Time-resolved Spectroscopy of V Sagittae

Marcos P. Diaz

An observational study of the peculiar binary V Sagittae is presented aiming to constrain the stellar masses and current models for the mass transfer in this system. The radial velocity curves of the Hb and HeII l 4686 emission lines at low photometric state are derived. Possible physical scenarios for the line forming region are discussed on the basis of the line profile orbital behavior. In addition, an exploratory analysis of the X-ray data on V Sagittae is made aiming to quantitatively address the proposed models for this binary.

Subject headings: binaries: eclipsing, cataclysmic variables, stars: individual (V Sagittae), stars: mass loss, cataclysmic variables, X-rays

1.1.  V Sagittae and Related Objects

V Sagittae is a very interesting close binary. Despite multi-wavelength observations and detailed wind modeling, the nature of this extensively observed system is still highly uncertain. With an orbital period of 12.34 hours it is one of the brightest cataclysmic variables known, challenging observers for time-resolved and high-dispersion spectroscopic studies. A closer look at V Sagittae available data in fact shows a very peculiar binary that does not fit in any the current cataclysmic variable classification categories, possibly reflecting a different physical scenario for the system. Some recent studies suggested that the V Sagittae phenomenon is not unique and other systems classified as CVs or Wolf-Rayet (WR) stars may present related phenomena. The photometric and spectroscopic similarities between V Sagittae and the supersoft sources (Kahabka & van den Heuvel 1997) were first claimed by Diaz & Steiner (1995, DS95 hereafter), who raised the problem of the inconsistently low X-ray flux for this new kind of binaries when compared to the LMC supersoft sources (SSS). More recently the properties of such systems have been summarized and a new class of close binaries with conspicuous spectroscopic and photometric characteristics named "V Sagittae Stars" has been proposed (Steiner & Diaz 1998). Identification of four of such systems has been suggested so far, namely WX Cen (DS95), V617 Sgr (Cieslinski, Diaz, & Steiner 1998), and WR46 (Oliveira, 1998). These systems share many observational characteristics which resemble both WR stars and SSS. They present strong OVI and NV permitted lines in their spectra and a HeII l 4686 / Hb ratio larger than 2 (see Steiner & Diaz 1998). In addition, HeI lines are not visible or very weak. Regardless of the long orbital period of V Sagittae stars (5-12 hours) the absorption spectrum from a stellar photospheric component has never been detected (see discussion in section 3). From the photometric perspective their orbital light curves are roughly sinusoidal or show double-eclipse profiles - a variety possibly explained by differences in the orbital inclination. Their absolute magnitude seems to range between -1.6 > M_V >1.6. However, these crude estimates contain large errors (see section IV for a brief discussion on V Sge distance value). The evolutionary status and nature of the stellar components in these systems have been a matter of debate. Besides the non-degenerate binary configuration first proposed by Herbig et al. (1965) for V Sagittae, spectroscopic solutions have shown primary masses that may be inconsistent with the white dwarf hypothesis. (e.g. WX Cen, DS95) while more extreme interpretations like a neutron star or black hole primary have been also explored (Koch et al. 1986).

1.2.  Previous Studies on V Sagittae

The classical reference on V Sagittae is the paper by Herbig et al. 1965 (HPSP hereafter). These authors presented phase resolved photometry identifying a broad "V" shaped primary eclipse and a shallow secondary eclipse. Together with the spectroscopic observations these authors arrive at a model for the binary with stellar components M₂ > M₁, where the mass ratio was taken from the radial velocity amplitude of O III Bowen fluorescence line (l l 3444,28 Å) components. After this pioneer study, V Sge has been observed in the UV by the IUE showing strong "wind" resonance lines (Koch et al. 1986). UV high-resolution spectra were taken by the HST/GHRS in 1993 and 1996. The former shows well-developed P-Cygni features in the CIV1549 profile. A wind model for the production of UV resonant lines was proposed by Vitello & Schlosman (1993) establishing the concept of a strong radiation driven wind in this system. Using UV+optical continuum and HeII recombination fluxes Hoare & Drew (1991) derived Zanstra boundary layer temperatures. Independent indication of wind activity comes from radio observations by Lockley, Eyres, & Wood (1997). A simple model for explaining the observed flux density at 8.46 GHz implies a mass-loss rate well above 10^-9 M¤ /yr.

