FUSE Observations of a Full Orbit of Hercules X-1: Signatures of Disk, Star, and Wind
Bram Boroson, Saeqa Dil Vrtilek, John C. Raymond, Martin Still
FFUSE Observations of a Full Orbit of Hercules X-1: Signatures ofDisk, Star, and Wind Bram S. Boroson [email protected] andSaeqa Dil Vrtilek and John C. Raymond
Smithsonian Astrophysical Observatory Mail Stop 83 Cambridge, MA [email protected], [email protected] andMartin Still
South African Astronomical Observatory PO Box 9 Observatory 7935 Cape Town, SouthAfrica [email protected] Based on observations made with the NASA-CNES-CSA Far Ultraviolet SpectroscopicExplorer. FUSE is operated for NASA by the Johns Hopkins University under NASA con-tract NAS5-32985
1. Introduction
Hercules X-1 (discovered by Tananbaum et al. 1972) is one of the most frequentlyobserved X-ray binary systems. The intermediate mass of the donor star, ≈ . (cid:12) , leadsto a wealth of behavior seen in both low mass and high mass systems. Although we suspectthe mass flow is primarily through Roche lobe overflow giving rise to an accretion disk, as inthe Low Mass X-ray Binaries (LMXB), the variable P Cygni profiles observed in UV linessuggest either a transient stellar wind or a stellar wind that is photoionized in some regions(Boroson, Kallman, & Vrtilek 2001). There are theoretical grounds as well to expect thatwinds may arise in this system when X-rays from the neutron star heat the surface of thenormal star or accretion disk (Arons 1973; Davidson & Ostriker 1973; Basko et al. 1977;London, McCray, & Auer 1981; Begelman, McKee, & Shields 1983; Begelman & McKee1983).Most LMXBs, including Z-sources and atoll-sources, do not show persistent pulsations,perhaps because they have neutron stars with low magnetic fields. These sources thus lack an a r X i v : . [ a s t r o - ph ] J un x = 13 .
86 seconds. The orbital period is slowly lengthening from massloss in the system (Deeter et al. 1991).Fortuitously, Her X-1 has high orbital inclination ( >
80 degrees), allowing total X-rayeclipses to constrain the size of the donor star, and the high galactic latitude offers only smallreddening, allowing the system to be observed at crucial UV and even EUV wavelengths.The system’s most mysterious variability is the 35-day X-ray high and low cycle (Giac-coni et al. 1973). For 8–11 days (the “Main-On state”) of this cycle Her X-1 emits X-rayswith a ∼ erg s − total X-ray luminosity. For a ∼ XMM (Jimenez-Garate et al.2002) shows a multitude of X-ray emission lines presumably from an accretion disk corona.The line ratios indicate that the gas is enhanced from CNO processing from a massiveprogenitor. Jimenez-Garate et al. (2005) confirmed the CNO enhancement by observations ofmore than two dozen emission lines originating in an accretion disk corona. Model predictionsof the disk corona’s response to illumination by the central X-ray source are in reasonableagreement with the observed fluxes for low and moderate Z elements ( O through S), but theFe xxv ,Fe xxvi lines are several times brighter than predicted (Jimenez-Garate et al. 2005).From observations of optical absorption lines (Reynolds et al. 1997), and from opticalpulsations that result from the X-rays from the neutron star periodically striking the surfaceof the normal star (Middleditch & Nelson 1976), we know that the normal star has a mass ≈ . (cid:12) and the neutron star has a mass 1.5 ± . (cid:12) . The optical spectrum showsabsorption lines from HZ Her, emission at the Bowen blend near 4640˚A (see Schachter,Filippenko, & Kahn 1989 for a discussion of the formation of these lines), and emission fromHe ii λ IUE , Vrtilek & Cheng 1996) showed that achange in the accretion disk precession could explain an anomalously low period of X-rayemission.To study global accretion one should observe gas at ionization stages and temperaturesresulting from X-ray illumination of the disk, and one would need to resolve Doppler-shiftedvelocities that correspond to the orbital motion of the neutron star (160 km s − ), motion in 4 –the accretion disk (expected to be ≈
300 km s − at the edge of the disk), and the velocitiesexpected in a disk or stellar wind ( ∼ − ).The strong UV resonance lines from N v , Si iv , and C iv , first seen with IUE (Howarth& Wilson 1983b), presumably result from photoionization of the accretion disk and HZ Her(Raymond 1993, Ko & Kallman 1994). These lines are much stronger than the strongestoptical high ionization line, He ii λ HST ) showed that these lines are still present at a few percent of maximum brightnessduring mid-eclipse when the disk and heated star should be entirely obscured (Anderson etal. 1994). The source of this emission may be an expanding wind.The Goddard High Resolution Spectrograph (GHRS) on
HST first resolved these emis-sion lines at ≈
35 km s − resolution (Boroson et al., 1996) to discern variable broad andnarrow emission components.The HST
Space Telescope Imaging Spectrograph (STIS) confirmed that the resonancelines have at least two components (Vrtilek et al. 2001). A broad component arises on theaccretion disk while a narrow line component may be associated with HZ Her. Prior tothe STIS observations, the accretion disk had only been observed as it contributed to thecontinuum light curve or obscured the central X-rays. During eclipse ingress and egress, thebroad lines seen with STIS behaved as expected for lines from an accretion disk rotatingprograde with the orbital direction. The blue edge of the line was obscured first in eclipseingress and appeared first in egress.Observations with the Far Ultraviolet Spectroscopic Explorer (
FUSE ) are complemen-tary to the existing
HST observations. Long-term variability in the system makes it impos-sible to combine rigorously data from different epochs. Analyzed separately, however, the
FUSE wavelength range of 900-1200˚A offers similar advantages and powerful consistencychecks to analysis of the
HST bandpass of 1200-1700˚A. Both wavelength ranges have strongresonance lines that respond to X-ray photoionization. Observations with the Hopkins Ul-traviolet Telescope (
HUT ) showed that the O vi doublet has flux comparable to the N v doublet, the brightest near UV line (Boroson et al. 1997).The resonance line doublets offer optical depth information through their doublet ra-tios, but if the lines are as broad as the doublet separation, it may be impossible todetermine the individual contribution of each line where they overlap. The separationsof C iv λλ , iv λλλ , v λλ . vi λλ , vi λλ , − , respectively. The far UVlines O vi and S vi compare favorably with the near UV lines (i.e. have greater separation 5 –and are less likely to overlap), except for Si iv , which suffers from confusion with an O iv blend near 1400˚A.For the present observations, we observed an entire 1.7 day binary orbit with FUSE . Amajor goal of this program was to apply the method of Doppler tomography ( §
