Naomi Havron
email: naomi.havron@mail.huji.ac.il

Alex A De Carvalho

Anne-Caroline Fiévet

Anne Christophe

Alex De Carvalho

3-4-year-old children rapidly adapt their predictions and use them to learn novel word meanings

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Prediction has been proposed to be a fundamental aspect of cognition, supporting multiple levels of cognitive processing and learning [START_REF] Clark | Whatever next? Predictive brains, situated agents, and the future of cognitive science[END_REF]. In language processing, for example, there is evidence that adults form predictions as to the likelihood of different syntactic structures, and update these predictions whenever they encounter a structure that does not match their expectations. Adults' initial expectations are based on a lifetime of linguistic experience, but as researchers manipulate exposure to structures in the input, the expectation to encounter these structures increases or decreases rapidly [START_REF] Fine | Rapid Expectation Adaptation during Syntactic Comprehension[END_REF][START_REF] Kaschak | What this construction needs is generalized[END_REF], though see also Harrington Stack, James & Watson, in press). Adults might have developed the ability to flexibly change their predictions through their lifelong expertise with language, as suggested by studies showing an increase in prediction in older ages (e.g., [START_REF] Huettig | Anticipatory eye movements are modulated by working memory capacity: Evidence from older adults[END_REF] and with literacy [START_REF] Mishra | Spoken language-mediated anticipatory eyemovements are modulated by reading ability-Evidence from Indian low and high literates[END_REF]. However, it may also be that adults' ability to adapt to the current linguistic environment is a consequence of language learning occurring through prediction and error-minimization. In this vein, several researchers have proposed that prediction is important for language acquisition (e.g., [START_REF] Chang | Becoming syntactic[END_REF]Gambi, Pickering, & Rabagliati, 2016;Sari Ylinen, Bosseler, Junttila, & Huotilainen, 2017). To explore this question, we examine whether 3-4 year-old children draw on recently encountered information to revise their predictions about the likely syntactic category of upcoming words, and exploit these revised predictions to infer novel words' meanings.

We draw on two lines of research: Findings from the priming literature suggesting that children revise their syntactic expectations both in production and comprehension (e.g., [START_REF] Peter | When and how do children develop knowledge of verb argument structure? Evidence from verb bias effects in a structural priming task[END_REF][START_REF] Thothathiri | Give and take: Syntactic priming during spoken language comprehension[END_REF]; and evidence that infants can use syntactic context to infer the meaning of novel words (e.g., [START_REF] Huang | Word learning in linguistic context: Processing and memory effects[END_REF][START_REF] Oshima-Takane | Early verb learning in 20-month-old Japanese-speaking children[END_REF][START_REF] Waxman | 24-Month-Old Infants Interpretations of Novel Verbs and Nouns in Dynamic Scenes[END_REF][START_REF] Bernal | Syntax constrains the acquisition of verb meaning[END_REF].

Research on syntactic priming in childrenthat is, their tendency to reuse recently encountered structures and process them fasterprovides evidence that children learn from the distribution of structures in their input. [START_REF] Branigan | Consistent and cumulative effects of syntactic experience in children's sentence production: Evidence for error-based implicit learning[END_REF] found that children's production of passives increased after priming, and increased even more in a second session held a week later. This suggests that priming is not just a result of activation of syntactic representations, but a manifestation of learning through adjusting expectations to the distribution of structures in the input. Recent studies also found that the more surprising or infrequent a prime is, the larger the priming effect children showas predicted by error-based learning models of priming (e.g., [START_REF] Peter | When and how do children develop knowledge of verb argument structure? Evidence from verb bias effects in a structural priming task[END_REF]. Nonetheless, these findings do not speak to the crucial question of whether children's revised expectations are used when encountering unfamiliar input, such as novel words. To test whether children use their adapted expectations to learn, we focus on children's prediction of a novel word's syntactic category from its linguistic context.

Children create expectations about the syntactic category of a following word, by relying on the distribution of structures in the input. For example, articles are usually followed by nouns (which tend to denote objects or agents), and pronouns are usually followed by verbs (which tend to denote actions).

Infants as young as 18-months can already use these contexts to infer the possible meaning of novel words.

When listening to a sentence like "It's a dax", they infer that "dax" refers to an object. Likewise, when listening to a sentence like "It's daxing", infants infer that "dax" refers to an action [START_REF] He | Verb learning in 14-and 18-month-old English-learning infants[END_REF]. This syntactic bootstrapping may account for children's ability to rapidly learn the meaning of novel words [START_REF] Gleitman | The Structural Sources of Verb Meanings[END_REF].

Although children are able to exploit context to build expectations about what will come next, there is little direct evidence that children update expectations rapidly enough to affect learning, and most importantly, no evidence that these updated expectations can guide the learning of novel linguistic information (Rabagliati, Gambi, & Pickering, 2015). In the current study we ask whether exposure to a small amount of input that children can successfully process, triggers changes to their predictions about syntactic categories, when confronted with novel words. We manipulate the distribution of familiar nouns and verbs, within a syntactic frame which can contain either a noun or a verb. We present one group of children with this frame preceding familiar nouns, and the other with this same frame preceding familiar verbs. We expect that children will use this distributional information to infer the syntactic category of a novel word appearing in this contextexpecting this novel word to be a noun if they have heard familiar nouns in this context, and to be a verb it they have heard familiar verbs in this context. If they do, this would be the first evidence that children's expectations are updated rapidly enough to allow prediction-based learning, and most importantly, that these adjusted expectations can guide language acquisition. This would simultaneously support a unified account of language processing and language learning, and shed light on the mystery of the speed and accuracy of children's language acquisition.

METHOD

All data and materials have been made publicly available via the Open Science Framework and can be accessed at https://osf.io/zzd9y/. The design and analysis plans were preregistered at the Open Science Framework and can also be accessed with the same link.

Participants

Our final sample consisted of 45 monolingual French-speaking children between the ages of 39.1 and 50.6 months (23 in the verb condition, 13 boys and 10 girls, mean age 45.3 months, SD = 3.26; 22 in the noun condition, 9 boys and 13 girls, mean age 45.4 months, SD = 3.3). They were recruited and tested in a middle-to high-socioeconomic status school in Paris, or in our babylab through direct contact with parents belonging to our database (these children can also be assumed to come from middle-to high-socioeconomic status homes). Out of 55 children originally tested, four were removed for technical difficulties, three for fussiness and crying, and one for naming the unfamiliar objects (e.g., saying "anteater" for a stuffed-animal we used in one video). We removed trials with more than 50% missing data, as well as any child with more than two missing trials, resulting in the exclusion of two more children. Written parental consent was obtained for all children.

We also tested 47 adult university students, 23 in the verb-condition and 24 in the noun condition, as a control group. We report their results briefly, with the full data and results available on the OSF.

Design

In French, la petite can either be followed by a noun (e.g., la petite grenouille, "the little frog") or by a verb (e.g., la petite dort, "the little one is sleeping"). It is more likely to be followed by a noun: a search in the Paris child-directed-speech corpus [START_REF] Morgenstern | What can child language tell us about prepositions ?[END_REF] found 720 instances where it was followed by a noun, and only 6 where it was followed by a verb. We manipulated the syntactic category that this context predicted by randomly assigning children to one of two conditionsa verb-condition and a noun-condition. In the induction phase, the verb-condition children were exposed to sentences in which la petite was predictive of verbs, that is, it was consistently followed by familiar verbs; while the nouncondition children were exposed to sentences in which it was predictive of nounsconsistently followed by familiar nouns. This phase was meant to create expectations for a different syntactic category in the different groups. In the test phase, we examined whether children utilize their adapted expectations to infer the meaning of novel words. If children adapted their expectations based on the few sentences they heard, then when hearing the same frame followed by a novel word (which could refer to either an action or an object), children from the verb-condition should be more likely to look at a girl performing a novel action, compared to children from the noun-condition; such a result would suggest they were more likely to categorize the novel word as a verb, on the basis of its preceding syntactic context.

Materials and Procedure

Participants were tested individually either in a quiet room in their school, or in our babylab in a soundattenuated double-walled booth. They were sitting facing a 27-in. screen positioned 70 cm away from them.

Eye gaze was recorded by Eyelink-1000 placed below the screen (operating in remote mode). We used a 5-point calibration.

