11institutetext: Instituto de Astrofísica e Ciências do Espaço, Universidade
do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal 22institutetext:
Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do
Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal. 33institutetext:
Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4
7AL, UK. 44institutetext: Centre for Exoplanets and Habitability, University
of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK. 55institutetext: Geneva
Observatory, University of Geneva, Chemin Pegasi 51, Versoix CH-1290,
Switzerland. 66institutetext: Institute for Computational Science, University
of Zurich,Winterthurerstr. 190, CH-8057 Zurich, Switzerland. 77institutetext:
Department of Physics, University of Oxford, OX13RH, Oxford, UK.
88institutetext: Centro de Astrobiología (CAB, CSIC-INTA), Depto. de
Astrofísica, ESAC campus 28692 Villanueva de la Cañada (Madrid), Spain.
99institutetext: Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France.
1010institutetext: Department of Physics and Astronomy, Vanderbilt University,
Nashville, TN 37235, USA. 1111institutetext: Univ. Grenoble Alpes, CNRS, IPAG,
F-38000 Grenoble, France. 1212institutetext: International Center for Advanced
Studies (ICAS) and ICIFI (CONICET), ECyT-UNSAM, Campus Miguelete, 25 de Mayo y
Francia, (1650) Buenos Aires, Argentina. 1313institutetext: European Southern
Observatory, Alonso de Córdova 3107, Santiago, Chile.

# The HD 137496 system:
A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.

T. A. Silva The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/<EMAIL_ADDRESS>The HD 137496 system:  A dense, hot
super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only available in
electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr
(130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD
137496 system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables
1 and 6 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/. O.D.S Demangeon The HD 137496 system:  A dense, hot super-
Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only available in
electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr
(130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD
137496 system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables
1 and 6 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/<EMAIL_ADDRESS>S. C. C. Barros The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. D. J. Armstrong The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. J. F. Otegi The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. D. Bossini The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. E. Delgado Mena The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. S. G. Sousa The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. V. Adibekyan The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. L. D. Nielsen The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. C. Dorn The HD 137496 system:
A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. J. Lillo-Box The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. N. C. Santos The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. S. Hoyer The HD 137496 system:
A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. K. G. Stassun The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. J. M. Almenara The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. D. Bayliss The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. D. Barrado The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. I. Boisse The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. D. J. A. Brown The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. R. F. Díaz The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. X. Dumusque The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. P. Figueira The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. A. Hadjigeorghiou The HD
137496 system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables
1 and 6 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. S. Hojjatpanah The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. O. Mousis The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. A. Osborn The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. A. Santerne The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. P. A. Strøm The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. S. Udry The HD 137496 system:
A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. P. J. Wheatley The HD 137496
system:  A dense, hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.The HD 137496 system:  A dense,
hot super-Mercury and a cold Jupiter††thanks: Tables 1 and 6 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.The HD 137496 system:  A dense, hot super-Mercury and a cold
Jupiter††thanks: Tables 1 and 6 are only available in electronic form at the
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.

(Received September 15, 1996; accepted March 16, 1997)

###### Abstract

Context. Most of the currently known planets are small worlds with radii
between that of the Earth and that of Neptune. The characterization of planets
in this regime shows a large diversity in compositions and system
architectures, with distributions hinting at a multitude of formation and
evolution scenarios. However, many planetary populations, such as high-density
planets, are significantly under-sampled, limiting our understanding of planet
formation and evolution.

Aims. NCORES is a large observing program conducted on the HARPS high-
resolution spectrograph that aims to confirm the planetary status and to
measure the masses of small transiting planetary candidates detected by
transit photometry surveys in order to constrain their internal composition.

Methods. Using photometry from the K2 satellite and radial velocities measured
with the HARPS and CORALIE spectrographs, we searched for planets around the
bright (V${}_{\textrm{mag}}$ = 10) and slightly evolved Sun-like star HD
137496.

Results. We precisely estimated the stellar parameters, $M_{*}$ = 1.035 $\pm$
0.022 $M_{\odot}$, $R_{*}$ = 1.587 $\pm$ 0.028 $R_{\odot}$, $T_{\text{eff}}$ =
5799 $\pm$ 61 K, together with the chemical composition (e.g. [Fe/H] = -0.027
$\pm$ 0.040 dex) of the slightly evolved star. We detect two planets orbiting
HD 137496. The inner planet, HD 137496 b, is a super-Mercury (an Earth-sized
planet with the density of Mercury) with a mass of $M_{b}$ = 4.04 $\pm$ 0.55
$M_{\oplus}$, a radius of $R_{b}=1.31_{-0.05}^{+0.06}\,R_{\oplus},$ and a
density of $\rho_{b}=10.49_{-1.82}^{+2.08}$ $\mathrm{g\,cm^{-3}}$. With an
interior modeling analysis, we find that the planet is composed mainly of
iron, with the core representing over 70% of the planet’s mass
($M_{core}/M_{total}=0.73^{+0.11}_{-0.12}$). The outer planet, HD 137496 c, is
an eccentric ($e$ = 0.477 $\pm$ 0.004), long period ($P$ =
$479.9_{-1.1}^{+1.0}$ days) giant planet ($M_{c}\sin i_{c}$ = 7.66 $\pm$ 0.11
$M_{Jup}$) for which we do not detect a transit.

Conclusions. HD 137496 b is one of the few super-Mercuries detected to date.
The accurate characterization reported here enhances its role as a key target
to better understand the formation and evolution of planetary systems. The
detection of an eccentric long period giant companion also reinforces the link
between the presence of small transiting inner planets and long period gas
giants.

###### Key Words.:

Techniques: photometric – Techniques: radial velocities - Stars: individual:
HD 137496 – Planets and satellites: detection – Planets and satellites:
composition

##  1 Introduction

In our quest to better understand planet frequency and formation, few missions
have been as influential as Kepler (Borucki et al. 2010), with upwards of 2500
validated planets111See the Extrasolar Planets Encyclopaedia (Schneider et al.
2011) or the NASA Exoplanet Archive (Akeson et al. 2013). and many others
awaiting confirmation. More than ten years have passed since its launch, and
astronomers are still able to reap the benefits of its data. In 2013, a second
failure occurred on Kepler’s reaction wheels. Despite this technical problem,
Kepler continued operations but surveyed the ecliptic plane for periods of
around 80 days called campaigns. This new operational setup of the Kepler
satellite became known as the K2 mission (Howell et al. 2014).

Together with other space-based missions and ground-based telescopes, Kepler
and K2 have discovered a large number of planets, many of them in
configurations foreign to our Solar System. Not only is the architecture of
the orbits distinct, the physical characteristics of these planets are also
significantly different, with a broad spectrum of sizes, masses, and plausible
compositions. Together with former results of Doppler radial velocity surveys
(e.g., Bonfils et al. 2013; Mayor et al. 2014), over the last decade it has
become clear that super-Earths and sub-Neptunes, planets with a radius between
that of Earth and and that of Neptune, are ubiquitous in our Galaxy despite
not being found in our Solar System (Howard et al. 2012; Zhu et al. 2018).

One of the most striking results for this population is the presence of a
radius gap (Fulton et al. 2017), where observed planets appear to prefer a
radius close to $\sim$1.3$R_{\oplus}$ or to $\sim$2.6$R_{\oplus}$. This gap
hints at two separate populations of exoplanets, where the smaller radius
planets are thought to be predominantly rocky, while planets with a radius
above the gap are expected to have lower densities and extended atmospheres
rich in volatiles. In order to explain this bimodal distribution (super-Earths
and sub-Neptunes), multiple theoretical models have been suggested. One of the
most prominent hypotheses is that this distribution is a result of
photoevaporation (Lopez et al. 2012; Owen & Wu 2017). Photoevaporation, the
erosion of the planetary atmosphere by the stellar irradiation, can strip the
atmosphere of a planet down to its core, while less irradiated and/or heavier
planets are able to retain their atmospheres and sustain a bigger radius. A
concurrent explanation is that the atmosphere of the planets can escape as a
result of the thermal emission generated by the planetary core (Gupta &
Schlichting 2019). Recent works also propose that the stellar environment of a
planetary system plays a crucial role in the observed radius distribution
(Kruijssen et al. 2020). The exoplanet community is now trying to characterize
more planets in this regime to identify which are the best hypotheses (e.g.,
Lopez & Rice 2018; Fulton & Petigura 2018; Van Eylen et al. 2018; Cloutier &
Menou 2020; Cloutier et al. 2020; Sozzetti et al. 2021; Leleu et al. 2021).

Within the rocky planet population, a variety of compositions are estimated,
from seemingly Earth-like compositions (e.g., Dressing et al. 2015) to high-
density Mercury-like planets (e.g., Santerne et al. 2018). When looking at
planets with interior compositions resembling that of Mercury, additional
formation and evolution scenarios are expected to take place to give origin to
an iron-enhanced planet. Such hypotheses include that some planets are
initially formed in iron-rich environments (e.g., Wurm et al. 2013; Santos et
al. 2017; Aguichine et al. 2020; Adibekyan et al. 2021), suffer from giant
impacts (Marcus et al. 2010; Inamdar & Schlichting 2015), or even experience
impact erosion from planetesimals (Shuvalov 2009; Wyatt et al. 2020).
Planetary dynamics can also play a significant role in the transition from gas
giants to high-density planets; this includes tidal disruption effects and
Roche-Lobe Overflow of matter and angular momentum transfers (Gu et al. 2003;
Li et al. 2010; Rappaport et al. 2013; Valsecchi et al. 2014, 2015; Jackson et
al. 2017). The detection of elusive Mercury-like exoplanets and the study of
their system architectures can provide unique and important clues regarding
the formation of these planets.

The large number of exoplanets discovered with Kepler and K2 shed new light on
the processes shaping these planets while also enabling more complete studies
on the architecture of planetary systems. A recent study using Kepler data
(Zhu & Wu 2018) found that there is a positive correlation between the
presence of hot super-Earths and ”cold” Jupiters in the same system. This work
was later corroborated by Bryan et al. (2019), where the authors
correspondingly find that $\sim$ 1/3 of close-in systems of super-Earths and
sub-Neptunes possess exterior giants companions (0.5-20 $M_{Jup}$ at 1–20 AU).
These results imply that the presence of outer gas giants does not prevent the
formation of super-Earths. On the other hand, Bitsch et al. (2020) showed in
their simulations that the eccentricity of these massive companions may play a
role in the presence of super-Earths, for which systems with eccentric
Jupiter-type planets are less likely to host inner super-Earths. Identifying
and studying such correlations is important to understanding the origin of
these planets, as it allows astronomers to test different models of planet
formation and migration and gather insights into the dynamics and the
architectures of planetary systems (Fang & Margot 2012).