2. FUSE Observations
With
FUSE (the Far Ultraviolet Spectroscopic Explorer) we extend observations in theUV spectral range to 900-1190˚A, a range observed only once before using
HUT , the HopkinsUltraviolet Telescope aboard the ASTRO-1, carried aboard the Space Shuttle but not placedin orbit (Boroson et al. 1997). While
HUT had a resolution of ≈ FUSE has a resolutionof ≈ . FUSE is a NASA
Origins mission operated by The Johns Hopkins University. Fouraligned telescopes feed two identical far-UV spectrographs. With resolution R= 20000 FUSEapproaches
HST in its utility for our program; the time coverage of the
HST
Space TelescopeImaging Spectrograph (STIS) was limited because the detectors were turned off when thespacecraft passed through the South Atlantic Anomaly. The FUSE mission is described inmore detail in Moos et al. (2000) and its on-orbit performance is described in Sahnow et.al. (2000).Our
FUSE observations began on June 9, 2001 at 7:47 UT. Table 2 shows the log ofexposures, each of which is integrated over each
FUSE orbit of the Earth, with gaps whenHer X-1 goes below the horizon. We use the orbital ephemeris of Deeter et al. (1991) todetermine the orbital phases of our observation. The exposure times listed in Table 2 arein most cases equal to the raw observation time. However, for cases such as observation13, interrupted by a passage through the South Atlantic Anomaly and not occultation bythe Earth, the Exptime listed is in general the minimum good exposure time for any
FUSE detector. The data were obtained through the LWRS aperature and in TIMETAG mode.We used the CalFUSE pipeline software version 3.0.8 to extract and calibrate the datafrom all four
FUSE telescopes. Below 1100˚A, where emission features are sharp, we addedan offset to each wavelength scale, in intervals of 0.025˚A, so that the absorption and emission 6 –features from each detector best agreed. We tested our wavelength calibration against theinterstellar Si ii λ . −
30 km s − . The standard deviation of the centroid of this line from orbit toorbit was ≈ . <
10 km s − .The S/N of the data was ≈ < ≈
10 near 1100˚A. The S/N within the O vi line had greater variation with orbital phase,as the doublet changed both in shape and in strength. At φ = 0 .
75, the peak S/N withinthe doublet was ≈
15 per 0.1˚A pixel, while at φ = 0 .
5, the peak S/N was ≈
25 per pixel.For further analysis, we skip the region between 1120–1160˚A in the 1B LiF detector.This region suffers from a systematic decrease in counts known as the worm..In Figures 1 and 2, we show average observed FUSE spectra at orbital phases when theemission is dominated by the disk and star, respectively. For the disk-dominated spectrum,we use observation number 20, at φ = 0 . φ = 0 . − − . FUSE spectra at orbital phases dominated by disk emission, we compare with theSTIS spectrum (observation root name O4V401010) during a Short-On state at φ = 0 . φ = 0 . § i Lyman- γ i i Lyman- β +O i i
3. Interstellar Lines
Interstellar features in the
FUSE spectra are interesting not only for the direct infor-mation they provide on the interstellar medium (ISM), but a proper accounting of thesefeatures can remove systematic errors from the analysis of the line and continuum emissionfrom the system itself.The neutral Hydrogen column density, N H , has previously been determined to be ≈ cm − (Boroson et al. 2000) from the wings of the saturated Lyman α line as observedwith the HST
STIS. The
FUSE bandpass includes further saturated lines in the Lymanseries, and these are consistent with N H ≈ cm − . This N H is also consistent with theE(B-V) value of 0.018 according to the Bohlin (1975) relation.From the galactic latitude of 37.52 ◦ we should expect a sightline with less H and H than typically seen through the galactic disk. Indeed, while absorption lines from rotationallevels J = 0 through J = 3 are readily identified, they are not saturated. Thus the levelpopulations should be easy to measure and it should be easy to compensate for the effectsof the absorption lines on the spectra.In Figure 3, we show a patch of the time-averaged FUSE spectrum, with the absorptionprofiles expected from source with a flat spectrum absorbed by columns of (2.8, 7.5, 4.1,3.4) × cm − for absorption from rotational levels J = 0 , , ,
3, respectively. We generatethe H profiles from the templates of McCandliss (2003), which are based on Abgrall et al.(1993a,b). We have assumed a line velocity parameter b = 10 km s − and have convolvedthe profiles with a Gaussian to simulate the FUSE
Line Spread Function.The two lowest rotational energy levels should have populations given by a Boltzmannfactor, taking into account the statistical weights of the two levels, g /g = 9. The energydifference between the levels is ∆ E = 170 . gas is T = 140 K. This is hotter than found for H gas from disk stars,consistent with the high galactic latitude of the line of sight (Gillmon, Shull, Tumlinson, &Danforth 2006).The average molecular fraction, defined by f H2 = 2N(H )N(H I) + 2N(H2) (1)is therefore > ∼ × − from the observed H lines, which have N(H ) ≈ × cm − . Ratiosof higher rotational levels than J /J are determined not by temperature and collisionalexcitation but by background FUV radiation. The H2 column density observed for Her X-1places it just above the boundary at which H2 clouds start to become optically thick to theFUV radiation. Gillmon et al. (2006) state that f H2 ≈ − is a typical molecular fractionbelow this boundary.Thus the first four levels of rotational excitation of H appear to match observed ab-sorption features and to be caused by H clouds that are not out of the ordinary. 8 –
4. Photometry of Emission Lines
The lines vary with the binary orbit in a manner similar to that previously observed inthe near UV with
HST . The flux peaks generally near φ = 0 .
5, when the X-ray heated faceof HZ Her points toward the observer, although there may be a dip very close to φ = 0 . vi λ .
4, S vi λ .
5, C iii λ iii λ vi λ .
9, O vi λ . iv λ v λ iii λ §
5. For the N iii line, we remove the flux of nearby airglow lines.In Table 3, we show the cross-correlation coefficients between the measured lightcurvesof the spectral lines and the lightcurves of the disk and star contributions to the continuumlightcurve, as determined by our continuum model.
