A photospheric and chromospheric activity analysis of the quiescent retrograde-planet host ν Octantis A
David Ramm, Paul Robertson, Sabine Reffert, Fraser Gunn, Trifon Trifonov, Karen Pollard, Faustine Cantalloube
aa r X i v : . [ a s t r o - ph . E P ] F e b Mon. Not. R. Astron. Soc. , ?? [2793]–15[2806] (2021) Printed 25 February 2021 (MN L A TEX style file v2.2)
A photospheric and chromospheric activity analysis of the quiescentretrograde-planet host ν Octantis A D . J . Ramm ⋆ † , P . Robertson , S . Reffert , F . Gunn , T . Trifonov , K . Pollard , F . Cantalloube School of Physical and Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand Department of Physics & Astronomy, The University of California, Irvine, Irvine, CA 92697, USA Landessternwarte, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, K¨onigstuhl 12, 69117, Heidelberg, Germany Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, Heidelberg 69117, Germany
25 February 2021
ABSTRACT
The single-lined spectroscopic binary ν Octantis provided evidence of the first conjectured cir-cumstellar planet demanding an orbit retrograde to the stellar orbits. The planet-like behaviouris now based on 1437 radial velocities (RVs) acquired from 2001 to 2013. ν Oct’s semimajoraxis is only 2.6 au with the candidate planet orbiting ν Oct A about midway between. Thesedetails seriously challenge our understanding of planet formation and our decisive modellingof orbit reconfiguration and stability scenarios. However, all non-planetary explanations arealso inconsistent with numerous qualitative and quantitative tests including previous spectro-scopic studies of bisectors and line-depth ratios, photometry from
Hipparcos and the morerecent space missions TESS and
Gaia (whose increased parallax classifies ν Oct A closerstill to a subgiant, ∼ K1 IV). We conducted the first large survey of ν Oct A ’s chromosphere:198 Ca II H-line and 1160 H α indices using spectra from a previous RV campaign (2009–2013). We also acquired 135 spectra (2018–2020) primarily used for additional line-depthratios, which are extremely sensitive to the photosphere’s temperature. We found no signif-icant RV-correlated variability. Our line-depth ratios indicate temperature variations of only ± K, as achieved previously. Our atypical Ca II analysis models the indices in terms of S/N and includes covariance significantly in their errors. The H α indices have a quasi-periodicvariability which we demonstrate is due to telluric lines. Our new evidence provides furthermultiple arguments realistically only in favor of the planet. Key words: methods: data analysis – stars: activity – binaries: spectroscopic – planetarysystems – individual: ν Octantis – planet-star interactions
A decade or so after the first exoplanets were described (Wolszczan& Frail 1992; Mayor & Queloz 1995), radial velocity (RV) evi-dence for the first retrograde planet appeared from a very unex-pected source, the compact single-lined spectroscopic binary ν Oc-tantis (Ramm 2004). However, these RVs shared the same initialfate as those from γ Cep A which almost hosted the first acknowl-edged RV-discovered planet (Campbell, Walker & Young 1988;Walker et al. 1992). γ Cep Ab was eventually confirmed 15 yr later(Hatzes et al. 2003), and was then the shortest period binary with aplanet ( P bin ∼ yr) – about 20 × longer than that for ν Oct. Bothinitial series of RVs led their discoverers to describe both planet andstellar rotation-related scenarios, the latter then being suspected as ⋆ E-mail: [email protected] † Research Fellow more likely causes. These two binaries have many other paralleldetails in their exoplanet histories and host star characteristics. Host stars may provide evidence that a candidate exoplanetorbit is retrograde relative to the star’s rotation (which we labeltype-1), and if in a binary system, relative to the two stellar orbits(our type-2). The first acknowledged retrograde planet was HAT-P-7b, promptly identified using the McLaughlin-Rossiter effect (ourtype-1; Winn et al. 2009; Narita et al. 2009). This had been pre-ceded in the same year by the first paper describing the conjecturedplanet ν Oct Ab , (Ramm et al. 2009; henceforth R09), which hasproven to be much more challenging for establishing its reality be-yond reasonable doubt. This is almost entirely due to the unprece- For example, and very significantly, both hosts were originally classifiedas giants, rare for early exoplanet claims – and both K0 III – which madea stellar origin for the RV signals more tenable. They also share a trivialnear-polar declination detail: | δ | = 77 ◦ .© 2021 RAS D. J. Ramm et al. dented geometry of the conjectured system, whose stars are sepa-rated by only 2–3 au with the circumstellar i.e. S-type planet aboutmidway between (see e.g. Gong & Ji 2018; Bonavita & Desidera2020; Quarles et al. 2020). Some details for ν Oct (HD 205478,HIP 107089) and its conjectured planet (based on the persistent RVcycle with a period P RV ∼ d) are listed in Table 1 and Table 2.The parallax was recently updated from Gaia observations, andcritically for the planet claim, increased by about 10 per cent (GaiaCollaboration 2018; Kervella et al. 2019 - whose work specificallyincludes nearby stars with stellar and substellar companions). The system’s geometry makes a prograde planet impossible(R09; Eberle & Cuntz 2010). An S2 (i.e. S-type, our type-2 ret-rograde) orbit has a significantly wider stability zone than its pro-grade equivalent (see e.g. Jefferys 1974; Wiegert & Holman 1997;Morais & Giuppone 2012). This opportunity for ν Oct Ab ’s re-ality was first investigated by Eberle & Cuntz (2010), and subse-quently by Quarles, Cuntz & Musielak (2012), Go´zdziewski et al.(2013) and Ramm et al. (2016; henceforth R16), all of whichfound retrograde solutions with merit but without being conclusive.Meanwhile, however, multiple other tests demonstrate that all otherexplanations (e.g. measurement artefacts, stellar variability, ν Octbeing a triple-star system) are substantially less credible than theplanet (R09; Ramm 2015 - henceforth R15; and R16). If the planetis an illusion, ν Oct A so far provides no evidence of its causativerole other than the persistent precise cycle of so far 1437 RVs over12.5 yr, and thus would have the alternative distinction of seriouslyconfronting our understanding of stellar variability. Go´zdziewski et al. identify a small number of nearby meanmotion resonances for coplanar S2 orbits in ν Oct including one atthe period ratio 5:2, this having been qualitatively suspected in R09.The unprecedented strong interactions suggest resonance is likelyto be a contributing factor for stability, as in other multi-body sys-tems (e.g. Campanella 2011; Robertson et al. 2012; Horner et al.2019; Stock et al. 2020). ν Oct Ab would never be confined to atypical narrow orbital path but would move endlessly throughout arather wide zone as Eberle & Cuntz (2010) first illustrated, leadingto significant challenges for competing models trying to character-ize different orbital geometries (Panichi et al. 2017).Many S-type planets have now been reported, though demandsfor any following an S2 orbit remains rare since the binary must bequite compact to lead to this conclusion. Scenarios that may cre-ate such orbits include star-hopping (Kratter & Perets 2012), per-haps facilitated by a scattering event, or significant system or orbitalchanges involving stellar winds, accretion/debris discs or evolutionto a white dwarf (WD) companion (see e.g. Tutukov & Ferorova2012). The WD scenario may have support for ν Oct from spec- Thus ν Oct A is less luminous and should be classified closer still to asubgiant, ∼ K1 IV, as now is also γ Cep A (Hatzes et al. 2003; Fuhrmann2004). § 3.5 will discuss this important revision. With zero evidence for retrograde status we label the orbit type-0 i.e. pro-grade, and assumed if not stated. If the host provides evidence of both type-1and 2 we would label it type-3 (1+2). The scheme is applicable to single starhosts i.e. type 0 or 1, and both S- (circumstellar) and P-type (circumbinary)planets (Dvorak 1986), i.e. type 0, 1, 2 or 3. The RVs were obtained using two CCDs and different calibration tech-niques ( I -cell and thorium-argon spectra) and therefore also different re-duction methods. No other star’s study using our instruments and methodsprovide any similar planet-like RVs. The primary star’s argument of pe-riastron, ω = 75 ◦ , has not changed significantly in 95 yr so any claimthat a hierarchical triple-star system is creating the planet-like RVs is alsounfounded (see R09 and R16 for details). Parameter ν Octantis A ReferenceSpectral type a K1IIIb-IV (1) V (mag) +3 . ± . (2)parallax (mas) . ± . (3) M V (mag) +2 . ± . our calculation BC V (mag) − . ± . (2) H p ( Hipparcos mag) . ± . (4)Mass ( M ⊙ ) a . ± . , . ± . (2), (5)Radius ( R ⊙ ) a . ± . , . ± . (2), (5) T eff (K) a ± , ± (2), (5) T LDR (K) b ± , ± (1), (6)Luminosity ( L ⊙ ) a ∼ (5) v sin i ( km s − ) ± . (2) P rot (d) a ≃ ± (6)Age (Gyr) ∼ . –3 (5)Observations (RVs) c I -cell, 257 CCF (1), (5)time span of RVs . − . (1), (5) Table 1.
