Eating planets makes you younger: The magnetic dynamo rejuvenation of GJ 504 by planetary engulfment

Astronomy & Astrophysics manuscript no. aa59144-26corr © ESO 2026 February 27, 2026 L etter to the E ditor Eating planets makes y ou y ounger: The magnetic dynamo rejuvenation of GJ 504 b y planetary engulfment S. Bellotti 1 , 2 , C. Pezzotti 3 , 4 , G. Buldgen 3 , A. A. V idotto 1 , D. Evensber get 1 , 5 , and E. Magaudda 6 1 Leiden Observatory , Leiden Univ ersity , PO Box 9513, 2300 RA Leiden, The Netherlands e-mail: bellotti@strw.leidenuniv.nl 2 Institut de Recherche en Astrophysique et Planétologie, Uni versité de T oulouse, CNRS, IRAP / UMR 5277, 14 avenue Edouard Belin, F-31400, T oulouse, France 3 ST AR Institute, Uni versité de Liège, Liège, Belgium 4 Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Roma, V ia Frascati 33, I-00040, Monteporzio Catone, Italy 5 Centre for Planetary Habitability (PHAB), Department for Geosciences, Univ ersity of Oslo, Oslo, Norway 6 Institut für Astronomie und Astrophysik, Eberhard-Karls Uni versität Tübingen, Sand 1, 72076 Tübingen, Germany Receiv ed ; accepted ABSTRA CT Conte xt. With the discov ery of a few thousand exoplanets, questions have been raised regarding star-planet interactions and whether the presence of a companion may a ff ect stellar properties. GJ 504 is an excellent tar get in this conte xt. This e volv ed ( ∼ 2 Gyr) Sun-like star has a short rotation period (3.4 d) and an intense magnetic activity lev el, as seen by the X-ray luminosity and the chromospheric diagnostics, which is in stark contrast with what would be expected at such an e volutionary stage. Aims. One possible explanation is that a close-in, Jupiter-mass planet was pushed starwards by the action of stellar tides, inducing a stellar spin-up and ultimately a rejuvenation of the stellar magnetic dynamo. By characterising the large-scale magnetic field and magnetised wind of GJ 504, we aim to provide additional observ ational constraints to test such scenario. Methods. W e analysed spectropolarimetric observations of GJ 504 collected with ESPaDOnS. Using Zeeman-Doppler imaging, we found a large-scale, dipolar , non-axisymmetric magnetic field with an average strength of 5.3 G, similar to that of evolv ed early- G type stars. W e fed the magnetic field information into our 3D magnetohydrodynamical simulation of the stellar wind and space en vironment of GJ 504, from which we constrained the wind-dri ven angular momentum loss ( ˙ J). W e then compared ˙ J to rotational ev olutionary tracks of GJ 504 for two scenarios: e volution with and without the engulfment of a close-in, Jupiter -mass companion. Results. Between the two scenarios, only the planetary engulfment can explain the observational constraints obtained previously in the literature, such as the stellar rotation and X-ray luminosity , and the ˙ J we derived and rescaled to account for underestimated magnetic field strength. Although there are many other stars with similar masses and rotation periods whose rotation evolution does not require planet engulfment, we also identified HD 75332 as a second candidate for planet engulfment, suggesting that GJ 504 may not be an isolated case. Ke y words. Stars: magnetic field – Stars: activity – Stars: e volution – Stars: winds – T echniques: polarimetric 1. Introduction Currently , 6042 e xoplanets ha ve been confirmed with v arious techniques (Nasa Exoplanet Archiv e 1 Christiansen et al. 2025). The precise characterisation of the exoplanet host stars is es- sential to fully understand the origin and history of these sys- tems (e.g. Danielski et al. 2022). On the one hand, stars gov ern and shape the ev olution of planetary systems, by determining the conditions for planetary formation, orbital migration, atmo- spheric erosion, and, notably , habitability . On the other hand, the fundamental properties of the host stars can be significantly in- fluenced by the presence of close-by planets, leading to mutual star-planet interactions (SPIs) of various types (tidal, radiative, magnetic, and wind; see V idotto 2025, for a recent revie w). An interesting target for studying SPIs is GJ 504, an iso- lated solar-like star (spectral type G0) with a mass of 1 . 22 M ⊙ , hosting a directly imaged substellar companion at a projected distance of ∼ 43 A U (Kuzuhara et al. 2013). The ev olution- ary state of GJ 504 is highly uncertain, with age estimations 1 As of Nov ember 2025, https: // exoplanetarchiv e.ipac.caltech.edu / varying from hundreds of millions of years to se veral gigayears. Previous studies on GJ 504 showed that the ages deriv ed from spectroscopic analyses (4 . 5 + 2 − 1 Gyr Fuhrmann & Chini 2015) and isochrone fitting (2 . 