5. UV Continuum Fits
The UV continuum varies, as the optical continuum does, with the 1.7 day orbitalperiod. The continuum generally peaks near φ = 0 .
5, when the X-ray heated face of theRoche lobe points towards the viewer, but a portion of the normal star may be blocked bythe accretion disk, and depending on long-term phase, the actual peak may occur within φ ± ∆ φ ≈ . ± . FUSE , we assume that X-ray heating of HZ Herand the accretion disk cause the entirety of continuum emission. The details of our simu-lation are similar to those of Vrtilek et al. (1990, especially the appendix), and Howarth &Wilson (1983a) (which was an elaboration on an earlier analysis of Gerend & Boynton, 1976),and binary simulation codes by Wilson & Devinney (1971). The method is summarized inAppendix A.We fit the spectrum using a reddening E ( B − V ) = 0 .
018 and for the extinction curve,we use Equation 5 in Cardelli, Clayton, & Mathis (1989).We also use a more modern determination of the distance to Her X-1 (Reynolds et al. 9 –1997). This greater distance requires a larger ˙ M to reach the same continuum flux. Thusthe scale of our ˙ M values are large compared with those reported earlier from IUE and
HST observations. The
IUE observations found a range of − log ˙ M = 8 .
30 to 8 .
68 (givenchanges in the long-term phase during an anomalous low state), whereas the
HST found − log ˙ M = 8 . ± . FUSE spectrum from each
FUSE obser-vation, we find a range of − log ˙ M = 8 .
12 to 8.38.For our fits we ignore wavelength regions that contain prominent emission or absorptionlines. We correct for absorption from the first 4 rotational energy levels of interstellar H bymultiplying the spectrum by the model presented in § M , which we allow to varyas a free parameter for each FUSE orbit. We also list the reduced χ .We have used our continuum fits to examine the continuum photometry. The modelallows us to separate the continuum emission into contributions from the heated face ofHZ Her and from the accretion disk. In Figure 5 we show the model flux near the O vi linessplit into disk and stellar components.
6. Eclipse Models
We made a simple model for emission from a symmetric precessing accretion disk un-dergoing eclipse by the Roche lobe of its companion. We then allowed free parameters ofthat model to vary in order to fit the observed O vi profiles during eclipse ingress and egress.The disk and Roche lobe geometry are based on the model of Howarth & Wilson (1983a),while the formation of the emission lines follows the model of Horne (1995), and is describedin Appendix B. We allow as free parameters the exponent of a radial power law of opticaldepth and elements of the Mach turbulence matrix. We allow the normalization of the lineflux at each orbital phase to vary as a free parameter.We calculate the eclipsing edge of the Roche lobe of HZ Her assuming corotation withthe orbit.Before fitting the model to the data, we subtracted the mid-eclipse spectrum from allspectra. The origin of the UV mid-eclipse spectra was explored by Anderson et al. (1994)who concluded that it probably does not arise in the accretion disk. The mid-eclipse O vi lines are broad, extending from -200 to +500 km s − heliocentric velocity. 10 –We also apply narrow gaussian absorption lines to our model spectra in order to simulatea possible C ii interstellar line near 1036˚A, a possible C ii ∗ line near 1037˚A, and a O i linenear 1039˚A. We also include narrow interstellar absorption near the rest wavelengths ofthe O vi doublet. A narrow absorption line can be seen near the blue component of thedoublet at λ = 1031 . × cm, following Cheng et al. (1995).The results are shown in Figure 6.The reduced χ of the fit was 2.8 with 1418 degrees of freedom.The power law index for the radial dependence on optical depth was α = − .
2, betweenthe α = − . v doublet by similar methods in Boroson et al. (2000)and the ≈ − .
55 value expected from the simulations of Raymond (1993).Although we based our fits on the model of Horne (1995) which allows for anisotropicturbulence, the fits do not unambiguously settle on particular values of the Mach matrix.Here, for simplicity, we present a model with isotropic Mach=1 turbulence.As with the resonance doublets in the near UV, the observed blue component of O vi near eclipse is stronger than the red component, which suggests that much of the line fluxis formed where τ < ∼
1. However, the doublet ratio is uncertain because strong interstellarC ii and O i absorption lines affect only the red O vi doublet component. Weaker interstellarlines, which we have not modeled, may be present as well, and may preferentially absorb oneor the other O vi component.The model lines are double-peaked outside of eclipse, but one peak of the red componentis absorbed by interstellar O i absorption. The observed line profiles are double-peaked at φ = 0 .
84 and double-peaked but broader at φ = 0 .
80. Observations at φ = 0 .
35 and φ = 0 . M impossible. In particular, we have considered the diskflat when it is probably warped, we have not calculated the ionization structure of the disk, 11 –we have ignored possible emission by the accretion stream, and we have ignored the role ofwinds in this system.Chiang (2001) presented models of accretion disk eclipse in Her X-1 that considereda disk wind. These models were motivated by the lack of double-peaked line profiles inany observations of UV resonance lines. Although the current model predicts double-peakedemission lines when the full disk is visible, the S/N is not strong enough to rule out a double-peaked structure. In addition, interstellar absorption lines coincide with three of the fourpeaks of the O vi doublet.It is clear that a model of a partially eclipsed accretion disk with parameters consideredstandard from previous work provides an excellent match to this data set. There appear tobe too many ways to improve the current fit to justify singling one out. φ = 0 . φ = 0 .
876 is particularly poor and we suggest that a process in addition tothe partial eclipse of a Keplerian accretion disk affects the line profile.Figure 6 shows that even though more of the disk is eclipsed than at φ = 0 . φ = 0 .
876 are actually stronger. There also appears to be an additionalabsorption component near the rest wavelength of O vi λ φ = 0 .
876 has not increased over the continuum at φ = 0 .
835 as muchas the line emission has increased. This is consistent with the earlier result that the X-rayillumination from our line and continuum models at other phases were not correlated.