Stellar parameters and RV observations for ν Oct A (all errors are ± σ , except H p which is the standard error on the median). 1: Ramm et al.(2016), 2: Fuhrmann & Chini (2012), 3: Kervella et al. (2019): this par-allax is a Bayesian ZP-corrected value from ESA’s Gaia mission (GRD2:Gaia Collaboration 2018), 4: ESA (1997), 5: Ramm et al. (2009), 6: Ramm(2015). a Reviewed in § 3.5. b LDR: line-depth ratio analysis. c See Foot-note 4.Parameter Binary planet, AbCompanion Mass . − . M ⊙ . − . M Jup
Object class K7 − M0V , or WD Jovian K km s − −
45 m s − a (au) . − . . − . P orb . ≃ . − d e . − . Table 2.
Basic orbital parameters for ν Oct and the conjectured S2-typeretrograde planet, summarised from R09, Go´zdziewski et al. (2013) andR16. The ratio of the orbital periods, P orb , is close to 5:2. Quarles et al.(2012) and Go´zdziewski et al. (2013) both favour a coplanar planetary orbitwhich R16 could not confirm. trophotometric observations nearly 50 yr ago (Arkharov, Hagen-Thorn & Ruban 2005). They reported unusually large variability( S ν = 0 . mag) in the near ultraviolet (345 nm) in the 1970s. Ofthe 172 ‘normal’ and 176 ‘suspect variable’ stars they catalogued,only two others had larger S ν , both in the latter group. This may bea clue to the nature of ν Oct B as it seems unlikely ν Oct A is thesource.The first close-planet candidate for a WD host was recentlyreported (WD1856+534; Vanderburg et al. 2020), discovered usingNASA’s Transiting Exoplanet Survey Satellite (TESS; Ricker et al.2015), another space mission that should help unravel the ν Octmystery. WD1856 b’s orbit ( P pl ∼ . d), is presumed to be dueto reconfiguration and migration processes (see e.g. Lin, Boden-heimer & Richardson 1996; Rasio & Ford 1996), which must haverelevance for any orbitally retrograde planet. Together with massloss/transfer processes inherent in WD evolution, these scenariosmay further complicate attempts to understand ν Oct Ab but alsoprovide some advantage since orbit reconfiguration (of the planetor the binary) would not require interaction from external or otherinternal masses, as anticipated with an unevolved secondary star.Two other recent claims are also relevant here. Firstly, another © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A S2-type planet, HD 59686 Ab, has been conjectured in this some-what wider but rather eccentric binary (Ortiz et al. 2016; Trifonovet al. 2018; K2 III, a bin ∼ . au, e bin ∼ . ). Interestingly,HD 59686 B is also suspected of being a WD, leading Ortiz et al.to investigate one possibility that the planet formed from a secondgeneration protoplanetary disc. It is tempting to speculate that ν Octand HD 59686 may be two early examples of relatively compact bi-naries with WD secondaries that created S2-type planets. Secondly,the first planet in a binary more compact than ν Oct was recentlyreported (HD 42936,
K0V + L dwarf; a bin ∼ . au; Barnes et al.2020). HD 42936-Ab is close to its host ( ∼ . au) so both itand WD1856 b are assumed to have reconfigured orbits, but withno evidence demanding either be retrograde.Understandable suspicion also persists that ν Oct A ’s RV sig-nal may be due to undetected surface activity. Hatzes et al. (2018)repeated this concern after γ Dra ’s anticipated single-planet claimdisappeared after more RV data was acquired. Oscillatory convec-tive modes (Saio et al. 2015) were instead promoted as the vari-able RVs more likely origin, just as Reichert et al. (2019) specu-late for Aldebaran – instead of its conjectured planet (Hatzes et al.2015). But unlike ν Oct A which is a relatively unevolved low-luminosity star (and so far has a persistent periodic RV signal), γ Dra ( ∼ L ⊙ , 50 R ⊙ ), and Aldebaran ( ∼ L ⊙ , 40 R ⊙ )typify the theoretical high-luminosity expectations of a star hav-ing these convective modes. Both are classified K5 III and are re-minders of the potential complications such evolved stars, both realand mistaken (e.g. ν Oct A and γ Cep A ) can present. Other radialand non-radial oscillations in stars similar to ν Oct A instead havea complex power spectrum that complicate asteroseismology stud-ies (see e.g. Dupret et al. 2009). This is not at all consistent withthe planet-like RV signal ν Oct A has provided to date. Hence, if ν Oct A is deceiving us, a more reasonable concern is that starsmore similar to it are more likely to be creating well-crafted il-lusions, such as γ Cep A . This possibility would create significantcomplications for other exoplanet claims now and in the future, andperhaps not restricted to similar subgiants.This background has motivated the photospheric and chromo-spheric studies reported here. Photospheric line variations are criti-cal for RVs but also for the extremely temperature-sensitive methodof line-depth ratios (LDRs; e.g. Hatzes, Cochran & Bakker 1998;Gray & Brown 2001; Kovtyukh et al. 2003; R15; R16). R15 andR16 demonstrate temperature constancy for ν Oct A to as little as ± K over 12 yr, with high consistency with the very low photo-metric variability recorded by
Hipparcos (see Table 1). This latestLDR series is also relevant as, more or less concurrently, observa-tions have also been obtained by NASA’s TESS mission which sig-nificantly support ν Oct A ’s photometric stability, as well as RVsfrom ESO’s HARPS spectrograph (Trifonov et al., in preparation).Chromosphere activity of ν Oct A has so far been limitedto three eye estimates of the Ca II K line from each of two spec-tra (Warner 1969), a single spectrum of Ca II H & K (R09) andH-line indices from 17 spectra (R16). All three papers concluded ν Oct A had minimal Ca II activity. Additionally, the Mg h + k chromospheric emission-line study by P´erez Mart´ınez, Schr¨oder &Cuntz (2011) found ν Oct A ’s activity to be very near their sam-ple’s empirically-derived basal flux of 177 cool giants. Here wereport on two much larger series: 198 line indices from the Ca II Hline and 1160 H α indices.Our work allows ν Oct A to be characterized in further detail,providing new evidence for the planet since significant activity isagain refuted. Even if the planet is eventually proven to be an illu-sion, which seems to be increasingly unlikely, our work adds to the fundamental knowledge of the star at the centre of this persistentlychallenging system.
