The Spectrum of SS 433 in the H and K Bands
E.L. Robinson, C.S. Froning, D.T. Jaffe, K.F. Kaplan, H. Kim, G.N. Mace, K.R. Sokal, J.-J. Lee
aa r X i v : . [ a s t r o - ph . S R ] A p r The Spectrum of SS 433 in the H and K Bands
Edward L. Robinson , Cynthia S. Froning , Daniel T. Jaffe , Kyle F. Kaplan , HwihyunKim , , Gregory N. Mace , Kimberly R. Sokal ,andJae-Joon Lee Received ; accepted Department of Astronomy, University of Texas at Austin, C1400, Austin, TX 78712;[email protected] Korea Astronomy and Space Science Institute, 776 Daeduk-daero, Yuseong-gu, Daejeon305-348, Republic of Korea 2 –
ABSTRACT
SS 433 is an X-ray binary and the source of sub-relativistic, precessing, bary-onic jets. We present high-resolution spectrograms of SS 433 in the infrared H and K bands. The spectrum is dominated by hydrogen and helium emissionlines. The precession phase of the emission lines from the jet continues to bedescribed by a constant period, P jet = 162 .
375 d. The limit on any secularlychanging period is | ˙ P | . − . The He I λ . µ m line has complex andvariable P-Cygni absorption features produced by an inhomogeneous wind witha maximum outflow velocity near 900 km s − . The He II emission lines in thespectrum also arise in this wind. The higher members of the hydrogen Brackettlines show a double-peaked profile with symmetric wings extending more than ± − from the line center. The lines display radial velocity variations inphase with the radial velocity variation expected of the compact star, and theyshow a distortion during disk eclipse that we interpret as a rotational distortion.We fit the line profiles with a model in which the emission comes from the surfaceof a symmetric, Keplerian accretion disk around the compact object. The outeredge of the disk has velocities that vary from 110 to 190 km s − . These compar-atively low velocities place an important constraint on the mass of the compactstar: Its mass must be less than 2 . M ⊙ and is probably less than 1 . M ⊙ . Subject headings: binaries: close — infrared: stars — stars: individual (SS 433) —stars: variables: other
1. Introduction
SS 433 is an eclipsing X-ray binary star with an orbital period P orb = 13 . ± . V jet ≈ . c ) baryonic jets (for a broadreview of the SS 433 jets see Fabrika (2004)). The jets originally revealed themselves astwo systems of hydrogen and helium emission lines, each system Doppler-shifted to the redor blue by up to hundreds of ˚Angstroms (Margon et al. 1979a; Liebert et al. 1979). Furtherobservations showed that the Doppler shifts of the two systems varied oppositely andsymmetrically about redshift z ≈ .
04 in a roughly sinusoidal pattern with a period near164 days (Margon et al. 1979b). Milgrom (1979a) and Fabian & Rees (1979) proposed thatthe two systems were produced by narrowly-columnated, oppositely-directed, precessingjets. A simple kinematic model based on this physical model is a good descriptor of theobserved jet redshifts (Abell & Margon 1979; Margon 1984). High resolution radio mapsof SS 433 are in accord with the optically-derived model (Roberts et al. 2008; Bell et al.2011). An update to the kinematic model by Eikenberry et al. (2001) yielded precise valuesfor the orbital inclination i = 78 . ◦ ± . ◦ , the angle between the jet and the precessionaxis θ = 20 . ◦ ± . ◦ , the precession period P jet = 162 . ± .
011 days, and the jetspeed β = V jet /c = 0 . ± . − β ) − / = 1 . P jet and P orb / α , H β , and Br γ emissionline with 4 to 6 Gaussians for each line. Two of the Gaussians were consistently displacedby ± (500 − − from the line centers. They associated these components withthe accretion disk. Filippenko et al. (1988) successfully modeled the broad, double-peakedprofiles of the stationary emission lines in the higher members of the Paschen series withtheoretical accretion disk line profiles, although Fabrika (2004) preferred to attribute theprofiles to disk winds and other gas outflows.A disk wind is certainly present (Fabrika 2004). The stationary Balmer lines aredominated by emission from this wind, not the disk itself, because they are produced ina volume large compared to the orbit of the binary star and because the radial velocityvariations of the lines are not in phase with the radial velocity variations expected for gasaround the compact star (Murden et al. 1980; Gies et al. 2002a). The wind also revealsitself in H β , He I λ ∼
150 to ∼ − ,increasing monotonically as the disk becomes more face on (Fabrika 1997). The maximumwind velocities inferred from models of these absorption features and of the broad wings of 5 –the He II emission lines imply that the maximum wind speed could be several times higherthan 1300 km s − (Fabrika 2004; Medvedev et al. 2013). The measured mass loss rates inthe wind generally cluster near 10 − M ⊙ yr − (but see Kotani et al. (1996)). The rate isless certain than the agreement among the measurements might suggest, though, becauseit depends on inter alia the adopted wind speed, the wind geometry, the clumpiness of thewind, and the mass of the compact star (Shklovskii 1981; Blundel et al. 2001; Fuchs et al.2002; Perez & Blundell 2009). Nevertheless, the mass loss rate is high and connotes anaccretion disk around the compact star that is supercritical and vertically extended, at leastnear the compact star (Fabrika 2004).The gas outflow is enhanced in the plane of the disk. The enhanced outflow is detectedfrom absorption lines with radial velocities near −
