Does the HR 6819 triple system contain a dormant black hole? Not necessarily
aa r X i v : . [ a s t r o - ph . S R ] J u l MNRAS , 1– ?? (2019) Preprint 20 July 2020 Compiled using MNRAS L A TEX style file v3.0
Does the HR 6819 triple system contain a dormantblack hole? Not necessarily
Tsevi Mazeh and Simchon Faigler
School of Physics and Astronomy, Faculty of Exact Sciences,Tel Aviv University, Tel Aviv 69978, Israel
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
A recent paper by Rivinius et al. proposed that HR 6819 is a triple system,with a distant Be star and a binary of 40-day orbit, composed of a B3 III giantand a dormant black hole (BH). We suggest that the evidence for this modelis not conclusive. In an alternative model, the companion of the giant is byitself a short-period binary in, say, a ∼ -day orbit, consisting, for example, oftwo A0 stars. Each of the two A0 stars should contribute ∼ of the totalbrightness of the system in the V band, and their spectral lines are moving dueto their assumed orbital motion with an unknown period. Therefore, only acareful analysis of the observed spectra can exclude such a model. Before suchan analysis is presented and upper limits for the depths of the hypotheticalA0 star absorption lines are derived, the model of a hidden close pair is moreprobable than the BH model. Key words: binaries: close – stars: black holes
HR 6819 is a nearby early-type Be star at a distance of ∼ pc. As reviewed by Rivinius et al.(2020, Ri20) in a recent intriguing paper, Maintz (2003) observed a series of sharp lines inthe spectrum of HR 6819 that do not come from the Be star, but instead are emanatingfrom another star, B3 III, in the system. The sharp lines revealed an orbital period of 40days, turning the system into a hierarchical triple system, [(?+B3 III)+Be], with the Be c (cid:13) Mazeh and Faigler star as the distant companion. Additional 51 spectra obtained by Ri20 and careful analysisrevealed an amplitude of ∼ km/s of the B3 III star.From the RV amplitude, together with some estimate of the giant mass, which Ri20claim to be at least ∼ M ⊙ , they conclude that the mass of the unseen companion is at least . M ⊙ . The key element of the argument of the Ri20 paper is that the unseen companioncannot be a main-sequence (MS) star. A . M ⊙ MS B star should have ∼ of the systemluminosity and its Balmer lines can have a depth of ∼ relative to its own continuum.Consequently, those lines should have a depth of ∼ relative to the combined continuumof the system. We note in passing that the location of the lines of the presumed . M ⊙ star is well known as a function of the 40-day orbital phase, making their detection easier.Nevertheless, such lines have not been seen in the many spectra obtained by the authors.Therefore, the Ri20 argument goes, the unseen object must be a BH. As no X rays wereobserved from the system, the BH is dormant, with no supply of material from its giantcompanion.BHs, dormant BHs in particular, are quite rare. See, for example, a report about thelarge search of the LAMOST spectroscopic database by Zheng et al. (2019), and a recentdiscussion of the Ri20 suggestion by Safarzadeh et al. (2020), published after this paperwas submitted. Consequently, one needs to check carefully if any other model for HR 6819,which might be more probable, is consistent with the observations. This short communicationsuggests that such a model exists, and some additional observations and/or analysis shouldbe done before one can conclude that the system contains a BH. We propose an alternative model for the HR 6819 system—the unseen companion is byitself a close binary of, say, a -day orbital period. This makes the HR 6819 a hierarchicalquadruple, composed of a distant Be star and a hierarchical triple, with the B3 III in a40-day orbit around the close pair. The close binary could be composed, for example, of twoA0 stars of ∼ . M ⊙ (e.g., Pecaut & Mamajek 2013), consistent with the RV modulation ofthe B3 III; see Figure 1 for a mobile diagram of the suggested system.We know of quite a few similar quadruple systems (see, for example, a discussion byHamers 2020). The period ratio of 10:1 we suggest for the close triple, [(A0+A0)+B3 III],assures that it is dynamically stable, especially because the outer orbit, that of the B3 III MNRAS , 1– ????