5 + 1 . 0 − 0 . 7 Gyr D’Orazi et al. 2017) are incompati- ble with the one based on activity indicators and gyrochronology ( ∼ 160 − 300 Myr Kuzuhara et al. 2013, e.g.), despite the large uncertainty . Moreo ver , the study of Bonnefo y et al. (2018) based on direct imaging and interferometry found plausible isochronal ages to be 21 ± 2 Myr and 4 . 0 ± 1 . 8 Gyr. As studied in Pezzotti et al. (2025), two possible scenarios can be in vok ed to reconcile the controversial findings of GJ 504’ s age. First, the rotational evolution of GJ 504 may hav e featured weakened magnetic braking (e.g. van Saders et al. 2016), dur - ing which the stellar large-scale magnetic field would not e ffi - ciently brake the stellar rotation. This is consistent with the ro- tation period value of 3.4 d. Second, the star possibly engulfed a close-by ( ≲ 1 A U) sub-stellar ( ≲ 3 M Jup ) companion, enhanc- ing its acti vity (Fuhrmann & Chini 2015; D’Orazi et al. 2017). This tidally dri ven SPI ev ent would increase the stellar rotation, leading to an enhanced X-ray luminosity and magnetic activ- Article number , page 1 of 9 A & A proofs: manuscript no. aa59144-26corr ity , overall rejuvenating the dynamo process sustaining the stel- lar magnetic field. The ev olutionary models for stellar rotation, Rossby number (that is, the ratio between rotation period and con vecti ve turnov er time), and X-ray luminosity of Pezzotti et al. (2025) corroborated that a planetary engulfment is a viable sce- nario and indicated an age of around 2 Gyr . The recent work of Lazovik & Barker (2026) shows that the dissipation of internal gravity wav es within stars is a ff ected by tidal SPIs. Specifically for GJ 504, a planetary engulfment can explain the short rotation period of the star . In this letter, we follow up on the work of Pezzotti et al. (2025) on GJ 504 and test whether the stellar wind-dri ven angu- lar momentum loss rate could be used as an additional constraint to discriminate between one of these two scenarios. W e anal- ysed spectropolarimetric observations of GJ 504 in order to re- construct the stellar lar ge-scale magnetic field and perform mag- netohydrodynamical simulations of the stellar wind. W e conte x- tualised these new observ ational constraints with the theoretical ev olution tracks of various quantities such as stellar rotation, X- ray luminosity , angular momentum loss, and total angular mo- mentum. Such a comparison allowed us to further discriminate whether GJ 504 ev olved without a planet or with a close-in, Jupiter mass planet that was engulfed. This letter is structured as follows. W e outline the large-scale magnetic field reconstruction in Sect. 2 and then describe the 3D magnetohydrodynamical simulations of the GJ 504’ s stel- lar wind in Sect. 3. The comparison between observational con- straints and stellar ev olutionary models is described in Sect. 4. W e finally draw our conclusions in Sect.5. 2. Magnetic imaging W e observed GJ 504 with ESPaDOnS in April 2025. W e pro- vide the fundamental properties of GJ 504 in T able 1 and a de- scription of the observations in Appendix A. W e characterised the large-scale component of GJ 504’ s magnetic field from cir- cularly polarised spectra by means of Zeeman-Doppler imaging (ZDI; for more information see Semel 1989; Donati et al. 1997). W e employed the zdipy code described in Folsom et al. (2018) and adopted the weak-field approximation, for which Stokes V is proportional to the deriv ativ e of Stokes I with respect to wa ve- length (e.g. Landi Degl’Innocenti 1992). As outlined in Folsom et al. (2018), the local unpolarised line profiles are modelled with a V oigt kernel. W e performed a χ 2 r minimisation between the me- dian of the observed Stokes I LSD profiles and its model to find the best-fitting parameters of the kernel. W e found the optimal values for depth, Gaussian width, and Lorentzian width to be 0.8, 1.63 km s − 1 , and 1.7 km s − 1 . For the ZDI input parameters, we used the values of the stel- lar rotation period (P rot = 3 . 4 d), projected equatorial velocity ( v eq sin( i ) = 6 . 3 km s − 1 ), and inclination ( i = 18 ◦ ) as listed in T able 1. W e set the maximum degree of spherical harmonic co- e ffi cients, ℓ max = 10, b ut a lower value could ha ve been used without changing the results as most of the magnetic energy is stored in the lo w- ℓ degrees. W e set the limb darkening coe ffi cient to 0.6 (Claret & Bloemen 2011). Finally , the di ff erential rotation search was inconclusi ve; hence, we assumed solid body rotation. The Stokes V LSD profiles and their ZDI fits are shown in Fig. B.1. The reconstructed ZDI map is sho wn in Fig. 1. The magnetic field has a mean strength of ⟨| B V |⟩ = 5 . 