On the mass of the neutron star in Cyg X-2
J. Casares, J.I. Gonzalez Hernandez, G. Israelian, R. Rebolo
aa r X i v : . [ a s t r o - ph . GA ] O c t Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 24 September 2018 (MN L A TEX style file v2.2)
On the Mass of the neutron star in Cyg X-2
J. Casares , J.I. Gonz´alez Hern´andez , , G. Israelian , R. Rebolo , Instituto de Astrof´ısica de Canarias, E-38200 La Laguna, Tenerife, Spain Cosmological Impact of the First STars (CIFIST) Marie Curie Excellence Team GEPI, Observatoire de Paris, CNRS, Universit´e Paris Diderot; Place Jules Janssen 92190, France Consejo Superior de Investigaciones Cient´ıficas, Spain
24 September 2018
ABSTRACT
We present new high resolution spectroscopy of the low mass X-ray binary Cyg X-2 which enables us to refine the orbital solution and rotational broadening of thedonor star. In contrast with Elebert et al (2009) we find a good agreement withresults reported in Casares et al. (1998). We measure P = 9 . ± . K = 86 . ± . − and V sin i = 33 . ± . − . These values imply q = M /M = 0 . ± .
02 and M = 1 . ± .
21 M ⊙ (for i = 62 . ± ◦ ). Therefore, theneutron star in Cyg X-2 can be more massive than canonical. We also find no evidencefor irradiation effects in our radial velocity curve which could explain the discrepancybetween Elebert et al’s and our K values. Key words: stars: accretion, accretion discs – binaries:close – stars: individual(Cygnus X-2) – X-rays:binaries
Dynamical studies in low mass X-ray binaries (LMXBs here-after) offer a promissing route to test the equation of state ofnuclear matter. Soft equations of state are not stable above1.6 M ⊙ (e.g. Brown & Bethe 1994) and hence finding a neu-tron star more massive than this limit would be a major ad-vance in our knowledge of nuclear matter physics. LMXBsand, in particular, accreting millisecond pulsars (AMPs) areexpected to harbour the most massive neutron stars becauseof the sustained accretion of matter during their long lifes(van den Heuvel & Bitzaraki 1995). Unfortunately, dynam-ical studies are hampered by (1) the overwhelming accre-tion luminosity in persistent LMXBs (which swamps thedonor star’s spectrum) and (2) the extreme faintness ofthe companion star in transient AMPs during quiescence(D’Avanzo et al. 2009).A promissing route to overcome these limitations wasproposed by Steeghs & Casares (2002). X-ray irradiateddonor stars can be betrayed by the detection of high ex-citation fluorescence NIII and CIII lines within the Bowenblend at ≃ P > K = 87 ± − . Almost 20 years later,this was refined by Casares et al. (1998) (C98) who find anA9 donor with orbital parameters P orb = 9 . ± . K = 88 . ± . − . This work also reports the firstdetermination of the rotational broadening of the donor’sabsorption features ( V sin i = 34 . ± . − ) which, inturn, implies a binary mass ratio q = M /M = 0 . ± . i = 62 . ± ◦ derived through ellipsoidal fitsto UBV light curves gives a neutron star mass of 1.78 ± ⊙ (Orosz & Kuulkers 1999) and, hence, a good can-didate for a massive neutron star. This result has been re-cently challenged by Elebert et al. (2009) (E09) who mea-sure K = 79 ± − and hence M =1.5 ± ⊙ .Here we present new high resolution spectroscopic ob-servations of Cyg X-2 with the main aim of refining the ro-tational broadening of the donor star and update the orbitalparameters. In contrast with E09, we find a good agreementwith previous results reported in C98 which give support tothe presence of a massive neutron star in Cyg X-2. c (cid:13) J. Casares et al.
