In this paper we discuss an alternative track for migration that can explain
the existence of Hot Jupiters observed in close orbits around their stars based
on a novel interpretation of established work. We also discuss the population
of sub-Earth rogue planets that would be created via this migration method,
which would be on the order of 2 to 40 billion, many of which would still be
present in the Galaxy and potentially detectable.Comment: 5 pages, 1 figure. Submitted to Acta Prima Aprili

Lund, Michael B.

English

arXiv

In this paper we discuss an alternative track for migration that can explain the existence of Hot Jupiters observed in close orbits around their stars based on a novel interpretation of established work. We also discuss the population of sub-Earth rogue planets that would be created via this migration method, which would be on the order of 2 to 40 billion, many of which would still be present in the Galaxy and potentially detectable

Caltech Authors - Main

Acta Prima Aprilia • April 2019 • Vol. V
Worlds in Migration
Michael B. Lund1
1CalTech/IPAC-NExScI
mlund@ipac.caltech.edu
Abstract
In this paper we discuss an alternative track for migration that can explain the existence of Hot Jupiters
observed in close orbits around their stars based on a novel interpretation of established work. We also
discuss the population of sub-Earth rogue planets that would be created via this migration method, which
would be on the order of 2 to 40 billion, many of which would still be present in the Galaxy and potentially
detectable.
I. Introduction
In the current era of astronomy, discover-ies of exoplanets have become frequent andalmost ubiquitous. Though the existence
of planets outside our solar system had been
discussed as a concept (such as by Bruno (1584)
and Struve (1952) to very different results), it
was surprising when some of the first plan-
ets found differed greatly from our own So-
lar System’s architecture, particularly as they
tended to be Jupiter-like planets orbiting in
very close orbits around their host stars (Mayor
and Queloz, 1995).
This has naturally led to the challenge to
understand how planetary formation processes
can have such diversity as to produce not just
our own solar system, but the myriad of plan-
etary systems that have now been discovered.
While there has been some suggestion that Hot
Jupiters are able to form in situ close to their
host stars (Batygin et al., 2016), there is also sig-
nificant evidence that some Hot Jupiters must
have migrated inward. Several discovered plan-
ets are known to be so close to their host stars
that they have high rates of mass loss, such
as GJ 3470b (Bourrier et al., 2018), WASP-12b
(Hebb et al., 2009; Lammer et al., 2009), and
KELT-9b (Gaudi et al., 2017). Multiple channels
have been proposed for how Hot Jupiters mi-
grate inward in their systems, including migra-
tion within the gas disk (D’Angelo and Lubow,
2008) or through planet-planet interactions and
the Kozai-Lidov mechanism (Kozai, 1962; Li-
dov, 1962). These pathways for Hot Jupiter for-
mation have already been compared in great
detail (Dawson and Johnson, 2018).
In this paper we propose a renewed consid-
eration of planetary migration as an extension
of some ideas initially proposed in Velikovsky
(1950), and which despite the criticism that they
have received (Goldsmith et al., 1977) may help
explain migration as observed in Hot Jupiters
when properly considered. We refer to this
mechanism as Type V migration.
II. Type V Migration
While Velikovsky (1950) does not present a
pathway for Hot Jupiter migration explicitly,
his work does outline a mechanism that can
be applied to characterize Hot Jupiter migra-
tion. Velikovsky presented work on the sudden
formation and migration of smaller terrestrial
planets on short timescales, on the order of
thousands of years. His work specifically fo-
cused on limited migration within our own
solar system, explaining how electromagnetic
forces could cause Venus to be ejected from
within Jupiter’s atmosphere before arriving
on its current orbit. Velikovsky’s hypothesis
was in part based on prior work regarding the
formation of new bodies directly from Jupiter
(Hesiod, 700BC).
We instead choose to focus on the influence
that such actions would have on Jupiter, or a
Jupiter-analogue, rather than on the smaller ter-
restrial body. The energy loss for the ejection
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Acta Prima Aprilia • April 2019 • Vol. V
of a single terrestrial object can be described
as a function of the mass and velocity of the
departing object:
∆E =
1
2
M♀v2 (1)
Due to the scope of this work we fix M♀ at 1
Venusian mass, or 0.815 M (Konopliv et al.,
1999). The velocity at time of ejection is a
slightly more complex problem. We examine
three different velocities, 100 km/s, 300 km/s,
and 1000 km/s, the first two representing the
velocities of most stars in the Milky Way, with
the last being typical of a hypervelocity star
(Boubert et al., 2017; Hills, 1988). Note that this
velocity is combined with the escape velocities
necessary for both escaping the mass of the
Jovian planet and the host star (as 1 M in this
work) and can be expressed using the equation
for escape velocity:
Vesc =
√
2GM
r
(2)
Here the mass in question is of the primary
object, and r represents the Jovian planetary