3 G and a maximum of | B max | = 12 . 9 G. The magnetic ener gy is ⟨ B 2 ⟩ = 0 . 35 × 10 2 G 2 and 88% of it is stored in the poloidal component. Of this component, 61% is stored in the dipolar component, 28% T able 1. Properties of GJ 504. Property V alue Spectral T ype G0V a V [mag] 5.22 b Distance [pc] 17.6 c T e ff [K] 6205 ± 20 b log g [cgs] 4 . 29 ± 0 . 07 b M / H [dex] 0 . 22 ± 0 . 04 b Mass [M ⊙ ] 1 . 29 ± 0 . 05 d Radius [R ⊙ ] 1 . 35 ± 0 . 04 e Age [Gyr] 2 . 11 ± 0 . 46 d Ro 0 . 62 d P rot [d] 3.4 b v eq sin i [km s − 1 ] 6 . 3 ± 1 . 0 b i [ ◦ ] 18 b Notes. The listed properties are: identifier , spectral type, V band magni- tude, distance, e ff ectiv e temperature, surface gravity , metallicity , stellar mass, stellar radius, stellar age, Rossby number, rotation period, equa- torial projected velocity , and inclination. The references are: a ) Gray et al. (2001), b ) D’Orazi et al. (2017), c ) Gaia Collaboration (2020), d ) Pezzotti et al. (2025), and e ) Di Mauro et al. (2022). in the quadrupolar component, and 9% in the octupolar compo- nent. The field is mostly non-axisymmetric, since only 25% of the magnetic ener gy is accounted in the ℓ > 0 and m = 0 modes. Finally , the axisymmetric-poloidal component accounts for 21% and the axisymmetric-toroidal component for 54%. 3. Stellar wind modelling W e simulated the stellar wind of GJ 504 using the Space W eather Modelling Framew ork ( SWMF , Tóth et al. 2012) and specifically the Alfvén wa ve solar model ( AWSoM , van der Holst et al. 2014) using the ZDI reconstructed map described in Sect 2 at the inner boundary of the model. A detailed description of the methodol- ogy behind the wind models can be found in the recent works of, for instance, Ó Fionnagáin et al. (2019) and Alv arado-Gómez et al. (2022). The models fix the radial magnetic field compo- nent at the inner boundary to the ZDI-deriv ed values (see Fig. 1), while the transv erse components are left to e v olve as the numer - ical solution relaxes towards steady state. Except for the stellar mass, radius, and rotation period, the other parameters used in the model are the same as those used for the solar wind and in our previous models (e.g. Ev ensberget et al. 2023). In Fig. 2, we present the steady-state output of our simu- lations centred on the star . The wind speed ( u ) increases with the distance from the star , while the local wind density ( ρ w ) and magnetic field (B w ) decrease. Furthermore, the wind exhibits a spiral shape owing to stellar rotation. The white streamlines in- dicate the magnetic field embedded in the stellar wind: open field lines are located at the stellar magnetic poles and closed field lines are visible in the regions where the magnetic polarity switches ov er . W e computed the mass loss rate of the wind ( ˙ M) by integrat- ing the mass flux over a closed spherical surface ( Σ ) centred on the star following Eq. 8 in V idotto et al. (2014b). W e estimated ˙ M = 1 . 07 × 10 − 13 M ⊙ / yr, which is about 5.4 times larger than the solar wind-mass loss rate. W e note that ˙ M should not vary with the choice of surface, Σ , as long as such surface encloses the star . W e found only a variation of 0.6% by varying the spherical sur- Article number , page 2 of 9 Bellotti et al.: The rejuvenated dynamo of GJ 504 Fig. 1. Reconstructed large-scale magnetic field map in flattened po- lar view . From the left, the radial, azimuthal, and meridional compo- nents of the magnetic field vector are illustrated. Concentric circles rep- resent di ff erent stellar latitudes: -30 ◦ , + 30 ◦ , and + 60 ◦ (dashed lines), as well as the equator (solid line). The radial ticks are located at the rotational phases when the observ ations were collected (see T able A.1). The colour indicates the polarity and strength of the magnetic field. face radius across the simulation domain. W e then computed the angular momentum loss rate ( ˙ J), which regulates the spin-down of the star with age, using Eq. 9 in V idotto et al. (2014b). W e estimated ˙ J = 7 . 53 × 10 31 erg , which is conserv ed at most within 5%. This value is a factor of 23 larger than the average mass loss rate of the Sun computed for cycle 23-24 (Finle y et al. 2019a). 4. Rotational ev olution models W e follo wed Pezzotti et al. (2025) and studied two e volution- ary scenarios for GJ 504 (see Appendix C for the model setup): one without tidally interacting Jupiter -mass companions and one in which the star was orbited by a Jupiter-mass, close-in planet with an initial orbital distance of a in = 0 . 