TOI-1670 b and c: An Inne Sub-Nep une wi h an Ou e Wa m Jupi e Unlikely o Ha e
O igina ed om High-eccen ici y Mig a ion
Quang H. T an
1
, B endan P. Bowle
1
, Michael Endl
1,2
, William D. Coch an
1,2
, Phillip J. MacQueen
2
, Da ide Gandolfi
3
,
Ca ina M. Pe sson
4
, Malcolm F idlund
4,5
, En ic Palle
6,7
, G zego z Nowak
6,7
, Hans J. Deeg
6,7
, Ra ael Luque
8
,
John H. Li ings on
9,10,11
, Pe Kabá h
12
, Ma ek Ska ka
12,13
, Ján Šubjak
12,14
, S e e B. Howell
15
,
Simon H. Alb ech
16
, Ka en A. Collins
17
, Massimiliano Esposi o
18
, Vincen Van Eylen
19
, Sascha G ziwa
20
,
Elisa Go o
3,18
, Chelsea X. Huang
21,29
, Jon M. Jenkins
15
, Ma ie Ka jalainen
12
, Raine Ka jalainen
12
,
Emil Knuds up
16
, Judi h Ko h
22
, K is ine W. F. Lam
23
, Da id W. La ham
17
, Alan M. Le ine
21
,
H. L. M. Osbo ne
19
, Samuel N. Quinn
17
, Se h Redfield
24
, Geo ge R. Ricke
21
, S. Seage
21,25,26
, Luisa Ma ia Se ano
3
,
Alexis M. S. Smi h
23
, Joseph D. Twicken
15,27
, and Joshua N. Winn
28
1
Depa men o As onomy, The Uni e si y o Texas a Aus in, 2515 Speedway, S op C1400, Aus in, TX 78712, USA; [email p o ec ed]
2
McDonald Obse a o y, The Uni e si y o Texas a Aus in, 2515 Speedway, S op C1400, Aus in, TX 78712, USA
3
Dipa imen o di Fisica, Uni e si à degli S udi di To ino, ia Pie o Giu ia 1, I-10125, To ino, I aly
4
Depa men o Space, Ea h and En i onmen , Chalme s Uni e si y o Technology, Onsala Space Obse a o y, SE-439 92 Onsala, Sweden
5
Leiden Obse a o y, Leiden Uni e si y, NL-2333 CA Leiden, The Ne he lands
6
Ins i u o de As o ísica de Cana ias (IAC), E-38205 La Laguna, Tene i e, Spain
7
Depa amen o de As o ísica, Uni e sidad de La Laguna (ULL), E-38206, La Laguna, Tene i e, Spain
8
Ins i u o de As o ísica de Andalucía (IAA-CSIC), Glo ie a de la As onomía s/n, E-18008 G anada, Spain
9
Depa men o As onomy, Uni e si y o Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
10
As obiology Cen e , 2-21-1 Osawa, Mi aka, Tokyo 181-8588, Japan
11
Na ional As onomical Obse a o y o Japan, NINS, 2-21-1 Osawa, Mi aka, Tokyo 181-8588, Japan
12
As onomical Ins i u e o he Czech Academy o Sciences, F ičo a 298, 25165, Ond
ejo , Czech Republic
13
Depa men o Theo e ical Physics and As ophysics, Masa yk Uni e si y, Ko lá ská 2, CZ-61137, B no, Czech Republic
14
As onomical Ins i u e o Cha les Uni e si y, V Holešo ičkách 2, 180 00, P aha, Czech Republic
15
NASA Ames Resea ch Cen e , Mo e Field, CA 94035, USA
16
S ella As ophysics Cen e, Depa men o Physics and As onomy, Aa hus Uni e si y, Ny Munkegade 120, DK-8000 Aa hus C, Denma k
17
Cen e o As ophysics |Ha a d & Smi hsonian, 60 Ga den S ee , Camb idge, MA 02138, USA
18
Thü inge Landess e nwa e Tau enbu g, S e nwa e 5, D-07778 Tau enbu g, Ge many
19
Mulla d Space Science Labo a o y, Uni e si y College London, Holmbu y S Ma y, Do king, Su ey RH5 6NT, UK
20
Rheinisches Ins i u ü Umwel o schung an de Uni e siä zu Köln, Aachene S aße 209, D-50931 Köln, Ge many
21
Depa men o Physics and Ka li Ins i u e o As ophysics and Space Resea ch, Massachuse s Ins i u e o Technology, Camb idge, MA 02139, USA
22
Depa men o Space, Ea h and En i onmen , As onomy and Plasma Physics, Chalme s Uni e si y o Technology, SE-412 96 Go henbu g, Sweden
23
Ins i u e o Plane a y Resea ch, Ge man Ae ospace Cen e (DLR), Ru he o ds aße 2, D-12489 Be lin, Ge many
24
As onomy Depa men and Van Vleck Obse a o y, Wesleyan Uni e si y, Middle own, CT 06459, USA
25
Depa men o Ea h, A mosphe ic and Plane a y Sciences, Massachuse s Ins i u e o Technology, Camb idge, MA 02139, USA
26
Depa men o Ae onau ics and As onau ics, Massachuse s Ins i u e o Technology, 77 Massachuse s A enue, Camb idge, MA 02139, USA
27
SETI Ins i u e, Moun ain View, CA 94043, USA
28
Depa men o As ophysical Sciences, Pey on Hall, 4 I y Lane, P ince on, NJ 08544, USA
Recei ed 2021 Sep embe 25; e ised 2022 Feb ua y 7; accep ed 2022 Ma ch 1; published 2022 Ap il 21
Abs ac
We epo he disco e y o wo ansi ing plane s a ound he b igh (V=9.9 mag)main-sequence F7 s a TOI-1670
by he T ansi ing Exoplane Su ey Sa elli e. TOI-1670 b is a sub-Nep une (=-
+
R
2.06
b0.15
0.19 R
⊕
)on a 10.9 day
o bi , and TOI-1670 c is a wa m Jupi e (=-
+
R
0.987
c0.025
0.02
5
R
Jup
)on a 40.7 day o bi . Using adial eloci y
obse a ions ga he ed wi h he Tull Coudé Spec og aph on he Ha lan J. Smi h elescope and HARPS-N on he
Telescopio Nazionale Galileo, we find a plane mass o =-
+
M0.63
c0.08
0.09 M
Jup
o he ou e wa m Jupi e , implying a
mean densi y o
=-
+
0.81
c0.11
0.13 gcm
−3
. The inne sub-Nep une is unde ec ed in ou adial eloci y da a (M
b
<0.13
M
Jup
a he 99% confidence le el). Mul iplane sys ems like TOI-1670 hos ing an ou e wa m Jupi e on a nea ly
ci cula o bi (=-
+
e0.09
c0.04
0.05)and one o mo e inne coplana plane s a e mo e consis en wi h “gen le” o ma ion
mechanisms such as disk mig a ion o in si u o ma ion a he han high-eccen ici y mig a ion. O he 11 known
sys ems wi h a wa m Jupi e and a smalle inne companion, eigh (73%)a e nea a low-o de mean-mo ion
esonance, which can be a signa u e o mig a ion. TOI-1670 joins wo o he sys ems (27% o his subsample)wi h
pe iod commensu abili ies g ea e han 3, a common ea u e o in si u o ma ion o hal ed inwa d mig a ion. TOI-
1670 and he hand ul o simila sys ems suppo a di e si y o o ma ion pa hways o wa m Jupi e s.
Unified As onomy Thesau us concep s: Exoplane as onomy (486);Radial eloci y (1332);Exoplane o ma ion
(492);T ansi pho ome y (1709)
1. In oduc ion
The o igin o gian plane s in e io o he wa e -ice line
emains an open ques ion. A numbe o heo ies ha e been
p oposed o explain he closes -in (P<10 days)gian plane s,
The As onomical Jou nal, 163:225 (16pp), 2022 May h ps://doi.o g/10.3847/1538-3881/ac5c4
© 2022. The Au ho (s). Published by he Ame ican As onomical Socie y.
29
Juan Ca los To es Fellow
O iginal con en om his wo k may be used unde he e ms
o he C ea i e Commons A ibu ion 4.0 licence. Any u he
dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s)and he i le
o he wo k, jou nal ci a ion and DOI.