radius or the orbital radius of the Jovian planet
for escape velocities from the planet and from
the star respectively. We treat the Jovian ra-
dius as 1RJ for our purposes. These energy
calculations neglect relativistic effects (Einstein,
1905).
By using the change in energy as calculated
by 1, we can then determine how the orbital
radius of the planet, in turn, changes by calcu-
lating the new orbital radius as a function of
∆E, Mplanet, M∗, and the current orbital radius,
as given in Eq.3.
r2 =
1
1
r1
− 2∆EGMplanet M∗
(3)
III. Simulations
In order to simulate the impact that Type V mi-
gration can have on a Jovian planet, we carry
out a suite of planetary migration simulations.
Our simulations use a range of Jovian planets
between 2 and 8 MJ , all of which we place at
a distance of 5 AU initially (Jewitt et al., 2007).
We then eject 500 Venusian-mass planets with
the three different final velocities mentioned
in §II, tracking how the planetary mass and
orbital radius change, as shown in Figure 1.
Our results show that it is quite possible
that a Jovian-mass planet can lose sufficient
mass and energy to migrate inward to the semi-
major axis regime of Hot Jupiters while still
maintaining sufficient mass to fit our observa-
tions. In the case of a 2MJ planet, all tracks
reach our final semi-major axis goal of 0.05 AU,
with the slowest process requiring somewhat
over 100 ejections. Alternatively, the hyperve-
locity ejections require fewer than 10 ejections
from the 2MJ planet to migrate to a 0.05 AU
orbital radius. Even in the high-mass case of
8MJ , the 0.05 AU distance is reached for all
tracks, although this does require more ejec-
tion events.
IV. Discussion
The natural product of this Type V migration
channel is a Galactic population of rogue plan-
ets. The existence of such planets has been
discussed in several prior works, including
some discussion of the dynamical histories
required to create them (Bear, 2000; Lissauer,
1987; Laughlin and Adams, 2000). Type V mi-
gration necessitates that the Jovian planet re-
mains in the system and only the terrestrial
planet is actually ejected. Therefore, our de-
scribed Type V migration mechanism is con-
sistent with more recent microlensing observa-
tions that have found that while there are not
many large rogue planets, there may be a large
number of terrestrial-sized rogue exoplanets
within the Milky Way (Mróz et al., 2017). These
ejected planets fall well within the sensitivity
range of the upcoming Wide-Field InfraRed
Survey Telescope (WFIRST) microlensing mis-
sion (Gehrels et al., 2015), which will be sensi-
tive to planets down to the size of Ganymede
(Penny et al., 2019).
The estimated fraction of stars that host
Hot Jupiters is around 1% (Wang et al., 2015).
With roughly 20 billion roughly sun-like stars
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Acta Prima Aprilia • April 2019 • Vol. V
Figure 1: The orbital radius of a Jovian planet as a function of remaining planetary mass for a range of initial planetary
masses. For each initial planetary mass we examine three different tracks (as indicated by the symbols) that
correspond to the resulting velocity of the ejected Venusian-mass bodies. The markers after the initial mass
represent Jovian mass-loss corresponding to 10, 50, 100, 250, and 500 Venusian masses. Our starting point
at the snow line is the red solid line at 5 AU, and the end point of 0.05 AU is the red dashed line.
in the galaxy (Plait, 2013), this translates to
200 million Hot Jupiters. Given the number of
terrestrial planet ejections needed to generate
this number of Hot Jupiters, our simulations
suggest a population of 2-40 billion rogue Venu-
sians in the Galaxy. We note, however, that if
a significant fraction of these ejections involve
hypervelocity planets, then the number still in
the galaxy may be notably reduced as these
bodies would be traveling in excess of galactic
escape velocities, and so could become inter-
galactic planetary bodies (Beastie Boys, 1998).
While their fates have not been the pri-
mary focus of this work, these rogue Venusians
(which have been speculated upon in previous
works (Lovecraft and Sterling, 1939; Heinlein,
1951; Sterling, 1961; Adamski and Leslie, 1977))
would also be prime candidates for Steppen-
wolf planets (Abbot and Switzer, 2011), since
they constitute a population of smaller terres-
trial planets with thick insulating atmospheres
that may be much more hospitable when not
subject to the high irradiation that Venus re-
ceives.
V. Summary
In this paper we have proposed that the work
of Velikovsky should be revisited in terms of
how the ejection of small terrestrial planets
from gas giants may provide an alternative mi-
gration track that can explain the observed pop-
ulation of Hot Jupiters. This would addition-
ally indicate a population of rogue Venusian
exoplanets numbering between 2 and 40 billion
that may be detected by future microlensing
missions such as WFIRST.
VI. Acknowledgements
The author thanks Savannah R. Jacklin for her
valuable feedback on this manuscript.
This research made use of Astropy,1 a
community-developed core Python package
1http://www.astropy.org
14
Acta Prima Aprilia • April 2019 • Vol. V
for Astronomy (Astropy Collaboration et al.,
2013; Price-Whelan et al., 2018).
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