oligarchic
phase of growth to become planetary embryos or protoplanets (Kokubo & Ida
1996, 1998). However, the situation becomes less clear in binary systems. On
one hand, the outcome of planetesimal-planetesimal collision is highly
sensitive to $V_{col}$ (Benz & Asphaug 1999; Stewart & Leinhardt 2009). On the
other hand, perturbations from a close binary companion can excite
planetesimal orbits and increase their mutual impact velocities, $V_{col}$, to
values that might exceed their escape velocities or even the critical
velocities for the onset of eroding collisions (Heppenheimer 1978; Whitmire et
al. 1998). This is a thorny problem for those binaries with separation of only
$\sim 20$ AU, such as $\gamma$ Cephei and HD 196885. Recently, many studies
have been performed to address this issue.

An earlier investigation by Marzari & Scholl (2000) found that the combination
of binary perturbations and local gas damping could force a strong orbital
alignment between planetesimal orbits, which significantly reduced $V_{col}$
despite relatively high planetesimal eccentricities. This mechanism was
thought to solve the problem of planetesimal growth until Thébault et al.
(2006) found the orbital alignment is size-dependent. Planetesimals of
different sizes align their orbits to different orientations, thus $V_{col}$
values between different sized planetesimals are still high enough to inhibit
planetesimal growth (Thébault et al. (2008, 2009) for S-type, and Meschiari
(2012) for P type). Moreover, the situation would become much more complicated
(probably unfavorable) for planetesimal growth if the eccentricity,
inclination and precession of the gas disk are also considered (Ciecielä G et
al. 2007; Paardekooper et al. 2008; Marzari et al. 2009; Beaugé et al. 2010;
Xie et al. 2011; Fragner et al. 2011; Batygin et al. 2011; Zhao et al. 2012).
Nevertheless, the problem could be somewhat simplified if the effects of a
dissipating gas disk are taken into account (Xie & Zhou 2008) and/or a smaller
inclination ($i_{B}<10^{\circ}$) between the binary orbit and the plane of the
protoplanetary disk is considered (Xie & Zhou 2009). Optimistically,
planetesimals may undergo a delayed runaway growth mode (called Type II
runaway) towards planets (Kortenkamp et al. 2001). In any case, however, it
seems that planetesimal-planetesimal collision is not an efficient way for
growing planetesimals in close binary systems.

An alternative way of growing planetesimals could be via accretion of dust
that they pass through in the disk. Both analytical studies and simulations
(Xie et al. 2010b; Paardekooper & Leinhardt 2010; Windmark et al. 2012) have
shown this could be promising to solve the problem of growing planetesimals
not only in binaries but also in single star systems (e.g., the well known
“meter-barrier” puzzle). For an efficient dust accretion to occur, one needs,
first, a source of dust, which could be either from the primordial
protoplanetary disk or from fragmentation of planetesimal-planetesimal
collisions, and second, weak disk turbulence to maintain a high volume density
of dust (Johansen et al. 2008).

####  3.3.2 Formation of Terrestrial and Gaseous Planets

Once planetesimals grew to 100-1000 km in radius (usually called planetary
embryos or protoplanets), they are no longer as fragile as before. Their own
gravity is strong enough to prevent them from fragmenting by mutual
collisions. In such a case, most collisions lead to mergers and thus growth of
planetesimals. Hence, one way to speed up growth is by increasing $V_{col}$,
which is readily available in a binary star system. For close binaries, such
as $\alpha$ Centauri AB, simulations (Barbieri et al. 2002; Quintana 2004;
Quintana & Lissauer 2006; Quintana et al. 2007; Haghighipour & Raymond  2007;
Guedes et al. 2008) have shown that Earth-like planets could be formed in
10-100 Myr.

If a protoplanet reaches several Earth masses, the critical mass for
triggering a runway gas accretion, before the gas disk is depleted, then it
could accrete the surrounding gas to become a gaseous planet. Generally,
planets would stop gas accretion after they have cleared all the surrounding
gas and opened a gap. However, because of the binary perturbation, gas could
be pushed inward to refill the gap and finally accreted by the planet (Kley
2001), leading to a higher gas accretion rate and more massive gaseous
planets. Such an effect could partially explain one of the observed facts:
gaseous planets in close binaries are slightly more massive than those in
single star systems.

###  3.4 Binary Effects on Planetary Dynamical Evolution

####  3.4.1 With a Gas Disk

Due to the complication of the problem itself, the studies of this aspect
mainly rely on numerical simulations. Kley & Nelson (2008) considered the
evolution of a low-mass planet (30 Earth masses) embedded in a gas disk of the
$\gamma$ Cephei system (S type). They found that the planet would rapid
migrate inward and accrete a large fraction of the disk’s gas to become a gas
giant planet, which is similar to the observed planet. For the circumbinary
case, i.e., P type, simulations (Pierens & Nelson 2007, 2008a, 2008b) showed
the results were sensitive to planet mass. Low mass planets (tens of Earth
masses) would successively migrate inward to the inner edge of the gas disk
and subsequently merge, scatter, and/or lock into a MMR. A high mass planet
($>$ Jupiter mass) would enter a 4:1 resonance with the binary, which pumped
up the eccentricity of the planet and probably led to instability. The model
favoring the low mass planet from the simulation is consistent with the recent
observation: the masses of the three confirmed circumbinary planets
(Kepler-16,-34,-35) are all $\leq$ Saturn’s mass.

####  3.4.2 Without a Gas Disk

As the lifetime of the disk, typically $\leq$ 10 Myr, is only less than 1% of
that of a planet (typically on the order of Gyr), the subsequent gas free
phase could dominate the evolution of planets after they have formed. In fact,
several mechanisms are found to play an important role in shaping the final
structure of planetary systems in binaries.

  * •

_Planet-planet scattering_. Multiple planets could form in a protoplanetary
disk, and because of damping from the gas disk , planets could maintain their
near circular orbits and thus avoid close encounters. Once the gas disk
dissipated, planet-planet interaction would excite the eccentricities of
planets, leading to close encounters and finally instability of the systems;
e.g., merger and/or ejection. Such a mechanism (usually called PPS) is thought
to explain the eccentricity distribution of observed giant planets (Ford &
Rasio 2008; Nagasawa et al. 2008; Chatterjee et al. 2008). In a binary system,
PPS would be more violent because of the additional perturbation from the
binary stars (Malmberg et al. 2007a). In S type binaries (especially those
with close separations and highly inclined and/or eccentric orbits),
simulations (Marzari et al. (2005), Xie et al. in prep.) have shown that PPS
often causes the system to finally have only a single planet, and the
remaining planet is usually the most massive one. Such results may explain one
observed fact: planets in close binaries are single and massive. In P type
binaries, PPS again favors a single planet. In addition, it predicts a
positive correlation between the planet’s orbital semimajor axis and
eccentricity (Gong et al. in prep.), which currently fit well to the three
confirmed circumbinary planets (Kepler-16,-34,-35). More P type planets
detected in the future will further test this correlation.