100 km s − that are strongest whenthe accretion disk is approximately edge-on (Crampton & Hutchings 1981; Fabrika 1997;Fabrika et al. 1997). This outflow is a likely source of some of the absorption seen atX-ray wavelengths (Kotani et al. 1996). Since the amount of absorption depends on thejet precession phase, Kotani et al. (1996) invoked circumbinary material in a precessingplane fed by gas “sprinkled” from the accretion disk. The geometry of the equatorialoutflow is uncertain. Fabrika (1997, 2004) pictures the material as a cometary tail comingfrom the A-type star. Or it may be an expanding spiral wave, perhaps extruded from theouter Lagrangian point or ejected by a propeller, or perhaps produced by a density wakein the stellar wind (Sawada et al. 1986; Welsh et al. 1998; Kim 2011). The outflowingmaterial in the equatorial plane is the likely source of the equatorial “ruff” observed atradio wavelengths (Doolin & Blundell 2009). In any case, there are good observational andtheoretical reasons to conclude that the circumbinary material is not confined to circularKeplerian orbits, and that the gas flow is affected by more than simple gravitationaldynamics. 6 –There is no agreement on the masses of the two stars, nor even whether the compactstar is a neutron star or a black hole. None of the properties that might uniquely identifya neutron star such as type I bursts or periodic flux modulations have been observed(Strohmayer & Bildsten 2006; van der Klis 2006), although quasi-periodic X-ray oscillationswith a frequency near 0.1 Hz have been seen (Kotani et al. 2006). Recent measurementsof the mass of the compact star range from M X = 1 . ± . M ⊙ (Goranskii 2011, 2013)to M X ≈ M ⊙ (Gies et al. 2002b; Blundell et al. 2008), and the measurements arenot converging (see Kubota et al. (2010) and Goranskii (2011) for reviews of the massmeasurements). The higher masses would imply that the compact star is a black hole, butthe lower masses would allow it to be a neutron star.These properties together make SS 433 unlike any other object that has been found inthe Galaxy. While it is often included among the microquasars because of the propertiesof its radio jets (Mirabel & Rodr´guez 1999), the underlying system is quite different fromthe other microquasars, most of which are low-mass and intermediate-mass X-ray binaries.Only recently has a sibling to SS 433 been found, but in another galaxy. M81 ULS-1, anultraluminous supersoft X-ray source in M81, has moving emission features reminiscent ofthe jet lines in SS 433 (Liu et al. 2015).We report here observations of the infrared spectrum of SS 433 in the H and K bandsat high spectral resolution, R = λ/ ∆ λ ≈ , H and K bands at a resolution near R ≈ ∼
10. They detected the P α jet line and stationary emission lines ofHe I and the hydrogen Brackett series. McAlary & McLaren (1980) and Fuchs et al. (2002)obtained spectrophotometry of SS 433 from 2.0 to 12 µ m with good S/N but R . K band at a resolution 7 –of ∼ ≈
400 at Br γ , but published only the Br γ data. Section 2 of ourpaper describes the observations and Section 3 gives the line identifications for both the jetand the stationary lines. Section 4 discusses the disk model for the higher members of theBrackett lines. Section 5 summarizes and discusses our results.
2. Observations and Data Reduction
The Immersion GRating INfrared Spectrograph (IGRINS) measures infrared spectrasimultaneously in the H - and K -bands (1.46-1.81 µ m and 1.93-2.47 µ m) at a resolvingpower of R ≃ The pipeline performs image calibration, spectrogram extraction, andwavelength calibration. We edited the comparison star spectrograms to flatten the intrinsicabsorption features of the A star, and then divided the SS 433 spectrograms by the A starspectrograms to remove telluric absorption and correct for the blaze profile of the spectralorders. We eliminated wavelengths where the signal-to-noise ratio of the A star spectrogramwas <
20 and/or the signal in the normalized SS 433 spectrogram dropped below 0.05. see also https://github.com/igrins/plp. 8 –Finally, we rebinned the spectrograms to a linear dispersion (0.00003 µ m/pixel or roughly1 resolution element) and combined the orders using weighted averages.There are two primary periodicities in SS 433: the orbital period and the jet precessionperiod. We calculated the orbital phases at which our data were obtained using the orbitalephemeris determined by Goranskii (2011) from data obtained between 1978 and 2007.In this ephemeris φ orb = 0 corresponds to the time of minimum of the deeper of the twooptical eclipses. The orbital phases are listed in Table 1. When extrapolated forward to theepochs of our observations, the formal error on φ orb is small, ± . ± . φ orb = ± . ∼ .
027 in phase after the mean times of eclipse in the opticaldata. If the X-ray emission arises close to the compact star, this suggests that true orbitalconjunction of the stars occurs at orbital phase ∆ φ orb ≈ . ± .
