SuppReferences

# A close-in giant planet escapes engulfment by its star

Marc Hon  NASA Hubble Fellow  Daniel Huber  Institute for Astronomy,
University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Sydney
Institute for Astronomy (SIfA), School of Physics, University of Sydney,
Camperdown, NSW 2006, Australia  Nicholas Z. Rui  TAPIR, Mailcode 350-17,
California Institute of Technology, Pasadena, CA 91125, USA  Jim Fuller
TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA
91125, USA  Dimitri Veras  Centre for Exoplanets and Habitability, University
of Warwick, Coventry CV4 7AL, UK  Centre for Space Domain Awareness,
University of Warwick, Coventry CV4 7AL, UK  Department of Physics, University
of Warwick, Coventry CV4 7AL, UK  James S. Kuszlewicz  Center for Astronomy
(Landessternwarte), Heidelberg University, Königstuhl 12, 69118 Heidelberg,
Germany  Stellar Astrophysics Centre, Department of Physics and Astronomy,
Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark  Oleg Kochukhov
Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala
75120, Sweden  Amalie Stokholm  Stellar Astrophysics Centre, Department of
Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C,
Denmark  Dipartimento di Fisica e Astronomia, Universit à degli Studi di
Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy  INAF – Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129
Bologna, Italy  Jakob Lysgaard Rørsted  Stellar Astrophysics Centre,
Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120,
DK-8000 Aarhus C, Denmark  Mutlu Yıldız  Department of Astronomy and Space
Sciences, Science Faculty, Ege University, 35100, Bornova,
$\dot{\mathrm{I}}$zmir, Turkey  Zeynep Çelik Orhan  Department of Astronomy
and Space Sciences, Science Faculty, Ege University, 35100, Bornova,
$\dot{\mathrm{I}}$zmir, Turkey  Sibel Örtel  Department of Astronomy and Space
Sciences, Science Faculty, Ege University, 35100, Bornova,
$\dot{\mathrm{I}}$zmir, Turkey  Chen Jiang  Max-Planck-Institut für
Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
Daniel R. Hey  Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn
Drive, Honolulu, HI 96822, USA  Howard Isaacson  Department of Astronomy,
University of California Berkeley, Berkeley CA 94720, USA  Jingwen Zhang
Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu,
HI 96822, USA  Mathieu Vrard  Department of Astronomy, The Ohio State
University, 140 West 18th Avenue, Columbus OH 43210, USA  Keivan G. Stassun
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN
37235, USA  Benjamin J. Shappee  Institute for Astronomy, University of
Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Jamie Tayar  Department
of Astronomy, University of Florida, Bryant Space Science Center, Stadium
Road, Gainesville, FL 32611, USA  Institute for Astronomy, University of
Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Zachary R. Claytor
Department of Astronomy, University of Florida, Bryant Space Science Center,
Stadium Road, Gainesville, FL 32611, USA  Institute for Astronomy, University
of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Corey Beard
Department of Physics and Astronomy, University of California Irvine, Irvine,
CA 92697, USA  Timothy R. Bedding  Sydney Institute for Astronomy (SIfA),
School of Physics, University of Sydney, Camperdown, NSW 2006, Australia
Casey Brinkman  Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn
Drive, Honolulu, HI 96822, USA  Tiago L. Campante  Instituto de Astrofísica e
Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762
Porto, Portugal  Departamento de Física e Astronomia, Faculdade de Ciências da
Universidade do Porto, Rua do Campo Alegre, s/n, 4169-007 Porto, Portugal
William J. Chaplin  School of Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham B15 2TT, United Kingdom  Ashley Chontos  Department of
Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544,
USA  Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive,
Honolulu, HI 96822, USA  Steven Giacalone  Max-Planck-Institut für
Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany  Rae
Holcomb  Department of Astronomy, University of Florida, Bryant Space Science
Center, Stadium Road, Gainesville, FL 32611, USA  Andrew W. Howard  Department
of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
Jack Lubin  Department of Astronomy, University of Florida, Bryant Space
Science Center, Stadium Road, Gainesville, FL 32611, USA  Mason MacDougall
Department of Physics and Astronomy, University of California Los Angeles, Los
Angeles, CA 90095, USA  Benjamin T. Montet  School of Physics, University of
New South Wales, Sydney, NSW 2052, Australia  UNSW Data Science Hub,
University of New South Wales, Sydney, NSW, 2052, Australia  Australian Centre
for Astrobiology, University of New South Wales, Sydney, NSW, 2052, Australia
Joseph M. A. Murphy  Department of Astronomy and Astrophysics, University of
California, Santa Cruz, CA 95064, USA  Joel Ong  Institute for Astronomy,
University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
Department of Astronomy, Yale University, New Haven, CT 06511, USA  NASA
Hubble Fellow  Daria Pidhorodetska  Department of Earth and Planetary
Sciences, University of California, Riverside, CA 92521, USA  Alex S. Polanski
Department of Physics and Astronomy, University of Kansas, 1082 Malott, 1251
Wescoe Hall Dr., Lawrence, KS 66045, USA  Malena Rice  Department of Physics
and Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  Department of Astronomy,
Yale University, New Haven, CT 06511, USA  Dennis Stello  School of Physics,
University of New South Wales, Sydney, NSW 2052, Australia  Sydney Institute
for Astronomy (SIfA), School of Physics, University of Sydney, Camperdown, NSW
2006, Australia  ARC Centre of Excellence for All Sky Astrophysics in Three
Dimensions (ASTRO-3D)  Dakotah Tyler  Department of Physics and Astronomy,
University of California Los Angeles, Los Angeles, CA 90095, USA  Judah Van
Zandt  Department of Physics and Astronomy, University of California Los
Angeles, Los Angeles, CA 90095, USA  Lauren Weiss  Department of Physics and
Astronomy, University of Notre Dame, Notre Dame, IN 46556

###### Abstract

When main-sequence stars expand into red giants, they are expected to engulf
close-in planets [1, 2, 3, 4, 5]. Until now, the absence of planets with short
orbital periods around post-expansion, core helium-burning red giants [6, 7,
8] has been interpreted as evidence that short-period planets around Sun-like
stars do not survive the giant expansion phase of their host stars [9]. Here,
we present the discovery that the giant planet 8 Ursae Minoris b [10] orbits a
core helium-burning red giant. At a distance of only 0.5 au from its host
star, the planet would have been engulfed by its host star, which is predicted
by standard single-star evolution to have previously expanded to a radius of
0.7 au. Given the brief lifetime of helium burning giants, the planet’s nearly
circular orbit is challenging to reconcile with scenarios whereby the planet
survives by having a distant orbit initially. Instead, the planet may have
avoided engulfment through the scenario of a stellar merger that either
altered the evolution of the host star or produced 8 Ursae Minoris b as a
second generation planet [11]. This system shows that core helium-burning red
giants can harbour close planets and provides evidence for the role of non-
canonical stellar evolution in the extended survival of late-stage
exoplanetary systems.

The red giant 8 Ursae Minoris (hereafter 8 UMi), known also as Baekdu, was
discovered to host the giant planet 8 UMi b (known also as Halla) on a close-
in, near-zero eccentricity ($e\simeq 0.06$) orbit with a period of $93.4\pm
4.5$ days based on observations from the Bohyunsan Optical Astronomy
Observatory (BOAO) [10]. Radial velocity detections of close-in planets
surrounding red giants are sometimes ambiguous [12, 13], and so we confirmed 8
UMi b’s detection by collecting 135 additional radial velocity measurements
using the HIRES spectrograph [14] on the Keck-I telescope at Maunakea, Hawaii.
A Keplerian orbit fit to the combined radial velocity data refines the
planet’s estimated orbital properties to a period of $93.31\pm 0.06$ days and
an eccentricity of $0.06\pm 0.03$ (Table 1), demonstrating phase coherence of
the radial velocity data across 12.5 years or 49 orbital cycles (Fig. 1). A
trend visible within the residuals of the combined fit suggests an additional,
outer companion in the planetary system, whose minimum distance was determined
with a 67% confidence to be 5 au.

The long term stability of 8 UMi’s 93-day radial velocity variations suggests
an orbiting companion rather than stellar activity modulated by the star’s
rotation. In support of this, we have found no evidence of a 93-day
photometric variability for the host star. Additional tests of chromospheric
and surface magnetic fields do not detect significant activity levels expected
for a red giant rotating with a period consistent with the RV data. These
tests, which are detailed in Methods, support the planetary nature of the
radial velocity variations.