The induction phase included six trials -four induction trials and two fillers. On each of these trials, the participant saw two videos played side-by-side-on the screen: one showing a little girl performing an action, and another showing the same girl holding an object. We showed the same girl on both sides of the screen to prevent participants from choosing which one is la petite based on which child they judge to be Two of the trials from the induction phase were filler items, which used an unambiguous syntactic structure (either c'est une Noun, "it's a Noun" or Elle Verb, "she's Verbing"'), and directed the children to look at the opposite video. For example, if a participant was in the verb-condition, they heard four la petite Verb sentences (e.g., la petite dort, "the little one is sleeping") and two C'est une Noun sentences (e.g., c'est une poussette, "this is a baby-stroller"). We used these two fillers so that participants are not always asked to look at the action (or the object in the noun-condition), but instead, realize that the woman can refer to either of the two videos. A difference between the two groups in the test phase should not therefore be attributed to them predicting that the woman in the experiment will always talk about the actions (or the objects), but to them predicting that the specific phrase la petite will be followed by either a verb or a noun.

The order of the trials was randomized.

In the test phase, consisting of three trials, participants still saw two videos, but this time the little girl in the videos was performing a novel action (which does not have a name in French) or holding an unfamiliar object (which does not have a name in French). While watching the videos play side by side, the participant heard Oh, regarde, la petite Novel-Word, "oh look, the little one is Novel-Wording" / "the little Novel-Word" (e.g., Oh, regarde, la petite nuve ! "Oh look, the little one is nuving" / "the little nuve!"). The three test trials featured three different novel words (nuve, dase, and bamoule), each presented with one novel object and one novel action. Children in both conditions saw the same videos and heard the exact same sentences. The prosody of the test sentences was the same as that of the induction sentencesambiguous as to whether the final word is a noun or a verb. Note that even if there remain some prosodic cues that bias towards one interpretation (verb or noun), this does not affect the validity of the experiment, since both groups hear the exact same sentence, while watching the same videos. Therefore, the prosody cannot create any artefactual difference between groups. In order to ascertain that it is possible to interpret the novel word in the test sentences as referring either to a noun or a verb, we conducted an online survey, in which 26 adult native French speakers were asked to listen to the test sentences (without the visual context), and choose whether the novel word referred to an object, or to an action that a girl is performing.

Participants judged the novel word to have referred to an action 31% of the time, confirming that the novel word could be interpreted as either a noun or a verb.

Each trial lasted less than a minute, with the full experiment lasting about 8 minutes.

All videos can be accessed on the OSF.

Additional information

In a fourth and final test-trial, participants watched a boy perform a novel action and the same boy holding a novel object, they were directed to look at le petit pirdale. Since participants were always exposed to la petite, and never to le petit (masculine version of la petite), we wanted to see whether what they have learned would generalize to le petit. This single trial is purely exploratory and we report the full results on the OSF.

Statistical Analysis

To test our hypothesis that children will use the information they were exposed to in the induction phase to infer the meaning of the novel words in the test phase, we conducted two statistical tests.

We first ran a cluster-based permutation analysis testing for a significant difference between conditions (as for example in Dautriche, Swingley, & Christophe, 2015; see [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF], for a formal presentation of the analysis itself). We used R (R core team, 2017) and the package eyetrackingR [START_REF] Dink | _eyetrackingR_. R package version 0.1[END_REF], and first down-sampled the data by averaging to one sample every 20 ms. For each time sample, the analysis runs a mixed-effects model testing for the effect of condition (on the arc-sin transformed proportion of looks toward the action video) with a random intercept for participant (we did not add a random intercept for item because there were only three items). Adjacent time-points with a tvalue greater than a predefined threshold (t = 1.5) are grouped together into a cluster. This analysis was conducted on the entire trial (0 to 10 seconds from the beginning of the trial). Note that an effect may exist from the beginning of the trial since participants have heard the sentence played one time before the videos reappeared. Our preregistered analysis was a cluster-based permutation analysis with a t-test, since at the time of preregistration, we had no way to run a mixed-effects permutation analysis. Results for the t-test permutation analysis are similar, and available on the OSF.

Our second analysis was a mixed-effects regression (using the lme4 package, [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF] comparing the overall looking time at the action video, averaged across the whole trial, between the two conditions. The analysis included a random intercept for participant. We added the analysis of the overall looking time for two reasons: First, the cluster-based permutation analysis is a conservative test. Since we make no prior assumptions about when our effect will happen, we lose power when the effect is not highly situated, which can be expected in such an ambiguous context. Second, even strong advocates for this analysis recommend to supplement it by a more standard comparison of looking time [START_REF] Delle Luche | Infant Behavior and Development A methodological investigation of the Intermodal Preferential Looking paradigm : Methods of analyses , picture selection and data rejection criteria[END_REF].

RESULTS

The cluster-based analysis revealed a marginally significant cluster (p = 0.054), between 3360 ms and 5100 ms after the beginning of the trial, coinciding with the first repetition of the target word during the test (see fig. 3): during that time-window, children from the verb-condition looked more at the action video than children from the noun-condition. Children from the verb-condition are consistently looking more at the action video than children from the noun condition (note that the target sentence was also heard once just before the beginning of the trial).

The mixed-effects regression conducted on the average overall looking time per participants found a large effect of condition: Children from the verb-condition (M = 0.602, SD = 0.117), were significantly more likely to look at the action video than children from the noun-condition (M = 0.482, SD = 0.139, β = .189, SE = .06, t= 3.142, p = .003, Cohen's d = 0.941), suggesting that children from the verb-condition were more likely to interpret the novel word as referring to the action than children in the noun-condition (see fig. 4).

Adult control group

We found the same effect of condition in adults as we did in young children, except that the difference between conditions was larger for adults. The full results can be accessed on the OSF

DISCUSSION

In the current study, we investigated whether children create predictions about the distribution of syntactic categories in a new environment, and draw on these to acquire word meanings. We found that children who heard examples of la petite + familiar verbs were more likely to infer that a novel word produced after la petite referred to an action, than children who heard la petite + familiar nouns sentences. This suggests that children did not only rapidly adapt their expectation to encounter a specific syntactic category (as was previously found in priming studies with children of this age, e.g., [START_REF] Thothathiri | Give and take: Syntactic priming during spoken language comprehension[END_REF], but also utilized their adapted predictions to learn. Importantly, our design included filler items within the induction phase, to exclude the possibility that children were biased to look at the action-video (or object-video) without having to take into account the specific sentencesit is thus unlikely that our effect is the result of a simple bias for either action or object-videos. This is the first study demonstrating that children adapt their predictions and use these adapted predictions to guide their learning of novel linguistic input.

One limitation of the present study is that since we do not have a control condition with no induction, it is possible that only children in one condition changed their predictions; for instance, children in the noun-condition might have looked at the novel object because it was the default choice of interpretation, meaning only the verb-condition children changed their predictions. This would be in-line with previous studies, which found larger priming effects for the less-frequent structure (e.g., [START_REF] Kholodova | Syntactic Priming in a Structurally Biased Language: The Role of Cross-Linguistic Differences in Language Learning, Talk presented at Many Paths to Language[END_REF].

Children showed different expectations after only four induction trials, which implies rapid adaptation and high sensitivity to structures in the input. This rapidity would be particulary useful since words seem to follow a "bursty" distribution in language [START_REF] Altmann | Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words[END_REF].

Parents may repeatedly use la petite+verb when talking about a doll or a little girl, but revert back to the more common la petite+noun when changing the subject. It would be interesting to test in the future whether children form predictions that are conditioned on the context or speaker, as has been found in adults (e.g., Kamide, 2012; Kroczek & Gunter, 2017)or whether they would also generalize to new speakers and contexts. This experiment could be interpreted as showing that information provided to the languageprocessing system affects the language-learning system. However, in the sense that processing changes children's expectations, it produces the same kind of effect that we would normally call learning, and there is no sense in talking about two different systems. Language acquisition is in fact a process by which the child is learning to process language [START_REF] Chang | Becoming syntactic[END_REF][START_REF] Pickering | An integrated theory of language production and comprehension[END_REF]. As the child hears la petite before familiar verbs, she processes these sentences to both comprehend them, and change the model she relies on for processing and learning novel linguistic materials. Thus, whether the next sentence contains a word she knows (processing) or she does not know (learning), she will rely on her adapted expectations, to predict to what category the word following la petite will belong.