7. Doppler Tomography
The Doppler tomography method, developed by Marsh and Horne (Marsh & Horne,1988, Marsh 2005) takes as input an emission line which is broadened by line of sight motion.The line must be observed over a good sampling of the binary orbit. In analogy with medicaltomography, a successful Doppler tomogram builds a higher-dimensional view of the objectfrom different observational slices.Analysis of Doppler shifted emission lines is prone to the confusion of different gassources which have been projected onto the same observed velocity. The tomographic methodpresents a transform of the same data into features separated not only by projected velocity,but also by orbital variability. 12 –The output tomogram is not a physical image of an accretion disk, but rather an image in“projected velocity space.” A component of the emission that varies sinusoidally in velocity(but remains constant in flux) is placed at a point in velocity space along a circle with aradius equal to the orbital velocity of that emission component. The phase of the sinusoiddetermines its position along that circle.The method assumes that all of the variation in a spectral line must be caused by theorbit changing the projection of the motion into the line of sight. (For example, the changein a spectrum must not be caused by a bright spot being obscured by an opaque object.)Even outside of the conditions in which it strictly applies, however, tomographic images canprovide a common view of the data and may suggest directions for further analysis.Technically, a Doppler tomogram is an inversion of f ( v, φ ) = (cid:90) ∞−∞ (cid:90) ∞−∞ I ( v x , v y ) g ( v − v R ) d v x d v y (2)which gives the flux F ( v, φ ) at the projected velocity v and the orbital phase φ as asummation of the velocity space tomogram I ( v x , v y ) with a line broadening function g ( V − V R ) which is usually narrow. This integral is an instance of a Radon transform. Theline broadening function for our FUSE spectra is approximately 0.05˚Aand for tomographicanalysis we assume it is a delta function.The relation between the radial velocity and the two axes of the Doppler tomogram, v x and v y is given by v R = γ − v x cos 2 πφ + v y sin 2 πφ (3)where γ is the systemic velocity of the system.The formation of the spectrum from the tomogram can be thought of as follows. Thephase φ determines a direction in the velocity space plane, and moving along that line,summing the intensity perpendicular to the line, one ideally forms the spectral line. At φ = 0 .
25, one views from the right in our figures, at φ = 0 . φ = 0 .
75 one views from the left.In this paper, we determine I ( v x , v y ) from F ( v, φ ) by means of Fourier-Filtered BackProjection, which inverts Equation 2 through I ( v x , v y ) = (cid:90) ¯ f ( γ − v x cos 2 πφ + v y sin 2 πφ, φ ) d φ (4) 13 –where to calculate ¯ f ( v, φ ) from f ( v, φ ), one takes its Fourier transform, multiplies by a rampfilter and a Wiener (optimal) filter based on the noise level, and then takes the inverse Fouriertransform.Although it may seem as if this filtering complicates the method of back-projection, aramp filter (multiplying the Fourier transform by the frequency) is required in order for backprojection to produce a rigorous inversion of Equation 2. Otherwise, back projection wouldonly produce a smeared version of the true tomogram.Unfortunately, using a ramp filter also magnifies pixel to pixel noise. We apply astandard Wiener filter that assumes a signal amid a noise component that is constant withfrequency. We find the power spectrum of the line spectra is well fit by several componentsof the form P ( ω ) = P exp( − kω ) (with k > ω , where the power spectrum is fit well by a constant noise level n . Theaction of the Wiener filter is then to multiply the power spectrum by P ( ω ) / ( n + P ( ω ), whichis nearly 1 when the signal dominates the noise and negligible at high frequencies where thespectrum is almost entirely noise. We used the same form of P ( ω ) for each line at eachorbital phase, and made a visual comparison between the actual power spectrum and thefunction P ( ω ). Because the filter adapts to different noise levels, the amount of smoothingvaries from line to line. For the lines with highest S/N, such as O vi λ vi λ In Figures 7–14 we show Doppler tomograms of the emission lines of S vi at 933 and944˚A, N iii λ vi at 1031˚A and 1037˚A, P v λ iv λ iii λ iii λ
977 is not shown as it is contaminated by the presence of saturated absorption.We have interpolated between orbital phases for the integration, which we perform between φ = 0 . φ = 0 .
85. The grayscale of the tomograms extends linearly from the minimumto the maximum.To understand the C iii multiplet, we consult
CHIANTI , a software package and atomicdatabase described in Dere et al. 1997 and Landi et al. 2006. The database, used extensivelyby stellar and solar astrophysicists, contains energy levels, wavelengths, radiative transition 14 –probabilities, and excitation data for many ions. The associated software package, writ-ten in IDL (Interactive Data Language), can be used to examine how line ratios vary withtemperature and density, subject to certain limiting assumptions. We find that C iii con-tains emission components at 0 , , , , − g ( V − V R )in Equation 2. We tried Gaussians of equal weight at velocities (0 , +168 , +367) km s − (Figure 14) and find there is a single bright spot near the Roche lobe.A further problem with the C iii multiplet is that the model of the continuum in thisregion predicts an absorption dip. To reduce artifacts, we use the simpler and smootherKurucz model atmospheres, with 1˚A resolution for all of the tomograms, instead of themodels based on actual stellar spectra observed with FUSE , which we have computed with0.1˚A resolution and which include some counting statistics noise.The signal in the tomograms, except as noted above, is concentrated in a peak offsetfrom the Roche lobe of HZ Her. The traditional signature of an accretion disk is not obviouslypresent. Accretion disks are expected to cause broad line emission that appears as a ring ina tomogram, with diminished flux within the velocity at the edge of the accretion disk, orabout 300 km s − for Hercules X-1. If the disk emission is symmetric, we expect it to becentered on the position of the neutron star in velocity space, ( vx, vy ) = (0 , − There is a simple interpretation of the tomograms in terms of P Cygni lines commonlyseen in stellar winds from massive stars (and in
HST spectra of Her X-1, Boroson, Kallman,& Vrtilek 2001). P Cygni lines, caused by resonance scattering, are characterized by red-shifted emission and absorption blue-shifted by velocities common in the wind. There is ahint of blue-shifted absorption in the trailed spectrograms at φ = 0 . − .
6, although theremay be an interstellar absorption line as well at these wavelengths and the gap between thepeaks of the accretion disk spectrum could also appear to be absorption.We note that for many tomograms in addition to the bright spot at ( vx, vy ) ≈ (150 , − vx, vy ) ≈ ( − , vi λ vi absorption.) Near the start ofthe phase range used by our tomograms, at φ ≈ .