  * •

_Lidov-Kozai Effect_. In an S type binary, if a planet is on a highly inclined
orbit666This could be either primordial or induced by planet-planet
scattering., then it could undergo the Lidov-Kozai effect (Kozai 1962; Lidov
1962). One of the most striking features of the effect is that the planet’s
eccentricity could be pumped to a very high value and oscillate with its
inclination out of phase. Recently, it has also been found that the planet
could flip its orbit back and forth when its eccentricity approaches unity
(Lithwick & Naoz  2011; Naoz et al. 2011a) if the binary orbit is eccentric,
hence exhibiting the so called eccentric Lidov-Kozai effect. One application
of this effect is that it could produce a HJ; when the planet oscillates to
very high eccentricity, with a very small periastron, tides from the central
star kick in and dampen its orbits to form a close planet (Wu & Murray 2003;
Fabrycky & Tremaine 2007). Recently, there have been examples of such
candidates showing evidence that they are on the way to being HJs via the
Lidov-Kozai effect (Socrates et al. 2012; Dawson & Johnson 2012). In addition,
as the planet could flip during the Lidov-Kozai evolution, there are
significant chances to form an HJ in a retrograde orbit (Naoz et al. 2011a),
which has been observed in some extrasolar systems (Triaud et al. 2010).
Nevertheless, depending on specific conditions, e.g, if general relativistic
effects and/or perturbation by another planet is relevant, the Lidov-Kozai
effect can be suppressed (Takeda et al. 2008; Saleh & Rasio 2009).

###  3.5 Non-Primordial Scenario

There is another possibility that a currently observed planet-bearing binary
was not the original one when the planet was born, namely the non-primordial
scenario. Various mechanisms can lead to such a result, and we briefly
summarize these two kinds as follows.

  * •

_Encounters with other stars and/or planets._ A binary star system has a
larger collisional cross section than a single star and thus a larger chance
to have a close encounter with other stars, during which they could have their
planets lost and/or exchanged (Pfahl 2005; Marti & Beauge 2012). In the end,
the binaries probably dramatically changed their orbits, and the surviving
planets were probably excited to highly eccentric and/or inclined
orbits(Malmberg et al. 2007b; Spurzem et al. 2009; Malmberg et al. 2011). In
addition, free floating planets(FFPs) could be recaptured by flyby binary
stellar systems (Perets & Kouwenhoven 2012).

  * •

_Steller Evolution._ If one of the binary component star evolves away from the
main sequence, it could induce instabilities in the planetary system in the
binary. Planets could bounce back and be forced between the space around the
two component binary stars (Kratter & Perets  2012). If a close binary star
evolve to some phase to have mass transfer, the mass lost from the donor star
could form a circumbinary disk, which could potentially harbor new planets
(Perets 2010).

##  4 Planet in star Clusters

Almost all the planets found now are around field stars. However the normal
theory of star formation predicts that most field stars are formed from a
molecular cloud, having the same initial mass function(IMF) as
stars($<3M_{\odot}$) in an open cluster indicating that these field stars
initially formed in clusters, e.g. our solar system’s, initial birth
environment was reviewed by Adams (2010). According to the chemical
composition of our solar system, our Sun may have formed in an environment
with thousands of stars, i.e. a star cluster or association. Thus scientists
are very interested in planet detection in clusters which would be more
effective than that around field stars due to many more objects existing in
the same size of a telescope’s field of view.

To survey planets around stars in a cluster, we have some advantages in
obtaining more effective and credible results. Some correlations between
planets occurrences as well as their properties and characteristics of their
host stars are not very clear due to the bias of measurements for these field
stars, such as age, mass, [Fe/H] etc. Large differences among these field
stars, especially the type of environment in the early stage, is a problem for
surveying the correlations. However, in one cluster, most of its members have
homogeneous physical parameters, i.e. age and [Fe/H]. The comparative study of
planets in clusters will provide more valid, credible correlations.

Unfortunately, except for some FFPs, few planets are found to be bounded
around members of either globular clusters(GCs) or open clusters(OCs). The
following sections will introduce the observational results and theoretical
works in both GCs and OCs respectively.

###  4.1 Planets in Globular Clusters

Because of the fruitful observation results of GCs and the huge number of
stars in GCs, especially main sequence stars(MSSs), people naturally expect to
find planets around these MSSs in GCs. As these stars are, on average about 50
times denser than field stars near the Sun, GCs have advantages for planet
searching. For example, in the two brightest GCs: $\omega$ Cen and 47 Tuc,
there are more than 60000 MSSs, approximately half of the total number of
Kepler targets. However, the extreme star density near the center of GCs
($10^{5}$ stars within a few arc min), requires an extremely high precision of
photometry. Until now, it has been hard to individually distinguish two nearby
stars in the core of GCs. The stars in the outer region of GCs are more widely
separated from each other, therefore they are more suitable for planet
searches.

The first planet system in GC was found in the nearest GC: M4, PSR B1620-26 b
(Backer et al. 1993), a $2.5M_{\rm J}$ planet around a binary radio pulsar
composed with a $1.35M_{\odot}$ pulsar and a $0.6M_{\odot}$ white dwarf.
However, if we focus on sun-like stars in GCs, no planets have been confirmed
until now.

To search for bounded planets around MSSs, some efforts have been made by
several groups. As the brightest GCs in the sky, 47 Tucanae and $\omega$
Centauri are good targets for planet searching by transiting. Using HST to
find planets in the core of 47 Tucanae, Gilliland et al. (2000) provided a
null result. In the outer halo, the same result was obtained by Weldrake et
al. (2005). Furthermore, Weldrake et al. (2007) found no bounded planets by
transiting in both of the two clusters, under the precision of $P<7$day,
$1.3-1.6R_{\rm J}$. The most recent works to find planets in the nearby
globular cluster NGC 6397 is contributed by Nascimbeni et al. (2012), butstill
no highly-significant planetary candidates have been detected for early-M type
cluster members.

Do the null results in GCs indicate the low occurrence of planets? For some
dense star environments, the stability of planets is crucial. Although planets
at $1$AU in the core of 47 Tuc can only survive around $10^{8}$yrs in such a
violent dynamical environment(Davies & Sigurdsson,  2001), planets at $10$AU
in the uncrowded halo of GCs can be preserved for several Gyrs (Bonnell et
al.,  2001). Therefore HJs with periods around a few days can survive much
longer in the halo. If HJs formed near these cluster members, they would have
a chance to be detected in GCs (Fregeau et al.,  2006).

The null results are mainly attributed to the low metallicity of these GCs.
Fischer & Valenti (2005) surveyed planet systems not far from the Sun, and
pointed out that the occurrence of gas giants depends on the metallicity of
their host stars. The most recent work by Mortier et al. (2012) found a
frequency of HJs $<1\%$ around metal-poor stars, while the frequency of gas
giants is $<2.36\%$ around stars with $[Fe/H]<-0.7$. Both 47 Tuc and $\omega$
Cen have a low [Fe/H](respectively -0.78 and $<-1$, from data collected by
Harris  (1996)). Hence, these two GCs contains few HJs. Higher frequencies of
giant planet are expected in GCs with higher [Fe/H].

Additionally, different properties of a circumstellar gas disk, especially its
structure, might influence the final architecture of planet systems, e.g. if
the gas disk in GCs is depleted much faster due to Extreme-Ultraviolet(EUV)
and Far-Ultraviolet(FUV) evaporation from nearby massive stars (Matsuyama et
al.,  2003), formation of gas giants may be unlikely, as well as the formation
of a hot planet. The different structure of a gas disk might not force the
planet to migrate inward enough to form hot planets, and naturally they are
hard to detect using transit.

In these old GCs, mass segregation is obvious due to energy equipartition,
i.e. massive objects concentrate in the center of the cluster while small
objects are easily ejected outside. Energy equipartition results in FFPs,
which might be ejected to become unbound by some mechanisms (Parker & Quanz
2012; Veras & Raymond,  2012) and have a lower-mass than stars. It is hard for
FFPs to stay in old GCs.

###  4.2 Planets in Open Clusters and Associations

None of the planets around solar-like stars are found in GCs,because of the
reasons mentioned before. OCs and associations which still contain lots of
MSSs, are also useful for planet searching. The main dissimilarities between
OCs and GCs are:

  1. 1.