In this paper, we present the discovery and characterization of such a system,
a new multi-planetary system around HD 137496, alias K2-364 (EPIC222EPIC
stands for Ecliptic Plane Input Catalog 249910734), a V${}_{\textrm{mag}}$=10,
mid-G star near the main sequence turn-off. HD 137496 b is a short period
super-Mercury, and HD 137496 c is a Jupiter-sized planet. HD 137496 b was
first identified based on photometric data from K2 Campaign 15 and confirmed
with radial velocity (RV) observations from the HARPS and CORALIE instruments.
These measurements revealed the presence of HD 137496 c, the second planet in
the system. This system’s radial velocities were obtained within the scope of
the NCORES program (ID 1102.C-0249, PI Armstrong). This HARPS program focuses
on improving our understanding of the origin and internal composition of such
close-in planets (e.g., Nielsen et al. 2020; Armstrong et al. 2020; Osborn et
al. 2021).

This paper is structured as follows. In Section 2, we describe the transit
discovery and characterization from the K2 photometry. We then check for
photometric contamination in Section 3. Next, we discuss the RV analysis and
stellar activity indicators in Section 4. The stellar properties are provided
in Section 5. The joint analysis of the RVs and photometry are reported in
Section 6, and the discussion and conclusions are given in Section 7.

##  2 K2 photometry

HD 137496 was observed by the Kepler spacecraft during Campaign 15 of the K2
mission from 23 August 2017 to 19 November 2017 - programs: GO15009 (PI:
Charbonneau), GO15021 (PI: Howard) and GO15028 (PI: Cochran). This target is
located at RA: 15:26:58.07, Dec: -16:30:31.68 (J2000) and was observed in the
long ($\sim$ 30 min) cadence mode.

The raw data were extracted through the Mikulski Archive for Space Telescopes
(MAST)333 http://archive.stsci.edu/k2/epic/search.php. portal. These include
the target pixel files, the simple aperture photometry (SAP) flux, and the
more processed version of SAP with artifact mitigation called the pre-search
data conditioning (PDCSAP) flux.

###  2.1 Detection of a transit signal with a period of 1.62 days

As most K2 light curves, the SAP and PDSCAP light curves suffer from a high
noise level with a 12 hr period. This is due to the rolling motion of the
satellite caused by solar pressure, which results from the loss of two
reaction wheels and the periodic corrections of this motion. For this reason,
we used the Planet candidates from OptimaL Aperture Reduction (POLAR) software
(Barros et al. 2016), which was specifically developed to mitigate this noise
source in order to assess the presence of transit signal in the light curve.
Using the box-fitting least-squares (BLS; Kovács et al. 2002) algorithm
implemented within the POLAR pipeline (see Barros et al. 2016, for more
details), we detected the presence of a transit signal with a period of 1.62
days in the light curve of HD 137496.

###  2.2 Comparison of POLAR, K2SFF, and EVEREST photometric performances

Similarly to POLAR, other software has been developed to provide additional
noise mitigation for data provided by the K2 mission. Such software includes
K2SFF (Vanderburg & Johnson 2014), which uses self-flat-fielding methods (as
POLAR does), and EVEREST (Luger et al. 2016, 2018), which uses pixel level
decorrelation; these have made their light curves publicly available. In order
to select the best light curve for the characterization of the discovered
transit signal, we compared the photometric precision of the three light
curves provided by POLAR444POLAR provides activity-corrected light curves as
well as instrumental detrended light curves., K2SFF, and EVEREST and present
this in Fig. 1.

####  2.2.1 Pre-treatment of the light curves

Both POLAR and K2SFF light curves are provided already detrended. This means
that long-term variations from residual instrumental noises or stellar
variability have been removed and the light curves are flat and ready for
transit detection and analysis. This is not the case with the EVEREST light
curves. Consequently, we detrended the EVEREST light curve using an adapted
Savitzky–Golay filter (Savitzky & Golay 1964). In our analysis, we used a
second-degree polynomial and a 1.45 day window. Before applying the filter, we
masked the transits identified using the period, the time of inferior
conjunction, and the duration of the transit provided by the POLAR BLS search.
Contrary to other implementations of the Savitzky–Golay filter (for example,
scipy.signal.savgol_filter provided within the widely used Python package
scipy), our implementation allows for unevenly sampled data555If the data
points are within half the Savtzky–Golay filter window width from the
beginning or end of the observation sequence, the coefficients of the closest
valid point were used instead of the usual full window width.. This is
critical to properly filtering the regions containing masked transit signals.
We detrended the original EVEREST light curve, dividing it by the result of
the Savitzky–Golay filtering.

Finally, for all light curves, the data points not flagged as QUALITY=0666More
details on the quality assessment can be found in Luger et al. (2018). in the
raw data were removed. During the first days of observation, there is also an
abrupt excess on the flux. This effect is observed in the photometry of
different targets of K2 Campaign 15 and can be explained by a thermal anomaly
on Kepler’s spacecraft (Hidalgo et al. 2020). For this reason, we removed all
observations taken before $t$ = 2 457 994.328 BJD777Barycentric Julian dates
throughout this work are computed from the coordinated universal time (UTC) in
the case of RVs and from the barycentric dynamical time (TDB) when regarding
the Kepler light curve..

Figure 1: Normalized flux from K2 photometry with systematics corrected via
the POLAR pipeline (top panel), K2SFF pipeline (middle panel), and EVEREST
pipeline with a Savitzky–Golay filtering (bottom panel). The red lines
indicate the expected transit positions for the short-period planet (HD 137496
b).

####  2.2.2 Photometric precision

In order to measure the photometric precision of each light curve, we computed
the 2 hr888Given the 2.17 hr duration of the detected transit, the 2 hr CDPP
is perfectly suited to select the best light curve for our analysis. CDPP
(combined differential photometric precision; Christiansen et al. 2012) using
the implementation provided with the EVEREST pipeline. The results are a CDPP
of 20.78 ppm for the POLAR light-curve, 19.89 ppm for the K2SFF one and 28.47
ppm for the EVEREST detrended light curve.

The POLAR and K2SFF methods have similar 2h-CDPP values and, from a visual
inspection, similar phase-folded light curves (see Fig. 2). With both
detrending methods presenting equivalent results, we decided to use the
POLAR999POLAR light curves are provided upon request to the authors. detrended
light curve (Table 6) for the rest of our analysis.

Figure 2: Phase-folded POLAR (top) and K2SFF (bottom) photometric transit data
(blue points). Represented in red are the 30 min bins.

##  3 Photometric contamination

From the GAIA DR3 (Gaia Collaboration et al. 2016, 2021) catalog, we find that
two additional stars101010GAIA DR3 ID sources: 6258809897751679360 and
6258809794673492864 fall within the K2 aperture. Their PSFs may contaminate
the pixels used by POLAR to extract the photometry. However, the combined flux
of these stars is four orders of magnitude smaller than the flux of our target
and the impact on the planetary parameter is thus negligible.

We observed HD 137496 with the AstraLux lucky-imaging instrument (Hormuth et
al. 2008) at Calar Alto Observatory (Almería, Spain) under Prog. ID
F20-2.2-014 (PI: J. Lillo-Box). The observations were carried out on the night
of 7 July 2020 under good observing conditions with seeing around 1 arcsec. By
using the lucky-imaging technique, we obtained 42730 frames with a 10 ms
exposure time using the Sloan Digital Sky Survey z filter (SDSSz) and
windowing the total field of view down to a 6$\times$6 arcsec frame. This
datacube of images is then reduced by the instrument pipeline (described in
Hormuth et al. 2008) by performing the basic bias subtraction and flat-
fielding and then selecting the top 10% of frames according to the Strehl
ratio metrics (Strehl 1902). Then, these best-quality images are aligned and
combined together to form a final high-spatial resolution image. No additional
sources are found in the final image within the sensitivity limits calculated
with our own developed astrasens
package111111https://github.com/jlillo/astrasens. The procedure is fully
described in Lillo-Box et al. (2012, 2014). The final sensitivity curve is
shown in Fig. 3. As shown, we can reach contrast magnitudes of 5 mag at 0.2
arcsec from the main target.

From our high-resolution image, we can also estimate the probability of an
undetected blended companion that could mimic the transit depth detected. We
call this the blended source confidence (BSC), and the steps for estimating
this probability are fully described in Lillo-Box et al. (2014). We used a
Python implementation of this technique (bsc, by J. Lillo-Box), which uses the
TRILEGAL5 galactic model (v1.6 Girardi et al. 2012) to retrieve a simulated
source population of the region around the corresponding target121212This is
done by using the Python implementation of astrobase by Bhatti et al. 2020..
From this simulated population, we derive the density of stars around the
target position (radius $r=1^{\circ}$) with the associated probability of
chance-alignment at a given contrast magnitude and separation. We used the
default parameters for the bulge, halo, thin and thick disks, and the
lognormal initial mass function from Chabrier (2001). The contrast curve was
then used to constrain this parameter space and estimate the final probability
of an undetected blended companion. We considered potentially contaminant
sources as those with a maximum contrast magnitude of $\Delta m_{\rm
max}=-2.5\log{\delta}$, with $\delta$ defined as the transit depth of the
candidate planet in the Kepler band. In this case, the transit depth of 6.8
ppt corresponds to a maximum contrast magnitude for relevant contaminants of
$\Delta m_{\rm max}=5$ mag. This represents the maximum magnitude that a
blended star can have to mimic this transit depth. We converted the depth in
the Kepler passband to the AstraLux SDSSz filter by simple conversions using
the KIC catalog and found that $\Delta m_{\rm Kep}=0.920\Delta m_{\rm SDSSz}$.
The result of this calculation provides a BSC of 1.034%.

Figure 3: Probability of a chance-aligned source at the target location (more
information in Section 3).

