Infrared Spectroscopy of Symbiotic Stars. XII. The Neutron Star SyXB System 4U 1700+24 = V934 Herculis
K. H. Hinkle, F. C. Fekel, R. R. Joyce, J. Mikołajewska, C. Galan, T. Lebzelter
aa r X i v : . [ a s t r o - ph . S R ] D ec INFRARED SPECTROSCOPY OF SYMBIOTIC STARS. XII.THE NEUTRON STAR SyXB SYSTEM 4U 1700+24 = V934 HERCULIS
KENNETH H. HINKLE
National Optical Astronomy ObservatoryP.O. Box 26732, Tucson, AZ 85726, USA [email protected]
FRANCIS C. FEKEL
Tennessee State University, Center of Excellence in Information Systems,3500 John A. Merritt Boulevard, Box 9501, Nashville, TN 37209, USA [email protected]
RICHARD R. JOYCE
National Optical Astronomy Observatory,P.O. Box 26732, Tucson, AZ 85726, USA [email protected]
JOANNA MIKO LAJEWSKA
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences,Bartycka 18, PL-00-716 Warsaw, Poland
CEZARY GA LAN
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences,Bartycka 18, PL-00-716 Warsaw, Poland
THOMAS LEBZELTER
University of Vienna, Department of AstrophysicsT¨urkenschanzstrasse 17, A-1180 Vienna, Austria [email protected]
ABSTRACT
V934 Her = 4U 1700+24 is an M giant–neutron star (NS) X-ray symbiotic (SyXB)system. Employing optical and infrared radial velocities spanning 29 years combinedwith the extensive velocities in the literature, we compute the spectroscopic orbit of 2 –the M giant in that system. We determine an orbital period of 4391 days or 12.0 yr,the longest for any SyXB, and far longer than the 404 day orbit commonly cited forthis system in the literature. In addition to the 12.0 yr orbital period we find a shorterperiod of 420 days, similar to the one previously found. Instead of orbital motion,we attribute this much shorter period to long secondary pulsation of the M3 III SRbvariable. Our new orbit supports earlier work that concluded that the orbit is seennearly pole on, which is why X-ray pulsations associated with the NS have not beendetected. We estimate an orbital inclination of 11 . ◦ ± . ◦
4. Arguments are made thatthis low inclination supports a pulsation origin for the 420 day long secondary period.We also measure CNO and Fe peak abundances of the M giant and find it to be slightlymetal poor compared to the Sun with no trace of the NS forming SN event. Basicproperties of the M giant and NS are derived. We discuss the possible evolutionarypaths that this system has taken to get to its current state.
Subject headings: stars: abundances — stars: binaries:symbiotic — stars: evolution— stars: individual (V934 Her) — stars: late-type
1. INTRODUCTION
Symbiotic X-ray binaries (SyXB) are a rare class of low-mass, hard X-ray binaries consisting ofa neutron star (NS) accreting mass from an M giant (M¨urset et al. 1997). The much more commonsymbiotic systems (SySt) contain a white dwarf accreting mass from, typically, a K or M giant.SySt are identified by emission lines in the optical that result from accretion processes. The SyXBdiffer from the SySt in having nearly normal optical spectra. Unlike SySt that are found becauseof their optical emission lines, typical SyXB are first identified as X-ray sources and then laterassociated with M giant optical counterparts.Since the companion to the NS is a low mass M giant, SyXB are also classified as low-massX-ray binaries (LMXB). As described by Liu et al. (2007), typical LMXB have orbital periods ofdays with the low-mass star transferring matter by Roche-lobe overflow to the NS primary. Thelow-mass star can be a white dwarf, a main-sequence star, or an F-G subgiant. SyXB differ fromthe larger group of LMXB in having a giant companion to the NS, an orbital period of years, andan exceedingly slow NS spin of minutes to hours (L¨u et al. 2012; Enoto et al. 2014). To date, thetotal number of confirmed SyXB systems is barely over a half dozen with the Galactic populationestimated to be ∼ ∼
2. A BRIEF REVIEW OF HD 154791 = V934 Her = 4U 1700+24
The X-ray source 4U 1700+24 was discovered roughly simultaneously by Cooke et al. (1978)in Ariel V scans for high-latitude X-ray sources and by Forman et al. (1978) from the Uhuru X-raycatalog. Garcia et al. (1983) found the Einstein X-ray position to be coincident with the V = 7.6mag normal M giant HD 154791. Using standard models for stellar wind accretion, Garcia et al.(1983) showed that a binary model with a NS accreting mass from an M giant was a plausibleexplanation for the X-ray luminosity and energy distribution. Lack of velocity variations & − over an eight month period suggested either that the system has a very long orbital period or thatit was viewed nearly face-on. 4 –Garcia et al. (1983) found three emission lines in the IUE ultraviolet spectrum of HD 154791that are not seen in normal M giant spectra. dal Fiume et al. (1990) found that these UV emissionlines have variable strengths associated with variations in the X-ray flux, strengthening the con-nection with an accretion process. In addition, Brown et al. (1990) found the He I 10830 ˚A line ispresent with strong emission and absorption. The He I 10830 ˚A 2 S - 2 P line has a metastablelower state 20 eV above the ground state and is diagnostic of binary star X-ray activity. However,Sokoloski et al. (2001) found no flickering in B with a limit of ∼
10 mmag.Garcia et al. (1983) identified the optical spectral type of HD 154791 as M3 II. However,Masetti et al. (2002) found its spectrum to be a poor fit to standard M3 II template spectra andpreferred M2 III. With standard values for the bolometric magnitude of an M2 III a distance of 420 ±
40 pc results, in good agreement with the
Hipparcos distance of 390 ±
130 pc. The connectionof the M giant and the X-ray source was cemented by the Masetti et al. (2006) measurement of aChandra position for the X-ray source with an uncertainty of ± . ′′
6, in excellent agreement with theoptical
Hipparcos position of the M giant. From time series photometry provided by the
Hipparcos team Kazarovets et al. (1999) assigned HD 154791 the variable star name V934 Her.Masetti et al. (2002) and Galloway et al. (2002) both noted that assuming a typical M2 IIIluminosity of 550 L ⊙ , the M giant is about 200 times more luminous than the X-ray source. Thisexplains the lack of rapid optical variations since the contribution from the X-ray source is negligiblecompared to the M giant optical and UV flux. This also explains why the optical spectrum is notpeculiar. In the case of the SyXB V2116 Oph/GX 1+4, a SyXB with symbiotic emission lines, thestellar luminosity is four times less than the X-ray luminosity.4U 1700+24, the variable X-ray source component of the binary , does not have any periodsdetectable in the 2 to 2700 sec range (Garcia et al. 1983). Galloway et al. (2002) similarly concludedthat 4U 1700+24 is different from other NSs detected in the X-ray region since no coherent orquasi-periodic oscillations could be seen in the X-ray data. Masetti et al. (2002) confirmed that 4U1700+24 has substantial X-ray variability but this lacks periodicity. This paper and Galloway et al.(2002) both concluded that the lack of periodicity results from viewing the NS nearly pole-on withthe magnetic axis aligned to the NS spin axis. In this geometry, hot spots on the NS will becontinuously in view.Masetti et al. (2002) found that the size of the X-ray emitting area to be on the order of tens ofmeters. This suggests that the accretion is funneled by the magnetic field onto the magnetic polarcap. Masetti et al. (2002) noted that the presence of an M giant wind was inferred from both theUV variability and the IRAS 12 and 25 µ m measurements of a mid-IR excess. An accretion rateof ∼ − M ⊙ yr − was shown to be consistent with normal values for both a red giant mass-lossrate, ∼ − M ⊙ yr − , and accretion efficiency onto a NS of ∼ − . In this paper we refer to the SyXB system observed in the optical and infrared as V934 Her and reserve the name4U 1700+24 for the X-ray source. However, as reflected in the title of this paper the optical and X-ray names arefully synonymous through most of the literature. σ period at about 410 days. An elliptical orbit wasthen fit to the data resulting in a 404 ± ± − and an eccentricity 0.26. Given an orbital period of ∼