3, the observer’s line of sight comes fromthe lower right in Figure 7. As the line of sight passes through both bright and dark spots,the observer at φ ≈ . φ ≈ . − .
6, the viewer looks at the system from the bottom of the plot, stack-ing pixels vertically. The result is red-shifted emission (the bright spot) and blue-shiftedabsorption (the dark spot).Although the blue-shifted absorption at φ = 0 . − . vi (bold), the spectrum expectedif the illuminated surface of HZ Her emits O vi Doppler shifted by the local rotationalvelocity (dashed), and an empirical Gaussian model of the emission lines. The Dopplershifts predicted from the rotation of the surface of HZ Her are less than observed in thenarrow emission lines.To model the narrow O vi emission lines we adapt our model of the continuum emission.This model takes into account the X-ray shadow cast by the disk and the eclipse of portionsof the normal star by the disk. The reprocessed O vi emission is proportional to the incidentX-ray flux. We also experimented with a model in which the X-ray illumination was non-isotropic, illuminating HZ Her with greater luminosity at φ = 0 .
25 than at φ = 0 .
75. Thismodel still does not account for the observed velocities.We also made an empirical model of the lines as Gaussians. The flux in the Gaussianline emission at each phase was proportional to the flux in the stellar component of ourcontinuum model using Kurucz model spectra. The central velocity in this model variessinusoidally with phase. We added Gaussian absorption to correspond to features seen in
HST
STIS spectra of the N v λ iv λ iv λ φ = 0 . − . φ = 0 .
5, but delayed by φ = 0 .
06, corresponding to a deflection of a windby the Coriolis effect. The absorption line has maximum covering fraction near φ = 0 . φ = 0. (Any wind is probably confined to the cylinder fromthe star towards the disk, as the emission lines seen in mid-eclipse are only ∼
1% of thepeak line strength, as observed with the
HST
FOS by Anderson et al. 1994). Both emissionand absorption components have constant width. Both emission and absorption componentsvary about a central velocity given by the L1 point.When these features are added to the model of the disk spectrum in §
6, assumed tomove with the neutron star’s 169 km s − orbit, and random counting statistics noise is added,the resulting tomogram (Figure 16) resembles the observed tomogram, while showing onlya hint of the presence of an accretion disk. Without the assumed phase delay of ∆ φ = 0 . vy = 0.
8. Line Ratio Diagnostics
The
FUSE spectra show emission lines that may serve as diagnostics of density, tem-perature, or optical depth. iii line diagnostics
The simultaneous measurement of C iii λ
977 and C iii λ iii n e = 10 cm − . At higher densities (up to n e ∼ ), the populations of the groundand metastable levels are entirely determined by collisions. In that regime, the 1176/977ratio depends only on temperature and the optical depths in the lines.We ignored flux from the FUSE
LiF2B detector near the C iii λ
977 line, even thoughthis detector recorded flux down to exactly 977˚A. The edge of the detector causes the fluxmeasured in this region was significantly lower than the other two detectors, so that includingthis data would have created an artificial dip at wavelengths λ > iii λ
977 are lower limits because of a saturated interstellarabsorption line at the rest wavelength. We correct the fluxes for interstellar reddening usingE(B-V)=0.018.We compare the fluxes of the two lines near φ = 0 .
6, when the fluxes peak. If theC iii λ
977 line behaves similarly to the O vi lines, then the bright narrow emission will, nearthis phase, have the greatest redshift. If so, the line may be redshifted away from theinterstellar absorption and the flux measurement may be more accurate near this phase. If 17 –the O vi λ iii λ
977 line,the flux at φ = 0 . ∼ iii λ
977 flux from the two phases surrounding φ = 0 . ± × − erg s − cm − , then we find a 1175/977 ratio of 0 . ± .
16. If we measurethe C iii λ
977 flux at exactly the peak at φ = 0 . ± . CHIANTI software, which usesatomic data from the
CHIANTI database and computes line ratios, given certain simplifyingassumptions (for example, the lines are optically thin and the gas is collisionally ionized andnot photoionized). If we consider a density of n e = 10 . cm − , the lower ratio found abovewould restrict the temperature to T > × K.The ratio is rendered uncertain observationally by the saturated interstellar absorptionline, and theoretically because of optical depth effects. Raymond (1993) presented models ofline emission from an X-ray illuminated accretion disk which took into account optical depththrough an escape probability formalism. One version of the model, “COS”, assumed cosmicabundances while the other, “CNO”, assumed that abundances had been altered by CNOprocessing. The CNO models should be more appropriate for Her X-1. In the two cases the I (1176) /I (977) ratios were 1.3 and 1.1, respectively. The observed emission at φ = 0 . iii λ emission The Bowen Fluorescence process (Schachter et al., 1989) arises because of the nearlyperfect coincidence of the He ii Ly α and the O iii – 2p3d resonance line ( λ iii near–UV primary cascades at λλ λ
374 backto the ground state. If conditions are right, an additional fluorescence occurs, since theO
III λ
374 line is almost coincident with the two N
III
2p – 3d resonance lines, resulting inN III optical primary cascades at λ ∼ ) in theHe II Ly α and O III λ pumping lines, because otherwise they will simply escape withoutconversion to a Bowen line.In the Sun, Raymond (1978) discovered O III λ
304 Bowen emission. It was found thatmeasurements of O
III λ ground-state Bowen cascade which, therefore, can also beproduced by collisional excitation, can serve as a density diagnostic, and compared favorably 18 –with other solar estimates of n e .We may use N iii λ III primary cascades (“ λ III and N
III ground-state cascades liebelow the Lyman limit and hence are unobservable).The intensity of N iii λ
990 resulting from Bowen fluorescence is related to the intensityof the Bowen lines at 4640˚Aby I f (991) = (4640 / B (3p2p) I (4640) (5)where B (3p2p) is the branching ratio of 2p-2s p
2D versus 3p-3s. From CHIANTI, we take B (3p2p) = 0 .