8 UMi was observed by NASA’s Transiting Survey Satellite (TESS) for 6 months
between July 2019 and June 2020, and for another 6 months between June 2021
and June 2022. The star’s oscillation modes are well-resolved within the TESS
data (Fig. 2a-b), such that its evolutionary state can be determined using
asteroseismology. The period spacing $\Delta\Pi$ of the seismic dipole ($l=1$)
oscillation modes for red giants can distinguish between red giants that are
expanding during their first ascent in the Hertzsprung-Russell diagram and
those that have previously swelled to their maximum size, but now reside in
the so-called red clump with smaller sizes [15]. First ascent red giants burn
hydrogen in a shell surrounding an inert helium core, resulting in a strong
density gradient between the contracting core and envelope, with $\Delta\Pi$
in the range $50-100$ s. Meanwhile, red clump stars burn helium within an
expanded, convective core, and have $\Delta\Pi$ in the range $250-400$ s [16].
We measured $\Delta\Pi=320$ s for 8 UMi, which unambiguously identifies the
star as a core-helium burning giant (Fig. 2c).

To determine the mass of the host star, we used established stellar modelling
techniques that compare the star’s observed properties to predicted
observables from stellar evolution models. Using observables from spectroscopy
and asteroseismology, we estimated the star’s mass to be $1.51\pm
0.05\,M_{\odot}$, which translates into a semi-major axis of $0.462\pm
0.006\,$au and a minimum planetary mass of $1.65\pm 0.06\,M_{J}$ for 8 UMi b.
Based on the host star’s mass and metallicity, stellar models predict that 8
UMi would have once expanded to about 0.7 AU. Depending on the choice of
model, we confirm with a 3–8$\sigma$ confidence that the expanding host star
would have surpassed the planet’s current orbital distance (Fig. 3).

While brown dwarfs [17] or low-mass stars may survive host star engulfment in
common-envelope scenarios, 8 UMi b is less massive than a brown dwarf with a
99.2% probability, assuming orbits are oriented randomly. Additionally,
astrometric data from ESA’s Gaia mission precludes unresolved companions more
massive than red dwarfs in a face-on orbit. Irrespective of the companion’s
mass, a common-envelope event with the host star is unlikely because the
resulting gravitational potential energy release could not have ejected the
host star’s envelope (see Methods). Additionally, the engulfed companion would
need only $10^{2}-10^{4}$ yr to spiral [9] into the star, in contrast to the
Myr timescale required for the star to complete its red giant expansion.

One possibility explaining 8 UMi b’s existence is that the planet initially
orbited at larger distances, but was pulled inwards by tidal interactions from
its expanding host star. However, simulations [18, 7, 8] indicate that this
scenario would require an exceptionally fine-tuned migration to halt further
orbital decay into the stellar envelope and reproduce the planet’s near-zero
eccentricity orbit. Alternatively, dynamical interactions may have scattered
the planet inwards on an eccentric orbit [19], which then tidally
circularized. However, the planet is then required to have attained its
current, near-circular orbit only after the host star has reached its maximum
size and commenced helium burning. Tidal circularization of the planet’s orbit
would thus need to occur within the 100 Myr that the host star spends in its
core helium-burning stage, which is unlikely given that the planet’s orbit
requires at minimum several Gyr to circularize at its current distance from
its host star.

Models of binary stellar evolution [20, 21] show that white dwarf–red giant
mergers can ignite core helium, resulting in the early termination of a red
giant’s expansion up the giant branch. Using Modules for Experiments in
Stellar Astrophysics [22], we modelled a binary history for 8 UMi and verified
that a circumbinary planet can remain dynamically stable throughout the binary
evolution of two low-mass stars that initially orbit each other at a 2-day
period before merging once forming a white dwarf–red giant pair. Therefore, 8
UMi may have been a close binary system whose merger prevented its components
from expanding sufficiently to engulf its circumbinary planet (Fig. 4). After
the merger, 8 UMi is expected to evolve as a typical red clump star, such that
the planet will eventually be engulfed once the star exhausts core helium and
expands up the asymptotic giant branch. According to this scenario, 8 UMi’s
progenitor once was an EL CVn-type binary [23]. These are binary systems with
an A- or F-type star orbiting a very low-mass white dwarf at periods shorter
than 3 days. Such systems frequently form the inner binaries of triple star
systems [24, 25], suggesting a stellar nature for the unresolved outer
companion in the 8 UMi system. A binary evolution scenario for 8 UMi is
further supported by predictions of surface lithium enrichment for the remnant
core-helium burning star based on simulations [26, 27] of white dwarf–red
giant mergers. In particular, measurements from previous spectroscopic surveys
[28, 29] have indicated that host star 8 UMi is over-abundant in lithium, with
$\mathrm{A(Li)}=2.0\pm 0.2$. With a 3$\sigma$ confidence, this is a factor of
ten to a hundred times larger than the lithium abundances of observed red
clump stars and single star model predictions at this mass [30, 31]. Besides a
circumbinary planet history, another possibility is that 8 UMi b formed as a
byproduct of the stellar merger event. Stellar ejecta from binary interactions
have been hypothesized to form protoplanetary disks [11], and so 8 UMi b may
have emerged from the debris disk surrounding the merger remnant.

As the first known close-in planet around a helium-burning red giant, 8 UMi b
demonstrates that stellar multiplicity, whose effect influences the fates of
planetary systems [32, 33], may result in pathways through which planets
survive the volatile evolution of their parent stars. Given the ubiquity of
binary systems, there may be a greater preponderance of exoplanets orbiting
post-main sequence host stars than previously assumed.

Table 1: Parameters of the fitted Keplerian orbit to the 8 UMi system. The
median values of the posterior distribution are reported. The lower- and
upper-bound uncertainties are the intervals between the median with the 16th
and 84th percentile values of the distribution, respectively. BOES, Bohyunsan
Observatory Echelle Spectrograph.; BJD, barycentric Julian date. Orbital
Parameters
---
Orbital period, $P$ |  $93.31\pm 0.06$ days
Radial velocity semi-amplitude, $K$ |  $56.1^{+1.7}_{-1.6}$ m/s
Eccentricity, $e$ | $0.062^{+0.028}_{-0.030}$
Argument of periapsis, $\omega$ |  $0.942^{+0.533}_{-0.463}$ rad
Time of periastron passage (BJD), $t_{P}$ | $2457601.379^{+7.844}_{-6.936}$
Instrumental Parameters
BOAO/BOES center of mass velocity, $\gamma_{\mathrm{BOES}}$ |  $13.33^{+7.42}_{-7.49}$ m/s
Keck/HIRES center of mass velocity, $\gamma_{\mathrm{HIRES}}$ |  $-46.91\pm 11.92$ m/s
BOAO/BOES jitter, $\sigma_{\mathrm{BOES}}$ |  $14.59^{+4.89}_{-4.12}$ m/s
Keck/HIRES jitter, $\sigma_{\mathrm{HIRES}}$ |  $12.65^{+0.86}_{-0.75}$ m/s
Linear acceleration, $\dot{\gamma}$ |  $0.014\pm 0.005$ m/s d-1
Curvature ($\times 10^{-5}$), $\ddot{\gamma}$ |  $0.49\pm 0.15$ m/s d-2
Derived Parameters
Planet mass, $M_{p}\sin i$ |  $1.65\pm 0.06$ $M_{J}$
Planet semi-major axis, $a_{\mathrm{pl}}$ |  $0.462\pm 0.006$ au

## Acknowledgements

The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has within the indigenous
Hawaiian community. We are most fortunate to have the opportunity to conduct
observations from this mountain. The data in this study were obtained at the
W. M. Keck Observatory, which is operated as a scientific partnership among
the California Institute of Technology, the University of California and the
National Aeronautics and Space Administration. The Observatory was made
possible by the generous financial support of the W. M. Keck Foundation.
Additional observations were obtained at the Canada-France-Hawaii Telescope
(CFHT), which is operated by the National Research Council (NRC) of Canada,
the Institut National des Sciences de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. M.H.
acknowledges support from NASA through the NASA Hubble Fellowship grant HST-
HF2-51459.001 awarded by the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy,
Incorporated, under NASA contract NAS5-26555. D.H. acknowledges support from
the Alfred P. Sloan Foundation, the National Aeronautics and Space
Administration (80NSSC21K0652, 80NSSC20K0593), and the Australian Research
Council (FT200100871). N.Z.R. acknowledges support from the National Science
Foundation Graduate Research Fellowship under Grant No. DGE-1745301. A.S.
acknowledges support from the European Research Council Consolidator Grant
funding scheme (project ASTEROCHRONOMETRY, G.A. n. 772293). O.K. acknowledges
support from the Swedish Research Council under the project grant 2019-03548.
M.V. acknowledges support from NASA grant 80NSSC18K1582. This work was
supported by Fundação para a Ciência e a Tecnologia (FCT) through research
grants UIDB/04434/2020 and UIDP/04434/2020. T.L.C. is supported by FCT in the
form of a work contract (CEECIND/00476/2018). T.R.B. acknowledges support from
the Australian Research Council through Discovery Project DP210103119 and
Laureate Fellowship FL220100117.