400 days and typical massesof 1.4 M ⊙ for the NS and 1.3 M ⊙ for the M giant, Masetti et al. (2002) found from Kepler’s thirdlaw a semi-major axis of ∼
300 R ⊙ and an orbital velocity of ∼
30 km s − . An inclination of . ◦ isrequired to match the observed velocity amplitude. The probability that a binary inclination willbe less than or equal to an inclination i is 1 − cos ( i ). An inclination of 5 ◦ or less has a probabilityof less than 0.5%.Tiengo et al. (2005) identified the O VIII Ly- α line red shifted by ∼ − at 19.19 ˚A inthe X-ray spectrum of 4U 1700+24. They found this is in agreement with the emitting gas beingaccreted by the NS at the magnetospheric radius. Nucita et al. (2014) found that this is ∼
3. NEW OBSERVATIONS AND REDUCTIONS
We observed the spectrum of V934 Her at high resolution in the optical and near-infrared on90 occasions using five telescopes at four different observatories and with six different instruments(Table 1). The extensive set of observations was made possible because V934 Her is bright, K ∼ H band spectrum withthe Phoenix cryogenic echelle spectrograph at the f/15 focus of the Kitt Peak National Observatory(KPNO) 2.1 m telescope. The most recent set of velocity observations, which have continued into2017, were acquired with the Fairborn 2 m telescope and fiber fed echelle spectrograph. Thus, ourvelocity data set spans 29 years.The first observation reported here was obtained with the KPNO 4 m telescope and FourierTransform Spectrometer (FTS) on 1988 Jul 3 as part of a program to study abundances. While 6 –FTS observations are a gold standard free from systematics in both frequencies and intensities, thetechnique suffers from multiplex disadvantage and is best applied to bright stars (Ridgway & Hinkle1987). The spectrum covers the K band at an apodized resolution, R = λ/ ∆ λ , of ∼ α Lyr that was observed on the same night. We analyzed this ratioed spectrum as part of ourabundance analysis. The FTS spectrum was also convolved to a resolution of 1.4 cm − (R ∼ H and K band.In 2000 October we observed a section of the H band spectrum using the KPNO 0.9 mcoud´e feed telescope and coud´e spectrograph. The detector was an infrared camera, NICMASS,developed at the University of Massachusetts. The 2-pixel resolving power is 44000 with theobservation centered at 1.623 µ m. V934 Her was also observed with the same detector, ordersorting filter, and support electronics at the Mount Stromlo Observatory (MSO) 1.88 m telescopeand coud´e spectrograph in 2001 and 2002. In the MSO data the 2-pixel resolving power is 24000.The experimental setup that used the NICMASS camera is described in Joyce et al. (1998) andFekel et al. (2000). The Canberra area bush fires of 2003 January destroyed the MSO 1.88 mtelescope, spectrograph, and the NICMASS camera.Following the loss of our equipment in Australia, we continued observations at KPNO usingthe 0.9 m coud´e feed telescope, coud´e spectrograph, and a CCD designated LB1A. The 1980 × µ m thick. Ourspectrograms, centered near 1.005 µ m, have a wavelength range of 420 ˚A and a resolving power of ∼ × µ m pixels (Fekel et al. 2013). Forty eight echelle orders are covered ranging in wavelength from3800–8260 ˚A. The observations were made with a fiber that produces a resolving power of ∼ δ Oph, an M giant IAU velocity standard, for which we adopted a radial velocity of − − from the work of Scarfe et al. (1990).Fekel et al. (2009) provide a general explanation of the velocity measurement of AST spectra.In the particular case of V934 Her we selected a subset of 40 lines from our solar-type star line listthat are relatively unblended in M giant spectra and range in wavelength from 5000 to 6800 ˚A.Our unpublished velocities of several IAU radial velocity standards from spectra obtained withthe 2 m AST have an average velocity difference of − − when compared to the results ofScarfe et al. (1990). Thus, we have added 0.6 km s − to each of our AST velocities.Figure 1 plots all our velocities as well as those from the Center for Astrophysics (CfA) thatwere provided by D. Galloway (private communication 2017) and are discussed in Section 4.On 2018 Apr 22 we obtained a spectrum of the H and K region of V934 Her at R=45000 usingIGRINS (Park et al. 2014) on Gemini South. The integration time was a few seconds, so the spec-trum does not contain OH night sky lines for velocity calibration. While the wavelength/velocitycalibration could be done using telluric absorption lines, for the current paper we opted to use thisspectrum only for abundance analysis. Since the spectrum has larger wavelength coverage thaneven the archival FTS spectrum, it became a key element in the abundance analysis. We used thepipeline reduced IGRINS spectrum, and to fit the continuum, we used the IRAF continuum routine splot ′ t ′ at low order. For our analysis it was necessary to join the echelle orders to produce a K band and an H band spectrum. We did this by comparing the overlap regions between the orders.Our H band analysis of this spectrum is based on the 1.5–1.7 µ m region that is utilized by theAPOGEE project (Majewski et al. 2016). Use of this region was facilitated by the comprehensiveline list developed by APOGEE (Shetrone et al. 2015).In addition to the IGRINS spectrum we selected seven other spectra for use in our chemicalabundance analysis of V934 Her. In Table 2 the observational details of the abundance analysisspectra are provided. An identifier (column 1) is given, which will be used later when it is necessaryto specify individual spectra. We analyzed the FTS spectrum since it covers the entire K bandroughly 20 years prior to the IGRINS observation. However, both the S/N and resolution areinferior to the IGRINS spectrum. To supplement these data we also included two K band Phoenixspectra that cover narrower ( ∼
100 ˚A) regions, one at 2.31 µ m and a second at 2.22 µ m, and three H band Phoenix spectra that cover a narrow region ( ∼
65 ˚A) at ∼ . µ m. For all the abundancedata a telluric reference spectrum of a hot star was observed at approximately the same time. With 8 –this reference spectrum the telluric lines have been ratioed from the V934 Her spectra.