55 and B (3d3p) = 0 . I c (991) = I (991) − I f (991).Taking into account the reddening toward Her X-1 implied by E(B-V)=0.018, we find apeak flux in the 991˚A line of 8 . ± . × − erg s − cm − . Non-simultaneous measurementsof the optical λ . ± . × − erg s − cm − (Still et al. 1997). The optical flux varies from orbit to orbit, and, moreover,probably includes contributions from C iii as well as N iii .These values imply that 20% of the N iii λ
991 line flux is the result of the Bowen fluo-rescence mechanism.We attempt to relate the density to the Bowen flux by I c (991) I f (991) = 4 (6)= n e N (N iii ) qB (3d3p) B (3p2p) N (N iii ) σI (374)= 4 . × n e /I (374)with N (N iii ) the density of N iii and q = 6 × − s − the excitation rate of the 991˚Atransition at T=30,000 K.We estimate an upper bound on the O iii λ
374 intensity (the line may be optically thick)from the O iii λ HST by Andersonet al. (1994). We account for the other O iii branches leading to the λ
374 line by using theobserved O iii
Bowen spectrum of RR Tel (Selvelli, Danziger, & Bonifacio 2007). We thenestimate I (374) < ∼ . D/R ) , with D = 6 . R theradius of the emitting region. Boroson et al. (2000) found log n e = 13 . ± . HST , and Howarth & Wilson (1983b) foundlog n e = 13 . IUE observations. Combining with Equation 6, we find
R < ∼ × cm.This is smaller than the size of the accretion disk ( R outer ≈ × cm). We note thatthe tomograms show emission from a small region in velocity space.Another test is provided by a comparison with theoretical models of N iii λ
991 emis-sion in the absence of the Bowen process. Raymond (1993) found ratios between the N iii line and C iii λ
977 for the COS model of I (991) /I (977) = 0 .
34 and for the CNO model of I (991) /I (977) = 0 .
53. The observed ratio of 0 . ± .
10 requires enhancement by Bowenfluorescence and provides an excellent match to the CNO model if only 70% of the N iii λ
9. Discussion
The far UV spectrum of Hercules X-1 shows clear evidence for a Keplerian accretiondisk. A simple model such a disk can fit the broad O vi emission lines near eclipse. Theorigin of brighter, narrow emission lines is still unknown. Doppler tomograms place thisemission apart from the Roche lobe of HZ Her.The bright narrow emission component generally follows the flux expected from theilluminated portion of the normal star. However, it appears brighter than expected at φ = 0 . φ = 0 . φ = 0 .
25 and φ = 0 .
75. Although such a model can bemade to reproduce the gross features of the line variation, there remain too many possiblealternate explanations for this to be convincing. There could be a source of variable emission,absorption, or scattering in addition to the normal star, for example, the gas stream or thesurface of the disk.In the presence of stellar winds, possibly transient or restricted in solid angle, tomogra-phy did not show a clear signature of an accretion disk in Hercules X-1.Although we found that a simple model of an accretion disk generally fit the spectraduring eclipse ingress and egress, there was an anomalous observation in which the O vi linesbrightened as the disk eclipse progressed. The phase φ = 0 .
876 is in the φ = 0 . − . absorption within the N v λλ , Constellation X may be able to resolve linesfrom more highly ionized species than the UV and Far UV resonance lines (Vrtilek et al.2004). If more highly ionized species track disk material better and are not as prevalent inthe narrow line region, we may be able to make reliable tomograms of the disk in this orsimilar systems. Hydrodynamic models of this system may be required to cut down on thevast parameter space of possible gas flows responsible for the spectral signatures observedhere.We would like to thank Jeff Bryant for helping us develop some
Mathematica routines forDoppler tomography. CHIANTI is a collaborative project involving the NRL (USA), RAL(UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and GeorgeMason University (USA). We would like to thank the anonymous referee for suggestionsthat improved the text and presentation, for pointing us to the S vi λλ ,
944 lines, andprompting us to analyze the interstellar molecular absorption lines.
A. Details of the Model of the Her X-1 Continuum
With one free parameter, the mass accretion rate ˙ M , we model the continuum emissionfrom the accretion disk and X-ray illuminated face of the normal star. We do this notby means of radiative transfer calculations, but by calculating the heated temperatures ofboth surfaces, and co-adding spectra appropriate for those temperatures, either blackbodyspectra, models of stellar spectra, or actual spectra of hot stars observed with FUSE .Our model of the far UV continuum emission of Her X-1 follows closely the methods ofVrtilek et al. (1990) and Cheng, Vrtilek, & Raymond (1995). We describe the method herein detail, including the minor departures we have made to extend the spectral simulation tothe far UV.The model of the accretion disk temperature as a function of radius, T ( r ), includesthe effects of both internal heating due to viscous forces and heating from X-rays from theneutron star.When we calculate the disk temperature as a function of radius, T ( r ), we include both 21 –the heat from viscous forces and X-rays from the neutron star. The local energy generatedby accretion is given by σT ( r ) = 3 GM ˙ M πr (cid:32) − (cid:114) Rr (cid:33) (A1)for Stefan-Boltzmann constant σ , neutron star mass M and radius R , and disk mass accretionrate ˙ M (Shakura & Sunyaev 1973).For local energy balance, the energy emitted must equal the energy generated plus theX-ray energy absorbed: σT ( r ) = σT ( r ) + aL x πr ∂ ( h/r ) ∂r (A2)where we choose the albedo a = 0 .