HR 6819 is a nearby early-type Be star at a distance of ∼ pc. As reviewed by Rivinius et al.(2020, Ri20) in a recent intriguing paper, Maintz (2003) observed a series of sharp lines inthe spectrum of HR 6819 that do not come from the Be star, but instead are emanatingfrom another star, B3 III, in the system. The sharp lines revealed an orbital period of 40days, turning the system into a hierarchical triple system, [(?+B3 III)+Be], with the Be c (cid:13) Mazeh and Faigler star as the distant companion. Additional 51 spectra obtained by Ri20 and careful analysisrevealed an amplitude of ∼ km/s of the B3 III star.From the RV amplitude, together with some estimate of the giant mass, which Ri20claim to be at least ∼ M ⊙ , they conclude that the mass of the unseen companion is at least . M ⊙ . The key element of the argument of the Ri20 paper is that the unseen companioncannot be a main-sequence (MS) star. A . M ⊙ MS B star should have ∼ of the systemluminosity and its Balmer lines can have a depth of ∼ relative to its own continuum.Consequently, those lines should have a depth of ∼ relative to the combined continuumof the system. We note in passing that the location of the lines of the presumed . M ⊙ star is well known as a function of the 40-day orbital phase, making their detection easier.Nevertheless, such lines have not been seen in the many spectra obtained by the authors.Therefore, the Ri20 argument goes, the unseen object must be a BH. As no X rays wereobserved from the system, the BH is dormant, with no supply of material from its giantcompanion.BHs, dormant BHs in particular, are quite rare. See, for example, a report about thelarge search of the LAMOST spectroscopic database by Zheng et al. (2019), and a recentdiscussion of the Ri20 suggestion by Safarzadeh et al. (2020), published after this paperwas submitted. Consequently, one needs to check carefully if any other model for HR 6819,which might be more probable, is consistent with the observations. This short communicationsuggests that such a model exists, and some additional observations and/or analysis shouldbe done before one can conclude that the system contains a BH. We propose an alternative model for the HR 6819 system—the unseen companion is byitself a close binary of, say, a -day orbital period. This makes the HR 6819 a hierarchicalquadruple, composed of a distant Be star and a hierarchical triple, with the B3 III in a40-day orbit around the close pair. The close binary could be composed, for example, of twoA0 stars of ∼ . M ⊙ (e.g., Pecaut & Mamajek 2013), consistent with the RV modulation ofthe B3 III; see Figure 1 for a mobile diagram of the suggested system.We know of quite a few similar quadruple systems (see, for example, a discussion byHamers 2020). The period ratio of 10:1 we suggest for the close triple, [(A0+A0)+B3 III],assures that it is dynamically stable, especially because the outer orbit, that of the B3 III MNRAS , 1– ???? (2019) R 6819 might not contain a dormant black hole Be Wide Binary
B3III
40 days~100R sun
A0A0 ~4 days~18R sun
Figure 1.
Mobile diagram of the proposed HR 6819 quadruple system. Diagram not to scale. star, is very close to being circular. Tokovinin (2008) considered a minimum ratio of 5:1for a triple to be dynamically stable, and his catalog contains quite a few triples close tothis ratio. In fact, the very existence of the giant as a distant companion to the two A-starsystem could push the pair into a close orbit by eccentricity pumping and relative inclinationmodulation (e.g., Mazeh & Shaham 1979) through the Kozai-Lidov effect, as suggested byFabrycky & Tremaine (2007).To estimate the relative luminosity of the A0 stars we use the apparent brightness of thesystem, V = . , and its distance, ∼ pc (see Ri20 discussion), to obtain M V ∼− . .The absolute magnitude of each of the two hypothetical A0 stars should be M V ∼ . (e.g.,Pecaut & Mamajek 2013). Ignoring interstellar extinction, this results in a contribution of ∼ of each of the A0 stars to the luminosity of the HR 6819 system in the V band. Asimilar calculation for the . M ⊙ presumed star considered by Ri20 results in a relativecontribution of ∼ and a Balmer-line depth of ∼ .We note that • A stars typically have absorption lines that can reach hundreds of km/s broadening(e.g., Zorec & Royer 2012), • their typical Balmer line depth can attain a depth of ∼ , and • in our model, the location of the lines changes due to the RV modulation of the A0stars in their orbital motion with an unknown orbital period. The amplitude of their RVmodulation in our specific model is ∼ km/s.These three features make the detection of the absorption lines of the presumed A0 stars MNRAS , 1– ?? (2019) Mazeh and Faigler quite challenging, given their ∼ depth relative