A Unicorn in Monoceros: the 3M_\odot dark companion to the bright, nearby red giant V723 Mon is a non-interacting, mass-gap black hole candidate
T. Jayasinghe, K. Z. Stanek, Todd A. Thompson, C. S. Kochanek, D. M. Rowan, P. J. Vallely, K. G. Strassmeier, M. Weber, J. T. Hinkle, F.-J. Hambsch, D. Martin, J. L. Prieto, T. Pessi, D. Huber, K. Auchettl, L. A. Lopez, I. Ilyin, C. Badenes, A. W. Howard, H. Isaacson, S. J. Murphy
MMNRAS , 1–25 (2021) Preprint 8 January 2021 Compiled using MNRAS L A TEX style file v3.0
A Unicorn in Monoceros: the 𝑀 (cid:12) dark companion to the bright, nearbyred giant V723 Mon is a non-interacting, mass-gap black hole candidate T. Jayasinghe , ★ , K. Z. Stanek , , Todd A. Thompson , , C. S. Kochanek , , D. M. Rowan , , P. J. Vallely , ,K. G. Strassmeier , M. Weber , J. T. Hinkle , F.-J. Hambsch , , , D. Martin , , J. L. Prieto , , T. Pessi ,D. Huber , K. Auchettl , , , L. A. Lopez , , I. Ilyin , C. Badenes , A. W. Howard ,H. Isaacson , , S. J. Murphy , Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA Center for Cosmology and Astroparticle Physics, The Ohio State University, 191 W. Woodruff Avenue, Columbus, OH 43210, USA Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Vereniging Voor Sterrenkunde (VVS), Oostmeers 122 C, 8000 Brugge, Belgium Bundesdeutsche Arbeitsgemeinschaft für Veränderliche Sterne e.V. (BAV), Munsterdamm 90, D-12169 Berlin, Germany American Association of Variable Star Observers (AAVSO), 49 Bay State Road, Cambridge, MA 02138, USA Fellow of the Swiss National Science Foundation Núcleo de Astronomía de la Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército 441, Santiago, Chile Millennium Institute of Astrophysics, Santiago, Chile School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D) Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA Department of Physics and Astronomy and Pittsburgh Particle Physics, Astrophysics and Cosmology Center (PITT PACC),University of Pittsburgh, 3941 O‘Hara Street, Pittsburgh, PA 15260, USA Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA Department of Astronomy, University of California Berkeley, Berkeley CA 94720, USA Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, Australia Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We report the discovery of the closest known black hole candidate as a binary companion to V723 Mon. V723 Mon is a nearby( 𝑑 ∼
460 pc), bright ( 𝑉 (cid:39) . 𝑓 ( 𝑀 ) = . ± . 𝑀 (cid:12) , nearly circular binary( 𝑃 = . 𝑒 (cid:39) 𝑇 eff , giant (cid:39) 𝐿 giant (cid:39) 𝐿 (cid:12) and 𝑅 giant (cid:39) 𝑅 (cid:12) . Matching these parameters to MIST evolutionary models indicates a mass of 𝑀 giant = . ± . 𝑀 (cid:12) . V723Mon is a known variable star, previously classified as an eclipsing binary, but its All-Sky Automated Survey (ASAS), KilodegreeExtremely Little Telescope (KELT), and Transiting Exoplanet Survey Satellite ( TESS ) light curves are those of a nearly edge-onellipsoidal variable. Detailed models of the light curves constrained by the period, radial velocities and stellar temperature givean inclination of 𝑖 = . ◦ ± . ◦ , a mass ratio of 𝑞 (cid:39) . ± .
02, a companion mass of 𝑀 comp = . ± . 𝑀 (cid:12) , a stellarradius of 𝑅 giant = . ± . 𝑅 (cid:12) , and a giant mass of 𝑀 giant = . ± . 𝑀 (cid:12) , consistent with our other estimates. We identifya likely non-stellar, diffuse veiling component with contributions in the 𝐵 and 𝑉 -band of ∼
64% and ∼ ∼ 𝐿 (cid:12) . The SED and the absence of continuum eclipses imply that the companion mass must be dominated by acompact object even if the companion is a binary. We do observe eclipses of the Balmer lines when the dark companion passesbehind the giant, but their velocity spreads are low compared to observed accretion disks. The X-ray luminosity of the systemis 𝐿 X (cid:39) . × ergs s − , corresponding to 𝐿 / 𝐿 edd ∼ − . The simplest explanation for the massive companion is a singlecompact object, most likely a black hole in the “mass gap”, although a double neutron star binary is possible. Key words: stars: black holes – (stars:) binaries: spectroscopic – stars: individual: V723 Mon ★ E-mail: [email protected] © a r X i v : . [ a s t r o - ph . S R ] J a n T. Jayasinghe et al.
The discovery and characterization of neutron stars and black holes inthe Milky Way is crucial for understanding core-collapse supernovaeand massive stars. This is inherently challenging, partly because iso-lated black holes are electromagnetically dark and partly becausecompact object progenitors (OB stars) are rare. To date, most massmeasurements for neutron stars and black holes come from pulsar andaccreting binary systems selected from radio, X-ray, and gamma-raysurveys (see, for e.g., Champion et al. 2008; Liu et al. 2006; Özelet al. 2010; Farr et al. 2011), and from the LIGO/Virgo detections ofmerging systems (see, for e.g., Abbott et al. 2016, 2017). Interactingand merging systems are however a biased sampling of compact ob-jects. A more complete census is needed to constrain their formationpathways.One important component of such a census is to identify non-interacting compact objects in binaries around luminous compan-ions. By their very nature, interacting black holes only sample anarrow range of binary configurations, and almost the entire pa-rameter space of binaries with black holes that are non-interactingremains unexplored. Interacting compact object binaries are onlyactive for relatively short periods of time, so most systems are quies-cent or non-interacting. The discovery and characterization of thesenon-interacting black holes are important for understanding the birthmass distribution of black holes and their formation mechanisms.With advances in time-domain astronomy and precision
Gaia as-trometry (Gaia Collaboration et al. 2018), a significant number ofthese systems should be discoverable. For example, Breivik et al.(2017) estimated that ∼ − non-interacting black holes aredetectable using astrometry from Gaia . Similarly, Shao & Li (2019)used binary population synthesis models to estimate that there are ∼ detached non-interacting black holes in the Milky Way, with10 of these systems having luminous companions that are brighterthan 𝐺 ∼
20 mag.Thompson et al. (2019) recently discovered the first low-mass( 𝑀 BH (cid:39) . + . − . 𝑀 (cid:12) ) non-interacting black hole candidate in thefield. It is in a circular orbit with P orb ∼
83 d around a spottedgiant star. Other non-interacting BH candidates have been discov-ered in globular clusters: one by Giesers et al. (2018) in NGC 3201(minimum black hole mass 𝑀 BH = . ± .
41 M (cid:12) ), and two byGiesers et al. (2019) in NGC 3201 ( 𝑀 BH sin ( 𝑖 ) = . ± .
50 M (cid:12) and 𝑀 BH sin ( 𝑖 ) = . ± . (cid:12) ). While obviously interesting intheir own right, these globular cluster systems likely have formationmechanisms that are very different from those of field black holebinaries.Other claims for non-interacting BH systems have been ruled out.For example, LB-1, which was initially thought to host an extremelymassive stellar black hole ( 𝑀 BH (cid:39) + − 𝑀 (cid:12) , Liu et al. 2019), waslater found to have a much less massive companion that was notnecessarily a compact object (see, for e.g., Irrgang et al. 2020; El-Badry & Quataert 2020b). Similarly, the naked-eye star HR 6819was claimed to be a triple system with a detached black hole with 𝑀 BH = . ± . 𝑀 (cid:12) (Rivinius et al. 2020), but was later arguedto contain a binary system with a rapidly rotating Be star and aslowly rotating B star (El-Badry & Quataert 2020a; Bodensteineret al. 2020).Here we discuss our discovery that the bright red giant V723 Monhas a dark, massive companion that is a good candidate for the closestknown black hole. We discuss the current classification of this systemin Section 2, and describe the archival data and new observations usedin our analysis in Section 3. In Section 4, we analyze photometricand spectroscopic observations to derive the parameters of the binary system and the red giant secondary. In Section 5, we discuss thenature of the dark companion. We present a summary of our resultsin Section 6. V723 Mon (HD 45762, SAO 133321, TIC 43077836) is a luminous( 𝑚 𝑉 (cid:39) . ) red-giant in the Monoceros constellation with J2000coordinates ( 𝛼, 𝛿 ) = ( . ◦ , − . ◦ ) . It was classified asa likely long period variable in the General Catalogue of VariableStars (GCVS; Kazarovets et al. 1999) after it was identified as a vari-able source in the Hipparcos catalogue with period P = .
97 d (ESA1997). Subsequently, the All-Sky Automated Survey (ASAS) (Poj-manski 1997, 2002) classified it as a contact/semi-detached binarywith P = .
87 d. The Variable Star Index (VSX; Watson et al. 2006)presently lists it as an eclipsing binary of the 𝛽 -Lyrae type (EB) withP = .
93 d.V723 Mon has a well determined spectroscopic orbit and is in-cluded in the The Ninth Catalogue of Spectroscopic Binary Orbits(Pourbaix et al. 2004). In particular, Griffin (2010) identified V723Mon as a single-lined spectroscopic binary (SB1) with a nearly circu-lar 𝑃 ∼
60 d orbit. Strassmeier et al. (2012) (hereafter S12) refined theorbit to 𝑃 orb = . ± . 𝑒 orb (cid:39) . ± . 𝑃 inner (cid:39) 𝑃 outer /
3. Griffin (2014) (hereafter G14) was unableto find a spectral feature indicative of a second companion in theircross-correlation functions. G14 discusses several peculiarities in theS12 RV solution. In particular, the radial velocity curve associatedwith the second component is unusual in structure compared to anyother system characterized by S12 and a triple system with this periodratio would almost certainly be dynamically unstable.The most striking feature of the well-measured 60 day RV curveis its large mass function of 𝑓 ( 𝑀 ) = 𝑃 orb 𝐾 ( − 𝑒 ) / ( 𝜋𝐺 ) = 𝑀 sin 𝑖 ( 𝑀 giant + 𝑀 comp ) (cid:39) . 𝑀 (cid:12) , (1)given 𝑃 orb = . 𝑒 = .
015 and 𝐾 = .
45 km s − from S12.If the observed giant has a mass of 𝑀 giant ∼ 𝑀 (cid:12) , the mass functionimplies a massive companion with a minimum mass of 𝑀 comp ∼ 𝑀 (cid:12) . Since the observed light is clearly dominated by the giant andthe companion has to be both much less luminous and significantlymore massive than the giant, V723 Mon is a prime candidate fora non-interacting, compact object binary. This realization led us toinvestigate V723 Mon in detail as part of a larger project to identifynon-interacting, compact object binaries. V723 Mon has previously been assigned a spectral type of G0 II (Houk &Swift 2000), however, in this work we find that it is more consistent with aK0/K1 III spectral type.MNRAS000
45 km s − from S12.If the observed giant has a mass of 𝑀 giant ∼ 𝑀 (cid:12) , the mass functionimplies a massive companion with a minimum mass of 𝑀 comp ∼ 𝑀 (cid:12) . Since the observed light is clearly dominated by the giant andthe companion has to be both much less luminous and significantlymore massive than the giant, V723 Mon is a prime candidate fora non-interacting, compact object binary. This realization led us toinvestigate V723 Mon in detail as part of a larger project to identifynon-interacting, compact object binaries. V723 Mon has previously been assigned a spectral type of G0 II (Houk &Swift 2000), however, in this work we find that it is more consistent with aK0/K1 III spectral type.MNRAS000 , 1–25 (2021)
723 Mon Here we present observations, both archival and newly acquired, thatare used in our analysis of V723 Mon. In Gaia
EDR3 (Gaia Collaboration et al. 2020), V723 Mon is source_id= 𝜛 EDR3 = . ± .
033 mas implies a distance of 𝑑 = / 𝜛 = ± Gaia
DR2 parallax of 𝜛 DR2 = . ± . 𝑑 = / 𝜛 = ±
15 pc (for DR2) and the more carefulestimate of 𝑑 = . + . − . pc by Bailer-Jones et al. (2018). Theastrometric solution has significant excess noise of Δ = .
22 mas,which is not surprising given that the motion of the giant should be ∼ . .
39, while larger than unity, is not indicative of problems in theparallax. We adopt a distance of 𝑑 =
460 pc for the remainder of thepaper. The distance uncertainties are unimportant for our analysis.V723 Mon has Galactic coordinates ( 𝑙, 𝑏 ) (cid:39) ( . ◦ , − . ◦ ) ,close to the Galactic disk, but away from the Galactic center. Atthe EDR3 distance, V723 Mon is ∼
32 pc below the midplane. Itsproper motion in EDR3 is 𝜇 𝛼 = − . ± .
032 mas yr − , and 𝜇 𝛿 = . ± .