The data analysed here were acquired in two series, one abouta decade ago and the other over the past two years. Both serieswere obtained at the University of Canterbury Mount John Obser-vatory using the 1-m McLellan telescope and HERCULES, a fibre-fed, thermally insulated, vacuum-housed spectrograph (Hearnshawet al. 2002). The CCD was a × detector cooled to ∼ − ◦ Cwhich recorded the ν Oct A spectra with a resolving power R ∼
70 000 . Further instrument details and our reduction methods forobtaining flat-fielded normalized spectra can be found in Ramm(2004), where the first tentative mention of the conjectured planet ismade, and R16. Our reduction software (HRSP; see Skuljan 2004)automatically provides both vacuum and air wavelengths. To makeother vacuum-to-air conversions we used the formulae of Morton(2000).The older series comprises nearly 1200 spectra obtained from2009.96–2013.96, i.e. four years, and allowed our chromospherestudies of the Ca II H line and H α . The spectra were almost all ob-tained using an iodine cell that reconfirmed the precise-RV planet-like signal (see R16). For our H α study, 1160 spectra were in-cluded in the final analysis, made possible by the higher S/N atthese longer wavelengths. The initial sample size for our Ca II anal-ysis was limited to 700 spectra as the Ca II lines were not includedin the first year or so of observations. More details of these data setswill follow in the relevant sections.A smaller set of 135 spectra were acquired more recently, from2018.34 until 2020.42 i.e. over about 25 months. As the I cellwas not used for these observations, we could not obtain furtherhigh-precision RVs but instead could use these spectra to obtaina new series primarily of line-depth ratios. The last spectrum ob-tained (2020.42; JD245 9002) has the highest S/N of our entireseries and was acquired to also extend that range of our Ca II spec-tra. The time span of all spectra considered here is from the firstLDR spectrum, 2001.85, until this last observation i.e. ∼ yr. We first present the results from our line-depth-ratio analysis of thenew spectra (2018–2020) and compare them to the previously pub-lished LDR results (2001–20013 ; R15 and R16) as well as again,the
Hipparcos photometry (1990–1993). The LDRs demonstratethe continued thermal stability of ν Oct A ’s photosphere and soare a useful prelude to our chromosphere studies.
We used the same methods and pipelines employed in R15 andR16: specifically, for each of the 135 new ν Oct A spectra we con-structed 22 LDRs and their errors from ten spectral lines in thewavelength region 6232–6257 ˚A. The principal equations for thesecalculations are given in R15.One significant advantage of LDRs is that they can be usedto derive a star’s temperature – which brings additional benefits –using a series of calibration stars whose temperatures allow pre-cise interpolation (see R15; their fig. 1). Further increases in ac-curacy and precision are achieved by modelling the influences of © 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al. temperature and luminosity (i.e. evolution) using linear regression(Press et al. 1994; algorithm fitexy ) leading to a modified LDR la-belled MLDR (see e.g. Gray & Brown 2001; Catalano et al. 2002;R15). R15 reported an accuracy of ± K for recovering the20 calibration stars’ temperatures but a precision as small as ± Kfor their 215 ν Oct A
LDRs, in excellent agreement with Gray &Brown (2001): their temperature precision from 92 giant stars was3.9 K. Neglecting these influences can yield significantly poorertemperature statistics as Gray & Brown discuss in the context ofother studies.R15 summarizes the strong relationship between the T − LDR regression line’s slope s reg and the ratio’s error ǫ r (see theirsec. 4.1). The slope is an indicator of sensitivity of each ratio to thecalibration stars’ temperatures. It therefore provides the error oneach ratio’s temperature estimate i.e. ǫ T r = s reg × ǫ r . Fig. 1 (a)shows the error on each LDR eventually rises exponentially asthe spectrum’s S/N drops, as anticipated. We estimated the
S/N solely from the photon noise so that
S/N ∼ √ F c where F c is thecontinuum flux at the spectral line, and calculated each ratio’s S/N from the average of the two lines. Our two examples show typicalsimilarities and differences (the relationship illustrated here for thefirst time), and how ǫ T r can vary between ratios even though all thelines are within about 25 ˚A ( ∼ − ˚A).The 22 T MLDR values next allow the mean and standard devia-tion, σ , for each spectrum to be derived, weighted by w r = 1 /ǫ T r .Our average temperatures have no adjustment for any zero-pointdifferences of the T MLDR values for the 22 ratios. The mean values, h T MLDR i , and their standard errors ( S.E. = σ/ √ ) are illustratedin Fig. 1 (b) and (c) respectively. The final standard deviations havean average ± K which is consistent with the temperature ac-curacy stated above.The total set of 398 T MLDR values comprises 217 spectra fromthe first observing series (2001.85–2007.16, 84 nights; R15 andR16), 46 spectra acquired during the I -RV campaign but with-out the I cell (2011.22–2013.74, 20 nights; R16), and our data (26nights). The distribution of all of these LDRs in terms of S/N isprovided in Fig. 1 (b). This shows that T MLDR becomes less scat-tered as
S/N increases, particularly for
S/N & , though thismay just be an artefact of the smaller sample size. It can also beseen that all of the spectra with S/N . were obtained in ourlatest series. The more recent 135 spectra give a weighted mean temperature T ν Oct = 4810 ± K, with no significant difference from the val-ues reported in R15 and R16. Our errors yield χ ν ∼ . whichindicates their average ( ∼ K) is somewhat more than what wouldbe consistent with our tiny temperature variations. The three se-ries combined have a weighted mean T ν Oct = 4811 ± K. If thetemperature-recovery accuracy given above ( ± K) is added inquadrature to this, the final temperature estimate for the 2018–2020spectra is ± K, equalling the other two LDR temperaturesin Table 1 – Ref. (1) and (6).Fig. 2 illustrates the distributions of the mean T MLDR valuesfor the 130 epochs of the LDR spectra acquired over 18.6 yr. Themeans are weighted by the standard errors w = 1 /ǫ T⋆ where weabbreviate T MLDR with T ⋆ . Our results display an extraordinarydegree of relative accuracy between the three T MLDR series – theoffset of the three mean temperatures is remarkably tiny at about1 K (see T ν Oct values in Fig. 2). So whilst the absolute accuracy of
Figure 1.
Temperatures ( T MLDR ) and errors from modified line-depth ra-tios in terms of
S/N . (a) Temperature-calibrated errors, ǫ T r , for two ratios;e.g. ‘3332’ labels the line pair 6233 ˚A and 6232 ˚A. (b) Averaged T MLDR values for 398 spectra: ‘ × ’ 217 LDRs (2001–2007), ‘ ♦ ’ 46 LDRs (2011–2013), ‘ • ’ 135 LDRs (2018–2020). (c) Standard errors on h T MLDR i . (a)and (c) include only the 135 new spectra. LDRs may be less impressive, there is extraordinary relative accu-racy even though their sensitivity may be imagined to make themvulnerable to variability from, for instance, measurement artefactsincluding subtle possibilities such as stray light within the spec-trograph (which is unexpected given the design of HERCULESand that our line-depths create ratios). Clearly our methods providepractically identical MLDR distributions of outstanding precisionover nearly 20 yr, despite two CCDs being used and many otherinstrumental and environmental parameters varying as well. Thuswe can be quite confident our LDRs are highly unlikely to be sig-nificantly compromised by any of these non-stellar variables.We searched our data for periodicity using the generalizedLomb-Scargle (GLS) periodogram as derived by Zechmeister &K¨urster (2009). The GLS is ideal for time series with uneven tem-poral sampling and nonuniform measurement errors as reportedhere. Our periodograms are normalized assuming the noise is Gaus-sian (Zechmeister & K¨urster; their eq. 22). In Fig. 2, we show theresult for our epoch-averaged MLDR temperatures, along with ap-proximate analytical P -values estimated according to Sturrock &Scargle (2010). We find no evidence for statistically significant pe-riodicity at any frequency. © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A Figure 2.