_Cluster ages_. OCs and associations are much younger than GCs, and have a
much larger [Fe/H], probably leading to more planets being formed around the
cluster members.

  2. 2.

_The dynamical environments_. The dynamical environment in OCs and
associations is still less violent than that in GCs because of lower star
density, which can preserve the two-body systems more easily than in GCs.

  3. 3.

_Binary fraction_. The much larger fraction of binary systems in OCs than GCs
is a good way to understand the formation of planet systems in binary stars.

Additionally, many more OCs and associations($\sim 1200$) are observed than
GCs ( $\sim 160$ ) in our galaxy. Due to these dissimilarities, a higher
probability of planet detection is expected.

As for the different properties of OCs, surveyed planets in OCs have their own
values. Some OCs are only a few Myr old, e.g. NGC6611(Bonatto et al.,  2006)
and NGC 2244 (Bonatto & Bica,  2009). Their ages are comparable with the
timescale of planet formation. Surveying planets and circumstellar disks in
these very young clusters will provide valuable samples to check and enhance
the current theories of planet formation, particularly the influences via
different environments in clusters during the early stages of planet
formation.

####  4.2.1 Bounded Planets and Debris Disks

Many groups have made efforts to search for planets by transits in OCs: e.g.
Bruntt et al. (2003) in NGC 6791, Bramich et al. (2005) in NGC 7789, Rosvick &
Robb (2006) in NGC 7086, Mochejska et al. (2006) in NGC 2158, etc. Only few
candidates were found but none were confirmed. The most significant progresses
were made in 2007. In NGC 2423, a gas giant with a minimum mass of $10.6M_{\rm
J}$ around a $2.4M_{\odot}$ red giant was found by Lovis & Mayor (2007) using
RV measurement. Another planet was soon found soon afterward by RV around the
giant star $\epsilon~{}$Tauri (Sato et al.,  (2007)) in the Hyades, the
nearest OC, with a minimum mass of $\sim 7.6M_{\rm J}$ and a period of $\sim
595$ days. Using transit, some smaller candidates have also been found without
RV confirmation, e.g. a single transit of a candidate $\sim 1.81M_{\rm J}$ in
NGC 7789 found by Bramich et al. (2005), which may indicate another exoplanet
with a long period. Most recent work by Quinn et al. (2012) claims that they
found two HJs by RV: Pr0201b and Pr0211b in Praesepe, these planet are the
first known HJs in OCs. Parameters describing these planets are listed in
Table 1 as well as properties of their host cluster.

Table 1: Parameters of the planets and their host stars in OCs, as well as
their host cluster. Data are from Lovis & Mayor (2007); Sato et al.,  (2007);
Harris  (1996); Quinn et al. (2012)

.  $M_{\rm p}\sin i$ Period semi-major ecc $M_{\rm star}$ host cluster age
[Fe/H] dist $(M_{\rm J})$ (day) axis (AU) $M_{\odot}$ (Gyr) (pc) $10.6$
$714.3$ $2.1$ $0.21$ $2.4$ $NGC2423$ $0.74$ $0.14$ $766$ $7.6$ $594.9$ $1.93$
$0.15$ $2.7$ $Hyades$ $0.6$ $0.19$ $47$

Compared with the null results in GCs, the encuraging results of planet
searching in OCs confirm the formation and survival ability of planets in
cluster environment, especially observations of the circumstellar disk in
young OCs, which is related to the occurrence of planet formation.

Haisch et al. (2001) showed the fraction of disks in OCs decayed with their
ages. Some recent results verify this correlation: $30-35\%$ of T-Tauri stars
have a disk in the $\sigma$ Ori cluster with ages $\sim 3$ Myr(Hernández et
al.,  2007). Using the Chandra X-ray Observatory, Wang et al. (2011) found a
K-excess disk frequency of $3.8\pm 0.7\%$ in the $5\sim 10r$My old cluster:
Trumpler 15.

Although the disk structures around cluster members are not well known, the
large fraction of gas disk in very young OCs makes the formation of planets
possible, especially for gas giants. The two confirmed planets found were not
HJs, but another two planets found most recently are HJs. However, lack of
more samples is a big problem in making a credible conclusion and surveying
the statistical characteristics of planet formation and evolution in OCs.

####  4.2.2 Free-Floating Planets

Ages, metallicity and star density are the main dissimilarities between OCs
and GCs. The formation of planets in OCs is thought to be common, but few
planets bound around stars have been observed. However a population of FFPs
has been found in OCs. In 2000, Lucas & Roche (2000) found a population of
FFPs in Orion. Bihain et al. (2009) also found three additional FFPs with
$4-6M_{\rm J}$ in the $\sim 3$ Myr old OC: $\sigma$ Orions. A huge number
(nearly twice the number around MSSs) of unbound planets have been found in
the direction of the Galactic Bulge (Sumi et al.,  2011).

These planets have multiple origins. They may also form around some cluster
members, but were ejected out of the original systems and cruise into clusters
(Sumi et al.,  2011). Because of their young ages, energy equipartition in OCs
is less effective than that in GCs. The dissolution timescale for objects to
escape from a cluster is $t_{\rm dis}\sim 2{\rm
Myr}\times\frac{N}{\ln(0.4N)}\times\frac{R_{\rm G}}{\rm kpc}$ (Baumgardt &
Makino,  2003). For a typical OC, with $N=1000$ stars at distance $R_{\rm
G}=1$kpc, $t_{\rm dis}\sim 0.1$Gyr and therefore FFPs can still stay in their
host clusters for most young OCs. It is hard to find the original host stars
of these FFPs, but surveying them is still useful for evaluating the frequency
of planet formation in OCs and GCs.

###  4.3 Planetary Systems in Clusters: theoretic works

The planet occurrent rate including formation rate and stability related with
the cluster environment is very important for predicting the rate of further
observations. From their respective dynamics, the large distinctions between
OCs and GCs generally predict more planets in OCs and HJs in halo of GCs.

Dynamical works focus on the stability and orbital architecture of planetary
systems in a cluster. Considering a fly-by event, the previous works show the
stability of planet systems depends on the bounded energy of planetary
systems, fly-by parameters as well as the star density of the environment,
which decides the occurrent rate of a fly-by event ($t_{\rm enc}\propto 1/n$,
Binney & Tremaine,  1987). Spurzem et al. (2009) used a strict N-body
simulation as well as a Monte Carlo method to survey the dynamical
characteristics, especially the effective cross section of planetary systems
with different orbital elements in a cluster’s gravity field. Adding
substructure of a young OC by Parker & Quanz (2012), the fraction of liberated
planet depends on the initial semi-major axis and virial parameter. The planet
systems in binary systems were also been surveyed by Malmberg et al. (2007a,
b, 2009). They considered encounters between a binary system and a single
star. After obvious changes of the inclination, a fraction of planets will
suffer the Kozai effect after encounters and consequently show instabilities.

The stability and orbital architecture of multi-planet systems in clusters
still need to be surveyed in further works, because planet-planet interactions
play an important role in deciding the final configuration of a planet system
after fly-bys. The dynamical evolution in clusters is much more complex than
in a single fly-by. In some very open clusters, the tidal effect can also
disrupt planet systems in the outer region. The effect of interstellar gas in
very young OCs is still uncertain. The fine structure of the circumstellar
disks still needs to be investigated during the formation of planet systems.