1
o ho Jupi e s (HJs; e.g., Dawson & Johnson 2018; Fo ney
e al. 2021). These scena ios a e p ima ily di ided be ween
dynamically “ iolen ”o “gen le”mechanisms. The o me
consis s o h ee-body dynamical in e ac ions such as plane –
plane sca e ing o high-eccen ici y idal mig a ion (e.g., Wu
& Mu ay 2003; Fab ycky & T emaine 2007; T iaud e al.
2010; Naoz e al. 2011; Ba ygin 2012). The la e e e s o disk
mig a ion (e.g., Wa d 1997; Alb ech e al. 2012; Kley &
Nelson 2012)o in si u o ma ion (e.g., Ba ygin e al. 2016;
Boley e al. 2016; Huang e al. 2016; Ande son e al. 2020).
These p ocesses ha e also been used o explain pa o he
a he -ou popula ion o wa m Jupi e s (WJs; defined he e o
ha e 10 days <P<200 days). Howe e , obse ed WJ
demog aphics sugges ha mul iple p ocesses a e p esen in
sculp ing hese mo e dis an gian sys ems.
WJs can be b oadly di ided in o wo classes. The fi s is a
ansien popula ion ha will likely e ol e in o HJs. In mo e
dis up i e o ma ion mechanisms, such as high-eccen ici y
idal mig a ion, gian plane s a compa a i ely wide sepa a ions
a e dis u bed on o highly eccen ic o bi s by a hi d body ia
plane –plane sca e ing o on Zeipel–Lido –Kozai oscilla-
ions and e en ually ci cula ize in o o bi s wi h sho e pe iods
(Kozai 1962; Lido 1962; Naoz 2016; I o & Oh suka 2019).
Eccen ic gian plane s unde going his idally damped inwa d
mig a ion a e caugh in a apid, empo a y s a e (Nae e al.
2001; Dawson & Johnson 2018; Dong e al. 2021; Jackson
e al. 2021). They a e expec ed o s a hei jou neys wi h
much highe eccen ici ies (e0.9; Vick e al. 2019), which
can decay as apidly as ∼1 My as hey se le in nea hei hos
s a (Pa a e al. 2020; Mancini e al. 2022). The majo i y o
WJs a e no expec ed o belong o his ansien classifica ion.
Ins ead, mos WJs a e a pa o a “s a ic”popula ion ha will
emain s able o e long ime pe iods. This g oup consis s o he
appa en ly single sys ems wi h low- o-mode a e eccen ici ies,
as well as coplana mul iplane sys ems con aining WJs wi h
low eccen ici ies. These WJs ha e pe iapses la ge han wha
is equi ed o e ficien idal damping o hei o bi s, which
occu s a 0.05 au (Ande son e al. 2016; Dong e al. 2021),so
hese plane s canno be unde going high-eccen ici y mig a ion.
I mos gian plane s o m beyond he wa e -ice line, o he
mig a ion mechanisms mus play a majo ole in sculp ing hese
WJ o bi al p ope ies and demog aphics (e.g., Ve as &
A mi age 2005; Fogg & Nelson 2009; Dong e al. 2014; O iz
e al. 2015; Huang e al. 2016; Ande son & Lai 2017; Ande son
e al. 2020; Schlecke e al. 2020). Howe e , he ela i e
impo ance o hese pa hways is s ill unknown. In es iga ing
WJ o bi al eccen ici ies can place addi ional cons ain s on he
dominan gian plane mig a ion mechanism, since each
scena io will p oduce di e en obse ed eccen ici y
dis ibu ions.
WJs ha e an eccen ici y dis ibu ion ha peaks a e=0.0
wi h a ail ha ex ends ou o e∼0.8 (Kipping 2013; Dong
e al. 2021). In o de o p oduce he popula ion o WJs wi h
mode a ely eccen ic o bi s (e∼0.2–0.7), a mechanism is
needed ha can exci e eccen ici ies. These po en ial exci a ion
scena ios include in e ac ions in ol ing a disk (e.g., Gold eich
& Sa i 2003; Pe o ich e al. 2019), secula eccen ici y
oscilla ions d i en by in e ac ions wi h a dis an inclined gian
plane (e.g., Ande son & Lai 2017), and plane –plane
sca e ing e en s (e.g., Mus ill e al. 2017; F elikh e al.
2019; Ma za i & Nagasawa 2019; Ande son e al. 2020).An
impo an clue is he obse ed dependence on me allici y o he
gian plane eccen ici y dis ibu ion, whe e me al- ich sys ems
( ha may mo e a o ably o m mul iple gian plane s)a e mo e
likely o hos eccen ic gas gian s (Dawson & Mu ay-
Clay 2013).
Sys ems hos ing WJs wi h low-mass inne companions on
coplana o bi s a e especially use ul labo a o ies o es hese
plane o ma ion and mig a ion heo ies. Thei small o bi al
eccen ici ies and low mu ual inclina ions sugges ha disk
mig a ion o in si u o ma ion likely helped c ea e his
popula ion. WJs ha e a ela i ely high close companion a e
o nea ly 50% (Huang e al. 2016). Howe e , hei in insically
low occu ence a e (∼1%–2%; Cumming e al. 2008)
combined wi h he di ficul y o de ec ing lowe -mass inne
plane s means ha only a hand ul o known mul iplane
sys ems hos a WJ (Johnson e al. 2010; San e ne e al. 2016;
Fe nandes e al. 2019). Inc easing he numbe o sys ems wi h
his mul iplane a chi ec u e may u he dis inguish his
subsample in o wo WJ popula ions, each o which likely
eflec s di e en o ma ion and mig a ion ou es.
He e we p esen he disco e y o he ansi ing mul iplane
sys em TOI-1670 bc, a WJ (TOI-1670 c)wi h an inne sub-
Nep une (TOI-1670 b) ound wi h he T ansi ing Exoplane
Su ey Sa elli e (TESS; Ricke e al. 2015). TOI-1670 b and c
we e o iginally iden ified by he TESS Science P ocessing
Ope a ions Cen e (SPOC; Jenkins e al. 2016)pipeline as wo
p omising ansi ing signals ha we e subsequen ly p omo ed
o TESS Objec o In e es (TOI; Gue e o e al. 2021)s a us.
TOI-1670 (TIC ID 441739020; 2MASS J17160415+7209402;
Gaia DR2 1651911084230149248)is a ela i ely inac i e
(log ¢=-
R
4.9
3
HK )old F7 dwa wi h a TESS appa en
magni ude o 9.5 mag and a mode a e p ojec ed o a ional
eloci y o ≈9kms
−1
(see Sec ion 3). In his wo k, we alida e
bo h plane s and measu e he mass o he ou e plane , TOI-
1670 c. In Sec ion 2, we desc ibe he TESS pho ome ic da a
and ollow-up adial eloci y (RV)obse a ions used in he
plane alida ion and mass measu emen . Ou cha ac e iza ion
o he sys em, including he hos s a and a global fi o he RVs
and ligh cu e, is p esen ed in Sec ion 3. We conclude in
Sec ion 4by con ex ualizing TOI-1670 in he pa adigm o WJs
and hei o ma ion.
2. Obse a ions
KESPRINT
30
is an in e na ional collabo a ion ocused on
he disco e y, confi ma ion, and cha ac e iza ion o exoplane
candida es om space-based missions (e.g., Gandolfie al.
2018; Pe sson e al. 2018; Li ings on e al. 2019; Lam e al.
2020;Šubjak e al. 2020). As pa o his conso ium, a se ies o
g ound-based ollow-up obse a ions o TOI-1670 we e aken.
These da a a e p ima ily used o ejec he possibili y o a alse-
posi i e scena io in which he obse ed ansi ing signal is
caused by some hing o he han a plane . Fo example, his
includes a low-mass eclipsing bina y (EB), a g azing ansi o
an EB, a backg ound EB, o a ansi ing plane a ound a
backg ound s a . Reconnaissance spec a a e used o exclude an
EB scena io by cons aining he maximum ampli ude o he RV
signal. High- esolu ion speckle images a e aken o exclude
bina y companions o TOI-1670 and nea by backg ound s a s.
High- esolu ion spec a a e used o cha ac e ize he hos s a
and, when possible, measu e he masses o he plane s.