004 after the time ofeclipse given by the Goranskij ephemeris. This seemingly small difference between the timesof true conjunction and eclipse will become important when we discuss the profiles of theBrackett lines.To calculate the expected phases and redshifts of the jet lines we used the jet ephemerisfrom Fabrika (2004). This is the same as the jet ephemeris determined by Eikenberry et al.(2001) except that phase zero is shifted to the times when the jet points most directly atthe Earth (when the H α − line reaches maximum blueshift), which are also the times whenthe positive and negative jet lines are most separated in wavelength. We denoted the phasecalculated from the Fabrika (2004) version of the ephemeris by Ψ (see Figure 4 in Fabrika(2004) and Figure 1 in Goranskii (2011)). The jet phases at the times of our observationsare also listed in Table 1. 9 –
3. Line Identifications3.1. The Stationary Lines
Figure 1 shows the infrared spectrum of SS 433 on 2015 May 27 when the jet lineswere weak, allowing the stationary emission features to be identified without confusion.The spectrum shows lines in the hydrogen Brackett series and Pfund series, neutral andionized helium, and the magnesium doublet at λλ . − . µ m (see Table 2). Fe II linesare often observed in the infrared spectra of early-type emission-lines stars, but are absentor too weak to be detected in the spectrum of SS 433 (Chojnowski et al. 2015). Nor do wedetect the Na I doublet at λλ . . µ m or any forbidden lines.The He I λ . µ m emission line, which arises from the metastable 2s S state,shows variable P-Cygni absorption features, the unambiguous signature of wind outflow.The lower panel of Figure 2 shows the He I line on 2014 May 24 and 2015 July 30. Thehorizontal axis in the figure has been converted to velocity shift with respect to the line’srest wavelength. The P-Cygni absorption features are variable and complex, showing thatthe wind is highly inhomogeneous. Individual components of the wind outflow can havevelocities up to ∼
900 km s − . These results agree qualitatively with earlier measurementsbased on absorption lines. Fabrika (1997), for example, deduced wind speeds between 200and 1300 km s − (see Figure 18 in Fabrika (2004)). In addition, Figure 5 in Gies et al.(2002a) suggests wind speeds between ∼
200 and ∼
600 km s − from the P-Cygni absorptionin the He I λ ∼
200 km s − . 10 –The emission feature near λ . µ m was an interesting puzzle. An emission featureat a similar wavelength is present in the spectra of many early-type emission-line stars andis usually identified as C I λ . µ m (Chojnowski et al. 2015). Medvedev et al. (2013)and Goranskii (2011) have shown that the wind should and does produce He II emissionlines. Prompted by their work, we instead identify the feature in SS 433 as Doppler-shiftedHe II λ . µ m arising in the high-velocity wind. To justify this identification, we notethat • The C I line in the spectra of Be stars is almost always weaker than Fe II λ . µ m,usually much weaker (see, eg, Figure 5 in Chojnowski et al. (2015)). Neither that Fe IIline nor, for that matter, any other Fe II lines are visible in the IGRINS spectrogramsof SS 433. Thus, if identified as C I, the feature at λ . µ m would be anomalouslystrong relative to other metal lines. • Although emission lines from carbon are seen in the optical spectrum of SS 433,they are always lines of ionized carbon(eg, C II λ / λ • If identified as He II, the feature has the wavelength and profile expected for emissionfrom the wind. The top panel of Figure 2 shows the profiles of the feature in the samespectrograms as the He I lines in the bottom panel of the figure. The horizontal axisin the top panel is again the velocity shift with respect to the rest wavelength of theHe II λ . µ m line. The λ . µ m emission feature lies on the steeply-slopingred wing of the strong Br11 line so its profile is distorted. Emission lines from thewind come from a different volume of the wind than that which causes the P-Cygniabsorption. Recognizing that the profiles of emission and absorption lines from aninhomogeneous wind will not, therefore, mimic each other precisely, we see that the 11 – λ . µ m emission feature aligns well with the P-Cygni absorption feature. • The λ . µ m line is produced by the 12-7 transition of He II. The He II at λ . µ m is produced by the 10-7 transition. If our identification is correct, the λ . µ m line must also be present and should be stronger than the λ . µ mline. Reference to Figure 1 shows that the λ . µ m line transition is, indeed,present and that it, too, is distorted and shifted, although not by as much as the λ . µ m line.Our identification of the λ . µ m has important implications. Since the red wingof the line is weaker than the blue wing, something, presumably the accretion disk, isobscuring the wind outflow at positive velocities. Also, since the He II emission comes froman inhomogeneous, variable, partially obscured wind, it is dangerous to use the velocity ofthe He II lines as a proxy for the orbital radial velocity variations of the compact star.The only absorption features other than the P-Cygni absorption that we could identifywith certainty are two diffuse interstellar absorption bands (DIBs) at 1.5273 and 1 . µ m(Geballe et al. 2011). The DIB at 1 . µ m is shown in Figure 3, where it shows up as anabsorption feature in the Br19 line that is not present in the Br18 or Br20 lines. Figure 4 shows the infrared spectrum of SS 433 on 2014 May 24 when the jet lineswere strong. All the jet lines we identified in this and the other four spectrograms are listedin Table 2, and come from neutral hydrogen and helium. The list includes lines that arenot normally in the IGRINS bandpasses but can move into the bandpasses when the jetDoppler shifts are large. We see one likely case of bullets in the jets: The P α − line on2014 May 24 (Figure 4) has three peaks that we interpret as coming from three different jet 12 –bullets. The half-width at half maximum of the P α jet line falls in the range 1000-2000 kms − , varying considerably from observation to observation. Although wide in an absolutesense, the jet lines are narrow compared to the total range of projected jet velocities overthe 162-day precession period. According to Vermeulen et al. (1993), the jet bullets aretypically separated by intervals of < ∼ cm or a few hundred AU before fading.The mean observed redshifts of the jet lines are given in Table 3 along with thethe values of Ψ calculated from the Fabrika (2004) ephemeris. The observed redshiftscorrespond to the peaks of the jet lines. The peaks are often difficult to identify forindividual lines, as in the case of the P α ± lines in Figure 4, but the mean redshifts areaccurate to better than ± . ≈ − .