4. ORBITAL ELEMENTS
The observed velocities (Fig. 1) suggest a long period orbit. We searched for an orbital periodin our radial velocity data using the least string method as implemented by T. Deeming (PDFND,Bopp et al. 1970). Given the small amplitude of any orbital velocity variation plus the uncertaintiesof the velocities the possible periods cover a broad range from about 4200 to 4950 days with a bestperiod at 4425 days. This means that our extensive velocity time series (Fig. 1), aside from ourinitial FTS spectrum, covers just 1.4 orbital cycles. With all our velocities given unit weight weobtained an orbital solution with the SB1 orbit program (Barker et al. 1967). Because of the broadrange of possible periods noted above, we tried starting values of the orbital period from both thelow end and the high end of the 4200 to 4950 day range. In each case, the orbit program convergedto the same set of orbital elements resulting in a period of 4479 days.While Galloway et al. (2002) discussed the Center for Astrophysics spectra and velocities forV934 Her, individual velocities were not published. Fortunately, D. Galloway (private communi-cation 2017) provided them to us. To check the compatibility of the zero-points for our velocitiesand those from CfA, we compared the orbital solution determined from our elements with the CfAvelocities. There was good agreement with the CfA velocities primarily being distributed in theorbit at phases where there was little orbital velocity variation. After comparing the variancesof the velocities in the two orbital solutions we combined the two data sets, assigning weights of0.6 to the CfA velocities, and obtained a combined-data solution for the orbital elements. In thecombined velocity solution the orbital period decreased to 4394 days, about a 2 σ change. Theeccentricity was likewise reduced by about 2 σ with the semi-amplitude increased by less than 1 σ .We next looked at the velocity residuals from the combined data orbital fit. A period searchfrom 100–600 days with the program PDFND was carried out on the CfA velocity residuals andresulted in a best period of 406 days, similar to the value found by Galloway et al. (2002). We thenmade a separate period search of the velocity residuals for our data. A period is clearly present inthe data at greater than 10 σ in the range 412 ±
10 days. Since both sets of velocities appear tohave a second periodicity of about 410 days, our last step was to analyze the two sets of velocitieswith the general least squares (GLS) program of Daniels (1966) to obtain a simultaneous solutionfor the short- and long-period velocity variations. This final solution resulted in periods of 420.2 ± ±
33 days, respectively. The uncertainties are 1 σ .Table 1 provides the individual radial velocities for both the CfA and our data. That tablelists for each observation the heliocentric Julian date, the observed total velocity, and the observedminus calculated velocity residual ( O − C ) to the combined orbit. Also computed and listed inthe table are the long period orbital phase, the long period velocity, which is equal to the totalvelocity minus the computed short period velocity, the short period orbital phase, and the short 9 –period velocity, which is equal to the total velocity minus the computed long period velocity. Thelast column gives the source of the observation. Table 3 provides the orbital elements for both theshort- and long-period variations. Although characterized by orbital parameters, the short-periodvariations, as will be discussed later, result from long secondary period (LSP) velocity changesrather than a third component of the system. The very small value of the long-period orbit massfunction, 0.0022 ± M ⊙ , suggests that our 4391 day orbit is seen nearly pole on. We willreturn to this point when defining the stellar parameters.Figure 2 presents the computed velocity curve of the long-period orbit compared with theradial velocities, where zero phase is a time of periastron. Each plotted velocity consists of thetotal observed velocity minus its calculated short-period velocity. Figure 3 shows the computedvelocity curve of the short-period “orbit” compared with the KPNO radial velocities, where zerophase is a time of periastron. Each plotted velocity consists of the total observed velocity minusits calculated long-period velocity.
5. STELLAR PARAMETERS5.1. Photometric Periods
Tomasella et al. (1997) acquired
U BV RI photometry on six nights over a two month periodand found no variability at V and B , although the values were a few 0.1 mag different from thosepreviously reported by Garcia et al. (1983). Hipparcos found that V934 Her varied by 0.16 magwith a possible period of 31 days. This forms the basis of the General Catalogue of Variable StarsSRb designation (Kazarovets et al. 1999). Goranskij et al. (2012), using precision photometry,found periods of 28, 31, and 44 days in V , 29, 44 and 405 days in B , and 44 and 415 days in U .Semi-regular variables characteristically have simultaneously excited closely separated periods fromthe same overtone (Hartig et al. 2014). The amplitudes in B and V are ∼ A common characteristic of SR variables is a long secondary period (LSP) to the dominantpulsation period. The LSP is typically 8–10 times longer than the dominant period (Nicholls et al.2009; Hartig et al. 2014). Taking the V934 Her photometric period to be 28–44 days (Goranskij et al.2012; Gromadzki et al. 2013), then the LSP is the ∼
400 day period.In M giants LSPs can be detected in both luminosity and velocity variations. As noted above,the first orbit for V934 Her was based on the Galloway et al. (2002) radial velocity period of 404 ± ω ∼ ◦ and e ∼ ω = 237 ◦ and e = 0.33. We also note the similarity ofthese numbers to the LSP “orbit”, ω = 229.5 ◦ e = 0.33, of the very well studied SySt CH Cyg(Hinkle et al. 2009).V934 Her presents an interesting case of LSP because the orientation of the star is known.Assuming that the rotation axis of the M giant is parallel to that of the orbit, the star is seen nearlypole on. In this case models for the LSP that require semidetached binaries (Wood et al. 1999;Soszy´nski 2007) and rotating spots with dust formation (Takayama et al. 2015) can be excluded.As discussed by Stothers (2010) and Saio et al. (2015), this narrows the explanations to pulsationmechanisms involving convection. A global pulsation mechanism for LSP now appears to be widelyaccepted if not fully understood (Trabucchi et al. 2017).LSPs are associated with increased mid-IR excess (Wood & Nicholls 2009). In the case ofV934 Her this is in agreement with the results of Masetti et al. (2002) who found a larger thanexpected IR excess. Masetti et al. (2002) reported a tentative period of ∼
400 days from RXTE ASMobservations. Galloway et al. (2002) analyzed the same data extended by an additional year andrefined this as a period of 404 ±
20 days. The existence of the LSP in the X-ray data would link theLSP to cyclic enhancements of mass loss from the M III. Corbet et al. (2008) analyzed Swift BATobservations and RXTE ASM observations including data previously analyzed by Masetti et al.(2002) and Galloway et al. (2002) but was not able to find the ∼
400 day period.