Our findings show that prediction does not only facilitate, but also guides learning. This means that predictions do not only help children learn by reducing the cost associated with processing the input, thus clearing resources for learningthey also structure the space of possibilities for meaning. As to the exact mechanisms by which children compute and use their expectations, there are several possible accounts.

Under the predictive-coding framework, the brain is thought of as a prediction machine, whose role is to capture the structure of input it encounters. The brain accomplishes this by predicting future input, and correcting its predictions when it encounters a prediction error. This is achieved through a hierarchical generative model that aims to minimize error within a bidirectional cascade of information [START_REF] Clark | Whatever next? Predictive brains, situated agents, and the future of cognitive science[END_REF][START_REF] Sohoglu | Predictive top-down integration of prior knowledge during speech perception[END_REF]. Our results are in line with such a mechanism, but they are also in line with other mechanisms of learning through prediction. For example, children could be creating predictions using analogy (see Bar, 2015); or they could be updating their predictions by cumulating frequenciesnot privileging evidence of error over correct predictions (for a discussion of the difference between this account and error-based predictions, see [START_REF] Corlett | Prediction error during retrospective revaluation of causal associations in humans: fMRI evidence in favor of an associative model of learning[END_REF].

The importance of our findings does not apply only to ambiguous sentences containing novel words. They might also explain how children initially learn unambiguous contexts. According to the semantic seed hypothesis [START_REF] Christophe | Bootstrapping the syntactic bootstrapper[END_REF], infants could manage to learn the meaning of a handful of very frequent words [START_REF] Bergelson | At 6-9 months, human infants know the meanings of many common nouns[END_REF][START_REF] Clark | Whatever next? Predictive brains, situated agents, and the future of cognitive science[END_REF], group them into objects and actions [START_REF] Carey | The origin of concepts[END_REF], and use these known words to learn to predict action-words after certain linguistic contexts, and object-words after others. They may then use these expectations to constrain the meaning of novel words [START_REF] Gleitman | The Structural Sources of Verb Meanings[END_REF][START_REF] He | Verb learning in 14-and 18-month-old English-learning infants[END_REF]. Our results illustrate how children rapidly form these predictions, and suggest a mechanism which could be useful not only in cases where the structure is ambiguous, but also for fully unambiguous syntactic contexts (such as articles and personal pronouns).

To conclude, it was previously suggested that children make rapid changes to their linguistic expectations following exposure to new linguistic evidence, and that they use this information when processing and learning new linguistic materials. We found that 3-4-year-old children indeed make rapid use of prediction at the syntactic level, and use newly-adjusted expectations to infer novel word meaning.

Prediction may thus be a key component not only in language processing in expert language users, but in children's language acquisition.

Fig. 1 :

 1 Fig. 1: Sample trial (target side is counterbalanced).

Figure 2 :

 2 Figure 2: Soundwave and pitch for one noun phrase (la petite balle, top), one verb phrase (la petite mange, middle), and one phrase with a novel word (la petite dase, bottom).

Figure 3 :

 3 Figure 3: Proportion of looks towards the action video in the test phase for the two conditions

Figure 4 :

 4 Figure 4: Mean overall proportion of looks towards the action video in the test phase for the two condition

smaller or younger. During the presentation of the two videos side-by-side, a women's voice (the last author) asked the child to look at one of the videos in a child-friendly fashion. For instance, for the pair of videos showing a girl holding a frog on one side, and a girl sleeping on the other side, participants assigned to the noun-condition would hear a sentence such as "Oh, regarde, la petite grenouille !" -"Oh look, the little frog!". In contrast, participants assigned to the verb-condition would hear "Oh, regarde, la petite dort !" -"Oh look, the little one is sleeping!". For a sample trial see Fig.1. The prosody was the same for noun and verb sentences. This was done by intentionally picking a prosody that is appropriate for both nouns or verbs, in which the three words belong to the same prosodic phrase; otherwise it would have been possible to disambiguate by using different prosodic structures (as shown in de Carvalho,[START_REF] De Carvalho | Phrasal prosody constrains syntactic analysis in toddlers[END_REF] de Carvalho, Dautriche, & Christophe, 2016; see Fig.2for a graphical depiction of the prosodic contour, see a full acoustic analysis on the OSF).

Acknowledgements

This work was supported by a postdoctoral grant to the first author from the French Embassy in Israel and

The Victor Smorgon Charitable Fund, and by the French Agence Nationale de la Recherche (grants n° ANR-13-APPR-0012, ANR-10-IDEX-0001-02 PSL* and ANR-10-LABX-0087 IEC). We thank Axel


Travis S Metcalfe

Jennifer L Van Saders

Sarbani Basu

Derek Buzasi

William J Chaplin

Ricky Egeland

Rafael A Garcia

Patrick Gaulme

Daniel Huber

Timo Reinhold

Hannah Schunker

Keivan G Stassun

Thierry Appourchaux

Warrick H Ball

Timothy R Bedding

Sébastien Deheuvels

Lucía González-Cuesta

Rasmus Handberg

Antonio Jiménez

Hans Kjeldsen

Tanda Li

Mikkel N Lu

Ma

Mos

Martin B Nielsen

Anthony Noll

Zeynep C ¸elik Orhan

Sibel Örtel

Ângela R G Santos

Mutlu Yildiz

Sallie Baliunas

Willie Soon

Typeset using L A T E X twocolumn style in AASTeX63

Keywords: Stellar activity, Stellar evolution, Stellar oscillations, Stellar rotation

Most previous efforts to calibrate how rotation and magnetic activity depend on stellar age and mass have relied on observations of clusters, where isochrones from stellar evolution models are used to determine the properties of the ensemble. Asteroseismology employs similar models to measure the properties of an individual star by matching its normal modes of oscillation, yielding the stellar age and mass with high precision. We use 27 days of photometry from the Transiting Exoplanet Survey Satellite to characterize solar-like oscillations in the G8 subgiant of the 94 Aqr triple system. The resulting stellar properties, when combined with a reanalysis of 35 yr of activity measurements from the Mount Wilson HK project, allow us to probe the evolution of rotation and magnetic activity in the system. The asteroseismic age of the subgiant agrees with a stellar isochrone fit, but the rotation period is much shorter than expected from standard models of angular momentum evolution. We conclude that weakened magnetic braking may be needed to reproduce the stellar properties, and that evolved subgiants in the hydrogen shell-burning phase can reinvigorate large-scale dynamo action and briefly sustain magnetic activity cycles before ascending the red giant branch.

INTRODUCTION

Studies of long-term magnetic variability in solar-type stars rely on measurements of chromospheric activity obtained over many decades. Fortunately, the collection of such observations started in the late 1960s from the Mount Wilson Observatory (Wilson 1978) and continued for more than 35 years. A similar program at Lowell Observatory (Hall et al. 2007) began in the early 1990s and is still ongoing, with the composite time-series for some stars now approaching half a century (Egeland 2017). With sufficiently frequent sampling during each observing season, the modulation from individual active regions can reveal the stellar rotation period (Baliunas et al. 1983), while changes between seasons can constrain latitudinal differential rotation from the slow migration of active regions through the magnetic cycle (Donahue et al. 1996). Such long-term data sets have provided high-quality snapshots of magnetic variability in dozens of solar-type stars (Böhm-Vitense 2007;Brandenburg et al. 2017), but the evolutionary thread that connects them is difficult to establish due to uncertainties in the basic stellar properties such as mass and age (Metcalfe & van Saders 2017).

Asteroseismology with the Transiting Exoplanet Survey Satellite (TESS, [START_REF] Ricker | Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series[END_REF]) is poised to revolutionize our understanding of the evolution of magnetic variability in solar-type stars. It provides nearly uninterrupted time-series photometry with a 2-minute cadence spanning at least 27 days, which is sufficient to detect solar-like oscillations in many F-and G-type dwarfs and subgiants down to V∼7 (Schofield et al. 2019). The detection of global oscillation properties such as the frequency of maximum oscillation power (ν max ) and the mean frequency spacing between consecutive radial overtones (∆ν), when combined with spectroscopic properties such as the effective temperature and metallicity (T eff , [Fe/H]), can typically determine the stellar mass with an uncertainty of 6% and the stellar age within about 20% (Serenelli et al. 2017). The identification of individual oscillation frequencies can cut these uncertainties in half (Creevey et al. 2017), and even larger improvements in the age precision are possible for subgiants that exhibit mixed-modes, which couple gravity-driven g mode oscillations in the stellar core with pressure-driven p mode oscillations in the envelope (Deheuvels & Michel 2011;[START_REF] Li | [END_REF].