03 or about 5 days would be enough to bring them into agreement with theobserved redshifts. Since jet nodding and intrinsic phase jitter can introduce phase residualsof 5 to 10 days (Eikenberry et al. 2001), and since we have only five epochs, this smallshift could have been introduced by statistical fluctuations. The most we can conclude isthat the Eikenberry et al. (2001)/Fabrika (2004) ephemeris predicts of the phase of the jetredshifts to | ∆Ψ | . . . µ m that appeared on2014 May 24 and 2015 July 30 but not in our other spectrograms (marked with a “?” inFigure 4). Although in a region with much telluric absorption, the feature is strong andlikely to be real. 13 –
4. A Disk Model for the Stationary Hydrogen Brackett Lines4.1. Previous Models for the Hydrogen Line Profiles
Most discussions of the stationary hydrogen emission lines have relied almost exclusivelyon observations of H α . The line is formed primarily in the disk wind and the wind emissionis so strong that it tends to drown out emission from other sources. There are occasionaldouble peaks near the center of H α that Blundell et al. (2008) and Bowler (2011, 2013)attributed to a rotating disk. Because they did not detect orbital radial velocity variationsin the double peaks, Blundell et al. (2008) concluded that the disk is a circumbinary disk orring. Bowler (2010) suggested that H α emission from an inner accretion disk around thecompact object became visible only during a flare in early 2004 November.The Paschen and Brackett lines appear to be less dominated by the wind emission,allowing emission from other parts of the SS 433 system to be more visible. Perez & Blundell(2009) fitted Br γ with six Gaussian distributions, which they attributed variously to amulticompenent wind, an inner accretion disk, and an outer accretion disk. The model fitsthe line profile well, but its functional form is not based on a physical model and it has atleast 19 parameters (three for each Gaussian and one for the continuum), so its uniquenessis an issue. Filippenko et al. (1988) observed the higher members of the Paschen series. Thelines varied rapidly but on average were double-peaked with broad wings. Filippenko et al.(1988) modeled the mean line profiles with emission from a single, Keplerian accretion diskaround the compact star. While the fits were not perfect, the model is physically based,testable, and requires only 6 parameters. 14 – Like the Paschen lines, the Brackett lines are usually double-peaked and have broadwings. We take, therefore, the same approach as Filippenko et al. (1988) and attemptto fit the Brackett lines with an accretion disk line profile. Our line model is essentiallythe same as that discussed by Stover (1981) and Smak (1981). The model disk is thin,circular, and in Keplerian motion around the compact star. We assume the line emissioncomes from an optically and physically thin layer sitting on top of an optically thickdisk. The distribution of line emission across the disk is axially symmetric and its radialdependence is given by a power law F ∝ r − α . The local line emission is Doppler broadenedby isotropic “turbulent” velocities, which we describe by a Gaussian distribution with astandard deviation σ = V turb /V circ , where V circ is the local circular velocity. Finally, theemitting layer has a ratio of outer radius to inner radius R max /R min . These are the innerand outer boundaries of the region producing the line emission, not necessarily the physicalboundaries of the disk. Thus the model line profile has three parameters: α , V turb /V circ , and R max /R min .Figure 6 shows how the model line profile varies as these three parameters are varied.The basic morphology of the profile – double-peaked with broad wings – is independent ofthe parameters over their ranges of interest. The dominant effect of varying R max /R min isto change the separation of the peaks relative to the total line width. The dominant effectof changing V turb /V circ is to change the depth of the minimum between the two peaks. Thedominant effect of changing α is to change the relative amount of flux in the wings. Anotherfour parameters are needed to fit the model line profiles to the observed line: the continuumlevel, the line strength, the wavelength of the line center, and a scale parameter for theline width that also absorbs the effect of disk inclination. Thus our model has a total ofseven parameters (turbulent broadening adds one parameter to the Filippenko et al. (1988) 15 –model).The observed line profiles are affected by physical processes not included in our modelsuch as absorption, wind emission, and patchiness in the distribution of the emissionwhatever its source. These effects systematically distort the observed line profiles, vitiatingany attempt to fit the profiles by, say, least squares. Instead, we fitted the profiles by eye,emphasizing the fits to the line wings. This approach precluded a formal error analysis. In part because Br γ is contaminated by jet emission or noise in all but two of ourobservations, but also because we suspect the higher member of the Brackett series are lesscontaminated by the wind emission seen in Br γ by Perez & Blundell (2009) and are morelikely to give a cleaner view of the accretion disk, we modeled only the higher members ofthe series. Figure 7 shows Br12 and Br13 from all our observations. The Br12 and Br13profiles agree well with each other, so we fit just the Br12 line, taking it as a proxy for allthe higher members of the Brackett series. The fits of the model profiles to the Br12 lineare shown in Figures 8 and 9, and the fitted model parameters are listed in Table 4. Thetable also gives the disk inclination, where we assume the disk is perpendicular to the jetand have calculated the jet inclination from the Eikenberry et al. (2001) jet model.We do not attach much significance to the fitted values of R max /R min and V turb /V circ .While the fitted values of R max /R min are all near R max /R min = 100, the values dependsensitively on the placement of the continuum, on noise, and on systematic distortions in theextreme wings of the line. The large values of the ratio mean only that the emission comesfrom most of the disk, not a narrow ring in the disk. The values of V turb /V circ all clustertightly near V turb /V circ = 0 .