The 130 nightly means of the T MLDR values from 398 LDR tem-peratures. Top: The distributions of the three LDR series defined in Fig. 1together with their ± σ error bars. The mean temperatures T ν Oct and theirstandard deviations are given below each series. Bottom: The GeneralizedLomb-Scargle periodogram and corresponding FAP levels. The pair of ver-tical dashed lines identify our revised ± σ range of ν Oct A ’s predictedrotation period (see § 3.5). The shorter bold line marks the planet-like RVperiod ( P RV ∼ d). Hipparcos and TESS
We next make a brief digression to describe photometric satellitedata which we will then compare to our LDR evidence. Since it hasbeen estimated that ν Oct B is at least 6 mag fainter than ν Oct A (R09, and see Table 2), the LDRs and photometry are assumed toonly record ν Oct A .Two satellites observed ν Oct, acquiring data whose end datesare separated by 30.6 yr. The first,
Hipparcos , achieved the longestbaseline ( ∼ d, 1989.45–1993.17; ESA 1997) and identified ν Oct A as one of its more stable targets (see Table 1). More re-cently, NASA’s TESS mission (Ricker et al. 2015) observed ν Octtwice in the 2-minute short-cadence mode. It was covered in Sec-tors 13 (2019 Jun 19 – Jul 18) and 27 (2020 Jul 5 – Jul 30), i.e. base-lines of about 28 and 24 days. We retrieved the Pre-search DataConditioning Simple Aperture Photometry (PDCSAP) using theL
IGHTKURVE software package (Lightkurve Collaboration, 2018).Approximately, this photometry has midtimes separated by 395 dand span 408 d. Therefore the two TESS records sample slightlydifferent phases of the RV cycle (assuming P RV ∼ d is stillrelevant), and together they include about 13 per cent of it. Thesehigh-precision records are also consistent with this bright spectro-scopic binary being exceptionally quiet, at least during these shortbaselines and within TESS’s spectral response capabilities (600–1000 nm bandpass; Ricker et al. 2015): the RMS scatter of eachPDCSAP dataset and both combined is just 0.02 per cent. ∆ m LDR from T MLDR
The temperature calibration enables one more significant bene-fit: the T MLDR values can be converted to a magnitude differ-ence ∆ m LDR using the Stefan-Boltzmann law ( L ∼ R T ). The Hipparcos and TESS photometry strongly support a claim that ∆ L ∼ , and the LDR results just as strongly record ∆ T ∼ . Figure 3.
Two time series for ν Oct acquired by NASA’s TESS missionduring mid-2019 ( N = 19 579 ) and mid-2020 ( N = 16 780 ). The RMSof each data set is 0.02%. PDCSAP: Pre-search Data Conditioning SimpleAperture Photometry. Therefore, though ν Oct A no doubt has some surface variability,as even less evolved stars do, we assume any radial changes are in-significant in our next calculation, a repeat of what was reported inR15 and R16. Eq. (1) provides the conversion to ∆ m LDR with thatassumption (i.e. ∆ R = 0 ): ∆ m LDR = −
10 log (cid:18) T ⋆ T ν (cid:19) ± s(cid:18) σ T⋆ T ⋆ (cid:19) + (cid:18) σ Tν T ν (cid:19) , (1)where we abbreviate T ν Oct (i.e. ± K) with T ν . Note that ∆ m LDR is extremely sensitive to the temperature: varying T ⋆ byonly one degree changes ∆ m LDR by about one millimagnitude.In Fig. 4 we compare these ∆ m LDR estimates to the magni-tude differences for the longer baseline photometry of
Hipparcos ,whose ∆ m Hip values relate to their mean. A striking similarityis evident between the four ∆ m distributions, all the more so asthere are no zero-point offsets applied to any T MLDR data. The lat-est MLDR series extends the time span of all ∆ m values to about30.5 yr. This graph also demonstrates that the more recent lower- S/N data do not significantly compromise the precision of these ∆ m values relative to the earlier data sets.Finally we note the small difference between the standard de-viations of ∆ m Hip and ∆ m LDR , where σ Hip ∼ . is greater than σ LDR ∼ . mmag. Of the various possible reasons one perhapsmore interesting to speculate is that this small difference recordsthe anticipated tiny contribution that ∆ R = 0 would make to the Hipparcos photometry, but not our LDRs which are more directlysensitive to temperature changes. Our evidence for this is too slimfor a credible claim but the idea might be successfully exploredwith more suitable data.This completes our work with LDRs. It confirms past conclu-sions: ν Oct A continues to have a very thermally-stable photo-sphere, which is difficult to reconcile with surface variability as wepresently understand its many variations. As discussed in consider-able detail in the LDR work reported in R15, neither star spots norpulsations are believable scenarios for creating the planet-like RVsin these circumstances. The same explanations there apply here. © 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al.
Figure 4.
The 398 magnitude differences, ∆ m LDR , derived using Eq. (1)and compared to ∆ m Hip from 116 best-quality ( flag = 0 ) Hipparcos ob-servations. The value above each series is the standard deviation of ∆ m (mmag) weighted by the standard errors. The upward arrows identify themidtimes of the two TESS photometric baselines (2019, 2020). Gaia and more clues negating a stellar origin for RVs
With the benefit of
Gaia ’s parallax (see Table 1) and our confir-mation of the photosphere’s stable temperature, we can also reviewseveral parameters that have some relevance here. The
Gaia par-allax is about 10 per cent greater than the three values reportedin R09, which includes that from
Hipparcos (ESA 1997). Con-sequently ν Oct A ’s luminosity is less, which we now estimateis about 14 L ⊙ (and M V = +2 . mag; Table 1). Based on theweighted mean of the five temperatures given above (i.e. ± K), ν Oct A ’s radius is also less i.e. . ± . R ⊙ (see R09,their eq. 3). The star is therefore now classified more closely as asubgiant, i.e. ∼ K1 IV , and placed in a sparsely populated part ofthe H-R diagram (very near γ Cep A ), well-separated from the so-called instability strip and other known classes of pulsating stars. Itremains to be seen if future revisions change this significantly.Such a star is not known to have a rotation period anywherenear as long as that of the RV cycle i.e. P RV ∼ d. In fact,the star’s v sin i ∼ − (see Table 1), our revised esti-mate for the radius, and assuming the rotational and orbital axesare parallel, i.e. i rot ∼ ◦ , predicts the star’s rotation period is P rot = 125 ± d. R09 devotes their sec. 4.1.7 to the considerableimprobability that rotation could be significant for the RV signal’sorigin. This scenario was made even more difficult to believe whenR16 doubled the time span of the persistent RV cycle to 12.5 yr,and is reduced even further by the new evidence presented here.Finally, we assess if solar-like oscillations have any chanceof influencing our observations of the now less-evolved ν Oct A .One way is to apply the formulae from Kjeldsen & Bedding (1995),specifically equations 7, 8 and 10 to our new values for [ R , T eff , L ] .Using the weighted mean for the stellar mass, . ± . M ⊙ , suchoscillations have a predicted velocity amplitude of about 2 m s − , amaximum-power period of only 1.5 hr and a luminosity amplitude δ L / L ∼ ppm at 6000 ˚A (the wavelength from Wein’s Displace-ment Law for the peak luminosity for our mean T eff ). These valuesare in excellent agreement with the graphical ones in Dupret et al.(2009) who studied both radial and non-radial oscillations. One oftheir stellar models is slightly evolved and similar to ν Oct A (their Case A, fig. 5, panel 3 at ν = 190 µ Hz). Its non-radial modes havesmaller amplitudes than the radial ones, and together these pro-duce a low-amplitude and very complex frequency spectrum, noth-ing like ν Oct A ’s planet-like RV signal. Such oscillations cannothave any significant impact on any of our data.We now report our analysis of the chromosphere-activity indi-cators, the Ca II H line and H α , the study of which benefits fromthe long series of precise LDR results – any photospheric contribu-tion to these indices is almost certainly insignificantly variable. Ca II AND H α INDICES
Many spectral lines have been identified as being useful for moni-toring chromosphere activity in late-type stars (see e.g. Lisogorsky,Jones & Feng 2019). One of the motivations for assessing suchbehaviour is the quest for increasingly precise RVs for exoplanetsearches. Whilst many photosphere lines can be used as indicatorsfor chromosphere activity, the classic ones with the strongest his-tory are the resonance doublet lines of Ca II H and K at 3968.47and 3933.66 ˚A close to the boundary of the ultraviolet and visible(see e.g. Wilson 1963; Linsky & Avrett 1970; Wilson 1978; Dun-can et al. 1991; Baliunas et al. 1995). However, these two lines havethe weakness, which will significantly influence our study, that theyare recorded in spectral regions that have inherently low
S/N .At the other end of the visible spectrum is H α ( . ˚A).This has the distinct advantages of much higher S/N than providedat Ca II H and K ( ∼ − × greater), and a better defined contin-uum without the complications of many neighbouring metal linesas Ca II H and K also have. However, as we will show, H α insteadhas the complication of telluric lines, and for a quiet star such as ν Oct A , these lines dominate the line-index variability. The
S/N differences resulted in our having a final set of about 200 Ca II H-line indices but nearly six times as many H α indices. An index is a conventional method to assess variability of a suitableline’s core for evidence of stellar activity (for its earlier history seeGriffin & Redman 1960). Our index, I , includes the line’s core in-terval F and two reference intervals F and F : I = 2 × F F + F , (2)where each flux interval i comprises N i bins having relative fluxes f i . Modern studies use either total fluxes or mean fluxes: the indexderived from mean fluxes h F i i exceeds that from total fluxes by N R /N (if N R = N = N ). If total fluxes are used, the error oneach flux ǫ i = σ i × √ N i . If mean fluxes are used ǫ i = σ i / √ N i ,i.e. the standard error on the mean, which ensures the index’s rela-tive error will be identical to that from total fluxes. We will alwaysuse mean fluxes.The index error ǫ I was calculated using error propagation: (cid:16) ǫ I I (cid:17) = (cid:18) ǫ F (cid:19) + ǫ + ǫ ( F + F ) = E + E , (3)where we introduce the error symbols E here and below for futurereference. Whilst this is the typical calculation for such an index,Eq. (3) may be incomplete since the flux errors are calculated from © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A Figure 5.
