Radial Velocity Discovery of an Eccentric Jovian World Orbiting at 18au
Sarah Blunt
1
,
2
,
18
, Michael Endl
3
, Lauren M. Weiss
4
,
19
, William D. Cochran
3
, Andrew W. Howard
1
,
Phillip J. MacQueen
3
, Benjamin J. Fulton
1
,
15
, Gregory W. Henry
14
, Marshall C. Johnson
3
,
12
, Molly R. Kosiarek
5
,
18
,
Kellen D. Lawson
8
, Bruce Macintosh
9
, Sean M. Mills
1
, Eric L. Nielsen
9
, Erik A. Petigura
1
, Glenn Schneider
7
,
Andrew Vanderburg
16
,
20
, John P. Wisniewski
8
, Robert A. Wittenmyer
3
,
13
, Erik Brugamyer
3
, Caroline Caldwell
3
,
Anita L. Cochran
3
, Artie P. Hatzes
10
, Lea A. Hirsch
9
, Howard Isaacson
6
,
17
, Paul Robertson
3
,
11
, Arpita Roy
1
, and
Zili Shen
3
1
Department of Astronomy, California Institute of Technology, Pasadena, CA, USA
2
Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA
3
McDonald Observatory and Department of Astronomy, The University of Texas at Austin, Austin, TX, USA
4
Institute for Astronomy, University of Hawai
‘
i, Honolulu, HI, USA
5
Department of Astronomy & Astrophysics, University of California, Santa Cruz, CA, USA
6
Astronomy Department, University of California, Berkeley, CA, USA
7
Steward Observatory, The University of Arizona, Tucson, AZ, USA
8
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA
9
Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA
10
Thüringer Landessternwarte, Tautenburg, Germany, EU
11
University of California, Irvine, CA, USA
12
Department of Astronomy, The Ohio State University, Columbus, OH, USA
13
Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, Australia
14
Center of Excellence in Information Systems, Tennessee State University, Nashville, TN, USA
15
IPAC-NASA Exoplanet Science Institute, Pasadena, CA, USA
16
Department of Astronomy, University of Texas at Austin, Austin, TX, USA
17
University of Southern Queensland, Toowoomba, QLD 4350, Australia
Received 2019 April 18; revised 2019 August 21; accepted 2019 August 21; published 2019 October 14
Abstract
Based on two decades of radial velocity
(
RV
)
observations using Keck
/
High Resolution Echelle Spectrometer
(
HIRES
)
and McDonald
/
Tull, and more recent observations using the Automated Planet Finder, we found that the
nearby star HR 5183
(
HD 120066
)
hosts a 3
M
J
minimum mass planet with an orbital period of
-
+
7
4
22
43
yr. The orbit
is highly eccentric
(
e
;
0.84
)
, shuttling the planet from within the orbit of Jupiter to beyond the orbit of Neptune.
Our careful survey design enabled high cadence observations before, during, and after the planet
’
s periastron
passage, yielding precise orbital parameter constraints. We searched for stellar or planetary companions that could
have excited the planet
’
s eccentricity, but found no candidates, potentially implying that the perturber was ejected
from the system. We did identify a bound stellar companion more than 15,000 au from the primary, but reasoned
that it is currently too widely separated to have an appreciable effect on HR 5183 b. Because HR 5183 b
’
s wide
orbit takes it more than 30 au
(
1
′′
)
from its star, we also explored the potential of complimentary studies with direct
imaging or stellar astrometry. We found that a
Gaia
detection is very likely, and that imaging at 10
μ
misa
promising avenue. This discovery highlights the value of long-baseline RV surveys for discovering and
characterizing long-period, eccentric Jovian planets. This population may offer important insights into the
dynamical evolution of planetary systems containing multiple massive planets.
Key words:
planets and satellites: detection
–
planets and satellites: fundamental parameters
–
stars: individual
(
HR 5183
)
Supporting material:
machine-readable table
1. Introduction
Radial velocity
(
RV
)
and transit surveys have characterized
very few planets beyond 5 au
(
Howard et al.
2010
; Mayor et al.
2011
; Fressin et al.
2013
; Petigura et al.
2013
)
,leavingthe
population characteristics of long-period planets largely unknown.
Direct imaging is sensitive to s
uch planets, but the current
generation of instruments is limited to planets several times the
mass of Jupiter orbiting young, massive stars
(
Bowler
2016
;
Nielsen et al.
2019
)
. Microlensing is also sensitive to planets at
large separations from their stars
, and microlensing results already
allow for occurrence calculations of planet mass as a function of
separation
(
Suzuki et al.
2016
)
. However, mircolensing results
will not enable detailed orbital or system architecture character-
ization. On the other hand, RV surveys are limited by their
baselines. Several authors have used RV trends or other
incomplete orbital arcs to constra
in the properties of long-period
planets and substellar objects
(
Wright et al.
2007
,
2009
; Knutson
et al.
2014
;Bouchyetal.
2016
; Bryan et al.
2016
; Rickman et al.
2019
)
, but it is challenging to pin do
wn the physical parameters of
planets with orbital periods much longer than the survey baseline.
Some authors assume circular orb
its in order to cut down the wide
parameter space of possible orbits
(
e.g., Knutson et al.
2014
)
, but
even so posteriors over semimajor axis and minimum mass span
wide ranges.