In this paper, we demonstrate the power of combining ground-based magnetic variability data with asteroseismic measurements of basic stellar properties from TESS. Our initial application is to the 94 Aqr triple system (HD 219834), which includes a blended primary consisting of a G8 subgiant (Aa) and a K3 dwarf (Ab) in a 6.3 year orbit, and a resolved secondary K2 dwarf (B) separated by 13 arcseconds (Fuhrmann 2008). In Section 2 we provide an overview of the observations, and in Section 3 we reanalyze the archive of chromospheric activity measurements from the Mount Wilson survey (Baliunas et al. 1995) for both the blended primary (A) and the resolved secondary (B) to determine the activity cycle and rotation periods. All three components are blended in the TESS observations, but the subgiant produces the only detectable asteroseismic signal because the K dwarfs oscillate with a much lower amplitude and higher frequency. In Section 4 we analyze and model the subgiant oscillations to determine the basic stellar properties from asteroseismology, and in Section 5 we establish the accuracy of these results with independent estimates of the subgiant radius, mass and age. In Section 6 we combine the rotation period from Mount Wilson data with the stellar mass and age from TESS to model the angular momentum evolution of the subgiant, demonstrating that weakened magnetic braking (van Saders et al. 2016) may be needed to explain the current rotation period. Finally, in Section 7 we summarize and discuss our results, including the idea that evolved subgiants can sustain a "born-again" dynamo before ascending the red giant branch.

OBSERVATIONS

Mount Wilson HK data

We use observations from the Mount Wilson Observatory (MWO) HK project (Wilson 1978;Vaughan et al. 1978;Baliunas et al. 1995) to study the long-and shortterm variability of magnetic activity in 94 Aqr A and B. The HK Project HKP-1 (1966HKP-1 ( -1978) ) and HKP-2 (1978HKP-2 ( -2003) ) spectrophotometers obtained counts through 1 Å triangular bandpasses centered on the Ca ii H & K (hereafter HK) line cores at 3968.470 Å and 3933.664 Å, respectively, as well as two 20 Å pseudo-continuum bands, R centered at 4001.067 Å, and V centered at 3901.068 Å (Vaughan et al. 1978). Emission in the HK line cores has long been known to be a signature of surface magnetic flux (see Linsky & Avrett 1970, for a review), and the disk-integrated HK emission from the Sun reveals the solar cycle (e.g. White & Livingston 1981;Egeland et al. 2017). The ratio of core to pseudo-continuum counts,

S = α MWO (N H + N K )/(N R + N V )
, where α MWO is a calibration factor, defines the now-standard S-index of magnetic activity. The pair 94 Aqr Aa and Ab were not resolved in the MWO observations, so the 94 Aqr A time series represents the sum of surface fluxes from these components. However, the G8 subgiant contributes approximately 97% of the flux in the relevant bandpasses (see Section 5.1).

TESS photometry

TESS observed 94 Aqr in 2-minute cadence for 27 days during Sector 2 of Cycle 1 (2018Aug 22-2018 Sep 20). We used the target pixel files produced by the TESS Science Processing Operations Center [START_REF] Jenkins | Proc. SPIE[END_REF] to extract light curves. A preliminary detection of solarlike oscillations was made with a light curve produced using simple aperture photometry, selecting all pixels with flux above three times the median absolute deviation of a median stacked image over the full observing sector. The final light curve was produced using the photometry pipeline 1 (Handberg et al., in prep.) maintained by the TESS Asteroseismic Science Operations Center (TASOC, Lund et al. 2017), which is based on software originally developed to generate light curves from data collected by the K2 mission (Lund et al. 2015).

Figure 1 shows the postage stamp for 94 Aqr. The large TESS pixels mean that the components of the 94 Aqr system are separated by less than one pixel on the detector. However, we made an effort to extract separate light curves for the two components. We built custom aperture masks around well-separated portions of the combined stellar image, conducted photometric extractions using those masks, and detrended the resulting light curves against spacecraft pointing data using a second-order two-dimensional polynomial fit, which has 1 https://tasoc.dk/code/ worked well for Kepler data in the past [START_REF] Buzasi | IAU General Assembly[END_REF]. Our goal was to construct aperture masks which were dominated by the wings of the images of the two stars, which might then allow us to separate the two stellar contributions. Despite our detrending efforts, light curves resulting from such aperture masks tended to be dominated by photometric jitter resulting from spacecraft motion, and we were unable to unequivocally separate the target light curves using this approach.

Derived luminosity

We derived an updated luminosity for 94 Aqr Aa from speckle observations of the close (0. 15) binary A component and the Gaia DR2 parallax of the resolved B component (see Section 5.2). The total V magnitude of the A component is 5.18 ± 0.01 (Fabricius et al. 2002), while the magnitude difference between Aa and Ab from speckle imaging is 3.1 (Tokovinin et al. 2015). The bolometric correction (-0.04) was deduced from an extrapolation of VandenBerg & Clem (2003, their Fig. 26), adopting T eff = 5461 ± 40 K from Gray et al. (2006) 2 , the parallax of 94 Aqr B adjusted for a small systematic offset (e.g., Stassun & Torres 2018;Zinn 2019), and interstellar extinction A V = 0.02 +0.07 -0.02 (see Section 5.1). The luminosity deduced from these parameters is L Aa = 3.31 +0.22 -0.07 L .

ACTIVITY CYCLES AND ROTATION

The resolved components of the 94 Aqr system (A and B) were observed by the Mount Wilson program during the years 1967-2003. The S-index was measured during annual observing seasons, each covering time spans between two and six months. From these data sets, we used several methods to estimate the activity cycle period and the rotation period for each star.

Each S-index time series shows long-term variability due to magnetic activity cycles. We computed the Lomb-Scargle periodogram of the full S-index time series for each component to search for the activity cycle period. We fit a sinusoid to the data using the highest periodogram peak as the initial period guess. The peak heights at the derived periods were used to estimate the period uncertainties. Following Montgomery & O'Donoghue (1999), we estimated the uncertainty of the peak with frequency f as σ(f ) = 6/N • σ(m)/(πT a), where N is the number of data points, T is the time baseline of the observations, and a is the amplitude of the sinusoid. We computed the root-mean-square deviation σ(m) = σ 2 • (1 -h peak ), where σ 2 is the variance of the zero-mean time series, and h peak is the normalized peak height at the derived period. We obtained activity cycle periods of 19.35 ± 0.18 yr and 9.13 ± 0.03 yr for 94 Aqr A and B, respectively (see Figure 2). We validated this analysis with two other methods, the autocorrelation function and a time-period analysis using a Morlet wavelet (Mathur et al. 2010;García et al. 2014;Buzasi et al. 2016). These analyses gave similar results.

The number of data points per observing season at Mount Wilson increased around 1980, revealing large variability which we attribute to active regions rotating in and out of view. From the seasonal data, Baliunas et al. (1996) measured rotation periods of 42 days and 43 days for the A and B components, while Olspert et al. (2018) found 43.4 ± 1.9 days and 34.8 ± 0.9 days, respectively. We performed an independent analysis of the Mount Wilson data sets, with three teams analyzing them seasonally and four teams analyzing the complete time series globally. The teams applied a range of different analysis techniques to both stars in the system, including application of the discrete Fourier transform (DFT), performing sinusoid fits to individual seasons and studying a histogram of the results, applying autocorrelation functions, and time-period wavelet analysis. In the case of 94 Aqr A, there was excellent agreement amongst the different methods, and we report a median rotation period of P rot = 46.9 ± 1.9 days (see Figure 3). For 94 Aqr B, the teams could not reach a consensus on the statistical significance of any potential detections of rotation from the seasonal data sets.

For the resolved B component, the activity cycle period can be attributed unambiguously to the K2 dwarf. For the blended A component, the G8 subgiant (Aa) contributes approximately 97% of the flux in the relevant bandpasses (see Section 5.1). Consequently, the 3% of the flux contributed by the K3 dwarf (Ab) would need to vary by roughly an order of magnitude to explain the observed S-index variation of up to 30% on both rotational and activity cycle timescales. Such modulations would be unprecedented (e.g., see Soon et al. 1994), so we identify the G8 subgiant as the source of the S-index variability. Note that comparable rotation periods have been observed in other G-type subgiants, including HD 182572 (41 days, Baliunas et al. 1996), andKIC 8524425 (42 ± 3 days, García et al. 2014). The implications of the observed activity cycle, and the possibility of a "born-again" dynamo in evolved subgiants, are discussed in Section 7.