Cyg X-2 was observed on the nights of 25-26 July 1999 us-ing the Utrech Echelle Spectrograph (UES) attached to the4.2 m William Herschel Telescope (WHT) at the Observa-torio del Roque de Los Muchachos. Ten 1800-3600s spec-tra were obtained with the E31 echelle grating and 2Kx2KSITe1 detector, covering the spectral range λλ − resolution. ThAr arc imageswere observed each night for the purpose of wavelength cal-ibration. The final wavelength calibration was verified usingthe OI skylines at λ λ − . These werecorrected from every individual spectrum.Eleven additional spectra were obtained on the nightsof 31 July 1999 and 9 July 2000 with the ISIS double-armspectrograph on the WHT. Here we employed the 1200Bgrating on the blue arm and different central wavelengthsresulting in wavelength coverages within λλ − . Frequent comparison CuAr+CuNe arc lampimages were taken every night for wavelength calibration.This was tested against sky lines and it was found to beaccurate to within 4 km s − . These small offsets were never-theless corrected from the individual spectra. The ISIS redarm was always centered redwards of 7600 ˚A but is notused in this paper due to its lower spectral resolution andthe paucity of absorption lines, which result in larger errorsin the cross-correlation analysis. The red arm spectra weremainly taken for the sake of abundance analysis and will bereported elsewhere (Gonz´alez Hern´andez et al. 2009). A logof the observations is presented in Table 1.For the purpose of radial velocity analysis we observedthe stellar template HR 114 (A7 III) using all different in-strumental configurations. This star has an intrinsic V sin i of 21 km s − i.e. comparable to the rotational broadeningof the donor star in Cyg X-2 (C98). Therefore, to refine ourprevious rotational broadening we decided also to observethe F3 V star HR 6189 with UES, which has a reportedupper limit V sin i <
15 km s − .All the images were processed following standard de-biasing and flat-fielding, and the spectra subsequently ex-tracted using conventional optimal extraction techniques inorder to optimize the signal-to-noise ratio of the output(Horne 1986). In C98 we measured the rotational broadening of the donorstar’s features in Cyg X-2 using 25 km s − resolution spectraand found V sin i = 34 . ± . − . Here we revisit thisdetermination using the 10 km s − UES spectra. We broad-ened the template star HR 6189 from 5 to 50 km s − in stepsof 1 km s − , using a Gray profile (Gray 1992) and a limb-darkening coefficient ǫ = 0 . f <
1, to account for their fractionalcontribution to the total light. These were subsequently sub-
Figure 1.
A section of the Doppler corrected average of the CygX-2 UES spectra in the rest frame of the donor star (top), to-gether with the F3V template HR 6189 broadened by 33.7 kms − (bottom). tracted from the Doppler corrected average of Cyg X-2, ob-tained using the orbital solution given in Sec. 4. The Cyg X-2average was also rectified through fitting a low order splineto the continuum, after masking out the main emission andatmospheric/IS absorption lines. The optimal broadening,based on a χ test on the residuals, is found for 34 . ± . − . A potential source of systematics is the assumptionof continuum limb-darkening coefficient in the computationof the rotational profile. Absorption lines in late-type starsare expected to have smaller core limb-darkening coefficientsthan the continuum (Collins & Truax 1995) and, therefore,assuming the continuum limb-darkening coefficient couldbias the result. This was tested by repeating the same anal-ysis using zero limb-darkening as a conservative lower limitand obtain V sin i = 32 . ± . − . Therefore, we decideto adopt the mean of the two limb-darkening values as a safeestimate of the true rotational broadening in Cyg X-2 i.e. V sin i = 33 . ± . − . This is in excellent agreementwith our determination in C98. We rectified the 21 individual spectra by subtracting a low-order spline fit to the continuum, after masking out themain emission and absorption features. The UES spectrawere subsequently rebinned into a uniform velocity scale of5 km s − pix − and the ISIS spectra into 27 km s − pix − .Radial velocities were extracted through cross-correlation ofevery individual spectrum of Cyg X-2 with its correspondingA7III template HR 114, observed with identical instrumen-tal setup. The template spectra were previously broadenedto 33 km s − to match the width of the donor photosphericlines (see previous section). Cross-correlation was performedin the spectral regions free from emission and telluric ab-sorption features. For consistency, new radial velocities wereextracted from the old database (C98) using a