025 A U at the moment of dispersal of the protoplanetary disc. The planet subsequently migrated starward due to tidal interactions. Pezzotti et al. (2025) found that the engulfment scenario agrees better with the short rotational period and bright X-ray luminosity of the star . Our results are shown in Fig. 3, where we compare the ev o- lutionary tracks of the normalised stellar rotation rate, Ω / Ω ⊙ (with Ω ⊙ = 2 . 9 × 10 − 6 Hz), the angular momentum loss, ˙ J wind , the X-ray luminosity , L X , and the angular momentum, J. The tracks were computed with initial values of Ω in ( Ω ⊙ ) = 3 . 2 , 5 , 18, which were chosen to reproduce the 25th, 50th, and 90th rota- tional percentiles in open clusters and stellar associations (e.g. Eggenberger et al. 2019). In the ˙ J wind panel, we include the angular momentum loss rate deriv ed in Sect. 3 ( ˙ J wind , ZDI ). This value alone is in agree- ment with the tracks of isolated e volution (solid lines), b ut these Fig. 2. Simulated stellar wind of GJ 504. The star is at the centre and its rotation axis lies along the positive z ⋆ . The x ⋆ − y ⋆ plane is coloured by the total wind v elocity . The Alfvén surf ace is the region of space where the local wind speed matches the Alfvén w ave speed, v A B w / p 4 πρ w (in cgs units), and is depicted as a translucent surface with two lobes, as ex- pected for stars with dominant dipolar large-scale field configurations. The colour bar indicates the total wind velocity (u tot ). same tracks fail to reproduce the observ ed rotation period, X- ray luminosity , and semi-empirical global angular momentum of the star . When the value ˙ J wind , ZDI is rescaled by a constant factor , motiv ated by the fact that ZDI is known to underesti- mate the magnetic field strength (Y adav et al. 2015; Lehmann et al. 2019), it becomes compatible with the planetary engulf- ment tracks. Specifically , the evolutionary tracks including en- gulfment (for Ω between 3.2 and 4 . 0 Ω ⊙ ) match all the four inde- pendent observational constraints. A more detailed explanation on the scaling factors can be found in Appendix D. 5. Conclusions W e followed up on the recent work of Pezzotti et al. (2025) on GJ 504, a Sun-like star that has a controversial e volution- ary state. Pezzotti et al. (2025) compared the rotation and X-ray luminosity of GJ 504 derived from stellar e volution models to observations. T o reconcile the observations with the theoretical tracks at the age of the star , the authors proposed a scenario in which GJ 504 engulfed a close-in, Jupiter-mass planet at an age of ∼ 1 − 2 Gyr . This tidally induced SPI may have spun up the star and in turn rejuvenated its dynamo, leading to enhanced mag- netic activity . With this work, we analysed the large-scale mag- netic field and magnetised wind of GJ 504 and found additional constraints that support the planetary engulfment scenario. W e compared the observational constraint on the stellar an- gular momentum loss to the evolutionary tracks of GJ 504 ob- tained from a scenario in which the star ev olved alone and an- other in which the star engulfed an exoplanet. If the star is as- sumed to ev olve in isolation, the computed ˙ J is the only quantity that matches the ev olution. Howe ver , if ˙ J is rescaled to counter- act the fact that Zeeman Doppler imaging may underestimate the magnetic field strength, ˙ J becomes incompatible with the star ev olving in isolation. When considering the engulfment of a planet instead, all observational constraints (stellar rotation, X-ray luminosity , total angular momentum, and rescaled ˙ J ) are Article number , page 3 of 9 A & A proofs: manuscript no. aa59144-26corr Fig. 3. Evolutionary tracks of GJ 504. The scenarios without (solid lines) and with engulfment (dashed lines) are shown. The spikes in the tracks correspond to the maximum transfer of angular momentum from the planetary orbit to the star , that occurs when the planet reaches the Roche limit. From the left: the stellar surface rotation rate, with the observational constraint taken from Di Mauro et al. (2022); stellar wind-driv en angular momentum loss tracks with the unscaled ˙ J wind deriv ed in Sect. 3 (white marker), the ˙ J wind , B × 5 obtained by scaling the magnetic field strength (orange marker), and ˙ J wind , ZDI rescaled by a factor of 20 (gray marker); X-ray luminosity , with the black dot indicating the observational constraint of Pezzotti et al. (2025); and global angular momentum, with the black dot showing the semi-empirical angular momentum, which is the model momentum of inertia multiplied by the surface rotation rate from Di Mauro et al. (2022). consistent with the ev olutionary tracks. Ultimately , this provides further support of the planetary engulfment scenario proposed