031 mas yr − . Combining this with the systemicradial velocity from § ( 𝑈, 𝑉, 𝑊 ) LSR = (− . ± . , . ± . , . ± . ) km s − using BANYAN (Gagné et al. 2018)for the calculations. We calculated the thin disk, thick disk and halomembership probabilities based on the
𝑈𝑉𝑊 velocities followingRamírez et al. (2013) to obtain 𝑃 ( thin ) (cid:39) 𝑃 ( thick ) (cid:39) 𝑃 ( halo ) (cid:39) Gaia
DR2 (Gaia Collaboration et al. 2018) also reports a lumi-nosity 𝐿 Gaia = . ± . (cid:12) , temperature 𝑇 eff , Gaia = + − K,and radius 𝑅 Gaia = . + . − . R (cid:12) , for the star that are consistent withan evolved red giant. While Gaia
DR2 does not report a value forthe reddening towards V723 Mon, Gontcharov & Mosenkov (2017)reports 𝐸 ( 𝐵 − 𝑉 ) (cid:39) .
10. The three-dimensional dust maps of Greenet al. (2019) give 𝐸 ( 𝐵 − 𝑉 ) (cid:39) . ± .
04 at the
Gaia distance,consistent with this estimate.
We analyzed well-sampled light curves from the All-Sky Auto-mated Survey (ASAS) and the Kilodegree Extremely Little Tele-scope (KELT), a densely sampled but phase-incomplete light curvefrom the Transiting Exoplanet Survey Telescope (TESS),
𝐵𝑉 𝑅 𝑐 𝐼 𝑐 light curves from the Remote Observatory Atacama Desert (ROAD)and a sparse ultraviolet (UV) light curve from the Neil Gehrels SwiftObservatory.ASAS (Pojmanski 1997, 2002) obtained a 𝑉 -band light curve ofV723 Mon spanning from November 2000 to December 2009 ( ∼ GRADE=A or GRADE=B for our analysis. V723 Mon clearly varies in the ASAS light curve,with two equal maxima but two unequal minima, when phased withthe orbital period from S12. We determined the photometric periodusing the
Period04 software (Lenz & Breger 2005). The dominantASAS period of 𝑃 ASAS (cid:39) . ± . 𝑃 orb / 𝑃 orb , ASAS = . ± . , (2)which agrees well with the spectroscopic periods from S12 and G14.Unfortunately, V723 Mon is saturated in the Automated Survey forSuperNovae (ASAS-SN; Shappee et al. 2014; Kochanek et al. 2017)images, and we could not use it to extend the time span of the V-banddata.The KELT (Pepper et al. 2007) light curve contains 1297 epochswhich we retrieved from the Exoplanet Archive . The KELT 𝑅 𝐾 filtercan be considered as a very broad Johnson R-band filter (Siverd et al.2012). However, there can be significant color corrections comparedto a standard Johnson R-band filter for very blue and very red stars(Pepper et al. 2007; Siverd et al. 2012). KELT observations weremade between September 2010 and February 2015 ( ∼
26 completeorbits). The dominant period in the KELT data ( 𝑃 KELT (cid:39) . ± . 𝑃 orb /
2. We find an orbital period of 𝑃 orb , KELT = . ± . . (3)The difference between the ASAS and KELT photometric periodestimates is not statistically significant.V723 Mon ( TIC
TESS (Ricker et al.2015) in Sector 6, and the 27 days of observations correspond to[0.46,0.82] in orbital phase where the phase of the RV maximum is0 .
75. We analyzed the
TESS data using the adaptation of the ASAS-SN image subtraction pipeline for analyzing
TESS full-frame images(FFIs) described in Vallely et al. (2020). While this pipeline producesprecise differential flux light curves, the large pixel scale of
TESS makes it difficult to obtain reliable measurements of the reference fluxof a given source. We normalized the light curve to have the reference
𝑇 𝐸𝑆𝑆 -band magnitude of 7.26 in the
TESS
Input Catalog (Stassunet al. 2019). Conveniently, the mean of the Sector 6 observations isapproximately the mean for a full orbital cycle (see Figure 4). Weuse a zero point of 20.44 electrons (
TESS
Instrument Handbook ).The light curve does not include epochs where the observations werecompromised by the spacecraft’s momentum dump maneuvers.We obtained 𝐵𝑉 𝑅 𝑐 𝐼 𝑐 light curves at the Remote ObservatoryAtacama Desert (ROAD; Hambsch 2012). All observations were ac-quired through Astrodon Photometric filters with an Orion Optics,UK Optimized Dall Kirkham 406/6.8 telescope and a FLI 16803CCD camera. Twilight sky-flat images were used for flatfield cor-rections. Reductions were performed with the MAXIM DL program and the photometry was carried out using the LesvePhotometry program. We obtained Swift UVOT (Roming et al. 2005) images in the
𝑈𝑉 𝑀
𝑈𝑉 𝑀
Swift
𝑈𝑉𝑊
𝑈𝑉𝑊 uvotimsum package. We then used uvotsource to extract source counts using a 5 . (cid:48)(cid:48) https://exoplanetarchive.ipac.caltech.edu/ https://archive.stsci.edu/files/live/sites/mast/files/home/missions-and-data/active-missions/tess/_documents/TESS_Instrument_Handbook_v0.1.pdf MNRAS , 1–25 (2021)
T. Jayasinghe et al. with radius of 40 . (cid:48)(cid:48) .The Swift 𝑈𝑉 𝑀
𝑈𝑉 𝑀
We used two sets of radial velocity (RV) measurements. The firstset, from Griffin (2014), was obtained between December 2008 andNovember 2013 as part of the Cambridge Observatory Radial Ve-locity Program and span 1805 days. The median RV error for thisdataset is ∼ .
80 km s − . These 41 RV epochs were retrieved from theNinth Catalogue of Spectroscopic Binary Orbits (SB9; Pourbaix et al.2004), converting the reported epochs to Barycentric Julian Dates(BJD) on the TDB system (Eastman et al. 2010) using barycorrpy (Kanodia & Wright 2018).The second set of RV data consists of 100 epochs obtained byS12 with the high resolution ( 𝑅 ≈ .
12 Å at 650 nm. Spectra were obtainedbetween November 2006 and April 2010, spanning a baseline of 1213days. The spectra were reduced following the standard proceduresdescribed in Strassmeier et al. (2012) and Weber et al. (2008). Of the100 spectra, 75 had S / N >
30 near 650 nm. There were 87 epochswith good RV measurements for the giant and the median RV erroris ∼ .
19 km s − . To better understand the V723 Mon system, and to test for possi-ble systematic errors, we obtained a number of additional high andmedium resolution spectra These observations are summarized inTable 7. Using the HIRES instrument (Vogt et al. 1994) on KeckI, we obtained 7 spectra with 𝑅 ≈ 𝑅 ≈ 𝜇 m fiber and6 cross-dispersers (CD). The data were processed as described inStrassmeier et al. (2018). The total integration time was 90 minutes,and the combined spectrum covers the entire wavelength range acces-sible to PEPSI (3840 − − =
260 in the range 7419 − 𝑅 ≈ . (cid:48)(cid:48) https://sb9.astro.ulb.ac.be/DisplayFull.cgi?3936+1 a standard combination of the modsccdred python package, andthe modsidl pipeline . The blue and red channels of both spectro-graphs were reduced independently, and the final MODS spectrumfor each night was obtained by averaging the MODS1 and MODS2spectra. The best weather conditions during this observing run oc-curred on Nov 20. The HIRES, PEPSI and MODS observations aresummarized in Table 7. We analyzed X-ray observations from the
Swift
X-Ray Telescope(XRT; Burrows et al. 2005) and
XMM-Newton (Jansen et al. 2001).The XRT data were taken simultaneously with the
𝑈𝑉 𝑀
Swift
XRT for 5594 seconds. AllXRT observations were reprocessed using the
Swift xrtpipeline ver-sion 0.13.2 and standard filter and screening criteria and the mostup-to-date calibration files. To increase the signal to noise of ourobservations, we combined all cleaned individual XRT observationsusing XSELECT version 2.4g. To place constraints on the presenceof X-ray emission, we used a source region with a radius of 30 arcseccentered on the position of V723 Mon and a source-free backgroundregion with a radius of 150 arcsec located at RA = 06:28:53.1, Dec= − XMM-Newton data obtained duringa ∼
10 ks observation of the nearby ultraluminous infrared galaxyIRAS 06269-0543 (Observation ID 0153100601; PI: N. Anabuki).However, V723 Mon is ∼ (cid:48) off-axis in these observations, resultingin a non-optimal PSF with a 90% enclosed energy radius of ∼ (cid:48) .We reduced the data using the XMM-Newton
Science System (SAS)Version 15.0.0 (Gabriel et al. 2004). We removed time intervalswith proton flares or high background after identifying them byproducing count-rate histograms using events with an energy between10–12 keV. For the data reduction, we used the standard screeningprocedures and the FLAGS recommended in the current SAS analysisthreads and XMM-Newton
Users Handbook . Here we present our analyses of the observations described in § § § § PHOEBE to derive themasses of the red giant and the dark companion. We also derive lim-its on companion eclipse depths. In § § § § http://swift.gsfc.nasa.gov/analysis/xrt_swguide_v1_2.pdf https://xmm-tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/ MNRAS000
Users Handbook . Here we present our analyses of the observations described in § § § § PHOEBE to derive themasses of the red giant and the dark companion. We also derive lim-its on companion eclipse depths. In § § § § http://swift.gsfc.nasa.gov/analysis/xrt_swguide_v1_2.pdf https://xmm-tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/ MNRAS000 , 1–25 (2021)
723 Mon We characterized the red giant using both fits to its overall SED andanalyses of the available spectra. For the SED we used photometryfrom APASS DR10 (Henden et al. 2018), SkyMapper DR2 (Onkenet al. 2019), 2MASS (Skrutskie et al. 2006) and AllWISE (Wrightet al. 2010). We used the
Swift
UVM2 photometry only as an upperlimit ( § . 𝑅 𝑉 = . 𝜒 / 𝑁 𝑑𝑜 𝑓 (cid:39)
1. Theexpanded uncertainties needed to reach 𝜒 / 𝑁 𝑑𝑜 𝑓 (cid:39) 𝑇 eff , giant = ±
500 K prior on the temperature and aprior of 𝐸 ( 𝐵 − 𝑉 ) = . ± .
04 on the extinction from Greenet al. (2019). The SED fit yields 𝑇 eff , giant (cid:39) ±
90 K, 𝐿 giant = ± 𝐿 (cid:12) , 𝑅 giant (cid:39) . ± . 𝑅 (cid:12) and 𝐸 ( 𝐵 − 𝑉 ) (cid:39) . ± . 𝜒 = . . 𝑅 giant = 𝑅 (cid:12) and 40 . 𝑅 giant = 𝑅 (cid:12) . Decreasingthe radius forces the star to become hotter (4800 K for 18 𝑅 (cid:12) ) tofit the SED at long wavelengths and more extincted to fit it at shortwavelengths. Constraints on a stellar companion to the giant fromthe SED are discussed in Section § ( D ) = . ± . ( D ) = . ± . 𝐸 ( 𝐵 − 𝑉 ) calibration in Poznanski et al. (2012), we find that 𝐸 ( 𝐵 − 𝑉 ) = . ± .
005 mag. This is consistent with the low foreground extinctionthat was derived from the SED models and the Green et al. (2019)extinction maps.All high resolution spectra indicate that the giant is rapidly rotat-ing. Strassmeier et al. (2012) derived a projected rotational velocityof 𝑣 rot sin 𝑖 = ± − using the SES spectra. Griffin (2014)found a similar average 𝑣 rot sin 𝑖 ∼
15 km s − but noted that the valuesseemed to depend on the orbital phase and ranged from 𝑣 rot sin 𝑖 ∼
10 km s − to 𝑣 rot sin 𝑖 ∼
20 km s − . We also find that 𝑣 rot sin 𝑖 variesfrom ∼ . − to ∼ . − in the SES spectra. The HIRESCPS pipeline (Petigura 2015) reports 𝑣 rot sin 𝑖 = . ± . − and we found 𝑣 rot sin 𝑖 = . ± . − from the PEPSI spec-trum using iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma2019). Assuming that the rotation of the giant is tidally synchronizedwith the orbit, the SES, PEPSI and HIRES measurements yield stel-lar radii of 𝑅 sin 𝑖 = . ± . 𝑅 (cid:12) , 𝑅 sin 𝑖 = . ± . 𝑅 (cid:12) and 𝑅 sin 𝑖 = . ± . 𝑅 (cid:12) , respectively, consistent both with estimatesfrom the SED and the radius derived for the giant from the PHOEBE models ( § 𝑖 (cid:39) PHOEBE models.To derive the surface temperature ( 𝑇 eff ), surface gravity (log ( 𝑔 ) ),and metallicity ( [ Fe / H ] ) of the giant, we use the spectral synthesiscodes FASMA (Tsantaki et al. 2020; Tsantaki et al. 2018) and iSpec . Figure 1.