Garcia et al. (1983) found that V934 Her had an optical spectral type of M3 II while Masetti et al.(2002) determined an optical spectral type of M2 III, which was confirmed by Goranskij et al.(2012). Their photometry of V934 Her does not show any measurable reddening. While Gaudenzi & Polcaro(1999) claimed the spectrum is abnormal, this has been refuted (see for instance Masetti et al. 2002).Other than the claim of Gaudenzi & Polcaro (1999), there is no evidence for spectral variability.Tomasella et al. (1997) were not able to detect changes in the optical spectrum of V934 Her duringa strong X-ray outburst.The FTS spectrum of V934 Her discussed earlier covers the 2.0–2.5 µ m near-IR K band.After apodizing to R ∼ − line. In V934 Herthis line is approximately intermediate in strength between the M2 III and M4 III spectra. Otheratomic features are also stronger than in the M2 spectrum. We assign a temperature classificationof M3. Importantly, the infrared spectrum of V934 Her looks like a normal star with no emissionfeatures in its K band spectrum.The distance to V934 Her has been discussed by both Garcia et al. (1983) and Masetti et al. 11 –(2002) with their results differing by a factor of two. This discrepancy has been resolved by the Gaia parallax of 1.837 ± +10 − pc (Gaia Collaboration 2018).Combining the distance with the galactic coordinates, V934 Her is 296 pc above the galactic plane.Goranskij et al. (2012) suggested that V934 Her is unreddened. Confirmation is provided by theimages of Schlafly & Finkbeiner (2011) who find E(B-V) is at most 0.038. Ignoring reddening, the2MASS (Cutri et al. 2003) m K = 2.988 mag results in an absolute K magnitude M K = − .
690 mag.Taking J − K = 1.181 mag, the 2MASS color of V934 Her, the K band bolometric correction fromBessell & Wood (1984) is 2.92 mag. The resulting bolometric magnitude for V934 Her is − . ± L ⊙ where the formal uncertainty is from the distance. Theuncertainties associated with the infrared photometry and bolometric correction are not available.van Belle et al. (1999) gives an effective temperature for an M3 III of 3573 ±
22 K. Alternately,using the V − K color of V934 Her, the V − K color– T eff relation of van Belle et al. (1999) yields3677 K. Dyck et al. (1996) suggests an effective temperature for an M3 III of 3650 K. Adopting a3650 K effective temperature as a mean value, the literature photometry for V934 Her/4U 1700+24is shown in Figure 5, fit with a 3650 K blackbody. The blackbody integrated flux is 1.4 ± × − W m − . Correcting for the Gaia distance of 544 pc the bolometric magnitude is − . ± L = 1367 ± L ⊙ .We adopt mean values for the temperature and luminosity with uncertainties embracing therange of values, L = 1200 ± L ⊙ and T eff = 3650 ±
100 K. The values for the temperature andluminosity are in good agreement with both the observational HRD and the evolutionary tracksfor an M3 III resulting from a low mass progenitor (Escorza et al. 2017). Similarly, using the
Gaia distance, K S , and J − K colors the relations of Lebzelter et al. (2018) confirm that V934 Her is oneither the RGB or faint AGB.We have argued that the ∼
410 day period of V934 Her is not an orbital period but is apulsational LSP. The Period-Luminosity relation of Wood (2000) can be applied to the photometricperiods. Goranskij et al. (2012) and Gromadzki et al. (2013) found periods of 28 and 44 days withan LSP of 410 days. The LSP is associated with a primary period on the first overtone B sequence(Wood et al. 1999; Trabucchi et al. 2017). We assume that the 44 day period is the first overtone,B sequence period and the 28 day period is the second overtone, A sequence period. From themid-line of the relations for 28 day, 44 day, and 410 day periods the corresponding LMC W JK from Figure 1 of Trabucchi et al. (2017) or Figure 2 of Soszy´nski et al. (2007) is 11.37. Assuminga distance modulus of m − M = 18.5 mag for the LMC, this corresponds to an M K = − .
3, 0.6mag brighter than measured. However, the P − L relations have a width > JK so the P − L bolometric magnitude is in agreement with the absolute K mag determined from the Gaia distance.The blackbody fit to the photometry yields the stellar radius as well as the flux. The uniformlyilluminated radius required for the blackbody is 91 +14 − R ⊙ . The Bourg´es et al. (2014) data basegives a limb-darkened angular diameter computed from the colors of V934 Her of 2 R = 1 . ±
12 –0.121 mas. Using the
Gaia distance the red giant radius is 90 R ⊙ . van Belle et al. (1999) give asmaller radius of 71 R ⊙ but the relationship has considerable width. From the models of Charbonnel et al. (1996) the luminosity of 1200 L ⊙ and T eff of 3650K place V934 Her on the early AGB of a solar metallicity 1.7 M ⊙ star. STAREVOL tracks byEscorza et al. (2017) suggest a mass a few 0.1 M ⊙ smaller. The NS companion in the V934 Hersystem has a limited range of mass. The upper limit to the mass of a NS occurs at ∼ M ⊙ when theinternal sound speed reaches the speed of light. Such a large mass for the NS seems unlikely. Massesof NSs in binary radio-pulsar systems are all very close to 1.35 M ⊙ (Thorsett & Chakrabarty 1999).Masses larger than 1.35 M ⊙ might occur (Lorimer & McLaughlin 2006) but masses measured forLMXB NSs, which can be uncertain, seldom exceed 1.5 M ⊙ (Casares et al. 2017).The mass function from the orbit of the M giant is f ( m ) = M NS sin ( i ) / ( M RG + M NS ) = 0 . M NS =1.35 M ⊙ and M RG =1.7 M ⊙ the orbital inclination is 11 . ◦
7. Lower massesfor the red giant from different evolution models or mass loss drive the inclination smaller. If,as suggested by L¨u et al. (2012), the NS has accreted mass from the giant, the inclination is alsosmaller. For example, an M giant mass of 1.4 M ⊙ reduces the inclination to 10 . ◦
9. We concludethat an orbital inclination in the range of 11 . ◦ ± . ◦ . ◦ M ⊙ , averaged between the evolutionary models,and a radius of 90 R ⊙ than the surface gravity is 5.4 cm s − , log g = 0.7, with the uncertainty inthe mass and radius resulting in a uncertainly in log g of ∼ T eff = 3650 K and log g = 0 .