## Author contributions statement

M.H. identified 8 UMi’s oscillations, led the observing program and data
analysis, and wrote most of the manuscript. D.H. organized observations,
interpreted the asteroseismic and radial velocity data, and contributed to
writing the manuscript. N.Z.R. and J.F. conducted binary simulations for the
host star, performed numerical calculations for planet survival scenarios, and
contributed to writing the manuscript. J.F. and D.V. interpreted formation
scenarios for the host star. J.S.K. and M.V. extracted oscillation parameters
from the TESS data. O.K. performed the spectropolarimetric analysis of the
host star and the control target. A.S., J.L.R., M.Y., Z.Ç.O., S.Ö., C.J., and
J.O. conducted grid-based modelling for 8 UMi. D.R.H. D.H., and M.H. fitted
the radial velocity data. H.I. measured chromospheric activity indices from
the HIRES data. J.Z. constrained the properties of the outer companion. K.G.S.
performed the SED analysis for the host star. B.J.S. extracted ASAS-SN
photometry for 8 UMi. J.T. and Z.R.C. provided interpolatable grids of
isochrones. T.R.B. and D.S. analyzed the asteroseismic data and helped guide
the strategy of the manuscript. B.T.M. identified and analyzed the lithium
richness of the control target. W.J.C., D.H., and T.L.C., are key architects
of TASC working groups on exoplanet hosts, including evolved stars. H.I. and
A.W.H. oversaw the California Planet Search observing program. A.C., S.G.,
C.B., J.L., R.H., J.M.A.M., J.V.Z., D.T., D.P., C.B., M.M. A.S.P., M.R., and
L.W. conducted Keck I/HIRES observations of 8 UMi and the control star. All
authors reviewed the manuscript.

## Competing interests

The authors declare that they have no competing financial interests.

## Correspondence

Correspondence and requests for materials should be addressed to M.H. (email:
mtyhon@hawaii.edu).

Figure 1: Radial velocity measurements of host star 8 UMi. (a) Radial velocity
time series from Keck/HIRES observations. The curve shows the best fit to the
radial velocity measurements whose error bars are 1$\sigma$ measurement
uncertainties added in quadrature with a fitted jitter value. (b) Residuals
after subtracting the best fit from the time series, fitted with a quadratic
trend in time as shown by the dash-dotted line. (c) Combined observations from
Keck/HIRES and BOAO/BOES. A quadratic trend in time has already been fitted
and subtracted to the data shown here to show variations from planet 8 UMi b
alone. (d) Residuals in the radial velocity data after subtracting the best
fit indicated by the curve in panel (c). (e) The phase-folded time series of
the combined and detrended radial velocity data. The dashed line shows the
phase-folded time series of the best fit to the orbit presented in panel (c).
Figure 2: Identification of the evolutionary state of host star 8 UMi as a
core helium-burning red giant. (a) Oscillation power spectrum of 8 UMi, as
observed by TESS. Oscillation modes are labelled by their angular degree $l$.
The inset presents a zoomed out view of the spectrum. (b) The frequency
échelle diagram of the spectrum. The symbols indicate the labelled oscillation
modes. (c) Fourier transform of the stretched period spectrum for the $l=1$
modes (see Methods). The asymptotic $l=1$ period spacing value for 8 UMi
corresponds to the value of $\Delta\Pi$ with the largest power, which is 320
s. Figure 3: Canonical single-star evolutionary models for the host star 8
UMi. (a) A 1.5$M_{\odot}$, solar-metallicity stellar model indicates that host
star 8 UMi would have reached a maximum size of $R_{\mathrm{tRGB}}$ during its
first ascent up the red giant branch. This maximum size exceeds the semi-major
axis of the planet 8 UMi b, $a_{\mathrm{pl}}=0.462\pm 0.006$ au (dashed-dotted
line). (b) Boundaries at which $R_{\mathrm{tRGB}}=a_{\mathrm{pl}}$ are shown
across a range of stellar mass and metallicity ([M/H]) values for different
stellar evolutionary codes. Each boundary comprises two lines, which reflect
the $\pm 1\sigma$ uncertainties of $a_{\mathrm{pl}}$. The mass and metallicity
measurements for 8 UMi, whose error bars indicate 1$\sigma$ (standard
deviation) uncertainties, locate the star in the region where
$R_{\mathrm{tRGB}}>a_{\mathrm{pl}}$ across all tested codes. This indicates
that the planet’s orbital distance is consistently shorter than the maximal
extent of its host star assuming single-star evolution.  Figure 4: A possible
history of host star 8 UMi in the form of a stellar merger. A primary, upon
its ascent up the red giant branch (RGB), is first stripped by its companion
into a helium white dwarf (WD). The white dwarf merges with the secondary when
it evolves off the main sequence and ascends the RGB. This binary scenario
produces a $M\approx 1.5M_{\odot}$ core helium burning star without requiring
the star’s radius to grow beyond the orbital distance of 8 UMi b.

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## Methods

### Orbital properties of the 8 UMi system

Radial velocity analysis: The first radial velocity dataset for 8 UMi
comprises measurements taken from the Bohyunsan Optical Astronomy Observatory
(BOAO) using the using the Bohyunsan Observatory Echelle Spectrograph Kim_2007
(BOES), which are available from the 8 UMi discovery paper Lee2015. We
obtained additional high-precision radial velocity observations (Extended Data
Table 1) using the HIRES spectrometer Vogt1994 at the Keck-1 Telescope on
Maunakea, Hawai‘i. All data was reduced using the standard procedure of the
California Planet Search Howard_2010 (CPS). For all observations we placed an
iodine-cell in the light path to project a series of fiducial absorption lines
onto the stellar spectrum. These references allow to track the instrumental
profile and precisely wavelength-calibrate the observed spectra. We also
collected a high signal-to-noise iodine-free template spectrum, which together
with the instrumental point-spread function (PSF) and iodine transmission
function is a component of the forward model employed by the CPS Doppler
analysis pipeline Howard_2010, Butler_1996.

We used the probabilistic modelling toolkit exoplanetexoplanet, pymc3 version
0.5.4 to fit a Keplerian orbit to the radial velocity time series. Radial
velocity offsets ($\gamma$) and jitter terms specific to BOAO
($\sigma_{\mathrm{BOAO}}$) and HIRES ($\sigma_{\mathrm{HIRES}}$) instruments
were included as free parameters in the fit. Additionally, long-term trends in
the radial velocity data were parameterized with a quadratic curve comprising
a linear acceleration term ($\dot{\gamma}$) and a curvature term
($\ddot{\gamma}$). The priors for period $P$ and semi-amplitude $K$ were
defined as normally distributed in log-space, such that
$\log(P)\sim\mathcal{N}(\log(93.5),10)$, and
$\log(K)\sim\mathcal{N}(\log(56.5),10)$. Those for $\omega$, $\dot{\gamma}$,
and $\ddot{\gamma}$ were uniformly distributed, where $\omega\sim\mathcal{U}$
($-2\pi,+2\pi$), $\dot{\gamma}\sim\mathcal{U}(0,0.1)$, and
$\ddot{\gamma}\sim\mathcal{U}(0,0.001)$. The eccentricity ($e$) prior was
described by Beta$\,(0.867,3.03)$, following a distribution tailored towards
empirical observations of extrasolar planet eccentricities Kipping_2013. The
priors for $\gamma$ of each instrument were normally distributed, with
$\gamma_{\mathrm{BOES}}\sim\mathcal{N}(-9.3,200)$,
$\gamma_{\mathrm{HIRES}}\sim\mathcal{N}(-2.4,200)$. Meanwhile, those for
$\sigma$ were parameterized with half-normal distributions, such that
$\sigma_{\mathrm{BOES}}\sim\lvert\ \mathcal{N}\rvert(0,100)$ and
$\sigma_{\mathrm{HIRES}}\sim\lvert\ \mathcal{N}\rvert(0,100)$. The time of
periastron passage, $t_{P}$ was fitted within the interval
$0.5t_{0}+\phi\times P$, where $\phi\sim\mathcal{U}(0,1)$ and $t_{0}$ is the
midpoint in time between the first and last radial velocity observations.

Following standard Markov chain Monte Carlo (MCMC) procedures, maximum a
posteriori estimates of the Keplerian orbital parameters were determined
through iterative fits to the time series, followed by the exploration of
parameter uncertainties using the No-U-Turn Sampler NUTS. We performed 5,000
tuning iterations and 5,000 draws from two chains during the posterior
sampling process, with random seeds of 39091 and 39095. The process resulted
in a Potential Scale Reduction Factor below 1.001 for each explored parameter,
indicating posterior convergence. The sampled posterior distribution is
presented in Extended Data Fig. 1. The fitted jitter terms from BOES and HIRES
are consistent with one another with values $\sim 10$ m/s, which is expected
from core-helium burning giants Yu_2018, Tayar_2019.