contempora-neous observation of the same template HR 114, obtained for c (cid:13) , 000–000 n the mass of the neutron star in Cyg X-2 the purpose of spectral classification. Radial velocities wereextracted following the method of Tonry & Davis (1979),where parabolic fits were performed to the peak of the cross-correlation functions, and the uncertainties are purely sta-tistical. The final errorbars were multiplied by a factor 2 sothat the minimum reduced χ of a sinewave fit model is 1.0.This yields the following parameters γ = − . ± . − P = 9 . ± . T = 2451387 . ± . K = 86 . ± . − where T corresponds to the inferior conjunction of thedonor star. All quoted errors are 68 per cent confidence. Thesystemic velocity γ has been corrected from the radial veloc-ity of HR 114, that we take as -10.2 ± − (Wilson1953). Fig. 2 displays the radial velocity points folded on theorbital period together with the best sine fit solution. Newradial velocities are marked with open circles whereas solidcircles indicate velocities from the old 1993-1997 database(C98). Our K velocity is consistent with C98 within 1- σ but not with E09 who finds K = 79 ± − . To ilustratethis point we also plot in dashed-line style the best sinewavefit for K = 79 km s − . This has χ ν = 3 for 60 degrees offreedom and hence it is far less significant than our K value(Lampton et al. 1976).E09 have suggested that the difference between the two K values could be caused by different levels of X-ray irra-diation between the two observing epochs. The detection ofHeII λ K (Wade & Horne 1988). It might be pos-sible that, by a chance coincidence, the E09 database wasobtained during an episode of lower X-ray activity than ourdata and we have looked for this using RXTE/ASM (AllSky Monitor) data. Contemporaneous X-ray observationsare available for the second half of the C98 campaign (since1996, when RXTE was launched) our new data from 1999-2000 and the entire E09 database but comparable levels ofX-ray activity are found, with the X-ray flux F X oscillatingbetween 35 and 50 ASM counts s − . Only one velocity pointin C98, obtained on the night of 5 Aug 1996, was taken dur-ing a dip in the X-ray light curve of ≃
18 counts s − . Interest-ingly, its orbital phase is φ = 0 .
63, almost identical to thatof another point obtained on 3 Aug 1997 ( φ = 0 . F X ≃
50 counts s − i.e. almost a factor 3 higher. Despitethe difference in X-ray flux both velocities are consistentwith our best orbital solution within 1 − σ . And one shouldnote that phase 0.65 is close to an orbital quadrature, whenvelocity distortions from a circular orbit should be largest(e.g. Davey & Smith 1992). This strongly suggests that the effects of X-ray irradiation in the radial velocity curve areunimportant.As a matter of fact, irradiation will distort the radialvelocity curve from a simple sine wave, introducing a ficti-tious eccentricity which should be measurable. Therefore, wehave also attempted to fit elliptical orbits to our database,following Friend et al. (1990). Our best fit yields null eccen-tricity ( e = 0 . ± . χ than asimple circular solution, another indication that irradiationis negligible at this level. Furthermore, Orosz & Kuulkers(1999) find no evidence for excess light at phase 0.5 in theiroptical light curves nor C98 observe any significant changeof spectral type with orbital phase. These two results alsosuggest that X-ray irradiation is not enough to explain thediscrepant K values. The lack of irradiation signatures isprobably due to the fact that the donor star is hot and theorbital separation large Orosz & Kuulkers (1999). The X-ray flux received by every surface element on the companionstar is too small to produce any disturbance in the radial ve-locity curve or light curve, despite the near Eddington X-rayluminosity of Cyg X-2.Looking at the radial velocity curve of E09 (shown infig. 4) we note a large scatter in the velocity points nearthe phase 0.25 quadrature. Two datapoints seem to lie sys-tematically lower than the rest by ∼
20 km s − and this iscertaintly dragging the K velocity to lower values. The au-thors admit that only one arc spectrum was obtained formost of the nights. Although sky lines were used to correctfor instrumental offsets, the fact that the strongest sky lineOIII λ ∼
160 km s − .In any case, new high resolution observations obtained atthe two orbital quadratures are clearly required to furtherconstrain K and confirm our result.Since the donor star is filling its Roche lobe and syn-chronized, we can combine our updated K and V sin i valuesto constrain the binary mass ratio through V sin i = K (1 + q ) 0 . q / . q / + ln (1 + q / ) (1)(Horne, Wade & Szkody 1986) which leads to q = 0 . ± .