The best-fitting, extinction-corrected SED model for V723 Monwithout considering veiling (see § Swift UVM2 detection (arrow;see Table 1) is treated as an upper limit and the error bars are expanded togive 𝜒 / 𝑁 𝑑𝑜 𝑓 (cid:39)
1. The SEDs for a main sequence companion of mass1 . 𝑀 (cid:12) , an equal mass binary consisting of two main sequence stars eachwith 0 . 𝑀 (cid:12) , and a binary with companion masses of 1 . 𝑀 (cid:12) and 0 . 𝑀 (cid:12) are shown as dashed lines (see § FASMA generates synthetic spectra based on the ATLAS-APOGEEatmospheres (Kurucz 1993; Mészáros et al. 2012) with
MOOG (Sneden1973) and outputs the best-fit stellar parameters following a 𝜒 min-imization process. iSpec carries out a similar minimization processwith synthetic spectra generated by SPECTRUM (Gray & Corbally1994) and MARCS model atmospheres (Gustafsson et al. 2008).The line lists used in this process span the wavelength range from480 nm to 680 nm. Since we are confident the companion should un-dergo eclipses (see § . < ∼ 𝜙 < ∼ .
52) when any companion would be eclipsed by thegiant. For the detailed fits, we fix the rotational velocity to the valueof 𝑣 rot sin 𝑖 = . ± . − found by iSpec for this spectrum.For the FASMA fits we initially keep the macroturbulent broadening( 𝑣 mac ) and the microturbulence ( 𝑣 micro ) fixed at 𝑣 mac = − and 𝑣 mic = − , but then allow them to be optimized once we have areasonable fit. This fits yield 𝑇 eff , giant = ±
50 K, log ( 𝑔 ) = . ± .
2, and [ Fe / H ] = − . ± .
1. In the iSpec fits, 𝑣 mic was kept as a freeparameter and we obtain similar results with 𝑇 eff , giant = ±
60 K,log ( 𝑔 ) = . ± . [ Fe / H ] = − . ± . [ 𝛼 / Fe ] = . ± .
1, and 𝑣 micro = . ± . − . We adopt the parameters from iSpec as our standard. The spectroscopic parameters derived for the giantare summarized in Table 2. These estimates of the spectroscopicparameters do not consider the effects of veiling on the observedspectrum (see § PHOEBE model in § ( 𝑔 ) PHOEBE = . ± . ( 𝑔 ) and the radius of the giant from § MNRAS , 1–25 (2021)
T. Jayasinghe et al.
Table 1.
Multi-band photometry measurements used in the construction of the SED for V723 Mon. Luminosities in each band are calculated assuming a nominaldistance of 𝑑 (cid:39)
460 pc. Filter Magnitude 𝜎 𝐹 𝜆 [ ergs s − cm − Å − ] 𝜆𝐿 𝜆 [ 𝐿 (cid:12) ] Reference
Swift
UVM2 14.11 0.07 1 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − 𝐾 𝑠 . × − . × − . × − . × − . × − spectroscopic mass is 𝑀 giant , spec = . ± . 𝑀 (cid:12) , consistent with themass of the giant derived from the PHOEBE model. The spectroscopictemperature is also consistent with that obtained from the SED fits.Based on the van Belle et al. (1999) temperature scale for giants, ourtemperature estimate is more consistent with a K0/K1 giant than thearchival classification of G0 ( ∼ 𝑉 -band magnitude ( 𝑀 𝑉 (cid:39) − . ± .
1) is consistent witha luminosity class of III (Straizys & Kuriliene 1981). From single-star evolution, the spectroscopic measurement of log ( 𝑔 ) suggests thatthe giant is currently evolving along the upper red giant branch. Thegiant has a luminosity larger than red clump stars, suggesting that ithas not yet undergone a helium flash.We used the spectroscopic parameters in Table 2 and the luminos-ity constraint from the SED fit as priors to infer the physical propertiesof the giant using MESA Isochrones and Stellar Tracks (MIST; Dot-ter 2016; Choi et al. 2016). We used the isochrones package for thefitting (Morton 2015). We find that 𝑀 giant , MIST = . ± . 𝑀 (cid:12) and 𝑅 giant , MIST = . ± . 𝑅 (cid:12) . The age of the giant from theMIST models is ∼ . + . − . Gyr. These results are consistent with theproperties of the giant derived from the spectra and the SED.
We fit Keplerian models both independently and jointly to the S12and G14 radial velocities using the Monte Carlo sampler
TheJoker (Price-Whelan et al. 2017). The results for the four fits are summa-rized in Table 3. We first fit each data set independently as an ellipticalorbit to verify that we obtain results consistent with the publishedresults. We then fit the joint data set using either a circular or an ellip-tical orbit. In the joint fits we include an additional parameter to allowfor any velocity zero point offsets between the S12 and G14 data.For the circular orbit we also set the argument of periastron 𝜔 = 𝑇 RV , max instead of theepoch of periastron. We define phases so that 𝑇 RV , max (BJD/TDB)corresponds to 𝜙 = .
75, the companion eclipses at 𝜙 = . 𝜙 =
0. After doing a first fit for the ellip-tical models, we did a further fit with 𝑃 , 𝐾 , 𝑒 , 𝛾 and 𝑇 RV , max fixedto their posterior values and further optimized 𝜔 using least-squaresminimization. Table 2.
Properties of the red giant in V723 Mon (not accounting for veiling,see § FASMA iSpec 𝑇 eff ( K ) ±
50 4570 ± ( 𝑔 ) . ± . . ± . [ Fe / H ] − . ± . − . ± . [ 𝛼 / Fe ] — 0 . ± . 𝑣 mic ( km s − ) . ± . 𝑣 mac ( km s − ) 𝑣 rot sin 𝑖 ( km s − ) ∗ . ± . 𝑅 ( 𝑅 (cid:12) ) . ± . 𝐿 ( 𝐿 (cid:12) ) ± 𝑀 ( 𝑀 (cid:12) ) . ± . ∗ 𝑣 rot sin 𝑖 varies with orbital phase The results of the fits are summarized in Table 3 and shown inFig. 2. The fits to the individual data sets agree well with the publishedresults, and the mass functions are well-constrained and mutuallyconsistent. The elliptical models all yield a small, non-zero ellipticity,consistent with G14’s arguments. We do find a small velocity offsetof Δ 𝑉 = . ± .
14 km s − for the elliptical model and Δ 𝑉 = . ± .
21 km s − for the circular model between the S12 and G14data. While the velocity residuals of the fits are small compared to 𝐾 ( (cid:46) . − versus 65 km s − ), they are large compared tothe measurement uncertainties. Thus, while the RV curve is clearlycompletely dominated by the orbital model, Fig. 2 also shows thatthere are significant velocity residuals for both joint fits. The circularfit is dominated by a residual of period 𝑃 orb / 𝑃 orb /
3. Fitting an elliptical orbitwith a circular orbit will show a dominant 𝑃 orb / 𝑃 orb / 𝑃 orb / MNRAS000
3. Fitting an elliptical orbitwith a circular orbit will show a dominant 𝑃 orb / 𝑃 orb / 𝑃 orb / MNRAS000 , 1–25 (2021)
723 Mon Phase O − C [ k m / s ] e O − C [ k m / s ] e = 0 R V [ k m / s ] P orb = 53 . ± . e = 0) Model , e = 0Model , e 0S12G14 Figure 2.
The observed radial velocities for V723 Mon as a function of orbital phase, defined with the epoch of maximal RV at 𝜙 = .
75 (top). The RVs fromStrassmeier et al. (2012) [S12] are shown as black circles and the RVs from Griffin (2014) [G14] are shown as blue squares. The joint, circular (elliptical) RVfit from Table 3 is shown in red (purple). The two models closely overlap and are hard to distinguish. The residuals from both the circular and elliptical fit to thecombined data are shown in the lower panels. The RV residuals are most likely a result of the ellipsoidal variability rather than the result of a triple system (seeappendix § A.) residuals do not however, resemble those of a Keplerian orbit. Wediscuss this hypothesis and the velocity residuals in Appendix A.Binaries with evolved components (log ( 𝑔 ) < .
5) and orbitalperiods shorter than ∼
100 days are expected to have gone throughtidal circularization and have circular orbits (e.g., Verbunt & Phinney1995; Price-Whelan & Goodman 2018). However, in the joint fits,the models with ellipticity are a better fit and have smaller RMSresiduals than the circular models. Griffin (2014) carried out an 𝐹 -test and noted that the ellipticity in their best-fit orbit for V723 Mon was significant, and concluded that it was very likely real. While weuse the circular orbit for the PHOEBE models in § . − . 𝑀 (cid:12) . The mass function itself is greaterthan the Chandrasekhar mass of ∼ . 𝑀 (cid:12) , immediately ruling out awhite dwarf companion. For an edge on orbit (see § 𝑀 giant (cid:39) MNRAS , 1–25 (2021)
T. Jayasinghe et al. 𝑀 (cid:12) , the companion mass is 𝑀 comp (cid:39) 𝑀 (cid:12) and the semi-majoraxis is 𝑎 (cid:39) 𝑅 (cid:12) . The Roche limits are approximately 𝑅 L , giant = . 𝑎 (cid:39) 𝑅 (cid:12) for the giant and 𝑅 L , comp = . 𝑎 (cid:39) 𝑅 (cid:12) for thecompanion. Based on the radius estimate from the SED fits ( § 𝑅 giant / 𝑅 L , giant (cid:39) .
66) but in the regime where we should be seeing strong ellipsoidalvariability due to the tidal deformation of the giant by the gravity ofthe companion (e.g., Morris 1985). Any stellar companion also has tobe well within its Roche lobe or it would dominate the SED becauseits Roche lobe is significantly larger. Hence, we can be confident thatwe have a detached binary whose light is dominated by a giant thatshould show ellipsoidal variability and might show eclipses.
While it has been previously claimed that V723 Mon is acontact/semi-detached binary of the 𝛽 -Lyrae type, we find that thisis very unlikely. As we just argued, both the giant and any compan-ion must lie well within their Roche lobes given the properties ofthe giant and the orbit. Additionally, the morphology of the lightcurve is inconsistent with those of detached and most semi-detachedeclipsing binaries. Here we interpret the light curves as ellipsoidalvariability and deduce limits on any eclipses of the companion foruse in § 𝑉 -band, KELT 𝑅 𝐾 -band and TESS 𝑇 -band lightcurves (Figure 4) using PHOEBE 2.3 (Prša et al. 2016; Horvat et al.2018; Conroy et al. 2020). Since the companion appears to be darkand producing no eclipses, we fix it to be a small ( 𝑅 = × − 𝑅 (cid:12) ),cold ( 𝑇 eff =
300 K) black body, use the simplest and fastest eclipsemodel ( eclipse_method=only_horizon ) and do not include theeffects of irradiation and reflection. We adopt the joint-circular RVsolution from Table 3 (period, 𝑒 =
0, systemic velocity, semi-majoraxis, and argument of periastron 𝜔 =
0) and keep the temperature ofthe giant fixed at 𝑇 eff , giant = 𝛽 = .
54, comparable to those obtained byClaret & Bloemen (2011) in the 𝑅 -band for stars with 𝑇 eff ∼ − (cid:46) [ Fe / H ] (cid:46) − . (cid:46) log ( 𝑔 ) (cid:46)
2. We did not find signifi-cant differences in the final parameters when we varied 𝛽 by ± PHOEBE models. A 20% change in 𝛽 roughly corresponds to Δ 𝑇 eff (cid:39)
500 K or Δ log ( 𝑔 ) (cid:39) . 𝑞 = 𝑀 giant / 𝑀 comp , orbital in-clination ( 𝑖 ), and the radius of the giant ( 𝑅 giant ). We simultaneouslyperform trial fits to the KELT and TESS light curves using the Nelder-Mead simplex optimization routine (Lagarias et al. 1998). The param-eters from the trial fit were then used to initialize a MCMC samplerwith 16 walkers, which was then run for 2000 iterations using the emcee (Foreman-Mackey et al. 2013) solver in
PHOEBE 2.3 . The er-rors in the parameters were derived from the MCMC chains. The cor-ner plot of the posterior samples are shown in Figure 3 and the resultsof the best-fitting
PHOEBE model are listed in Table 4. Our model is agood fit to the KELT 𝑅 𝐾 -band and TESS 𝑇 -band light curves, shownin Figure 4. The PHOEBE model indicates that the orbital inclinationof V723 Mon is nearly edge on (87 . + . − . deg). The semi-major axisof the binary is 𝑎 orb sin 𝑖 = 𝑎 giant sin 𝑖 + 𝑎 c sin 𝑖 = . ± . 𝑅 (cid:12) . Theradius derived from the PHOEBE model (23 . ± . 𝑅 (cid:12) ) agrees wellwith those obtained from the SED fits and the MIST evolutionarymodels in § PHOEBE model for the ellipsoidal variations, we are able to directly +1.01.0 R . . . . . i o r b () +1.01.0
20 22 24 26 R equiv,RG (R ) . . . . . q o r b . . . . . i orb ( ) .
24 0 .