Long-baseline RV surveys dating back to the mid-1980s
(
Campbell
1983
; Marcy
1983
; Mayor & Maurice
1985
;
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
https:
//
doi.org
/
10.3847
/
1538-3881
/
ab3e63
© 2019. The American Astronomical Society. All rights reserved.
18
NSF Graduate Research Fellow.
19
Beatrice Watson Parrent Fellow.
20
NASA Sagan Fellow.
1
Campbell et al.
1988
; Marcy & Benitz
1989
; Marmier et al.
2013
; Zechmeister et al.
2013
; Fischer et al.
2014
; Wittenmyer
et al.
2014
; Moutou et al.
2015
; Endl et al.
2016
)
are beginning
to
fi
ll this characterization gap as their time baselines increase.
The long-period
(
>
1yr
)
planets discovered by these surveys
share characteristics with the directly imaged planets and the
shorter-period RV-discovered planets. As these surveys
mature, they will allow us to characterize the transition from
older, less massive, shorter-period RV-detected planets to
younger, more massive, longer-period imaged planets. These
new discoveries will also enable us to calculate the funda-
mental properties of planets in wider mass and age ranges than
those currently accessible to direct imaging alone, examine the
rarity of the Earth
–
Jupiter
–
Saturn architecture, and test giant
planet formation theories
(
Cumming et al.
2008
; Wittenmyer
et al.
2006
,
2011
,
2016
)
.
Here, we present the discovery of HR 5183 b, a highly
eccentric planet with a semimajor axis of
-
+
18
4
6
au orbiting a
V
=
6.3 G0 star. HR 5183 has been monitored for more than
20 yr as part of the California Planet Search at Keck
/
High
Resolution Echelle Spectrometer
(
HIRES
)
and the long-
duration RV planet survey at McDonald Observatory. After
over 10 yr of relatively constant RV measurements, HR 5183
began rapidly accelerating. In 2018, the RV measurements
fl
attened out and turned over, an event associated with the
planet
’
s periastron passage. As we discuss later in the paper,
this periastron passage event was information-rich, and allowed
precise constraints on the planet
’
s orbital parameters even
without RV coverage over the entire orbital period. With an
orbital period of
-
+
7
4
22
43
yr, HR 5183 b is the longest-period
planet with a well-constrained orbital period and minimum
mass detected with the RV technique.
This paper is organized as follows. In Section
2
, we present
our RV measurements of HR 5183. In Section
3
, we provide
precise estimates of the stellar parameters of HR 5183, and in
Section
4
, we characterize the planet HR 5183 b. In Section
5
,
we describe an extremely widely separated
(
>
15,000 au
)
stellar
companion to HD 5183, and present the results of searches for
additional stellar and planetary companions. In Section
6
,we
discuss prospects for multi-method detection of HR 5183 b. In
Section
7
, we relate HR 5183 b to other exoplanet systems,
comment on formation scenarios, and conclude.
2. High-resolution Spectra
We began Doppler monitoring of HR 5183 in 1997 at Keck
/
HIRES and in 1999 at McDonald
/
Tull. We have also
monitored HR 5183 on the Automated Planet Finder
(
APF
)
with high cadence since its commissioning in 2013. The RVs
from all three spectrographs are shown in Figure
1
and
tabulated in Table
1
.
2.1. HIRES Spectra
We obtained 78 high-resolution
(
R
=
60,000
)
spectra of HR
5183 with the HIRES spectrograph
(
Vogt et al.
1994
;Cumming
et al.
2008
;Howardetal.
2010
)
between 1997 and 2019. HIRES
underwent major upgrades in 2004, so for modeling purposes we
treat pre- and post-upgrade HIRES measurements independently
(
see Section
4
)
. Wavelength calibration for each RV measurement
was performed with a warm iodin
e-gas cell placed in the light
path in front of the slit, producing a convolved spectrum of the
star, iodine gas, and point-spread function
(
PSF
)
. Each spectrum
was forward-modeled with a deconvolved stellar spectrum
template, an atlas iodine spect
rum, and a line-spread function
(
Butler et al.
1996
)
. This technique is stable at the 2
–
3ms
−
1
level
on timescales of more than a decade
(
Howard & Fulton
2016
)
.
To monitor chromospheric and stellar spot activity, we
extracted spectral information at and near the Ca
II
H and K
lines to calculate a Mt. Wilson style
S
-index value
(
following
Wright et al.
2004
and Isaacson & Fischer
2010
)
for
measurements taken after the 2004 instrument upgrade.
S
-
index values for HIRES measurements taken before 2004 were
pulled directly from Wright et al.
(
2004
)
. These values do not
correlate signi
fi
cantly with time, the RV measurements, or the
RV residuals from the maximum a posteriori
(
MAP
)
orbit
(
see
Section
4
)
. In particular, the
S
-index values show no trends or
correlations with RV measurements on the timescale of the
proposed planet period.
2.2. Tull Spectra
Between 1999 and 2019, we collected 175 high-resolution
(
R
=
60,000
)
spectra with the Tull Coudé Spectrograph
(
Tull
et al.
1995
)
on the 2.7 m Harlan J. Smith telescope as part of
the McDonald Observatory planet search
(
Cochran et al.
1997
;
Hatzes et al.
2000
)
. For all observations, we inserted an iodine
absorption cell into the light path to obtain a precise
wavelength calibration. Combined with a template stellar
spectrum, this allowed us to reconstruct the shape of the
instrumental PSF at the time of each observation. We used the
RV modeling code
Austral
(
Endl et al.