Four ν Oct A Ca II H-line spectra for representative epochs, preliminary indices and
S/N values. In each plot the core width represented is 1.0 ˚A.Top: The highest
S/N spectrum across three orders. The core width and two reference intervals are marked with bold horizontal lines. The core is magnifiedbelow in (a). Below: The cores of four spectra with both decreasing
S/N and index I CaH . Included are the I CaH , observation date, and
S/N . the fluxes which, if suitably chosen, should be highly correlated.This suggests covariance deserves consideration.The expression for the total covariance CoV must be added toEq. (3):
CoV = − ǫ ǫ T F ( F + F ) ρ , T + 2 ǫ ǫ ( F + F ) ρ , = E + E , (4)where ρ is a correlation coefficient, T represents the sum of the ref-erence fluxes, and ǫ T is calculated by also including its covarianceterm, i.e., ǫ T = q ǫ + ǫ + 2 ǫ ǫ ρ , . (5)The sign of ρ , T and ρ , will determine if E and/or E increaseor decrease the total error, or if E + E → . If only one refer-ence interval is used and covariance taken into consideration, thecontribution of E to the total error is absent. Ca II H line spectra and data set
When seventeen Ca II H-line indices were reported in R16, thespectra we analyse here were available. However, most of the 700archived Ca II spectra, have quite low S/N ( . ), and previouslyhad been considered probably useless for any definitive study basedon expectations and a preliminary sample’s analysis.As a definitive understanding of the ν Oct system is yet to be attained, we took a second look at this large pool of spectra to re-view the earlier decision. We decided that it was a poor strategy toco-add spectra since the few available for most nights result in verylittle advantage and co-adding many across multiple epochs wouldprovide fewer final indices, most obtained with greater complica-tion and risk for errors as for instance Zechmeister et al. (2018)warns. Instead, a rather more novel approach was undertaken whena distinctive distribution that could be modelled revealed itself froma larger sample of indices.The HERCULES archive provided an initial sample of 482spectra. Many of the original 700 spectra could not be properlyprocessed due to more prevalent cosmic rays and other complica-tions. We restricted our analysis to the record of the Ca II H line in n = 143 as its S/N is about 40 per cent greater than its duplicatein n = 144 and both records of Ca II K. The 218 discarded spectrahave
S/N . at the H line record we used. Four H-line spectraof varying S/N are illustrated in Fig. 5 showing ν Oct A ’s mini-mal chromospheric activity and the extent of slight infilling whichvaries primarily due to spectral noise. Ca II indices and errors The origin of the dominant chromospheric flux is in the vicin-ity of the temperature minimum (Linsky & Avrett 1970) whichis presumably highly correlated with the LDR temperatures justdescribed. The Ca II H line has variable amounts of infilling andactivity depending on, for instance, the star’s luminosity (Wilson& Bappu 1957). Typically the Ca II H-line core of main-sequencestars is sampled with an interval of about 1–1.1 ˚A (e.g. Wilson © 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al.
Figure 6.
The preliminary Ca II H indices from 482 ν Oct A spectra fora core width W = 1 . ˚A. (a) The indices, with the total for each subsetbounded by S/N = 30 , , given above. The dotted horizontal lineidentifies the weighted mean for the 27 spectra with S/N > . (b) Theweighted mean indices for each h S/N i bin. The bold curve is the parabolicfit to the 13 h S/N i bins in the range [39, 60]. (c) The linear fit for S/N > . In (b) and (c) the y-scale is magnified for clarity and the vertical solidlines represent ± σ . ν Oct A , which in any case has a verythermally-stable photosphere from evidence summarized in Fig. 2.Our H-line cores have a width of about 1.0 ˚A; see Fig. 5. Thisdetail provides further indirect evidence for ν Oct A ’s revised less-evolved luminosity class (see § 3.5). Rather than commit to a singleinterval width W we used a series in 0.1 ˚A steps from 0.9 ˚A to1.5 ˚A. We selected two reference intervals, R1 and R2, each 10 ˚Awide, centered at λ air = 4015 ˚A in order n = 142 and at λ air =3990 ˚A in order n = 143 (see top panel Fig. 5). The second redderreference interval was chosen so that it would have a slightly higher S/N motivated by our mostly low-quality spectra.Our preliminary 482 indices are shown in Fig. 6 (a), given inrelation to their
S/N . These distributions fall into four ranges de-lineated by the vertical dotted lines in each panel at
S/N = 30 , 40and 60. In Fig. 6 (a) the anticipated near constancy of the indicesfor a quiet star such as ν Oct A is evident for
S/N > . The dis-tributions of E . . . E and their sum are illustrated in Fig. 7. Ourerrors yield ρ , T ∼ − . and ρ , ∼ +0 . , so that both E and E are positive, and E is about as significant as E . E is alwaysthe dominant term, but its contribution decreases as S/N increases.The error terms tend to plateau just above the threshold
S/N ∼ ,particularly for E and E . Below this threshold, the total error in-creases exponentially (Fig. 7b), and above it, the minimum errorsbegin and average . ± . . This error, incorporating thecovariance terms, is equivalent to about 3.4 per cent of the indexand about . × greater than the error without covariance included,a significant difference. Figure 7.