6. ABUNDANCES6.1. Methods
Abundances were measured with the spectral synthesis technique in the classical way, i.e.,employing local thermodynamic equilibrium (LTE) analysis based on a 1D, hydrostatic model at-mospheres (MARCS, Gustafsson et al. 2008). Synthetic spectra were calculated with the code de-veloped by M. Schmidt (WIDMO, Schmidt et al. 2006). The general characteristics of the adoptedmethod together with its justification is discussed in a series of papers on chemical compositionanalysis in SySt giants (Ga lan et al. 2016, and references therein). In summary the abundance 13 –calculations for given model atmospheres were performed as follows. The initial–starting valuesfor the free parameters were obtained by adjusting roughly by eye the synthetic to the observedspectrum through several iterations. Next, the simplex algorithm (Brandt 1998) was used for χ minimization in the parameter space. Besides the relevant abundances and isotopic ratios, addi-tional free parameters were the line broadening for each spectrum expressed as a macroturbulentvelocity, ζ t , and a microturbulent velocity, ξ t . For the V934 Her analysis ξ t was found by examiningthe large range of excitation potentials and line strengths, especially from C O lines over thebroad wavelength range of the IGRINS spectrum.The excitation potentials and gf-values for transitions in the case of atomic lines in the narrow H -band region of the Phoenix spectra were taken from the list by M´elendez & Barbuy (1999) andfor the K -band region from the Vienna Atomic Line Database (VALD, Kupka et al. 1999). Forthe molecular data in the K -band region we used line lists by Goorvitch (1994) for CO, Kurucz(1999) for OH, and Sneden et al. (2014) for CN. For the H -band IGRINS spectrum we used theDR12 release of the APOGEE line lists (Shetrone et al. 2015).The spectrum synthesis was run with model stellar atmospheres covering a broad range ofeffective temperature from 2900 to 4250 K, surface gravity from 0 . .
0, and metallicity from − . .
0. The data sets were fit separately since the data covered a range of resolution andsignal-to-noise ratio. The regions of the spectra contaminated with artifacts or with insufficientlywell-reduced telluric absorption features were excluded from the analysis.
The parameters derived above for V934 Her, T eff =3650 K, log g = +0.5, and approximatesolar metallicity, resulted in synthetic spectra that were excellent fits to the H band spectra (Fig. 6).However, to our surprise, the strong lines in the K -band region were best fit with a significantlylower effective temperature, T eff = 3100 K (FTS spectrum) and T eff = 3000 K (IGRINS spectrum).The surface gravity remained log g = 0 . H -band second overtone CO linesare fit by T eff =3650 K while the first overtone CO lines in K -band region appear to require a ∼ K and H spectra were taken simultaneously, hence, explanations for thelower excitation temperature that invoke time variability can be ruled out. Since weak lines arefit by a 3650 K effective temperature while strong lines are not, the outer layers of the modelatmosphere must be too hot. To further investigate this problem we did a curve-of-growth analysisof the CO lines. This technique, discussed by Hinkle et al. (2016), requires large spectral coverage,which was made possible by our IGRINS observation. Using the CO second overtone lines, we 14 –found a CO excitation temperature of 3375 K. The CO second overtone lines are generally weak,at most ∼
30% deep. Comparison to a similar analysis of spectral standard M giants shows that a3375 K excitation temperature corresponds to an effective temperature of ∼ K band region of the V934 Her spectrum contains measurable lines from the CO isotopo-logues C O and C O. These lines are not nearly as strong as the C O 2-0 lines. There arealso clear upper limits for 2-0 C O lines. With T exc =3375 K curves-of-growth were computedfor the isotopologues. Shifts between these curves-of-growth give the isotopic abundances (Fig. 8).We find C/ C = 10 ± O/ O = 2500 +1500 − , and O/ O = 262 ± H -band C O with similar strength isotopic lines in the K -band. Spectrum synthesisuses a model atmosphere to fit a spectral interval. The failure of the synthetic spectrum to fit thestrong lines must not be a problem related to wavelength since the model works for both H and Kweak lines. We also measured the CO lines in the K band FTS spectrum. The equivalent widthsfrom the FTS and IGRINS spectra are in reasonable agreement, again demonstrating that there isnot a time dependent problem.Tsuji (1988) reports similar difficulties in fitting the CO first overtone lines. Tsuji found thatextra absorption in low excitation first overtone CO lines is a common property of late-type spectra.He attributed the low temperature absorption to a quasi-static, turbulent, 1000–2000 K extendedregion in the outer atmospheres of these stars.Chakrabarty & Roche (1997) suggested that the NS in the SyXB V2116 Oph system heats thered giant, altering the TiO band strengths and impacting estimates of the spectral class based onthis molecule. The orbit of V2116 Oph is close to edge on. Chakrabarty & Roche (1997) deriveda mean spectral class of M5. In our analysis of V2116 Oph (Hinkle et al. 2006) we found that theM5 III effective temperature, T eff = 3400 K, agreed with the effective temperature determined fromspectral synthesis of the infrared spectrum. This analysis was based on Phoenix spectra coveringsmall regions of the spectrum. In 2018 April we observed V2116 Oph with IGRINS. Using thisobservation, we obtained T exc = 3200 K for the CO second overtone. This corresponds to T eff =3370 K, so it is in good agreement the Chakrabarty & Roche (1997) spectral type. The separationof the NS and M giant in V934 Her is about two times larger than it is in V2116 Oph, so NS heatingshould be even less in V934 Her. Table 5 lists final values of abundances obtained from the spectra for T eff = 3650 K and log g = 0.5. Resulting values for the broadening parameters are presented in Table 6. The contributions 15 –to the uncertainties in the abundances are given in Table 7. Uncertainties in the abundances comemainly from uncertainties in stellar parameters. The final uncertainty in Table 7 is the quadraturesum of uncertainties of each model parameter. IGRINS results derived entirely from the H -bandare similar to FTS and Phoenix results from the K -band. In spite of the difficulties in fitting thespectra with a consistent model atmosphere, the K - and H -band results (Table 5) are similar withthe exception of the N abundance derived from the FTS spectrum. We attribute this to the lowerquality of that spectrum. However, to err on the side of caution, in the subsequent discussion weuse only the H -band results with the exception of the C and O isotopes.