27 0 .
30 0 .
33 0 . q orb +0.020.02 Figure 3.
The corner plot (Foreman-Mackey 2016) for the posterior samplesin the best-fitting PHOEBE model to the KELT and
TESS light curves. determine the masses of the two components. The mass of the com-panion is 𝑀 comp = 𝑓 ( 𝑀 )( + 𝑞 ) sin 𝑖 (cid:39) . 𝑀 (cid:12) sin 𝑖 (cid:18) 𝑓 ( 𝑀 ) . 𝑀 (cid:12) (cid:19) (cid:18) + 𝑞 . (cid:19) (4)and from the PHOEBE models, we find that the red giant has a mass 𝑀 giant (cid:39) . ± . 𝑀 (cid:12) and the companion has a mass 𝑀 comp (cid:39) . ± . 𝑀 (cid:12) . The reported errors are purely statistical and donot consider systematic effects (veiling, etc.) in the derivation ofthe binary solution. However, our results in § 𝑀 comp (cid:39) . ± . 𝑀 (cid:12) ) is that it is a non-interacting black hole in the“mass-gap” between 3 − 𝑀 (cid:12) (Özel et al. 2010; Farr et al. 2011).We discuss other scenarios in §
5. The estimated mass of the redgiant ( 𝑀 giant (cid:39) . ± . 𝑀 (cid:12) ) places it towards the lower end ofmeasured red giant masses in the APOKASC catalog (Pinsonneaultet al. 2018). Of the APOKASC sources with measured asteroseismicmasses, only ∼
5% had masses lower than 0 . 𝑀 (cid:12) . The mass is ∼ . 𝑀 (cid:12) smaller than the MIST estimate in § ∼ 𝑅 (cid:12) ), a companion with a radius of 1 𝑅 (cid:12) should be eclipsedfor inclination angles 𝑖 (cid:38) ◦ . Figure 5 shows the eclipses predictedfor the ASAS, KELT and TESS light curves for main sequence starswith masses of 1 𝑀 (cid:12) , 1 . 𝑀 (cid:12) and 2 𝑀 (cid:12) . Any such stars wouldhave produced relatively easy to detect eclipses. We will focus on theKELT limits because these data have higher S/N compared to ASASphotometry, and TESS only observed the eclipse of the red giantand not of the companion. At the expected phase of the eclipse, the
MNRAS000
MNRAS000 , 1–25 (2021)
723 Mon Phase
ROAD : B f second , B ’ ASAS : V f second , V ’ Model + Second LightModel
KELT : R
Phase
TESS : T N o r m a li ze d F l u x Figure 4.
The normalized ROAD 𝐵 -band, ASAS, KELT and TESS light curves for V723 Mon as a function of orbital phase (defined with the epoch of maximalRV at 𝜙 = . § 𝐵 ( 𝑓 second , B ∼ 𝑉 -band ( 𝑓 second , V ∼ , 1–25 (2021) T. Jayasinghe et al.
Table 3.
Orbital Elements for V723 MonParameter S12 G14 S12 + G14 S12 + G14 𝑃 orb ( d ) . ± . . ± . . ± . . ± . 𝐾 ( km s − ) . ± .
068 65 . ± .
117 65 . ± .
081 65 . ± . 𝑒 . ± . . ± . . ± . 𝜔 ( ◦ ) . ± . . ± . . ± . 𝛾 ( km s − ) . ± .
053 3 . ± .
07 1 . ± .
07 1 . ± . 𝑎 giant sin 𝑖 ( 𝑅 (cid:12) ) . ± .
081 77 . ± .
139 77 . ± .
096 77 . ± . 𝑇 RV , max (BJD-2450000) 4096 . ± .
696 4098 . ± .
954 4096 . ± .
773 4096 . ± . ( km s − ) 𝑓 ( 𝑀 ) ( 𝑀 (cid:12) ) . ± .
005 1 . ± .
009 1 . ± .
006 1 . ± . Table 4.
Fundamental Binary Parameters for V723 Mon obtained through bi-nary modelling for the dark companion primary (DC) and red giant secondary(RG) Parameter DC RG 𝑃 orb (d) 59.9398 (fixed) 𝜔 ( ◦ ) 𝑒 𝛾 ( km s − ) 𝑎 sin 𝑖 ( 𝑅 (cid:12) ) . + . − . .
187 (fixed) 𝑖 ( ◦ ) . + . − . 𝑇 eff ( 𝐾 )
300 (fixed) 4600 (fixed) 𝑅 ( 𝑅 (cid:12) ) × − (fixed) 23 . ± . 𝑞 . + . − . 𝑀 ( 𝑀 (cid:12) ) . ± .
08 0 . ± . RMS of the KELT data relative to the eclipse-free ellipsoidal (ELL)model is only 0 .
84% for phases from 0.46 to 0.54. If we bin the data0.01 in phase, the RMS of the binned data is only 0 . Swift , ASAS and ROAD light curves, we will adopteclipse limits of 10%, 3% and 2% for the
𝑈𝑉 𝑀 𝐵 and 𝑉 bands,respectively. The Swift
𝑈𝑉 𝑀
𝑈𝑉 𝑀 𝜙 (cid:39) . ∼
10% at the expectedphases 0 . (cid:46) 𝜙 (cid:46) .
54. While the
TESS light curve does not coverthe eclipse of the companion at 𝜙 = .
5, it does cover the eclipse ofthe giant at 𝜙 =
0. For this eclipse, we estimate a conservative limiton the
TESS band eclipse depth of ∼ . After the KELT 𝑅 𝐾 -band and TESS 𝑇 -band light curves were jointlyfit, we compared the resulting model 𝑉 -band light curve to the ASASobservations, and found that the observed 𝑉 -band variability ampli-tude was smaller than predicted by our model. Lower amplitudesat (usually) bluer wavelengths are generally attributed to an addi-tional source of diluting (“second”) light. For X-ray binaries, it is also known as “disk veiling” due to additional light from accretion(e.g., Hynes et al. 2005; Wu et al. 2015). The amount of additionalflux is usually characterized either by the ratio 𝑟 of the veiling fluxto the stellar flux or the veiling flux as a fraction of the total flux 𝑓 = 𝑟 /( + 𝑟 ) . Interacting X-ray binaries are frequently observed tohave veiling factors upwards of 𝑓 disk ∼ 𝑟 ∼ TESS light curves and fit for additional flux (second light) inthe 𝑉 -band. The fit to the ASAS 𝑉 -band light curve is consistent withan additional flux amounting to 𝑓 second , V = ±
2% of the mean fluxin the 𝑉 -band. Figure 4 shows the PHOEBE model fit for the 𝑉 -bandafter accounting for this additional flux. The redder ROAD 𝑅 𝑐 and 𝐼 𝑐 light curves agree well with the PHOEBE model without additionalflux. The ROAD observations also agree with the
PHOEBE modelfor the 𝑉 -band with the additional flux ( 𝑓 second , V = ± 𝐵 -band light curve and a model withoutextra flux is even larger than for the 𝑉 -band. Fitting the 𝐵 -band datarequires a larger second light contribution of 𝑓 second , B = ± 𝐵 − 𝑉 = − . ± . 𝑇 eff ranging from ∼ ,
000 K to ∼ ,
000 K (Papaj et al. 1993).However, no hot star could have a rapidly rising SED from 𝑉 to 𝐵 and then drop rapidly from 𝐵 to the 𝑈𝑉 𝑀 § 𝑟 ( 𝜆 ) = 𝑉 ( 𝜆 ) 𝑆 ( 𝜆 ) , (5)where 𝑉 ( 𝜆 ) is the veiling spectrum and 𝑆 ( 𝜆 ) is the uncontaminatedspectrum of the star (Casares et al. 1993). The ratio 𝑟 ( 𝜆 ) is related tothe second light ( 𝐹 ) as 𝐹 = 𝑟 ( 𝜆 ) 𝐹 giant , (6)where 𝐹 giant is the flux from the giant. The observed spectrum of thestar is a function of the veiling factor 𝐹 veil ( 𝜆 ) = + 𝑟 ( 𝜆 ) 𝑟 ( 𝜆 ) = 𝐴 ( 𝜆 ) 𝑆 ( 𝜆 ) 𝐹 veil ( 𝜆 ) , (7)where 𝐴 ( 𝜆 ) is a normalization factor. The monochromatic veiling MNRAS000
000 K (Papaj et al. 1993).However, no hot star could have a rapidly rising SED from 𝑉 to 𝐵 and then drop rapidly from 𝐵 to the 𝑈𝑉 𝑀 § 𝑟 ( 𝜆 ) = 𝑉 ( 𝜆 ) 𝑆 ( 𝜆 ) , (5)where 𝑉 ( 𝜆 ) is the veiling spectrum and 𝑆 ( 𝜆 ) is the uncontaminatedspectrum of the star (Casares et al. 1993). The ratio 𝑟 ( 𝜆 ) is related tothe second light ( 𝐹 ) as 𝐹 = 𝑟 ( 𝜆 ) 𝐹 giant , (6)where 𝐹 giant is the flux from the giant. The observed spectrum of thestar is a function of the veiling factor 𝐹 veil ( 𝜆 ) = + 𝑟 ( 𝜆 ) 𝑟 ( 𝜆 ) = 𝐴 ( 𝜆 ) 𝑆 ( 𝜆 ) 𝐹 veil ( 𝜆 ) , (7)where 𝐴 ( 𝜆 ) is a normalization factor. The monochromatic veiling MNRAS000 , 1–25 (2021)
723 Mon Phase N o r m a li ze d F l u x ASAS : V
Eclipse depths : ∼ . , ∼ . , ∼ . PHOEBE Model
Phase N o r m a li ze d F l u x KELT : R
Eclipse depths : ∼ . , ∼ . , ∼ . Phase N o r m a li ze d F l u x TESS : T
Eclipse depths : ∼ . , ∼ . , ∼ . Model T eff ’ K , R ’ R fl , M ’ M fl T eff ’ K , R ’ R fl , M ’ M fl T eff ’ K , R ’ R fl , M ’ M fl Figure 5.
The observed ASAS, KELT and
TESS light curves compared to various eclipsing models with main sequence companions to the red giant. Theellipsoidal model is shown in red. The depths of the eclipses at 𝜙 = . 𝑀 single > . 𝑀 (cid:12) and 𝑀 binary > . 𝑀 (cid:12) (see § , 1–25 (2021) T. Jayasinghe et al.
Phase UV M [ m ag ] Figure 6.
The
Swift
UVM2 light curve. The expected eclipse duration ( ∼ . factor 𝐹 veil = EW s EW obs (8)is the ratio of the observed equivalent widths to those predicted fromthe standard/synthetic spectrum.We calculated the monochromatic veiling factors for various Ca iand Fe i absorption lines in the SES spectra and the red side of thePEPSI spectrum ( 𝜆 >
500 nm). For the Ca lines, we assumed anabundance of [ Ca / H ] = . ± .
02 derived from the PEPSI spec-trum. We generated a synthetic iSpec / SPECTRUM (Gray & Corbally1994) spectrum for the red giant using the atmospheric parametersin Table 2. Since the 𝑅 ≈ ,
000 PEPSI spectrum has lower S/N atblue wavelengths, we use the mean veiling factors in the SES spectrafor the absorption lines blue-ward of 500 nm. We use the standarddeviations of the estimates from the individual SES spectra to es-timate the uncertainties. For the redder lines at >
500 nm, we usethe veiling factors derived from the PEPSI spectrum at 𝜙 (cid:39) .
63 andassign errors of ± .
10 in 𝑟 ( 𝜆 ) . This method can have large systematicuncertainties (see Casares et al. 1993), but it provides a way to inde-pendently test the estimates from the dependence of the ellipsoidalvariability amplitudes on wavelength.Figure 7 shows that the fractional veiling and second light as afunction of wavelength 𝑟 ( 𝜆 ) rises steeply towards bluer wavelengths,with a power-law ( 𝜆 𝛼 ) index of 𝛼 (cid:39) − . ± .
5, steeper than thatexpected from the Rayleigh-Jeans law ( 𝛼 = − 𝑅 𝐾 and TESS 𝑇 filtersthat are used for our primary fits to the ellipsoidal variations. As aprecaution, we ran PHOEBE models adding 10 −
20% extra flux in theKELT 𝑅 𝐾 band, and found that the masses of the red giant and darkcompanion are comparable to those obtained without consideringveiling given the error estimates. The fractional second light in the 𝑉 -band from the PHOEBE fits is comparable to that derived from theline veiling estimates. The
PHOEBE estimate of the second light in the 𝐵 -band is somewhat larger than that seen in the line veiling, howeverboth estimates indicate a large contribution to the 𝐵 -band flux. Basedon the lack of eclipses in the light curves (see § 𝜆 (cid:46)
600 nm, the inferred propertiesof the star from § 𝑇 eff , giant (cid:39) ±
100 K, 𝐿 giant = ± 𝐿 (cid:12) , 𝑅 giant (cid:39) . ± . 𝑅 (cid:12) and 𝐸 ( 𝐵 − 𝑉 ) (cid:39) . ± .
044 (Figure 8). The veiling componentcontributes ∼
12% of the total SED flux, with most of the flux in thebluer wavelengths. We perform iSpec fits to the PEPSI spectrumafter truncating it to the redder wavelengths at 𝜆 >
600 nm thatare minimally affected by veiling. We obtain 𝑇 eff = ±
50 K,log ( 𝑔 ) = . ± . [ Fe / H ] = − . ± . [ 𝛼 / Fe ] = . ± .
1, and 𝑣 micro = . ± . − . From the parameters listed in Table 2, thesediffer by Δ 𝑇 eff , giant (cid:39)
220 K, Δ log ( 𝑔 ) (cid:39) .
3, and Δ [ Fe / H ] (cid:39) .