by Pezzotti et al. (2025). T o understand whether GJ 504 is an isolated case, we per- formed a similar analysis for HD 75332, which is another Sun- like star lying in the vicinity of GJ 504 in terms of mass, rota- tion period, and magnetic field properties (see Appendix E). W e found analogous results to GJ 504, although other stars with sim- ilar properties do not show this anomaly (Pezzotti et al. 2026). Additional observ ations from a dedicated campaign are required to provide more constraints on these phenomena, such as radial velocity follow-ups to study oscillations and constrain the age of GJ 504. In general, from both spectroscopic studies of chem- ical enrichment (e.g. Soares et al. 2025) and tidal SPI studies (Lazovik & Barker 2026), an occurrence rate of 20% for plane- tary engulfments with detectable signatures for Sun-like stars is expected. Acknowledgements. SB and AA V acknowledge funding by the Dutch Research Council (NWO) under the project "Exo-space weather and contemporaneous sig- natures of star-planet interactions" (with project number OCENW .M.22.215 of the research programme "Open Competition Domain Science- M"). AA V and DE acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 817540, ASTR OFLOW). AA V acknowledges funding from the Dutch Research Council (NWO), with project number VI.C.232.041 of the T al- ent Programme V ici. GB acknowledges funding from the Fonds National de la Recherche Scientifique (FNRS) as a postdoctoral researcher. CP thanks the Bel- gian Federal Science Policy O ffi ce (BELSPO) for the financial support in the framew ork of the PRODEX Program of the European Space Agency (ESA) un- der contract number 4000141194. EM is supported by the Deutsche F orschungs- gemeinschaft under grant STE 1068 / 8. 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The data were reduced with the LIBRE-ESPRIT pipeline (Donati et al. 1997). The first observation on April 5th recorded a significantly lo wer signal-to-noise ratio (S / N) compared to the other observations, due to the presence of clouds that attenuated the signal. For this reason the observ ation was discarded from the analyses described in the following sections. The signal-to-noise ratio at 650 nm per resolution element (2 . 6 km s − 1 velocity bin) per polarimetric sequence of the other observ ations ranges between 146 and 390, with an a verage of 329. In the ne xt sections, the observ ations will be phased with the following ephemeris HJD = HJD 0 + P rot · n cyc , (A.1) where HJD 0 is the heliocentric Julian Date reference (the first one of the time series for each star , see T able A.1), P rot is the rotation period of the star (see T able 1), and n cyc represents the rotation cycle. W e applied least-squares decon v olution (LSD Donati et al. 1997; K ochukhov et al. 2010) to the Stok es I and V spectra using the lsdpy code which is part of the Specpolflow software (Folsom et al. 2025) 2 . This is a cross-correlation technique that decon volves an observ ed spectrum with a line list to obtain an av erage, high-S / N line profile. W e used the V ienna Atomic Line Database 3 (V ALD, Ryabchikov a et al. 2015) to generate a synthetic line list corresponding to a stellar temperature of 6250 K and surface gravity of log g = 4 . 5 (cm s − 2 ). When performing LSD, we excluded spectral regions a ff ected by telluric bands and the H α line: [627,632], [655.5,657], [686,697], [716,734], [759,770], [813,835], and [895,986] nm. In total, we used 7100 atomic spectral lines and we adopted a normalisation wa velength and Landé factor (that is, the magnetic sensitivity of the line indicated as g e ff ) of 700 nm and 1.2 (see Kochukho v et al. 2010, for more details). The output is Stokes I and V LSD profiles with augmented S / N. W e re-normalised the Stokes I LSD profiles continuum to unity by fitting a linear model to the region outside the line, to include residuals of continuum normalisation at the le vel of the spectra. The Stokes V profiles were correspondingly rescaled with the same fit. Appendix B: ZDI fit of Stokes V LSD profiles W e fitted the observed Stokes V LSD profiles down to χ 2 r = 1 . 