##  4 Radial velocities

###  4.1 HARPS

Radial velocity measurements of HD 137496 were obtained with the HARPS
spectrograph (R=115,000) mounted on the 3.6m telescope at ESO’s La Silla
Observatory (Mayor et al. 2003). A total of 142 observations were taken
between 1 March 2019 and 1 March 2021 in the high-accuracy mode, as part of
the NCORES large program (ID 1102.C-0249, PI Armstrong). An exposure time of
1500s was used, giving a signal-to-noise ratio (S/N) of $\sim$70 per pixel.
Typically, the star was observed two-to-three times per night. The data were
reduced with the standard HARPS pipeline. RV measurements were derived using a
weighted cross-correlation function (CCF) method using a G2V template (Baranne
et al. 1996; Pepe et al. 2002). The bisector inverse slope (BIS) and the full
width at half maximum (FWHM) were measured using the methods of Boisse et al.
(2011).

###  4.2 CORALIE

HD 137496 was also observed with the CORALIE spectrograph (R=60,000) mounted
on the 1.2m Swiss Euler telescope at La Silla Observatory (Queloz et al.
2001). Thirty observations were taken between 9 July 2019 and 21 August 2021.
An exposure time of 1200s was used, yielding a S/N of $\sim$25 per pixel (at
5500Å). Similarly to HARPS, the RV measurements were obtained through cross-
correlation of the spectra with a binary G2V template (Baranne et al. 1996;
Pepe et al. 2002). The FWHM, BIS, and other line-profile diagnostics were
computed using the standard CORALIE DRS. Both CORALIE and HARPS spectra and
derived RVs will be made public through the DACE
portal131313https://dace.unige.ch/radialVelocities/?pattern=HD%20137496 hosted
at the University of Geneva (Buchschacher et al. 2015).

###  4.3 RV analysis

In Figure 4, we present our RV time series. As is clearly seen, the data show
a long-term and high-amplitude trend (semi-amplitude of $\sim
200\,\mbox{m\,s${}^{-1}$}$), typical of the signature of a long period giant
planet.

Figure 4: HARPS (orange) and CORALIE (blue) radial velocities. The calculation
of the fit model (green) is explained on Section 6.  Table 1: RVs and stellar
activity indicators measured with HARPS and CORALIE.

BJD - 2400000 | RV (m s-1) | FWHM (m s-1) | BIS (m s-1) | … | Instrument
---|---|---|---|---|---
58543.91 | $-2687.67\pm 1.28$ | $7246.28\pm 10.25$ | $11.39\pm 1.8$ | … | HARPS
58547.80 | $-2685.88\pm 1.44$ | $7247.69\pm 10.25$ | $7.41\pm 2.0$ | … | HARPS
58547.90 | $-2685.67\pm 1.58$ | $7242.47\pm 10.24$ | $8.42\pm 2.2$ | … | HARPS
… | … | … | … | … | …
141414The complete table will be made available in machine-readable form in
the online journal.

In the top panel of Fig. 5, we plot the generalized Lomb-Scargle periodogram
(GLSP, Lomb 1976; Scargle 1982) of the RV time series. We notice that a high-
significance, low false-alarm probability (FAP) peak is observed around a
period of 500 days. After fitting a Keplerian to this signal and removing it
from the RVs, the GLSP shown in the second panel of Fig. 5 displays a
significant peak at the period detected in K2 photometric data by the BLS,
$P=1.62$ days. The other significant peak (period of 2.6 days) in this GLSP
corresponds to an alias of this 1.62 days peak.

Figure 5: Generalized Lomb-Scargle periodogram of the RVs before (top) and
after the fitting and removal of the signal from planet c (second from the
top) and planet b (third from the top). The levels corresponding to a FAP of
10%, 1%, and 0.1% are represented by the horizontal dashed lines. In the
bottom panel, we show the GLSP of the window function, W($\nu$).

From the HARPS and CORALIE data (Table 1), we evaluated activity indicators:
FWHM, BIS, contrast of the CCF, $H_{\alpha}$ emission, Na-doublet and the
Mount Wilson S-index (HARPS) or directly the Calcium H and K lines (CORALIE).
The GLSPs of these indicators are plotted in Figs. 6 and 7 with a logarithmic
scale in frequency and in Appendix B with a linear scale. No significant peak
is observed in the GLSP of the activity indicators at the period of the
suspected planet b or c151515The period of both planets and the RV offset
between the instruments were all fit in the Markov chain Monte Carlo (MCMC)
process described on Section 6.. We also evaluated the correlation between
these indicators and the radial velocities from HARPS through the Bayesian
framework presented in Figueira et al. (2016)161616The code is available in
the git repository: https://bitbucket.org/pedrofigueira/bayesiancorrelation/..
No significant correlation was observed between the RVs and the BIS, FWHM, or
$S_{HK}$ (Pearson correlation coefficient of $\rho_{FWHM}=0.15\pm 0.08$;
$\rho_{BIS}=0.04\pm 0.08$; $\rho_{S_{HK}}=0.01\pm 0.08$).

Figure 6: GLS periodograms of the stellar activity indicators from HARPS RVs.
Figure 7: GLS periodograms of the stellar activity indicators from CORALIE
RVs.

##  5 Stellar characterization

For the determination of the stellar parameters, we have used the high-
resolution, high S/N, HARPS spectra. The individual HARPS spectra were
corrected from the RV and co-added in order to produce a unique spectrum with
a high S/N. The spectroscopic stellar parameters were derived using the
commonly used equivalent width (EW) method “ARES+MOOG” (we used ARES v2 and
MOOG2014; see Sousa 2014 for details). The spectral analysis is based on the
excitation and ionization balance of iron abundance. The equivalent widths
(EWs) of the lines were consistently measured with the ARES code (Sousa et al.
2007, 2015) and the abundances derived in local thermodynamic equilibrium
(LTE) with the MOOG code (Sneden 1973). A grid of plane-parallel Kurucz ATLAS9
model atmospheres was used (Kurucz 1993). The line list used in this analysis
was the same as that used in Sousa et al. (2008). This is the same method
applied to derive homogeneous spectroscopic parameters for the Sweet-CAT
catalog (Santos et al. 2013; Sousa et al. 2018).

In order to have accurate estimates of the planetary mass and radius, it is
critical to determine those same parameters accurately for the host star. By
using the parameters already determined by the spectroscopy analysis as
inputs, we then determine the mass, $M_{*}$, radius, $R_{*}$, age, and
extinction of HD 137496 through the use of the Bayesian tool PARAM v1.5
(Rodrigues et al. 2017). This pipeline employs Bayesian methods to compute the
probability density functions of stellar fundamental properties through the
use of a pre-computed grid of stellar evolutionary tracks. The derived stellar
parameters are presented in Table 2. We then performed independent stellar
parameter estimations with different methods using the spectral energy
distribution (SED) and isochrones (for more information on these methods, see
Appendix C). We found that the mass and radius estimates were compatible
across different tools within the 1-$\sigma$ uncertainties. The ages were also
compatible within the 1-$\sigma$ uncertainties, with the exceptions of NextGen
(see Appendix C.2) and the chemical clocks (see Appendix C.5). However, these
two methods rely on empirical relations, contrary to all the other methods
(including PARAM), which rely on stellar models. The fact that all the methods
based on stellar models provide similar estimates despite the use of different
stellar evolutionary tracks strengthens our choice to adopt the mass, radius,
and age derived with PARAM.

Finally, we derived stellar abundances of several elements using the same
tools and models as for the stellar spectroscopic parameter determination, as
well as using the classical curve-of-growth analysis method assuming local
thermodynamic equilibrium. Although the EWs of the spectral lines were
automatically measured with ARES, for the elements with only two-three lines
available, we performed a careful visual inspection of the EW measurements.
For the derivation of chemical abundances of refractory elements, we closely
followed the methods described in Adibekyan et al. (2012, 2015); Delgado Mena
et al. (2014, 2017). Abundances of the volatile elements, C and O, were
derived following the method of Delgado Mena et al. (2010) and Bertran de Lis
et al. (2015). Since the two spectral lines of oxygen are usually weak and the
6300.3Å line is blended with Ni and CN lines, the EWs of these lines were
manually measured with the task splot in IRAF. Lithium and sulfur abundances
were derived by performing spectral synthesis with MOOG following the works by
Delgado Mena et al. (2014) and Costa Silva et al. (2020), respectively. All
the [X/H] ratios are obtained by doing a differential analysis with respect to
a high S/N solar (reflected from Vesta) spectrum from HARPS. The stellar
abundances of the elements are presented in Table 3.

We find that the [X/Fe] ratios of most elements are close to solar, as
expected for a star with near-solar metallicity. Moreover, we used the
chemical abundances of some elements to derive ages through the so-called
chemical clocks (i.e., certain chemical abundance ratios that have a strong
correlation with age: e.g., Nissen 2015). For more details regarding this
estimation, we advise the reader to consult Appendix C.5.

The kinematics of the star can also reveal important information about the
primordial place where this system was born in the Galaxy. Through the use of
Gaia’s accurate distance and radial velocity measurements, we were able to
calculate the 3D velocities $U$, $V,$ and $W$171717U, V, and W are,
respectively, the positive in the directions of Galactic center, Galactic
rotation, and the North Galactic Pole.. These velocities were then adjusted to
the space velocities of the Local Standard of Rest (LSR) using the recent
LAMOST data (Tian et al. 2015): $U_{\odot}=9.58$ km/s, $V_{\odot}=10.52$ km/s,
and $W_{\odot}=7.01$ km/s. We then calculated the probability of this star
belonging to specific populations, the thick disk (TD), thin disk (D), or the
stellar halo (H), according to the classical method of Bensby et al. (2003).
For HD 137496, we find a TD/D = 0.01, making it clear that this star belongs
to the thin disk.

Table 2: IDs, coordinates, and magnitudes of the planet-host star.