Characterizing the outer companion: An underlying long-term trend in the
radial velocity data, as determined by non-zero values of first-
($\dot{\gamma}$) and second-order ($\ddot{\gamma}$) velocity derivatives,
suggests the presence of an additional, outer companion to the system. These
derivatives were defined with respect to a reference time,
$t_{\mathrm{ref}}=2457508.0173445$. We compared radial velocity models with
and without these additional terms, using the Watanabe-Akaike Information
Criterion Watanabe_2010 (WAIC) metric. The score was measured as a deviance
value, where smaller scores indicate better predictive accuracy. We found the
model including a trend (WAIC = 1265.80) was favoured over the one without
(WAIC = 1282.37). The improvement in WAIC in using the trended model is
significantly greater than the standard error in WAIC differences between the
two models ($d_{\mathrm{WAIC}}=7.64$) and therefore the RV variations are
better predicted with a trend, and suggest the presence of an outer companion
with a longer period than our combined observational baseline of 12.5 years.

To constrain the mass and semi-major axis of the outer companion, we fitted a
Keplerian orbit using joint constraints from the host star’s long-term radial
velocity trend and astrometric acceleration Lubin_2022. A broad range of
masses, semi-major axes, $i$, $\omega$, $e$, and mean anomaly values were
explored using MCMC procedures to identify orbits that fit the radial velocity
derivatives ($\dot{\gamma},\ddot{\gamma}$). To apply the astrometric
constraints, we computed the expected proper motion vectors for each
calculated orbit in the Hipparcos and Gaia DR3 epochs, which were then
contrasted against the observed change in proper motion for host star 8 UMi
between the two epochs Brandt_2021. The results from separately and jointly
fitting the radial velocity and astrometry constraints are shown in Extended
Data Fig. 2, where we conclude that the outer companion orbits at a distance
greater than 5 au at a 67% confidence level.

### Stellar activity

Previously, the discovery of 8 UMi b was established using the lack of
correlations between radial velocity measurements with H-$\alpha$ line
variations, spectral line bisectors, and Hipparcos photometry Lee2015. We
further established the planet’s existence in this work using measured Ca II H
and K spectral line variations and spectropolarimetric observations of the
host star to estimate its stellar activity level. We computed Ca II H and K
indices ($S_{HK}$) following established calibration methods Isaacson_2010 for
Keck data. The results in Extended Data Fig. 3 indicate no significant
correlation between 8 UMi’s radial velocity measurements with $S_{HK}$ and no
significant 93-day variation within its computed Generalized Lomb-Scargle
(GLS) periodogram Zechmeister_2009. The absence of strong chromospheric
activity for 8 UMi is further evidenced in Extended Data Fig. 4a-b by its lack
of strong Ca II H and K emission features. Extended Data Fig. 4c demonstrates
the lithium-richness of 8 UMi at the 6707.8Å Li I absorption line in
comparison with the Li-normal Liu_2014 core helium-burning giant $\mu$ Pegasi
polarbase. We adopt a lithium abundance as $\mathrm{A(Li)}=2.0\pm 0.2$ for 8
UMi, which is the average and standard deviation of previously published
Kumar_2011_supp, Charbonnel_2020_supp Local Thermodynamic Equilibrium (LTE)
measurements of lithium for the star.

To estimate the strength of magnetic fields potentially present at the surface
of the host star, we collected four spectropolarimetric observations between
February 2022 and July 2022 with ESPaDOnS at the Canada-France-Hawaii
Telescope (CFHT). The observed data comprised intensity ($I$), Stokes $V$, and
null ($N$) polarisation spectra, reduced with the Libre-Esprit Donati_1997 and
Upena pipelines at CFHT. To detect the presence of Zeeman signatures within
the spectra, we applied the improved Least Squares Deconvolution technique
Donati_1997, Kochukhov_2010 using line masks from the Vienna Atomic Line
Database Kupka_1999 corresponding to a model atmosphere of
$T_{\mathrm{eff}}=4750$K and $\log(g)=2.5$ dex. All LSD profiles for 8 UMi in
Extended Data Fig. 5 show null detection of Stokes V Zeeman signatures, which
correspond to false alarm probabilities (FAP) Donati_1997 $>1\times 10^{-3}$.
This firmly excludes the presence of a $\sim 5\,$G mean longitudinal magnetic
field strength expected for an active red giant rotating at a period of 90
days Auriere_2015.

These observations are benchmarked against the known active red giant TYC
3542-1885-1 (KIC 8879518). This active star has a measured Kepler photometric
rotation period of $109$ days Gaulme_2020, and was chosen as a control target
by virtue of having a similar evolutionary state, mass ($M=1.61\,M_{\odot}$)
and radius ($R=10.89\,R_{\odot}$) to the host star 8 UMi. Additionally, TYC
3542-1885-1 is also lithium-rich Wheeler_2021, albeit with higher abundance
levels to 8 UMi (Extended Data Fig. 4c). From our Keck/HIRES observations of
TYC 3542-1885-1 between 2 April 2022 and 1 August 2022 (Extended Data Fig. 3),
the star exhibits a quasi-periodic $\sim 65\,$d radial velocity variation that
correlates strongly with its measured $S_{HK}$, inferred to be caused by a
secondary starspot feature. Despite lower SNR spectropolarimetric data,
ESPaDOnS observations of TYC 3542-1885-1 show marginal ($1\times
10^{-5}<\mathrm{FAP}\leq 1\times 10^{-3}$) evidence of a mean longitudinal
magnetic field (Extended Data Fig. 5) at strengths of $\sim 3\,$G, which is
broadly consistent with the expected field strength for a 100-200 d rotating
red giant Auriere_2015. From our analysis of the control target, we expect the
host star 8 UMi to show similar patterns in chromospheric and surface magnetic
activity levels if its 93-day radial velocity variations are stellar in
nature, but such activity signatures were not observed.

Extended Data Fig. 6 shows our analysis of 8 UMi’s photometry from different
sources. A starspot mimicking 8 UMi’s $\sim 50\,$m/s radial velocity
variations would show photometric variability at the $2.5-3$% level, based on
simulated results of a generic starspot (e.g., 600 K spot contrast, 3% visible
hemisphere coverage, $60^{\circ}$ longitude) using the Spot Oscillation And
Planet 2.0 tool Dumusque_2014. We found 8 UMi’s time series from Hipparcos
Hipparcos and from ASAS-SN Shappee_2014, Kochanek_2017 3-pixel ($\sim 24$
arcsec) radius aperture photometry to be constant to within $0.5\%$ and
showing no significant 93-day periodic variation within their computed GLS
periodograms. Additionally, we examined TESS short-cadence Simple Aperture
Photometry light curves corrected using the TESS Systematics-Insensitive
Periodogram (TESS-SIP) Hedges_2020, which confirmed the same null result from
a search of periods spanning 20-200 days. We thus conclude that 8 UMi’s radial
velocity variations are planetary in nature.

### Asteroseismic measurements

We used all TESS light curves for 8 UMi across Cycles 2 and 4 (total of 12
Sectors) that were produced by the TESS Science Operations Center Jenkins_2016
(SPOC), which are available at the Mikulski Archive for Space Telescopes
(MAST) as of January 2023. We determined the oscillation frequency at maximum
power, $\nu_{\mathrm{max}}=45.29\pm 0.43\,\mu$Hz, by fitting the light curve’s
power density spectrum with a model comprising a Gaussian oscillation power
envelope superimposed upon a background of three granulation parameters and
white noise Themessl_2020. We identified oscillation modes using a well-tested
automated peak detection method Montellano_2018 to fit Lorentzian-like models
to the resonant peaks within the power envelope. We determined the large
frequency spacing, $\Delta\nu=4.80\pm 0.01\,\mu$Hz, by fitting the detected
radial modes to the red giant oscillation pattern Mosser_2011 following the
asymptotic relation of stellar acoustic modes Tassoul_1980.

We measured the dipole mode period spacing, $\Delta\Pi$, by converting the
frequency axis of the oscillation spectrum into stretched periods Mosser_2015.
Following established automated procedures Vrard_2016_supp, stretched period
spectra were computed over trial values of $\Delta\Pi$ and mixed mode coupling
factors ($q_{c}$), with the best solution providing the highest power in the
Fourier transform of the resulting stretched period spectrum. By searching
between $\Delta\Pi$ of 40-400 s and $q_{c}$ of $0.05-0.80$, we determined the
solution at $(\Delta\Pi,q_{c})=(320\,$s$,0.35)$ as the global maximum, which
firmly identifies 8 UMi as a core helium-burning giant Mosser_2017.