26, from an initial value of 2.0 which corresponds to a featureless magnetic map. In this ZDI reconstruction, we remo ved the observation on April 5th at 10:43:38 UT since the S / N was visibly lo wer than the other observations, which allo wed us to improv e the target χ 2 r . The de viation of the χ 2 r from 1.0 may come from the unaccounted intrinsic e volution of magnetic features, as well as the assumption of solid body rotation. Donahue et al. (1996) measured P rot values for GJ 504 between 3.23 d and 3.41 d, and attributed this variation to di ff erential rotation. The fact that we cannot constrain such phenomenon from our GJ 504 data does not imply a null surf ace shear . Rather , the limiting f actor is likely the time span of our observations, which is too short for the surface latitudinal shear to hav e distorted the magnetic features enough to be detected. Appendix C: Rotational ev olution model setup T o compute the rotational and X-ray luminosity tracks of GJ 504 for the ev olutionary scenarios with and without engulfment, we provided the structural tracks computed with the CLES stellar ev olution code (Scuflaire et al. 2008) to a SPI code (Pri vitera et al. 2016; Rao et al. 2018; Pezzotti et al. 2021, 2025). In this code, the treatment of two main SPIs is implemented: the gra vitational-tidal one, accounting for the exchange of angular momentum between the host star’ s surface and the planetary orbit, and the radiative one, through which the mass loss from planetary atmosphere due to the host star high energy radiation is estimated. For the e volution of the host star surface rotation rate, the impact of magnetised winds is considered by means of the solar calibrated prescription of Matt et al. (2015, 2019). Solid body rotation is assumed for GJ 504 on the pre-main sequence and main sequence phases (Rao et al. 2021). The ev olution of the X-ray luminosity is consistently computed with respect to the one of the surface rotation rate, by using the recalibrated R x − R o relationship of Johnstone et al. (2021), as in Pezzotti et al. (2021), where R x is the ratio between the X-ray and the bolometric luminosity , and Ro is the stellar Rossby number . Appendix D: Scaling the torque The normalisation factors used to reconcile the angular momentum loss estimated from ZDI maps with the ones from rotational models depend on the considered braking law and modelling assumptions (see e.g. Evensber get & V idotto 2024). In Finley et al. (2019b), the authors found that torque estimates based on rotation-e volution models, as in Matt et al. (2015) are systematically larger than the ones derived from ZDI-based wind models (e.g. Finley & Matt 2018). They suggest sev eral causes at the source of this discrepancy , among which potential issues with the rotation-ev olution models or systematic e ff ects from the ZDI technique in underestimating field strengths. 2 A vailable at https: // github .com / folsomcp / LSDpy 3 http://vald.astro.uu.se/ Article number , page 5 of 9 A & A proofs: manuscript no. aa59144-26corr T able A.1. Journal of ESPaDOnS observ ations for GJ 504. Date UT HJD n cyc S / N σ LSD B ℓ S index log R ′ HK H α index Ca ii IR T [hh:mm:ss] [10 − 5 I c ] [G] *Apr 05 09:00:26 2460770.8805 0.00 88 24.4 . . . . . . . . . . . . . . . Apr 05 09:05:18 2460770.8839 0.00 233 8.1 12 . 01 ± 4 . 25 0 . 361 ± 0 . 132 − 4 . 362 ± 0 . 213 0 . 320 ± 0 . 003 0 . 861 ± 0 . 004 Apr 05 10:43:38 2460770.9522 0.02 146 14.6 10 . 01 ± 7 . 02 0 . 414 ± 0 . 266 − 4 . 284 ± 0 . 360 0 . 320 ± 0 . 004 0 . 860 ± 0 . 007 Apr 06 07:57:57 2460771.8372 0.28 390 5.0 2 . 53 ± 2 . 53 0 . 344 ± 0 . 066 − 4 . 391 ± 0 . 115 0 . 319 ± 0 . 002 0 . 853 ± 0 . 003 Apr 06 09:33:16 2460771.9034 0.30 369 5.1 1 . 67 ± 2 . 58 0 . 353 ± 0 . 067 − 4 . 374 ± 0 . 112 0 . 319 ± 0 . 002 0 . 855 ± 0 . 003 Apr 06 11:24:55 2460771.9809 0.32 382 5.5 4 . 88 ± 2 . 50 0 . 354 ± 0 . 066 − 4 . 374 ± 0 . 110 0 . 319 ± 0 . 002 0 . 852 ± 0 . 003 Apr 06 12:57:43 2460772.0453 0.34 373 5.0 2 . 96 ± 2 . 59 0 . 355 ± 0 . 069 − 4 . 372 ± 0 . 115 0 . 320 ± 0 . 002 0 . 850 ± 0 . 003 Apr 06 14:02:05 2460772.0900 0.36 372 4.8 5 . 02 ± 2 . 61 0 . 333 ± 0 . 072 − 4 . 409 ± 0 . 131 0 . 319 ± 0 . 002 0 . 851 ± 0 . 003 Apr 07 07:53:26 2460772.8340 0.57 358 5.9 3 . 26 ± 2 . 82 0 . 365 ± 0 . 077 − 4 . 356 ± 0 . 124 0 . 320 ± 0 . 002 0 . 855 ± 0 . 003 Apr 07 09:40:27 2460772.9083 0.60 318 6.0 5 . 96 ± 3 . 11 0 . 345 ± 0 . 088 − 4 . 388 ± 0 . 151 0 . 319 ± 0 . 002 0 . 858 ± 0 . 003 Apr 07 11:10:03 2460772.9706 0.61 300 6.8 6 . 30 ± 3 . 29 0 . 352 ± 0 . 094 − 4 . 376 ± 0 . 158 0 . 319 ± 0 . 002 0 . 856 ± 0 . 003 Apr 07 12:52:14 2460773.0415 0.64 351 6.1 5 . 36 ± 2 . 84 0 . 345 ± 0 . 080 − 4 . 389 ± 0 . 139 0 . 320 ± 0 . 002 0 . 859 ± 0 . 003 Apr 07 14:34:45 2460773.1127 0.66 254 8.2 15 . 60 ± 4 . 12 0 . 346 ± 0 . 149 − 4 . 386 ± 0 . 254 0 . 319 ± 0 . 003 0 . 860 ± 0 . 004 Apr 08 08:11:11 2460773.8464 0.87 334 5.7 3 . 87 ± 2 . 94 0 . 374 ± 0 . 083 − 4 . 341 ± 0 . 129 0 . 322 ± 0 . 002 0 . 863 ± 0 . 003 Apr 08 10:05:34 2460773.9258 0.90 305 6.8 − 1 . 14 ± 3 . 30 0 . 357 ± 0 . 095 − 4 . 368 ± 0 . 156 0 . 320 ± 0 . 002 0 . 862 ± 0 . 003 Apr 08 12:19:40 2460774.0189 0.92 369 4.6 − 3 . 72 ± 2 . 67 0 . 362 ± 0 . 072 − 4 . 360 ± 0 . 116 0 . 320 ± 0 . 