Parameter | Value | Source
---|---|---
Identifying Information |  |
R.A. (J2000) | $15^{h}26^{m}58^{s}.07$ | Gaia DR2$a$$a$footnotetext:
DEC (J2000) | $-16^{h}30^{m}31^{s}.69$ | Gaia DR2$a$$a$footnotetext:
HD | 137496 |
K2 ID | 364 |
EPIC ID | 249910734 |
Distance and Velocities |  |
$PM_{R.A.}$ ($masyr^{-1}$) | 20.54 $\pm$ 0.1 | Gaia DR2$a$$a$footnotetext:
$PM_{DEC}$ ($masyr^{-1}$) | -46.86 $\pm$ 0.08 | Gaia DR2$a$$a$footnotetext:
$\pi$, Parallax (mas) | 6.41 $\pm$ 0.07 | Gaia DR2$a$$a$footnotetext:
$v_{rad}$ (km s-1) | -2.65 $\pm$ 0.34 | Gaia DR2$a$$a$footnotetext:
$d$, Distance (pc) | 156 $\pm$ 14 | This work
$U$ (km s-1) | -10.35 $\pm$ 0.31 | This work
$V$ (km s-1) | -24.34 $\pm$ 0.60 | This work
$W$ (km s-1) | -7.89 $\pm$ 0.35 | This work
Magnitudes |  |
$K_{p}$ (mag) | 9.833 | MAST EPIC$b$$b$footnotetext:  $G$ (mag) | 9.77 $\pm$ 0.34 | Gaia DR2$a$$a$footnotetext:  $B_{p}$ (mag) | 10.16 $\pm$ 0.34 | Gaia DR2$a$$a$footnotetext:  $R_{p}$ (mag) | 9.25 $\pm$ 0.34 | Gaia DR2$a$$a$footnotetext:  $B$ (mag) | 10.63 $\pm$ 0.024 | APASS$c$$c$footnotetext:  $V$ (mag) | 9.996 $\pm$ 0.028 | APASS$c$$c$footnotetext:  $J$ (mag) | 8.646 $\pm$ 0.024 | 2MASS$d$$d$footnotetext:  $H$ (mag) | 8.366 $\pm$ 0.046 | 2MASS$d$$d$footnotetext:  $K$ (mag) | 8.244 $\pm$ 0.036 | 2MASS$d$$d$footnotetext:  $A_{V}$ (mag) | 0.211 $\pm$ 0.067 | This work
Stellar Parameters |  |
$T_{\textrm{eff}}$ (K) | 5799 $\pm$ 61 | This work
log $g$ (cgs) | 4.05 $\pm$ 0.1 | This work
[Fe/H] (dex) | -0.03 $\pm$ 0.04 | This work
$v_{\textrm{turb}}$ (km s-1) | 1.16 $\pm$ 0.02 | This work
$M_{*}$$e$$e$footnotetext: ($M_{\odot}$) | 1.04 $\pm$ 0.02 | This work
$R_{*}$$e$$e$footnotetext: ($R_{\odot}$) | 1.59 $\pm$ 0.03 | This work
$\rho_{*}$ ($\mathrm{g\,cm^{-3}}$) | 0.259 $\pm$ 0.014 | This work
Age$e$$e$footnotetext: (Gyr) | 8.3 $\pm$ 0.7 | This work

181818 $a$$a$footnotetext:  Gaia Collaboration et al. (2018)
$b$$b$footnotetext:  http://archive.stsci.edu/k2/epic/search.php
$c$$c$footnotetext: Munari et al. (2014)
$d$$d$footnotetext: Cutri et al. (2003)
$e$$e$footnotetext: We provide here the estimates obtained with PARAM, but we
also derived these quantities using other tools (see Section 5 and Appendix
C).

Table 3: Stellar abundances. Species | Value
---|---
Abundances |
[C I/H] | -0.104 $\pm$ 0.017
[O I/H] | 0.045 $\pm$ 0.077
[Na I/H] | -0.064 $\pm$ 0.013
[Mg I/H] | 0.008 $\pm$ 0.016
[Al I/H] | 0.018 $\pm$ 0.015
[Si I/H] | -0.029 $\pm$ 0.025
[Ca I/H] | -0.016 $\pm$ 0.041
[Ti I/H] | -0.002 $\pm$ 0.022
[Cr I/H] | -0.043 $\pm$ 0.029
[Ni I/H] | -0.080 $\pm$ 0.014
[Cu I/H] | -0.065 $\pm$ 0.027
[Zn I/H] | -0.076 $\pm$ 0.020
[Sr I/H] | -0.172 $\pm$ 0.077
[Y I/H] | -0.134 $\pm$ 0.048
[Zr I/H] | -0.143 $\pm$ 0.036
[Ba I/H] | -0.081 $\pm$ 0.025
[Ce I/H] | -0.058 $\pm$ 0.040
[Nd I/H] | -0.063 $\pm$ 0.034
[S I/H] | -0.16 $\pm$ 0.05
A(Li) | 2.02 $\pm$ 0.04

##  6 Joint analysis: RV & photometry

In order to estimate the planetary parameters, we performed a joint analysis
by simultaneously fitting the already normalized K2 light curve and the RVs
from HARPS and CORALIE, using the approach and tools described in Demangeon et
al. (2018). A Markov chain Monte Carlo (MCMC) algorithm, implemented in the
emcee Python package (Foreman-Mackey et al. 2013), was used to sample the
posterior probability density function.

To generate the model light curves that are compared to the K2 light curve, we
used the batman191919Available at https://github.com/lkreidberg/batman. Python
package (Kreidberg 2015). Since the observations from K2 were taken in long-
cadence mode (30-min), we super-sampled202020Integration times can cause
morphological distortions to the transit light curve, since we are using long-
cadence observations this effect is amplified. Super-sampling is a correction
that takes into account the extended exposure times, with the factor of 10
being widely used for K2 and Kepler. This number arises from a comparison with
the work of Kipping (2010), where the authors studied three targets of Kepler
with similar magnitudes and computed that an oversampling factor of 5 is
sufficient. In order to avoid any issue regarding the accuracy of our model,
due to subtle differences between the targets and HD 137496, we chose an
oversampling factor twice as large (10), which is thus more than enough in
terms of accuracy while still manageable in terms of computation time. the
model by a factor of 10.

To compute the model of the RVs to be compared with the HARPS and CORALIE
data, we used the RadVel212121Available at https://github.com/California-
Planet-Search/radvel. Python package (Fulton et al. 2018). Since we are using
data from two different spectographs, the model includes an RV offset between
the two instruments on top of the systemic velocity, $\gamma_{RV,HARPS}$, as
measured by HARPS.

For the two planets, we estimated the period $P$, the time of inferior
conjunction $t_{\textrm{ic}}$, the RV semi-amplitude $K$, and the projected
eccentricity components, $e\cos\omega$ and $e\sin\omega,$ where $e$ and
$\omega$ are the eccentricity and the argument of periastron, respectively;
thus, we improve the exploration of the parameter space for low-eccentricity
solutions. For the transiting planet, we also estimated the radius ratio
$R_{p}/R_{*}$ and the cosine of the orbital inclination $\cos i_{\textrm{p}}$.
Finally, the transit signal also enables the derivation of the stellar density
$\rho_{*}$.

To account for sources of noise that would have been ignored during the
computation of the error bars provided with the data, we used a jitter
parameter added in quadrature to the error bar for the standard deviation of
the Gaussian likelihood function (e.g., Baluev 2009). We used one jitter
parameter per dataset (K2, HARPS, CORALIE). The priors used are provided in
Table 4, and more information regarding the reasons behind the choice of
priors can be found in Appendix D.

In order to quicken the convergence despite the use of broad priors, we drew
the initial values of the MCMC chains for the planetary parameters $K$, $P$,
$t_{ic}$, the cosine of the inclination of planet b, and $\rho_{*}$ from the
posterior distribution of a first fit realized with tighter priors (see
Appendix E). Before running the emcee MCMC exploration, we carried out a pre-
optimization of the parameter’s values using the downhill simplex (aka amoeba)
algorithm. We performed one optimization for each walker and used the results
as initial values of the emcee exploration. The number of walkers was defined
as three times the number of free parameters rounded to the closest even
number. We computed 100,000 steps for each Markov chain walker. After the run,
we removed the burn-in from the chains and studied the convergence using a
modified Geweke diagnostic (Geweke et al. 1991). The planetary parameters were
then estimated by the median of the resulting marginalized posterior
distributions and the borders of the 68 % confidence interval as the 16th and
84th percentiles.

The full list of fitted parameters along with the obtained values and
confidence intervals are shown in Table 4. The phase-folded light curve and
RVs and the best-fit model using the estimated parameters are shown in Fig. 8.

Table 4: Instrumental, stellar, and planetary parameters derived from the
joint analysis on the photometric and radial velocity data.

Parameter | Results - This work | Prior$a$$a$footnotetext:
---|---|---
Instrument parameters |  |
Systemic velocity $\gamma_{RV,HARPS}$ [m s-1] | $-2988.9_{-1.0}^{+1.1}$ |  $\mathcal{G}$ [-2921.8, 130]
K2 jitter [ppm] | $66.8_{-1.38}^{+1.43}$ |  $\mathcal{J}$ [$1.9\cdot 10^{-6}$, $1.9\cdot 10^{-4}$]$b$$b$footnotetext:
HARPS radial velocity jitter [m s-1] | $1.52_{-0.23}^{+0.23}$ |  $\mathcal{J}$ [0.017, 17]$b$$b$footnotetext:
CORALIE radial velocity jitter [m s-1] | $0.72_{-0.51}^{+1.88}$ |  $\mathcal{J}$ [0.12, 120]$b$$b$footnotetext:
$\Delta\text{RV}$ CORALIE to HARPS [m s-1] | $-18.64_{-2.46}^{+2.48}$ |  $\mathcal{U}$ [-111, 11]
Stellar parameters |  |
Stellar density $\rho_{*}$ [$\textrm{g.cm}^{-3}$] | $0.259_{-0.014}^{+0.014}$ |  $\mathcal{G}$ [0.2590, 0.0150]
Limb-darkening coefficient $u1$ | $0.5325_{-0.0061}^{+0.0061}$ |  $\mathcal{G}$ [0.5324, 0.0061]
Limb-darkening coefficient $u2$ | $0.1056_{-0.0089}^{+0.0090}$ |  $\mathcal{G}$ [0.1056, 0.0091]
HD 137496 b
Period $P_{b}$ [days] | $1.62116_{-8.06\,10^{-5}}^{+7.91\,10^{-5}}$ |  $\mathcal{J}$ [0.09, 1400]
RV semi-amplitude $K_{b}$ [m s-1] | $2.14\pm 0.29$ |  $\mathcal{U}$ [0.0, 50.0]
Radius ratio $R_{p,b}/R_{*}$ | $0.0076_{-0.00029}^{+0.00030}$ |  $\mathcal{U}$ [0.0, 1.0]
Impact parameter $b_{b}$ | $0.27_{-0.17}^{+0.14}$ |  $\mathcal{U}$ [0.0, 2.0]
Eccentricity $e_{b}$ | 0 | Fixed at 0
Time of inferior conjunction $t_{ic,b}$ [BJD-2450000] | $8039.1317_{-0.0029}^{+0.0028}$ |  $\phi$ : $\mathcal{U}(0,1)$$c$$c$footnotetext:
Transit depth [ppm] | $57.5_{-4.28}^{+4.61}$ | -
Transit duration $T_{b}$ [hr] | $3.28_{-0.14}^{+0.10}$ | -
Ingress to egress duration $\tau_{b}$ [hr] | $3.23_{-0.15}^{+0.11}$ | -
Scaled semi-major axis $a_{b}/R_{*}$ | $3.70\pm 0.07$ | -
Semi-major axis $a_{b}$ [AU] | $0.02732\pm 0.00019$ | -
Inclination $i_{b}$ [º] | $85.8_{-2.2}^{+2.6}$ | -
Radius $R_{b}$ [$R_{\oplus}$] | $1.31_{-0.05}^{+0.06}$ | -
Mass $M_{b}$ [$M_{\oplus}$] | $4.04\pm 0.55$ | -
Density $\rho_{b}$ [$\mathrm{g\,cm^{-3}}$] | $10.49_{-1.82}^{+2.08}$ | -
Equilibrium temperature $T_{eq,b}$ [K] | $2130_{-29}^{+30}$ | -
HD 137496 c
Period $P_{c}$ [days] | $479.9_{-1.0}^{+1.1}$ |  $\mathcal{J}$ [0.09, 1400]
RV semi-amplitude $K_{c}$ [m s-1] | $221.25_{-0.82}^{+0.83}$ |  $\mathcal{U}$ [0, 444]
Eccentricity $e_{c}$ | $0.477\pm 0.004$ |  $\mathcal{B}$ [0.867, 3.03]
Time of inferior conjunction $t_{ic,c}$ [BJD-2450000] | $8629.21\pm 0.41$ |  $\phi$ : $\mathcal{U}(0,1)$$c$$c$footnotetext:
Argument of periastron [deg] $\omega_{c}$ | $-39.01_{-0.47}^{+0.46}$ | -
Semi-major axis $a_{c}$ [AU] | $1.2163_{-0.0088}^{+0.0087}$ | -
Minimum mass $M_{c}\sin i_{c}$ [$M_{Jup}$] | $7.66\pm 0.11$ | -
Equilibrium Temperature $T_{eq,c}$ [K] | $370\pm 5$ | -