20, but these values should also be viewed with skepticism. The 16 –only mechanism available to the model for filling the dip between the peaks of the line isturbulent velocity. Many other physical processes could do the same. The rather high valueof V turb /V circ means only that some mechanism is producing low velocity emission thattends to fill the dip.The fitted values of α , which are dominated by the fits to the wings of the lines,are more meaningful. Except for the profile on 2014 November 21 (Figure 9), which iscontaminated by a jet line, the disk model fits the wings of the observed profiles well. Thefitted values of α differ from observation to observation and these differences correspond toreal differences among the observed profiles. This can be seen by comparing the rapidlydropping wings of the profile on 2015 May 27, which yielded α = 1 .
4, to the slowly droppingwings of the profile on 2014 May 24, which yielded α = 2 .
1. All the values lie in therelatively narrow range 1 . ≤ α ≤ .
2, bracketing the best-fit value α = 1 . α that have beenmeasured from the hydrogen emission lines produced by the accretion disks in cataclysmicvariables and low-mass X-ray binaries (Stover 1981; Smak 1981; Johnston et al. 1989;Horne & Saar 1991). Like SS 433, a single cataclysmic variable can also have differentvalues of α on different nights. Thus, the value of α ranges from 1.7 to 2.25 in the dwarfnova Z Cha (Horne & Saar 1991).Although the disk model predicts that double peaks near the line center should alwaysbe present, the peaks can be distorted or missing altogether from the observed profiles of theBrackett lines. Both peaks are missing from the Br12 profile on 2015 July 30 (Figure 8).We attribute this to absorption by the accretion disk. On that date the inclination ofthe disk was 98 ◦ , so the disk was nearly edge-on to the Earth. If, as is widely suspected,the disk is vertically extended (Fabrika 2004), the rim of the disk would hide much of theemitting surface layer of the disk. We expect our disk model to fail under these conditions, 17 –especially at the low velocities where the hydrogen lines would be prone to self absorption.The profiles of the Brackett lines on 2014 November 21 (Figure 9) were single peaked– the blue peak of the line was missing. The orbital phase predicted by the Goranskii(2011) ephemeris for this observation is 0 . ± . γ line profiles. One of them was obtained at a similar orbitalphase ( φ orb = 0 .
96) and was almost identical to the profile we observed. Following thediscussion in Section 2, the orbital phase of our observation probably corresponds to a phase − .
023 before true conjunction of the stars. Thus, our observation and the observation byPerez & Blundell (2009) were both made during eclipse but prior to mid-eclipse. At thisphase the accretion disk is partly eclipsed and the eclipse would systematically block offparts of the disk with low velocity gas approaching the Earth. The profile would be missingthe blue-shifted peak. The line profile can therefore be interpreted as a classical rotationaldisturbance similar to the rotational disturbance observed in the He II λ − . The velocities on the individual observations range from 107 to191 km s − , and inspection of Figure 8 shows that these differences correspond to large,real differences in the peak separations from profile to profile. In fact, these deprojectedvelocities may be too low because broadening of the lines by turbulence moves the doublepeaks towards each other with respect to the line wings. For V turb /V circ = 0 .
20 this effectreduces the separation of the peaks by about 15%. Correcting for this effect would increasethe mean deprojected velocity at the outer edge of the disk to ∼
170 km s − . If, on the 18 –other hand, the shallowness of the dip between the peaks has nothing to do with turbulentbroadening, no correction is needed. The most we can say is that the mean circular velocityat the outer edge of the disk lies somewhere in the range 150-170 km s − .The wavelengths of the centers of the fitted profiles are given in the last column ofTable 4. Figure 10 plots the radial velocities of the line centers against the orbital phasecalculated from the Goranskii (2011) orbital ephemeris (column 3 of Table 1). If the Br12emission line comes from an accretion disk around the compact star, its radial velocityshould be vary sinusoidally with a maximum approaching velocity near phase 0.25. Thesolid line in the figure is a sine curve fitted to the observed velocities by least squares. Themeasurements are sparse and poorly distributed in orbital phase, so the fitted values ofthe amplitude and mean velocity of the sine curve are not meaningful. The phase of thesine curve is, however, fairly well constrained. The phase of maximum approaching velocityoccurs at φ orb = 0 . ± .