002 0 . 858 ± 0 . 003 Apr 09 06:41:40 2460774.7842 1.15 331 6.2 0 . 04 ± 3 . 03 0 . 333 ± 0 . 090 − 4 . 410 ± 0 . 162 0 . 319 ± 0 . 002 0 . 856 ± 0 . 003 Apr 09 08:04:19 2460774.8416 1.17 361 5.4 0 . 94 ± 2 . 70 0 . 358 ± 0 . 072 − 4 . 367 ± 0 . 119 0 . 319 ± 0 . 002 0 . 854 ± 0 . 003 Apr 09 09:39:25 2460774.9076 1.18 368 5.1 − 1 . 03 ± 2 . 62 0 . 352 ± 0 . 069 − 4 . 377 ± 0 . 116 0 . 318 ± 0 . 002 0 . 854 ± 0 . 003 Apr 09 11:04:47 2460774.9669 1.20 345 5.6 − 1 . 65 ± 2 . 85 0 . 345 ± 0 . 079 − 4 . 389 ± 0 . 136 0 . 319 ± 0 . 002 0 . 855 ± 0 . 003 Notes. The columns are the following: 1) date of the observation, 2) universal time of the observation, 3) heliocentric Julian date, 4) rotational cycle as computed from Eq. A.1, 5) signal-to-noise ratio per resolution element per polarimetric sequence at 650 nm, 6) RMS noise le vel of Stokes V signal in units of unpolarised continuum, 7) longitudinal magnetic field, 8) S -index, 9) log R ′ HK index, 10) H α index, and 11) Ca ii infrared triplet index. The first observ ation marked with * was not used due to lo w signal-to-noise ratio. Article number , page 6 of 9 Bellotti et al.: The rejuvenated dynamo of GJ 504 Fig. B.1. Time series of Stokes V LSD profiles and the ZDI models for GJ 504. The observations are shown in black and the models in red. The numbers on the right indicate the rotational cycle computed from Eq. A.1. The horizontal dashed line represents the zero point of the profiles, which is shifted vertically based on the rotational phase for visualisation purposes. In Finle y et al. (2019b), they sho w that multiplying the ˙ J estimates by 20, for their sample of stars with ZDI-based wind models, a general better overlap is obtained with respect to the torques estimated from rotation-ev olution models. By comparing rotational tracks computed for a standard solar model, with the same method and braking law as in Pezzotti et al. (2025), we found that a factor of 20 is indeed needed to reconcile the rotational tracks at at the solar age with the torque determined at the solar maximum. For consistency , in this work we multiplied the ˙ J deriv ed in Sect.3 by a factor 20 to reconcile the predictions from theoretical rotational tracks with the semi-empirical estimates of the torque. In the ˙ J wind panel of Fig. 3, we indicated the angular momentum loss we deriv ed in Sect. 3 multiplied by 20 ( ˙ J wind , ZDI × 20 = 1 . 51 × 10 33 erg). W e also note that the minimum amount of scaling for ˙ J wind , ZDI to be compatible with the engulfment scenario (precisely , the ev olutionary track of 3 . 2 Ω ⊙ ) is a factor of approximately four . Owing to the f act that ZDI recov ers only a fraction of the total magnetic field strength (see e.g. Y adav et al. 2015), we decided to perform a simulation of the stellar wind with augmented magnetic field strength. In practice, we follo wed Evensber get et al. (2023) and multiplied the input radial magnetic field strength of ZDI by a factor of fiv e, and then characterised the wind properties in a similar manner to Sect. 3. W e obtained ˙ J wind , B × 5 = 7 . 15 × 10 32 erg. As sho wn in Fig. 3, both the rescaled values of ˙ J are compatible with the planetary engulfment scenario. Appendix E: Comparative analysis with HD 75332 GJ 504 fundamental parameters are close to τ Boo (M = 1 . 39 M ⊙ , P rot = 3 . 1 d, age = 1 . 9 Gyr) and HD 75332 (M = 1 . 21 M ⊙ , P rot = 3 . 56 d, age = 0 . 9 Gyr), as can be seen in T able 1. In this appendix, we present a similar analysis for HD 75332 to that described in Sect. 4, using the magnetic properties provided in Bro wn et al. (2021), in order to assess whether it could have undergone an ev olutionary history similar to GJ 504. τ Boo is excluded from this comparison because the star is known to host a hot Jupiter planet (Butler et al. 1997), hence the engulfment scenario of a tidally interacting hot Jupiter would render the analysis inconsistent. W e searched for the optimal fundamental stellar parameters of HD 75332 by means of a global minimisation technique carried out with SPInS (Lebreton & Reese 2020), on the basis of a grid of stellar tracks computed with the CLES stellar ev olution code (Scuflaire et al. 2008). W e used T e ff [K] = 6258 ± 44, log g = 4 . 34 ± 0 . 03 and [M / H] = 0 . 05 ± 0 . 03 from Brown et al. (2021), and the bolometric luminosity derived from the Gaia DR3 (Gaia Collaboration 2020) G-band (L bol [L ⊙ ] = 1 . 99 ± 0 . 01) as in Buldgen et al. (2019), as constraints for the modelling. The optimal v alues that we found are: M = 1 . 15 ± 0 . 06 M ⊙ , R = 1 . 19 ± 0 . 03 R ⊙ , Age = 1 . 78 ± 0 . 