222222In the column on the right, we display our prior choices: $\mathcal{U}$
\- Uniform; $\mathcal{G}$ \- Gaussian; $\mathcal{J}$ \- Jeffreys;
$\mathcal{B}$ \- beta distribution.
$a$$a$footnotetext: For more information, see Appendix D.
$b$$b$footnotetext: The Gaussian prior distribution is truncated to only
consider positive values.
$c$$c$footnotetext: We define $\phi$ the orbital phase of the time of inferior
conjunction as $\phi$ = ($t_{ic}$ \- $t_{ref}$) / $P$, where $t_{ref}$ is an
arbitrarily chosen reference time. We then considered a uniform prior between
0 and 1 to $\phi$. We chose $t_{ref}$ to be 8039 and 8620 BJD-2450000 for
planets b and c, respectively.

(a)

(b)

Figure 8: Left: Phase-folded and binned transit with residuals for HD 137496 b
together with the best fitting model. Root mean square (rms) of the K2
residuals: 71 ppm and 10 ppm for bins in phase corresponding to 20 min. Right:
Phase-folded RV fit with residuals for HD 137496 b (left) and HD 137496 c
(right). Rms of ths HARPS residuals: 3.4 m/s; CORALIE residuals: 6.6 m/s.

##  7 Discussion

In this work, we present the HD 137496 system, composed of two planets
orbiting a G-type star near the main-sequence turn-off. To characterize the
two planets, we acquired high precision radial velocity observations with the
HARPS and CORALIE spectrographs together with K2 photometry which exhibits
transits of HD 137496 b. We present a mass measurement for HD 137496 b of
$M=4.04\pm 0.55$ $M_{\oplus}$ with a radius of $R=1.31_{-0.05}^{+0.06}$
$R_{\oplus}$ and a density of $\rho$ = $10.49_{-1.82}^{+2.08}$
$\mathrm{g\,cm^{-3}}$, while the non-transiting HD 137496 c has a minimum mass
of $7.66\pm 0.11$ $M_{\textrm{Jup}}$.

###  7.1 A low-mass inner planet with a cold distant companion

This system is composed of an eccentric cold Jupiter and a hot super-Mercury
(or dense super-Earth). This planetary architecture has gained traction in the
exoplanet field in recent years (Santos et al. 2016; Huang et al. 2017; Zhu &
Wu 2018; Bitsch et al. 2020). As mentioned in Section 1, Zhu & Wu (2018) found
a correlation between the presence of inner super-Earths and long-period
Jupiter-like planets with Kepler data. The authors derived that cold Jupiters
appear three times more often around hosts of super-Earths than they do around
field stars, suggesting that cold Jupiters do not directly compete with inner
super-Earths for solid material, thus allowing their formation. However, the
recent study by Bitsch et al. (2020) brings to light the eccentricity of the
distant massive companion in these statistics. The authors argue that if the
giant planet has an eccentric orbit, it is very unlikely that the system
harbors any inner super-Earths (making the HD 137496 system a counter
example). Nevertheless, the presence of a low-mass inner planet together with
a cold Jupiter in eccentric and/or mutually inclined orbits has been the
object of recent studies (Hansen 2017; Mills et al. 2019; Carrera et al. 2019;
Masuda et al. 2020; Poon & Nelson 2020; Pu & Lai 2021). This highlights the
need for accurate characterization of such systems for our understanding of
planet formation and evolution and stresses the importance of the HD 137496
system.

The high eccentricity of the orbit of HD 137496 c ($e\simeq 0.48$) is expected
for high-mass planets (Ribas & Miralda-Escudé 2007; Adibekyan et al. 2013),
hinting at a dynamically ”hot”232323By dynamically “hot” we mean that strong
planet-planet dynamic interactions caused significant changes to their orbital
parameters. evolution (Bitsch et al. 2013; Ida et al. 2013; Raymond &
Morbidelli 2020). In light of these recent works, this could be interpreted as
the effect of formation and migration mechanisms for which the orbit of HD
137496 b was tidally circularized at the currently observed short orbital
period.

###  7.2 Composition of HD 137496 b

In Fig. 9, we show HD 137496 b in the mass-radius diagram alongside all the
small planets ($M<20M_{\oplus}$) extracted from TEPcat242424Available at
http://www.astro.keele.ac.uk/jkt/tepcat/. (Southworth 2011) whose masses are
known with a precision better than 20%. According to the models of Zeng et al.
(2016), HD 137496 b has the bulk density of a planet composed mostly of iron
(consistent within the uncertainties). In the literature, very few planets
appear to have densities as high as HD 137496 b, making it a reference and a
compelling target for the study of interior models and planet formation.

Figure 9: Mass–radius diagram for planets with radii below 5 $R_{\oplus}$ and
masses below 20 $M_{\oplus}$, with mass uncertainties under 20%. Planets are
color-coded according to their incident flux. Data retrieved from TEPcat
(Southworth 2011) as of March 2021. For reference, Venus and Earth are also
plotted. Colored lines represent the theoretical models for internal
composition of small planets (Zeng et al. 2016). The experiment-based mass-
radius relationship for a hypothetical pure iron planet from Smith et al.
(2018) is shown in brown, with data from the National Ignition Facility (NIF).
The gray line and shaded area represent the limit by maximum collisional
stripping curve according to Marcus et al. (2010). The small planet discovered
and characterized in this paper is plotted in the red circle.

####  7.2.1 Modeling of the internal structure of HD 137496 b

Using the estimated mass and radius, we computed a marginal core radius
fraction (CRF) of 81% $\pm$ 11% using hardCORE252525Available at
https://github.com/gsuissa/hardCORE/blob/master/hardcore.py. (Suissa et al.
2018). This simple model assumes that the planet is fully differentiated with
a maximum density layer no denser than iron. The model then calculates the
minimum and maximum core radius fractions for which a marginal CRF can be
sampled. The core radius fraction is related (Zeng & Jacobsen 2017) to the
core mass fraction (CMF) by

$CRF\approx\sqrt{CMF}.$ (1)

This translates to a CMF of 78% $\pm$ 11 % using this model.

As an alternative method, we characterized the internal structure of HD 137496
b considering a pure-iron core, a silicate mantle, and a pure-water layer
using a Bayesian inference analysis. We did not add hydrogen and helium to the
model since such a dense (10.49$\leavevmode\nobreak\ g$/$cm^{3}$) and hot
($T_{\textrm{eq}}=2130$ K) planet is not expected to retain a significant
volatile envelope (e.g., Seager et al. 2007). The equations of state (EOS)
used for the iron core are taken from Hakim et al. (2018), the EOS of the
silicate-mantle is calculated with PERPLE_X from Connolly (2009) assuming
Earth-like abundances, and we used the AQUA EOS from Haldemann et al. (2020)
for the pure-water layer. The thickness of the planetary layers were set by
defining their masses and solving the structure equations.

---
Figure 10: Ternary diagram of inferred internal composition of HD 137496 b. We
show the parameter space covered by the posterior distributions in mass (left)
and radius (right).

In order to quantify the degeneracy between various interior parameters and
produce posterior probability distributions, we used a generalized Bayesian
inference analysis with a nested sampling scheme (Buchner et al. 2014). Fig.
10 shows ternary diagrams of the inferred composition of HD 137496 b, which
shows the degeneracy linked to the determination of the composition of
exoplanets. The degeneracy of internal compositions leading to the observed
mass and radius is relatively low since a planet with such a high density
needs to have a large iron core. We find an iron mass fraction (IMF) of
$0.73\pm 0.12$, which is in agreement with the estimate from hardCORE.

The silicon mantle and water layer have estimated relative mass fractions of
23% and 7%, respectively. The stellar abundance ratios can be used as a proxy
for the bulk abundances of the planet, reducing the degeneracy of internal
models leading to the same mass and radius (Dorn et al. 2015; Adibekyan et al.
2021). However, the planet bulk density of HD 137496 b is relatively large,
while the stellar abundance does not show any particularly iron-rich
refractory composition.

In fact, if we assume that the ratios of Fe/Si and Mg/Si measured in the host
star reflect the planetary ratios, we are not able to match the observed mass
and radius. This is illustrated in Figure 9, where the planet sits well below
the area that represents purely rocky interiors reflecting the host star
abundance within 1-$\sigma$.