### Stellar modelling

Four different codes Rodrigues_2014, Rodrigues_2017, Yildiz_2016, Jiang_2021,
Silva-Aguirre_2022 were used to model host star 8 UMi and estimate its
fundamental stellar properties. We constrained the modelling to core helium-
burning stars and used as inputs asteroseismic parameters $\Delta\nu$ and
$\nu_{\mathrm{max}}$, along with atmospheric parameters
$T_{\mathrm{eff}}=4847\pm 100\,$K and [M/H]$=-0.03\pm 0.10\,$ dex. These were
adopted from the discovery paper Lee2015, with the uncertainties (standard
deviation) inflated from their original published values Tayar_2022. We report
the best-fitting estimates across the modelling codes, which are $M=1.51\pm
0.05$ (stat) $\pm 0.04$ (sys) $\,M_{\odot}$ , $R=10.73\pm 0.11$ (stat) $\pm
0.08$ (sys) $\,R_{\odot}$, $L=52.9\pm 4.9$ (stat) $\pm 3.3\,L_{\odot}$ (sys).
The central values were provided by one of the codes Yildiz_2016 that showed
the smallest difference to the median derived mass, with systematic
uncertainties as the standard deviation of an estimated parameter over all
codes. By combining errors in quadrature, these results translate to average
uncertainties of $0.06\,M_{\odot}$ for mass, $0.14\,R_{\odot}$ for radius, and
$5.9\,L_{\odot}$ for luminosity.

We verified our modelled results using independent estimation methods, where
for each the 1$\sigma$ uncertainty is reported as that method’s standard
deviation. Using model-calibrated asteroseismic scaling relations Sharma_2016,
Stello_2022, we measured $M_{\mathrm{scal}}=1.54\pm 0.06\,M_{\odot}$ and
$R_{\mathrm{scal}}=10.72\pm 0.16\,R_{\odot}$. Additionally, we fitted Kurucz
stellar atmosphere models to the broadband (0.2–22 $\mu$m) spectral energy
distribution (SED) of the host star Stassun:2016,Stassun:2017,Stassun:2018
(see Extended Data Fig. 7), including extinction based on the maximum line-of-
sight value from published Galactic dust maps Schlegel:1998. Integration of
the unreddened model SED, combined with a Gaia DR3 parallax
$\varpi=6.128\,$mas (with no systematic offset applied StassunTorres:2021),
resulted in $L_{\mathrm{SED}}=53.81\pm 1.84\,L_{\odot}$ and subsequently
$R_{\mathrm{SED}}=10.19\pm 0.36\,R_{\odot}$, which are in agreement to within
1$\sigma$ with our modelled estimates.

We determined theoretical estimates of the maximum size of a pre-core helium-
burning star by interpolating the radius of its stellar envelope at the tip of
the red giant branch ($R_{\mathrm{tRGB}}$) across mass and metallicity using
various Choi_2016, Hidalgo_2018, Dotter_2008, Tayar_2022, Bressan_2012,
Weiss_2008 isochrone grids, all of which are based on canonical single-star
evolution. The interpolation produces a boundary above which the current semi-
major axis of 8 UMi b would be smaller than $R_{\mathrm{tRGB}}$ of its host
star (see main text Fig. 3). We measured the closest extent of each
isochrone’s boundary to 8 UMi’s mass and metallicity and found with a
3-8$\sigma$ confidence that 8 UMi b, had it formed in-situ at 0.46 AU, would
have been within its host star’s stellar envelope during the giant branch
phase assuming canonical stellar evolution.

### Exploring survival scenarios

Tidal migration and circularization: Assuming a constant quality factor $Q$,
the tidal migration timescale $\tau_{\mathrm{tide}}$ is roughly the
evolutionary timescale of the semi-major axis due to tides:

$\left\lvert\frac{\dot{e}}{e}\right\rvert_{\mathrm{tide}}\sim\left\lvert\frac{\dot{r}}{r}\right\rvert_{\mathrm{tide}}=\frac{1}{\tau_{\mathrm{tide}}}=\frac{1}{\tau^{\star}_{\mathrm{tide}}}+\frac{1}{\tau^{p}_{\mathrm{tide}}}\simeq\frac{1}{\mathrm{min}(\tau^{\star}_{\mathrm{tide}},\tau^{p}_{\mathrm{tide}})}$
(1)

where $\tau^{\star}_{\mathrm{tide}}$ and $\tau^{p}_{\mathrm{tide}}$ account
for tidal dissipation in the star and planet, respectively. These timescales
are estimated asgoldreich1966q

$\displaystyle\tau^{\star}_{\mathrm{tide}}\simeq\frac{1}{9\pi}Q_{\star}\frac{M_{\star}}{M_{p}}\left(\frac{a}{R_{\star}}\right)^{5}P\approx
60\,\mathrm{Gyr}\left(\frac{Q_{\star}}{10^{5}}\right)\left(\frac{M_{\star}}{1.51\,M_{\odot}}\right)^{1/2}\left(\frac{M_{p}}{1.65\,M_{J}}\right)^{-1}\left(\frac{a}{0.46\,\mathrm{au}}\right)^{13/2}\left(\frac{R_{\star}}{10.73\,R_{\odot}}\right)^{-5}$
(2a)
$\displaystyle\tau^{p}_{\mathrm{tide}}\simeq\frac{1}{9\pi}Q_{p}\frac{M_{p}}{M_{\star}}\left(\frac{a}{R_{p}}\right)^{5}P\approx
10^{5}\,\mathrm{Gyr}\left(\frac{Q_{p}}{10^{5}}\right)\left(\frac{M_{p}}{1.65\,M_{J}}\right)\left(\frac{M_{\star}}{1.51\,M_{\odot}}\right)^{-3/2}\left(\frac{a}{0.46\,\mathrm{au}}\right)^{13/2}\left(\frac{R_{p}}{1.50\,R_{J}}\right)^{-5}$
(2b)

where the star and planet tidal quality factors $Q_{\star}$ and $Q_{p}$ are
scaled to the lower end of $Q$ values reported in literature for Jovian
planetswu2005origin and red giantsessick2015orbital with $Q_{\star}\sim
Q_{p}\gtrsim 10^{5}$, and assuming a representative Jovian planet radius
Fortney_2021 of $1.5R_{J}$. Hence, present-day tidal circularization and
migration takes place on timescales characteristically larger than a Hubble
time, and can be ignored.

Of course, during the red giant’s expansion prior to the helium flash, its
radius would have greatly exceeded its current-day value, significantly
enhancing the tidal dissipation and dramatically shortening the orbit’s
circularization timescale. If, during this expansion, the outer radius of the
star barely grazed the planet’s orbit at its helium-flash radius $a\approx
R_{\star}\approx 0.7\,\mathrm{au}$, a similar calculation yields a minimal
dissipation timescale $\tau^{\star,\mathrm{flash}}_{\mathrm{tide}}\simeq
1.6\,\mathrm{Myr}$. This approximates a lower bound to the planet’s migration
timescale in the most extreme scenario where a very fine-tuned dynamical
process brings the planet as close to the star as possible during its helium
flash. This timescale should be compared to the timescale of $\sim
50\,\mathrm{kyr}$ on which the star shrinks following the initial helium
flash, when its radius is largest. Hence, the planet could not migrate inwards
as fast as the star contracts following the helium flash. Even under these
fine-tuned scenarios, tidal circularization and migration cannot act fast
enough to deliver the planet to its current orbital separation and
eccentricity.

8 UMi b mass constraints: Assuming orbits are randomly oriented, the
probability of an orbit having inclination $i$ is proportional to $\sin i$.
Given 8 UMi b’s mass of $M_{p}\sin i=1.65\,M_{J}$, the planet’s orbit would
need to be nearly face-on ($i\leq 7.3^{\circ}$) for its mass to exceed
$13\,M_{J}$, which is a threshold adopted as the deuterium-burning limit for
brown dwarfs Spiegel_2011. This range of $i$ occurs with a probability of
0.8%, based on draws from an isotropic distribution.

Host star 8 UMi has low astrometric excess noise as reported by the Gaia space
mission. This noise is quantified by the Re-normalized Unit Weight Error
(RUWE), and has a value of $\rho_{\mathrm{DR2}}=1.09$ for Gaia Data Release 2
(DR2) during which 17 visibility periods were reported over the observing
baseline. The angular perturbation to the single source of the photocentre as
fitted by Gaia can be estimated Belokurov_2020 as $\delta{\theta}\approx
0.53\sigma_{\varpi}\sqrt{N(\rho_{\mathrm{DR2}}-1)}=0.076\,$mas , where
$\sigma_{\varpi}$ is the star’s parallax error of 0.024 mas and $N=192$ is the
number of good along-scan Gaia observations. Given the near-zero eccentricity
constraint from the radial velocity data, we considered perturbations in the
limit of a face-on alignment for a circular orbit Penoyre_2020, such that

$\delta{\theta}=\frac{\varpi a|q-l_{r}|}{(1+q)(1+l_{r})},$ (3)

where the DR2 parallax $\varpi=6.123\,$mas, the semi-major axis $a=0.462\,$au,
$q=M_{\mathrm{planet}}/M_{\star}$ is the mass ratio, and
$l_{r}=L_{\mathrm{planet}}/L_{\star}$ is the luminosity ratio, which we
approximate as zero. Assuming the perturbation comes purely from the orbiting
companion, $q$ is predicted to be $\sim 0.028$ to yield a sufficiently large
$\delta{\theta}$ that produces the observed $\rho_{\mathrm{DR2}}$. This
suggests that companion masses above $0.043M_{\odot}$ or $45\,M_{J}$ would
induce larger astrometric noise excesses than as measured by
$\rho_{\mathrm{DR2}}$ and therefore rules out 8 UMi b as a stellar companion.
In Gaia Data Release 3 (DR3), 8 UMi is reported to have a high astrometric
fidelity Rybizki_2022 (value = 1), with a nearly identical parallax of
$\varpi_{\mathrm{DR3}}=6.128\,$mas and $\rho_{\mathrm{DR3}}=0.80$ based on 23
visibility periods. This value of $\rho_{\mathrm{DR3}}$, when considered in
tandem with $\rho_{\mathrm{DR2}}$, is again inconsistent with excess
astrometric scatter from a close stellar companion Penoyre_2022.