High state phase-resolved spectroscopy of V Sge has been published by Williams et al. (1986), Robertson, Honeycutt & Pier (1997), Lockley (1997), and by Gies, Shafter & Wiggs (1998). The emission lines during the high photometric state present a broad flat-topped component which was understood as formed in the high velocity wind. The profile variations with orbital phase were interpreted using a colliding wind model (Lockley 1997) as the formation mechanism of these lines. Radial velocity semi-amplitudes were found by this author (K = 225 km/s) and by Gies, Shafter & Wiggs (1998) to fall in the range from 134 km/s to 378 km/s. The near infrared spectrum of V Sagittae is discussed by Ramseyer et al. (1993).

Extensive photometric data has been compiled and published by various authors. Simon (1996a) analyzed historic data from 1932 to 1994 showing the bimodal distribution of brightness levels in low (m_v ~ 12.3) and high (m_v ~ 10.8) states. More recent photometric observations by Robertson, Honeycutt, & Pier (1997) confirmed the presence of low and high brightness states with a characteristic transition time-scale of 15-30 days. The original orbital ephemeris from HPSP has been improved by Smak (1995), Simon (1996b), Mader & Shafter (1997), and Patterson et al. (1998). These three analysis agreed in finding a secular period decrease at a rate within the range  = -(2.6-5.1)´ 10^-10. Mader & Shafter (1997) conclude that if this period derivative reflects the mass transfer in the system, then a lower limit to the mass loss rate of 4´ 10^-7 M¤ /yr can be inferred. This limit depends, however, on the assumptions made in their calculations. These authors also performed a light curve fitting analysis starting from their UBV data and HPSP effective temperatures. No acceptable solutions were found for the hypothesis of a double-contact system nor a fully detached system. What is more important, no solutions in agreement with a secondary donor in a semi-detached, non-degenerate configuration were found. Successful light-curve models were obtained in which the primary is a hot subdwarf filling its Roche lobe while the companion is well contained within its Roche surface. Alternatively to the accreting primary scenario that will be proposed in the present work, Lockley (1997) and Gies, Shafter & Wiggs (1998) presented a picture where the mass outflow from a hot subdwarf and the companion colliding wind may explain the emission line formation and their profiles.

The primary eclipse full-width in V Sagittae comprises more than 40% of the orbit - a forbidden situation for a Roche-lobe-limited accretion disk in a semi-detached system. However, as claimed by DS95, the orbital light curve of V Sge is surprisingly similar to the double-eclipsing SSS CAL 87, where the very broad eclipses have been explained by a combined effect of secondary illumination, disk occultation and secondary eclipse by the disk (Schandl, Meyer-Hoffmeister, & Meyer 1997). In the non-degenerate model of Mader & Shafter (1997), the wide eclipses are explained by the ellipsoidal (tidal) variation of the primary's flux.

The radiation field in V Sge should be capable of photoionizing the line emitting gas to a level consistent with the ionization states observed in the optical and UV spectrum. This object was detected by the Einstein Observatory (Koch et al. 1986) as a faint and soft source (Eracleus, Halpern & Patterson 1991). The serendipitous detection of V Sge in the ROSAT/PSPC field of the symbiotic nova PU Vul is discussed by Hoard, Wallerstein & Willson (1996) who found significant X-ray flux modulation at high harmonics of the orbital period.