To emphasize the unusual high density of HD 137496 b, we compare the planet’s
inferred iron mass fraction (IMFplanet) to its stellar counterpart (IMFstar)
in Figure 11. The IMFstar is calculated from [Fe/H], [Si/H], and [Mg/H]
(Tables 2 and 3), assuming that all Mg and Si are oxidized (Seager et al.
2007; Rogers & Seager 2010; Dorn et al. 2015; Unterborn et al. 2016; Wang et
al. 2018). Similarly, the calculation of IMFplanet assumes that the core is
pure iron. Clearly, the IMFplanet is similar to Mercury and the 2-$\sigma$
regions of both IMFstar and IMFplanet do not overlap. This means that the
probability of the planet reflecting the stellar refractory abundances is less
than 0.04%.

This high IMF is also beyond the values expected for a star with a solar-like
chemical composition. As shown in Valencia et al. (2007), by assuming a solar
nebula composition, we have a [Fe/Si] ratio constrained to $\sim$ 65%. The
star we studied here is similar to the Sun ($M=1.035\pm\ 0.022\;M_{\odot}$),
with abundances derived from the HARPS spectrum shown in Table 3. From Tables
2 and 3, we have [Fe/H] = -0.027 $\pm$ 0.04 and [Si/H] = -0.029 $\pm$ 0.025,
resulting in [Fe/Si] = 0.002 $\pm$ 0.027 signaling a Fe/Si close to the one
observed in the Sun.

Similar iron-enriched planets were recently identified Santerne et al. (2018);
Plotnykov & Valencia (2020); Schulze et al. (2021). Among the best
characterized planets, there are only a few such super-Mercury planets (Otegi
et al. 2020; Adibekyan et al. 2021), and only a handful for which stellar
abundances were measured (e.g., Kepler 107 c, Bonomo et al. 2019). HD 137496 b
is thus a precious object when it comes to understanding the formation of
super-Mercuries.

Table 5: Inferred interior structure properties of HD 137496 b. $M_{core}/M_{total}$ |  |  |  | $0.73^{+0.11}_{-0.12}$
---|---|---|---|---
$M_{mantle}/M_{total}$ |  |  |  | $0.21^{+0.16}_{-0.14}$
$M_{water}/M_{total}$ |  |  |  | $0.06^{+0.05}_{-0.04}$
Figure 11: Posterior distribution for estimated iron mass fractions (IMF) as
inferred from stellar refractory abundances (red) and the planet mass and
radii (gray). All IMF calculations assume that the cores are pure iron and
silicate mantles are iron-free. The 2-$\sigma$ regions of both posterior
distributions do not overlap, solidifying arguments in favor of a likely
super-Mercury interior of HD 137496 b with high IMF.

####  7.2.2 Formation of high-density planets

Considering the collisional history during planet formation, Scora et al.
(2020) found that it is difficult to form super-Mercuries and that a series of
extremely energetic impacts would be needed to form iron-rich planets.
Furthermore, such impact events are rare and IMFs are expected to only
increase by a factor of 2 in extreme cases. Within observational
uncertainties, this can, in principle, explain the iron enrichment of HD
137496 b, but the most common spread in IMF within a system is on the order of
only 10% (Scora et al. 2020), which is insufficient to explain the iron
enrichment of HD 137496 b. Interestingly, by invoking giant impacts, Marcus et
al. (2010) argue that the formation of super-Mercuries might be limited to
masses below 5 $\mathrm{M}_{\Earth}$, similar to that of HD 137496 b. This is
because an even larger impactor of more than 10 $\mathrm{M}_{\Earth}$would be
required and most planets of such high masses have thick volatile envelopes,
which might lead to very different collision outcomes. The special conditions
required to form high-density planets is consistent with the fact that these
objects are mostly uncommon.

As in the giant impact scenario, favored by a small semi-major axis and their
associated high orbital velocity, other processes are enhanced by the close
proximity to the host star. As theorized in the studies of Mercury, the close
proximity to the host star, and the ensuing high surface temperature of the
planet can cause the evaporation of the silicate-rich mantle (Cameron 1985;
Perez-Becker & Chiang 2013), increasing the estimated iron-mass fraction. The
planet’s environment in the proto-planetary disk can also heavily influence
its density (Adibekyan et al. 2021). Processes such as photophoresis (Wurm et
al. 2013), rocklines (Aguichine et al. 2020), magnetic erosion (Hubbard 2014),
magnetic boost (Kruss & Wurm 2018, 2020), and others can cause the formation
of Mercury-like planets in the innermost regions of the disk.

A combination of all these phenomena may explain the density observed on HD
137496 b. Nonetheless, more ”exotic” scenarios are also a possibility. An
example is that we may be observing a planetary core that is still compressed
(Mocquet et al. 2014). If a recent (¡ a few gigayears ago) event like the
Roche lobe overflow (Valsecchi et al. 2014, 2015; Jackson et al. 2016; Königl
et al. 2017; Ginzburg & Sari 2017), an increased evaporation rate of the
planet’s gaseous envelope (e.g., caused by an abrupt decrease of the star-
planet distance due to orbital tidal decay or migration), or another unknown
process that freshly peeled off the atmosphere of a gaseous planet, the
ensuing core-remnant would then sustain an exceptionally high density.
Regardless of which mechanisms are at play here, HD 137496 b, with well-
characterized planetary and stellar parameters, is an ideal target for future
works regarding the formation of high-density planets.

###  7.3 Future observations

As observed in Mercury (Potter & Morgan 1997; Pfleger et al. 2015), this
planet may host a mineral atmosphere and is a promising target to search for
an elongated comet-like planet’s exosphere. The small distance to the star,
together with an internal structure that resembles that of Mercury, might
create the conditions for an exospheric emission of the heavy refractory
elements present at the planet’s surface. Such a tail could extend within
several planetary radii and disclose relevant clues regarding the planet’s
chemical composition (Mura et al. 2011; Merkel et al. 2018; Vidotto et al.
2018). Future transmission spectroscopy observations could bring into sight
possible spectral signatures from this planetary tail. As studied in previous
systems (e.g., $\pi$ Men c - Damasso et al. 2020; Kunovac Hodžić et al. 2021),
measurements of the planetary inclinations and spin-orbit alignment would also
help to constrain the formation and evolution models for this system.

##  8 Conclusion

We report the discovery of a planetary system orbiting HD 137496 (K2-364).
With photometry from K2 and precise RVs from both HARPS and CORALIE spanning
over two years, we are able accurately characterize the stellar host, study
its chemical composition, and put strong constraints on the planetary
companions. We found the planetary system to be composed of a cold ($a=1.22\pm
0.01$ AU), massive ($M=7.66\pm 0.11M_{Jup}$) giant planet together with an
inner ($a=0.02732\pm 0.00019$ AU) super-Mercury, for which we achieve a
precise determination ($\sim$20 % of relative precision) of the bulk density
($\rho$ = $10.49_{-1.82}^{+2.08}$ $\mathrm{g\,cm^{-3}}$; $M=4.04\pm 0.55$
$M_{\oplus}$ and $R=1.31_{-0.05}^{+0.06}$ $R_{\oplus}$). Our interior modeling
analysis shows that this small planet has an iron-dominated composition with
the core representing over 70% of the planet’s mass.

HD 137496 b (K2-364 b) joins the small sample of well-characterized dense
planets, making it an interesting target for testing planet formation
theories, density enhancing mechanisms, and even the possible presence of an
extended comet-like mineral rich exosphere. Together with HD 137496 c (K2-364
c), a high-mass (mass ratio $m_{c}/m_{b}$¿400), high-eccentricity planet, this
system presents an interesting architecture for planetary evolution studies.
Future astrometric observations could also provide significant constraints on
the relative inclination of the planetary orbits, unraveling new opportunities
to discover the system’s dynamical history.

###### Acknowledgements.

We thank Morgan Deal and Nuno Moedas for helpful discussion on the effects of
atomic diffusion on chemical abundances. This work was supported by Fundação
para a Ciência e a Tecnologia (FCT) and Fundo Europeu de Desenvolvimento
Regional (FEDER) via COMPETE2020 through the research grants UIDB/04434/2020,
UIDP/04434/2020, PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113,
PTDC/FIS-AST/28953/2017, PTDC/FIS-AST/3388/2020 & POCI-01-0145-FEDER-028953.
The French group acknowledges financial support from the French Programme
National de Planétologie (PNP, INSU).
We thank the Swiss National Science Foundation (SNSF) and the Geneva
University for their continuous support to our planet search programs. This
work has been in particular carried out in the frame of the National Centre
for Competence in Research PlanetS supported by the Swiss National Science
Foundation (SNSF).
This publication makes use of The Data & Analysis Center for Exoplanets
(DACE), which is a facility based at the University of Geneva (CH) dedicated
to extrasolar planets data visualisation, exchange and analysis. DACE is a
platform of the Swiss National Centre of Competence in Research (NCCR)
PlanetS, federating the Swiss expertise in Exoplanet research. The DACE
platform is available at https://dace.unige.ch.
This study is based on observations collected at the European Southern
Observatory under ESO programme 1102.C-0249.
This paper includes data collected by the Kepler mission and obtained from the
MAST data archive at the Space Telescope Science Institute (STScI). Funding
for the Kepler mission is provided by the NASA Science Mission Directorate.
STScI is operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5–26555.
This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.
T.A.S acknowledges support from the Fundação para a Ciência e a Tecnologia
(FCT) through the Fellowship PD/BD/150416/2019 and POCH/FSE (EC). O.D.S.D. is
supported in the form of work contract (DL 57/2016/CP1364/CT0004) funded by
FCT. D.J.A. acknowledges support from the STFC via an Ernest Rutherford
Fellowship (ST/R00384X/1). E.D.M. acknowledges the support by the Investigador
FCT contract IF/00849/2015/CP1273/CT0003. V.A. acknowledges the support from
FCT through Investigador FCT contract nr. IF/00650/2015/CP1273/CT0001 L.D.N.
is funded by the Swiss National Science Foundation (P2GEP2_200044). C.D.
acknowledges support from the Swiss National Science Foundation under grant
PZ00P2_174028. J.L-B. acknowledges financial support received from ”la Caixa”
Foundation (ID 100010434) and from the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie grant agreement No
847648, with fellowship code LCF/BQ/PI20/11760023. DJAB acknowledges support
from the UK Space Agency. A.H. acknowledges support from an STFC studentship.
S.H. acknowledges CNES funding through the grant 837319. O.M. acknowledges
support from CNES. A.O. acknowledges support from an STFC studenship. P.J.W.
acknowledges support from STFC consolidated grants (ST/P000495/1 and
ST/T000406/1).