30
h p://kesp in .science/
2
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
2.1. TESS Pho ome y
TOI-1670 was obse ed by TESS a 2 minu e cadence o e
11 sec o s (15, 16, 18, 19, 20, 21, 22, 23, 24, 25, and 26) o a
o al o 323 days. Images we e educed and ligh cu es we e
analyzed o ansi signals wi h he TESS SPOC pipeline
(Jenkins e al. 2016), which iden ified wo po en ial ansi
signals (Jenkins 2002; Jenkins e al. 2010,2020)wi h pe iods
o 40.7 (TOI-1670.01)and 10.9 (TOI-1670.02)days. The
SPOC e ing es s (Twicken e al. 2018; Li e al. 2019)
alida ed bo h signals as consis en wi h plane s, and hey we e
designa ed as TOIs (Gue e o e al. 2021)by he TESS Science
O fice.
We downloaded he SPOC P e-sea ch Da a Condi ioning
Simple Ape u e Pho ome y (PDCSAP)ligh cu e (Smi h
e al. 2012; S umpe e al. 2012,2014) om he MAST da a
a chi e
31
using he ligh ku e (Ligh ku e Collabo a ion
e al. 2018)so wa e package. We emo ed all o he
pho ome ic measu emen s ha a e flagged as poo quali y by
he SPOC pipeline (DQUALITY >0)o whe e ei he he flux
o flux e o is lis ed as NaN. Ou lie ejec ion was pe o med a
3σ o posi i e ou lie s and 10σ o nega i e ou lie s o allow
o ansi e en s. The ligh cu e was fla ened by emo ing
low- equency ends using a Sa i zky–Golay fil e (Sa i zky
& Golay 1964)a e all ansi e en s we e masked ou . The
final ligh cu e o TOI-1670 is shown in Figu e 1. The
pho ome ic poin s used in he global model fi a e shown in
pu ple and pink. These co e he ansi e en s o TOI-1670 b
and c, espec i ely, and hei imes o ansi a e u he deno ed
by he co esponding colo ed iangles along he ime axis.
2.2. TRES Reconnaissance Spec oscopy
We ob ained six spec a o TOI-1670 wi h he Tillinghas
Reflec o Echelle Spec og aph (TRES; Fű ész 2008)on he 1.5
m Tillinghas elescope a he F ed L. Whipple Obse a o y on
UT 2020 Feb ua y 2 and 20; UT 2020 Ma ch 6, 9, and 16; and
UT 2020 July 7. Exposu e imes anged om 300 o 650 s and
ha e an a e age signal- o-noise a io (S/N)o 32 ±5. The RVs
we e ex ac ed ollowing Buchha e e al. (2010). The spec a
ha e an a e age measu emen e o o 53 m s
−1
and an ms o
54 m s
−1
, which excludes he possibili y o an EB scena io;
howe e , hese spec a a e no used as pa o he o bi fi .
Table A1 in Appendix A epo s he RV measu emen s.
2.3. OES Reconnaissance Spec oscopy
We collec ed 32 spec a using he Ond
ejo Echelle
Spec og aph (OES)on he 2 m Pe ek elescope a he
Ond
ejo Obse a o y in he Czech Republic (Kabá h e al.
2020). These obse a ions we e ob ained be ween UT 2020
Feb ua y and UT 2020 Sep embe a a cadence o 3–5 RVs pe
mon h. We ex ac ed he spec a and pe o med he bias, fla -
field, and cosmic- ay co ec ions using s anda d IRAF 2.16
ou ines (Tody 1993). The RVs we e ex ac ed using he IRAF
c oss-co ela ion xco , aking he highes -S/N spec um as a
empla e. The a e age measu emen e o is 110 m s
−1
, and he
RV ms is 116 m s
−1
. The Dopple signals o TOI-1670 b and
c a e no de ec ed in his da a se , so hey a e no used in he
o bi fi . Howe e , hey a e used o ejec an EB scena io and
jus i y u he ollow-up o TOI-1670 wi h p ecise RV
measu emen s. The econnaissance RV measu emen s a e
epo ed in Table A1 in Appendix A.
2.4. Tull CoudéSpec oscopy
We used he Tull Coudé Spec og aph on he 2.7 m Ha lan J.
Smi h elescope a McDonald Obse a o y o ob ain 49 spec a
o TOI-1670 be ween UT 2020 Ap il and UT 2021 Sep embe .
The Tull Coudé Spec og aph is a c oss-dispe sed echelle
spec og aph wi h a wa eleng h co e age anging om 3750 o
10200 Å(Tull e al. 1995). Ou configu a ion uses a 1 2 sli ,
which yields a esol ing powe o R=60,000. P ecise
wa eleng h calib a ion and ins umen al p ofile econs uc ion
a e achie ed wi h a empe a u e-con olled iodine apo (I
2
)
cell ha is moun ed in on o he en ance sli .
The RVs a e ex ac ed using he RV educ ion pipeline
Aus al (Endl e al. 2000). The I
2
cell imp in s a well-
unde s ood e e ence abso p ion spec um on o he s ella
spec a. P ecise di e en ial RVs a e hen calcula ed by
Figu e 1. De ended TESS ligh cu e o TOI-1670. The ull ligh cu e is shown in black. Pu ple and pink poin s a e ela i e pho ome y wi hin ou ansi du a ions
be o e and a e ansi s o TOI-1670 b and c, espec i ely, and a e used in he global RV and ligh -cu e model fi . Times o ansi a e also ma ked by iangles
plo ed along he ime axis. Gaps in he ligh cu e co espond o pe iods whe e TESS uploaded da a, esul om da a quali y cu s, o a e du ing Sec o 17, when TOI-
1670 was no obse ed. TESS sec o s a e shown in blue abo e he ligh cu e.
31
h ps://a chi e.s sci.edu/missions-and-da a/ ess/
3
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
compa ing each s ella -plus-iodine spec um wi h a high-S/N
s ella empla e de oid o iodine lines. The S-index ac i i y
me ic o each spec um is also calcula ed and calib a ed on o
he M . Wilson S-index sys em ollowing he desc ip ion in
Paulson e al. (2002). Table A2 in Appendix A epo s he
esul ing RVs, ac i i y indices, and ela ed measu emen e o s.
2.5. FIES Spec oscopy
We acqui ed se en spec a o TOI-1670 using he Fibe - ed
Echelle Spec og aph (FIES; F andsen & Lindbe g 1999;
Tel ing e al. 2014)a he 2.56 m No dic Op ical Telescope
(Djup ik & Ande sen 2010)o Roque de los Muchachos
Obse a o y (La Palma, Spain). The obse a ions we e ca ied
ou be ween UT 2020 May 25 and UT 2020 Sep embe 6 as
pa o he Spanish CAT obse ing p og am 59–210. We used
he FIES high- esolu ion mode, which p o ides a esol ing
powe o R=67,000 in he spec al ange 3760–8220 Å.We
aced he RV d i o he ins umen by acqui ing long-exposed
ThA spec a (exposu e ime o 90 s)immedia ely be o e and
a e each science obse a ion. The science exposu e ime was
se o 1200–1800 s, depending on he sky condi ions and
scheduling cons ain s. The da a educ ion ollows he s eps
desc ibed in Buchha e e al. (2010)and Gandolfie al. (2015)
and includes bias sub ac ion, fla -fielding, o de acing and
ex ac ion, and wa eleng h calib a ion. The RVs we e de i ed
ia mul io de c oss-co ela ions using he fi s s ella spec um
as a empla e. The S/N pe pixel a 5500 Å anges be ween 40
and 65. The a e age RV unce ain y is 13.4 ±2.4 m s
−1
.
2.6. HARPS-N Spec oscopy
We obse ed TOI-1670 wi h he HARPS-N spec og aph
(R≈115,000)on he 3.59 m Telescopio Nazionale Galileoa
Roque de los Muchachos Obse a o y loca ed in La Palma, Spain,
be ween UT 2020 Augus and UT 2020 Sep embe (Cosen ino
e al. 2012,2014)du ing obse ing p og am A40TAC_22 (PI:
Gandolfi). A o al o eigh spec a we e aken; se en spec a had an
exposu e ime o 1800 s, and one had an exposu e ime o 215 s.
This esul edinana e ageS/N a 550 nm o 84 ±16 o he fi s
se enspec aandanS/N o 15 o he sho e exposu e.