2000
)
to compute
precise differential RVs.
We typically reach a long-term RV precision of 4
–
6
-
m
s
1
for inactive FGK-type stars with the Tull spectrograph. A major
advantage of the Tull RV survey is that the instrumental setup
has not been modi
fi
ed over the duration of the program. For
nearly 20 yr, we have been using the same CCD detector, the
same iodine cell, and the same positions of the Echelle grating
and cross-disperser prism. This assures that there are no RV
zero-point offsets introduced into the RV time series.
We determined the
S
-index values from the Ca
II
H and K
lines in the blue orders of the Tull spectra using the method
outlined in Paulson et al.
(
2002
)
. These
S
-index values also
show no trend or correlation with RV measurements over the
duration of the observations.
2.3. APF Spectra
Finally, we obtained 104 spectra of HR 5183 with the APF
(
Radovan et al.
2014
;Vogtetal.
2014
)
between 2013 and 2019.
The APF is an automated 2.4 meter telescope at Lick Observatory
on Mt. Hamilton, California. It
is equipped with the Levy
Spectrograph, a dedicated high-re
solution echelle spectrometer
that sits at a Nasmyth focus. The Levy Spectrograph achieves
R
>
120,000 and covers a wavelength range of 374.3
–
980.0 nm.
Spectra of HR 5183 were observed through a warm iodine-gas
cell for wavelength calibration. The RVs were calculated with the
pipeline described in Fulton et al.
(
2015
)
, which descends from
the Butler et al.
(
1996
)
pipeline, and is essentially identical to the
HIRES reduction pipelin
e discussed in Section
2.1
. As with the
HIRES data, we calculate
S
-index values following Isaacson &
Fischer
(
2010
)
.These
S
-index values similarly appear independent
of the RV measurements over the duration of the observations.
2
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
3. Stellar Properties
HR 5183 is a nearby slightly evolved G0 star. We derived
precise stellar parameters for HR 5183 using the method
described in Fulton et al.
(
2018
)
. Brie
fl
y, this method uses
Gaia
DR2 parallaxes
(
Gaia Collaboration et al.
2018
)
, spectroscopic
effective temperatures computed from our Keck template
spectrum with the
SpecMatch
code
(
Petigura
2015
)
, and
Two Micron All Sky Survey
(
2MASS
)
photometry
(
Skrutskie
et al.
2006
)
to compute precise stellar radii. log
g
,
[
Fe
/
H
]
, and
v
sin
i
are also calculated from the Keck spectrum using
Figure 1.
Top: RVs of HR 5183 from the Keck-HIRES, McDonald-Tull, and APF-Levy spectrographs as a function of time. Error bars show observational errors and
instrument-speci
fi
c jitter values added in quadrature. The best-
fi
t Keplerian orbit is shown
(
blue solid line
)
. Residuals are inset below. Bottom: close-up of the gray
region in top plot. The RV curve peaks in 2018 January during periastron passage, and declines monotonically afterward in all three data sets.
3
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
SpecMatch
. Stellar mass, age, and distance are derived using
the
isoclassify
21
package
(
Huber et al.
2017
)
. The stellar
properties derived from this analysis are presented in Table
2
,
along with other useful stellar parameters.
Allen & Monroy-Rodríguez
(
2014
)
found evidence that HR
5183 is in the halo of the Milky Way using reduced proper
motion diagrams following Salim & Gould
(
2003
)
. However,
HR 5183 is younger and more metal-rich than typical galactic
halo objects
(
Carollo et al.
2016
)
, which led us to scrutinize this
claim. To investigate the galactic population membership of
HD 5183, we performed a kinematic analysis of its galactic
orbit, following Johnson et al.
(
2018
)
. We used the
galpy
22
package
(
Bovy
2015
)
to compute 50 random realizations of
galactic positions and
U
,
V
,
W
space velocities for HR 5183
consistent with its
Gaia
DR2 parameters
(
Gaia Collaboration
et al.
2018
)
. For each realization, we then calculated the
galactic orbit of HR 5138 in
galpy
ʼ
s
“
MWPotential2014
”
galactic potential. The resulting orbits never achieve a height
above the galactic midplane of more than 200 pc. This result
supports the claim that HR 5183 is a thin-disk member, and not
a halo object.
4. Planet Properties
The curvature we saw in the RVs
(
see Figure
1
)
alerted us to
the existence of HR 5138 b, and motivated us to characterize its
orbital properties. We modeled the RV time series using the
open-source toolkit
radvel
23
(
Fulton et al.
2018
)
. The code
and data used to perform the analysis in this paper are available
on GitHub.
24
We chose to perform this
fi
t using the following
parameterization of the Keplerian RV function: log
P
,
T
C
,
w
e
cos
,
w
e
sin
, and log
K
. We imposed uninformative
uniform priors on each of these parameters except log
P
, for
which we de
fi
ned as an informative baseline prior. Because we
detected a long-period planet by observing a single, short-
duration event
(
the planet
’
s periastron passage
)
, we made an
analogy to detection by transit and de
fi
ned the following prior
on period, often used in the exoplanet transit community
(
e.g.,
Vanderburg et al.