Planet formation in star clusters must have a strong dependence on the
physical and dynamical environments of their host stars. The environments in
clusters are very different from that around field stars, or binary pairs,
e.g. the different properties of the circumstellar disk, dynamical
instabilities in different stages during planet formation, as well as the
stability of a planetary system after the planets are formed. The protoplanet
gas disk plays a very important role in the formation of gas giant planets. A
comparison between the timescale of gas disk dispersion and that of gas giant
formation is a crucial clue to judge the formation rate of giant planets. On
the other hand, the observation of circumstellar disks and giant planets
(including FFPs) in some very young OCs, can also give a limit on the rate
that a planetary gas disk is preserved, which is related to the planet
formation rate in a cluster environment. The distinctions in the different
environments for OCs and small bounded planet samples in OCs have limited our
knowledge about the formation of planets in clusters.

##  5 Conclusions

With the increasing data of observed exoplanets, the study of orbital
architectures for multiple planet systems becomes timely. Unlike the
relatively mature theory for formation of a single planet (except for some
bottleneck problems), the properties of planet’s architecture is relatively
far from clear. Dynamical factors, such as interactions among planets, tidal
interactions with the host star and a protostellar disk, or in some cases
perturbations from a third companion (a star or brown dwarf), etc, tend to
sculpt the orbital evolution and sculpt the final architectures of the planet
systems.

According to our present knowledge, we tentatively classify the planet systems
around single stars into three major catalogs: HJ systems, standard systems
and distanct giant planet systems. The standard systems can be further
categorized into three sub-types under different circumstances: solar-like
systems, hot super-Earth systems and sub-giant planet systems. The
classification is based on the major process that occurred in their history.
It may help to predict unseen planets, as well as to understand the possible
composition of planets, since through the history of their evolution, we can
judge whether large orbital mixing has occurred.

Due to the presence of a third companion, planet formation in a binary
environment has raised some more challenging problems, especially for the
stage of planetesimal formation. Anyway, the observed exoplanets around binary
stars, especially the circumbinary exoplanets like Kepler 34b and 35b,
indicate that planet formation is a robust procedure around solar type stars.

Planets in clusters will provide a useful clue for understanding the formation
of planets in a cluster environment. Although only very limited observational
results have been obtained, theories can still predict some properties of
exoplanets in clusters. Planet samples in some young OCs might be especially
interesting for revealing the difference between planet formation around field
stars and members of clusters.

###### Acknowledgements.

We would like to thank Drs. G.Marcy, S.Udry, N.Haghighipour,M.Nagasawa, Y.Q.
Wu, A.V.Tutukov and R.Wittenmyer, I.Boisse for their helpful suggestions. The
work is supported by the National Natural Science Foundations of China
(Nos.10833001,10925313,11078001 and 11003010), Fundamental Research Funds for
the Central Universities(No.1112020102), the Research Fund for the Doctoral
Program of Higher Education of China(No.20090091110002 and 20090091120025).