ASTEROSEISMOLOGY OF 94 Aqr Aa

Extracting the oscillation parameters

We compute the power spectral density (PSD) of the TESS light curve (see Section 2.2) to analyze the stellar oscillations. Because the signal to noise ratio (S/N) of the oscillations is relatively low, six teams analyzed the oscillation spectrum to agree on a frequency set. The frequency analysis involves taking into account the background noise caused by surface granulation (e.g., Harvey et al. 1988), then extracting the star's eigenmodes (see Figure 4). Because we are dealing with a subgiant star, the latter involves considering mixed dipolar (l = 1) modes, where acoustic waves excited in the convective envelope couple with internal gravity waves in the core.

By definition, a mixed mode has a dual character, being both a p mode and a g mode. The solution of the continuity equation by Shibahashi (1979) led to an implicit expression for the mixed mode frequency ν pg as

tan θ p = q tan θ g , (1)
where θ p and θ g are the phase functions of ν pg with respect to the p mode and g mode frequencies, and q is the coupling factor. The phase function θ p is given by:

θ p = π (ν pg -ν np,1 ) ∆ν(n p ) (2)
where ∆ν

(n p ) = [1 + α(n p -n max )] ∆ν (3)
and θ g is given by:

θ g = π 1 P 1 1 ν pg - 1 ν ng,1 . (4)
When there is no coupling, q = 0 and there are no mixed modes, so ν pg = ν np,1 . Otherwise, the solutions to Eq. ( 1) provide the frequencies of the mixed modes.

Our computation of mixed modes is based upon Mosser et al. (2015). We first assume that the frequencies of radial modes ν np,0 are given by:

ν np,0 = n p + + α 2 (n p -n max ) 2 ∆ν (5)
where n p is the radial order, is a phase offset, α is the mean curvature of the l = 0 pattern as a function of frequency, n max is the closest radial order to ν max , and ∆ν is the mean large frequency separation between consecutive radial overtones. The frequencies of the dipolar p modes are given by: where d 01 is the mean separation between l = 0 and l = 1 modes of a given order n, relative to ∆ν. The periods of dipolar g modes P ng,1 are given by:

ν np,1 = ν np,0 + 1 2 -d 01 ∆ν (6)
P ng,1 = (n g + α 1 )P 1 (7)
where n g is the g mode order, α 1 is a constant and P 1 is the period spacing of dipolar modes. The values deduced from Eq. (1) for 94 Aqr Aa are P 1 = 290.8 ± 0.5 seconds, with q = 0.16 ± 0.025. These values are similar to stars with comparable ∆ν (see Mosser et al. 2014). We used the resulting asymptotic l = 1 mode frequencies as a guide for identification and subsequent fitting.

The observed oscillation spectrum is typical of a subgiant star, where all l = 1 modes are of mixed nature, leading to the impression of an irregular mode distribution as a function of frequency. Due to the rather low S/N, our estimate of the frequency of maximum oscillation power suffers from a relatively large uncertainty at ν max = 875 ± 12 µHz. Similarly, the determination of ∆ν was initially ambiguous, with estimates ranging from about 40 to 60 µHz. We converged to the value ∆ν = 50.2 ± 0.4 µHz, which is simultaneously compatible with a fit to both the radial and non-radial modes.

From a consensus of the individual teams, we identified four radial (l=0), five dipole (l=1), and two quadrupole (l=2) modes above our significance threshold (S/N ≥ 5). The identified frequencies from the team that was most representative of the consensus are listed in Table 1 and marked with blue triangles in the bottom panel of Figure 4. The two sets of closely-spaced triangles at the lower end of the frequency range are pairs of l=2 and l=0 modes, while the two largest peaks are strongly mixed l=1 modes. Slightly below the frequency range with identified modes, there are a few marginal peaks that may be additional l=1 and l=2 modes for which we did not reach a consensus. Finally, there are three peaks above our significance threshold that remain unidentified: a relatively strong peak near 935 µHz, a weaker peak adjacent to a mixed mode near 843 µHz, and a marginal peak close to an l=2/l=0 pair at 826 µHz. Future TESS observations in Sector 29 may help to clarify these ambiguities.

Modeling the oscillation modes

To determine the fundamental properties of 94 Aqr Aa, several teams attempted to match the observed oscillation frequencies identified above, us-ing stellar evolution models from MESA (Paxton et al. 2011), ASTEC (Christensen-Dalsgaard 2008), and the Yale Rotating Evolution Code (YREC, Demarque et al. 2008) in its non-rotating configuration. We found reasonable agreement between the resulting determinations of asteroseismic radius, mass, and age, with relative dispersions of 2%, 7%, and 22%, respectively. For consistency with our subsequent analysis of the angular momentum evolution (see Section 6), below we provide details only for the results obtained with YREC.

We initially constructed a grid of models with masses in the range 1.16 M to 1.32 M with a spacing of 0.01 M . For each mass, models were created with five values of the mixing length parameter spanning α MLT = 1.5 to 2.3, initial helium abundances from the primordial helium abundance of 0.248 (Steigman 2010) to 0.30 in steps of 0.01, and initial [Fe/H] in the range +0.15 to +0.33 in steps of 0.01. We use the Grevesse & Sauval (1998) solar mixture to convert [Fe/H] to Z/X. For each of the parameters, the models were evolved from the zero-age main-sequence (ZAMS) to an age of 11 Gyr. Models were output at intermediate ages.

The models were constructed using OPAL opacities (Iglesias & Rogers 1996) supplemented with low temperature opacities from Ferguson et al. (2005). The OPAL equation of state (Rogers & Nayfonov 2002) was used. All nuclear reaction rates are obtained from Adelberger et al. (1998), except for that of the 14 N (p, γ) 15 O reaction, which we adopt from Formicola et al. (2004). All models included gravitational settling of helium and heavy elements using the formulation of Thoul et al. (1994). The oscillation frequencies of the models were calculated with the code of Antia & Basu (1994).

The fits to the observations were done in two steps: we first looked for models that provided a good match to the frequencies of the l=0 and l=2 modes, in addition to showing consistency with spectroscopic constraints (Gray et al. 2006, T eff = 5461 ± 40 K; [Fe/H] = +0.23 ± 0.08) and the derived luminosity from Section 2.3 (L Aa = 3.31 +0.22 -0.07 L ). The quality of the fit was defined as follows. For each observable, T eff , [Fe/H] and luminosity L, we define a likelihood. For instance, the likelihood for effective temperature was defined as

L(T eff ) = D exp(-χ 2 (T eff )/2), (8)
with

χ 2 (T eff ) = (T obs eff -T mod eff ) 2 σ 2 T , (9)
where σ T is the uncertainty on the effective temperature, and D is a normalization constant. We define the likelihoods for [Fe/H] and L in a similar manner. For the frequencies, we first corrected for surface effects using the two-term surface correction proposed by Ball & Gizon (2014)

δν nl ≡ ν obs nl -ν mod nl (10) = 1 I nl a ν nl ν ac -1 + b ν nl ν ac 3 , (11)
where δν nl is the difference in frequency for a mode of degree l and radial order n between the observations and the model, ν nl is the frequency and I nl is the inertia of the mode, and ν ac is the acoustic cut-off frequency, with coefficients a and b determined from a generalized leastsquares fit to the frequency difference of the l = 0 modes. This allows us to define a likelihood for frequencies. We define ν cor nl = ν mod nl -S, where S is defined by the righthand side of Eq. ( 11) but now applied to both l = 0 and l = 2 modes.

χ 2 (ν) = (ν obs nl -ν cor nl ) 2 σ obs nl . (12)
Consequently

L(ν) = C exp - χ 2 (ν) 2 , ( 13
)
where C is a normalization constant. The total likelihood for each model is then

L total = L(ν)L(T eff )L([Fe/H])L(L). ( 14
)
The medians of the marginalized likelihoods of the ensemble of models were used to determine the most likely stellar properties, after converting them to a probability density by normalizing the likelihood by the prior distribution of each parameter. A finer grid in mass and age was created around the most likely values of these parameters in order to fit the l = 1 modes, improving both the accuracy of the stellar age and the sampling of the posterior distributions. The likelihoods were calculated again, except that now in Eq. ( 12) we also used the l = 1 modes. The optimal asteroseismic properties were derived from the new probability density, and they are listed in Table 2 along with independent estimates (see Section 5) and the other available constraints. Note that because YREC did not use a global optimization technique, it is possible that a better fit to the observations exists.