3. Incontrast, the parameters derived from the
PHOEBE fits (Table 4) donot change significantly if we change 𝑇 eff , giant . Because the modelsof the veiled SED are driven to larger, cooler stars, models forcingthe star to be more compact are even more disfavored than in theunveiled models. The best model of the veiled SED has 𝜒 = . . 𝑅 giant = 𝑅 (cid:12) and to 64 . 𝑅 giant = 𝑅 (cid:12) .The origin of this veiling component remains unclear although itis clearly non-stellar in nature. However, the morphology of the veil-ing component is broadly compatible with the spectra of advectiondominated accretion flows (ADAF). ADAF spectra can be describedby contributions due to synchrotron emission, Compton scatteringand Bremsstrahlung radiation (Quataert & Narayan 1999). The mostluminous feature in the ADAF models come from the synchrotronpeak and for stellar mass black holes, this peak falls in the opticalwavelengths (Quataert & Narayan 1999). In their ADAF models forquiescent black hole binaries ( 𝑀 BH = 𝑀 (cid:12) ) with low accretion rates(log ( (cid:164) 𝑀 / (cid:164) 𝑀 edd ) ∼ − MNRAS000
PHOEBE fits (Table 4) donot change significantly if we change 𝑇 eff , giant . Because the modelsof the veiled SED are driven to larger, cooler stars, models forcingthe star to be more compact are even more disfavored than in theunveiled models. The best model of the veiled SED has 𝜒 = . . 𝑅 giant = 𝑅 (cid:12) and to 64 . 𝑅 giant = 𝑅 (cid:12) .The origin of this veiling component remains unclear although itis clearly non-stellar in nature. However, the morphology of the veil-ing component is broadly compatible with the spectra of advectiondominated accretion flows (ADAF). ADAF spectra can be describedby contributions due to synchrotron emission, Compton scatteringand Bremsstrahlung radiation (Quataert & Narayan 1999). The mostluminous feature in the ADAF models come from the synchrotronpeak and for stellar mass black holes, this peak falls in the opticalwavelengths (Quataert & Narayan 1999). In their ADAF models forquiescent black hole binaries ( 𝑀 BH = 𝑀 (cid:12) ) with low accretion rates(log ( (cid:164) 𝑀 / (cid:164) 𝑀 edd ) ∼ − MNRAS000 , 1–25 (2021)
723 Mon Wavelength [ Å ] r ( λ ) B − b a nd V − b a nd K E L T R K − b a nd T E SS T − b a nd Ca I linesFe I lines
Wavelength [ Å ] F / ( F + F g i a n t ) V − band (PHOEBE)B − band (PHOEBE) Figure 7.
The fractional veiling 𝑟 ( 𝜆 ) (Equation 5) [left] and second light (Equation 6) [right] calculated using Ca i and Fe i absorption lines as a function ofwavelength. The fractional second light in the 𝐵𝑉 -bands as calculated from PHOEBE are shown as filled diamonds. Power-law fits are shown as blue dashedlines. The effective wavelengths of the 𝐵𝑉 𝑅 𝐾 𝑇 -bands are shown as dashed lines. Figure 8.
The best-fitting SED model for V723 Mon after correcting for theveiling component (red triangles). The uncorrected SED from Figure 1 isalso shown (dashed line). Note that the SED of the veiling component is verydifferent from the SEDs of stars, as can be seen by comparing to Figure 1.
We can constrain the presence of luminous companions using eitherthe SED or the absence of eclipses. The limits using only the SEDwill be weaker than those using the eclipses, but are also independentof any knowledge of the inclination. For the SED constraints, we require that the companion contributes less than 100%, 60% and20% of the light in the
𝑈𝑉 𝑀 𝐵 and 𝑉 bands respectively. The 𝐵 and 𝑉 band limits correspond to the estimated veiling source from§4.4 and are conservative since the SED of the veiling light appearsto be inconsistent with a star, and the 𝑈𝑉 𝑀
𝑈𝑉 𝑀 𝐵 , 𝑉 and 𝑅 bands based on the eclipse models in §4.3. While we didnot use the 𝑈𝑉 𝑀 [ Fe / H ] = − . 𝑀 (cid:12) (log ( age ) = . 𝐿 = . 𝐿 (cid:12) , 𝑇 = MNRAS , 1–25 (2021) T. Jayasinghe et al. initial drop in temperature weakens the constraints more than therise in luminosity (see Figure 1). There are two maximum masses formodels with two stars. The lower age peak corresponds to pairing aslightly evolved star with a lower mass main sequence star. The totalmass of 1 . 𝑀 (cid:12) comes from combining a 1 . 𝑀 (cid:12) ( 𝐿 = . 𝐿 (cid:12) , 𝑇 = . 𝑀 (cid:12) ( 𝐿 = . 𝐿 (cid:12) , 𝑇 = ( age ) = .
45. The higher age peak comes from combining twostars of the same mass. The total mass is again 1 . 𝑀 (cid:12) and the twocomponents each have 𝑀 = . 𝑀 (cid:12) (log ( age ) = . 𝐿 = . 𝐿 (cid:12) , 𝑇 = 𝑈𝑉 𝑀 𝜆𝐿 𝜆 ≈ 𝐿 (cid:12) (aftercorrecting for extinction). Models normalized by this luminosity onlyhave total luminosities of 4 𝐿 (cid:12) , 5 𝐿 (cid:12) and 75 𝐿 (cid:12) , for temperatures of10 K, 3 × K and 10 K respectively, much too low for a massiveHe star companion. For example, a Helium star with 𝑇 ∼ K willhave 𝑀 ∼ 𝑀 (cid:12) and 𝐿 ∼ , 𝐿 (cid:12) (Gräfener et al. 2012). For anyhot companion with a luminosity approaching that of the giant, wewould also expect to see the effects of irradiation of the giant on itslight curve and phase dependent spectra, but no such perturbationsare seen.Given the size of the orbit and the size of the giant, compan-ions with radii similar to those allowed by the SED will be eclipsedprovided the inclination angle is 𝑖 (cid:38) ◦ . While the systematic uncer-tainties on the estimated inclination of 𝑖 (cid:39) ◦ ± ◦ may be moderatelylarger, the light curve shapes at inclinations anywhere approachingthis upper limit for seeing eclipses are grossly incompatible with theobservations. Fig. 9 also shows the limits on masses using the fluxlimits on the companion required to avoid visible eclipses, and theyare stronger than those from the SED as expected. The biggest changeis that they eliminate the “bumps” associated with stars starting tomove off the main sequence because they more directly constrainthe size of any companion. The improvements are otherwise modestbecause the (blue) luminosities are such strong functions of massthat moderate changes in the limits on the luminosity produce verymodest changes in the limits on the mass. The single star limit is now0 . 𝑀 (cid:12) and the two star limit is 1 . 𝑀 (cid:12) where the two star limitis always weakest for the stars being twins. These limits are smallerthan the binary mass function for this system (see § H 𝛼 and H 𝛽 emission We find that the Balmer H 𝛼 and H 𝛽 lines appear to significantly varywith phase (Figure 10) and this is unusual for a red giant. Given ourphase convention, the dark companion will be eclipsed by the giant at 𝜙 = .
50 with an eclipse duration of 𝑡 ecl (cid:39) . 𝜙 = .
50 should isolate its contribution. Toexplore this, we subtracted the SES spectrum of the red giant near 𝜙 (cid:39) . 𝑆 / 𝑁 > 𝛼 , H 𝛽 , Ca i 𝜆 𝜆 § ∼
12 km s − (Figure 11). This is also seen in the spec- Figure 9.
Limits on the mass of a companion that is comprised of either one(black) or two (red) luminous stars based on either the lack of KELT eclipses(solid) or the SED (dashed) as a function of the age of the stars. From theselimits, the maximum allowed mass for a single star is 1 . 𝑀 (cid:12) (SED) and0 . 𝑀 (cid:12) (eclipses). For two stars, the maximum allowed mass is 1 . 𝑀 (cid:12) (SED) and 1 . 𝑀 (cid:12) (eclipses). tra close to conjunction at 𝜙 = . 𝜆 𝜆 𝛼 and H 𝛽 emissionclearly varies with orbital phase. We do not see the Ca ii H and Klines in emission, so the changes in the Balmer lines are unlikely tobe caused by chromospheric activity. The Balmer emission could becaused by mass loss from the red giant through a stellar wind.The typical Gaussian FWHM of the H 𝛼 and H 𝛽 emission profilesis ∼
290 km s − . The median equivalent width of the residual H 𝛼 and H 𝛽 lines is EW ( H 𝛼 ) = . ± .
02 and EW ( H 𝛽 ) = . ± .
02 respectively. We can convert the H 𝛼 equivalent width to theflux at the stellar surface using 𝐹 H 𝛼 = 𝐹 𝑐 EW ( H 𝛼 ) (see for e.g.,Soderblom et al. 1993; González Hernández & Casares 2010). 𝐹 𝑐 isthe continuum flux which we derive using Hall (1996) as log ( 𝐹 𝑐 ) = . − . ( 𝐵 − 𝑉 ) . For V723 Mon, we find ( 𝐵 − 𝑉 ) = . ± .
06 mag, using the APASS DR10 photometry and the 𝐸 ( 𝐵 − 𝑉 ) from the SED fits. We obtain log ( 𝐹 𝑐 ) = . ± .
06 and 𝐹 H 𝛼 = . ± . − s − . Normalizing the H 𝛼 flux to the bolometricflux (i.e. 𝑅 H 𝛼 = 𝐹 H 𝛼 / 𝜎𝑇 ), we obtain log ( 𝑅 H 𝛼 ) = − . ± . ( 𝑅 H 𝛼 ) is usually compared to the Rossby number 𝑅 = 𝑃 rot / 𝜏 𝑐 ∼ .
84, where 𝜏 𝑐 ≈ . 𝑅 , V723 Mon has a value of log ( 𝑅 H 𝛼 ) higher thanany of the chromospherically active single stars from López-Santiagoet al. (2010) (see figure 5 in González Hernández & Casares 2010).This also indicates that the observed H 𝛼 emission is not just fromchromospheric activity.Another argument against chromospheric activity is that thechanges in the Balmer lines with phase are coherent over the ∼ . MNRAS000
84, where 𝜏 𝑐 ≈ . 𝑅 , V723 Mon has a value of log ( 𝑅 H 𝛼 ) higher thanany of the chromospherically active single stars from López-Santiagoet al. (2010) (see figure 5 in González Hernández & Casares 2010).This also indicates that the observed H 𝛼 emission is not just fromchromospheric activity.Another argument against chromospheric activity is that thechanges in the Balmer lines with phase are coherent over the ∼ . MNRAS000 , 1–25 (2021)
723 Mon dominated by chromospheric activity, we would expect the structureto change with time as the spot patterns evolve. At RV quadrature( 𝜙 (cid:39) .
25 and 𝜙 (cid:39) . 𝜆 𝜙 (cid:39) . 𝜙 (cid:39) . 𝛼 emission component isrelatively stationary at ∼−
35 km s − . The median separation betweenthe absorption and emission components in H 𝛼 is Δ 𝑉 ∼
115 km s − ,however this appears to vary with orbital phase. The separation islargest for 0 ≤ 𝜙 ≤ .
25, with Δ 𝑉 ∼
148 km s − , and drops there-after. The smallest separation between the two components is seenat phases 0 . ≤ 𝜙 ≤ .
75, with Δ 𝑉 ∼
104 km s − . Much like with theSES spectra, we also see clear variability in the H 𝛼 line profiles inthe HIRES spectra (Figure 13), and the asymmetry in the HIRES lineprofiles also reverses after 𝜙 = . 𝜙 (cid:39) .
5) there is very little Balmeremission (Figure 12). Both the Balmer and photospheric lines aremodulated with the ellipsoidal variations (Figure 10), however, near 𝜙 (cid:39) .