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##  Appendix A K2 PDCsap photometric data and the reduced data through the
POLAR pipeline

Table 6: Photometric data.

| K2 PDCsap | POLAR
---|---|---
BJD - 2400000 | Flux [e-/s] | Error [e-/s] | Flux | Error
57994.328188 | 1654310.8 | 34.72 | 0.99997539 | 1.939$2\text{\times}{10}^{-5}$
57994.348620 | 1654281.0 | 34.70 | 0.99999547 | 1.939$3\text{\times}{10}^{-5}$
… | … | … | … | …
262626The complete table will be made available in machine-readable form in
the online journal.

##  Appendix B Linear-scaled GLS periodograms

Figure 12: GLS periodograms of stellar activity indicators from HARPS RVs. The
last panel represents the observational window function.  Figure 13: GLS
periodograms of stellar activity indicators from CORALIE RVs. The last panel
represents the observational window function.

##  Appendix C Stellar parameter estimation

As explained in Section 5, we chose to use PARAM to estimate the stellar mass,
radius, and age of HD 137496. In order to test the reliability of these
estimates, we applied different tools to independently determine these
parameters. In the following sections, we provide additional details on the
analysis made with PARAM (Section C.1) and present the other approaches and
their results (Sections C.2 \- C.5).

###  C.1 Stellar modeling with PARAM

Together with the parallax, $T_{\textrm{eff}}$, log $g,$ and [Fe/H] (Table 2),
PARAM v1.5 can either perform a spectral energy distribution (SED) fit, using
the magnitudes B, V, J, H, and K, or just consider the K272727The K band is
usually less affected by reddening, and the effect of low reddening can be
included in the error bars. magnitude and no SED fit. Both these methods
provide very compatible age estimates, differing only by 0.1 Gyr, which is
well within the error bars. However, our age estimate is very precise at 8.3
$\pm$ 0.7 Gyr. This is due to the proximity of the star to the turn-off
region, in which the age has a greater impact on the shape of the isochrone,
constraining the fit. The high precision on the derived metallicity
additionally constrains the possible isochrones and results in such a small
uncertainty. All the estimated values can be found in Table 2.

###  C.2 Stellar modeling with NextGen

We performed an analysis of the broadband spectral energy distribution (SED)
of the star together with the Gaia EDR3 parallax (with no systematic offset
applied; see, e.g., Stassun & Torres 2021) following the procedures described
in Stassun & Torres (2016) and Stassun et al. (2017, 2018). We pulled the
$B_{T}V_{T}$ magnitudes from Tycho-2, the $BVgri$ magnitudes from APASS, the
$JHK_{S}$ magnitudes from 2MASS, the W1–W4 magnitudes from WISE, the $G_{\rm
BP}G_{\rm RP}$ magnitudes from Gaia, and the NUV magnitude from GALEX.
Together, the available photometry spans the full stellar SED over the
wavelength range 0.2–22 $\mu$m (see Figure 14).

We performed a fit using NextGen stellar atmosphere models, with the effective
temperature ($T_{\rm eff}$), metallicity ([Fe/H]), and surface gravity ($\log
g$) adopted from the spectroscopic analysis. The remaining free parameter is
the extinction $A_{V}$, which we limited to the maximum line-of-sight value
from the Galactic dust maps of Schlegel et al. (1998). The resulting fit
(Figure 14) has a best-fit $A_{V}=0.29\pm 0.04$ and a reduced $\chi^{2}$ of
1.3, but we note that the GALEX NUV flux indicates a mild level of
chromospheric activity (see below). Integrating the (unreddened) model SED
gives the bolometric flux at Earth, $F_{\rm bol}=3.534\pm 0.041\times 10^{-9}$
erg s-1 cm-2. Taking the $F_{\rm bol}$ and $T_{\rm eff}$ together with the
Gaia parallax gives the stellar radius, $R_{\star}=1.621\pm 0.036$ R⊙, which
is consistent with a modestly evolved star. In addition, we can estimate the
stellar mass from the empirical relations of Torres et al. (2010), giving
$M_{\star}=1.17\pm 0.07$ M⊙, which is consistent with the (less precise)
estimate of $M_{\star}=1.08\pm 0.12$ M⊙ obtained directly from $R_{\star}$
together with the spectroscopic $\log g$.

Finally, we can use the star’s NUV excess (Fig. 14) to estimate a rotation
period and age via empirical rotation-activity-age relations. The observed NUV
excess implies a chromospheric activity of $\log R^{\prime}_{rmHK}=-5.11\pm
0.06$ via the empirical relations of Findeisen et al. (2011). This in turn
implies a stellar rotation period of $P_{\rm rot}=32\pm 2$ d via the empirical
relations of Mamajek & Hillenbrand (2008), which could, in principle, be
checked against a future $v\sin i$ and/or rotation period measurement,
although these will be difficult given the very low level of activity of this
evidently old star. Finally, the NUV estimated activity implies an age of
$\tau_{\star}=10.2\pm 1.7$ Gyr via the empirical relations of Mamajek &
Hillenbrand (2008). This result is compatible with PARAM at a 1.1-$\sigma$
level, and the larger uncertainty can be expected since this estimate relies
on an empirical relation.

Figure 14: Spectral energy distribution of HD 137496. Red symbols represent
the observed photometric measurements, where the horizontal bars represent the
effective width of the passband. Blue symbols are the model fluxes from the
best-fit NextGen atmosphere model (black).

###  C.3 Stellar modeling with PASTIS

We also performed a Bayesian analysis of the stellar SED using the Planet
Analysis and Small Transit Investigation Software (PASTIS; Díaz et al. 2014;
Santerne et al. 2015). PASTIS allows us to model the host star by fitting the
SED to the BT-Settl atmosphere models (Allard et al. 2012) and Dartmouth
evolutionary tracks (Dotter et al. 2008). For this, we used the $B$, $V$, $J$,
$H,$ and $K$ magnitudes from Table 2 as input. The star was modeled for the
effective temperature, T${}_{\text{eff}}$; surface gravity, $\log$ $g$;
metallicity, [M/H]; distance, $d$; and color excess, E(B$-$V). For these
parameters, we used normal distributions defined by the spectroscopic values
reported in Table 2 as priors. Among other parameters (see Table 7), we
obtained a stellar age of 8.19 $\pm$ 0.69 Gyr, which is fully compatible with
what was derived in the spectral analysis using PARAM.

Table 7:  Stellar modeling with the PASTIS Bayesian code based on SED fitting. Parameter | Value
---|---
Age (Gyr) | 8.19 $\pm$ 0.69
$log\,g$ (cgs) | 4.066 $\pm$ 0.020
$R_{*}(R_{\odot})$ | 1.580 $\pm$ 0.035
$M_{*}(M_{\odot})$ | 1.060 $\pm$ 0.023
$T_{\text{eff}}$ (K) | 5811 $\pm$ 58
E(B$-$V) (mag) | 0.042 $\pm$ 0.026
[M/H] (dex) | -0.033 $\pm$ 0.040

###  C.4 Stellar modeling with $q^{2}$

We also estimated the mass, radius, and age of the host star through the use
of the Qoyllur-Quipu (or $q^{2}$) Python package282828Available at
https://github.com/astroChasqui/q2 (Ramírez et al. 2014) by inputting the
T${}_{\text{eff}}$, [Fe/H] and $\log$ $g$ presented in Table 2. As suggested
by (Ramírez et al. 2014), we first applied a -0.04 dex offset to the
metallicity, and then we estimated $M_{\star}=1.090\pm 0.069$ $M_{\odot}$;
$R_{\star}=1.617\pm 0.235$ $R_{\odot}$ and age = 7.406 $\pm$ 1.328 Gyr by
fitting the Yonsei–Yale isochrones (Kim et al. 2002). All these quantities are
once again fully compatible with the PARAM analysis. The larger uncertainties
can also be expected since, unlike the other approaches, this method does not
take into account the parallax, SED, or any magnitudes.

###  C.5 Chemical clocks

We applied the 3D formulas described in Table 10 of Delgado Mena et al.
(2019), which also consider the variation in age produced by the effective
temperature and iron abundance. The chemical clocks[Y/Mg], [Y/Zn], [Y/Ti],
[Sr/Ti], [Sr/Mg], [Y/Si], [Sr/Si], and [Y/Al] were used from which we obtain a
weighted average of 6.7 Gyr (see Table 8). For the uncertainty, since the age
estimates are derived from abundance ratios involving common species, assuming
that all estimates are perfectly correlated we obtain a weighted error of 0.6
Gyr. However, the relations used to derive the age from each abundance ratio
are derived empirically based on high-precision stellar abundances. As a
consequence, the high precision of our abundance measurements of HD 137496
results in a precise age estimate which might not reflect the true uncertainty
of the method.

By using 1D formulas (as described in Table 5 of Delgado Mena et al. 2019), we
obtain a similar age (see Table 9). The age from chemical clocks is lower than
the age derived through isochrones with PARAM but still shows that this star
is clearly older than the Sun. Interestingly, we find quite a high value of Li
abundance (2.02 dex) for an almost solar twin in terms of $T_{\rm eff}$ and
[Fe/H]. Several works have found that solar analogs hosting giant planets tend
to present enhanced Li depletion (e.g., Delgado Mena et al. 2014; Figueira et
al. 2014; Gonzalez 2015, and references therein) when compared to similar
stars with no detected planets, but this is not the case of HD 137496.
However, this star has a low $\log g$ value, indicating that it might be
slightly evolved. The works by Delgado Mena et al. (2014) and Baumann et al.
(2010) show that stars with $\log g$$\lesssim$ 4.2 dex increase their Li as
$\log g$ decreases, regardless of the presence of planets. The higher Li
abundances of these somewhat evolved stars could be explained by the fact that
they were hotter on the main sequence and did not deplete as much Li due to
their thinner convective envelopes. The Li abundance, $\log g$ value and the
radius larger than the Sun support the fact that this star is entering the
subgiant phase. This indicates an older age than the 6.8 $\pm$ 0.7 Gyr derived
from the chemical clocks and is more compatible with the 8.3 $\pm$ 0.7 Gyr
derived using PARAM. We also note that our chemical clock analysis assumes
that the star is in on the main sequence. Liu et al. (2019) showed that atomic
diffusion can significantly alter the measured abundances when a star leaves
the main sequence and thus might bias the age estimate provided by chemical
clocks. We thus favored the PARAM age estimate over the one provided by the
chemical clocks.