We used he s anda d HARPS-N Da a Reduc ion So wa e
(DRS)wi h a G2 nume ical mask o ex ac he RVs (Pepe e al.
2002). The RVs, hei measu emen e o s, and he associa ed
ac i i y indica o s, such as he bisec o in e se slope (BIS),
FWHM o he c oss-co ela ion unc ion, and S-index p oduced
by he HARPS-N DRS, a e lis ed in Table A2 o Appendix A.
2.7. High- esolu ion Imaging
On he nigh s o UT 2021 Ap il 5 and June 24, TOI-1670
was obse ed wi h he NESSI and ‘Alopeke speckle image s
(Sco e al. 2018; Sco 2019), moun ed on he 3.5 m WIYN
elescope a Ki Peak and he 8.1 m Gemini No h elescope on
Maunakea, espec i ely. Bo h ins umen s simul aneously
acqui e da a in wo bands cen e ed a 562 and 832 nm using
high-speed elec on-mul iplying CCDs. Obse a ions o TOI-
1670 we e pe o med in he 562 and 832 nm bands ollowing
he p ocedu es desc ibed in Howell e al. (2011). The esul ing
econs uc ed images ha e a 5σdel a magni ude con as o 4 o
8 magni udes a angula sepa a ions om 20 mas o 1 2 in he
832 nm band (Figu e 2). No o he companion sou ces a e
de ec ed in he econs uc ed images wi hin hese angula limi s
down o he con as s ob ained. These angula limi s
co espond o spa ial sepa a ions o 3.3–200 au a he dis ance
o TOI-1670.
3. Analysis
3.1. S ella Pa ame e s
Plane a y pa ame e s measu ed om he global join fi o
he ansi and RV da a depend on p ecise s ella mass and
adius measu emen s. In pa icula , R
p
is de e mined om he
ansi dep h and M
p
om he RV semiampli ude, which a e
dependen on R
*
and M
*
, espec i ely. The s ella mass and
adius can be in e ed wi h a mosphe ic and e olu iona y
models using he spec oscopic pa ame e s (T
e
, log g,[Fe/H],
sin i). We de e mine bo h o hese spec oscopic and
undamen al pa ame e s o TOI-1670 using se e al app oaches
desc ibed below.
3.1.1. Spec al Analysis
We analyzed he coadded HARPS-N (S/N=180)spec um
wi h he spec al analysis package Spec oscopy Made Easy
(SME; Valen i & Piskuno 1996; Valen i & Fische 2005;
Piskuno & Valen i 2017). The spec al fi ing echnique o
SME minimizes he χ
2
alue by fi ing syn he ic spec a o s a s
based on g ids o a mosphe e models and obse a ions. We fi
Figu e 2. Recons uc ed speckle images o TOI-1670 om NESSI ( op)and
‘Alopeke (bo om)in he 562 and 832 nm bands and hei co esponding 5σ
con as cu es. No h is up, and eas is o he le .
4
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
he coadded HARPS-N spec um wi h he ATLAS12 model
spec a (Ku ucz 2013)using he non-local he modynamic
equilib ium SME e sion 5.2.2 ollowing he p ocedu e
desc ibed in F idlund e al. (2017) o compu e T
e
, log g,
sin i, and chemical abundances. The s ella su ace g a i y, log
g, was es ima ed using he spec al wings o he Ca I6102,
6122, 6162 Å iple and he Ca I6439 Åline. The mic oscopic
and mac oscopic u bulences, V
mic
and V
mac
, we e held fixed o
he alues de e mined in he calib a ion o s a s wi h simila
T
e
and log g om B un e al. (2010)and Doyle e al. (2014),
espec i ely.
We also de i e he s ella pa ame e s using he publicly
a ailable SpecMa ch-Emp so wa e package (Yee e al.
2017).SpecMa ch-Emp compa es he HARPS-N empla e
spec um o a high- esolu ion (R∼55,000), high-S/N(>100)
Keck/HIRES op ical spec al lib a y o 404 well-cha ac e ized
ea ly- o la e- ype dwa s (F1 o M5). The empi ical spec a a e
calib a ed using in e e ome y, so SpecMa ch-Emp p o-
duces es ima es o T
e
,[Fe/H], and R
*
(ins ead o log g). P io
o unning he code, we con e he HARPS-N spec um
empla e on o he Keck/HIRES o ma ollowing he p ocedu e
desc ibed in Hi ano e al. (2018).
The s ella pa ame e s de i ed om SME and SpecMa ch-
Emp a e in good ag eemen wi h each o he (Table 1). F om
SME, we find an e ec i e empe a u e o T
e
=6170 ±61 K
and me allici y o [Fe/H]=0.09 ±0.07 dex, while Spec-
Ma ch-Emp gi es T
e
=6048 ±110 K and [Fe/
H]=0.05 ±0.09 dex; hese a e consis en wi h each o he
wi hin 1σ. These esul s a e also in good ag eemen wi h he
pho ome ically de i ed e ec i e empe a u e om Gaia DR2
(=-
+
T6162
e 175
162 K)and ag ee a he 2σle el wi h he TESS
Inpu Ca alog (TIC) 8 (Gue e o e al. 2021) alue o
6345 ±121 K. Fo his wo k, we adop he spec oscopic
pa ame e s om SME as i p oduces all a mosphe ic
pa ame e s. The final adop ed s ella pa ame e s a e epo ed in
Table 3.
3.1.2. S ella Mass and Radius
We in e he s ella adius by fi ing he spec al ene gy
dis ibu ion (SED)o TOI-1670 using he so wa e package
ARIADNE.
32
ARIADNE u ilizes a Bayesian model a e aging
amewo k ha con ol es ou s ella a mosphe e models—
Phoenix 2 (Husse e al. 2013), BT-Se l (Alla d e al.
2011), Ku ucz (1993), and Cas elli & Ku ucz (2003)—wi h he
esponse unc ions o commonly a ailable b oadband fil e s.
Fo ou SED fi ing, we use he Two Mic on All Sky Su ey
(2MASS)JHK
s
, Gaia DR2 (G,G
BP
,B
RP
), Johnson Vand B,
and Wide-field In a ed Su ey Explo e (WISE; W1 and W2)
bandpasses. Syn he ic SEDs a e c ea ed by in e pola ing in
T
e
–glog –[Fe/H]space. Dis ance, adius, A
V
, and excess
pho ome ic unce ain y e ms a e ee pa ame e s in he fi ing
p ocess. We se he p io s o T
e
, log g, and [Fe/H] o he
alues we ound in Sec ion 3.1.1, he dis ance p io o he
Baile -Jones e al. (2021)Bayesian-based alue (-
+
165.72 0.38
0.32
pc), and he s ella adius p io o he Gaia DR2 alue
(=-
+
R
1.38 0.07
0.08
*R
e
). The ex inc ion, A
V
, has a fla p io limi ed
by he maximum line-o -sigh eddening acco ding o he
ecalib a ed SFD galaxy dus map (Schlegel e al. 1998;
Schlafly & Finkbeine 2011). The excess pho ome ic noise
pa ame e s all ha e Gaussian p io s cen e ed a ze o wi h a
s anda d de ia ion equal o 10 imes he epo ed pho ome ic
e o . The SED o TOI-1670 and bes -fi ing model a e shown
in Figu e 3.
We es ima e he mass o TOI-1670 using he s ella
isoch one so wa e package isoch ones (Mo on 2015a)
and he MESA Isoch ones and S ella T acks (Do e 2016;
Choi e al. 2016)e olu iona y model g ids. The isoch ones
package in e s undamen al s ella pa ame e s by compa ing a
a ie y o obse a ional inpu s o in e pola ed model alues.
We inpu he Gaia DR2 pa allax, b oadband pho ome y
(2MASS JHK
s
; Gaia DR2 G,G
BP
, and B
RP
; Johnson Vand B;
and WISE W1 and W2), and he SME spec oscopic alues
(T
e
, log g, and [Fe/H])as p io s. The pos e io s a e sampled
using he Mul iNes (Fe oz e al. 2009,2019)sampling
algo i hm.