2016
; Kipping
2018
)
:
=
-<
+
pP t B
Pt B
BtP
,,
1if
else
,1
d
d
d
⎧
⎨
⎩
()
()
()
where
t
d
is the duration of the event
(
in this case, the periastron
passage
)
,
P
is the orbital period, and
B
is the observing
baseline. See Section
4.1
for a justi
fi
cation of this choice of
prior and a detailed comparison to other possible models and
prior parameterizations. Unlike in the case of a transit
detection, the duration of the periastron passage event of HR
5183 is not easily de
fi
ned. We performed
fi
ts with
t
d
=
0 and
t
d
=
3.5 yr, ultimately
fi
nding that the results were indis-
tinguishable and sidestepping this issue. We adopted
t
d
=
0 for
convenience.
We also included jitter
(
σ
)
and RV offset
(
γ
)
terms for each
of our four RV data sets
(
we treated HIRES pre-2004 and post-
2004 measurements as separate data sets in our
fi
t; see
Section
2.1
)
. We assumed uninformative uniform priors on
each of these instrumental terms as well. The logarithm of the
complete likelihood for this model is
å
ss
ps s
=-
-
+
++
=
vM
ln
1
2
2ln 2
, 2
i
n
ii
ii
ii
0
2
jit,
2
2
jit,
2
1
2
⎡
⎣
⎢
⎤
⎦
⎥
()
()
()()
where
n
is the total number of RV measurements,
v
i
is the
i
th
RV measurement,
σ
i
is its uncertainty,
M
i
is the Keplerian
model prediction for observation
i
, and
σ
jit,
i
is the jitter
parameter for the instrument that took observation
i
(
Fulton
et al.
2016
)
.
We computed the MAP
fi
t with
radvel
, obtaining an
orbital period of 72.85 yr, a minimum mass of 3.24
M
J
, and an
eccentricity of 0.84. This orbital solution is shown in Figure
1
,
and a bird
’
s-eye view comparing this orbit to the orbits of the
solar system planets is shown in Figure
2
. We next performed
an Af
fi
ne-invariant Markov chain Monte Carlo
(
MCMC
)
Table 1
RVs and
S
-index Values
Time
RV
RV Unc.
Inst.
S
HK
a
S
HK
Unc.
(
BJD - 2440000
)(
ms
−
1
)(
ms
−
1
)
10463.1705
−
63.5
1.09
HIRES
b
0.14
0.01
10547.042
−
67.93
1.16
HIRES
b
0.14
0.01
10838.155
−
59.22
1.08
HIRES
b
0.14
0.01
10954.9271
−
63.3
1.61
HIRES
b
0.14
0.01
11200.1185
−
57.71
1.24
HIRES
b
0.14
0.01
11213.9789
−
51.69
9.03
TULL
0.15
0.02
11241.8948
−
35.6
4.08
TULL
0.15
0.02
11274.8541
−
49.01
8.4
TULL
0.16
0.02
11310.9479
−
63.84
1.34
HIRES
b
0.14
0.01
11329.7947
−
36.45
4.72
TULL
0.15
0.02
Notes.
a
Note that the
S
HK
values for each instrument do not have the same zero point.
Pre- and post-upgrade HIRES
S
-values should be treated independently.
b
Pre-upgrade HIRES measurement.
(
This table is available in its entirety in machine-readable form.
)
Table 2
Stellar Properties
Parameter
Value
Unit
R.A.
13 46 57
hh:mm:ss
Decl.
+
06 20 59
dd:mm:ss
HD Name
HD 120066
L
2MASS ID
J13465711
+
0621013
L
Gaia
Source ID
3721126409323324416
L
Parallax
31.757
±
0.039
mas
K
4.85
±
0.02
mag
V
6.30
mag
T
eff
5794
±
100
K
log
g
4.02
±
0.1
dex
[
Fe
/
H
]
0.10
±
0.06
dex
v
sin
i
3
±
1kms
−
1
R
*
-
+
1
.53
0.05
0.06
R
e
M
*
1.07
±
0.04
M
e
Age
-
+
7
.7
1.2
1.
4
Gyr
Distance
31.49
±
0.04
pc
Note.
T
eff
, log
g
,
[
Fe
/
H
]
, and
v
sin
i
were calculated from the stellar spectrum
using the
SpecMatch
code.
R
*
was calculated as described in Section
3
.
M
*
,
age, and distance were calculated using the
isoclassify
code.
21
GitHub.com
/
danxhuber
/
isoclassify
22
GitHub.com
/
jobovy
/
galpy
23
https:
//
radvel.readthedocs.io
/
en
/
latest
24
https:
//
github.com
/
California-Planet-Search
/
planet-pi
4
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
exploration of the parameter space with the ensemble sampler
emcee
25
(
Foreman-Mackey et al.
2013
)
. Our MCMC analysis
used 8 ensembles of 50 walkers and ran for 1552 steps per
walker, achieving a maximum Gelman
–
Rubin
(
Gelman et al.
2003
)
statistic of 1.001. A corner plot showing posterior
distributions and covariances between
T
P
,
P
,
M
sin
i
,
a
,
a
(
1
−
e
)
,
e
, and
ω
is shown in Figure
3
. These values are also
recorded in Table
3
.