to the combined continuum of the system,and the presence of the absorption lines of the two B stars and the emission lines of the Bestar.There are two key differences between the two A0 model and the . M ⊙ -star modelrejected by Ri20. First, the Balmer lines of the A0 stars are of ∼ depth, whereas thelines of the . M ⊙ star should have ∼ depth. Second, the lines of the two A0 stars aremoving with a high amplitude and an unknown period, while the position of the lines of therejected model are well known.Therefore, although the . M ⊙ -star model is rejected by Ri20, the two A0 model is stillviable. Before a search in the observed spectra for the two A0 absorption lines is carefullydone and accurate upper limits are derived, the burden of proving that a BH is hidden inthe HR 6819 system is not lifted.A close pair like we suggest has a separation of ∼ R ⊙ . With the two stars of ∼ R ⊙ ,the system should display eclipses, unless its orbital inclination is smaller than ∼ ◦ . A fulleclipse should have a depth of ∼ . The TESS light curve of HR 6819 (TIC 118842700)could easily show such an eclipse, despite the erratic modulation of the system, as shown byRi20 who searched for a periodic sinusoidal signal. In any case, the fact that an eclipse isnot seen suggests that the inclination of the presumed binary is less than ∼ ◦ ; below thatangle any eclipse should be quite shallow.The same consideration goes for a possible eclipse of the B3 III by the A stars. Theseparation of the 40-day orbit is somewhat larger than 100 R ⊙ . An eclipse is unlikely, unlessthe inclination is larger than ∼ ◦ . On the other hand, in our model the 40-day orbit cannothave a too low inclination, below, say, ◦ , otherwise the masses of the close pair get toolarge, and their luminosity too bright for hiding their absorption lines in the spectra. Wetherefore conclude that even if we assume coplanarity for the close-pair and the 40-day orbits,our model allows for inclination in the range between ◦ and ◦ . The probability for suchan inclination range is ∼ . , assuming an isotropic distribution of the angular-momentumvector of the system. Assuming relative inclination between the two orbital planes, which isnot so surprising (e.g., Tokovinin 2008), makes our model less restrictive. MNRAS , 1– ????
Mobile diagram of the proposed HR 6819 quadruple system. Diagram not to scale. star, is very close to being circular. Tokovinin (2008) considered a minimum ratio of 5:1for a triple to be dynamically stable, and his catalog contains quite a few triples close tothis ratio. In fact, the very existence of the giant as a distant companion to the two A-starsystem could push the pair into a close orbit by eccentricity pumping and relative inclinationmodulation (e.g., Mazeh & Shaham 1979) through the Kozai-Lidov effect, as suggested byFabrycky & Tremaine (2007).To estimate the relative luminosity of the A0 stars we use the apparent brightness of thesystem, V = . , and its distance, ∼ pc (see Ri20 discussion), to obtain M V ∼− . .The absolute magnitude of each of the two hypothetical A0 stars should be M V ∼ . (e.g.,Pecaut & Mamajek 2013). Ignoring interstellar extinction, this results in a contribution of ∼ of each of the A0 stars to the luminosity of the HR 6819 system in the V band. Asimilar calculation for the . M ⊙ presumed star considered by Ri20 results in a relativecontribution of ∼ and a Balmer-line depth of ∼ .We note that • A stars typically have absorption lines that can reach hundreds of km/s broadening(e.g., Zorec & Royer 2012), • their typical Balmer line depth can attain a depth of ∼ , and • in our model, the location of the lines changes due to the RV modulation of the A0stars in their orbital motion with an unknown orbital period. The amplitude of their RVmodulation in our specific model is ∼ km/s.These three features make the detection of the absorption lines of the presumed A0 stars MNRAS , 1– ?? (2019) Mazeh and Faigler quite challenging, given their ∼ depth relative to the combined continuum of the system,and the presence of the absorption lines of the two B stars and the emission lines of the Bestar.There are two key differences between the two A0 model and the . M ⊙ -star modelrejected by Ri20. First, the Balmer lines of the A0 stars are of ∼ depth, whereas thelines of the . M ⊙ star should have ∼ depth. Second, the lines of the two A0 stars aremoving with a high amplitude and an unknown period, while the position of the lines of therejected model are well known.Therefore, although the . M ⊙ -star model is rejected by Ri20, the two A0 model is stillviable. Before a search in the observed spectra for the two A0 absorption lines is carefullydone and accurate upper limits are derived, the burden of proving that a BH is hidden inthe HR 