All alues o he s ella adius and mass a e epo ed in
Table 2. We include alues om he TIC and Gaia DR2, as
well as he ypical mass and adius o an F7V dwa o
e e ence (Cox 2000). The SpecMa ch-Emp fi also de i es a
s ella adius, which we couple o he calib a ion equa ions
om To es e al. (2010) o in e a su ace g a i y o log
g=4.14 ±0.07 dex and a s ella mass o 1.25 ±0.09 M
e
. All
alues a e in good ag eemen wi h each o he . We adop he
ARIADNE adius (R
*
=1.316 ±0.019 R
e
)and he iso-
ch ones mass (M
*
=1.21 ±0.02 M
e
)as he s ella pa a-
me e s o be used in he global fi and epo all adop ed
physical, pho ome ic, and kinema ic p ope ies o TOI-1670 in
Table 3.
Table 1
Spec oscopic Pa ame e s o TOI-1670 De i ed Using SME and SpecMa ch-Emp
Me hod T
e
(K)log g(gcm
−3
)[Fe/H](dex) sin i(km s
−1
)
SME 6170 ±61 4.29 ±0.11 0.09 ±0.07 9.2 ±0.6
SpecMa ch-Emp 6048 ±110 L0.05 ±0.09 L
Figu e 3. The SED o TOI-1670. B oadband pho ome y (Table 3)is shown
wi h o ange ci cles, wi h ho izon al e o s ep esen ing he bandpass wid h. The
bes -fi ing model SED is shown in black, and he blue diamonds a e he model
flux in eg a ed o e each bandpass. The esiduals no malized by he
pho ome ic e o s a e shown in he bo om panel.
32
h ps://gi hub.com/j ines/as oARIADNE
5
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
3.2. S ella Ac i i y
S ella ac i i y in he o m o o a ionally modula ed
s a spo s and g anula ion can bo h mimic and mask he signals
o plane s in ligh cu es (Llama & Shkolnik 2015,2016)and
RVs (e.g., Figuei a e al. 2013). Thus, p io o unning he
global model fi , we fi s examine whe he s ella ac i i y
significan ly influences he ligh cu e and RV ime se ies o
TOI-1670. We measu ed a low a e age alue o
log ¢=-
R
4.93 0.01
HK om he HARPS-N spec a, which
sugges s ha TOI-1670 is a quie s a no domina ed by s ella
ac i i y (Mamajek & Hillenb and 2008). The TESS ligh cu e
p io o de ending also does no exhibi any significan o a ion
o ac i i y-induced a iabili y.
A common s a is ical ool used o de ec pe iodic signals in
une enly sampled ime se ies da a is he Lomb–Sca gle
pe iodog am (Lomb 1976; Sca gle 1982). We u ilize his
algo i hm o sea ch o pe iodici y in bo h he TESS
pho ome y and RV ac i i y indica o s o dis inguish s ella
ac i i y–based signals om hose induced by plane a y mo ion.
We compu e he gene alized Lomb–Sca gle (GLS)pe iod-
og ams (Zechmeis e & Kü s e 2009) o he “unde ended”
PDCSAP ligh cu e wi h he ansi e en s emo ed, he RVs,
he a o emen ioned ac i i y indica o s, and he spec al window
unc ion o e he equency ange 0.0005–0.5 day
−1
(2–2000
days)in Figu e 4. The GLS powe h esholds co esponding o
alse-ala m p obabili y (FAP)le els o 1% and 0.1% compu ed
ia a boo s ap app oach a e shown as blue do ed lines
(Kue s e e al. 1997). The GLS pe iodog am o he RVs was
compu ed o he combined HARPS-N and Tull Coudé da a
a e sub ac ing he sys ema ic eloci y o se s as epo ed in
Table 4. The pe iodog am o he TESS pho ome y has e y
low powe wi h no peaks ha ha e significance highe han he
1% FAP le el. This is consis en wi h he fla na u e o he
unde ended PDCSAP ligh cu e and indica es ha TOI-1670
does no ha e a la ge s a spo co e age ac ion. The s onges
signal in he pe iodog am o he RVs is a he ∼40.7 day o bi al
pe iod o TOI-1670 c, which has an FAP <0.1%. This peak
has no coun e pa s in he pe iodog ams o he ac i i y indices,
which would be he case i ha signal o igina ed om s ella
ac i i y. Ac i i y signals can also appea a he equency o he
s ella o a ion pe iod. Using he s ella adius and sin i,we
can place a lowe limi o P
o
7.2 days ( 0.138 day
−1
).No
significan peaks a e isible in he GLS pe iodog am o he S-
indices a his equency.
3.3. S a is ical Valida ion o TOI-1670 b
Al hough TOI-1670 b is no significan ly de ec ed in he RV
da a se , ou model is able o place an uppe limi on i s mass.
The 3σuppe limi o he fi ed RV semiampli ude is 14.5 m
s
−1
, which co esponds o an uppe limi o 0.18 M
Jup
o TOI-
1670 b, assuming an eccen ici y o ze o.
An es ima e o he RV p ecision equi ed o obus ly de ec
TOI-1670 b can be made om a p edic ed mass in e ed om
i s adius. Inpu ing he s ella and plane a y pa ame e s
measu ed in Sec ion 3in o a p obabilis ic mass– adius ela ion
using he open so wa e package o ecas e (Chen &
Kipping 2017)yields a mass es ima e o -
+
5
.2 2.0
4.0 M
⊕
o TOI-
1670 b. Assuming a ci cula o bi , his co esponds o an RV
semiampli ude o ∼1.3 m s
−1
. Robus ly de ec ing an RV signal
a his le el equi es ins umen p ecision a he 1 m s
−1
le el
and a well-beha ed s a .
We can exclude alse-posi i e scena ios o suppo TOI-1670
b as a likely plane using ollow-up obse a ions. F om Gaia
Table 2
S ella Mass and Radius o TOI-1670 De i ed om Di e en Me hods
Me hod M
*
(M
e
)R
*
(R
e
)
ARIADNE
a
1.16 ±0.16 1.316 ±0.019
isoch ones 1.21 ±0.02 1.316 ±0.007
SpecMa ch-Emp+To es
b
1.25 ±0.09 1.57 ±0.18
TIC
c
1.25 ±0.18 1.312 ±0.057
Gaia DR2
d
L-
+
1
.38 0.07
0.08
Typical F7V dwa
e
1.21 1.32
Adop ed 1.21 ±0.02 1.316 ±0.019
No es.
a
Mass calcula ed using de i ed adius and log g.
b
Mass calcula ed using SpecMa ch-Emp pa ame e s and calib a ion
equa ions om To es e al. (2010).
c
S assun e al. (2019).
d
Gaia Collabo a ion e al. (2018).
e
Cox (2000).
Table 3
Adop ed Physical, Pho ome ic, and Kinema ic P ope ies o TOI-1670
Pa ame e Value Sou ce
TIC ID 441739020 1
TOI ID 1670 1
Gaia ID 1651911084230149248 2
2MASS ID J17160415 +7209402 3
Gaia α(J2000.0)17:16:04.16 2
Gaia δ(J2000.0)+72:09:40.17 2
Gaia epoch 2015.5 2
Gaia pa allax (mas)5.92 ±0.02 2
Dis ance (pc)-
+
1
65.72 0.38
0.32 4
Gaia μ
α
cos δ(mas y
−1
)−6.09 ±0.05 2
Gaia μ
δ
(mas y
−1
)5.154 ±0.05 2
B(mag)10.43 ±0.03 5
V(mag)9.89 ±0.03 5
T(mag)9.423 ±0.0061 1
G(mag)9.8232 ±0.0004 2
G
RP
(mag)9.4145 ±0.0014 2
G
BP
(mag)10.0747 ±0.0010 2
J(mag)8.97 ±0.02 3
H(mag)8.75 ±0.03 3
K
s
(mag)8.724 ±0.02 3
W1(mag)8.689 ±0.023 6
W2(mag)8.702 ±0.020 6
T
e
(K)6170 ±61 This wo k
log g(gcm
−3
)4.29 ±0.11 This wo k
[Fe/H](dex)0.09 ±0.07 This wo k
sin i(km s
−1
)9.2 ±0.6 This wo k
M
*
(M
e
)1.21 ±0.02 This wo k
R
*
(R
e
)1.316 ±0.019 This wo k
ρ
*
(gcm
−3
)0.752 ±0.036 This wo k
Age (Gy )2.53 ±0.43 This wo k
A
V
(mag)0.010 ±0.006 This wo k
Re e ences. (1)S assun e al. (2019),(2)Gaia Collabo a ion e al. (2018),(3)
Cu i e al. (2003),(4)Baile -Jones e al. (2021),(5)Høg e al. (2000),(6)Cu i
e al. (2021).