4.1. Model Choice
We performed three additional orbit
fi
ts to evaluate our choice
of model. First, we performed two
fi
ts without informative
baseline priors on log
P
: one
fi
tting in
P
and
K
(
as opposed to
log
P
and log
K
)
, and another in log
P
(
fi
tting in log
P
versus
P
imposes an implicit Jeffrey
’
s prior on
P
)
. Period posteriors
obtained from these two models and the informative prior are
compiled in Table
4
. All three orbital period posteriors are
consistent within 1
σ
, but the informative baseline prior pushes the
median orbital period to shorter v
alues. Neither of these priors
signi
fi
cantly change the posteriors on the other orbital parameters;
for example,
fi
tting in log
P
gives
M
sin
i
=
-
+
3
.28
0.15
0.16
M
J
and
e
=
0.87
±
0.05. The slight dependence of the solution on our
prior choice ultimately points to the need for more data, but in the
meantime we adopt the informative prior.
Next, we performed a
fi
t including a
g
̇
parameter to account
for potential additional wider-separation companions in
fl
uen-
cing the RV signal of the star. Adding this free parameter has
the effect of pushing the eccentricity posterior to higher values
(
e
=
0.92
±
0.03
)
and the period posterior to lower values
(
P
=
-
+
7
1.87
27.07
52.2
6
yr
)
, but the posterior distribution of
g
̇
is
consistent with 0
(
g
̇
=
-
+
0
.12
0.19
0.22
ms
−
1
yr
−
1
)
. The adopted
model has lower bayesian information criterion
(
BIC
)
(
Δ
BIC
=
5.4
)
and Akaike information criterion
(
AIC
)
values
(
Δ
AIC
=
1.7
)
, indicating that the added free parameter does
not substantially improve the
fi
t. We cannot unequivocally rule
out a trend, but since including one is not statistically warranted
and does not affect the conclusions of the paper, we adopt the
fi
t with no trend.
The lack of an unambiguous trend in the RVs is consistent
with our failure to detect companion objects in the
Hubble
Space Telescope
(
HST
)
and Nasmyth Adaptive Optics System
(
NAOS
)
Near-Infrared Imager and Spectrograph
(
CONICA
)
,
hereafter NaCo, images
(
see Section
3
and Appendix
B
)
. The
possible bound companion at 15,000 au
(
Section
5.2.1
)
would
not produce a measurable
g
̇
.
4.2. Orbit Information Density
Our measurements of the properties of this planet may seem
surprisingly precise
(
see Table
3
)
given observations spanning
only about one-third of the orbit. These constraints are possible
because we tracked the system through periastron passage,
when the information density of the Keplerian signal is highest.
High-eccentricity orbits have unique shapes that sensitively
depend on
e
and
ω
(
see Figure 2 of Howard & Fulton
2016
for
a helpful visualization
)
. The shape of the HR 5183 RV curve is
fi
t only by a narrow range of these parameters, as Figure
3
shows.
The relatively
fl
at RV curve from
∼
1998 to 2015 followed
by a sharp uptick and subsequent turnover are consistent only
with
e
;
0.8 and
ω
;
−
0.4. All other Keplerian curves have
shapes that are inconsistent with our measurements. More
complicated models involving additional planets or a
g
̇
term
are also excluded by the peculiar RV pattern.
We offer two arguments to build intuition. First, imagine
decomposing the RV
fi
tting into a process that matches three
orbital properties of the Keplerian curve:
(
1
)
the shape
(
from
e
and
ω
)
,
(
2
)
the vertical scale
(
K
)
, and
(
3
)
the horizontal scale
(
P
)
. Once the shape has been determined by matching the
appropriate Keplerian curve, the horizontal and vertical scales
can be measured using RVs spanning less than a full orbit,
provided the information-rich close approach is covered.
Second, consider the how the planet
’
s speed varies over its
orbit. We can de
fi
ne the fastest half orbit as the portion of an
orbit near closest approach, when the true anomaly
(
f
)
is
between
−
π
/
2 and
π
/
2. The time for the planet to pass through
the fastest half orbit,
t
fho
, can be computed using the
relationship between
f
and time
(
t
)
,
p
=-
df
P
e
a
r
dt
2
1, 3
2
2
⎜⎟
⎛
⎝
⎞
⎠
()
where
r
is the distance between the orbiting planet and the star
(
Seager
2010
, Equation
(
2.44
))
. Substituting an expression for
r
(
f
)(
Seager
2010
, Equation
(
2.20
))
,
ò
p
=
-
+
p
p
-
t
Pe
df
ef
1
21cos
.4
fho
232
2
2
()
()
For a circular orbit,
t
fho
integrates to
P
/
2, as expected.
Eccentric orbits have much shorter timescales of close
approach though. Numerically integrating Equation
(
4
)
with
Figure 2.
MAP orbit of HR 5183 b compared to the orbits of the planets in our
solar system
(
blue: Neptune, teal: Uranus, purple: Saturn, red: Jupiter, gray:
Mars, and black dashed: HR 5183 b
)
. The sizes of the colored circles show the
relative sizes of the solar system planets
(
not to scale with respect to their
orbits
)
. We assume a radius of 1
R
J
for HR 5183 b. The orbital locations of the
planets were computed on 2019 July 31, approximately 1.5 yr after the
periastron passage of HR 5183 b. HR 5183 b
’
s
Ω
and
i
are set to arbitrary
values. At periastron, HR 5183 b is closer to its star than our asteroid belt is to
the Sun, and at apastron, it is more distant than Neptune.
25
GitHub.com
/
dfm
/
emcee
5
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
e
=
0.84, we
fi
nd
t
fho
≈
P
/
18.6. That is, the planet completes
the fastest half of its orbit nearly an order of magnitude more
quickly than in the circular case. While our
fi
tting procedure
did not actually measure
t
fho
and scale it by a factor of 18.6 to
determine
P
, this exercise illustrates how highly eccentric
orbits contain information related to orbital period on short
timescales, and thus allow us to measure
P
with higher
precision than one might expect.