5, the equivalent width of the Balmer lines increases abruptly,signalling a dramatic drop in Balmer emission. A similar EW increaseis not seen in the photospheric lines. This feature is coincident withthe eclipse of the unseen companion by the red giant and has theexpected duration. The MODS spectra were taken around the eclipseof the dark companion by the red giant at 𝜙 (cid:39) . 𝛼 and H 𝛽 absorption features also deependuring the eclipse.While we have clear evidence to show the presence of Balmeremission that is correlated with the orbital motion of the putativeblack hole ( § 𝐿 ). At 𝜙 =
0, the inner La-grangian point is directed toward the observer. This also coincideswith the deeper minimum in the light curve because the surfacegravity and brightness is smallest at 𝐿 (Beech 1985). Conversely,at 𝜙 = . 𝐿 points away from the observer. It is possible thatthe Balmer emission is associated with the photoionization of matterstreaming through the inner Lagrangian point. The nearly-constantvelocity offset of the emission peak from the secondary is also consis-tent with this interpretation. However, this scenario requires a sourceof photoionization. The neutron star binary 1FGL J1417.7 − 𝛼 line with a complex morphology (Strader et al.2015; Swihart et al. 2018). Instead of an accretion disk, the authorsattributed this behavior to the interaction between the magneticallydriven wind from the secondary and the pulsar wind. Balmer photonsoriginating from an interbinary shock or the wind from the secondarywill have a velocity offset from the secondary. This is also seen inV723 Mon. However, the 𝐻𝛼 line in 1FGL J1417.7 − 𝐵 and 𝑉 -band light curves for V723 Mon.In summary, we see evidence of broad Balmer emission in thespectra. The Balmer line profiles prior to when the unseen compan- ion is eclipsed by the giant (0 ≤ 𝜙 (cid:46) .
46) resemble P-Cygni profiles,with a blue shifted emission component and a red shifted absorptioncomponent in the rest-frame of the giant. When the unseen com-panion is behind the giant at 𝜙 (cid:39) .
5, both the Balmer componentsdisappear and the Balmer absorption features from the giant becomedeeper. When the unseen companion re-emerges after the eclipse atphases 0 . (cid:46) 𝜙 ≤
1, we see a clear change in the P-Cygni-likeline profile, with both the absorption and emission components blueshifted. However, the absorption component is blue shifted morethan the emission and the P-Cygni profile is reversed. We also seesignificant changes in the Balmer line depths at 𝜙 = . Although there are no significant detections in the individual epochs,we detect a source with 9 . ± . ( . ± . ) × − counts/second in the merged Swift
XRT data. Assuming that 𝐸 ( 𝐵 − 𝑉 ) (cid:39) .
086 from § 𝑁 H , V723 (cid:39) . × cm − . This is considerably smaller thanthe total column density in the line of sight towards V723 Mon( 𝑁 H , LOS = . × cm − ). Assuming an absorbed power-lawwith a photon index of 2 and the Galactic column density estimate 𝑁 H , V723 , the
Swift
XRT count rate corresponds to an absorbed fluxof ( . ± . ) × − ergs cm − s − or an unabsorbed flux of ( . ± . ) × − ergs cm − s − in the 0.3-2.0 keV energy range.At the Gaia
EDR3 distance, we obtain absorbed and unabsorbedX-ray luminosities of ( . ± . ) × ergs s − and ( . ± . ) × ergs s − , respectively. If we use a 0.3-10.0 keV energy range,we obtain a similar number of counts as there is very little emission > . We also derive a limit on the hardness ratio of − . XMM-Newton observation, V723 Mon is not detected abovethe background, so we derive an upper-limit on 𝐿 X . We find a 3 𝜎 upper-limit count rate of 4.17 × − counts/second in the 0.5-8.0keV band within a 60 (cid:48)(cid:48) aperture (consistent with the off-axis PSFat the source position). Assuming an absorbed power-law with aphoton index of 2 and the Galactic column density of 𝑁 H , V723 , wefind an upper-limit absorbed flux of 1.0 × − erg cm − s − andan unabsorbed flux of 1.1 × − erg cm − s − . Adopting the Gaia
EDR3 distance, the latter quantity yields an X-ray luminosity upper-limit of 2.7 × erg s − in the 0.5-8.0 keV band.The Swift
XRT estimate of the X-ray luminosity is comparable tothe 𝐿 X ∼ − ergs s − observed for quiescent X-ray binaries(Dinçer et al. 2018) and the 𝐿 X ∼ − ergs s − observedfor chromospherically active RS CVn systems (Demircan 1987). Ifthe X-ray luminosity originates from an accretion disk, the putative We derive a 3 𝜎 upperlimit of 7 × − to the 2.0-10.0 keV count rate,which corresponds to an absorbed flux of 6 . × ergs s − or an unabsorbedflux of 7 . × ergs s − . Here the hardness ratio is defined as
𝐻 𝑅 = ( 𝐻 − 𝑆 )/( 𝐻 + 𝑆 ) where 𝐻 is the number of counts in the 2.0-10.0 keV energy range and 𝑆 is the numberof counts in the 0.3-2.0 keV energy range. MNRAS , 1–25 (2021) T. Jayasinghe et al.
200 100 0 100 200
Velocity[kms − ] H α H α
200 100 0 100 200
Velocity[kms − ] H α
200 0 2004858 4860 4862 4864 48660.20.40.60.81.0 H β H β
200 0 2004858 4860 4862 4864 48660.40.20.00.20.4 H β
200 100 0 100 2006436 6438 6440 6442 64440.60.70.80.91.01.11.2
CaI λ CaI λ
200 100 0 100 2006436 6438 6440 6442 64440.40.20.00.20.4
CaI λ
200 100 0 100 2006458 6460 6462 6464 6466
Wavelength [ Å ] CaI λ Phase (Φ)
CaI λ
200 100 0 100 2006458 6460 6462 6464 6466
Wavelength [ Å ] CaI λ P h a s e N o r m a li ze d F l u x E W ( Φ ) / E W ( Φ ’ ) R e s i du a l s Figure 10.
SES line profiles for the Balmer H 𝛼 , H 𝛽 , Ca i 𝜆 𝜆 𝜙 (cid:39) 𝜆 ∼ .000
SES line profiles for the Balmer H 𝛼 , H 𝛽 , Ca i 𝜆 𝜆 𝜙 (cid:39) 𝜆 ∼ .000 , 1–25 (2021)
723 Mon
80 60 40 20 0 20 40 60 80
Velocity [km s − ] N o r m a li ze d F l u x H α
80 60 40 20 0 20 40 60 80
Velocity [km s − ] N o r m a li ze d F l u x H β PEPSIModel
80 60 40 20 0 20 40 60 80
Velocity [km s − ] N o r m a li ze d F l u x Ca I λ
80 60 40 20 0 20 40 60 80
Velocity [km s − ] N o r m a li ze d F l u x Ca I λ Figure 11.
LBT/PEPSI line profiles for the Balmer H 𝛼 , H 𝛽 , Ca i 𝜆 𝜆 § ∼
12 km s − ) from the rest frame of the giant. black hole accretes at a very low luminosity of ∼ − 𝐿 edd . Thereis observational evidence which indicates that the X-ray luminosityfrom quiescent black holes is significantly fainter than that from neu-tron stars (see for e.g., Asai et al. 1998; Menou et al. 1999). Whiledebated, this has been attributed to advection-dominated accretionflows (ADAF; see, for e.g.,Narayan & Yi 1995) and the existence ofevent horizons for black holes. However, given the rapid rotation ofthe giant, some of the observed X-ray luminosity may originate fromthe giant’s chromosphere (Gondoin 2007). The X-ray spectra of X-ray binaries are generally harder (hotter), with average temperatures 𝑘𝑇 > 𝑘𝑇 < Swift
XRT analysis, it appears that the X-ray emission is relativelysoft, which appears to be consistent with a chromospheric origin.However, to fully characterize this X-ray emission, followup X-rayspectra of significantly better S/N are necessary.We can estimate the mass loss rate from the giant as (cid:164) 𝑀 = × − 𝜂 𝑅 𝐿𝑅𝑀 𝑀 (cid:12) yr − ≈ × − 𝑀 (cid:12) yr − , (9)(Reimers 1975) where 𝐿 , 𝑅 and 𝑀 are in solar units and 𝜂 𝑅 (cid:39) .
477 (McDonald & Zijlstra 2015). The velocity of the wind fromthe giant is assumed to be the escape velocity, which is 𝑉 wind ≈ 𝑉 esc ∼
120 km s − . For a scenario where the black hole accretesmass through the stellar wind, Thompson et al. (2019) approximatedthe amount of material gathered at the sphere of influence of the black hole as (cid:164) 𝑀 acc ∼ (cid:164) 𝑀 ( 𝜋𝑎 ) 𝜋 (cid:32) 𝐺 𝑀 BH 𝑉 (cid:33) ∼ × − M (cid:12) yr − (cid:164) 𝑀 − (cid:18) 𝑀 BH 𝑀 (cid:12) (cid:19) (cid:18) 𝑉 wind
120 km s − (cid:19) − , (10)where (cid:164) 𝑀 − = (cid:164) 𝑀 / − M (cid:12) yr − . For radiatively efficient accretiononto the black hole, the accretion luminosity can be approximated by 𝐿 acc ∼ . (cid:164) 𝑀 acc 𝑐 (cid:39) 𝐿 (cid:12) . (11)For radiatively inefficient accretion, the luminosity can be much lower(Narayan & Yi 1995). This estimate of the accretion luminosity ismuch larger than the observed X-ray luminosity of this system ( § 𝐿 acc ≈ 𝐿 veil ). Given the observed properties of the system and the modeling resultsfrom § §
4, we next systematically discuss the nature of thecompanion. We first discuss the uncertainties in the mass of thecompanion and then systematically consider the possible single andbinary possibilities for its composition.Ultimately, our knowledge of the mass of the companion is de-termined by how well we can constrain the properties of the giant.
MNRAS , 1–25 (2021) T. Jayasinghe et al.
200 100 0 100 2000.20.00.20.4 R e s i du a l F l u x φ ’ = 0 H α Ca IH β
200 100 0 100 2000.20.00.20.4 R e s i du a l F l u x φ ’ = 0 .
200 100 0 100 2000.20.00.20.4 R e s i du a l F l u x φ ’ = 0 .
200 100 0 100 2000.20.00.20.4 R e s i du a l F l u x φ ’ = 0 .
200 100 0 100 2000.20.00.20.4 R e s i du a l F l u x φ ’ = 0 .
200 100 0 100 200
Velocity [km s − ] R e s i du a l F l u x φ ’ = 0 . Figure 12.
The right panels show the template subtracted H 𝛼 (red dot-dashed), H 𝛽 (blue dashed) and Ca i 𝜆000
The right panels show the template subtracted H 𝛼 (red dot-dashed), H 𝛽 (blue dashed) and Ca i 𝜆000 , 1–25 (2021)
723 Mon
200 100 0 100 200
Velocity [km s − ] Wavelength [ Å ] R e s i du a l s H α HIRES P h a s e Figure 13.
The HIRES H 𝛼 line profiles as a function of orbital phase. Thetemplate SES spectrum at 𝜙 (cid:39) . § Estimates of the mass through either the radius and gravity or stellarevolution models give relatively crude limits of 1 . ± . 𝑀 (cid:12) and1 . ± . 𝑀 (cid:12) , respectively ( § 𝑀 core is (cid:18) 𝐿𝐿 (cid:12) (cid:19) ≈ (cid:18) 𝑀 core . 𝑀 (cid:12) (cid:19) . (12)(Boothroyd & Sackmann 1988), so we must have 𝑀 giant > 𝑀 core (cid:39) . 𝑀 (cid:12) for 𝐿 ∼ 𝐿 (cid:12) . This implies a lower bound for the com-panion mass of 𝑀 comp (cid:38) . 𝑀 (cid:12) , above the mass of the mostmassive neutron star observed and larger than the limits for singleand binary stellar companions in § PHOEBE mod-els of the ellipsoidal variability in § 𝑞 because (to leadingorder) the amplitude of the 𝑃 orb / 𝜖 ∼ ( 𝑅 / 𝑎 ) / 𝑞 while the amplitudes of the 𝑃 orb and 𝑃 orb / ( 𝑅 giant / 𝑎 ) / 𝑞 (e.g., Morris 1985; Gomel et al. 2020). Since the semi-major axis is determined by the period, mass function and mass ratio, 𝑎 ∝ 𝑃 𝑓 ( + 𝑞 ) , the ellipsoidal variability can constrain both 𝑅 giant and 𝑞 . This also means that the radius of the giant is an importantindependent constraint. Given the period, mass function and ampli-tude 𝜖 , the mass of the giant 𝑀 giant = 𝑓 𝑞 ( + 𝑞 ) ∝ 𝑅 simplyscales with the radius of the giant. The mass of the companion, 𝑀 comp = 𝑓 ( + 𝑞 ) , is less dependent on the radius because the massratio 𝑞 is small. We can verify this correlation using PHOEBE modelswith the radius of the giant fixed to 𝑅 giant =
18, 20, 22, 24, and 26 𝑅 (cid:12) .The mass of the giant increases monotonically and fairly rapidly withradius, 𝑀 giant = .
44, 0.57, 0.74, 0.93, and 1 . 𝑀 (cid:12) , while the massof the companion increases more slowly, 𝑀 comp = .