ACCURACY OF THE STELLAR PROPERTIES

Radius from SED

We performed a fit to the broadband photometry of 94 Aqr A in order to make an independent determination of the stellar radius (see Figure 5). We followed the procedures described in Stassun & Torres (2016); Stassun et al. (2017Stassun et al. ( , 2018)). Briefly, we adopted the best available spectroscopic values for T eff and [Fe/H], and then fit a standard stellar atmosphere model [START_REF] Kurucz | The Stellar Populations of Galaxies[END_REF] to the broadband spectral energy distribution (SED) in order to determine empirically the bolometric flux at Earth (F bol ). The free parameter of the fit was the interstellar extinction. Using the Gaia DR2 parallax, adjusted for the known small systematic offset (-82 µas, Stassun & Torres 2018), the stellar radius was then determined via the Stefan-Boltzmann relation.

We adopted the Johnson U BV magnitudes from the Mermilliod (2006) homogenized photometric catalog of bright stars, the B T V T magnitudes from Tycho-2, the Strömgren ubvy magnitudes from Paunzen (2015), the JHK S magnitudes from 2MASS, the W3-W4 magnitudes from WISE, and the G magnitude from Gaia. Together, the available photometry spans the full stellar SED over the wavelength range 0.35-22 µm. We adopted the spectroscopic parameters from Gray et al. (2006), doubling the quoted uncertainty on T eff to a more realistic 80 K. We also adopted the parameters for the blended Ab component from Docobo et al. (2018), and similarly fit its SED, in order to correct the F bol of 94 Aqr Aa for contamination of light in the broadband photometry from the close companion.

The fit has a reduced χ 2 = 3.3 and an extinction of A V = 0.02 +0.07 -0.02 . The resulting bolometric flux is F bol = (2.18 ± 0.25) × 10 -7 erg s -1 cm -2 , which with the parallax gives R Aa = 2.07 ± 0.13 R , consistent with the asteroseismic value (R = 2.06 ± 0.03 R ). A similar analysis of 94 Aqr B, adopting the spectroscopic constraints from Fuhrmann (2008), yields R B = 0.85 ± 0.03 R .

Mass from astrometry and spectroscopy

To derive the individual masses of 94 Aqr Aa and Ab, we used the available data from astrometry and spectroscopy. For astrometry, we used the same data available to Docobo et al. (2018). For spectroscopy, we used radial velocities measured by Sarma (1962) and Katoh et al. (2013). We then jointly fit the astrometric and spectroscopic data using an MCMC approach as described in Marcadon et al. (2018). The orbital parameters are given in Table 3, and the results are illustrated in Figure 6. Docobo et al. (2018) used the Gaia parallax for the Aa/Ab system to derive the masses of the two components. Unfortunately, Gaia DR2 does not account for binarity. This means the parallax of 94 Aqr A is not useful, because the period of the orbit is about 6.3 years. Instead, we used the parallax of 94 Aqr B (π = 44.515±0.055 mas; Gaia Collaboration et al. 2018), which has an orbital period around A that is longer than a few hundred years (Mason et al. 2001).

We derived individual masses for Aa and Ab following the same approach as Docobo et al. (2018). The error propagation was done using the MCMC solution, thereby taking into account the intrinsic correlations between the various orbital parameters. We found M Aa = 1.22 ± 0.08 M , in agreement with the asteroseismic value (M = 1.22±0.03 M ), and M Ab = 0.81±0.04 M .

Age from isochrone fitting

Because 94 Aqr Aa is on the subgiant branch and experiencing relatively rapid evolution, its age is well constrained from simple isochrone fitting. We use the methods described in Section 6 to find a best fit stellar model from the observed surface constraints on radius, T eff , and [Fe/H] in the "Other" column of Table 2. We adopt a broad prior on the age of 5.0 ± 5.0 Gyr, while the priors on mass, [Fe/H], and mixing length are taken directly from Table 2. We estimate an age of t iso = 6.2 +0.9 -0.7 Gyr, which is consistent with the asteroseismic value (t = 6.2 ± 0.2 Gyr).

ANGULAR MOMENTUM EVOLUTION

By combining the stellar properties from asteroseismology with the rotation period determined from the Mount Wilson HK data, we can finally model the angular momentum evolution of 94 Aqr Aa using magnetic braking formulations from van Saders & Pinsonneault (2013), van Saders et al. (2016) and van Saders et al. (2019). We examined two distinct classes of braking models: "standard" and "weakened" magnetic braking.

The standard models are described in van Saders & Pinsonneault (2013). We model rotational evolution using the rotevol code (as in van Saders & Pinsonneault 2013;van Saders et al. 2016;Somers & Pinsonneault 2016) atop formally non-rotating YREC stellar evolution tracks manipulated with the isochrone tools in kiauhoku (Claytor et al. 2020). The stellar model grid physics are the same as described in van Saders & Pinsonneault ( 2013) with the addition of gravitational settling and diffusion, the wider metallicity range of van Saders et al. (2016), and an Eddington atmosphere. The magnetic braking law has four free parameters which are tuned to reproduce the observed rotation periods in young open clusters and the Sun: the overall normalization of the braking law, f k ; the period and duration of the disk locking phase P disk and T disk , which set the initial rotation rate; and the angular rotation velocity at which the spin-down transitions from the saturated to unsaturated regime, ω crit . For stars near or beyond the end of the main-sequence, only f k is important; the strong dependence of the spin-down on rotational velocity means that the late-time evolution is insensitive to variations in parameters that affect early-time evolution (ω crit , T disk , P disk ). In this prescription, the spin-down is smooth at late times in much the same manner as fully empirical gyrochronology relations (e.g., Barnes 2010).

The weakened braking models are identical to the standard models except for one additional free parameter that affects the late-time evolution: a critical Rossby number Ro crit beyond which magnetic braking ceases and angular momentum is conserved. Due to the weakened braking, the modified model generally predicts faster rotation periods than the standard model, which allows it to reproduce the rotation periods of old asteroseismic calibrator stars (van Saders et al. 2016). With a fixed f k = 6.6 (and ω crit = 3.4 × 10 -5 s -1 , P disk = 8.1, T disk = 0.28), van Saders et al. (2016) found Ro crit = 2.16 when calibrating against 21 Kepler asteroseismic targets.

Rotational modeling of 94 Aqr Aa

For 94 Aqr Aa, we used the asteroseismically constrained properties to predict the observed rotation period under the two different braking prescriptions. In contrast to the main-sequence, envelope expansion on the subgiant branch (SGB) increasingly dominates over magnetic braking in the rotational evolution as the star approaches the base of the giant branch. This means that the predicted rotation is tied strongly to age, but also to both HR diagram position and stellar mass.

We used a Monte Carlo approach (emcee, Foreman-Mackey et al. 2013) to search our model grids in mass, age, bulk composition (Z/X), and mixing length (α MLT ) to match the best fit values of T eff , [Fe/H], and radius from the "Asteroseismic" column in Table 2. We adopted Gaussian priors on the mass, age, [Fe/H], and α MLT centered on 1.22 M , 6.2 Gyr, +0.15 dex, and 1.78 with 1σ widths of 0.03 M , 0.2 Gyr, 0.05 dex, and 0.2, respectively. A total of 8 chains were run for 100000 steps each, with the first 5000 steps discarded as burnin. Such a run corresponds to > 1000 autocorrelation times in all variables of interest.

We predict a rotation period for the standard braking model of P = 76 +11 -13 days with the asteroseismic surface constraints. For a weakened braking model with Ro crit , we predict P = 49 +7 -9 days, in good agreement with the observed period of 46.9 ± 1.9 days (see Figure 7). If instead we adopt the spectroscopic values for T eff and [Fe/H], we would predict P = 63 +12 -11 days for the standard model, and P = 41 ± 8 days for weakened braking. In both cases the weakened braking model provides better agreement with the observed rotation.

Robustness to assumptions

There are two types of physical assumptions that can affect our conclusions: assumptions about the magnetic braking and angular momentum transport itself, and physical uncertainties in the underlying stellar models. We argue that the latter are of most concern for the weakened braking interpretation.