68 Gyr. Article number , page 7 of 9 A & A proofs: manuscript no. aa59144-26corr W e then computed ev olutionary tracks for HD 75332 as shown in Fig. E.1. W e assumed the same two scenarios as for GJ 504: ev olution without planet, and with an inward migration of a giant planet. In the scenario without planet, we considered three initial surface rotation rates Ω in = 3 . 2 , 5 , 18 Ω ⊙ and in the scenario with a planet, we considered a 3 M J companion at initial orbital distance a in (A U) = 0 . 025, and host star initial surface rotation rate Ω in ( Ω ⊙ ) = 3 . 5. W e selected this value for the initial surface rotation rate for analogy with the case of GJ 504, for which the engulfment and consequent compatibility with the observational and semi-empirical constraints for Ω , L X , ˙ J wind and J is obtained for models with Ω in ( Ω ⊙ ) ∼ 3 . 2 − 4. In this scenario, the planet is engulfed by the host star at ∼ 1 . 5 Gyr. It is worth recalling that the choice of initial mass orbital distance for the planet, together with the initial surf ace rotation rate for the host star , is degenerate. Therefore, choosing a di ff erent set of initial parameters may lead to a similar result, as discussed in Pezzotti et al. (2025). In Fig. E.1, we show the comparison between observ ational constraints and the ev olutionary tracks for Ω in , angular momentum loss, L X , and total angular momentum. The observational constraints of Ω in and L X were taken from Brown et al. (2021) and V idotto et al. (2014a), respectively . For the angular momentum loss, the black circle indicates the value computed using the prescription of Finley & Matt (2018). The dipolar , quadrupolar and octupolar components of the large-scale poloidal magnetic field of HD 75332 were taken from T able 3 in Brown et al. (2021). In Fig. E.1, the solid lines indicate the scenario without planet engulfment, while the dashed line represents the track relative to the engulfment scenario. W e find that all the observational constraints (stellar rota- tion, angular momentum, X-ray luminosity , and total angular momentum) are reconciled with the theoretical tracks only with the engulfment scenario, in a similar manner as for GJ 504. Analogously , the observed angular momentum loss is consistent with the ev olutionary track associated with the planetary engulfment when multiplied by a factor of 20. From this comparative analysis, we infer that GJ 504 and HD 75332 may ha ve e xperienced a similar ev olutionary history , potentially in volving the engulfment of a giant planet. Howe ver , se veral uncertainties persist regarding the magnetic properties of stars occupying this particular region of the mass–period parameter space. In other words, the magnetic properties of only GJ 504, HD 75322 and τ Boo have been reconstructed in the literature. Pezzotti et al. (2026) in vestigate the activity–rotation–age relation for 13 G-type and F-type stars with high-quality asteroseismic constraints from the Kepler LEGACY sample. The authors report that none of these K e pler stars, despite having highly accurate and precise fundamental parameters like rotation periods and eR OSIT A X-ray luminosities, exhibit anomalous properties similar to those of GJ 504 and HD 75332. Specifically , the rotation periods are not substantially shorter than model predictions and the X-ray luminosities are not enhanced giv en their stellar age. Article number , page 8 of 9 Bellotti et al.: The rejuvenated dynamo of GJ 504 Fig. E.1. Evolutionary tracks computed for HD 75332. The scenarios without (solid lines) and with (dashed line) the engulfment of a 3 M J planet at an initial orbital distance a in = 0 . 025 A U are included. F or the stellar initial surface rotation rate, we considered v alues of Ω in ( Ω ⊙ ) = 3 . 2 , 5 . 0 , 18, as representativ e of the ev olution as slow , moderate and fast rotator (Eggenberger et al. 2019). The spike featured by the dashed line indicates the e ff ect the planetary engulfment has on the stellar property . In the top-left panel, the black dot sho ws the observ ed surface rotation rate as in Brown et al. (2021). In the top-right panel, the black dots shows the estimates of angular momentum loss derived by using the prescription in Finley & Matt (2018) and the values in T able 2 of Bro wn et al. (2021). The gray square shows the mean value of the angular momentum loss estimates multiplied by a f actor 20. In the bottom-left panel, the back dot sho ws the observ ational value of the X-ray luminosity from V idotto et al. (2014a). In the bottom-right panel, the black dot sho ws the semi-empirical angular momentum obtained by multiplying the best-fit stellar model momentum of inertia by the surface rotation rate in Bro wn et al. (2021). Article number , page 9 of 9