6819 system is not lifted.A close pair like we suggest has a separation of ∼ R ⊙ . With the two stars of ∼ R ⊙ ,the system should display eclipses, unless its orbital inclination is smaller than ∼ ◦ . A fulleclipse should have a depth of ∼ . The TESS light curve of HR 6819 (TIC 118842700)could easily show such an eclipse, despite the erratic modulation of the system, as shown byRi20 who searched for a periodic sinusoidal signal. In any case, the fact that an eclipse isnot seen suggests that the inclination of the presumed binary is less than ∼ ◦ ; below thatangle any eclipse should be quite shallow.The same consideration goes for a possible eclipse of the B3 III by the A stars. Theseparation of the 40-day orbit is somewhat larger than 100 R ⊙ . An eclipse is unlikely, unlessthe inclination is larger than ∼ ◦ . On the other hand, in our model the 40-day orbit cannothave a too low inclination, below, say, ◦ , otherwise the masses of the close pair get toolarge, and their luminosity too bright for hiding their absorption lines in the spectra. Wetherefore conclude that even if we assume coplanarity for the close-pair and the 40-day orbits,our model allows for inclination in the range between ◦ and ◦ . The probability for suchan inclination range is ∼ . , assuming an isotropic distribution of the angular-momentumvector of the system. Assuming relative inclination between the two orbital planes, which isnot so surprising (e.g., Tokovinin 2008), makes our model less restrictive. MNRAS , 1– ???? (2019) R 6819 might not contain a dormant black hole We have shown that a viable model for HR 6819, consistent with the available observations,is a quadruple system, with a close pair composed of two A0 stars, instead of the BHconjecture. We hope that the coming paper of Hadrava et al., reported by Ri20, which isgoing to include a careful analysis of the spectra, can shed some light on the nature of thecompanion of the B3 III star.Furthermore, the separation between the two components of the 40-day binary is ∼ . milli-arcsec (mas). At such separation, Gravity (Gravity Collaboration et al. 2017) and maybeGaia (e.g., Gaia Collaboration et al. 2016) could resolve the A0-star binary from their B3 IIIgiant companion, as their combined luminosity is ∼ of that of the giant. Alternatively,a few precise astrometric measurements might be able to detect the orbital motion of thegiant, as its amplitude is expected to be of ∼ . mas, and its orbital period and eccentricityare well known.While writing this short letter we noticed a recent publication by van den Heuvel & Tauris(2020, van20) with regard to the suggestion that the red giant 2MASS J05215658+4359220has a BH companion (Thompson et al. 2019). Similarly, van20 conjecture that the unseencompanion in that system is a close binary. Questions have also been raised (El-Badry & Quataert2020; Abdul-Masih et al. 2020; Eldridge et al. 2019) about the identification of a M ⊙ BHas a companion to the B star by Liu et al. (2019), but see Liu et al. (2020) for a rebuttal.It seems that reaching the goal of confidentially finding dormant BHs in close binaries, ascompanions to giants in particular, is still further ahead.
DATA AVAILABILITY
No new data were generated or analysed in support of this research.
ACKNOWLEDGMENTS
We are indebted to the referee for extremely useful suggestions. We thank Micha Engel forhis kind assistance, and Laurent Eyer and Berry Holl for carefully reading the paper and fortheir comments. This research was supported by grant No. 2016069 of the United States-Israel Binational Science Foundation (BSF) and by the grant no. I-1498-303.7/2019 of theGerman-Israeli Foundation.
MNRAS , 1– ?? (2019) Mazeh and Faigler
REFERENCES
Abdul-Masih M., et al., 2020, Nature, 580, E11El-Badry K., Quataert E., 2020, MNRAS, 493, L22Eldridge J. J., Stanway E. R., Breivik K., Casey A. R., Steeghs D. T. H., Stevance H. F., 2019, arXiv e-prints,p. arXiv:1912.03599Fabrycky D., Tremaine S., 2007, ApJ, 669, 1298Gaia Collaboration et al., 2016, A&A, 595, A1Gravity Collaboration et al., 2017, A&A, 602, A94Hamers A. S., 2020, MNRAS,Liu J., et al., 2019, Nature, 575, 618Liu J., Soria R., Zheng Z., Zhang H., Lu Y., Wang S., Yuan H., 2020, Nature, 580, E16Maintz M., 2003, PhD Thesis, Univ. of Heidelberg, GermanyMazeh T., Shaham J., 1979, A&A, 77, 145Pecaut M. J., Mamajek E. E., 2013, ApJS, 208, 9Rivinius T., Baade D., Hadrava P., Heida M., Klement R., 2020, A&A, 637, L3Safarzadeh M., Toonen S., Loeb A., 2020, arXiv e-prints, p. arXiv:2006.11872Thompson T. A., et al., 2019, Science, 366, 637Tokovinin A., 2008, MNRAS, 389, 925Zheng L.-L., et al., 2019, AJ, 158, 179Zorec J., Royer F., 2012, A&A, 537, A120van den Heuvel E. P. J., Tauris T. M., 2020, arXiv e-prints, p. arXiv:2005.04896 MNRAS , 1– ????