6
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
EDR3, we no e ha TOI-1670 has ze o excess as ome ic
noise and a eno malized uni weigh e o o 1.07, indica ing
ha he single-s a model is a good fi o he as ome ic
solu ion (Gaia Collabo a ion e al. 2018; Lindeg en e al. 2018).
F om ou RVs, we find ha he o e all RV a iabili y is
<110 m s
−1
om OES, <54 m s
−1
om TRES, <34 m s
−1
om he Tull Coudé, and <16 m s
−1
om HARPS-N, all o
which obus ly exclude an EB scena io o he hos s a .
Finally, we use TRICERATOPS (Giacalone e al. 2021) o
s a is ically e alua e he p obabili y o possible alse-posi i e
scena ios in ol ing nea by con aminan s a s, including back-
g ound EBs. TRICERATOPS is a Bayesian ool o alida ing
ansi ing plane candida es by modeling and calcula ing he
p obabili y o di e en scena ios ha p oduce ansi -like ligh
cu es. Based on he lack o a close s ella companion om
Gaia as ome y, ou high- esolu ion imaging, and ou RVs, we
omi he op ional alse-posi i e calcula ions o he EB and
un esol ed s ella companion scena ios in he TRICERATOPS
code.
33
TRICERATOPS e u ns a alse-posi i e p obabili y ( he
o al p obabili y o a alse-posi i e scena io in ol ing he
p ima y s a )o <0.015 and a nea by alse-posi i e p obabili y
( he sum o all alse-posi i e p obabili ies o scena ios
in ol ing nea by s a s)o <10
−2
. The RV confi ma ion o
he ou e coplana ansi ing WJ u he suppo s he plane a y
na u e o TOI-1670 b, as mul iplane sys ems a e unlikely o be
alse posi i es (Lissaue e al. 2012; Rowe e al. 2014).
3.4. Join Modeling o RVs and Pho ome y
We pe o m a mul iplane global fi o he a ailable RV and
ansi obse a ions o TOI-1670 using he pyane i modeling
sui e (Ba agán e al. 2019). As he plane a y Dopple signals
a e no eco e ed a a significan le el in he TRES and
Ond
ejo spec a, we only use he 49 Tull Coudé and eigh
HARPS-N RVs in he modeling. We limi he ligh -cu e da a
o pho ome y spanning ou ull ansi du a ions be o e and
a e all ansi e en s o TOI-1670 b and c o imp o e
compu a ion e ficiency; his esul s in a o al o 24,772
pho ome ic poin s. These egions a e shown in pu ple and
pink in Figu e 1 o TOI-1670 b and c, espec i ely.
We simul aneously fi he Keple ian o bi and TESS ligh
cu e o eigh pa ame e s: o bi al pe iod (P), cen al ime o
ansi (T
0
), RV semiampli ude (K), ansi impac pa ame e
(b), plane a y- o-s ella adius (R
p
/R
*
), scaled semimajo axis
(a/R
*
), and pa ame e ized o ms o eccen ici y and a gumen
o pe ias on (
w
esin and
w
ecos ). This las pa ame e -
iza ion by Ande son e al. (2011)is used because he
eccen ici y pos e io dis ibu ion o o bi s wi h low eand
b oad ωis poo ly sampled by Ma ko chains (e.g., Lucy &
Sweeney 1971; Fo d 2006; Wang & Fo d 2011).Bydefining e
and ωin a pola o m, we a oid unca ing he pos e io
dis ibu ion a ze o and impose a uni o m p io on e. We also
adop he pa ame e iza ion o bas defined by Winn (2010),
w
=-
+
⎜⎟
⎛
⎝⎞
⎠
bai
R
e
e
cos 1
1sin,1
2
()
*
**
whe e i
*
is he s ella inclina ion, in o de o impose p io s ha
exclude non ansi ing o bi s >+b1R
R
p
(
)
*
.
We se na ow uni o m p io s on bo h o bi al pe iod and ime
o ansi based on isual inspec ion o he ligh cu e and he
SPOC p elimina y pa ame e s. Fo he inne sub-Nep une, he
anges a e =T1721.92, 1721.99
b0, ()in uni s o (BJD
TDB
–
2,457,000)days, =P10.980, 10.988
b()days, and
=K0.0, 10.0
b(
)
ms
−1
. Fo he ou e Jupi e , he anges
a e =T1750.82, 1750.92
c0, ()in uni s o (BJD
TDB
–
2,457,000)days, =P40.7485, 40.7505
c(
)
days, and
=K10.0, 100.0
c()ms
−1
. The s ella mass and adius a e
also ee pa ame e s wi h Gaussian p io s o
=
MM1.215, 0.023()
*and =
R
R1.316, 0.019()
*.
34
These pa ame e s a e u he cons ained by he s ella mean
densi y, which is a ec ed by Pand a/R
*
(Seage & Mallén-
O nelas 2003; Winn 2010). We assumed a quad a ic limb-
da kening law ollowing he equa ions om Mandel & Agol
(2002), who defined he linea and quad a ic coe ficien s as u
1
and u
2
, espec i ely. The pa ame e iza ion o =+quu
112
2
()
and =+
-
quuu0.5
211 21
()
om Kipping (2013)is adop ed. We
se b oad uni o m p io s o all o he pa ame e s and epo
hem in Table 4.A“ji e ” e m is added o he RVs o accoun
Figu e 4. Lomb–Sca gle pe iodog ams o he unde ended TESS pho ome y
a e emo ing ansi signals (fi s panel), combined Tull Coudé and HARPS-
N RVs a e sub ac ing he sys emic eloci ies (second panel), combined M .
Wilson S-index om Tull Coudé and HARPS-N spec a ( hi d panel), and
spec al window unc ion ( ou h panel). The 1% and 0.1% FAP (blue dashed
and do ed, espec i ely)lines a e calcula ed using boo s ap esampling. The
pu ple and pink e ical lines a e he ∼10.9 and ∼40.7 day plane a y signals
de e mined by he TESS SPOC, espec i ely. The highes peak o each
pe iodog am is shown as a dashed black e ical line. The e a e no coun e pa
peaks in he pe iodog am o he S-index ha co espond o he ∼40.7 day
signal seen in he pe iodog am o he RV, and no peaks ise abo e he 1% FAP
h eshold. No peaks a e isible in he spec al window unc ion pe iodog am.
The only significan pe iod (<0.1% FAP)in he RVs is a 41.1 days, consis en
wi h he WJ (TOI-1670 c).
33
Giacalone e al. (2021)no ed ha using ollow-up obse a ions o ule ou
un esol ed s ella companion scena ios p oduces simila esul s o bo h
TRICERATOPS and he a ge alida ion code espa (Mo on 2015b; Mo on
e al. 2016).
34
He e and
e e o he uni o m and no mal dis ibu ions, espec i ely,
whe e he la e is defined as ms,(
)
.
7
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
o any sys ema ic and as ophysical a iance no epo ed in
he obse a ional unce ain ies.
35
Pos e io dis ibu ions o fi ed and de i ed pa ame e s we e
sampled using a Ma ko Chain Mon e Ca lo Me opolis–
Has ing algo i hm ollowing he desc ip ion by Sha ma (2017)
as implemen ed by pyane i. The dis ibu ions we e sampled
using 50 chains o 10,000 i e a ions wi h a hinning ac o o
10. The con e gence o each chain was de e mined wi h he
Gelman–Rubin diagnos ic es (Gelman & Rubin 1992).
Using he TESS pho ome y and RVs, we join ly model he
ansi s o TOI-1670 b and c and he RV cu e o TOI-1670 c
using he p io s as p e iously desc ibed.
36
The pos e io alues
o he fi ed and de i ed sys em pa ame e s om pyane i o
TOI-1670 a e gi en in Table 4. The bes -fi ing phased TESS
ligh cu es o TOI-1670 b and c and RV model o TOI-1670
c a e plo ed in Figu es 5–7. Figu e C1 in Appendix Cdisplays
he pos e io dis ibu ions o he fi ed pa ame e s. We find a
mass, adius, and densi y o TOI-1670 c o =-
+
M0.63
c0.08
0.09
M
Jup
,=-
+
R
0.987
c0.025
0.02
5
R
Jup
, and
=-
+
0.81
c0.11
0.13 gcm
−3
,
espec i ely. Fo TOI-1670 b, we find a adius o -
+
2
.06 0.15
0.19
R
⊕
and a 3σmass uppe limi o M
b
<0.13 M
Jup
.