02. The revised mass function is thus f ( M ) = M sin i/ (1 + q ) = P K / π G = 0 . ± .
03 and hence M sin i = 1 . ± .
06 M ⊙ . Assuming i = 62 . ± ◦ (Orosz & Kuulkers 1999) we find M = 1 . ± .
21 M ⊙ . Theerror budget is clearly dominated by the uncertainty in theinclination angle and thus ellipsoidal model fits to new lightcurves are urgently needed to better constraint the stellarmasses. We have revisited the determination of the system parame-ters in Cyg X-2 with 21 new high-resolution spectra obtainedduring 1999 and 2000. The new solution does not supportthe conclusions of E09 who claim for a significantly lowervalue for the radial velocity semiamplitude of the donorstar. Instead, our results confirm previous determinations c (cid:13) , 000–000 J. Casares et al.
Figure 2.
Radial velocity curve folded on the ephemeris listedin Sect. 4 with the best sine-wave solution overplotted. New UESand ISIS velocities from 1999-2000 are marked with open circleswhereas solid circles indicate velocities from the 1993-1997 ISISdatabase. The dashed line depicts the orbital solution of E09. reported in C98. The discrepancy cannot be explained byX-ray irradiation because the sinusoidal shape of the radialvelocity curve is not disturbed. In particular, we find (i) noevidence for orbital eccentricity and (ii) no significant de-viations between two velocity points at phase ∼ ∼
3. Our refined orbital parame-ters are P = 9 . ± . K = 86 . ± . − and V sin i = 33 . ± . − , which lead to q = 0 . ± . M sin i = 1 . ± .
06 M ⊙ . Assuming i = 62 . ± ◦ fromOrosz & Kuulkers (1999) leads to M = 1 . ± .
21 M ⊙ and,therefore, the possibility that Cyg X-2 harbours a neutronstar more massive than canonical. We thank the anonymous referee for helpful comments tothe manuscript. MOLLY software developed by T. R. Marshis gratefully acknowledged. Partly funded by the SpanishMEC under the Consolider-Ingenio 2010 Program grantCSD2006-00070: first science with the GTC. J.C. acknowl-edges support from the Spanish Misitry of Sience and Tech-nology through the project AYA2007-66887. J. I. G. H. ac-knowledges support from the EU contract MEXT-CT-2004-014265 (CIFIST). The INT is operated on the island of LaPalma by the Isaac Newton Group in the Spanish Observa-torio del Roque de Los Muchachos of the Instituto de As-trof´ısica de Canarias (IAC).
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Log of the observations.
Date Instrument Wav. Range Exp. time Dispersion Resolution λλ (s) (˚A pix − ) (km s − )25-26/07/1999 UES 5300-9000 3200,3x(1800,2700,3600) 0.11 1031/07/1999 ISIS 5885-6665 3x1800 0.45 349/07/2000 ISIS 3545-4460 6x1800 0.45 449/07/2000 ISIS 4350-5250 100, 1800 0.45 54 c (cid:13)000