The preliminary Ca II H index errors from 482 ν Oct A spec-tra. (a) The percentage fraction each error term contributes to the total. Thesingle isolated symbols label the values from mid-2020 (JD245 9002). Thethree dotted vertical lines are as in Fig. 6. The errors are for a core width W = 1 . ˚A since narrower widths have E , E and E increasingly co-incident, approaching a mutual minimum contribution of about − %.(b) The total errors given by the sum E + E + E + E . The apparently near-constant 27 indices with
S/N > inFig. 6 (a) in fact delineate a fairly well-defined sloping line asshown below in Fig. 6 (c), even without the high- S/N anchor. Thiswe modelled with a linear fit weighting each index by /ǫ I to giveour modified indices: I ′ = I − ( a S + a ) + h I i , (6)where S represents S/N and h I i is the weighted mean of these27 indices and defines our zero-point for I ′ . Note that if our spectrahad S/N limited to [60, 90] the implied slope of the distribution
S/N > would disappear. The modelled indices have larger er-rors determined by the rescaled original index error created by thefitting process, the RMS of the linear fit (which varies with the corewidth of the H line), and the standard deviation of the original mean σ h I i = 0 . , each added in quadrature.It is impossible to guess what the average behaviour of the427 indices is in the interval [30, 60] in Fig. 6 (a), so we created aseries of narrow S/N bins, typically with ∆ S/N = 1 . Starting at
S/N = 30 we extended the ∆ S/N range in one unit steps untilwe had at least ten indices in each bin. This provided 23 bins. Foreach bin we calculated the average and standard deviation of the
S/N and the indices, each index weighted by its error as above. © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A Figure 8. χ ν values from our final indices and errors in terms of S cut .The results for four Ca II H-line core widths W are shown. The numberabove each S cut is the total number of indices included in each parabolicfit (shown in Fig. 6 b), these finally combined with the 27 high- S/N indices.
These statistics, in relation to each bin’s mean
S/N are plotted inFig. 6 (b).For
S/N > the indices are adequately fit by a parabola.This fit though requires further care as it is not obvious what is itslower limit, which we label as S cut . Its choice is another balanc-ing act between precision and sample size for our final time seriessince the binned indices have increasingly higher standard devia-tions as S/N decreases. We discarded 221 spectra in ten bins with
S/N < as they have the largest standard deviations and are leastconsistent with our intended parabolic fit (marked with crosses ‘ × ’in Fig. 6 (b). For the 13 remaining h S/N i bins, which include 261original indices, we calculated the model-fitted final indices andtheir errors for core widths of W = [0 . , . ˚A. These four widthsencompass those considered most suitable for our spectra (i.e. 1.0and 1.1 ˚A; see Fig. 5). χ ν Of the original 700 archived spectra, ∼ per cent are discardedfrom our complete analysis which somewhat vindicates the deci-sion several years ago. Our errors and indices are now final. The er-rors each comprise two conventional terms E and E , two covari-ance terms E and E and three terms from each model dependingon the spectrum’s S/N , making a total of seven terms. Each erroris approximately doubled by the model-fitting calculations.We calculated χ ν for our final indices and errors for our gridof four H-line core widths and thirteen S cut values. Fig. 8 showsthat our atypical analysis of mostly low- S/N spectra and the in-clusion of covariance ultimately provides strong evidence for theconsistency of our indices, errors and models. For example, for theH-line core width W = 1 . ˚A, χ ν ≈ . for the four consecu-tive parabolic fit thresholds S cut = [41 , . Without covariance χ ν = 2 . Our final relative errors average about seven per cent forthe 198 indices defined by S cut = 41 . In Fig. 9 we illustrate our fi-nal indices and errors for the time series defined by S cut = 41 and W = 1 . ˚A which corresponds to χ ν = 0 . . This example is ap-proximately normally distributed as the lower two panels illustrate.We also derived χ ν = 0 . for the 27 indices from the spectra with S/N > . Figure 9.
Two distributions of indices based on the Ca II H-line core width W = 1 . ˚A. Top panels: The dashed and dotted horizontal lines identify themean and ± and ± σ . The error bars are ± σ and the y-scales are iden-tical. (a) 27 indices with S/N > , χ ν = 0 . . The right arrow pointsto the mid-2020 (JD245 9002) index. (b) 171 indices with S/N > , χ ν = 1 . . (c) Frequency distribution of 198 indices. Open: (a) indices.Hashed: (b) indices. (d) Normal probability plot of 196 indices within ± σ of the mean in (b), and the regression line based on the index mean andstandard deviation. Figure 10.
GLS periodogram of the final series of 198 H-line indices using S cut = 41 , with the corresponding FAP levels. The pair of vertical linesidentify the boundaries of our revised predicted ± σ range of ν Oct A ’srotation period (see § 3.5) and the bolder line the planet-like RV period( P RV ∼ d).© 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al.
As we found with our LDR work, within our errors, there isnothing here that suggests anything but quite randomly distributeddata, regardless of the temptation to perhaps imagine some signifi-cantly periodic behaviour in Fig. 9 (b) where removal of only a veryfew data points would make such a suspicion far less likely. OurGLS periodogram search as described in § 3.1 confirms this (seeFig. 10). It was created using the indices plotted in Fig. 9. There isno significant peak corresponding to ν Oct A ’s predicted rotationperiod ( P rot ∼ d) or the planet-like RV period ( P RV ∼ d)where a deep trough is in fact evident. Unfortunately, our lack ofany detection of a credible rotation period (both here and with ourLDR data) means we are still limited to estimates of P rot as in Ta-ble 1 and § 3.5 (where, in any case, we noted rotation remains ahighly unlikely explanation for the RV cycle). H α spectra and data set ν Oct A ’s unique planet claim demands certainty about any con-clusions relating to any index variability similar to the RV signal.Our H α indices have this characteristic, having a quasi-periodicityin the vicinity of the conjectured planet’s period. We intend to pro-vide robust proof that this is caused solely by telluric lines. H α is a prominent photospheric absorption line in late-typestellar spectra. Its core can also include chromospheric activity.It was this profile variability that led to H α being studied for β Cephei in 1979 using one of the first digital detectors, an ex-perimental Fairchild CCD (Young, Furenlid & Snowden 1981).We employed a long time series of H α indices as denselysampled as possible, corresponding to the I -cell RVs reported inR16. Such a sample is critical for demonstrating the cause of thedominant variability in our indices. The 1160 spectra archived overfour years comprise 229 epochs. Thirty spectra (from 18 epochs)were acquired without I which are useful to compare our indiceswith and without I involvement. For the majority with I lines,our I cell benefited from a temperature controller designed to min-imise variability ( . ± . C), so that the density and extent ofthe I forest was assumed to be quite constant. H α is recordedin two HERCULES spectral orders, n = 86 and 87. The S/N inorder 87 is about twice that in 86 so we used only n = 87 , theirrange at H α being S/N ∼ [90 , and their mean 220.Our first evidence of the role of telluric lines is presented be-fore indices are calculated. The high S/N region where H α re-sides is also uncomplicated by large numbers of other photosphericlines such as the metal lines near Ca II H and K. It is thereforevery suitable for making a preliminary visual comparison of all ofour spectra with respect to a reference. This has the advantage thatthe entire H α region can be assessed for significant flux variationswhich may be concealed by the solitary line index. We ensured allour spectra have an essentially level continuum with a maximumrelative flux f max = 1 . , and that each H α core centre is measuredaccurately to within a pixel by also comparing the fitted centre ofthe sharp Ca I line ( ∼ . ˚A) redward of H α with each H α core fit. We calculated the relative flux differences ∆ f i betweeneach spectrum and our reference (see Fig. 11).This plot alone is strong evidence that H α has very lit-tle core activity since the ∆ f i variations for the core interval [ − , +15] km s − are actually the least of the wide range shown.Instead we see time-dependent line movement contaminating both We will discuss the absence of any significant impact of the I forest onour H α indices in the final paragraph of § 4.3.2. Figure 11. H α flux-difference curves ( ∆ f i ) relative to the ν Oct A reference spectrum plotted above. The core boundaries of our H α indicesare identified with dotted vertical lines at [ − , +15] , [ − , +35] , and [ − , +70] km s − . The small arrowed feature is likely to be due to acosmic ray since it does not appear in the duplicate record in order 86. shoulders of H α , but particularly the redward one, which subse-quent evidence will prove are telluric lines. We were fortunate thatthe strongest telluric lines did not engulf our line cores as may oc-cur in other circumstances. ν Oct A ’s absolute RV
All of our spectra include telluric lines and most also the I for-est. An example of these non-stellar lines in a HERCULES spec-trum of the fast-rotating Be star Achernar ( α Eri, B6V, v sin i ∼
250 km s − ) is provided in Fig. 12. About a dozen prominent tel-luric lines are recorded but the H α region includes many morefainter ones. ν Oct A ’s absolute RV is intimately connected to the relativebehaviour of its lines and any non-stellar lines. We measured theabsolute radial velocity ( RV abs ) of ν Oct A using the shift fromthe rest wavelength of the Ca I line at ∼ . ˚A. This line is rec-ognized for its relative stability (e.g. K¨urster et al. 2003; Robertsonet al. 2013), and for our purposes, the resulting low-precision RVsare adequate. Our RV abs estimates and the best-fitting curve areprovided in Fig. 13. Vertical lines identify the RV minima whichhave different time spans ∆ t between them making them ideal forconnecting the RV abs variations to our index variations that we willnext describe. Note that all of the ∆ t intervals differ from the or-bital period of the conjectured planet and the predicted rotationperiod of ν Oct A , and critically, the ∆ t differences are due to ν Oct A ’s orbital RVs that a single star would not provide.Fig. 14 includes the H α spectrum with the highest S/N , acartoon representation of the strongest telluric lines recorded inFig. 12, and identifies the Ca I line. The reference intervals R1 andR2 are defined in the next section. For instance, within the 95 ˚A shown in Fig. 12, the online database HI-TRANonline (https://hitran.org) lists 576 water vapour lines, the principalspecies contributing to the telluric spectrum. For details of its latest releasesee Gordon et al. (2017). © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A Figure 12.