We have made a host of assumptions about the braking, most of which we expect cannot shift the standard model prediction toward the shorter observed rotation period. We've assumed a single set of initial conditions despite the fact that stars in nature display a range of birth rotation rates, but even if we had launched our best fit models rotating at breakup velocity on the ZAMS (3 times faster than assumed in our models, which have a ZAMS period of less than 1 day) the predicted period for the standard model would differ by only 1 day. We haven't allowed for differential rotation, but for cases in which the core rotationally decouples from the envelope (e.g. Denissenkov et al. 2010;MacGregor & Brenner 1991) we expect slower observed envelope rotation rates, not faster (Deheuvels et al. 2014). If the star had a strong radial differential rotation on the mainsequence it could result in faster-than-expected rotation on the SGB, but indications are that main-sequence and early SGB stars have little radial differential rotation (e.g. Thompson et al. 1996;Saio et al. 2015;Benomar et al. 2015;Deheuvels et al. 2020). 94 Aqr Aa is not a single star, but its 6.3 year orbit is sufficiently wide that we expect it to behave as a single star in terms of rotational evolution.

By contrast, reasonable changes to the underlying stellar physics have the ability to shift the predicted rotation period in the standard model by more than 10 days. The asteroseismic fits in Section 4.2 allowed the mixing length to be a free parameter, rather than fixing it to the solar value as is the norm in most non-seismic analyses. We have found that our results are sensitive to the choice of mixing length.

Smaller values of α MLT yield models with shorter periods. Changing the mixing length tends to shift subgiant tracks along the SGB, meaning that constraints in temperature, radius, and luminosity can be matched with a model of essentially the same stellar mass. However, at a fixed location in the HR diagram, models of the same mass but different mixing lengths will have different convective overturn timescales, affecting the predicted rotation period. A 1.2 M , 0.2 dex model at 2.0 R with a mixing length of 1.8 has a period of 60 days, but the same model with a mixing length of 1.6 has a period of 46 days at 2.0 R -a difference comparable to that between period predictions for a standard and weakened model of magnetic braking. While we have allowed the mixing length to vary in our fit and incorporated the (fairly broad) asteroseismic prior on α MLT , the sensitivity of the period to the choice of mixing length means that we cannot rule out the possibility that the tension between the observed and predicted period for standard braking arises from an inappropriate choice of the mixing length.

Efforts to quantify how the mixing length should vary as a function of stellar properties have yielded conflicting results. Observational estimates from asteroseismology (Bonaca et al. 2012;Creevey et al. 2017;Tayar et al. 2017;Viani et al. 2018) find that the mixing length should increase as the metallicity increases, while simulations of convection generally arrive at the opposite conclusion (Magic et al. 2015). Viani et al. (2018) predicts that a star with the surface gravity, temperature and metallicity of 94 Aqr Aa should have a supersolar mixing length for any of the relations they provide. Larger mixing lengths result in longer rotation periods, and would reinforce the tension between the standard model and the observed rotation. We note that, in contrast to these predictions, the asteroseismic mixing length for 94 Aqr Aa in Table 2 is sub-solar (α MLT, = 1.98).

The apparent need for weakened braking could also be spurious if our stellar mass is underestimated. Rotation rate is a very strong function of mass, particularly near the Kraft (1967) break, where stars above the break in mass rotate rapidly, while less massive stars rotate more slowly. The dichotomy is a result of the diminishing convective envelopes in more massive stars, and the consequently weak large-scale fields and magnetic braking. If we fix the mixing length to α MLT = 1.78 and broaden the priors on mass, age, and metallicity to 1σ Gaussian widths of 0.5 M , 2.0 Gyr, and 0.2 dex, the resulting increase of 0.05 M in mass is sufficient to shift the predicted rotation period from ∼71 days to 55 days. However, we note that changing the mixing length to ∼1.5 can match the observed rotation period with no upward adjustment to the mass, so we consider the poorly constrained mixing length to be the more intractable source of uncertainty.

These issues are connected to challenges inherent in stellar modeling that have stood for decades, and the solution is unlikely to emerge from this article. In the following section, we explore the possibility that 94 Aqr Aa has experienced weakened magnetic braking, but we caution the reader about the sizable caveats to this interpretation that we have outlined above.

SUMMARY AND DISCUSSION

By combining Mount Wilson observations of magnetic variability with TESS asteroseismic measurements of the G8 subgiant 94 Aqr Aa, we have discovered new evidence for weakened magnetic braking (van Saders et al. 2016) and the possibility of a "born-again" dynamo in evolved stars, as we discuss below.

A reanalysis of 35 years of HK observations (Section 3) yielded rotation and magnetic activity cycle periods for 94 Aqr Aa (P Aa rot = 46.9±1.9 days, P Aa cyc = 19.35±0.18 yr) and a cycle period for 94 Aqr B (P B cyc = 9.13 ± 0.03 yr). The amplitude of the observed variability in the blended A component allowed us to attribute these properties to the subgiant (Aa) because it contributes 97% of the light in the relevant bandpasses.

Asteroseismology of 94 Aqr Aa from TESS observations (Section 4) yielded precise determinations of the stellar radius (R = 2.06 ± 0.03 R ), mass (M = 1.22 ± 0.03 M ) and age (t = 6.2 ± 0.2 Gyr). We established the absolute accuracy of these properties (Section 5) with independent estimates of the stellar radius from SED fitting (R Aa = 2.07 ± 0.13 R ), the stellar mass from a close binary orbit (M Aa = 1.22 ± 0.08 M ), and the age from isochrone fitting (t iso = 6.2 +0.9 -0.7 Gyr). Using the asteroseismic properties from Section 4, we attempted to reproduce the observed rotation period from Section 3 with angular momentum evolution models (Section 6) that adopted either standard spindown or the weakened magnetic braking proposed by van Saders et al. (2016). The standard model predicts a rotation period (P = 76 +11 -13 days) that is substantially longer than suggested by the observations, while the model with weakened magnetic braking (P = 49 +7 -9 days) more closely reproduces the observed rotation period with stalled spin-down at a critical Rossby number Ro crit = 2.16 (van Saders et al. 2016). Note that with these models, the Rossby number of the Sun is Ro ∼ 2.2, comparable to the critical value.

The fact that the G8 subgiant shows a magnetic activity cycle provides an interesting constraint on stellar dynamo models. According to the scenario proposed by Metcalfe & van Saders (2017), activity cycles should gradually grow longer with the rotation period along the two sequences identified by Böhm-Vitense (2007). When a star reaches the critical Rossby number suggested by van Saders et al. (2016), the rotation period remains relatively constant while the activity cycle appears to grow longer and weaker before disappearing entirely. The resulting "flat activity" star still shows magnetic activity on small scales, allowing rotation periods to be measured, but the mean activity level is approximately constant on longer timescales. Such stars have previously been interpreted as Maunder minimum candidates (Judge et al. 2004), but at least some of them may be the end-states of large-scale stellar dynamos.

If the critical Rossby number represents a threshold above which large-scale dynamos no longer operate (Tripathi et al. 2018), then models with weakened magnetic braking may help to explain the existence of a cycle in 94 Aqr Aa. The mass of this G8 subgiant suggests that it evolved from an F-type star on the main-sequence. As such, it may have had a relatively short activity cycle until it reached the critical Rossby number after about 2.5 Gyr (see Figure 8) at a rotation period near 15 days (e.g., see Metcalfe et al. 2019, their Fig. 1). The cycle would have then grown longer and weaker for about 2 Gyr at nearly constant Rossby number. When hydrogen core-burning ceased, the core would have contracted and the star would become hotter with a thinner convection zone, pushing it above Ro crit and making it a "flat activity" star. However, the star would subsequently expand and cool when hydrogen shell-burning began, slowing its rotation through conservation of angular momentum and deepening the outer convection zone. For a small range of masses above the solar value, these evolutionary effects (solid line in Figure 8) can push the Rossby number back below Ro crit so the star can reinvigorate large-scale dynamo action and briefly sustain an activity cycle before ascending the red giant branch. This scenario for a "born-again" dynamo is simply not possible with standard models (dashed line in Figure 8).