In the present work, time-resolved spectrophotometry of V Sagittae taken during a low state is analyzed. It will be shown in section 3 that the emission seen during low state may be dominated by the gas undergoing mass transfer, in contrast to the primarily wind emission seen at high states. The measurements aim to define the primary radial velocity amplitude and constrain the mass ratio. In section 4 the SSS scenario is further explored constraining the X-ray luminosity and source temperature with an analysis of ROSAT observations. The next section details the observational procedures used for obtaining and reducing the spectroscopic data. Finally, the conclusions are summarized in section 5.

The spectroscopic data were taken with a B&C Cassegrain spectrograph at the 1.6m telescope of LNA at Itajubá, Brazil (table 1). The detectors employed were a coated, front-illuminated CCD GEC (770´ 1152) with 22.5m pixels and a back-illuminated SITe (1024´ 1024) with 24m pixels. The instrumental PSF was sampled by 2-2.5 pixels yielding a spectral resolution of 1.7 to 2.0 Å. The spectral coverage ranged from 4050 Å to 5080 Å with the use of a 1200 gr./mm grating. Bias frames and dome+twilight flatfielding were made to correct for readout pattern, 2D sensitivity and illumination effects. Negligible dark current was measured in both detectors while the readout zero point was taken from overscan sections in each exposure. The slit was opened to roughly match the best seeing conditions, preserving resolution and assuring wavelength stability. He-Ar comparison lamp exposures bracketed the target observations. A low-order solution was interpolated for each V Sge observation between comparison frames. Typical RMS residuals in wavelength calibrations are smaller than 30 mÅ. The reduction procedure was carried using IRAF utilities including the minimum variance extraction of spectra taken under significant sky background.

A bright comparison star ~65 arcsec away from V Sge was included in the slit at PA @  87° . This flux fiducial was simultaneously measured with the variable to correct for slit losses (including the atmospheric dispersion effect in first order) and small sky transparency variations. Wide slit (9 arcsec) exposures of the slit comparison star and standard (Hamuy et al. 1994) extinction sequences completed the differential spectrophotometric calibration of the time-series. This procedure was repeated for each run. U,B,V,R_KC,I_KC simultaneous photoelectric photometry of V Sge was taken in August, 26, 1993 with a 24 inch telescope at the same site. The broad band magnitudes V=11.35(3); U-B=-0.81(5); B-V=0.07(3); V-R=0.24(4) and R-I=0.12(5) were compared with synthetic photometry made on the final spectra yielding consistent results. A total of 131 narrow and wide slit spectra of V Sge were taken during low and high photometric states. A medium-term orbit average was achieved for low-state runs (figure 1). The time-resolved line analysis will focus on the low state data.

3.1  The Average Spectrum

The average spectrum of V Sge is well described by HPSP as a high ionization spectrum with a blue continuum. Balmer lines, HeII, NV l l 4603,4933,4945, the CIII+NIII complex and possibly OV l 4930 are seen in observed range (table 2). The high-state spectrum of V Sge shows broader emission lines when compared to the average low-state spectrum while the line flux has a larger increase than the continuum at high-state. In other words, a clear increase in the EW of HeII and Balmer lines is observed in high states. The Balmer lines show "absorption" structures in the profile during high and low states. This seems to occur over a wider phase interval during high-state. No sign of an absorption spectrum was found and the previous claim of the presence of the CH "G" band (Echevarria et al. 1989) could not be confirmed with the low-state data at hand.

3.2.  The Radial Velocity Curves

The revised linear ephemeris for the primary minimum by Mader & Shafter (1997): T(min) = 2437889.913(5) + 0.514195(4)´ E was used to derive the orbital phase scale in our study. Departures from the linear ephemeris are smaller than 0.01 and therefore unrelevant to the present analysis. The phasing of the spectra was confirmed by the continuum light curve. Synthetic photometry indicates B < 14.1 over the whole spectrum series, which of course include the primary eclipses.