## References

  * Aarseth et al. (1993) Aarseth, S. J., Lin, D. N. C., & Palmer, P. L., 1993, ApJ, 403, 351
  * Adams (2010) Adams, F. C., 2010, ARA&A, 48, 47
  * Agol et al. (2005) Agol, E., Steffen, J., Sari, R., & Clarkson, W., 2005, MNRAS, 359, 567
  * Armitage (2007) Armitage, P. J., 2007, arXiv:astro-ph/0701485
  * Artymowicz & Lubow (1994) Artymowicz, P., & Lubow, S. H., 1994, ApJ, 421, 651
  * Backer et al. (1993) Backer, D. C., Foster, R. S., & Sallmen, S., 1993, Nature, 365, 817
  * Batalha et al. (2012) Batalha et al. 2012, arXiv: 1202. 5852
  * Barbieri et al. (2002) Barbieri, M., Marzari, F., & Scholl, H., 2002, A&A, 396, 219
  * Batygin et al. (2011) Batygin, K., Morbidelli, A., & Tsiganis, K., 2011, A&A, 533, A7
  * Batygin & Morbidelli (2012) Batygin, K., & Morbidelli, A., 2012, arXiv: 1204. 2791
  * Baumgardt & Makino, (2003) Baumgardt, H, & Makino, J., 2003, MNRAS, 340,227
  * Beaugé et al. (2010) Beaugé, C., Leiva, A. M., Haghighipour, N., & Otto, J. C., 2010, MNRAS, 408, 503
  * Benz & Asphaug (1999) Benz, W., & Asphaug, E., 1999, Icarus, 142, 5B
  * Beuermann et al. (2010) Beuermann, K., Hessman, F. V., Dreizler, S., et al., 2010, A&A, 521, L60
  * Bihain et al. (2009) Bihain, G., Rebolo, R., Zapatero, O. M. R., et al. 2009, A&A, 506, 1169
  * Binney & Tremaine, (1987) Binney, J., Tremaine, S., 1987, Galactic Dynamics. Princeton Univ. Press, Princeton, NJ
  * Blum & Wurm (2008) Blum, J., & Wurm, G., 2008, ARA&A, 46, 21
  * Bodenheimer & Pollack (1986) Bodenheimer, P., & Pollack, J. B. 1986, Icarus, 67, 391
  * Boisse et al. (2012) Boisse,I. Pepe, F., Perrier,C., et al.,2012, Arxiv:1205.5835
  * Bonatto et al., (2006) Bonatto, C., Santos Jr. J. F. C., & Bica, E. 2006, A&A 445,567
  * Bonatto & Bica, (2009) Bonatto, C., & Bica1, E. 2009, MNRAS, 394, 2127B
  * Bonnell et al., (2001) Bonnell, I. A., Smith, K. W., Davies, M. B., & Horne, K. 2001, MNRAS, 322, 859
  * Borucki et al. (2011) Borucki, W. J., Koch, D. G., Basri, G., et al., 2011, ApJ, 736, 19
  * Boss (1997) Boss A. P., 1997, Science, 276, 1836
  * Bramich et al. (2005) Bramich, D. M., Horne, K., Bond, I. A., et al., 2005, MNRAS, 359, 1096
  * Brown et al. (2012) Brown, D. J. A., Cameron, A. C., Anderson, D. R., et al., 2012, MNRAS, 423, 1503
  * Bruntt et al. (2003) Bruntt, H., Grundahl, F., Tingley, B., et al., 2003, A&A, 410, 323
  * Burkert & Ida (2007) Burkert, A. , & Ida, S., 2007, ApJ, 660, 845
  * Butler & Marcy (1996) Butler, R.P., & Marcy G. W., 1996. ApJL, 464, L153
  * Butler et al. (2006) Butler, R. P., et al., 2006, ApJ, 646, 505
  * Chambers & Wetherill (1998) Chambers, J. E., & Wetherill, G. W., 1998, Icarus, 136, 304
  * Chambers (2001) Chambers, J. E., 2001, Icarus, 152, 205
  * Chambers (2004) Chambers, J. E., 2004, E&PSL, 223, 241
  * Chatterjee et al. (2008) Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A., 2008, ApJ, 686, 580
  * Chauvin et al. (2011) Chauvin, G., Beust, H., Lagrange, A.-M., & Eggenberger, A., 2011, A&A, 528, A8
  * Chiang & Youdin (2010) Chiang, E., & Youdin, A. N., 2010, AREPS, 38, 493
  * Ciecielä G et al. (2007) Ciecielä G, P., Ida, S., Gawryszczak, A., & Burkert, A., 2007, A&A, 470, 367
  * Cieza et al. (2009) Cieza, L. A., Padgett, D. L., Allen, L. E., et al., 2009, ApJ, 696, L84
  * Correia et al. (2008) Correia, A. C. M.; Udry, S.; Mayor, M.; et al. 2008, A&A, 479,271
  * Csizmadia etal. (2010) Csizmadia, S., Renner, S., Barge, P., et al., 2010, A&A, 510, A94
  * Cumming et al. (2008) Cumming, A., Butler, R. P., Marcy, G. W., et al., 2008, PASP, 120, 531
  * Cuzzi et al. (2008) Cuzzi, J. N., Hogan, R. C. & Shariff, K., 2008, ApJ, 687, 1432
  * Dai et al. (2010) Dai, Z.-B., Qian, S.-B., Fernández Lajús, E., & Baume, G. L., 2010, MNRAS, 409, 1195
  * Davies & Sigurdsson, (2001) Davies, M. B., & Sigurdsson, S., 2001, MNRAS, 324, 612
  * Dawson & Johnson (2012) Dawson, R. I., & Johnson, J. A., 2012, arXiv: 1203. 5537
  * Desidera & Barbieri (2007) Desidera, S., & Barbieri, M., 2007, A&A, 462, 345
  * Doyle et al. (2011) Doyle, L. R., Carter, J. A., Fabrycky, D. C., et al., 2011, Science, 333, 1602
  * Duquennoy & Mayor (1991) Duquennoy, A., & Mayor, M., 1991, A&A, 248, 485
  * Eggleton & Kiseleva-Eggleton (2001) Eggleton, P. P., & Kiseleva-Eggleton, L., 2001, ApJ, 562, 1012
  * Eggenberger et al. (2011) Eggenberger, A., Udry, S., Chauvin, G., et al., 2011, IAUS, 276, 409
  * Michael et al. (2006) Endl, M., Cochran, W. D., Kürster, M., 2006, ApJ, 649, 436
  * Fabrycky & Tremaine (2007) Fabrycky, D., & Tremaine, S., 2007, ApJ, 669, 1298
  * Fabrycky et al. (2012) Fabrycky, D. C., Kepler Science Team, 2012, DDA, 43,0103F
  * Figueira et al. (2012) Figueira, P.,Marmier, M., Bou , G., et al. 2012, A&A541, A139
  * Fischer & Valenti (2005) Fischer, D. A. & Valenti, J., 2005, ApJ, 622, 1102
  * Ford et al. (2001) Ford, E. B., Havlickova, M., & Rasio, F. A., 2001, Icarus, 150, 303
  * Ford& Rasio (2006) Ford, E. B., & Rasio, F. A., 2006, ApJ, 638, L45
  * Ford & Rasio (2008) Ford, E. B., & Rasio, F. A., 2008, ApJ, 686, 621
  * Fortney et al. (2003) Fortney, J. J., Sudarsky, D., Hubeny, I., et al., 2003, ApJ 589, 615
  * Fragner & Nelson (2010) Fragner, M. M., & Nelson, R. P., 2010, A&A, 511, A77
  * Fragner et al. (2011) Fragner, M. M., Nelson, R. P., & Kley, W., 2011, A&A, 528, A40
  * Fregeau et al., (2006) Fregeau, J. M., Chatterjee, S., & Rasio, F. A., 2006, ApJ, 640, 1086
  * Gaudi et al. (2005) Gaudi, B. S., Seager, S., & Mallen-Ornelas, G., 2005, ApJ, 623, 472
  * Gerlach & Haghighipour (2012) Gerlach, E. &Haghighipour, N. 2012, accepted by publication in Cel. Mech. Dyn. Astron. arXiv:1202.5865
  * Gilliland et al. (2000) Gilliland, R. L., Brown, T. M., Guhathakurta, P., et al. 2000, ApJ, 545, L47
  * Goldreich & Ward (1973) Goldreich, P., & Ward, W. R., 1973, ApJ, 183, 1051
  * Goldreich & Tremaine (1979) Goldreich, P., & Tremaine, S., 1979, ApJ, 233, 857
  * Goldreich & Tremaine (1980) Goldreich, P. & Tremaine, S., 1980, ApJ, 241, 425