04, which is consistent with the value expected for an accretiondisk around the compact object.
5. Summary and Discussion
In summary, our most important results are: • The precession phases of the jet differ from the phases predicted by theEikenberry et al. (2001) ephemeris by ∆Ψ ≈ − .
03. Because this small phaseshift could have been caused by a combination of jet nodding and intrinsic phasejitter, we conclude only that the Eikenberry et al. (2001) ephemeris still predicts thejet redshift phase to | ∆Ψ | . .
03. This means that the clock underlying the phaseof the jet precession has had a single, constant period for more than 37 years. Wecan place an upper limit on any secular changes to the period by attributing all 19 –the observed phase shift to a slowly-changing precession period. The implied upperlimit to the rate of change of the period is, then, | ˙ P jet | . | ∆Ψ | /E ≈ − , where E = 83 is the number of elapsed cycles, and the time scale for any period changeis P jet / | ˙ P jet | & ,
000 years. The superhumps in the light curves of the SU UMasubclass of cataclysmic variables are caused by precession of the accretion disks inthese systems, although it is generally the precession of an elliptical disk lying flat inthe plane of the orbit, not a tilted disk (Patterson 2001). For comparison, the rates ofchange of the periods of superhumps are generally greater than | ˙ P hump | ≈ × − ,but a few well-determined values of | ˙ P hump | are somewhat less than 10 − (Kato et al.2009). The superhump periods of SU UMa stars are typically just a few hours,however, so for even the most stable of them P hump / ˙ P hump ≈
30 years. • The multicomponent, variable, P-Cygni profile of the He I λ . µ m emission lineis direct evidence for an inhomogeneous and variable wind outflow. The maximumobserved wind speed is ∼
900 km s − . These properties compare favorably withearlier measurements of the wind properties (Fabrika 2004; Medvedev et al. 2013),although we do not see the strong dependence of wind speed on disk inclinationfound by Fabrika (1997). The He II emission from the 12-7 and 10-7 transitions at λ . µ m and λ . µ m respectively also come from this wind. We agree withMedvedev et al. (2013) that the redshifted part of the He II wind emission is obscured,greatly obscured in the case of the λ . µ m line. Because of this obscuration andbecause the obscuration is variable, the profiles of the lines are distorted and thedistortions vary with time (see also the discussion of He II emission lines in Goranskii(2011)). • The broad, usually double-peaked, emission in the higher members of the Brackettseries are produced in an accretion disk around the compact star. Three lines of 20 –evidence lead to this conclusion. First, the observed line profiles generally agreewith model profiles produced by accretion disks. We attribute the disagreementsbetween the observed and model profiles on two of the observing dates to a rotationaldisturbance during eclipse and to obscuration by the optically-thick edge of the diskwhen the disk is edge-on, neither of which effects are included in the model. Second,the derived distribution of line flux across the disk is similar to the distribution of lineflux across the surfaces of disks in cataclysmic variables and low-mass X-ray binaries.Third, the phase of the radial velocity curve of the Brackett lines agrees with thephase expected for an accretion disk around the compact star. Our conclusion issimilar to that of Filippenko et al. (1988) who showed that the higher members of thePaschen lines could be modeled by emission from an accretion disk.Our model differs from essentially every published model for the Balmer emissionlines, especially the H α line (Fabrika 2004). We attribute the difference to a differencein the physical processes producing the lines: Emission from the wind dominates thelower members of the Balmer series, drowning out emission from other sources. Windemission is much weaker in the higher members of the Paschen series and Brackettseries, allowing contributions from other components of the SS 433 system to dominate.Our model also disagrees with the interpretation of Br γ by Perez & Blundell (2009).In part this is due to our application of the model to the higher members of theBrackett series, but another factor is also at work. The observed Br12 line profile thatdiffered the most from our model was obtained on 2015 July 30, when the accretiondisk was almost edge-on and the low-velocity line emission was strongly self absorbed.All of the spectrograms obtained by Perez & Blundell (2009) were obtained near thissame disk orientation. They did not detect the accretion disk because much of it washidden at that precession phase. 21 –Our results place an important limit the mass of the compact object. We first reviewthe uncertainties in previous measurements of the masses of the stars in SS 433, thencalculate the new upper limit on the mass of the compact object. The direct way todetermine the masses of stars in binaries is to measure the radial velocity curves of thetwo stars. The most recent determination of the masses of the stars in SS 433 based onradial velocities was by Kubota et al. (2010), who found 1 . M ⊙ ≤ M X ≤ . M ⊙ . Theyalso carefully analyzed the uncertainties in the masses derived this way. Because of heating,the radial velocity of the A-star can be measured during only half the orbit. Furthermore,considerable judgement must be exercised when choosing which of its absorption lines tomeasure and when estimating corrections to the measured velocities to account for theheating. The radial velocity of the compact star must be measured from the emission linesarising in gas thought to