This is not to say that we have ruled out 100 yr or more
periods and higher
(
;
0.91
)
eccentricities. Such orbits appear in
our posterior, but because there is less posterior volume in this
region of parameter space, they are less probable overall.
5. Additional Bound Companions
5.1. Search for Additional Planets in the System
We searched for other signi
fi
cant periodic signals in the RV
data using the
χ
2
difference technique described in Howard &
Fulton
(
2016
)
. In brief, we started by calculating the
χ
2
of a
fl
at
line
fi
t to the RVs, and injecting additional Keplerian orbits into
Figure 3.
Corner plot displaying posterior distributions and covariances of HR 5183 b orbital parameters of interest: time of periastron passage
(
T
P
)
, orbital period
(
P
)
,
minimum mass
(
M
sin
i
)
, semimajor axis
(
a
)
, minimum orbital separation
(
a
(
1
−
e
))
, eccentricity
(
e
)
, and argument of periastron
(
ω
)
. Importantly, these probability
distributions were derived from the
fi
tted posteriors; among the parameters shown here, only
T
P
is actually a parameter in the
fi
t. Time of periastron passage, minimum
mass, and minimum orbital separation are very well constrained, while orbital period remains uncertain and correlated with eccentricity.
6
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
the model. We calculated the change in
χ
2
(
Δ
χ
2
)
when
including each additional Keplerian orbit over a grid of periods
and eccentricities. We constructed a periodogram of the
Δ
χ
2
values as a function of trial period and
fi
t the distribution of
periodogram peak heights to infer an empirical false alarm
probability
(
eFAP
)
for each detected peak. We detected no
signals with an eFAP greater than 1%, indicating no additional
planetary companions down to our sensitivity limits.
We characterized our sensitivity limits over a grid of
semimajor axes and
M
sin
i
values by applying the search
algorithm described above to each injected planetary signal.
The results of this analysis are shown in Figure
4
. As expected,
we are most sensitive to Jupiter-mass and heavier planets with
a
<
30 au. Our data are not sensitive to Earth-mass planets. HR
5183 b itself is at our detection limits because of its large
semimajor axis, but its high eccentricity makes it detectable.
We also searched for transit signals in ground-based
photometric observations of HR 5183,
fi
nding no signi
fi
cant
signals above our sensitivity limits. These data and analysis are
described in Appendix
A
.
5.2. Search for Stellar Companions to HR 5138
We used a two-pronged approach to search for additional
bound companions to HR 5183: analyzing archival corona-
graphic images of the star and searching the
Gaia
DR2
database for stars with similar 3D locations and kinematic
properties. HR 5138 b is likely much below the detection limit
of current coronagraphic imagers
(
see Section
6
)
, and we did
not expect to detect it in these images. We found several
archival images of HR 5183: one set of images taken with
NaCo on the Very Large Telescope
(
VLT
)
and one set taken
with the
HST
Imaging Spectrograph
(
HST
/
STIS
)
. Details about
the observations and data reduction are presented in
Appendix
B
. We used these images to derive contrast curves
illustrating our detection limits for HR 5183
(
Figure
5
)
, and
found no evidence for companions, with sensitivity down to
Δ
mag
=
20 at 4
′′
.
While our scrutiny of coronagraphic images revealed no
companions, through our
Gaia
DR2 search and the analysis
described below, we found that HIP 67291 is likely an
eccentric, widely separated
(
>
15,000 au
)
stellar companion to
HR 5138. However, even if this star is gravitationally bound to
HR 5183, it is too widely separated to affect the planet HR
5183 b. In addition, it would not be in the
fi
eld of view of any
of the images described in Appendix
B
.
5.2.1. HIP 67291: A Wide Stellar Companion to HR 5183
Several papers in the literature have presented evidence that
HIP 67291, a K7V star
(
Alonso-Floriano et al.
2015
)
with a
projected separation of more than 15,000 au, is bound to HR
5183
(
Allen et al.
2000
; Allen & Monroy-Rodríguez
2014
;
Tokovinin
2014
)
. Using kinematic parameters from
Gaia
DR2
and an isochrone-derived mass for HIP 67291, we investigated
the probability that these two stars are gravitationally bound,
and present orbital parameters for the system. This analysis is
Table 3
Fit Parameters and Derived Planet Properties
Parameter
Median Value and
68% CI
MAP Value
Unit
ln
P
-
+
1
0.21
0.35
0.4
6
10.2
ln
(
days
)
T
c
-
+
1
8965
40
4
4
18964
JD -
2440000
w
e
cos
0.86
±
0.02
0.86
w
e
sin
−
0.32
±
0.03
−
0.32
ln
K
3.64
±
0.01
3.64
ln
(
-
ms
1
)
σ
(
HIRES pre-
upgrade
)
-
+
3
.4
0.6
0.8
3.09
-
ms
1
σ
(
HIRES post-
upgrade
)
3.3
±
0.4
3.16
-
ms
1
σ
(
Tull
)
-
+
5
.8
0.5
0.6
5.67
-
ms
1
σ
(
APF
)
-
+
3
.7
0.4
0.5
3.58
-
ms
1
γ
(
HIRES pre-
upgrade
)
-
-
+
52.6
1.5
1.3
−
52.5
-
ms
1
γ
(
HIRES post-
upgrade
)
-
-
+
52.4
2.1
2.0
−
52.4
-
ms
1
γ
(
Tull
)
-
-
+
19.2
2.1
1.9
−
19
-
ms
1
γ
(
APF
)
-
-
+
47.2
2.2
2.0
−
47.2
-
ms
1
P
-
+
7
4
22
43
72.85
yr
K
-
+
3
8.25
0.55
0.58
38.21
m s
−
1
e
0.84
±
0.04
0.84
ω
−
0.35
±
0.03
−
0.35
rad
T
P
58121
±
12
58120.0
JD -
2440000
M
sin
i
-
+
3
.23
0.14
0.15
3.24
M
J
a
-
+
1
8
4
6
18.0
au
a
(
1
−
e
)
-
+
2
.88
0.08
0.09
2.89
au
T
eq
(
peri
)
-
+
1
71.0
5.1
5.2
170.94
K
T
eq
(
apo
)
-
+
5
0.2
7.6
7.0
50.58
K
Note.