  * Gomes et al. (2005) Gomes, R., Levison,H. F., Tsiganis, K., & Morbidelli, A., 2005, Nature, 435, 466
  * Gonzalez (1997) Gonzalez, G., 1997, MNRAS, 285, 403
  * Gould et al. (2006) Gould, A., Dorsher, S., Gaudi, B. S., & Udalski, A., 2006, AcA, 56, 1
  * Greenberg et al. (1978) Greenberg, R., Hartmann,W. K., Chapman, C. R., & Wacker, J. F., 1978, Icarus, 35, 1
  * Guedes et al. (2008) Guedes, J. M., Rivera, E. J., Davis, E., et al., 2008, ApJ, 679, 1582
  * Haghighipour (2010) Haghighipour, N. 2010, Planets in Binary Star Systems (editor), Astrophysics and Space Science Library, 366. Springer Science.
  * Haghighipour (2011) Haghighipour, N. 2011, Contemporary Physics, 52, 403
  * Haghighipour et al. (2010) Haghighipour, N., Dvorak, R., & Pilat-Lohinger, E., 2010, Astrophysics and Space Science Library, vol. 366, ed. N. Haghighipour, 285
  * Haghighipour & Kirste (2011) Haghighipour, N. & Kirste, S. 2011, CMDA, 111,267
  * Haghighipour & Raymond (2007) Haghighipour, N. & Raymond, S. N. 2007, 666, 436
  * Haisch et al. (2001) Haisch, K. E., Lada, E. A., & Lada, C. J., 2001, ApJ, 553, L153
  * Harris (1996) Harris, W. E., 1996, AJ, 112, 1487
  * Hatzes et al. (2003) Hatzes, A. P., Cochran, W. D., Endl, M., et al., 2003, ApJ, 599, 1383
  * Hayashi (1981) Hayashi, C., 1981, PThPS, 70, 35
  * Hébrard etal. (2010) Hébrard, G., Bonfils, X., Ségransan, D., et al., 2010, A&A, 513, A69
  * Heppenheimer (1978) Heppenheimer, T. A., 1978, A&A, 65, 421
  * Hernández et al., (2007) Hernández, J., Hartmann, L., Megeath, T., et al., 2007, ApJ, 662, 1067
  * Hinse et al. (2012) Hinse, T. C., Lee, J. W., Goździewski, K., et al., 2012, MNRAS, 420, 3609
  * Holman & Wiegert (1999) Holman, M. J., & Wiegert, P. A., 1999, AJ, 117, 621
  * Holman& Murray (2005) Holman, M. J., & Murray, N. W., 2005, Science, 307, 1288
  * Howard et al. (2010) Howard, A. W., Marcy, G. W., Johnson, J. A., et al., 2010, Science, 330, 653
  * Howard & Marcy (2011) Howard, A. W, Marcy, G., Bryson, S. T., The Kepler Team, 2012, ApJS, 201, 15
  * Hrudková et al. (2010) Hrudková, M., Skillen, I., Benn, C. R., et al., 2010, MNRAS, 403, 2111
  * Ida & Lin (2004) Ida, S., & Lin, D. N. C. 2004, ApJ, 604, 388
  * Ida & Lin (2005) Ida, S., & Lin, D. N. C. 2005, ApJ, 626, 1045
  * Ida & Lin (2008) Ida, S., & Lin, D. N. C. 2008, ApJ, 673, 487
  * Ida & Lin (2010) Ida, S., & Lin, D. N. C. 2010, ApJ, 719, 810
  * Ikoma et al. (2000) Ikoma, M., Nakazawa, K., & Emori, E., 2000, ApJ, 537, 1013
  * Jang-Condell (2007) Jang-Condell, H., 2007, ApJ, 654, 641
  * Johansen et al. (2007) Johansen, A., Oishi, J. S., Mac, L. M.-M., et al., 2007, Nature 448, 1022
  * Johansen et al. (2008) Johansen, A., Brauer, F., Dullemond, C., et al., 2008, A&A, 486, 597
  * Johnson et al. (2007) Johnson, J. A. , Butler, R. P. , Marcy, G. W., et al. 2007, ApJ, 670, 833
  * Johnson et al. (2009) Johnson, J. A., Winn, J. N., Albrecht, S., et al., 2009, PASP, 121, 1104
  * Johnson et al. (2010) Johnson, J. A., et al., 2010, PASP, 122, 905J
  * Johnson & Li (2012) Johnson, J. L., & Li, H., ApJ, 751,81
  * Jones et al. (2003) Jones, H. R. A. , Butler, R. P. , Tinney, C. G., et al., 2003, MNRAS, 341, 948
  * Juric & Tremaine (2008) Juricć, Mario & Tremaine, Scott, 2008, ApJ, 686, 603
  * Kaib et al. (2012) Kaib, N. A., Duncan, M. J., & Raymond, S. N., 2012, in AAS/Division of Dynamical Astronomy Meeting, 43, 0506
  * Kalas et al. (2008) Kalas,P., Graham,J.R., Chiang. E., et al., 2008, Science 322,1345
  * Kennedy & Kenyon (2008) Kennedy, G. M. , & Kenyon, S. J., 2008, ApJ, 673, 502
  * Kley (2001) Kley, W., 2001, IAUS, 200, 511
  * Kley & Nelson (2008) Kley, W., & Nelson, R. P., 2008, A&A, 486, 617
  * Kley & Nelson (2012) Kley, W., & Nelson, R. P., 2012, arxiv: 1203. 1184
  * Königl (1991) Königl, A., 1991, ApJ, 370, L39
  * Kokubo & Ida (1996) Kokubo, E., & Ida, S., 1996, Icarus, 123, 180
  * Kokubo & Ida (1998) Kokubo, E., & Ida, S., 1998, Icarus, 131, 171
  * Kokubo & Ida (2000) Kokubo, E., & Ida, S., 2000, Icarus, 143, 15
  * Kokubo et al. (2006) Kokubo, E., Kominami, J., & Ida, S., 2006, ApJ, 642, 1131
  * Kortenkamp et al. (2001) Kortenkamp, S. J., Wetherill, G. W., & Inaba, S., 2001, Science, 293, 1127
  * Kozai (1962) Kozai, Y., 1962, AJ, 67, 591
  * Kratter & Perets (2012) Kratter, K. M., & Perets, H. B., 2012, ApJ, 753, 91
  * Lai et al. (2011) Lai, D., Foucart, F., & Lin, D. N. C., 2011, MNRAS, 412, 2790
  * Lagrange et al. (2009) Lagrange,A.-M., Gratadour, D., Chauvin, G., Fusco, T., et al. 2009, A&A, 493, L21-L25
  * Larwood et al. (1996) Larwood, J. D., Nelson, R. P., Papaloizou, J. C. B., & Terquem, C., 1996, MNRAS, 282, 597
  * Laughlin et al. (2004) Laughlin, G. , Bodenheimer, P. , & Adams, F. C. 2004, ApJ, 612, L73
  * Lee at al. (2009) Lee, J. W., Kim, S. L., Kim, C. H., et al., 2009, AJ, 137, 3181
  * Lee & Peale (2002) Lee, M. H., & Peale, S. J., 2003, ApJ, 567, 596
  * Levison & Agnor (2003) Levison, H. F., & Agnor, C., 2003, AJ, 125, 2692
  * Lidov (1962) Lidov, M. L., 1962, Planet. Space Sci., 9, 719
  * Lin et al. (1996) Lin, D.N.C., Bodenheimer, P., & Richardson, D. C., 1996, Nature, 380, 606L
  * Lin & Papaloizou (1986) Lin, D.N.C., & Papaloizou, J.C.B., 1986, ApJ, 309, 846L
  * Lin & Papaloizou (1996) Lin, D.N.C., & Papaloizou, J.C.B., 1996, ARA&A 34,703
  * Lissauer (1993) Lissauer, J. J., 1993, ARA&A, 31, 129
  * Lissauer (1995) Lissauer, J. J., 1995, Icarus, 114, 217
  * Lissauer et al. (2011) Lissauer, J. J., Fabrycky, D. C., Ford, E. B., et al., 2011, Nature, 470,53
  * Liu et al. (2011) Liu, H.-G., Zhou,J.-L., & Wang, S., 2011, ApJ, 732,66
  * Lithwick & Naoz (2011) Lithwick, Y., & Naoz, S., 2011, ApJ, 742, 94
  * Lithwick & Wu (2011) Lithwick, Y., & Wu, Y., 2012, arXiv: 1204. 2555
  * Lovis & Mayor (2007) Lovis, C. & Mayor, M., 2007, A&A, 472, 657
  * Lovis et al. (2011) Lovis, C., Ségransan, D., Mayor, M., et al., 2011, A&A, 528, A112
  * Lucas & Roche (2000) Lucas, P. W., & Roche, P. F., 2000, MNRAS, 314, 858
  * Malmberg et al. (2007a) Malmberg, D., Davies, M. B., & Chambers, J. E., 2007, MNRAS, 377, L1