4. Discussion
The exis ence o WJ sys ems hos ing one o mo e smalle
coplana inne companions such as TOI-1670 is inconsis en
Table 4
P io s and Pos e io s on he Global Sys em Pa ame e s o TOI-1670 b and c
Pa ame e Adop ed P io Pos e io Values
Fi ed Pa ame e s bcbc
T
0
(BJD
TDB
−2,457,000)1721.92, 1721.99(
)
1750.82, 1750.92(
)
-
+
1
721.9423 0.0062
0.0071 -
+
1
750.88286 0.00083
0.00085
P(days)10.980, 10.988()40.7485, 40.7505(
)
-
+
1
0.98462 0.00051
0.0004
6
-
+
4
0.74976 0.00021
0.000022
K(ms
−1
)0.0, 10.0(
)
10.0, 100(
)
-
+
4
.6 3.0
3.3 -
+
3
2.7 4.3
4.7
b0.0, 1.0(
)
0.0, 1.0(
)
-
+
0.61 0.37
0.22 -
+
0.76 0.04
0.02
a/R
*
1.1, 20.0(
)
1.1, 50.0(
)
-
+
1
6.88 0.27
0.27 -
+
4
0.68 0.66
0.6
6
R
p
/R
*
0.0, 0.05(
)
0.0, 0.15(
)
-
+
0.014 0.001
0.001 -
+
0.077 0.002
0.002
esin ω-1.0, 1.0(
)
-1.0, 1.0(
)
-
+
0.18 0.44
0.3
6
-
+
0.27 0.1
0
0.0
8
ecos ω-1.0, 1.0(
)
-1.0, 1.0(
)
--
+
0.63 0.21
0.62 --
+
0.07 0.13
0.1
4
De i ed Pa ame e s
M
p
LL
-
+
1
3.8 8.7
9.5 M
⊕
-
+
0.63 0.08
0.09 M
Jup
R
p
LL
-
+
2
.06 0.15
0.19 R
⊕
-
+
0.987 0.025
0.025 R
Jup
ρ
p
(gcm
−3
)LL
-
+
8.6 5.6
6.9 -
+
0.81 0.11
0.13
eLL
-
+
0.59 0.26
0.17 -
+
0.09 0.04
0.05
ω(deg)LL
-
+
1
63.6 53.7
41.7 -
+
1
05.5 29.4
28.
6
i(deg)LL
-
+
86.87 1.07
1.1
6
-
+
88.84 0.04
0.0
4
a(au)LL
-
+
0.103 0.002
0.002 -
+
0.249 0.005
0.005
T
14
(h )LL
-
+
2
.80
0.19
0.16
-
+
5
.40 0.05
0.0
6
T
eq
(K)LL
-
+
1
062 13
1
4
-
+
684 9
9
Addi ional Pa ame e s
M
*
( om scaled pa ame e s)(M
e
)1.215, 0.023(
)
-
+
1
.218 0.07
6
0.081 -
+
1
.239 0.079
0.08
4
ρ
*
( om ansi )(gcm
−3
)L-
+
0.754 0.035
0.037 -
+
0.767 0.037
0.038
q
1
0.0, 1.0(
)
-
+
0.35 0.11
0.19
q
2
0.0, 1.0(
)
-
+
0.32
0.23
0.39
γ
Tull
(km s
−1
)--3.6849, 3.3299(
)
--
+
3.5132 0.0043
0.0042
γ
FIES
(km s
−1
)-0.1217, 0.1139(
)
--
+
0.0108 0.0061
0.0061
γ
HARPS−N
(km s
−1
)--11.6134, 11.3602(
)
--
+
11.4805 0.0027
0.0025
RV ji e (Tull)(ms
−1
)L-
+
2
2.5 3.6
3.9
RV ji e (FIES)(ms
−1
)L-
+
5
.3 3.8
7.2
RV ji e (HARPS-N)(ms
−1
)L-
+
4
.3 2.8
4.5
Figu e 5. T ansi ligh cu e olded o he o bi al pe iod o TOI-1670 b. The
TESS pho ome y is shown in pu ple, and he solid black line is he bes -fi ing
ansi model. The black ci cles a e he pho ome ic da a binned o e 20 minu e
in e als. The middle panel zooms in on he bes -fi ansi model and binned
da a poin s. The fi esiduals a e shown in he lowe panel.
35
We also fi o a noise e m in he pho ome y and find a alue 2 o de s o
magni ude less han he ypical unce ain y wi h no app eciable change in o he
model pa ame e s. We choose no o include his e m in he final join
model fi .
36
We also conside less complex models in Appendix B. We ul ima ely
choose o apply a ull global fi o obus ly assess he pa ame e unce ain ies.
8
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
wi h dynamical mig a ion ou es. Du ing high-eccen ici y idal
mig a ion, mul iple close-in plane s would likely in e ac wi h
each o he and po en ially lead o ejec ions o collisions (e.g.,
Rasio & Fo d 1996; Cha e jee e al. 2008; Mus ill e al. 2015).
Simila ly, plane –plane sca e ing and on Zeipel–Lido –
Kozai in e ac ions equi e an ou e companion (Ve as &
A mi age 2005; Ande son & Lai 2017). Mul iplane sys ems
hos ing a WJ wi h low eccen ici y ep esen ano he ype o
sys em ha expe ienced compa a i ely gen le dynamical
his o ies, such as inwa d disk mig a ion o in si u o ma ion.
TOI-1670 joins a hand ul o confi med sys ems wi h an ou e
wa m gian exoplane (M
p
>0.25 M
Jup
, 10 days <P<200
days)and a leas one inne smalle companion (see Table 5).
Figu e 8shows he eccen ici y e sus semimajo axis o he
confi med WJs. The WJs in all 11 sys ems (including TOI-
1670)wi h simila configu a ions ha e low eccen ici ies,
whe eas he eccen ici ies o o he WJs wi hou known inne
companions a e widely dis ibu ed. This di e gence u he
sugges s ha his g oup o TOI-1670-like sys ems may ha e
o med and mig a ed along a simila e olu iona y pa hway.
One way o disen angle whe he disk mig a ion o in si u
o ma ion plays he dominan ole in sculp ing hese mul iplane
sys ems is by examining hei pe iod a ios in sea ch o nea
mean-mo ion esonances (MMRs). Disk mig a ion is expec ed o
e ficien ly cap u e gian plane s in o MMRs close o small in ege
pe iod a ios such as 2:1, 3:1, 3:2, and 4:3 (e.g., Gold eich &
T emaine 1980;Lee&Peale2001;A mi age2010;Winn&
Fab ycky 2015). In si u o ma ion can also c ea e plane s in o bi al
esonances, ei he coinciden ally o by eccen ici y damping ia
in e ac ions wi h he p o oplane a y o plane esimal disk (Dawson
e al. 2016;Mo isone al.2020). In his o ma ion scena io, he e
should be a popula ion o sys ems ha cong ega e a o nea hese
di e en in ege a ios.
Wi hin he sample o 11 known sys ems ha ha e a gian plane
wi h a small inne companion, eigh WJs (73%)a e in o nea a
2:1 o 3:1 esonance wi h he inne plane (Table 5). Wi h a pe iod
a io o 3.7, TOI-1670 joins wo o he sys ems, K2-290 and HIP
57274, ha ha e non-MMR o bi al pe iod a ios g ea e han 3.
The plane s in hese sys ems may ha e o med in si u o mig a ed
inwa d oge he . Al e na i ely, ha he plane s in hese sys ems
a e no locked in an MMR could also indica e ha hey o med
independen ly and did no mig a e oge he o became uns able
o e ime (Pe i e al.2020; Pichie i & Mo bidelli 2020;Izido o
e al. 2021). This may hin a a di ision wi hin his small class o
WJs in mul iplane sys ems in which some mig a e in o place ia
disk mig a ion ( hose wi h in ege pe iod a ios), while o he s
o med whe e we see hem oday o expe ienced u he
dynamical in e ac ion la e in hei li e ime. This hypo hesis can
be u he in es iga ed by inc easing he numbe o wa m gian
plane s wi h smalle inne companions and examining popula ion
ends wi hin his sample.