T
eq
values were calculated assuming a visible albedo of 0.5.
ω
refers to
the orbit of the star HR 5183 induced by the planet HR 5183 b.
Table 4
Period Prior Comparison
Prior
Median Period and 68% CI
uniform in
P
and
K
-
+
1
25
54
113
yr
uniform in
P
log
and
K
log
-
+
1
03
41
103
yr
inf. baseline prior
(
adopted
)
-
+
7
4
22
43
yr
Figure 4.
Sensitivity of the HR 5183 RV time series to injected planetary
signals as a function of semimajor axis
(
a
)
and minimum mass
(
M
sin
i
)
. Each
point corresponds to an injected RV signal. Blue dots were detected, while red
dots were not. The solid color background shows the fraction of signals that
were recovered, corresponding to the probability of detection. The parameters
of HR 5183 b are shown as a black point with error bars
(
the uncertainty on
M
sin
i
is too small see
)
. Our data are sensitive to less massive, shorter-period
planets out to the orbit of HR 5183 b.
7
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
meant to be exploratory and not de
fi
nitive; additional
undetected companions orbiting HIP 67291 would affect these
calculations, for example.
We performed an isochrone
fi
t for HIP 67291 using the
isochrones
26
Python package
(
Morton
2015
)
to interface
with the MESA Isochrones & Stellar Tracks
(
MIST
)
stellar
evolution models
(
Paxton et al.
2011
,
2013
,
2015
; Choi et al.
2016
; Dotter
2016
)
.Wede
fi
ned priors on
[
Fe
/
H
]
and log
g
using the values and precisions used in the template to compute
the
Gaia
RV of HIP 67291
(
rv
_
template
_
fe
_
h
and
rv
_
template
_
logg
in the
Gaia
DR2 database, respec-
tively
)
. In addition, we placed Gaussian priors on parallax and
T
eff
, informed by the
Gaia
DR2 values and uncertainties
reported for HIP 67291. We also placed a Gaussian prior on the
age of HIP 67291, informed by the age of HR 5183 derived in
Section
3
, but found that this constraint did not affect the mass
of HIP 67291. We obtained a mass of 0.67
±
0.05
M
from
this analysis, which is consistent with the K7V spectral type
derived in Alonso-Floriano et al.
(
2015
)
.
Given the mass of HIP 67291, the mass of HR 5183 derived
in Section
3
, and the respective parallaxes, R.A.
/
decl. values,
proper motions, and RVs of both stars from
Gaia
DR2
(
compiled in Table
5
)
, the orbit of the two stars is in principle
completely speci
fi
ed. In practice, the uncertainties on these
parameters are signi
fi
cant enough to permit large uncertainties
in the orbital parameters. To quantify these uncertainties, we
drew samples from Gaussian distributions over both stellar
masses and each of the six positional and velocity measure-
ments for each star, then calculated the resulting orbital
parameters. We found that 44% of these generated orbits had
e
<
1
(
i.e., are bound
)
. Histograms of the orbital parameters
derived from this sampling method
(
the likelihood over
possible bound and unbound
/
hyperbolic orbital parameters
)
are shown in Figure
6
. Highly eccentric, edge-on orbits are
preferred.
While the likelihood that these two stars are bound is only
44%, the two possible physical explanations for the 66% of
hyperbolic orbits
(
that the two stars are currently
fl
ying by one
another and that they were bound in the past and recently
became unbound
)
likely have low prior probabilities. There-
fore, the posterior probability that the two stars are bound is
likely much higher than 44%.
While the presence of an extremely wide stellar companion
to HR 5183 is certainly interesting, HIP 67291 is simply too far
away from the planet HR 5183 b to affect its orbit in the current
orbital con
fi
guration. The median periastron distance of the
HIP 67291-HR 5183 orbit
(
neglecting hyperbolic solutions
)
is
∼
10,000 au, well beyond the theorized minimum Sun
–
Oort-
cloud separation of 2000 au
(
Morbidelli
2005
)
. In the Oort
cloud, the galactic potential due to the overall galactic mass
distribution is an important driver of orbital evolution, which
tells us that even when HIP 67291 is closest to HR 5183 b, its
gravitational in
fl
uence is at most comparable to that of the
galactic potential.