Common-envelope evolution: The observed orbital separation $\approx
0.5\,\mathrm{au}$ eliminates the possibility of 8 UMi b initiating a
successful common envelope, independent of its mass. Assuming that 8 UMi b
starts at an orbital separation $a_{i}\approx 0.7\,\mathrm{au}$ (the tip of
the red giant branch), the orbital energy available to unbind the envelope is

$\Delta
E_{\mathrm{orb}}\simeq\frac{GM_{p}M_{c}}{2a_{f}}-\frac{GM_{p}M_{\star}}{2a_{i}}=\frac{1}{2}GM_{p}\left(\frac{M_{c}}{a_{f}}-\frac{M_{*}}{a_{i}}\right)$
(4)

where $M_{*}\approx 1.5\,M_{\odot}$, $M_{c}\approx 0.25\,M_{\odot}$, and
$a_{f}\approx 0.5\,\mathrm{au}$. However, because $M_{c}/M_{*}<a_{f}/a_{i}$,
we find that $\Delta E_{\mathrm{orb}}<0$, which implies that the planet ends
up less bound than before. The observed semi-major axis of 8 UMi b therefore
precludes the orbit from having shrunk enough to unbind any of the envelope,
regardless of the value of $M_{p}$. Even in the absence of a common-envelope
event, the companion would almost certainly not survive temporary engulfment
by the host star. The maximum inspiral timescale $t_{\mathrm{insp}}$ for a
$0.1\,M_{\odot}$ red dwarf in the envelope of 8 UMi can be estimated as the
time for the companion’s orbital energy to be reduced by ram pressure
Macleod_2018_supp. For a drag force $F_{D}$ and orbital velocity $v$, the
inspiral time is $t_{\mathrm{insp}}\sim E_{\mathrm{orb}}/F_{D}v\propto
M_{p}/R_{p}^{2}\sim 10^{2}-10^{4}\,\mathrm{yr}$. Assuming that the host star
had previously engulfed the planet at its current orbital distance of
$0.5\,$au, the calculated inspiral timescale is much smaller than the $\sim
2\,\mathrm{Myr}$ required for the host star to reach $R_{\mathrm{tRGB}}$ as
estimated by stellar models Choi_2016 .

### Modelling the binary merger scenario

Using Modules for Experiments in Stellar Astrophysics (mesa, version
r22.05.1paxton2010modules,paxton2013modules,paxton2015modules,paxton2018modules,paxton2019modules),
we simulated coupled orbit—stellar binary evolution scenarios resulting in a
merger of a red giant with a helium white dwarf companion as a pathway for 8
UMi b’s survival. These scenarios aimed to simulate a first, stable mass
transfer phase that stably strips the primary followed by a second, unstable
mass transfer phase that merges the two stars. Leading up to the first mass
transfer phase, we simulated the stellar evolution and orbits of both stars
together until the primary has been totally stripped into a helium white
dwarf. After the first mass transfer phase, we modelled the primary purely as
a point mass with the mass of the primary’s stripped core while still evolving
the orbits of both stars. As observational constraints, the simulated initial
component masses $M_{1}$ and $M_{2}$ were set such that the final mass of the
remnant, $M$, is 8 UMi’s observed stellar mass of $\approx 1.5\,M_{\odot}$.
Additionally, to avoid dynamically destabilizing the planet, the semi-major
axis of the simulated binary throughout its evolution cannot exceed $\gtrsim
30\%$ of the planet’s own semi-major axisholman1999long, which evolves to
conserve orbital angular momentum.

We included magnetic braking and tidal synchronization in our modelling, where
we assume that tides instantaneously synchronize the stellar spins to the
orbital frequency, which is a good approximation at short orbital periods. The
magnetic braking torque is a strong function of spin frequency, with
$\dot{J}\propto\Omega^{3}$ in standard magnetic braking
prescriptionsrappaport1983new, resulting in the high sensitivity of the
simulation outcomes to the initial orbital separation. Additionally, we
assumed mass transfer in the form of fast wind off of the accretor. This form
of mass loss is governed by the $\beta$ parametertauris2006formation, with
$\beta=0$ indicating that no mass is lost from the system and $\beta=1$
indicating that all mass is lost and therefore no mass is transferred to the
accretor. Assuming no mass is lost during the merger, the final mass of the
remnant is given by

$M=(1-\beta)(M_{1}-M_{c})+M_{c}+M_{2}$ (5)

where $M_{c}$ is the maximum mass of the primary’s core (i.e., the mass of the
stripped helium white dwarf). We determined $M_{1}$ and $M_{2}$ by specifying
$\beta$ and a mass ratio $q$, assuming $M\approx 1.50\,M_{\odot}$ and
$M_{c}\approx 0.25\,M_{\odot}$. A fully conservative mass transfer ($\beta=0$)
was found to result in an unstable first mass transfer phase, while fully non-
conservative mass transfer ($\beta=1$) destabilized the planet through
excessive orbital expansion. We thus used a fiducial choice of parameters
$q=0.7$ and $\beta=0.6$ ($M_{1}=1.23\,M_{\odot}$, $M_{2}=0.86\,M_{\odot}$),
and subsequently identified that models with initial orbital periods
$1.7\,\mathrm{d}\lesssim P_{\mathrm{init}}\lesssim 2.3\,\mathrm{d}$ can stably
strip the envelope of the primary completely, with lower period models either
evolving into contact binaries (or merging prematurely) and higher period
models undergoing unstable mass transfer immediately. These initial orbital
periods and the corresponding fiducial parameters are values that have been
observed in solar-type binaries raghavan2010survey, with previously reported
statistics Moe_2017 estimating the frequency of companions per decade of
orbital period of short-period ($\simeq 3\,$days) binary systems with $q>0.3$
to be $0.017\pm 0.007$.

Extended Data Fig. 8 shows an example fiducial model with
$P_{\mathrm{init}}=2\,\mathrm{d}$. Magnetic braking on the main sequence
reduces the orbital separation by a factor of $\sim 2$ until the onset of the
first stable mass transfer phase, which is when the donor reaches the red
giant branch. During this time ($t\sim 4.2$–$5.6$ Gyr in Extended Data Fig. 8)
the envelope of the primary is stripped, the secondary accretes mass, and the
binary’s semi-major axis increases to $\sim 1.7$ times its initial value, but
not enough to destabilize the planet’s orbit. The resulting binary system
forms an EL CVn-like binary with a period shorter than 10 days.

The mesa simulations of Chen et al.Chen_2017 predicted that a range of
$1.9\,$d $\lesssim P_{\mathrm{init}}\lesssim 2.4\,$d and $0.67\lesssim
q\lesssim 1$ can yield donors that undergo mass transfer at the base of the
red giant branch for $1.1M_{\odot}<M_{1}<1.25M_{\odot}$ ($\beta=0.5$ has been
assumed in this case), which is consistent with our fiducial model. They
additionally performed a population synthesis study and estimated a steady
production rate of EL CVn binaries $\approx 0.015\,\mathrm{yr}^{-1}$ over the
last few $\mathrm{Gyr}$, assuming a Miller & Scalo initial mass function in
the range $0.08$–$100$ $M_{\odot}$miller1979initial,eggleton1989distribution
and a constant star formation rate $5\,M_{\odot}\,\mathrm{yr}^{-1}$. We
calculate such a model to yield a $\approx 0.6\,\mathrm{yr}^{-1}$ production
rate of $1$–$2\,M_{\odot}$ stars, which implies that $\sim 2$–$3\%$ of red
clump stars may have formed from merging EL CVn-like binaries.

