A FIRST LOOK AT THE ECLIPSING CATACLYSMIC VARIABLE LANNING 10

Keith Horne

Palomar Observatory, California Institute of Technology

Howard H. Lanning

Mount Wilson and Las Campanas Observatories, Carnegie Institution of Washington

and

Richard H. Gomer

Palomar Observatory, California Institute of Technology

[Published 1982, Ap. J. 252, 681]

ABSTRACT

Our spectra show broad H-alpha and He I 6678 emission lines from the accretion disk and a weak absorption feature from the red dwarf. Radial velocity measurements of the H-alpha emission line vary systematically with binary phase. The observed velocity amplitude, K(em)=240 km/s, gives the mass function f(M)=0.46 M(sun). A phase shift of the velocity curve relative to the eclipse ephemeris indicates that a brightness asymmetry exists in the inner parts of the disk. The unusual dynamical state of the system is discussed.

Subject headings: stars: eclipsing binaries--stars: individual--stars: white dwarfs

I. INTRODUCTION

Cataclysmic variables are close binary systems in which a red dwarf star, filling its Roche lobe, spills material into the Roche lobe of its white dwarf companion. The expelled gas plummets in a stream toward the white dwarf, but is compelled by its angular momentum to form a disk in which viscous processes regulate the accretion onto the white dwarf. The impact of the gas stream produces a rapidly fluctuating bright spot on the outer rim of the disk. Visible light from the system is often dominated by emission from the accreting gas. A thorough review of work on cataclysmic binaries is provided by Robinson (1976).

In this paper, we present a detailed study of the new cataclysmic variable, Lanning 10. The star was discovered by Lanning (1973) in his Palomar 48 inch (1.2 m) Schmidt survey for ultraviolet-bright objects in the galactic plane. Low resolution spectra of Lanning 10 (Margon and Downes 1981) show broad Balmer and He II emission lines which characterize the spectra of many cataclysmic variables. The energy distribution (Szkody and Crosa 1981) resembles that of an F5-G0 star at a distance of ~1 kpc plus a Rayleigh-Jeans component that dominates in the ultraviolet. The ultraviolet spectrum of Lanning 10 is much steeper than that of many cataclysmic systems (Szkody 1981; Greenstein and Oke, unpublished data).

We have found that Lanning 10 is an eclipsing cataclysmic variable. In Section II we present high-speed and multicolor photometry and discuss the eclipses and flickering behavior of Lanning 10. An analysis of the light curve with the aid of a numberical simulation of the eclipse of the disk is given in Section III. Spectroscopic observations are presented in Section IV, and the dynamical implications of the present observations are considered in Section V.

II. PHOTOMETRY

Our photometric observations of Lanning 10 were made during 1980 November and December with the Mount Wilson 1.5 m telescope. A single-channel Cassegrain photometer with an S-20 phototube was used. Offset guiding kept Lanning 10 safely inside a 13" focal plane aperture during the observations. The sky and two nearby reference stars were monitored at roughly 10 and 40 minute intervals to permit background subtraction and correction for atmospheric extinction.

Four nights were devoted to high-speed photometry with 0.25 s time resolution. An absolute timing accuracy of 1 ms was achieved with a stable crystal oscillator and WWVB broadcasts. A broad-band (1900 A FWHM) filter with peak response near 4550 A was used. These data, which resulted in the discovery of the eclipses, serve to define the time scale of flickering activity (~10 minutes) and the shape of the eclipse profile. Figure 1 shows an orbital light curve obtained on a night when two eclipses were observed.

Figure 1: Lanning 10 Light Curve

Broad-band orbital light curve of Lanning 10 on 1980 Dec 18. The data have been sky-subtracted, corrected for atmospheric extinction, and rebinned in 30 s intervals. Clouds prevented observations between phases 0.4 and 0.6. Ticks along the top mark 20 minute intervals.

Table 1 lists specific data for five individual eclipses.

I(min) is the instrumental magnitude at mid-eclipse relative to a nearby reference star
ΔI is the eclipse depth in magnitudes
ΔΦ is the full phase width of the eclipse at half-depth
Φ(1) and Φ(2) are phases at which abrupt slope changes occur

Multicolor observations were acquired on four additional nights to determine the color of the flickering and to check for color variations during the eclipse. Integrations of 10s duration were made in U, B, V, and (on 2 nights) r filters. Light curves for each filter thus hav a time resolution of 30-40 s, sufficient to fully resolve the slow flickering. The data were reduced to magnitude differences relative to one of the two reference stars. Light curves and color indices are presented in Figure 2. Eclipse depths at different wavelengths are given for five individual eclipses in Table 2.