follow its motion, usually He II λ λ , α and Br γ emission lines into sets of up to six Gaussian functions, and identified a pair of red- andblue-displaced Gaussians as emission from a circumbinary disk of gas in a circular Keplerianmotion. They equated the velocities of the Gaussians with the orbital velocity, whichyielded a lower limit on the mass enclosed by the circumbinary disk. After subtracting the 22 –mass of the A-star, they derived a mass of ∼ M ⊙ for the compact star and its accretiondisk. Even if the decomposition of the line profiles into Gaussians were to have physicalmeaning, the enhanced gas flow in the plane of the orbit is observed to have a large radialoutflow velocity (Crampton & Hutchings 1981; Fabrika 1997; Fabrika et al. 1997; Fabrika2004). The gas does not follow a circular Keplerian orbit, compromising masses based onthe assumption that it does.Finally, as typified by the work of Goranskii (2011, 2013), it is possible to measurethe mass of the compact star in SS 433 without resorting to radial velocity measurements.Brinkmann et al. (1989) assumed that the A-star exactly fills its Roche lobe and that theX-ray eclipse in SS 433 is an eclipse by the A star of a thin jet of X-rays near the compactstar. Since the orbital inclination of SS 433 is known, they were able to derive a mass ratio q = M X /M A = 0 . M A is the mass of the A star. Using only its photometricproperties and distance, Goranskii (2013) derived a mass for the A-star and, from the massratio, a mass for the compact star. The assumption that the surface of A-star is identicalto the surface of its Roche lobe is insecure, though, especially since the A-star might be atilted rotator as required by slaved disk models for the jet precession (van den Heuvel et al.1980). The derivation of the A-star mass from its photometric properties is, furthermore, amulti-step process, each step prone to its own uncertainties.While we cannot fully determine the mass of the compact star in SS 433, we canuse the profiles of the Brackett lines to place an independent constraint on its mass. Theseparation of the two stars in SS 433 is given by a = G ( M X + M A ) P orb / π . Previousmeasurements of the masses of the stars tend to fall into two distinct groups: one with totalmasses near 30 M ⊙ and one with total masses near 15 M ⊙ (Kubota et al. 2010; Goranskii2011). For the 30 M ⊙ group, the separation of the two stars is ∼ . × cm; while forthe 15 M ⊙ group, the separation is ∼ . × cm. If we assume that the tidal truncation 23 –radius of an accretion disk around the compact object is about 25% of the separation of thestars (Frank, King, & Raine 1992), the maximum disk radius is 1 . − . × cm.If the disk is Keplerian, the radius of the outer edge of the disk is given by R max = GM X /V R max , which leads to the mass limit M X ≤ R max V R max /G . All the variousvalues one might adopt for R max and V R max yield low upper limits to M X , indicatinga low total mass for SS 433. We will, therefore, restrict our discussion to the smallerradius for the disk, R max = 1 . × cm. The most stringent constraint on the massof the compact star comes from adopting the smallest measured value of the deprojectedrotational velocity, V R max = 107 km s − as measured on on 2015 June 11. This yieldsa mass limit of M X ≤ . M ⊙ . A more realistic upper limit comes from adopting themean deprojected rotational velocity, V R max = 148 km s − , which yields M X ≤ . M ⊙ .The most relaxed upper limit comes from increasing the adopted V R max by another 15%,to V R max = 170 km s − , to account for the possible effects of turbulent broadening onthe line profile. In this case the mass limit increases to M X ≤ . M ⊙ . The only recentmass determinations that are consistent with these limits are that of Goranskii (2011),who found M X = 1 . ± . M ⊙ , and (barely) that of Kubota et al. (2010), who found1 . M ⊙ ≤ M X ≤ . M ⊙ . These limits place the mass of the compact star much below therange of measured black hole masses but within the range of measured neutron star masses(Ozel et al. 2012).In closing we note that our results are based on data from just five nights ofobservations. It is encouraging that the new data are in accord with previously publisheddata where comparison is possible, notably with the Paschen line profiles observed byFilippenko et al. (1988) and with the Br γ line profiles observed by Perez & Blundell(2009), at least at those orbital phases where our data overlaps theirs. Nevertheless, theobservational properties of SS 433 are complex and not easily disentangled. The mass limit 24 –we have derive for the compact star in SS 433 should be viewed with some caution until itis tested against a larger set of data.This work used the Immersion Grating Infrared Spectrograph (IGRINS) that wasdeveloped under a collaboration between the University of Texas at Austin and the KoreaAstronomy and Space Science Institute (KASI) with the financial support of the USNational Science Foundation under grant AST-1229522, of the University of Texas atAustin, and of the Korean GMT Project of KASI.McDonald Observatory (IGRINS). 25 – REFERENCES
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147 1.64135(05 )2014 Nov 21 110 1.7 0.20 57 ◦
148 1.64190(10)2015 May 27 100 1.4 0.22 66 ◦
191 1.64120(05)2015 Jun 11 100 2.2 0.20 77 ◦
107 1.64155(10)2015 Jul 30 80 1.7 0.22 98 ◦ · · · a The disk is assumed to be perpendicular to the jet, whose inclinationis determined from the jet precession ephemeris. At an inclination of90 ◦ the disk is edge-on. b Deprojected orbital velocity at the outer edge of the disk. 35 –