42, 2.57, 2.77,2.98, and 3 . 𝑀 (cid:12) , as expected. In fact, the numerical results al- most exactly track the expected scalings from holding 𝜖 fixed whilevarying the radius of the star.The PHOEBE models on their own found a radius of 𝑅 giant = . ± . 𝑅 (cid:12) , which agrees well with the independent results from the SEDfits. Without the correction for veiling, these fits gave 22 . ± . 𝑅 (cid:12) and with the correction for veiling they gave 24 . ± . 𝑅 (cid:12) . Thesefits use a much more complete SED model than used for the GaiaDR2 estimate of ∼ 𝑅 (cid:12) , but even for this smaller estimate thecompanion mass is 𝑀 comp = . 𝑀 (cid:12) . Since the radius estimatesfrom the SED and the ellipsoidal variability agree, we will proceedunder the assumption that the resulting mass estimates of 𝑀 giant = . ± . 𝑀 (cid:12) and 𝑀 comp = . ± . 𝑀 (cid:12) are essentially correct.We next consider all the possible scenarios for the composition ofthe companion, with Table 5 providing a summary. If the companionis a single object, the options are a star, a white dwarf (WD), aneutron star (NS) or a black hole (BH). A star is ruled out by theeclipse and SED limits from §4.5, with 𝑀 comp < . 𝑀 (cid:12) based onthe lack of eclipses. A WD is ruled out because its mass wouldexceed the Chandrasekhar mass limit of 1 . 𝑀 (cid:12) . A NS is technicallypossible, since a companion mass of 𝑀 comp (cid:39) . 𝑀 (cid:12) is stillslightly less than the maximum passable mass of a neutron star( 𝑀 ∼ 𝑀 (cid:12) ; Lattimer & Prakash 2001). However, the mass is wellabove the maximum observed masses of 𝑀 (cid:39) . ± . 𝑀 (cid:12) and 𝑀 (cid:39) . + . − . 𝑀 (cid:12) found for the neutron stars PSR J0348+0432 andMSP J0740+6620, respectively (Antoniadis et al. 2013; Cromartieet al. 2020), so we view a NS as unlikely. The mass of the darkcompanion is slightly larger than the 𝑀 (cid:39) . + . − . 𝑀 (cid:12) mass-gapcompact object in the LIGO/VIRGO gravitational wave merger eventGW190814 (Abbott et al. 2020), and it is comparable in mass to the 𝑀 BH (cid:39) . + . − . 𝑀 (cid:12) non-interacting black hole identified around thered giant 2MASS J05215658+4359220 by Thompson et al. (2019).The mass estimates for V723 Mon, due to its ellipsoidal variability,are much tighter than for 2MASS J05215658+4359220. Thus, thesimplest explanation of observed V723 Mon system properties isthat the binary companion is a black hole near the lower end of themass gap.There are many more possible scenarios if the companion is abinary. The orbit of such a binary has to be fairly compact (seeAppendix A), but not too compact, or the system would merge toorapidly (see below). While a single phase of common envelope evo-lution can likely lead to the simple binary models, any of these triplesolutions likely requires a more complex evolutionary pathway whichwe will not attempt to explore here. Based on our analyses in § 𝑀 binary < . 𝑀 (cid:12) from the eclipse constraints (Figure9). The companion must contain at least one compact object.Combining a star with a compact object seems unlikely. With thestellar mass < . 𝑀 (cid:12) based on the lack of eclipses, the compactobject mass must be > . 𝑀 (cid:12) . A WD is ruled out because thisexceeds the Chandrasekhar limit. A NS is possible, but the mass is ator above the maximum observed NS masses. A BH is also possible,but a single more massive BH seems far more plausible than a BHwith a NS-like mass combined with a star to form the inner binaryof a triple system.A double WD binary requires that both WDs are very close to theChandrasekhar limit or above it. Given that such massive WDs arequite rare (Tremblay et al. 2016), putting two of them into such asystem is unlikely even if the masses can be kept just below the limit.Combining a WD and a NS is allowed, and the NS mass is in theobserved range if the WD mass is > . 𝑀 (cid:12) . Combining a WD with aBH is possible, but has the same plausibility problems as combininga star with a BH. A double NS binary is feasible. They would need MNRAS , 1–25 (2021) T. Jayasinghe et al. to be of similar mass, since a mass ratio > . . 𝑀 (cid:12) (Suwaet al. 2018). Combining a NS with a BH and a double BH binaryseem implausible because they both require BH masses in the rangeobserved for neutron stars.An additional consideration for any compact object binary modelfor the companion is its lifetime due to the emission of gravitationalwaves. For an equal mass, 2 . 𝑀 (cid:12) binary in a circular orbit withsemi-major axis 𝑎 in , the merger time is 𝑡 merge = . × years (cid:18) 𝑎 in 𝑅 (cid:12) (cid:19) (cid:18) . 𝑀 (cid:12) 𝑀 comp (cid:19) . (13)If the age of the system must be > ( ) Gyr to allow time for thered giant to evolve, then 𝑎 in > . 𝑅 (cid:12) ( . 𝑅 (cid:12) ) . Unfortunately, abinary with such a long life time is too weak a gravitational wavesource to be detected by the Laser Interferometer Space Antenna(LISA, Robson et al. 2019). As discussed in Appendix A, dynamicalstability requires 𝑎 in < 𝑅 (cid:12) (significantly inside the Roche loberadius of the companion, ∼ 𝑅 (cid:12) ), so a long-lived, dynamicallystable binary is possible for 4 𝑅 (cid:12) < ∼ 𝑎 in < ∼ 𝑅 (cid:12) . This does notguarantee secular stability, and for much of this range of semi-majoraxes we would also expect to see dynamical perturbations of the outerorbit and additional tidal interactions (see Appendix A).In summary, while it is difficult to rule out more complex scenarioswhere the companion to the giant is a binary consisting of at least onecompact object, the simplest explanation is that the dark companionis a low-mass black hole. This would make V723 Mon a uniquesystem, as it would contain both the lowest mass BH in a binaryand be the closest known black hole yet discovered. The low X-rayluminosity ( 𝐿 / 𝐿 edd ∼ − ) of this system likely also suggests a blackhole companion, as quiescent black holes are known to be X-ray faint(see § The nearby ( 𝑑 (cid:39)
460 pc), bright ( 𝑉 (cid:39) . 𝑇 eff , giant (cid:39) 𝐿 giant (cid:39) 𝐿 (cid:12) ) V723 Mon is in a high massfunction, 𝑓 ( 𝑀 ) = . ± . 𝑀 (cid:12) , nearly circular binary ( 𝑃 = . 𝑒 (cid:39)
0) with a dark companion of mass 𝑀 comp = . ± . 𝑀 (cid:12) .V723 Mon is a known variable that had been typically classified as aneclipsing binary, but the ASAS, KELT and TESS light curves indicatethat is in fact a nearly edge-on ellipsoidal variable ( § § 𝑖 (cid:39) § . 𝑀 (cid:12) < 𝑀 comp < . 𝑀 (cid:12) for 0 . 𝑀 (cid:12) < 𝑀 giant < . 𝑀 (cid:12) . We modeled the light curves with PHOEBE using constraints on the period, radial velocities and stellartemperature to derive an inclination of 𝑖 = ◦ ± ◦ , a mass ratio of 𝑞 (cid:39) . ± .
02, a companion mass of 𝑀 comp = . ± . 𝑀 (cid:12) ,a stellar radius of 𝑅 giant = . ± . 𝑅 (cid:12) , and a giant mass of 𝑀 giant = . ± . 𝑀 (cid:12) consistent with the earlier estimates ( § 𝐵 and 𝑉 -band lightcurves ( § ∼ ∼
23% of the total flux in the 𝐵 -band and 𝑉 -band respectively.The SED of the veiling component decays rapidly towards both bluerand redder wavelengths, strongly inconsistent with a stellar SED.Given that we do not see eclipses in the light curves, we infer thatthe veiling component has to be diffuse. We find no evidence for a luminous stellar companion and can ruleout both single and binary main sequence companions based on theSED and limits on eclipses ( 𝑀 single < . 𝑀 (cid:12) , 𝑀 binary < . 𝑀 (cid:12) )from the light curves ( § § §
5, Figure 9).Once the spectrum of the red giant is subtracted, we also findevidence of Balmer H 𝛼 and H 𝛽 emission ( § 𝐿 X (cid:39) . × ergs s − ( 𝐿 / 𝐿 edd ∼ − ) using 𝑆𝑤𝑖 𝑓 𝑡
XRT data ( § §
5, Ta-ble 5). Prior to this discovery, A0620-00 (V616 Mon) was the closestconfirmed black hole at an estimated distance of ∼ . 𝐻𝑢𝑏𝑏𝑙𝑒 space telescope will constrain the natureof the veiling component, and X-ray light curves will be useful tounderstand the nature of the compact object in this system. Futuredata releases from
Gaia will also confirm the orbital inclination.We can very crudely estimate the expected number of similarsystems based on the fraction of the thin disk mass from whichV723 Mon was selected. We assume a simple exponential disk modelwith density 𝜌 = 𝜌 𝑒 − 𝑅 / 𝑅 𝑑 −| 𝑧 |/ ℎ , (14)where 𝑅 d ≈ ℎ and densitynormalization 𝜌 are not needed. The total disk mass is 4 𝜋𝜌 ℎ𝑅 𝑑 .If we assume that V723 Mon was selected from a cylinder of radius 𝑅 at the Galactocentric radius of the Sun, 𝑅 (cid:12) (cid:39) 𝜋ℎ𝑅 exp (− 𝑅 sun / 𝑅 𝑑 ) , so thefraction of the disk mass surveyed is approximately (cid:18) 𝑅𝑅 𝑑 (cid:19) exp (− 𝑅 sun / 𝑅 𝑑 ) (cid:39) .
008 (15)if we assume 𝑅 (cid:39) .
002 if we use the distance 𝑅 (cid:39) . to 10 ) of non-interacting black hole binaries in the Galaxy based on populationsynthesis models (see, for e.g., Breivik et al. 2017; Shao & Li 2019).A number of large spectroscopy projects such as APOGEE (Ma-jewski et al. 2017) and LAMOST (Cui et al. 2012) are in the process ofphysically characterizing (kinematics, temperature, abundances, etc.)millions of Galactic stars. These surveys frequently obtain their spec-tra in multiple visits, providing sparse radial velocity (RV) curves forhuge numbers of stars. A particularly important synergy is the abilityto combine photometric surveys with these spectroscopic surveys tosearch for non-interacting compact object binaries like V723 Mon. MNRAS000
002 if we use the distance 𝑅 (cid:39) . to 10 ) of non-interacting black hole binaries in the Galaxy based on populationsynthesis models (see, for e.g., Breivik et al. 2017; Shao & Li 2019).A number of large spectroscopy projects such as APOGEE (Ma-jewski et al. 2017) and LAMOST (Cui et al. 2012) are in the process ofphysically characterizing (kinematics, temperature, abundances, etc.)millions of Galactic stars. These surveys frequently obtain their spec-tra in multiple visits, providing sparse radial velocity (RV) curves forhuge numbers of stars. A particularly important synergy is the abilityto combine photometric surveys with these spectroscopic surveys tosearch for non-interacting compact object binaries like V723 Mon. MNRAS000 , 1–25 (2021)
723 Mon Table 5.
Comparison of the possible scenarios involving stellar companions (*), white dwarfs (WD), neutron stars (NS) and black holes (BH) that can explainthe nature of the dark companion. We assumed 𝑀 comp = . ± . 𝑀 (cid:12) from § (cid:51) ’ indicates that the scenario is possible, a ‘?’ indicates thatwhile the scenario is technically possible, it is very unlikely and a ‘ (cid:55) ’ indicates that the scenario is ruled out. The simplest explanation is that of a single lowmass black hole, indicated with ‘ (cid:51)(cid:51) ’.Dark Companion Possibility CommentSingle Star (cid:55) Ruled out by SED/eclipse limits from § 𝑀 ∗ (cid:46) . 𝑀 (cid:12) ).Single WD (cid:55) WD will exceed Chandrasekhar limit ( 𝑀 WD > . 𝑀 (cid:12) ).Single NS ? Requires an extreme NS equation of state.Single BH (cid:51)(cid:51) Simplest explanation.Star + Star (cid:55)
Ruled out by SED/eclipse limits from § 𝑀 binary (cid:46) . 𝑀 (cid:12) ).Star + WD (cid:55) For 𝑀 ∗ (cid:46) . 𝑀 (cid:12) ( § 𝑀 ∗ < . 𝑀 (cid:12) , the NS mass exceeds 2 . 𝑀 (cid:12) .Star + BH ? BH mass is even lower than with no star.WD + WD (cid:55) Both WD components near or above Chandrasekhar limit.NS + WD (cid:51)
NS mass is in the observed range if 𝑀 WD > . 𝑀 (cid:12) BH + WD ? BH mass is even lower than with no WD.NS + BH (cid:55)
The BH must have a NS-like mass.NS + NS (cid:51)
Both NS components should have 𝑀 NS (cid:38) . 𝑀 (cid:12) , so 𝑞 inner (cid:38) . (cid:55) The BHs have NS masses.