7. DISCUSSION7.1. Stellar Evolution
The probability of forming a binary system outside of a globular cluster by gravitational captureis nearly zero. Stellar evolutionary tracks show that the main sequence mass of the V934 Her giantwas in the range ∼ M ⊙ , so the unevolved system was a binary consisting of the massiveprogenitor of the NS and a ∼ M ⊙ companion. The O/ O oxygen isotope ratio is very large, ≥ . ⊙ (Smith 1990; Hinkle et al. 2016). The agreement of masses from the evolutionary tracks andabundances requires that mass transfer from the proto-SN supergiant to the current M giant, ifany, was no more than a few 0.1 M ⊙ . The main sequence lifetime for a 1.6 M ⊙ star is ∼ > ⊙ star is .
100 Myrs (Vassiliadis & Wood1993; Tauris & van den Heuvel 2006). Thus the age of the NS is ∼ C and nitrogen N abundances of the M III (Table 5) reflect mixing duringthe first dredge-up. This is confirmed by the low carbon isotope ratio, C/ C ∼ α /Fe] = +0.27 fromthe average of the Mg, Si, and Ca abundances. The [ α /Fe] versus [Fe/H] is close to the meanrelation (Lambert 1987) and shows no notable peculiarity for this star. The α element and Feabundances are similar to the abundances of many other SySt giants (Ga lan et al. 2016, 2017).Casares et al. (2017) report that in LMXB many of the low-mass stars show enhancements of Feand α elements. Modeling suggests that this results from the capture of SN ejecta by the dwarfcompanion. We conclude that in the SyXB giants any SN ejecta on the surface has been mixedinto the interior as the star evolved up the giant branch.L¨u et al. (2012) discussed Monte Carlo simulations of the SyXB population including CCS,electron-capture SN (ECS), and accretion-induced collapses (AIC). Their study concludes thatbetween 70% and 98% of SyXB NSs are formed via core collapse with the remainder formed viaECS. The simulation finds that systems forming via ECS have short initial periods and have passedthrough a common envelope phase. Similar scenarios are discussed by Willems & Kolb (2002). 16 –The simulated SyXB population of L¨u et al. (2012) has typical parameters similar to V934 Her.Perhaps the existence of binary systems that survived a CCS should not be surprising since allmassive stars have at least one companion (Duchˆene & Kraus 2013) and the number of binarysurvivors of a SN is very small. In the case of V934 Her the Gaia proper motions of − ± − in right ascension and − ± − in declination correspond to velocities of − − − at the Gaia distance of 544 pc. The γ velocity for the binary is − ± − so the space velocity of this star is not unusually large.Assuming a NS mass of 1.35 M ⊙ , a mass of 1.6 M ⊙ for the M giant, and an orbital period of12.0 years, Kepler’s third law gives a semimajor axis a of 7.52 AU for V934 Her. At periastron theseparation is a (1 − e ) = 4.86 AU. From the formula of Eggleton (1983) the M giant Roche lobeat periastron is 1.93 AU or 415 R ⊙ , which is much larger than the current stellar radius of ∼ R ⊙ . As a tip AGB star the stellar radius will increase to ∼ R ⊙ (Ohnaka et al. 2006). At thesame time the mass-loss rate will increase from the current ∼ − M ⊙ yr − to ∼ − M ⊙ yr − .Over the 10 yr TP AGB lifetime (Vassiliadis & Wood 1993) the current 1.6 M ⊙ M III will lose ∼ ⊙ to become a 0.6 M ⊙ white dwarf (Si et al. 2018). As the mass loss increases, mass transferto the NS will decrease the orbital separation. Simulations by Wiktorowicz et al. (2017) predictthe evolution of ultra-luminous X-ray (ULX) sources from NS–low mass star binaries with massesnearly identical to those in the V934 Her system. A complicating factor is the increased absorptionof the X-ray flux due to the 10 increase in mass loss . From radial velocity observations Famaey et al. (2009) obtained orbits for non-symbiotic Mgiant stars in the
Hipparcos survey and combined the results with M giant orbits from the literatureto produce a sample of 29 systems. In a follow-up paper Jorissen et al. (2009) examined the ( e –log P ) diagram of those 29 M giant binaries from Famaey et al. (2009). Although V934 Her has adegenerate companion it has an unremarkable optical spectrum. Thus, we compare V934 Her withthe M giant sample of Famaey et al. (2009).Figure 1 of Jorissen et al. (2009) shows that M giants with periods up to about 1500 days allhave eccentricities below 0.25. For M giants with longer period orbits, except for one nearly circularorbit system, the eccentricities range from about 0.3 to 0.75. V934 Her with its period of 4391days and eccentricity of 0.35 clearly has a very non-circular orbit but is situated near the lower endof the eccentricity distribution. The kick velocity resulting from asymmetry during a CCS can besubstantial to the point of disrupting the binary (Lyne & Lorimer 1994). Given the large, 4.8 AU,periastron separation for V934 Her, tidal forces have not substantially acted to circularize the orbit.The eccentricity near the lower bound of M giants may well reflect the primordial eccentricity of Noted by the anonymous referee
17 –the system and apparently was not significantly increased as a result of the SN event. This suggeststhat the NS resulted from an ECS that has low kick velocity (L¨u et al. 2012).
The presence of a LSP pulsation of the M giant is supported by both spectroscopy and photom-etry. The 420 day spectroscopic “orbit” is a close match to the velocity variations observed in otherLSP variables (Hinkle et al. 2002). The luminosity derived from
Gaia places the 44 day photometricperiod of V934 Her on the AGB pulsation first overtone, the 28 day period on the second overtone,and the 404 day photometric period on the LSP sequence (Trabucchi et al. 2017). Assuming thestellar equator is aligned with the plane of the orbit, the M giant is seen nearly pole on. Thisnarrows the list of possible LSP mechanisms to those favoring convection (Trabucchi et al. 2017).Strong absorption lines in the M giant spectrum are not well fit by a standard model atmosphere.A connection between the atmospheric structure and LSP is an area for future investigation.Published observations show a tentative connection between the LSP and X-ray activity, pre-sumably driven by changes in the mass loss. In the SyXB/StSt system V2116 Oph/GX 1+4 activityis enhanced near periastron passage (I lkiewicz et al. 2017). Although the V934 Her orbit is signif-icantly more eccentric than that of V2116 Oph, the periastron separation, 2.28 AU, is still abouttwice that of V2116 Oph/GX 1+4. It would be interesting to confirm the connection between LSPand X-ray activity and to see if the activity of V934 Her also increases near periastron.