This number is roughly comparable to the fraction of clump stars which are
lithium-rich ($\sim 1\%$sneden1984search,yan2018nature,Zhang_2020_supp) or
R-type carbon stars ($\sim 0.1\%$izzard2007origin), which are thought to form
from similar merger processes. It is also broadly consistent with the rate of
merger remnantsrui2021asteroseismic inferred for red giants from transient
statisticskochanek2014stellar, close binary surveysraghavan2010survey, and red
giant binarityprice2020close. When applying the inferred EL CVn-like binary
merger fraction to the $>140$ substellar companions detected around red giants
RCdatabase, roughly 1 in $\sim 10^{2}$ companions may indeed orbit helium
white dwarf–red giant merger remnants if we assume that an order-unity
fraction of these exoplanet hosts are core helium-burning. Therefore, the
hypothesis that 8 UMi is such a remnant is plausible.

Unstable mass transfer begins at the end of the simulation using our fiducial
model when both the secondary’s core mass and the helium white dwarf’s mass
are $\approx\\!0.25\,M_{\odot}$, such that a stellar merger results in a
helium core mass of $\approx 0.5\,M_{\odot}$, similar to ordinary red clump
stars. To determine if the second, unstable mass transfer phase results in a
merger, we estimated the final semi-major axis $a_{f}$ of the binary from its
initial semi-major axis $a_{i}$ by assuming that some fixed fraction
$\alpha_{\mathrm{CE}}$ of the change in orbital energy is used to move the
envelope to infinityivanova2013common:

$|E_{\mathrm{bind}}|\sim\alpha_{\mathrm{CE}}\left(\frac{GM_{1c}M_{2c}}{2a_{f}}-\frac{GM_{1c}M_{2i}}{2a_{i}}\right),$
(6)

where $M_{1c}$ is the mass of the stripped helium white dwarf, and $M_{2i}$
and $M_{2c}$ are the total and core masses of the red giant prior to the
merger event. We calculated the binding energy of the envelope directly from
our stellar models, including internal (thermal) energy and recombination
energy, as

$|E_{\mathrm{bind}}|=\int^{M}_{M_{2c}}\left[u(m)+\epsilon(m)\right]\mathrm{d}m\,.$
(7)

Here, $u(m)$ and $\epsilon(m)$ are the specific potential and internal
energies of the red giant, respectively, and we defined the boundary of the
helium core to be where the hydrogen fraction falls below $1\%$. We used
$\alpha_{\mathrm{CE}}=1/3$, which is consistent with observed helium white
dwarf binariesscherbakCE. A stellar merger event is predicted when the post-
common-envelope orbital separation is sufficiently small such that the helium
core (of radius $R_{2c}$) of the giant is disrupted by the inspiraling helium
white dwarf. This occurs at an orbital separation $a_{*}=R_{2c}/f(q_{f})$,
where $q_{f}$ is the ratio of the masses of the red giant core and helium
white dwarf, and $f(q_{f})$ is an order-unity function given by Eggleton’s
formulaeggleton1983approximations ($f(q_{f})\approx 0.38$ for equal-mass
binaries). As demonstrated in Extended Data Fig. 9, all our models with
$P_{\mathrm{init}}\lesssim 2.3\,{\rm d}$ were predicted to attain final
orbital separations $a_{f}<a_{*}$ and thus resulted in stellar mergers. Our
mergers were assumed to occur with no mass loss, which we justify with the
observed low eccentricity of 8 UMi b. Given a planetary post-mass-loss
eccentricity of $e=\Delta M/M$, and assuming an initially circular orbit with
instantaneous mass loss, the star mass loss $\Delta M$ cannot be more than
$\sim\\!0.1\,M_{\odot}$ in a time shorter than the planet’s orbital period if
the planet’s nearly circular orbit is to be maintained.

## Data availability

TESS light curves processed by the SPOC pipeline are available from MAST
(https://archive.stsci.edu/). The spectra for $\mu\,$Pegasi is accessible at
http://polarbase.irap.omp.eu/. Astrometric measurements for 8 UMi are openly
available from the Gaia archive (https://gea.esac.esa.int/archive/). The HIRES
radial velocity measurements, ESPaDOnS spectra and spectropolarimetric data
products, ASAS-SN time series, traces of the MCMC sampling from the radial
velocity fits, MESA binary simulation inlists, and SED data are available at
https://zenodo.org/record/7668534.

## Code availability

The radial velocity fitting was performed using the exoplanet code
(docs.exoplanet.codes/). The Generalized Lomb-Scargle periodogram
implementation is available at (https://github.com/mzechmeister/GLS). TESS-SIP
for correcting TESS systematics is provided at
(https://github.com/christinahedges/TESS-SIP). The asteroseismic modelling was
performed using BASTA (https://github.com/BASTAcode/BASTA), the PARAM web tool
(http://stev.oapd.inaf.it/cgi-bin/param), MESA (https://docs.mesastar.org).
The binary module of MESA was used for binary simulations. Calibrated
asteroseismic scaling relations used asfgrid
(http://www.physics.usyd.edu.au/k2gap/Asfgrid/). Grids of isochrones publicly
available are MIST (https://waps.cfa.harvard.edu/MIST/), PARSEC
(https://github.com/philrosenfield/padova_tracks/releases/tag/v2.0), Dartmouth
and GARSTEC (https://zenodo.org/record/6597404), and BASTI (http://albione.oa-
teramo.inaf.it/).

Extended Data Figure 1: Posterior probability distribution of the fit to the
combined BOES/HIRES radial velocity data. The 16th, 50th, and 84th percentile
values of each fitted parameter are indicated with dashed lines. Extended Data
Figure 2: Constraints to the outer companion in the 8 UMi planetary system.
Contours indicate 67% highest density intervals of permissible mass and
separation values of the outer companion as estimated from the residuals of
radial velocity measurements in Figure 2 (purple), and from measurements of 8
UMi’s Gaia DR3-Hipparcos astrometric acceleration (green). These two
measurements jointly constrain the outer companion’s mass and separation,
which corresponds to the locus indicated by the shaded region between the
contours. Extended Data Figure 3: Stellar activity of the host star 8 UMi and
active red giant TYC 3542-1885-1. The chromospheric activity of both stars are
estimated using Ca II H and K indices ($S_{HK}$) computed from Keck/HIRES
spectra, with error bars indicating 1$\sigma$ (standard deviation)
uncertainties. (a-b) Variations of $S_{HK}$ with radial velocity from each
star. Included for each are the Spearman correlation factors ($R$) and two-
sided p-values ($p$) for the test whose null hypothesis is that $S_{HK}$ and
radial velocity are uncorrelated. (c-d) Generalized Lomb Scargle (GLS)
periodograms of radial velocity measurements and $S_{HK}$. The vertical dashed
line indicates 8 UMi b’s orbital period, and the horizontal lines indicate the
periodogram’s False Alarm Probability (FAP). Extended Data Figure 4: Spectral
features of 8 UMi and active red giant TYC 3542-1885-1.. Comparisons are
additionally made with the inactive, Li-normal giant $\mu$ Pegasi. (a-b) The
Ca II H and K absorption lines. (c) The 6707.8Å Li I absorption line.
Extended Data Figure 5: ESPaDOnS spectropolarimetry of the host star 8 UMi and
active red giant TYC 3542-1885-1 The least-squares deconvolution profiles in
each panel, from top to bottom, are that of Stokes V, null polarisation $N$,
and Stokes I, respectively. Error bars indicate 1$\sigma$ (standard deviation)
uncertainties for the profiles. Included are the Stokes $V$ mean longitudinal
magnetic field strength ($B_{Z}$) and its corresponding 1$\sigma$ (standard
deviation) uncertainty, polarimetric signal-to-noise ratio (SNR), and
observation times ($t$) in BJD - 2459000. Extended Data Figure 6:  Observed
photometric variations of 8 UMi. Time series photometry from (a) Hipparcos,
(b) ASAS-SN, and (c) systematics-corrected TESS Simple Aperture Photometry.
The standard deviation uncertainty for each photometric measurement is shown
with error bars. These are visible for the Hipparcos data, but smaller than
the symbol sizes for ASAS-SN and TESS data. The dispersion of the Hipparcos
and ASAS-SN time series, $\sigma_{\mathrm{disp}}$, are quantified as a
fraction of the star’s apparent magnitude. Generalized Lomb Scargle (GLS)
periodograms for the (d) Hipparcos, (e) ASAS-SN, and (f) systematics-corrected
TESS Simple Aperture Photometry light curves. The vertical dashed line
indicates 8 UMi b’s orbital period, and the horizontal lines indicate the
periodogram’s False Alarm Probability (FAP).  Extended Data Figure 7: Spectral
energy distribution of 8 UMi. The distribution was estimated using
$B_{T}V_{T}$ magnitudes from Tycho-2, the $JHK_{S}$ magnitudes from 2MASS, the
W1–W4 magnitudes from WISE, the $GG_{\rm BP}G_{\rm RP}$ magnitudes from Gaia,
and the NUV magnitude from GALEX. Red symbols represent the observed
photometric measurements, where the horizontal error bars represent the
effective width of the passband while the vertical error bars are 1$\sigma$
(standard deviation) photometric uncertainties. Blue symbols are the model
fluxes from the best-fit Kurucz atmosphere model (black), which have a reduced
$\chi^{2}$ of 1.3, with extinction $A_{V}=0.06\pm 0.02$ mag, $T_{\rm
eff}=4900\pm 75$ K, surface gravity $\log g=2.5\pm 0.5$ dex, and [Fe/H] =
$-0.5\pm 0.3$ dex. Integration of the (unreddened) model SED gives the
bolometric flux at Earth, $F_{\rm bol}=6.48\pm 0.22\times 10^{-8}$ erg s-1
cm-2.  Extended Data Figure 8:  Simulation of a stellar binary history for 8
UMi leading up to a stellar merger. This fiducial model is simulated using
$\beta=0.6$, $q=0.7$, and $P_{\mathrm{init}}=2\,\mathrm{d}$, with the stellar
merger occuring at the onset of unstable mass transfer at $t\approx 8.6\,{\rm
Gyr}$. (a) Binary separation (semi-major axis, s.a.) (purple solid line) and
orbital period (green dashed line) versus time for the simulated binary model.
(b) Primary total and core masses versus time. (c) Secondary total/core mass
versus time. Extended Data Figure 9:  Simulated white dwarf–red giant binaries
that successfully merge to produce a core-helium burning giant like 8 UMi.
These models are simulated using $\beta=0.6$ and $q=0.7$, with
$M_{1}=1.23\,M_{\odot}$ and $M_{2}=0.86\,M_{\odot}$. (a) Final total mass
$M_{\mathrm{tot,f}}$ and final helium core mass $M_{\mathrm{c,f}}$ of the
merger remnant. (b) Binary separation (semi-major axis, s.a.) and orbital
period before ($a_{\mathrm{i}}$) and after ($a_{\mathrm{f}}$) the common-
envelope event. The orange region represents $a_{\mathrm{f}}$ values that
result in a stellar merger. Extended Data Table 1:  Radial velocity
measurements of 8 UMi collected using the HIRES spectrograph atop the Keck-I
telescope from 19 May 2021 to 1 August 2022. Reported uncertainties are
1$\sigma$ (standard deviation) uncertainties.