Fig. 1.— The spectrum of SS 433 obtained on 27 May 2015. The jet lines were unusuallyweak at that time, allowing the stationary lines to be identified without confusion. Thestationary lines are marked and identified above the spectrum. The jet lines are marked andidentified below the spectrum. 36 – -1000 0 100011.52 -1000 0 100011.11.2
Fig. 2.— The bottom panel shows the profiles of the He I λ . µ m line on 2015 July 30when the accretion disk was nearly edge on ( i = 98 ◦ ), and 2014 May 24 when the disk wasmost nearly face on ( i = 63 ◦ ). The telluric lines have been masked out in both spectrogramsand the spectrum on 2015 July 30 has been shifted vertically for clarity. The wavelengthscale has been converted to velocity shift from the rest wavelength of the line. The blue-shifted absorption features betray the presence of a complex and variable wind outflow. Thetop panel shows the profiles of the He II λ . µ m line on the same dates and, once again,the spectrum on 2015 July 30 has been shifted for clarity. This weak line lies on the steeplysloping red wing of the strong Br11 line. The He II line is shifted and broadened to roughlythe same velocities as the wind features in the He I line, showing that it, too, arises in thedisk wind. 37 – Fig. 3.— The Br18 (rightmost), Br19, and Br20 emission lines in all five spectrograms,labeled with the dates on which the data were obtained. The forest of narrow features presentin all the spectrograms, but especially evident in the spectrogram obtained on 2015 June 11,are caused by incompletely removed terrestrial absorption lines. The profiles of all theBrackett lines are generally similar, as can be seen by comparing the profiles of the Br18 andBr20 lines. The broad absorption feature near 1.5273 µ m that distorts the profile of Br19 isa diffuse interstellar band. 38 – Fig. 4.— The spectrum of SS 433 obtained on 24 May 2014. The stationary lines are markedand identified above the spectrum, while the jet lines are marked and identified below thespectrum. The velocity shifts of the jet lines placed the P α − and P α + lines on top of thestationary Br10 and Br γ lines respectively, greatly distorting the profiles of those stationarylines. We interpret the multi-peaked profile of the P α − line sitting on top of Br10 as causedby “bullets” in the jet. 39 – Fig. 5.— The filled squares and triangles are the measured redshifts of the jet lines in ourdata. At the scale of this plot the error bars are smaller than the symbols. The curves arethe redshifts predicted by the Eikenberry et al. (2001) model for the jet reshifts. A shift ofthe predicted redshift curves by ∆Ψ ≈ − .
03 or about 5 days would bring the observed andpredicted redshifts to the same phase. 40 –
Fig. 6.— Model emission line profiles. The basic morphology of the profile – double-peakedwith broad wings – is independent of the model parameters over their ranges of interest.The upper left panel shows the effect of varying the parameter R max /R min . The dominanteffect is to increase the separation of the peaks relative to the total line width as R max /R min decreases. The upper right panel shows the effect of varying the parameter α , where theline flux from the disk is given by the power law F ∝ r − α . The dominant effect is to throwmore flux into the line wings as α decreases. The lower panel shows the effect of varyingthe turbulent velocity of the gas in the disk. The dominant effect of changing V turb /V circ is to decrease the depth of the minimum between the two peaks as the turbulent velocityincreases. 41 – Fig. 7.— The Br12 and Br13 lines in all five spectrograms, labeled with the dates and theorbital phases at which the data were obtained. The forest of narrow features present in allthe spectrograms, but especially evident in the spectrogram obtained on 2014 November 21,are caused by incompletely removed terrestrial absorption lines. Features near 1.625 µ m areartifacts introduced by inaccurate flat-fielding at the ends of orders. The broad feature at1.655 µ m in the spectrum obtained on 2014 November 21 is the jet line Br9 − . 42 – Fig. 8.— Fits of the accretion disk line profile model to the Br12 emission line on thedates labeled in the upper left corner of each panel. According to the Eikenberry et al.(2001) ephemeris, the inclinations of the jet to the line of sight were θ = 63 ◦ and 66 ◦ inthe upper two panels, and θ = 77 ◦ and 98 ◦ in the lower two panels. If the accretion disk isperpendicular to the jet, the disk was viewed nearly edge-on in the lower right panel, perhapsexplaining the missing horns of the line profile at that time. 43 – Fig. 9.— A fit of the accretion disk line profile model to the Br12 emission line on 2015November 21. The rising flux on the right side of the spectrum is caused by the jet line Br9 − .According to the Goranskii (2011) ephemeris, the orbital phase of SS 433 was φ orb = 0 . γ line at φ orb = 0 .
96 shown Figure 1 in Perez & Blundell (2009). Although thesample is small, we suggest that the distortion of the line profile near and just before eclipseis repeatable. We interpret the distortion as being caused by a partial eclipse of the accretiondisk. 44 –
Fig. 10.— The data points are the radial velocities of the Br12 emission line plotted againstthe orbital phase calculated from the Goranskii (2011) orbital ephemeris. If the Br12 emissionline comes from a symmetric accretion disk around the compact star, its radial velocity shouldvary sinusoidally with a maximum approaching velocity at phase 0.25. The solid line is a sinecurve fitted to the data points. The measured velocities are sparse and poorly distributedin orbital phase, so the values of the amplitude and mean velocity are not meaningful. Thephase of the sine curve is, however, fairly well constrained and is φ orb = 0 . ± ..