  * Malmberg et al. (2007b) Malmberg, D., de Angeli, F., Davies, M. B., et al., 2007, MNRAS, 378, 1207
  * Malmberg et al. (2009) Malmberg, D., & Davies M. B., 2009, MNRAS, 394, L26
  * Malmberg et al. (2011) Malmberg, D., Davies, M. B., & Heggie, D. C., 2011, MNRAS, 411, 859
  * Marcy & Butler (1996) Marcy G. W., & Butler R. P., 1996, ApJL, 464, L147
  * Marcy et al. (2005a) Marcy, G., Butler, R. P., Fischer, D., et al., 2005a, PThPS, 158, 24
  * Marois et al. (2008) Marois, C. , Macintosh,B., Barman T., et al., 2008, Science, 322, 1348
  * Marti & Beauge (2012) Marti, J., & Beauge, C., 2012, arXiv: 1206. 4875
  * Marzari & Scholl (2000) Marzari, F., & Scholl, H., 2000, ApJ, 543, 328
  * Marzari et al. (2005) Marzari, F., Weidenschilling, S. J., Barbieri, M., & Granata, V., 2005, ApJ, 618, 502
  * Marzari et al. (2009) Marzari, F., Thébault, P., & Scholl, H., 2009, A&A, 507, 505
  * Matsuyama et al., (2003) Matsuyama, I., Johnstone, D., & Hartman, L., 2003, ApJ, 582, 893
  * Matsumura et al. (2010) Matsumura, S., Thommes, E. W., Chatterjee, S., & Rasio, F. A., 2010, ApJ, 714, 194
  * Mayer et al. (2010) Mayer, L., Boss, A., & Nelson, A. F., 2010, ASSL, 366, 195
  * Mayor & Queloz (1995) Mayor, M., & Queloz, D., 1995, Nature, 378, 355
  * Mayor et al. (2003) Mayor, M., Pepe, F., Queloz, D., et al., 2003, Msngr, 114, 20M
  * Mayor et al. (2011) Mayor, M., Marmier, M., Lovis, C., et al., 2011, arXiv: 1109. 2497
  * McLaughlin (1924) McLaughlin D. B., 1924, ApJ, 60, 22
  * Meschiari (2012) Meschiari, S., 2012, ApJ, 752, 71
  * Mizuno (1980) Mizuno, H., 1980, PThPS, 64, 544
  * Mochejska et al. (2006) Mochejska, B. J., Stanek, K. Z., Sasselov, D. D., et al., 2006, AJ, 131, 1090
  * Morbidelli et al. (2005) Morbidelli, A., Levison, H. F., Tsiganis, K. & Gomes, R., 2005, Nature, 435, 462
  * Mordasini et al. (2009a) Mordasini, C., Alibert, Y., & Benz, W., 2009a, A&A, 501, 1139
  * Mordasini et al. (2009b) Mordasini, C., Alibert, Y., Benz, W., & Naef, D., 2009b, A&A, 501, 1161
  * Mordasini et al. (20012) Mordasini, C., Alibert, Y., Benz, W., Klahr, H., & Henning, T., 2012, A&A, 541, A97
  * Mortier et al. (2012) Mortier, A., Santos, N. C., Sozzetti, A., et al., 2012, A&A, 543, A45
  * Mugrauer & Neuhäuser (2009) Mugrauer, M., & Neuhäuser, R., 2009, A&A, 494, 373
  * Müller & Kley (2012) Müller, T. W. A., & Kley, W., 2012, A&A, 539, A18
  * Murray & Dermott (1999) Murray, C. D., & Dermott, S. F., 1999, Solar system Dynamics, Cambridge University Press
  * Nagasawa et al. (2003) Nagasawa, M., Lin, D. N. C. & Ida, S. , 2003, ApJ, 586, 1374N
  * Nagasawa et al. (2008) Nagasawa, M., Ida, S., & Bessho, T., 2008, ApJ, 678, 498
  * Nagasawa et al. (2011) Nagasawa, M. & Ida, S., 2011, ApJ, 742, 72N
  * Nascimbeni et al. (2012) Nascimbeni, V., Bedin, L. R., Piotto1, G., Marchi, F. De, & Rich, R. M., 2012, A&A, 541, 144
  * Naoz et al. (2011a) Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J., 2011, Nature, 473, 187
  * Naoz et al. (2011b) Naoz, S.; Farr, W.M; Lithwick, Y.., Rasio, F.A., & Teyssandier, J., 2011, arXiv: 1107. 2414
  * Ormel & Kobayashi (2012) Ormel, C. W., & Kobayashi, H., 2012, ApJ, 747, 115
  * Paardekooper & Leinhardt (2010) Paardekooper, S.-J., & Leinhardt, Z. M., 2010, MNRAS, 403, L64
  * Paardekooper et al. (2008) Paardekooper, S.-J., Thébault, P., & Mellema, G., 2008, MNRAS, 386, 973
  * Parker & Quanz (2012) Parker, R. J., & Quanz, S. P., 2012, MNRAS, 419, 2448P
  * Papaloizou & Terquem (2001) Papaloizou, J. C. B., & Terquem, C., 2001, MNRAS, 325, 221
  * Pascucci et al. (2008) Pascucci, I., Apai, D., Hardegree-Ullman, E. E., et al., 2008, ApJ, 673, 477
  * Pätzold& Rauer (2002) Pätzold, M., & Rauer, H., 2002, ApJ, 568, L117
  * Perets (2010) Perets, H. B., 2010, arXiv: 1001. 0581
  * Perets & Kouwenhoven (2012) Perets, H. B., & Kouwenhoven, M. B. N., 2012, ApJ, 750, 83
  * Pfahl (2005) Pfahl, E., 2005, ApJ, 635, L89
  * Pichardo et al. (2005) Pichardo, B., Sparke, L. S., & Aguilar, L. A., 2005, MNRAS, 359, 521
  * Pierens & Nelson (2007) Pierens, A., & Nelson, R. P., 2007, A&A, 472, 993
  * Pierens & Nelson (2008a) Pierens, A., & Nelson, R. P., 2008, A&A, 478, 939
  * Pierens & Nelson (2008b) Pierens, A., & Nelson, R. P., 2008, A&A, 483, 633
  * Pollack et al. (1996) Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al., 1996, Icarus, 124, 62
  * Potter et al. (2011) Potter, S. B., Romero-Colmenero, E., Ramsay, G., et al., 2011, MNRAS, 416, 2202
  * Qian et al. (2010) Qian, S.-B., Liao, W.-P., Zhu, L.-Y., & Dai, Z.-B., 2010, ApJ, 708, L66
  * Queloz et al. (2000b) Queloz, D., Mayor, M., Weber, L., et al., 2000, A&A, 354, 99
  * Quinn et al. (2012) Quinn, S. N., White, R. J., Latham, D. W., et al. arXiv:1207.0818
  * Quintana (2004) Quintana, E. V., 2004, Ph.D. Thesis,
  * Quintana & Lissauer (2006) Quintana, E. V., & Lissauer, J. J., 2006, Icarus, 185, 1Q
  * Quintana et al. (2007) Quintana, E. V., Adams, F. C., Lissauer, J. J., & Chambers, J. E., 2007, ApJ, 660, 807
  * Rabus etal. (2009) Rabus, M., Deeg, H. J., Alonso, R., Belmonte, J. A., & Almenara, J. M., 2009, A&A, 508, 1011
  * Rafikov (2003) Rafikov, R. R., 2003, AJ, 125, 942
  * Rafikov (2004) Rafikov, R. R., 2004, AJ, 128, 1348
  * Raghavan et al. (2006) Raghavan, D., Henry, T. J., Mason, B. D., et al., 2006, ApJ, 646, 523
  * Raghavan et al. (2010) Raghavan, D., McAlister, H. A., Henry, T. J., et al., 2010, ApJS, 190, 1
  * Rasio & Ford (1996) Rasio, F. A. & Ford, E. B., 1996, Science, 274, 954R
  * Rivera et al. (2010) Rivera, E. J.; Laughlin, G.; Butler, R. P. et al. 2010,ApJ, 719,890
  * Raymond et al. (2006) Raymond, S. N., Mandell, A. M. & Sigurdsson, S., 2006, Science, 313, 1413R
  * Raymond et al. (2008) Raymond, S. N., Barnes, R., & Mandell, A., 2008, MNRAS, 384, 663
  * Roell et al. (2012) Roell, T., Neuh auser, R., Seifahrt, A., & Mugrauer, M. 2012, A&A, 542, A92
  * Rosvick & Robb (2006) Rosvick, J. M., & Robb, R., 2006, AJ, 132, 2309
  * Rossiter (1924) Rossiter R. A., 1924, ApJ, 60, 15
  * Saleh & Rasio (2009) Saleh, L. A., & Rasio, F. A., 2009, ApJ, 694, 1566