A similar mechanism may help explain the existence of magnetic cycles in subgiants that evolved from more massive F-type stars, which had never previously sustained a large-scale dynamo. For example, Egeland (2018) used Mount Wilson and Lowell observations to identify an activity cycle in the subgiant component of the HD 81809 system. The mass of this star (1.58 ± 0.26 M ) would place it above the Kraft break on the main-sequence, without a substantial outer convection zone to help build a large-scale magnetic field. Consequently, it would not have experienced significant magnetic braking during its main-sequence lifetime, and it would only have slowed to its current rotation period (40.2 ± 2.3 days) through expansion on the subgiant branch. The deeper convection zone during this evolutionary phase could finally support large-scale dynamo action for the first time in its life, explaining the observed activity cycle.

The results presented above demonstrate the power of combining magnetic variability data from Mount Wilson and other programs with new asteroseismic observations from TESS. With accurate determinations of the basic stellar properties such as radius, mass, and age, we can finally reveal the evolutionary threads that connect stars with known rotation rates and magnetic activity cycles. Over the coming years, this approach promises to yield additional insights about magnetic stellar evolution, particularly beyond the middle of main-sequence lifetimes.

Figure 1 .

 1 Figure 1. The mean TESS postage stamp (3. 9 × 9. 1) for 94 Aqr, averaged over the complete time series. Counts are shown on a logarithmic scale to allow visibility of the full range, and overlying circles indicate stellar locations from Gaia DR2, with a limiting G magnitude of 14. Blending of the A and B components near image center is apparent.

Figure 2 .

 2 Figure 2. Long-term variability of 94 Aqr A (top) and 94 Aqr B (bottom) from the Mount Wilson S-index data.The reported activity cycle period and uncertainty come from fitting a sinusoid (red curves) to each time series.

Figure 3 .

 3 Figure 3. Time series Ca HK measurements of 94 Aqr A from a representative observing season near cycle maximum in 1998 (top). The corresponding periodogram (bottom)shows a clear detection of rotation (blue point) with a period similar to the median value reported in the text. The detected period is shown with a red line in the top panel.

Figure 4 .

 4 Figure 4. Top: power spectral density (PSD) of the TESS light curve as a function of frequency in µHz.The red line represents a fit to the background noise, and the white line includes the excess power due to oscillations. Bottom: ratio of the power spectrum to the background noise as a function of frequency in the range where oscillation modes are detected. Within this frequency interval, peaks above the red line have < 1% probability of being due to noise, with the false alarm probability decreasing exponentially at higher S/N.

Figure 5 .

 5 Figure 5. Spectral energy distribution (SED) fit to broadband photometry of 94 Aqr A. The fit to 94 Aqr Aa is shown in black, with observed fluxes as red symbols and bandpass integrated model fluxes as blue symbols. The red curve shows the SED of the companion (Ab), which is used to correct for light contamination in the SED of 94 Aqr Aa.

Figure 6 .

 6 Figure 6. Results of a simultaneous fit to the astrometry (top) and spectroscopy (bottom) of 94 Aqr A. Data are shown with blue points, and the fit is shown in black.

Figure 7 .

 7 Figure 7. Predictions from a standard spin-down model (purple) and weakened braking model (orange) for the rotation period of 94 Aqr Aa. The observed rotation period from Mount Wilson data is shown with black vertical lines.

Figure 8 .

 8 Figure8. Predictions from a standard spin-down model (purple/dashed) and weakened braking model (orange/solid) for the evolution of the Rossby number in 94 Aqr Aa. For each model, the best-fit combination of mass and composition is shown as a dark line and the best fit age is marked with a solid point. In addition, 250 randomly drawn posterior samples of mass and composition are shown, truncated at the end of the subgiant branch.

Table 1 .

 1 Identified Oscillation Frequencies.

	n l	ν obs nl (µHz)	ν mod nl	(µHz) ν cor nl (µHz)
	15 0 771.39 ± 0.19	773.63	771.32
	16 0 821.62 ± 2.85	826.39	821.73
	18 0 921.29 ± 0.23	933.78	921.93
	19 0 971.64 ± 0.29	987.71	970.81
	15 1 794.37 ± 0.14	801.01	797.96
	16 1 837.02 ± 0.12	839.83	837.48
	16 1 860.61 ± 0.14	862.92	858.32
	17 1 899.76 ± 0.17	909.41	900.14
	18 1 950.49 ± 1.21	960.71	947.10
	19 1 996.11 ± 0.15	1010.47	994.33
	14 2 767.21 ± 0.31	768.71	766.60
	15 2 815.28 ± 0.15	821.81	817.46

Table 2 .

 2 Stellar Properties of 94 Aqr Aa.

		Asteroseismic	Other	Source
	Radius (R )	2.06 ± 0.03	2.07 ± 0.13	(1)
	Mass (M )	1.22 ± 0.03	1.22 ± 0.08	(2)
	Age (Gyr)	6.2 ± 0.2	6.2 +0.9 -0.7	(3)
	T eff (K)	5411 ± 31	5461 ± 40	(4)
	[Fe/H] (dex)	+0.15 ± 0.05 +0.23 ± 0.08	(4)
	Luminosity (L )	3.30 ± 0.06	3.31 +0.22 -0.07	(5)
	αMLT	1.78 ± 0.20	• • •
	References-(1) Section 5.1; (2) Section 5.2; (3) Section 5.3;
	(4) Gray et al. (2006); (5) Section 2.3

Table 3 .

 3 Orbital Parameters of 94 Aqr A.

	Parameter	Value
	Period (years)	6.317 ± 0.005
	T (year)	2012.37 ± 0.02
	e	0.1628 ± 0.0022
	a (arcsec)	0.1925 ± 0.0032
	i ( • )	46.72 ± 1.86
	Ω ( • )	341.62 ± 1.11
	ω ( • )	33.20 ± 0.88
	K (km s -1 )	6.022 ± 0.012
	π (mas)	44.515 ± 0.055

Note that the quoted uncertainty on T eff does not account for systematics between different methods and the fundamental T eff scale set by the accuracy of interferometric angular diameters, which can be 2%[START_REF] Casagrande | [END_REF]White et al. 2018).

ACKNOWLEDGMENTS T.S.M. acknowledges support from NSF grant AST-1812634, NASA grants NNX16AB97G and 80NSSC20K0458, and a Visiting Fellowship at the Max Planck Institute for Solar System Research. Computational time at the Texas Advanced Computing Center was provided through XSEDE allocation TG-AST090107. J.v.S. acknowledges support from NASA through the TESS Guest Investigator Program (80NSSC18K1584). S.B. acknowledges NASA grant 80NSSC19K0374. D.B. acknowledges support from NASA through the Living With A Star Program (NNX16AB76G) and from the TESS GI Program under awards 80NSSC18K1585 and 80NSSC19K0385. W.J.C., W.H.B. and M.B.N. acknowledge support from the UK Space Agency. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement no.: DNRF106). R.E. was supported by the NCAR Advanced Study Program Postdoctoral Fellowship. The National Center for Atmospheric Research is sponsored by the National Science Foundation. R.A.G. and B.M. acknowledge support from the CNES PLATO grant. P.G. acknowledges funding from the German Aerospace Center (Deutsches Zentrum für Luft-und Raumfahrt) under PLATO Data Center grant 50OO1501. D.H. acknowledges support from NASA through the TESS Guest Investigator Program (80NSSC18K1585, 80NSSC19K0379). T.R. acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 715947). T.A. acknowledges support from the Programme de Physique Stellaire et Planétaire. T.R.B. acknowledges support from the Australian Research Council. L.G.C. acknowledges support from grant FPI-SO from the Spanish Ministry of Economy and Competitiveness (MINECO) (research project SEV-2015-0548-17-2 and predoctoral contract BES-2017-082610). A.J. Acknowledges support from the State Research Agency (AEI) of the Spanish Ministry of Science, Innovation and Universities (MCIU). H.K. acknowledges support from the European Social Fund via the Lithuanian Science Council (LMTLT) grant No. 09.3.3-LMT-K-712-01-0103. M.N.L. acknowledges support from the ESA PRODEX programme. S.M. acknowledges support from the Spanish Ministry with the Ramon y Cajal fellowship number RYC-2015-17697. Z.C ¸.O., S. Ö. and M.Y. acknowledge support from the Scientific and Technological Research Council of Turkey (T ÜB İTAK:118F352). A.R.G.S. acknowledges support from NASA grant NNX17AF27G. This work benefited from discussions within the international team "The Solar and Stellar Wind Connection: Heating processes and angular momentum loss" at the International Space Science Institute (ISSI).