Table 6.
Swift UVM2 observationsBJD Date Phase UVM2 (mag) 𝜎 (mag)2459144.44160 2020-10-21 0.975 14.10 0.042459150.61009 2020-10-28 0.078 14.06 0.042459155.04343 2020-11-01 0.152 14.07 0.042459158.71169 2020-11-05 0.213 14.17 0.042459162.69297 2020-11-09 0.279 14.12 0.042459166.86925 2020-11-13 0.345 14.32 0.062459172.83661 2020-11-19 0.449 14.10 0.042459173.77366 2020-11-20 0.464 14.16 0.042459175.50175 2020-11-22 0.493 14.12 0.042459175.75777 2020-11-22 0.497 14.13 0.042459176.62881 2020-11-23 0.512 14.13 0.042459184.19318 2020-11-30 0.634 14.06 0.042459203.85574 2020-12-20 0.966 14.04 0.042459209.83580 2020-12-26 0.066 14.09 0.04 For example, for the vast majority of these relatively bright stars,the ASAS-SN survey (Shappee et al. 2014; Kochanek et al. 2017;Jayasinghe et al. 2018, 2020) will supply all-sky, well-sampled lightcurves spanning multiple years. If we make a conservative assump-tion that ASAS-SN can characterize the variability of most giantsup to ∼ ∼
20 red giants with non-interacting companions that have ASAS-SNlight curves. However, there is a significant cost to confirming thesesystems. In particular, a well sampled set of RV measurements isrequired to accurately measure the mass function and to constrainthe properties of any companion. Nonetheless, as the spectroscopicsurveys expand from a few 10 to a few 10 stars during the next 5years, this approach will become a major probe of compact objectbinaries. ACKNOWLEDGEMENTS
We thank Dr. Jennifer Johnson, Dr. Marc Pinsonneault and Dr. JimFuller for useful discussions on this manuscript. We thank Dr. JayStrader for a careful reading of this manuscript. We thank Dr. RickPogge for his help with obtaining the LBT/MODS spectra.The ASAS-SN team at OSU is supported by the Gordon andBetty Moore Foundation through grant GBMF5490 to the Ohio StateUniversity, and NSF grant AST-1908570.TJ, KZS and CSK are supported by NSF grants AST-1814440and AST-1908570. AT is supported in part by NASA grant80NSSC20K0531. TAT acknowledges previous support from Scia-log Scholar grant 24216 from the Research Corporation, fromwhich this effort germinated. J.T.H. is supported by NASA award80NSSC21K0136. Support for JLP is provided in part by the Min-istry of Economy, Development, and Tourism’s Millennium ScienceInitiative through grant IC120009, awarded to The Millennium In-stitute of Astrophysics, MAS. D.H. acknowledges support from theAlfred P. Sloan Foundation, the National Aeronautics and SpaceAdministration (80NSSC18K1585, 80NSSC19K0379), and the Na-tional Science Foundation (AST-1717000). CB acknowledges sup-port from the National Science Foundation grant AST-1909022.Parts of this research were supported by the Australian ResearchCouncil Centre of Excellence for All Sky Astrophysics in 3 Dimen-sions (ASTRO 3D), through project number CE170100013.The LBT is an international collaboration among institutions in theUnited States, Italy and Germany. LBT Corporation partners are: TheUniversity of Arizona on behalf of the Arizona Board of Regents;Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft,Germany, representing the Max-Planck Society, The Leibniz Institutefor Astrophysics Potsdam, and Heidelberg University; The Ohio StateUniversity, representing OSU, University of Notre Dame, Universityof Minnesota and University of Virginia.STELLA and PEPSI were made possible by funding through theState of Brandenburg (MWFK) and the German Federal Ministry of
MNRAS , 1–25 (2021) T. Jayasinghe et al.
Table 7.
Spectroscopic observations from HIRES, MODS and PEPSI.BJD [TDB] Date Phase RV (kms − ) 𝜎 𝑅𝑉 (kms − ) Instrument2459143.09532 2020-10-20 0.952 24.39 0.10 HIRES2459153.99899 2020-10-31 0.134 -47.28 0.10 HIRES2459162.02289 2020-11-08 0.268 -63.27 0.10 HIRES2459188.01112 2020-12-04 0.702 62.67 0.10 HIRES2459208.01826 2020-12-24 0.036 -12.23 0.10 HIRES2459208.89679 2020-12-25 0.050 -17.51 0.10 HIRES2459209.98247 2020-12-26 0.068 -24.92 0.10 HIRES2459171.94982 2020-11-18 0.434 — — MODS2459173.86921 2020-11-20 0.466 — — MODS2459174.89034 2020-11-21 0.483 — — MODS2459175.77657 2020-11-22 0.498 — — MODS2459183.77896 2020-11-30 0.631 48.74 0.25 PEPSI Education and Research (BMBF) through their Verbundforschunggrants 05AL2BA1/3 and 05A08BAC.Some of the data presented herein were obtained at the W. M. KeckObservatory, which is operated as a scientific partnership among theCalifornia Institute of Technology, the University of California andthe National Aeronautics and Space Administration. The Observatorywas made possible by the generous financial support of the W. M.Keck Foundation.The authors wish to recognize and acknowledge the very signif-icant cultural role and reverence that the summit of Maunakea hasalways had within the indigenous Hawaiian community. We are mostfortunate to have the opportunity to conduct observations from thismountain.We thank the ASAS and KELT projects for making their light curvedata publicly available. This research has made use of the VizieRcatalogue access tool, CDS, Strasbourg, France. This research alsomade use of Astropy, a community-developed core Python packagefor Astronomy (Astropy Collaboration et al. 2013, 2018).
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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APPENDIX A: THE ORIGIN OF THE RADIAL VELOCITYRESIDUALS
S12 interpreted V723 Mon as a triple system where the companionis a binary with period 𝑃 in = 𝑃 orb / (cid:39)
20 days. G14 argued againstthis hypothesis, but there are significant RV residuals at 𝑃 orb / 𝑃 orb / ∼
20 day inner binary is the dynamicalstability argument raised by G14. For our nominal parameters, theouter orbit has a total mass of (cid:39) 𝑀 (cid:12) (in round numbers) and asemi-major axis of 100 𝑅 (cid:12) while the inner orbit has a mass of 3 𝑀 (cid:12) .The 45 𝑅 (cid:12) semi-major axis of a 20 day binary is very close to theRoche limit around the companion of 49 𝑅 (cid:12) . A rough estimate ofthe largest semi-major axis that could be dynamically stable giventhe outer orbit and the mass ratios is 32 𝑅 (cid:12) based on Mardling &Aarseth (2001). In short, G14 was correct to hypothesize that suchan orbit should be dynamically unstable.We experimented with numerically integrating planar 3-body or-bits starting from nominally circular orbits as initial conditions for ∼
100 orbits of the outer binary and varying mass ratios of the innerbinary. High mass ratio inner binaries were generally very unstable,presumably because the lighter star in the inner binary is trying tomaintain an orbital radius close to the full semi-major axis of 45 𝑅 (cid:12) in this limit. Equal mass inner binaries tended to be more stable,presumably because each star now only has an orbit of ∼ 𝑅 (cid:12) about the center of mass of the inner binary. Nonetheless, many trialsresulted in the destruction of the system well before 100 orbits werecompleted. These results were not unique to picking a truly resonant 𝑃 orb / ∼
12 days to satisfy the dynamical stability criterion, although suchsystems may still be secularly unstable.The other problem with longer period inner binaries is that theyperturb the outer orbit and produce time varying tidal forces on thegiant even if stable. In particular, the wider inner binaries wouldgenerally drive the outer orbit to be significantly elliptical in ournumerical experiments even if they were stable over the 100 orbits.Making the companion a binary also means that the tidal forces onthe giant are time variable. If the companion is a single star, theamplitude of the elliptical variability depends on ( 𝑅 giant / 𝑎 ) whileif it is an equal mass binary it depends on 𝑥 (cid:18) 𝑅 giant 𝑑 (cid:19) + − 𝑥 (cid:18) 𝑅 giant 𝑑 (cid:19) (A1)where 𝑑 and 𝑑 are the distances to the two stars which comprisefractions 𝑥 and 1 − 𝑥 of the mass of the inner binary. Compared toa single companion, there is a fractional fluctuating tidal amplitudefor circular orbits of order3 ( − 𝑥 ) 𝑎 𝑖𝑛 𝑎 cos 𝜔 𝑡 𝑡 + (cid:16) − 𝑥 + 𝑥 (cid:17) 𝑎 𝑖𝑛 𝑎 cos 2 𝜔 𝑡 𝑡 (A2)where the frequency 𝜔 𝑡 = 𝜔 in − 𝜔 is the frequency difference betweenthe inner and outer binaries. In particular, for an equal mass ( 𝑥 = / (cid:16) 𝑎 in 𝑎 (cid:17) , (A3) so a 𝑃 in =
20 day period inner binary would produce ∼
38% peak-to-peak fluctuations in the tidal force with a period of 15 days. Nosuch residuals are seen in the residuals from the ellipsoidal modelof the light curves at this or any similar period (see Appendix B).To have fractional fluctuations in the tidal forcing smaller than 𝑓 = . 𝑓 requires an equal mass inner binary to be more compact than 𝑎 in < 𝑓 / 𝑅 (cid:12) and to have a period 𝑃 in < . 𝑓 / days.These arguments appear to strongly rule out the inner binary pro-posed by S12. We instead suspect that the RV residuals and much ofthe evidence for a binary companion are driven by the consequencesof making RV observations of a high amplitude ELL variable. Thevery similar issues for observations of stars with dynamical tideshave been discussed (e.g. Arras et al. 2012, Penoyre & Stone 2019)recently, but we could find no previous discussion in the context ofa tidally locked system. A tidally locked star is simply rotating atthe orbital frequency, so the rotation velocity at the surface scaleswith the cylindrical radius from the rotation axis. Thus, the rotationalvelocity is larger on the long axis of the star than on the short axis.When viewed along a principal axis, there is the usual cancellationof the contributions from the parts of the star rotating towards andaway from the observer. However, when viewed at an intermediatedirection, the contribution of one sign of the rotation comes from theslower moving short axis while the contribution from the other signcomes from the faster moving long axis. This makes a contributionto the observed radial velocities with a period 𝑃 orb / 𝑚 = 𝑃 orb /
3, and we think this is the likely origin of the 𝑃 orb / APPENDIX B: SHORT TIMESCALE VARIABILITY
We searched for additional variability on three broad time scales.First, we looked for extra variability on the time scales of weeks orlonger in the residuals of the ASAS and KELT light curves after sub-tracting the best model for the ellipsoidal variability. Next, we lookedfor variability on the time scale of days in the residuals of the TESSlight curve. Finally, we searched for very short time scale variabilityduring several periods of very high cadence ROAD observations.As discussed in Appendix A, a sufficiently wide binary secondarywill produce strong fluctuations in the strength of the tides on the giantat periods with frequencies that are either the difference in frequencybetween the inner and outer binary 𝑤 𝑡 or twice that frequency, withthe perturbations at 𝑤 𝑡 requiring an un-equal mass binary companion.In particular, for the 20 day period inner binary proposed by S12,we would expect strong fluctuating tides on periods of 30 and 15days, although the 30 day period could be partly absorbed into theELL fit. We looked for periodic signals in the residuals of the fits tothe ASAS and KELT light curves using Period04 (Lenz & Breger2005), and found none that were significant (a signal-to-noise ratio
MNRAS , 1–25 (2021)
723 Mon > TESS residuals on shorttime scales (Figure B1) with an amplitude of 0 . 𝜈 max = 𝜈 max , (cid:12) (cid:18) 𝑔𝑔 (cid:12) (cid:19) (cid:18) 𝑇 eff 𝑇 eff , (cid:12) (cid:19) − / , (B1)where 𝜈 max , (cid:12) = 𝜇 Hz, 𝑇 eff , (cid:12) = 𝑔 (cid:12) = . × cm / s (Brown et al. 1991; Kjeldsen & Bedding 1995). Given thespectroscopic parameters in § 𝜈 max ≈ . 𝜇 Hz,which corresponds to a period of 𝑃 osc ≈ . 𝐵 -bandexposures. We have reduced these data using the ASAS-SN versionof the Alard (2000) image subtraction software. We do not find anyevidence for short ( < 𝐵 -band variability, with therms scatter during individual nights below 0 .
01 mag. Given that the“second light” contribution to the total 𝐵 -band flux of V723 Mon isabout 60%, this translates to the short-timescale variability of thiscomponent being less that ∼ 𝐵 -band variability at the ∼
2% level is still possible(on top of the observed ellipsoidal modulations discussed in § This paper has been typeset from a TEX/L A TEX file prepared by the author. MNRAS , 1–25 (2021) T. Jayasinghe et al.
BJD − O − C [ % ] TESS : T
Figure B1.
The
TESS residuals after the PHOEBE model is subtracted.MNRAS000