6. Prospects for Direct Imaging and Detection with
Gaia
Transit probability is given by
w
=
+
+
-
p
RR
a
e
e
1sin
1
5
p
tra
2
*
⎜⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
()
(
Winn
2010
)
. Assuming a Jupiter radius for HR 5183 b,
p
tra
=
0.00185
±
0.00010. Although this probability is lottery-
ticket-like, the prospects for detecting HR 5183 b with stellar
astrometry and thermal direct imaging are promising. Detection
with either of these methods could address the sin
i
degeneracy,
allowing us to obtain a direct mass measurement.
To investigate prospects for imaging HR 5183 b, we used the
orbit-solving code from
orbitize
27
(
Blunt et al.
2019
)
,an
orbit-
fi
tting toolkit for direct imaging astrometry. First, we
determined the angular separation posterior as a function of
time. We randomly sampled from the RV orbit posteriors
described in the previous section, assigned each sample orbit an
inclination
(
randomly drawn from a uniform distribution in
cos
i
)
and an
Ω
(
randomly drawn from a uniform distribution
)
,
and used
orbitize
to solve for the projected angular
Figure 5.
1
σ
point-source detection limits for HR 5183 computed with NaCo
on the VLT in the
Ks
band, and with
HST
/
STIS using WedgeA-0.6
(
W6
)
and
WedgeA-1.0
(
W1
)
. See Appendix
B
for details. We did not detect companions
to HR 5183 in these images.
Table 5
Gaia
DR2 Parameters for HR 5183 and HIP 67291
Parameter
HR 5183 Value
Unc.
HIP 67291 Value
Unc.
Unit
Unc. Unit
R.A.
206.74
0.034
206.87
0.042
deg
mas
Decl.
6.35
0.029
6.32
0.028
deg
mas
Parallax
31.76
0.04
31.92
0.05
mas
mas
Proper motion
(
R.A.
)
−
510.45
0.07
−
509.44
0.08
mas yr
−
1
mas yr
−
1
Proper motion
(
decl.
)
−
110.22
0.06
−
111.02
0.06
mas yr
−
1
mas yr
−
1
RV
−
30.42
0.20
−
30.67
0.15
km s
−
1
km s
−
1
26
GitHub.com
/
timothydmorton
/
isochrones
27
GitHub.com
/
sblunt
/
orbitize
8
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.
separation,
ρ
, at several future epochs. Posterior distributions in
ρ
calculated using this procedure for three future epochs are
shown in Figure
7
. Since the planet passed periastron so
recently, the median of its projected separation posterior
generally increases with time over the next 5 yr.
Next, we calculated contrast posteriors, in both re
fl
ected
visible and thermal infrared
(
10
μ
m
)
wavelengths, using the
angular separation posterior. To calculate visible re
fl
ected-light
contrast, we approximated HR 5183 b as a Lambertian disk
with an albedo of 0.5, and assumed that the star emits as a
blackbody. These results are shown in Figure
8
on 2025
January 1, along with estimated and required predicted contrast
capabilities for future re
fl
ected-light coronagraphs. For refer-
ence, the phase angle
(
angle between the observer
’
s line of
sight, the planet
’
s location, and the star
’
s location
)
will be
-
+
137
19
10
°
on this date. Robustly calculating the thermal infrared
contrast requires knowing the planet
’
s
T
eff
(
which in turn
requires knowledge of non-blackbody effects, such as wave-
length-dependent emissivity and age
)
, but as a
fi
rst optimistic
approximation we calculated contrast posteriors assuming the
planet emits as a blackbody with temperature given by
T
eq
at its
periastron distance. These results are shown in Figure
9
, along
with contrast capabilities of two current-generation infrared
imagers. In visible re
fl
ected light, HR 5183 b appears to be
likely beyond the capabilities of even HabEx
/
LUVOIR, but
infrared thermal emission may be a different story. Within 5 yr,
the planet will most likely be separated from its star by more
than 200 mas, and its contrast at 10
μ
m, in this optimistic
approximation, would be comparable to the performance
fl
oors
of current-generation infrared imagers like the Gemini Planet
Imager
(
GPI
)
and SPHERE. Instrument concepts like TIKI
(
Blain et al.
2018
)
, which aim for 1
e
−
7 contrast at the
approximate projected separation of HR 5183 b, are well suited
for this endeavor.
Another imminent dual-detection prospect for HR 5183 b is
with stellar astrometry from
Gaia. Gaia
will release astrometric
Figure 6.
Bound
(
gray solid
)
and all
(
red line
)
solutions for the orbit of HIP
67291 and HR 5183. These are normalized, so even though the gray probability
density function
(
PDF
)
is a subset of the red PDF, the gray exceeds the red in
places. These solutions may not be accurate if there are undetected massive
companions around HIP 67291. High eccentricities and edge-on orbits are
preferred. Although small values of
a
(
1
−
e
)(
neglecting unbound hyperbolic
orbits
)
are possible, the most probable value occurs at 1000 au, and the median
at 10,000 au, too widely separated to affect the planet HR 5183 b. The most
probable orbital period is almost 1 Myr.
Figure 7.
Posterior distributions of the projected separation
(
ρ
)
of HR 5183 b
from its primary at three future epochs. The time of periastron passage is
precisely constrained to be 2018 January from the RVs, and accordingly, the
separation posterior generally increases over the next 5 yr. In 2024, HR 5183 b
will be separated from its host by more than 200 mas with 95% con
fi
dence.
9
The Astronomical Journal,
158:181
(
15pp
)
, 2019 November
Blunt et al.