  * Santos et al. (2001) Santos, N. C., Israelian, G., & Mayor, M., 2001, A&A, 373, 1019
  * Santos et al. (2004) Santos, N. C., Israelian, G., & Mayor, M., 2004, A&A, 415, 1153
  * Sato et al., (2007) Sato, B., Izumiura, H., Toyota, E., et al., 2007, ApJ, 661, 527
  * Schlaufman & Laughlin (2011) Schlaufman, K. C. & Laughlin, G., 2011, ApJ738, 177
  * Sara & Drake (2010) Seager, S., & Deming, D., 2010, ARA&A, 48, 631
  * Socrates et al. (2012) Socrates, A., Katz, B., Dong, S., & Tremaine, S., 2012, ApJ, 750, 106
  * Sousa et al. (2008) Sousa, S. G., Santos, N. C., Mayor, M., et al., 2008, A&A, 487, 373
  * Sousa et al. (2011) Sousa, S. G., Santos, N. C., Israelian, G., Mayor, M., & Udry, S., 2011, A&A, 533, A141
  * Sozzetti et al. (2009) Sozzetti, A., Torres, G., Latham, D. W., et al., 2009, ApJ, 697, 544
  * Spurzem et al. (2009) Spurzem, R., Giersz, M., Heggie, D. C., & Lin D. N. C. 2009, ApJ, 697, 458
  * Steffen et al. (2012) Steffen, J. H., Ragozzine, D., Faabrycky, D. C., et al., 2012, arXiv: 1205. 2309S
  * Stewart & Leinhardt (2009) Stewart, S. T., & Leinhardt, Z. M., 2009, ApJ, 691, L133
  * Sumi et al., (2011) Sumi, T., Kamiya, K., Bennett, D. P., et al., 2011, Nature, 473, 349
  * Tabachnik & Tremaine (2002) Tabachnik, S. , & Tremaine, S., 2002, MNRAS, 335, 151
  * Takeda et al. (2008) Takeda, G., Kita, R., & Rasio, F. A., 2008, ApJ, 683, 1063
  * Tanaka et al. (2002) Tanaka, H., Takeuchi, T., & Ward, W. R. 2002, ApJ, 565, 1257
  * Terquem & Papaloizou, (2007) Terquem, C., & Papaloizou, J. C. B., 2007, ApJ, 654, 1110
  * Thébault et al. (2006) Thébault, P., Marzari, F., & Scholl, H., 2006, Icarus, 183, 193
  * Thébault et al. (2008) Thébault, P., Marzari, F., & Scholl, H., 2008, MNRAS, 388, 1528
  * Thébault et al. (2009) Thébault, P., Marzari, F., & Scholl, H., 2009, MNRAS, 393, L21
  * Thommes et al. (2008) Thommes, E. W., Matsumura, S., & Rasio, F. A., 2008, Science, 312, 814
  * Tremaine & Dong (2012) Tremaine, S. & Dong, S. B., 2012, AJ, 143, 94
  * Triaud et al. (2010) Triaud, A., et al., 2010, A&A, 524, A25
  * Tsiganis et al. (2005) Tsiganis, K., Gomes, R., Morbidelli, A., & Levison, H. F., Nature, 435, 459
  * Tutukov & Fedorva (2012) Tutukov, A.V., & Fedorova, A. V. 2012, Astronomy Report, 56,305
  * Udry et al. (2002) Udry, S. , Mayor, M. , Naef, D., et al., 2002, A&A, 390, 267
  * Udry et al. (2003) Udry, S. , Mayor, M. , & Santos, N. C., 2003, A&A, 407, 369
  * Udry & Santos (2007) Udry, S. & Santos, N. C., 2007, ARA&A, 45, 397
  * Udry et al. (2006) Udry, S., Mayor, M., Benz, W., et al., 2006, A&A, 447, 361
  * Veras & Raymond, (2012) Veras, D., & Raymond, S. N., 2012, MNRAS, 421L. 117V
  * Wang et al. (2012) Wang, S., Ji,J.H., & Zhou, J.-L., 2012, ApJ, 753, 170
  * Wang et al. (2011) Wang, J., Feigelson, E. D., Townsley, L. K., et al., 2011, ApJS, 194, 11W
  * Ward (1986) Ward, W. R., 1986, Icarus, 67, 164
  * Ward (1997) Ward, W. R., 1997, Icarus, 126, 261
  * Weidenschilling & Cuzzi (1993) Weidenschilling, S. J., & Cuzzi, J. N., 1993, in Protostars and Planets III, ed. E. H. Levy & J. I. Lunine (Tucson: Univ. Arizona Press), 1031
  * Weidenschilling (1997) Weidenschilling, S. J., 1997, Icarus, 127, 290
  * Weldrake et al. (2005) Weldrake, D. T. F., Sackett, P. D., Bridges, T. J., & Freeman,K. C., 2005, ApJ, 620, 1043
  * Weldrake et al. (2007) Weldrake, D. T. F.; Sackett, P. D., & Bridges, T. J., 2007, ASPC, 366, 289W
  * Welsh et al. (2012) Welsh, W. F., Orosz, J. A., Carter, J. A., et al., 2012, Nature, 481, 475
  * Wetherill & Stewart (1989) Wetherill, G. W., & Stewart, G. R., 1989, Icarus, 77, 330
  * Wetherill (1990) Wetherill G. W., 1990, AREPS, 18, 205
  * Whitmire et al. (1998) Whitmire, D. P., Matese, J. J., Criswell, L., & Mikkola, S., 1998, Icarus, 132, 196
  * Windmark et al. (2012) Windmark, F., Birnstiel, T., Güttler, C., et al., 2012, A&A, 540, A73
  * Winn et al. (2010) Winn J. N., Fabrycky D., Albrecht S. & Johnson J. A., 2010, ApJL, 718, L145
  * Wittenmyer et al. (2010) Wittenmyer, R. A.; O’Toole, S. J.; Jones, et al. 2010 ApJ, 722, 1854
  * Wittenmyer et al. (2011a) Wittenmyer, R. A.; Tinney, C. G.; O’Toole, S. J. et al. 2011a, ApJ, 727, 102
  * Wittenmyer et al. (2011b) Wittenmyer, R. A.; Tinney, C. G.; Butler, R. P., et al. 2011b, ApJ, 738, 81
  * Wright et al. (2009) Wright J. T., et al., 2009, ApJ, 693, 1084
  * Wright et al. (2011) Wright J. T., Veras, D., Ford, E., et al., 2011, ApJ, 730, 93,
  * Wright et al. (2012) Wright J. T., Marcy G. W., Howard A. W., et al., 2012, ApJ, 753, 160
  * Wu & Murray (2003) Wu, Y., & Murray, N., 2003, ApJ, 589, 605
  * Wu et al. (2007) Wu, Y., Murray, N. W., & Ramsahai, J. M., 2007, ApJ, 670, 820
  * Wu & Lithwick (2011) Wu, Y., & Lithwick, Y., 2011, ApJ, 735, 109
  * Xie & Zhou (2008) Xie, J.-W., & Zhou, J.-L., 2008, ApJ, 686, 570
  * Xie & Zhou (2009) Xie, J.-W., & Zhou, J.-L., 2009, ApJ, 698, 2066
  * Xie et al. (2010b) Xie, J.-W., Payne, M. J., Thébault, P., Zhou, J.-L., & Ge, J., 2010, ApJ, 724, 1153
  * Xie et al. (2011) Xie, J.-W., Payne, M. J., Thébault, P., Zhou, J.-L., & Ge, J. 2011, ApJ, 735, 10
  * Yasui et al. (2009) Yasui, C., Kobayashi, N., Tokunaga, A. T., Saito, M. & Tokoku, C., 2009, ApJ, 705, 54
  * Youdin & Shu (2002) Youdin, A. N. & Shu, F. H.,2002, ApJ, 580, 494
  * Zhang & Zhou (2010a) Zhang,H.& Zhou,J.-L., 2010a, ApJ, 714,532
  * Zhang & Zhou (2010b) Zhang,H.& Zhou,J.-L., 2010b, ApJ, 719,671
  * Zhao et al. (2012) Zhao, G., Xie, J.-W., Zhou, J.-L., & Lin, D. N. C., 2012, ApJ, 749, 172
  * Zhou et al. (2010) Zhou, J.-L., 2010, EAS, 42, 255
  * Zhou et al. (2005) Zhou, J.-L., Aarseth, S. J., Lin, D. N. C., & Nagasawa, M., 2005 ApJ, 631:L85
  * Zhou at al. (2007) Zhou, J.-L., Lin, D. N. C. & Sun, Y.-S., 2007, ApJ, 666, 423
  * Zucker & Mazeh (2002) Zucker, S., & Mazeh, T., 2002, ApJ, 568, L113
  * Zucker& Mazeh (2003) Zucker, S., & Mazeh, T., 2003, ASPC, 294, 31
  * Zucker et al. (2004) Zucker, S., Mazeh, T., Santos, N. C., Udry, S., & Mayor, M., 2004, A&A, 426, 695