5, and the disk height at radius r is h ( r ). The X-rayluminosity is related to the gravitational potential released by accreting matter: L x = 0 . GM ˙ MR (A3)These equations, together with vertical hydrostatic equilibrium, can be solved numer-ically to determine T ( r ). The surface of the noncollapsed star is also assumed to have analbedo a = 0 . T ( r ) is compared with thecritical disk temperature, T dc . If T ( r ) > T dc , then we assume that the disk region radiateslike a blackbody. If T ( r ) < T dc , then we interpolate through our library of actual stellarspectra to find a spectrum appropriate for temperature T ( r ). From experience fitting HST
FOS spectra and fitting the Balmer jump, we fix T dc = 10000 K so that in practice thedisk almost always has blackbody spectra, except at its edge where it is not illuminated byX-rays.The stellar library from 1150 to 7500˚A is described in Cannizzo & Kenyon (1987). Thenear UV spectra were obtained with IUE and are described in Wu et al. (1982). All thespectra are normalized to have constant flux in the V bandpass and are then scaled to theirabsolute magnitudes using their V-R colors and the Barnes-Evans relation (Barnes, Evans,& Moffett 1978).For this paper, we have extended the library of stellar spectra further into the UV byusing
FUSE spectra of main sequence stars between O 9.5 and A 7. These observations aredescribed briefly in Table 5. Stars of temperature greater than T sc = 18 ,
900 K are not usedin the fits to Her X-1 and are not included in the table. We have interpolated over thosewavelengths we expect are affected by interstellar atomic or molecular absorption, and wehave applied a filter designed to smooth interstellar lines while retaining stellar features. We 22 –de-reddened each spectrum and scaled the flux according to the star’s visual magnitude V.We have tested the method and the use of these stellar spectra by using model stellar spectraas predicted by Kurucz (1979). Plots of far UV spectra in our library, normalized to have aconstant V magnitude, are shown in Figure 17.For the purpose of computing the disk shadow, the disk is assumed to have a fixedopening angle and a fixed tilt from the orbital inclination, although the direction of the disknormal precesses with the X-ray cycle in a manner described by Gerend & Boynton (1976)and Howarth & Wilson (1983a). Because of the finite disk opening angle, the outer regionsof the disk can occult the inner regions, and the disk edge itself can radiate, although it isnot illuminated by the central X-rays.The noncollapsed star is assumed to fill its Roche lobe, and its shape, visibility, andillumination by the X-ray source are treated according to methods evolved from Wilson &Devinney (1971) to Howarth & Wilson (1983a). Following those references, we model theeclipse of the disk using the Roche potential. We take into account both limb darkening andthe gravity-darkening appropriate for a late-type star. If the temperature of some region onthe surface of the star, after X-ray illumination, is greater than some critical temperature T sc ,we assume the region emits as a blackbody. If the local temperature is less than T sc , we againinterpolate through our stellar library to find the appropriate stellar spectrum with whichthe spot radiates. From earlier experience fitting Her X-1 UV spectra, we fix T sc = 18900(Cheng, Vrtilek, & Raymond 1995).The model, as currently realized, does not account for emission or shadowing by a gasstream between the noncollapsed star and disk. B. Details of the Model of the Disk Lines in Eclipse
Accretion disks in theory have emission lines with a double-peaked shape, with peaksseparated by a velocity given approximately by the projection into the line of sight of theorbital velocity at the edge of the accretion disk. For Hercules X-1, with typical neutronstar mass, an nearly edge-on inclination, and an outer disk radius of R ≈ × cm, weexpect the peaks to occur at ±
300 km s − . While greater velocities are found within theouter disk radius, each ring at a fixed radius emits down to a Doppler velocity of 0 wherethe gas moves tangential to the line of sight. Regions of high Doppler velocity arise fromprogressively smaller regions in the disk, and contribute less to the overall line shape.We have calculated detailed models of emission from an accretion disk and have fit theseto the profiles observed in Her X-1 during eclipse ingress and egress. In reality, the disk is 23 –likely to be warped, and in future work we will test individual models of this warped shape.The importance of the demonstration in this paper is that it shows how easy it is to getgeneral agreement with the observed line profiles given the standard picture of the accretiondisk.The method in detail follows that of Horne (1995), which allows for nonisotropic turbu-lence and for Keplerian shear, that is, the local dispersion in disk velocity as a result of theKeplerian flow itself. This introduces free parameters for the “Mach matrix” describing theturbulent flow, in addition to the power law exponent that we use to as a phenomenologicaldescription the strength of the emission line as a function of radius in the disk. For simplicity,we keep the elements of the Mach matrix constant with radius in the disk.Following Horne (1995), the local line profile is given by I ν ∝ (1 − e − τ ν ) (B1)where the optical depth τ ν at frequency ν is given by τ ν = τ e ( V − V ) / V (B2)for a given line center optical depth τ .The nonisotropic turbulence and shear enter through ∆ V , given by∆ V = ∆ V + ∆ V + ∆ V (B3)or ∆ V /C s = µγA + ( Q sin i tan i sin 2 θ ) + sin i ( M RR cos θ − M Rθ cos θ sin θ (B4)+ M θθ sin θ ) + 2 sin i cos i ( M ZR cos θ − M Zθ sin θ ) + cos iM ZZ (B5)where i is the orbital inclination, µ is the mean molecular weight, γ = 5 /
3, and A is theatomic weight. The shear parameter Q is given by Q = 34 HR V
Kep C s ∆ Z H (B6)and, for simplicity, is set to 3 /