Although the locus of the line formation region is not yet well known, we adopted the classical double-gaussian convolution method (Schneider & Young 1980) for measuring the radial velocities of the emission lines in V Sge. It will be shown in the next section that the line cores are highly structured. Therefore, by selecting the line wings the effect of the line reversals on the derived velocities can be controlled and minimized. The original data set was binned into 25 and 20 independent phase bins for HeII l 4686 and Hb , respectively. This procedure enables the measurement of small fractions of the line wings. Each bin contains typically about 75 minutes total exposure time. Both HeII and Hb line wings were sampled by narrow (FWHM = 120 km/s and 180 km/s, respectively) Gaussian masks for velocities "a" ranging from 400 km/s to 1600 km/s along the profile. Single sinusoidal fitting to the radial velocity curves were computed with free semiamplitude, K, and phase of positive-to-negative velocity v-g crossing (f ₀), resulting in the diagnostic diagram shown in figure 2. Consistent results were found for both lines up to a = 1000 km/s. Unfortunately, the HeII l 4686 wings could not be explored beyond this velocity due to the significant contamination by the CIII+NIII complex in its blue wing. Besides the agreement between HeII l 4686 and Hb the semi-amplitude plot shows a plateau at ~230 km/s. The phase of zero crossing at high velocities (f ₀ = 0.93) shows a small but significant shift relative to the expected phase of superior conjunction of the primary. Note however, that the zero-crossing phase at high state (f ₀ = 0.142) reported by Gies, Shafter & Wiggs (1998) for Ha wings is well out of our measurement errors. The velocity could be sensed up to a »  1300 km/s in the wings, where the errors increase rapidly. Sample radial velocity curves for a = 800 km/s (HeII) and a = 1100 km/s (Hb ) are shown in figure 3. A closer inspection of the residuals and average line profiles suggests that some deviations seen around phase 0.65 and 1.15 are not produced by data noise but indeed reflect sudden orbital changes in the profile shape. An average over HeII and Hb velocities between 800 < a < 1100 km/s gives K = 226 ±  8 km/s. This value is in very good agreement with the previous determination by Lockley (1997) based on high state data. The photometric phase of the radial velocity curves suggests that the HeII and Hb line forming region share the orbital velocity direction with the continuum eclipsed component. The phase shift between the eclipses and r.v. curve of 25 degrees has yet to be explained

3.3.  The Emission Line Profiles and Doppler Tomography

While the Ha line wings during high-state extends from -1300 km/s to +2000 km/s (Gies, Shafter, & Wiggs 1998), the low-state Hb wing are more symmetric with maximum velocities of +/- 1400 km/s (figure 4). It is interesting to note that the photometric eclipse depth reaches more than 1 mag in U while the Hb line flux does not show a decrease. In fact, the Hb line flux presents a sharp maximum during phase 0.0 indicating that the Balmer line forming region is not eclipsed. A secondary sharp and bright Hb profile is seen close to phase 0.5. The classical explanation for this feature in CV's is the presence of a secondary illumination effect. In this particular binary, however, this interpretation may not be necessarily true. A blue shifted absorption is seen at maximum strength during photometric phase 0.15-0.20. In an accreting primary scenario, this behavior may be tentatively explained in the context of an optically thick wind seen against the bright-spot. Some extension of the bright-spot along the prograde side of the disk is required by the observed absorption phase interval. A less structured profile is seen in the HeII 4686 trailed spectrogram (figure 5)indicating that self-absorption effect is possibly milder in this line. A minimum is visible close to phase 0.0 and maxima at phases 0.7 and 0.45 are seen. In this case the primary minimum in the continuum is roughly followed by the HeII emission flux. This behavior may suggest a partial eclipse of the highly ionized regions in the primary Roche-lobe.

In order to further explore the line profile variations in V Sge, HeII l 4686 and Hb Doppler maps (Marsh & Horne 1988) were computed. The filtered back-projection algorithm (Rosenfeld & Kak 1982) was employed to produce velocity maps that follow the usual coordinate definition, i.e. the origin is at binary rest, the X-axis points from the primary to the secondary while the Y-axis points in the direction of secondary orbital motion.