Above: the weak but dense I -line forest in the vicinity of H α (from a white+ I spectrum). Below: A spectrum of the fast-rotating α Eri(B6V, v sin i ∼
250 km s − ) including I and about 15 more promi-nent telluric lines. The wavelength range is about × greater than theequivalent of the RV scale in Fig. 11. The telluric line marked with ‘ × ’( ∼ . ˚A) also dominates the redward shoulder of the ∆ f i curves inFig. 11. Figure 13.
The absolute radial velocity of 1160 ν Oct A spectra based onthe wavelength shift ∆ λ of the Ca I line at λ air = 6572 . ˚A. The verticaldashed lines mark successive RV abs minima with the time interval ∆ t tothe integer day between them (their average is 365.6 d). The curve is basedon the barycentric RV corrections ( ∼ [ − , +16] km s − ) and the orbitalsolutions for ν Oct A and the conjectured planet (Ramm et al. 2016), andour best-fitting estimate of the systemic RV ( +37 . − ). H α indices The literature describes many choices for the flux intervals for H α indices. For a survey of their variety see e.g. K¨urster et al. (2003);Cincunegui et al. (2007); Gomes da Silva et al. (2011); Ortiz et al.(2016); Zechmeister et al. (2018). We used three H α core widths,with the centre defining the RV zero-point for all flux intervals.The narrowest, [ − , +15] km s − , is suggested by the evidencein Fig. 11, and is similar to that used by K¨urster et al. (2003).We also included the wider interval [ − , +35] km s − (similar toZechmeister et al. 2018) and one twice that, [ − , +70] km s − ,chosen to be just beyond the maximum absolute RV of ν Oct A ( ∼
61 km s − ). We used the two reference intervals R1 and R2 de-fined by Zechmeister et al. (2018), namely [ − , − − and [+100 , +300] km s − and calculated the index errors includ-ing covariance as described earlier. Unlike our Ca II indices, there is no correlation between S/N and our H α indices ( ρ ∼ +0 . ). However, none of the index dis-tributions (see Fig. 15) appear to be strictly random – they all haveevidence of cyclic behaviour with the dominant period of about oneyear, although this doesn’t become better defined until the indexuses the two wider H α regions, the main reason for their inclu-sion. Only the widest core width provides a significant maximumpeak power in a periodogram and this is at 365.5 d (coincidently themean of the approximated RV abs timespans in Fig. 13 is 365.6 d).This quasi-periodicity close to one year strongly implies the pri-mary cause has a non-stellar origin, i.e. telluric lines.For the first time we demonstrate the usefulness of the five RV abs minima lines as evidence that telluric lines are the dominantcause of our index variations: the set of lines has been offset in timeby − d for the [ − , +35] km s − core width but unadjusted forthe widest one, and these included in Fig. 15 for the top two panels.Not only is adequate alignment found, simply made by eye, but thetwo offsets are unequal. The relative contributions of stellar andtelluric lines vary if the flux intervals differ and this explains whythe time shift to make this alignment is unequal for the two widercore widths that we can more easily assess – in fact, for this reason,it is also more likely the shifts will differ. The more precise indexvariations of the widest core interval is perhaps explained by themore prominent roles of both the very stable photosphere and theadditional telluric lines found here (which are also present in thereference intervals).Thirty spectra were acquired without the I cell, the benefit ofwhich is also clear from Fig. 15: the no- I indices have a distribu-tion that is consistent with those with I . To confirm this similarity,we also derived indices from our 135 new spectra (used for ourLDR study) whose spectra also have no I lines. Their distributionis far less dense and uniform than our much larger series (whichis the principal reason the former were not otherwise included for H α ) but are statistically indistinguishable from that derived fromspectra with I . This demonstrates that the previous concern for us-ing spectra including the I forest for an H α study was unfounded,and duplicate the claim made in K¨urster et al. (2003) that I in-volvement made no significant impact on their H α and Ca I in-dices for Barnard’s star. That the complete absence or inclusion of I lines makes no significant difference to these indices also makesit clear that any temperature variations of the I cell leading to vari-ability of the forest’s extent is highly unlikely to make any differ-ence either. Several more pieces of evidence ensure our H α variations aredominated by telluric lines. Firstly, Bergmann (2015) used HER-CULES to also measure H α indices for τ Cet, δ Pav and α Cen Aand B in the same time span and frequently on the same nightsas our ν Oct A spectra. These indices use a wider core interval [ − , +115] km s − and different reference intervals but still We also calculated all of our indices using the reference intervals definedby K¨urster et al. and Cincunegui et al., which are distinctly different fromZechmeister et al. These index distributions were indistinguishable for thenarrowest core width and barely so for the mid-width core. The indices wederived with the Zechmeister et al. reference intervals were significantlymore precise for the widest core interval, which is why they are reported.© 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al.
Figure 14.