Table 8: Age estimation from 3D relations (more information can be found in Delgado Mena et al. 2019). Formula | Age
---|---
$T_{\text{eff}}$ \+ [Fe/H] + [Sr/Si] | 7.41 $\pm$ 2.31
$T_{\text{eff}}$ \+ [Fe/H] + [Sr/Si] | 7.41 $\pm$ 2.16
$T_{\text{eff}}$ \+ [Fe/H] + [Sr/Mg] | 7.67 $\pm$ 1.72
$T_{\text{eff}}$ \+ [Fe/H] + [Y/Mg] | 6.72 $\pm$ 1.21
$T_{\text{eff}}$ \+ [Fe/H] + [Y/Si] | 6.10 $\pm$ 1.67
$T_{\text{eff}}$ \+ [Fe/H] + [Y/Ti] | 6.34 $\pm$ 1.46
$T_{\text{eff}}$ \+ [Fe/H] + [Y/Zn] | 6.66 $\pm$ 1.38
Table 9: Age estimation from 1D relations (more information can be found in Delgado Mena et al. 2019). Formula | Age
---|---
[Sr/Ti] | 6.88 $\pm$ 2.31
[Sr/Mg] | 6.82 $\pm$ 2.06
[Sr/Si] | 6.58 $\pm$ 1.21
[Sr/Zn] | 6.34 $\pm$ 1.09
[Y/Al] | 6.61 $\pm$ 0.50
[Y/Mg] | 6.86 $\pm$ 0.76
[Y/Si] | 6.97 $\pm$ 0.91
[Y/Ti] | 6.91 $\pm$ 0.94
[Y/Zn] | 6.58 $\pm$ 0.82

##  Appendix D Selection of priors

###  D.1 Instrumental parameters

For the systemic velocity $\gamma_{RV,HARPS,}$ we considered a Gaussian prior
with the median and standard deviation matching that of the HARPS data.
Regarding the jitter parameters, we chose Jeffreys priors evaluated between
$10^{-2}$ and 10 times the median error bar for each of the datasets. The
prior of the RV shift between the CORALIE and HARPS data was set as a uniform
prior between the median plus and minus the square root of the sum of the
variances computed from all data after 2458673 BJD, when both instruments
observed the target.

###  D.2 Stellar parameters

For the limb-darkening coefficients, we use the PyLDTk292929Available at
https://github.com/hpparvi/ldtk (Parviainen & Aigrain 2015) toolkit. By
applying this method for the Kepler bandpass and taking the previously
determined $T_{\text{eff}}$ and log $g$ as inputs, the result for the limb-
darkening model coefficients of the quadratic model are $u1=0.5324\pm 0.0061$
and $u2=0.1056\pm 0.0091$. We used these estimates as priors. Finally, for the
stellar density, we used the estimate obtained by the stellar characterization
analysis (see Section 5).

###  D.3 Planetary parameters

With respect to the planetary periods, we have broad Jeffreys priors set
between the shortest orbital period for a known planet (0.09 days - Bailes et
al. 2011) and the time span of our data (1400 days). With regards to the RV
semi-amplitudes, $K$, we again set broad priors. For planet b, we considered a
uniform prior between 0 and 50 m/s, so as to safely cover all realistic
scenarios for a planet with the observed transit depth. For planet c, we
considered a uniform prior between 0 and 444 m/s, the range of RVs in our
HARPS dataset.

Joint priors are used in this work as a way to better convey our prior
knowledge of the system. They consist of the conversion of one set of jumping
parameters into a different but equivalent set of parameters, allowing for a
more physically motivated prior while helping the convergence of the MCMC
analysis.

One example is the joint prior on the jumping parameter $e\cos\omega$ and
$e\sin\omega$. It is not possible to set two independent priors on these two
quantities that would be equivalent to a prior on $e$ between 0 and 1 and a
prior on $\omega$ between -$\pi$ and $\pi$. To solve this problem, we used a
joint prior on $e\cos\omega$ and $e\sin\omega$ which converts this set of
parameters into $e$ and $\omega$. We can then set priors directly on $e$ and
$\omega$, while $e\cos\omega$ and $e\sin\omega$ remain the jumping parameters,
which is important for a better convergence Eastman et al. (2013). For planet
c, we used a uniform prior between $-\pi$ and $\pi$ for $\omega$ and a Beta
distribution (with $a=0.867$ and $b=3.03$) for $e$ (Kipping 2013). In the case
of planet b, due to its short orbital period and the age of the system, the
orbit is expected to be circular. Since from Equation (1) of Dobbs-Dixon et
al. (2004) we can expect a timescale associated with an eccentricity damping
of 1.44 Myr, for this calculation we assume a modified tidal quality factor
$Q^{\prime}_{p}$ of 100.

Another joint parameter used in this work is the joint parameter on $P$ and
$t_{ic}$ for planet c. We do not have prior knowledge of any of these two
parameters; to reflect this lack of constraints, we need to set broad
uninformative priors on both these quantities. However, by definition $t_{ic}$
is a degenerate variable as the values of $t_{ic}$ and $t_{ic}$ \+ $P$ are
equivalent in our model. To avoid this degeneracy, we used a joint prior that
transforms the set of parameters $P$ and $t_{ic}$, into $P$ and $\phi$, where
$\phi$ is the orbital phase defined by $\phi$ = ($t_{ic}$ \- $t_{ref}$) / $P$.
In this equation, $t_{ref}$ is a reference time arbitrarily chosen as the
rounded value of the first RV measurement. With this new set of parameters, we
can easily set broad and uninformative priors while removing the degeneracy.
We chose a Jeffreys prior between 0.09 and 1400 days on $P$ and a uniform
prior between 0 and 1 on $\phi$.

Our final joint prior is designed to translate the prior knowledge that a
planet is transiting. From our previous analysis on the photometric (Section
2) data, we know that planet b is transiting. The S/R of the transit of planet
b is low (see Fig. 2), and it is too easy for the MCMC exploration to wander
off into scenarios where planet b is not transiting. We can significantly
improve the MCMC convergence by limiting the parameter space to a region where
planet b is transiting. The parameters used in this model are the period, $P$,
impact parameter, $b$, radius ratio, $R_{p}/R_{*}$, and stellar density,
$\rho_{*}$ (Seager & Mallen-Ornelas 2003). Both $\rho_{*}$ or $a/R_{*}$,
together with $P$, $b$ and $R_{p}/R_{*}$ would accurately model the transit.
In this work, since we have strong constraints on $\rho_{*}$ from the stellar
analysis (Section 5), we can use this information to achieve a better
convergence on the MCMC and improve the results on our posterior distribution
of $b$. If not for our prior information on the stellar density, a degeneracy
could arise between $\rho_{*}$ and $b$, as both are capable of affecting the
transit duration. By using a joint prior, we compute $b$ alongside
$R_{p}/R_{*}$, allowing us to always determine if the planet is transiting for
each set of parameters. By imposing the conditions 0 ¡ $R_{p}/R_{*}$ ¡ 1 and 0
¡ $b$ ¡ 2, we include every non-grazing and grazing scenario.

##  Appendix E Early run: Prior and posterior

For the joint fit used to derive the final estimates of the parameters of the
system (Section 6), we chose broad prior distributions (see Table 4 and
Appendix D) that reflected any prior knowledge on the system and did not
unjustifiably constrain the parameters. However, in the attempts that we made,
when we drew the initial position of the MCMC chains from these priors, we did
not converge to the best solution. From the preliminary analysis of the light
curve (see Section 2) and the RV (see Section 4), we obtained a rough
knowledge of the best values for $P_{b}$, $t_{ic,b}$, $P_{,}c$ and $K_{c}$.
This knowledge could not be used to define the prior distributions since it
arose from the data that we were analyzing. However, to circumvent the
problem, we carried out a two-stage analysis: a first run to converge to the
best region of the parameter space and a second to derive robust estimates for
the value of the parameters. So, we did a first run, which used the knowledge
of $P_{b}$, $t_{ic,b}$, $P_{c},$ and $K_{c}$ extracted from our preliminary
analyses to define their prior distribution (see Table 10). We then performed
a second run (Section 6) that used the broader priors defined in Table 4 but
the posterior distributions of the parameters listed in Table 10, coming from
the first run, to draw the initial values of the MCMC chains.

Table 10:  Prior and posterior distributions for our first run designed to
converge to the best region of the parameter space quickly ($\mathcal{U}$ \-
Uniform; $\mathcal{G}$ \- Gaussian; $\mathcal{J}$ \- Jeffreys; $\mathcal{B}$
\- beta distribution).

Parameter | Prior | Posterior$a$$a$footnotetext:
---|---|---
Stellar density $\rho_{*}$ [$\textrm{g.cm}^{-3}$] |  $\mathcal{G}$ [0.2590, 0.0150] |  $\mathcal{G}$ [0.257, 0.02]
HD 137496 b
Period $P_{b}$ [days] |  $\mathcal{G}$ [1.621, 0.0005] |  $\mathcal{G}$ [1.6211, 0.0001]
RV semi-amplitude $K_{b}$ [m s-1] |  $\mathcal{U}$ [0.0, 50.0] |  $\mathcal{G}$ [2.14, 0.3]
Radius ratio $R_{p,b}/R_{*}$ |  $\mathcal{U}$ [0.0, 1.0] |  $\mathcal{G}$ [0.0076, 0.0003]
Time of inferior conjunction $t_{ic,b}$ [BJD-2450000] |  $\phi$ : $\mathcal{U}(0.08,0.006)$$b$$b$footnotetext:  |  $\mathcal{G}$ [58039.132, 0.003]
Cos inclination $\cos i_{b}$ [º] | - |  $\mathcal{G}$ [0.072, 0.06]
HD 137496 c
Period $P_{c}$ [days] |  $\mathcal{J}$ [0.1, 740] |  $\mathcal{G}$ [481.6, 3.0]
RV semi-amplitude $K_{c}$ [m s-1] |  $\mathcal{G}$ [230, 100] |  $\mathcal{G}$ [221.26, 0.9]
Time of inferior conjunction $t_{ic,c}$ [BJD-2450000] |  $\phi$ : $\mathcal{U}(0.0,1.0)$$b$$b$footnotetext:  |  $\mathcal{G}$ [58629.22, 0.5]
303030 $a$$a$footnotetext: Starting distribution from which the samples were
drawn for the first step in our MCMC analysis.
$b$$b$footnotetext: As defined in Table 4.