During the interpretation of Doppler tomography in V Sge one should keep in mind that line opacity effects (especially in Hb ) may mask the intrinsic emissivity distribution. Disentangling these effects depends on detailed radiation transfer modeling for this particular system that was not attempted. Therefore, the tomography interpretation will concentrate on the HeII mapping, which presents a substantially different intensity distribution when compared to the Hb mapping (see figures 6 and 7). In the HeII tomogram (figure 7) we see an absorption close to rest which may be explained by self-absorption in this particular transition. This effect is redundantly seen in the phased line profiles as a small reversal. A similar effect was detected in the HeII tomography of WX Cen by DS1995. The other conspicuous feature of this map is an enhanced emission at V_Y ~ -40 km/s and V_X ~ -230 km/s. All the (V_X<0, V_Y<0) quadrant is brighter in HeII, in clear contrast with the Hb distribution. This may be tentatively explained in terms of the illumination by the central source of gas that overflows the hot-spot, spilling over the disk in ballistic trajectories (e.g. V617 Sgr, Cieslinski, Diaz & Steiner 1998). In the context of a colliding wind model as proposed by Lockley (1997), this enhanced emission may be eventually understood as the dominant secondary flow producing a significant fraction of the HeII line between the stars.

4.1.  Constraints on Stellar Masses

Although the radial velocity curves at high velocities are well described by a single sinusoid it is, however, important to recognize that the assumption of exactly tracing the primary orbital motion by the emission line wings may be questionable. If the line wing's radial velocity correctly reflects the stellar velocity then the semi-amplitude derived in section 3.2 has some direct dynamical consequences. The orbital inclination is highly uncertain at this stage although the presence of both primary and secondary eclipses indicate a very high orbital inclination. Mass functions were calculated for a wide interval between 75°  and 90° . By examining the resulting mass diagram (figure 8), one may find that the common mass ratio domain for CVs (q º  M₂/M₁ <1) occurs at a very high mass range. Seen from the radial velocity measurements, an inverse mass ratio still opens the possibility of a degenerate primary with mass below 1.4 M¤ . The stellar masses proposed by HPSP; M₁ = 0.74 M¤ and M₂ = 2.80 M¤ were derived assuming K₁ = 320 km/s and exhibit a significant discrepancy when compared to our mass function. On the other hand, eclipse photometric solutions by Mader & Shafter support q = 4.1. This value combined with the K₁ found in the present work yield M₁ = 0.3 M¤ and M₂ = 1.2 M¤ . If the primary in V Sagittae is a white dwarf then the secondary mass implied by our mass function is below 2.1 M¤ . This possibility points towards a (non-degenerate) secondary overfilling its Roche lobe and transferring mass on a Kelvin-Helmholtz time-scale. In principle, this process may last until the secondary becomes the less massive component in the system (Paczynski 1971). Mass transfer rates ³ 10^-7 M¤ /yr can be achieved with this mechanism for a donor close to the main sequence.

4.2.  Constraints on X-Ray Emission

It has been claimed that V Sge and similar objects may be the galactic counterparts of SSS (DS95, Steiner & Diaz 1998, Patterson et al. 1998). The low or even absent X-ray flux from these peculiar binaries has been qualitatively explained by interstellar and/or intrinsic absorption combined with a very soft intrinsic spectrum. As the V Sge class prototype was observed by ROSAT, some quantitative effort can be made to constrain the source properties, supporting or rejecting the SSS model.

The most popular model for SSS proposes a binary system that contains an accreting white dwarf (Kahabka & van den Heuvel 1997). Mass accretion rates above the critical limit for degenerate outbursts (>1´ 10^-7 M¤ /yr) feed a steady hydrogen burning shell (Fujimoto, 1982). The energy production in this situation is self-regulated by radiation pressure close to the Eddington limit, which implies a bolometric luminosity close to 10³⁷ - 10³⁸ erg/s, depending on the white dwarf mass and chemical composition of the burning shell. Even for such a high luminosity the radiation from the shell can be quite soft, depending on the effective radius of the source. For a typical white dwarf radius, the implied blackbody temperature should be around a few tens eV. In fact, that is the range of temperatures derived from the X-ray spectrum of several SSS.