We hank Benjamin To flemi e, Daniel K olikowski,
Michael Gully-San iago, and E ik Pe igu a o insigh ul
discussions on he gene alized Lomb–Sca gle pe iodog am,
gas gian occu ence a e, and ligh -cu e analysis.
Q.H.T. and B.P.B. acknowledge suppo om a NASA
FINESST g an (80NSSC20K1554). This wo k benefi ed om
in ol emen in ExoExplo e s, which is sponso ed by he
Exoplane s P og am Analysis G oup (ExoPAG)and NASAʼs
Exoplane Explo a ion P og am O fice (ExEP). B.P.B.
acknowledges suppo om Na ional Science Founda ion g an
AST-1909209 and NASA Exoplane Resea ch P og am g an
20-XRP20_2-0119.
C.M.P. and M.F. g a e ully acknowledge he suppo o he
Swedish Na ional Space Agency (DNR 65/19 and 177/19).
J.K. g a e ully acknowledges he suppo o he Swedish
Na ional Space Agency (SNSA; DNR 2020-00104). P.K.,
M.S., J.S., and R.K. acknowledge he financial suppo o In e -
ans e g an No. LTT-20015. M.K. acknowledges suppo
om ESAs PEA4000127913. M.E. acknowledges he suppo
o he DFG p io i y p og am SPP 1992 “Explo ing he
Di e si y o Ex asola Plane s”(HA 3279/12-1). Funding
o he S ella As ophysics Cen e is p o ided by he Danish
Na ional Resea ch Founda ion (g an ag eemen No.
DNRF106). D.G. and L.M.S. g a e ully acknowledge financial
suppo om he Cassa di Rispa mio di To ino (CRT)
ounda ion unde g an No. 2018.2323 “Gaseous o ocky?
Un eiling he na u e o small wo lds.”This wo k is pa ly
suppo ed by JSPS KAKENHI g an No. JP20K14518 and
SATELLITE Resea ch om As obiology Cen e (AB022006).
Funding o he TESS mission is p o ided by NASA’s Science
Mission Di ec o a e. This esea ch has made use o he Exoplane
Follow-up Obse a ion P og am websi e, which is ope a ed by he
Cali o nia Ins i u e o Technology, unde con ac wi h he
Figu e 6. T ansi ligh cu e olded o he o bi al pe iod o TOI-1670 c. The
TESS pho ome y is shown in pink, and he solid black line is he bes -fi ing
ansi model. Black poin s a e he pho ome ic da a binned o e 20 minu e
in e als.
Figu e 7. The RV cu e o TOI-1670, phase- olded o he o bi al pe iod o he
WJ, TOI-1670 c, wi h he con ibu ions o he inne companion emo ed. The
di e en colo ed poin s deno e he di e en spec og aphs, and he bes -fi ing
RV model is shown by he solid black line. The fi esiduals a e shown in he
lowe panel. The colo ed e o ba s a e nominal RV e o s, and he g ay e o
ba s include he sys ema ic ji e e m.
9
The As onomical Jou nal, 163:225 (16pp), 2022 May T an e al.
Pa a, K. C., Winn, J. N., Holman, M. J., e al. 2020, AJ,159, 150
Paulson, D. B., Saa , S. H., Coch an, W. D., & Ha zes, A. P. 2002, AJ,
124, 572
Pepe, F., Mayo , M., Galland, F., e al. 2002, A&A,388, 632
Pe sson, C. M., F idlund, M., Ba agán, O., e al. 2018, A&A,618, A33
Pe i , A. C., Pe igu a, E. A., Da ies, M. B., & Johansen, A. 2020, MNRAS,
496, 3101
Pe o ich, C., Wu, Y., & Ali-Dib, M. 2019, AJ,157, 5
Pichie i, G., & Mo bidelli, A. 2020, MNRAS,494, 4950
Piskuno , N., & Valen i, J. A. 2017, A&A,597, A16
Ra e y, A. E. 1986, Am. Sociol. Re ., 51, 145
Rasio, F. A., & Fo d, E. B. 1996, Sci,274, 954
Ricke , G. R., Winn, J. N., Vande spek, R., e al. 2015, JATIS,1, 014003
Rowe, J. F., B yson, S. T., Ma cy, G. W., e al. 2014, ApJ,784, 45
Sanchis-Ojeda, R., Fab ycky, D. C., Winn, J. N., e al. 2012, Na u ,487, 449
San e ne, A., Mou ou, C., Tsan aki, M., e al. 2016, A&A,587, A64
Sa i zky, A., & Golay, M. J. E. 1964, AnaCh, 36, 1627
Sca gle, J. D. 1982, ApJ,263, 835
Schlafly, E. F., & Finkbeine , D. P. 2011, ApJ,737, 103
Schlecke , M., Kossakowski, D., B ahm, R., e al. 2020, AJ,160, 275
Schlegel, D. J., Finkbeine , D. P., & Da is, M. 1998, ApJ,500, 525
Schmi , J. R., Agol, E., Deck, K. M., e al. 2014, ApJ,795, 167
Schneide , J., Dedieu, C., Le Sidane , P., Sa alle, R., & Zolo ukhin, I. 2011,
A&A,532, A79
Schwa z, G. 1978, The Annals o S a is ics,6, 461
Sco , N. J. 2019, AAS Abs ac s, 51, 330.15
Sco , N. J., Howell, S. B., Ho ch, E. P., & E e e , M. E. 2018, PASP,130,
054502
Seage , S., & Mallén-O nelas, G. 2003, ApJ,585, 1038
Sha ma, S. 2017, ARA&A,55, 213
Smi h, J. C., S umpe, M. C., Van Cle e, J. E., e al. 2012, PASP,124, 1000
S assun, K. G., Oelke s, R. J., Paege , M., e al. 2019, AJ,158, 138
S umpe, M. C., Smi h, J. C., Ca anza i e, J. H., e al. 2014, PASP,126, 100
S umpe, M. C., Smi h, J. C., Van Cle e, J. E., e al. 2012, PASP,124, 985
Sugiu a, N. 1978, Communica ions in S a is ics—Theo y and Me hods, Vol. 7
(Abingdon-on-Thames: Taylo & F ancis),13
Tel ing, J. H., A ila, G., Buchha e, L., e al. 2014, AN,335, 41
Tody, D. 1993, ASP Con . Se . 52, As onomical Da a Analysis So wa e and
Sys ems II, ed. R. J. Hanisch, R. J. V. B issenden, & J. Ba nes (San
F ancisco, CA: ASP), 173
To es, G., Ande sen, J., & Giménez, A. 2010, A&AR ,18, 67
T iaud, A. H. M. J., Collie Came on, A., Queloz, D., e al. 2010, A&A,
524, A25
T i ono , T., Kü s e , M., Zechmeis e , M., e al. 2018, A&A,609, A117
Tull, R. G., MacQueen, P. J., Sneden, C., & Lambe , D. L. 1995, PASP,
107, 251
Twicken, J. D., Ca anza i e, J. H., Cla ke, B. D., e al. 2018, PASP,130,
064502
Valen i, J. A., & Fische , D. A. 2005, ApJS,159, 141
Valen i, J. A., & Piskuno , N. 1996, A&AS, 118, 595
Ve as, D., & A mi age, P. J. 2005, ApJL,620, L111
Vick, M., Lai, D., & Ande son, K. R. 2019, MNRAS,484, 5645
Šubjak, J., Sha ma, R., Ca michael, T. W., e al. 2020, AJ,159, 151
Wang, J., & Fo d, E. B. 2011, MNRAS,418, 1822
Wa d, W. R. 1997, Ica ,126, 261
Weiss, L. M., Ma cy, G. W., Rowe, J. F., e al. 2013, ApJ,768, 14
Weiss, L. M., Fab ycky, D. C., Agol, E., e al. 2020, AJ,159, 242
Winn, J. N. 2010, a Xi :1001.2010
Winn, J. N., & Fab ycky, D. C. 2015, ARA&A,53, 409
Wu, Y., & Mu ay, N. 2003, ApJ,589, 605
Yee, S. W., Pe igu a, E. A., & on B aun, K. 2017, ApJ,836, 77
Zechmeis e , M., & Kü s e , M. 2009, A&A,496, 577
16
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