The H α region of our ν Oct A spectrum with the highest
S/N ∼ . It has RV abs ∼ +35 . − which coincidentally is about midwayin the range of RV values depicted in Fig. 13. The core centre is marked with a vertical dashed line at RV core = 0 and our two reference intervals R1 andR2 located accordingly. The stellar spectrum and RV core scale will move relative to the wavelength scale due to RV abs , whereas the cartoon of telluric linesabove the spectrum is fixed. Note this spectrum’s Ca I line is bounded by two strong telluric lines separated by ∼
130 km s − and is discussed in § 4.3.3. those distributions and ours are very similar. Bergmann’s four starsand ν Oct A all have similar RV abs ranges ( ∼ −
55 km s − ) soall had H α moving relative to telluric lines in quite similar ways.Secondly, Bergmann’s strategies to manage stray-light contamina-tion between α Cen A & B were strictly defined by his evidencehis distributions were also substantially due to telluric line involve-ment, and more specifically, water vapour. Thirdly, Bergmann’s re-duction pipeline differed from ours so the chances of the two du-plicating a reduction artefact is also highly unlikely.The final evidence comes from indices of the recognized ‘sta-ble’ Ca I line used for our absolute RV estimates. We also calcu-lated these using a series of core widths: the [ − , +15] km s − interval that is very similar to that used by K¨urster et al. and Robert-son et al. (2013) for their Ca I indices, and a series in 10 km s − steps from 10–70 km s − . We found [ − , +30] km s − providedthe least variation (half that provided by [ − , +15] km s − ).Again, the core interval [ − , +70] km s − recorded most dis-tinctly the influence of telluric lines (see Fig. 16). Note that thiswider interval is more than the separation of the two strong telluriclines bounding Ca I in Fig. 14, and so both influence some Ca I indices. Our RV abs minima lines are again successfully aligned tothe dominant cycles for the wider core interval. These results showthat 1. the index distribution of the stable Ca I line closely mimicsour H α indices and has the least variation of all our indices (themean for [ − , +30] km s − is . ± . ≡ Ca I or any other lineis best studied when less likely to be contaminated by tellurics. H α index errors and final comments We calculated our index errors E . . . E using the same methodsdescribed in § 4.1. Given the significant impact of the covarianceterms E and E to our Ca II index errors, it was somewhat sur-prising that they make little difference to our H α errors, since themean fluxes of the reference intervals are again highly correlated,just as they were for our Ca II indices ( H α : ρ , ∼ . ). However,perhaps related to the influence of telluric lines, the associated er-rors ( ǫ = σ/ √ N ) are not at all highly correlated, regardless of thecore or reference intervals used, since we also checked this resultwith the K¨urster et al. reference intervals. If this result is commonin other H α index studies it shows that the absence of the covari-ance terms also made no significant difference to their errors.The core width that is most suitable for our originalpurpose – assessing H α ’s activity – is the narrowest one, [ − , +15] km s − . That index distribution is in the bottom panelof Fig. 15. E is again by far the dominant error term. The relativecontributions of the four error terms to their total are (0.962, 0.046,0.005, − . ). The relative total errors have a mean . ± . percent which yield χ ν = 0 . . Both E and E are practically zerofor two different reasons: E ∼ as ρ , T = − . , and E ∼ primarily because the error portion is ∼ (and ρ , = − . , sothat E actually reduces the total error, but only insignificantly).That we can precisely correlate the tiny effects of telluric linesin terms of RV abs suggests our methods are reliable and any H α activity is likely to be significantly less. Also, as a final minor detail,having established the origin of the dominant variations, we cannow speculate that contributions to the almost nightly variationsmay be differences with the observations’ airmasses and the hu- © 2021 RAS, MNRAS , ?? [2793]–15[2806] nactivity of the retrograde-planet host ν Oct A Figure 15. H α line indices from 1160 ν Oct A spectra for three core inter-vals. ‘ ◦ ’: 1130 indices with I , ‘ × ’: 30 indices without I . (a) The dashedvertical lines are unshifted relative to their zero-point time in Fig. 13, butin (b) are shifted by − d, so these two 5-line sets are offset from eachother. The y-axes all span the same range i.e. 0.085. The mean percent-age errors for the ± , ± and ±
70 km s − indices are respectively . ± . , . ± . and . ± . per cent. Figure 16. Ca I indices from 1160 ν Oct A spectra for two core widths.‘ ◦ ’: 1130 indices with I , ‘ × ’: 30 indices without I . The axis ranges areas in Fig. 15. The dashed vertical lines in (a) are shifted relative to theirzero-point in Fig. 13 by − d. midity that the telluric lines’ primary component, i.e. water vapour,also records. We report five new independent series of precise data that all indi-cate ν Oct A is a very quiet star: two photometric series from TESS(2019, 2020), which more or less coincide with our LDR study ofits photosphere (2018–2020), and our two large surveys of its chro-mosphere whose origin is the I -cell RV time series (2009–2013).The TESS photometry bounds the 1437 RVs (2001–2013) with Hipparcos observations three decades before (1989–1993). A sixthline of new evidence is the
Gaia parallax that indicates ν Oct A is less luminous, and so more probably approximately K1 IV. Thisalso strongly favours the quiet-star classification, as does our re-view of solar-like oscillation scenarios. These results are consistentwith all previous surveys, for instance, more recently, two bisectorstudies (R09 and R16), and two other LDR studies (R15 and R16).There is no significant variability of any of these many pho-tometric or spectroscopic time series, and certainly none corre-lated with the planet-like RVs. Other facts are against ν Oct be-ing a heirarchical triple-star system or the cause being related to ν Oct A ’s rotation. Thus this overwhelming evidence demonstratesall non-planetary solutions continue to be implausible, which in-stead we interpret is only compatible with a retrograde planetwhose properties are approximated in Table 2.With thousands of planets now described, ν Oct Ab remainsunprecedented in terms of the system’s geometry. It still providesmany opportunities for exploring unexpected dynamical models ofplanet formation and orbit stability, as well as exceptional observa-tional opportunities for such a bright, short-period system’s orbitalbehaviour. Recently found evidence that the secondary star may bea white dwarf was reported in the Introduction which would have asignificant bearing on such studies. As more evidence accumulatesonly in favour of the planet, the flip-side of irrefutable evidencethat the planet is instead an illusion is how unexpected any non-planetary alternative would then be.We began by confirming how thermally-stable ν Oct A ’s pho-tosphere continues to be. This allowed us to confidently claimthe photosphere, which has produced the enigmatic RVs for overa decade, is highly unlikely to contribute any variability to ourchromosphere indices, nor be the source of the planet-like signal.Knowing the thermal stability of the photosphere is a useful advan-tage for any chromosphere study, a detail not commonly reported.It is no doubt partly due to ν Oct A ’s quiescence that has al-lowed our study of its Ca II spectra with such low S/N and suc-cessfully pursue our atypical methods. It is also this stability thathas helped us critically examine the telluric line contribution to our H α spectra and quite clearly reveal its quasi-periodic behaviourand origin. All our results strongly imply they record mostly ran-dom processes and not something systematically cyclic.Because similar studies use data that may be at least moder-ately correlated it seems that covariance deserves closer scrutiny insuch cases. Even though the covariance terms have opposite signs,the correlation coefficients may still cause the covariance terms toincrease the errors significantly – as our Ca II results demonstrate.Our methods for analysing low- S/N spectra may allow other so-farneglected archival material to be recovered usefully as we quite sur-prisingly achieved here. Finally, we introduced a simply describedclassification system for retrograde orbits that appears effective forour purposes, and may be of sufficient merit for use by others. © 2021 RAS, MNRAS , ?? [2793]–15[2806] D. J. Ramm et al.
ACKNOWLEDGEMENTS
We appreciate the anonymous referee’s several suggestions that ledto helpful improvements. DJR thanks M. F. Reid, then Physics &Astronomy HoD, for renewing his Research Fellow status (2018–2020) allowing continuing access to academic and IT resources in-cluding the assistance of O. K. L. Petterson. DJR is also grateful tothe UC Mt. John Observatory director K. R. Pollard and the presentHoS R. Marquez for the generous allocation of observing time andresearch support for this project that provided us the opportunityto obtain more data for ν Oct. We thank the observing technicianF. Gunn for obtaining the spectra 2018–2020 and K. R. Pollard andR. Marquez of the School of Physical and Chemical Sciences, Uni-versity of Canterbury for sourcing observing and technical supportfor this project at the UC Mt John Observatory, including fundingfrom The Brian Mason Trust, UC Foundation, The School of Phys-ical and Chemical Sciences and The Otago Museum. DJR thanksM. K¨urster (MPIA) and K. J. Moore (Christchurch) for helpful con-tributions. This research made use of L
IGHTKURVE , a Pythonpackage for Kepler and TESS data analysis (Lightkurve Collab-oration, 2018).
DATA AVAILABILITY
The data underlying this article will be shared on reasonable re-quest to the corresponding author.
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