8. CONCLUSIONS
The NS–M giant symbiotic binary V934 Her is shown to have a 12 year orbit with an eccentricityof 0.35. The period previously found in the velocity data, 404 days and revised here to 420 days,is not the binary orbit but the LSP pulsation of the M giant. We find the M giant to have aspectral type of M3 III and to have slightly subsolar abundances. The O/ O is consistent with aprogenitor main sequence star having a mass similar to that determined from the observed stellarparameters and evolutionary tracks. As is the case for the SyXB star V2116 Oph, the elementalabundances do not show any peculiarities that would suggest either a previous common envelopestage with the proto-NS massive star or that mass was transferred during the SN event. Thevelocity and orbit of V934 Her also appear to be little affected by the SN suggesting it was an ECS.The main sequence lifetime of the M giant progenitor was ∼ Gaia ( ), processed bythe Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been pro-vided by national institutions, in particular the institutions participating in the Gaia
MultilateralAgreement.This research was based in part on observations obtained at the Gemini Observatory, whichis operated by the Association of Universities for Research in Astronomy, Inc., under a coopera-tive agreement with the NSF on behalf of the Gemini partnership: the National Science Founda-tion (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio deCiencia, Tecnolog´ıa e Innovaci´on Productiva (Argentina), and Minist´erio da Ciˆencia, Tecnologia eInova¸c˜ao (Brazil). The Phoenix spectrograph was developed by NOAO. IGRINS was developedunder a collaboration between the University of Texas at Austin and the Korea Astronomy andSpace Science Institute (KASI) with the financial support of the US National Science Foundationunder grant AST-1229522, of the University of Texas at Austin, and of the Korean GMT Projectof KASI.The National Optical Astronomy Observatory is operated by the Association of Universitiesfor Research in Astronomy under cooperative agreement with the National Science Foundation.KH and RJ express their thanks to the Office of Science for support of their research. The researchat Tennessee State University was supported in part by the State of Tennessee through its Centersof Excellence program. JM has been financed by Polish National Science Centre (NSC) grants2015/18/A/ST9/00746 and 2017/27/B/ST9/01940 and CG by NSC grant SONATA No. DEC- 19 –2015/19/D/ST9/02974. 20 –
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This preprint was prepared with the AAS L A TEX macros v5.2.
25 –Fig. 1.— Radial velocity data (Table 1) for V934 Her as a function of time. Solid circles = ourvelocities, x = Center of Astrophysics. 26 –Fig. 2.— The computed velocity curve of the 4391 day (12.0 yr) long-period orbit compared withour radial velocities and those from CfA. Star = KPNO FTS, solid circle = KPNO coud´e, opencircle = Fairborn Observatory, solid triangle = Mount Stromlo Observatory and KPNO NICMASS,open triangle = KPNO and Gemini South Phoenix, x = Center for Astrophysics. Each plottedvelocity consists of the total observed velocity minus its calculated short-period velocity. Zero phaseis a time of periastron. 27 –Fig. 3.— The computed velocity curve of the 420.2 day velocity variation interpreted as anorbit and compared with the velocity residuals. CfA velocities = open circles, our velocities = solidcircles. Each plotted velocity consists of the total observed velocity minus its calculated long-periodvelocity. Zero phase is a time of periastron. 28 –
Fig. 4.— K -band FTS spectra at R ∼ (cid:2)(cid:3)(cid:4)(cid:5)(cid:1)(cid:6)(cid:7)(cid:8) (cid:9)(cid:10)(cid:11)(cid:7)(cid:12)(cid:7)(cid:13)(cid:14)(cid:15)(cid:16)(cid:1)(cid:17)(cid:18)(cid:19)(cid:20)(cid:8)(cid:21)(cid:13)(cid:22)(cid:23) (cid:24)(cid:25)(cid:26) (cid:26) (cid:26)(cid:24) (cid:26)(cid:24)(cid:24) (cid:27) (cid:12) (cid:28) (cid:29) (cid:1) (cid:17) (cid:30)(cid:31) (cid:23) (cid:24)(cid:25)(cid:24)(cid:24)(cid:24)(cid:26)(cid:24)(cid:25)(cid:24)(cid:24)(cid:26)(cid:24)(cid:25)(cid:24)(cid:26)(cid:24)(cid:25)(cid:26)(cid:26)(cid:26)(cid:24)(cid:26)(cid:24)(cid:24) Fig. 5.— Photometry of V934 Her/4U 1700+24 from the literature compared to a 3650 K black-body. The dashed line is a best fit while the two solid lines correspond to high and low envelopes.The blackbody integrated flux is 1.4 × − W m − . Assuming the Gaia distance of 544 pc thebolometric magnitude is − R ⊙ . The blackbody fit shows IR excess suggesting a modest mass loss rate and UVexcess due to the NS. 30 – Ca ITi I V IFe I Ni I12CO 13COOH CN N o r m a li ze d F l u x [ F l / F c o n t ] Heliocentric wavelengths l [ Å ]−0.1 0 0.1 16100 16120 16140 16160 16180 16200 16220 16240 16260 O − C Na I Ca ITi I V IFe I Ni I12CO 13COOH CN N o r m a li ze d F l u x [ F l / F c o n t ] Heliocentric wavelengths l [ Å ]−0.1 0 0.1 16260 16280 16300 16320 16340 16360 16380 16400 16420 16440 O − C Fig. 6.— IGRINS H -band spectrum (blue line) shown as normalized flux as a function of wave-length in ˚angstr¨oms in the region 16100–16440 ˚A compared to the synthetic spectrum (red line)calculated with the final abundances (Table 5). Individual lines are identified with dashes belowthe spectrum. The C O 6-3 head is at 16190 ˚A and the C O 7-4 band head is at 16400 ˚A.Residuals (O-C) to the fit are shown in the box above the spectrum. 31 –