Time | Radial velocity | Uncertainty
---|---|---
BJD - 2459000 | m/s | m/s
353.842103 | 34.810319 | 0.957495
361.902204 | 69.348529 | 0.888507
368.784719 | 48.809886 | 0.911906
373.801558 | 51.160183 | 0.869466
378.834098 | 5.876205 | 0.842353
378.835070 | 7.768937 | 0.847276
378.835996 | 4.595331 | 0.859393
378.870140 | -0.197723 | 0.894331
378.871077 | -1.580994 | 0.891074
378.872026 | -4.547195 | 0.912844
378.979199 | 14.606174 | 0.857701
378.980125 | 17.859138 | 0.896076
378.981074 | 16.502770 | 0.848254
384.890366 | -2.409111 | 0.990540
384.892484 | -4.921133 | 0.958773
384.894429 | -2.751882 | 0.903895
389.914801 | -19.275643 | 0.834250
389.915738 | -17.315992 | 0.936139
389.916674 | -15.740141 | 0.951262
395.864380 | -39.513886 | 0.955047
395.865318 | -37.492119 | 0.956622
395.866209 | -39.848328 | 0.941511
399.827438 | -31.820359 | 0.972085
399.828607 | -34.245779 | 1.021377
399.829741 | -33.843625 | 0.971329
406.739231 | -60.907537 | 1.026887
406.740134 | -60.100727 | 0.900744
406.741048 | -58.346060 | 0.952770
415.752084 | -27.386193 | 1.087321
415.753681 | -30.211521 | 1.063041
415.754700 | -26.923308 | 1.070932
415.757998 | -27.737135 | 1.078141
420.829269 | -49.413959 | 1.134881
420.830415 | -44.291389 | 1.021217
420.831688 | -45.008137 | 1.095143
435.773916 | 19.435892 | 1.090663
435.774865 | 19.687407 | 1.025351
435.775814 | 18.302992 | 1.008119
443.730761 | 24.779948 | 1.039300
443.731675 | 25.534491 | 1.101412
443.732636 | 23.593110 | 1.041690
450.766041 | 69.011527 | 1.207604
450.767025 | 68.430295 | 1.194408
450.768009 | 69.318575 | 1.264927
455.740426 | 62.917694 | 1.017182
455.741352 | 56.633304 | 1.050469
455.742266 | 58.825162 | 1.011381
470.711559 | 37.405981 | 1.119984
470.712497 | 35.467619 | 1.096883

Time | Radial velocity | Uncertainty
---|---|---
BJD - 2459000 | m/s | m/s
470.713446 | 35.582958 | 1.120459
478.709022 | -4.443548 | 1.153627
478.715029 | -7.003524 | 1.268035
478.720607 | -7.905698 | 1.112496
483.753253 | -50.993642 | 1.066348
483.754468 | -52.206761 | 1.257434
483.755672 | -49.098157 | 1.205983
489.704354 | -67.520930 | 1.201372
489.705523 | -70.438690 | 1.325950
489.706692 | -71.966822 | 1.216982
497.701247 | -59.438410 | 1.199675
497.702809 | -59.489978 | 1.199892
506.689152 | -57.215682 | 1.253242
506.690240 | -59.439143 | 1.182603
506.691351 | -59.210949 | 1.178573
513.697277 | -46.329758 | 1.231641
513.698481 | -48.825172 | 1.310779
513.699719 | -49.372107 | 1.139539
622.113710 | 28.831742 | 1.029991
622.114740 | 26.803767 | 1.150842
622.115794 | 29.397291 | 1.097965
626.086114 | 29.669555 | 1.173846
626.087202 | 29.863729 | 1.058872
626.088325 | 30.465299 | 1.134471
632.073919 | 42.695454 | 0.957066
632.074868 | 44.096309 | 0.999416
632.075828 | 43.932892 | 0.996506
655.010662 | 43.071189 | 0.939295
655.011599 | 41.502631 | 0.898865
655.012525 | 43.082613 | 0.915619
661.035709 | 33.081970 | 0.956038
661.036901 | 37.172227 | 0.894799
661.038059 | 32.319343 | 0.939563
672.030706 | -1.852284 | 0.967251
672.031759 | -3.129297 | 1.031975
672.032870 | -4.028580 | 0.936177
681.007997 | -43.712090 | 0.982126
681.008888 | -48.960588 | 0.960503
681.009791 | -47.199496 | 1.010990
691.000779 | -48.491071 | 1.150332
691.001717 | -46.239763 | 1.064292
691.002654 | -45.255098 | 0.997759
695.013168 | -47.220558 | 1.019411
695.014082 | -43.609635 | 1.043123
695.014996 | -45.622370 | 0.948686
700.948879 | -20.122784 | 1.002295
700.952375 | -19.824926 | 1.230983
711.897946 | 13.432848 | 0.980607
711.898907 | 11.327911 | 0.985397

Extended Data Table 1 (continued):  Time | Radial velocity | Uncertainty
---|---|---
BJD - 2459000 | m/s | m/s
711.899856 | 13.267244 | 1.085308
715.974755 | 37.686341 | 0.961920
715.975693 | 39.381356 | 0.998087
715.976630 | 37.921361 | 0.917527
737.813506 | 76.820012 | 0.909781
737.814536 | 76.766067 | 0.996631
737.815566 | 74.604152 | 0.918539
740.799098 | 62.368957 | 0.937384
740.800070 | 65.637292 | 0.875799
740.801019 | 67.465725 | 0.915763
741.796518 | 54.978361 | 0.888018
741.797409 | 51.933870 | 0.965281
741.798323 | 53.079849 | 0.865434
747.917120 | 33.196888 | 0.951404
747.918335 | 33.229634 | 0.994584
747.919574 | 36.687595 | 0.950376
749.986941 | 23.051076 | 0.871991
749.988017 | 18.465904 | 0.846402
749.989071 | 23.438575 | 0.963685
756.960219 | 2.667942 | 0.956022
756.961353 | -1.127702 | 0.926351
756.962418 | -0.344195 | 0.903171
759.944743 | -14.055632 | 0.993686
759.945773 | -14.769997 | 0.991786
759.946757 | -15.594268 | 0.884224
771.854751 | -50.035824 | 0.973484
771.855862 | -48.483816 | 1.025444
771.856973 | -49.680070 | 1.070451
789.800968 | -11.766739 | 1.007803
789.802218 | -10.835423 | 1.091427
789.803537 | -7.329680 | 1.093144
791.806519 | -13.067793 | 1.080876
791.807607 | -10.685886 | 1.084655
791.808834 | -10.084930 | 1.104502
792.739494 | -29.757211 | 1.138764
792.740535 | -28.673963 | 1.135497
792.741589 | -27.545748 | 1.123028

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