V Sge is a low-latitude (l^II = 62° , b^II = -9° ) source, a fact that may imply significant X-ray absorption in the galaxy. Sparse information concerning the interstellar reddening and hydrogen column density can be found in the literature. Koch et al. (1986) estimate E(B-V) = 0.2 from the strength of the 2200 Å bump. From nearby stars and assuming an exponential vertical n_H galaxy structure, HPSP found E(B-V) = 0.4. Patterson et al. (1998) adopt E(B-V) = 0.33. From the values above and using a standard n_H ´  extinction relation (e.g. Gorenstein, 1975) one finds 1.5 ´ 10²¹ < n_H < 3´ 10²¹ cm^-2. Alternatively, Eracleus, Halpern, & Patterson (1991) suggested n_H < 8´ 10²⁰ cm^-2 from Einstein X-ray spectrum fitting. Finally, the "nH ftool" interpolation suggests n_H @  1.8´ 10²¹ cm^-2 for the galactic hydrogen column density in this direction (Dickey & Lockman 1990). The distance to the system is highly uncertain. Reddening values may suggest a distance of 2.8 kpc (HPSP). In our exploratory analysis the fluxes were computed using d = 3.0 kpc. Trivial scaling can be applied while adjusting the column density. A slice in observed flux contours (in units of ROSAT/PSPC cts/s) is shown in figure 9 for a wide range in temperature and column density. A typical bolometric luminosity for an SSS was chosen while the X-ray spectrum is considered a simple blackbody. The observed ROSAT/PSPC count rate of 0.0090(± 10) cts/s in a 27057 second exposure defined a source S/N = 9.2. This count rate was corrected for off-axis vignetting to 0.011(± 1) cts/s. Such a level defines a contour region that covers a reasonable interval in temperatures and column densities. For the simple analysis performed here, the total column density may or may not include intrinsic circumstellar gas. Extremely soft spectra, on the other hand, are not allowed by the highest ionization state observed (OVI) which should require a blackbody source with temperature above or around 20 eV. On the opposite side, the source temperature should not much exceed 100 eV, to account for the Einstein spectrum and ROSAT/PSPC hardness ratios (Hoard et al. 1996). It is interesting to mention that such a luminous blackbody in the "permitted" area of figure 9 should fall bellow EUVE detection limits for a source at 3.0 kpc.

The presence of significant flickering activity in V Sagittae has been observed in the past. This indicates the operation of a mass loss mechanism and suggests mass transfer and accretion phenomena. Subsidiary information supporting mass transfer may be derived from the secular orbital period decrease at a relatively high rate. It is shown in the present work that the Hb line forming region is not eclipsed while the HeII region is only partially eclipsed, suggesting a vertically extended and possibly structured source. Both lines present the positive-to-negative radial velocity crossing close to the primary photometric minimum. A detailed determination of the emission line radial velocities yields a sinusoidal semi-amplitude of 226± 8 km/s with a phase shift of 0.07. The white dwarf hypothesis for the primary star in V Sagittae is supported by the mass function found. In this case, the heavier secondary mass is constrained to less than 2.1 M¤ . This fact leads to scenario where a Roche-lobe overfilling companion is experiencing a very rapid episode in the history of the binary. The ROSAT detection of V Sge was reanalyzed in the context of the SSS model for this class of objects. A well defined region in the temperature versus n_H domain satisfies the proposal of a hydrogen burning white dwarf with plausible parameters.

This work is partially based on optical data obtained at LNA/CNPq. I wish to thank the referee for constructive remarks, A. Bruch for obtaining the photometry data and K. Mukai for help on the use of PIMMS package. This study made use of bibliographical information provided by the SIMBAD database. ROSAT and EUVE data searches were performed using HEASARC/GSFC databases. This research was partially supported by CNPq grant No. 301029 and FAPEMIG grant No. 183696.