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This preprint was prepared with the AAS L A TEX macros v5.2.
27 –Symbol Adopted value Meaning Reference q M ns (cid:12) ) R inner Inner radius of accretion disk (cm) Cheng, Vrtilek, & Raymond 1995 R outer × Outer radius of accretion disk (cm) CVR a D B − V ∗ . θ d α d a ∗ × Orbital separation, centers of mass (cm) H&W i vi (double-peak gap?)B0080101006 52069.67566 52069.71106 0.387799 2800 Dip in O vi B0080101007 52069.74947 52069.78043 0.429904 2675B0080101008 52069.82233 52069.84980 0.471734 2374B0080101009 52069.89492 52069.91917 0.513482 2095B0080101010 52069.96775 52069.98854 0.555305 1796B0080101011 52070.04000 52070.05792 0.596954 1548B0080101012 52070.11058 52070.12730 0.638113 1442B0080101013 52070.15631 52070.16500 0.662651 644B0080101014 52070.18235 52070.19666 0.679620 1231B0080101015 52070.22613 52070.26604 0.712899 3447B0080101016 52070.29521 52070.33540 0.753612 3472B0080101017 52070.36448 52070.40475 0.794380 3479 O vi λ vi λ FUSE
Her X-1 observations. 29 –Exposure Orbital Phase Duration (s) ˙ M (Kurucz) χ (Kurucz) ˙ M ( FUSE ) χ ν ( FUSE )( − log M (cid:12) ) ( − log M (cid:12) )1 0.182 3418 8.04 2.7 8.06 2.72 0.223 3498 8.07 2.9 8.10 3.03 0.264 3501 8.09 3.1 8.19 3.24 0.305 3497 8.16 2.9 8.26 3.05 0.346 3486 8.21 2.7 8.32 2.96 0.388 3059 8.24 2.5 8.33 2.77 0.430 2675 8.29 2.4 8.38 2.88 0.472 2374 8.20 2.3 8.30 2.59 0.513 2095 8.07 2.6 8.18 2.710 0.555 1796 8.08 2.4 8.17 2.711 0.597 1548 8.13 2.5 8.21 2.612 0.638 1444 8.20 2.2 8.27 2.313 0.663 751 8.22 1.2 8.30 1.314 0.680 1236 8.19 1.6 8.27 1.615 0.713 3448 8.17 2.5 8.27 2.616 0.754 3473 8.20 2.5 8.22 2.617 0.794 3480 8.18 2.3 8.19 2.318 0.835 3478 8.22 2.2 8.22 2.219 0.876 3469 8.17 2.2 8.18 2.220 0.917 3472 8.29 1.7 8.28 1.721 0.958 3204 NA NA NA NA22 0.001 2826 NA NA NA NA23 0.042 2503 NA NA NA NA24 0.084 2000 8.10 1.7 8.12 1.7Table 3: Fits to the Her X-1 continuum as observed with FUSE . ˙ M (Kurucz) and χ (Kurucz)give the mass accretion rate and goodness of fit parameter for the model fit that uses Kuruczspectra while ˙ M (FUSE) and χ (FUSE) give those parameters for fits using a library of FUSE spectra. 30 –Ion Wavelength (˚A) r star r disk r continuum CommentsS vi vi iii
977 0.90 0.45 0.76 Affected by strong ISM lineN iii
992 0.80 0.62 0.91 Near strong airglow linesO vi vi iv v iii § eff (K) FUSE Rootname E(B-V) VHD 146813 B 1.5 V 24000 P1014901 0.02 9.06HD 74662 B 3 V 18000 A1290201 0.09 8.87(Interpolated) B 4 V 16500HD 92288 B 6 V 14000 Z9012801 0.05 7.9(HD 21672,HD 92536) B 8 V 11500 (Z9011401,Z9012901) (0.09,0.04) (6.63,6.32)HD 149630 B 9 V 10800 B0910101 0.04 4.2(HD 109573,HD 181296) A 0 V 10000 (B0910401,P2500101) (0.0,0.01) (5.78,5.03)HD 31647 A 1 V 9300 C0380901 0.0 4.989HD 115892 A 2 V 9050 A0410505 0.0 2.75HD 43940 A 3 V 8850 C0380101 0.0 5.87HD 11636 A 5 V 8500 A0410101 0.0 2.64(Interpolated) A 6 V 8350HD 187642 A 7 V 8050 D0990101 0.0 0.77Table 5: FUSE spectra used to form a library of stellar continua versus effective temperaturein the far UV. 31 –
900 950 1000 1050 1100Wavelength (A)0.00.51.01.52.0 F l u x ( − e r g s − c m − Å − ) O VIC IIIS VI S IVS IVN IIIS VI 1100 1150 1200 1250 1300Wavelength (A)0.00.51.01.52.0 F l u x ( − e r g s − c m − Å − ) C IIIP V N V1300 1350 1400 1450 1500Wavelength (A)0.00.51.01.52.0 F l u x ( − e r g s − c m − Å − ) Si IVO V N IV 1500 1550 1600 1650 1700Wavelength (A)0.00.51.01.52.0 F l u x ( − e r g s − c m − Å − ) C IV He II
Fig. 1.— The mean Her X-1 far UV spectrum observed with FUSE ( < HST
STIS ( >
900 950 1000 1050 1100Wavelength (A)012345 F l u x ( − e r g s − c m − Å − ) O VIC IIIS VI S IVS IVN IIIS VI 1100 1150 1200 1250 1300Wavelength (A)012345 F l u x ( − e r g s − c m − Å − ) C IIIP V N V1300 1350 1400 1450 1500Wavelength (A)012345 F l u x ( − e r g s − c m − Å − ) Si IVO V N IV 1500 1550 1600 1650 1700Wavelength (A)012345 F l u x ( − e r g s − c m − Å − ) C IV He II
Fig. 2.— The mean Her X-1 far UV spectrum observed with FUSE ( < HST
STIS ( > W a v e l eng t h ( A ) . . . . . Flux (10 −13 erg s −1 cm −2 Å −1 ) Fig. 3.— A sample of the H absorption lines in the spectrum of Her X-1, and a model(dotted lines) with flat normalization, of absorption from rotational levels J = 0 through J = 3. 34 – 35 –Fig. 4.— Light curves of prominent lines in the FUSE spectrum of Hercules X-1. A modelof the continuum flux has been subtracted. Errors at the 1 σ level are shown. Emissionlines shown: (a) S vi λ .
4, (b) S vi λ .
5, (c) C iii λ iii λ vi λ .
9, (f)O vi λ .
6, (g) S iv λ v λ iii λ φ in our model of the continuum flux in the wavelengthrange of the O vi doublet. The continuum is separated into disk and stellar components. 37 –Fig. 6.— Fits to the O vi lines at phases when the accretion disk is partially eclipsed. 38 –Fig. 7.— A Fourier-filtered back-projected Doppler tomogram using the FUSE spectra ofS vi λ
933 from φ = 0 . φ = 0 .
85. The grayscale runs from the minimum to the maximum.Top: the trailed spectrogram (left) and filtered trailed spectrogram (right). Middle: the back-projected tomogram (left) and filtered tomogram (right). Bottom: the trailed spectrograminverted from the back-projected tomogram (left) and from the filtered tomogram (right). 39 –Fig. 8.— A Fourier-filtered back-projected Doppler tomogram using the FUSE spectra ofS vi λ
944 presented as in Figure 7. 40 –Fig. 9.— A Fourier-filtered back-projected Doppler tomogram using the FUSE spectra ofN iii λ . vi λ . vi λ . iv λ v λ iii λ vi λ FUSE exposures (thickcurve), a model of O vi emission on the surface of the noncollapsed star (dashed), and anempirical model of Gaussian emission and absorption models. Both models include flux froma model of the accretion disk. 47 –Fig. 16.— A Doppler tomogram of a simple simulation of the O vi λ
900 950 1000 1050 1100 1150 1200Wavelength (Å)0.0010.0100.1001.00010.000100.0001000.000 F l u x ( e r g s − c m − Å − ) B 1.5 V B 6 VB 8 V A 3 VA 1 V
Fig. 17.— Sample spectra, with spectral type labelled, in the library of
FUSE spectra weuse to complement our library of