COCN N o r m a li ze d F l u x [ F l / F c o n t ] Heliocentric wavelengths l [ Å ] FeI TiI ScI SiIFeI FeIFeI −0.1 0 0.1 23060 23080 23100 23120 23140 23160 O − C Fig. 7.— Lower box. Phoenix spectrum of V934 Her observed 2012 June 8 (blue line) comparedto synthetic spectra obtained with two different adopted effective temperatures T eff = 3100 K (redline) and 3600 K (green line). The spectrum is dominated by strong CO bands superimposed on abackground of weak CN and atomic lines. The hotter atmosphere does not give a good fit to thealternating high and low excitation 2-0 C O lines. Dashes below spectrum and upper box as inFigure 5. 32 –Fig. 8.— Curves-of-growth for the weak CO isotopologue lines in V934 Her. Measurements fromthe IGRINS and FTS spectra are shown separately. The IGRINS spectrum has a much higherS/N. The IGRINS spectrum covers the CO ∆v=3 and ∆v=2 regions while the FTS spectrum onlycovers the CO ∆v=2 region. ∆v=3 lines from the rare isotopologues were not detected. The shiftsbetween the curves-of-growth give the isotopic ratios (labelled). 33 –Table 1. Radial Velocities of V934 HerHelio. JD RV O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a b O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a c d O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a e f g
37 –Table 1—ContinuedHelio. JD RV O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a O − C RV L RV S − − (km s − ) φ L (km s − ) φ S (km s − ) Source a a CfA = Center for Astrophysics, KPNO1 = KPNO 4m + FTS, KPNO2 = KPNO2.1m + Phoenix, KPNO3 = KPNO coud´e feed + NICMASS, MSO = Mount StromloObservatory 1.88m + NICMASS, GemS = Gemini South 8m + Phoenix, KPNO4= KPNO coud´e feed + LB1A, KPNO5 = KPNO 4m + Phoenix, Fair = FairbornObservatory b µ m c µ m d µ m, R = 70000 e µ m f µ m g µ m 39 –Table 2. Spectra used for abundance analysisID Date Helio. JD Spec. Region Instrument Res. S/N(UT) (˚A) ( λ/ ∆ λ )Ph1 2000 Jul 13 2451738.77 15590 – 15662 Phx/KPNO 2.1 50000 ∼ ∼ ∼ ∼ ∼ > > P (days) 420.17 ± ± P (yr) 1.150 ± ± T (HJD) 2457894 ±
22 2457118 ± γ (km s − ) ... − ± K (km s − ) 0.634 ± ± e ± ± ω (deg) 237 ±
23 50.7 ± a sin i (10 km) 3.45 ± ± f ( m ) ( M ⊙ ) 0.0000093 ± ± − ) 0.6 0.6 40 –Table 4. Parameters of the V934 Her M IIIParameter Value SourceDistance 544 ±
10 pc
Gaia
Spec Type M3 III Fig. 3; T eff & luminosity T eff ±
100 K Sp.Ty.; V-K; CO T exc
Luminosity 1200 ±
200 L ⊙ See text; Fig. 4Radius 90 ±
20 R ⊙ Fig. 4; van Belle et al. (1999)Mass 1.6 +0 . − . M ⊙ Evol. tracks & mass lossSurface gravity (log g) 0.7 ± − ) Mass and radiusInclination a . ◦ ± . ◦ F e/H ] -0.60 ± α/H ] -0.33 ± ∼ a Equator to plane of sky 41 –Table 5. Abundance SummaryElement FTS Phoenix IGRINS a log ǫ ( X ) b [ X ] c log ǫ ( X ) b [ X ] c log ǫ ( X ) b [ X ] c C 7 . ± . − . ± .
10 7 . ± . − . ± .
08 7 . ± . − . ± .
06N 8 . ± .
11 +0 . ± .
16 7 . ± . − . ± .
11 7 . ± . − . ± .
08O 8 . ± . − . ± .
12 8 . ± . − . ± .
08 8 . ± . − . ± . . ± . − . ± . · · · · · · . ± . − . ± . · · · · · · · · · · · · . ± . − . ± . . ± .
18 +0 . ± . · · · · · · . ± . − . ± . . ± .
13 +0 . ± . · · · · · · . ± . − . ± .
08S 7 . ± . − . ± . · · · · · · · · · · · · K · · · · · · · · · · · · . ± . − . ± . . ± . − . ± . · · · · · · . ± . − . ± . . ± .
10 +0 . ± .
14 2 . ± . − . ± . · · · · · · Ti 4 . ± . − . ± .
15 4 . ± . − . ± .
19 4 . ± . − . ± . · · · · · · · · · · · · . ± . − . ± . · · · · · · · · · · · · . ± . − . ± . · · · · · · · · · · · · . ± . − . ± . . ± . − . ± .
12 6 . ± . − . ± .
11 6 . ± . − . ± . · · · · · · · · · · · · . ± . − . ± . . ± .
29 +0 . ± .
33 5 . ± . − . ± .
19 5 . ± . − . ± . C/ C 6 . ± . · · · . ± . O/ O 4500 ± · · · ± d16 O/ O 390 ± · · · ± da From H band spectrum b log ǫ ( X ) = log ( N ( X ) N ( H ) − ) + 12 .
0. Uncertainty is σ from the fit. See Table 7 for the totaluncertainty. Abundances in dex. c Relative to the Sun [ X ] abundances in respect to the solar composition of Asplund et al. (2009),Scott et al. (2015 a) and Scott et al. (2015 b) d From K band spectrum 42 –Table 6. Line Broadening ParametersSpectrum ζ t (km s − ) ξ t (km s − )FTS 5 . ± .
74 2 . ± . . ± .
65 2 . ± . . ± .
59 2 . ± . . ± .
51 2 . ± . . ± .
35 2 . ± . . ± .
52 2 . ± . . ± .
34 2 . ± .
07 43 –Table 7. Abundance Uncertainty Summary a Element ∆ T eff = +100 K ∆ log g = +0 . ξ t = +0 . b C +0 .
04 +0 .
19 0 . ± .
20N +0 . − .
06 +0 . ± .
08O +0 .
12 +0 . − . ± . . − . − . ± . . − .
09 +0 . ± . . − . − . ± . − .
04 +0 .
11 +0 . ± .
12K +0 .
03 +0 . − . ± . .
05 +0 . − . ± . .
07 +0 . − . ± .
12V +0 .
07 +0 . − . ± . .
05 +0 . − . ± . − .
01 +0 .
09 0 . ± . − .
02 +0 . − . ± . .
01 +0 .
12 +0 . ± . − .
02 +0 .
11 0 . ± . a H -band IGRINS data and model atmospheres with parameters T eff =3600 K, log g = 0 .
5, and ξ t = +2 . b [(∆ T eff ) + (∆ log g ) + (∆ ξ t ) ] ..