Our eclipse ephemeris, reported previously by Lanning, Horne, and Gomer (1981), is given below:

      HJD = 2,444,557.94957(17) + 0.3212534(15)E.         (1)

The Lanning 10 eclipse is shallower but similar in shape to the eclipses of UX UMa (Nathe and Robinson 1974) and DQ Her (Nather and Warner 1969). A round-bottomed minimum is flanked by asymmetric wings which extend to phases 0.88 and 0.15. There appear to be changes in slope at phases phi(1)~0.96 and phi(2)~0.04 which mark the transitions between the main body of the eclipse and the wings (see Table 1). The full width at half-depth is ΔΦ~0.07, and the eclipse depth is about 1 mag. A more detailed analysis of the eclipse profile will follow in Section III.

The system becomes slightly redder and show no relative increase in Balmer continuum emission during the eclipse. U-B and B-V color indices shown in Figure 2 redden by ~0.1 mag during the eclipse, and the eclipse depths listed in Table 2 are smaller at longer wavelengths. The central part of the disk is bluer than other sources of light (red dwarf, outer parts of the disk, circumstellar material) which remain visible during the eclipse.

Outside of the eclipse, Lanning 10 exhibits flickering activity with a 10% amplitude and a time scale of 10 minutes. This slow flickering contrasts sharply with that of U Gem (Warner and Nather 1971) and LX Ser (Horne 1980) which reach amplitudes up to 30% and time scales as short as a few seconds. The flickering is blue in color. Several 10 minute flares as large as 0.2 mag are visible in the U light curve (Fig. 2), but are less prominent in the B and V light curves. Blue flickering is characteristic of systems with an accretion disk rather than a magnetic accretion funnel. Optical cyclotron emission in the magnetic funnel produces red flickering in AM Her (Priedhorsky and Kzreminski 1978) and EF Eri (Horne and Gomer, unpublished data).

Power spectra of the high-speed data revealed no persistent periodic signals with semi-amplitudes larger than 0.59% (99% confidence) and periods in the range of 1-100 s. The limit quoted is for our longest run, shown in Figure 1.

A 10% brightening and enhanced flickering occur between phases 0.6 and 0.9. Many cataclysmic variables develop a large hump in their light curve during this part of the orbit, when the bright spot is located on the forward side of the disk. The bright spot in Lanning 10 appears to be weak or at least weakly modulated with binary phase. We also note a bump in B-V near phase 0.5. This feature could result from an eclipse of the red dwarf by the disk, or from the ellipsoidal variations of the tidally distored red dwarf. Confirming observations are needed.

III. LIGHT CURVE SIMULATIONS

The eclipse light curve harbors information about the geometry of the binary system (inclination, mass ratio) and about the structure of the accretion disk. We have used a numerical simulation to compute synthetic eclipse light curves for comparison with the observations. The disk is assumed to lie in the orbital plane concentric with the white dwarf. We employ a simple power law to approximate the radial variation of the surface brightness of the disk. The light curve model thus has four parameters, the mass ratio q=M(R)/M(W), the inclination i, the outer radius of the disk R(D), and the power-law exponent alpha.

The mass ratio q and inclination i are highly correlated parameters. Because the red swarf fills its Roche lobe, its radius r(R) relative to the binary separation alpha is controlled by q. Increasing q produces a broader and deeper eclipse which may be compensated for by decreasing the inclination. Our simulation results agree closely with the approximate expressions

which together define a relationship between q and i. Equation (2) is a approximation given by Paczynski (1971) for the size of the Roche lobe, while equation (3) describes the eclipse of a point source by a spherical body. ΔΦ is the phase width of the eclipse. For Lanning 10, the appropriate value of ΔΦ is 0.07+/-0.01.

The shape of the eclipse profile is largely independent of the assumed mass ratio, provided the inclination is adjusted to keep a fixed eclipse depth. The disk parameters may thus be well determined despite a large uncertainty in q. The outer radius of the disk R(D) is determined by the width of the wings of the eclipse profile. Our simulations confirm the result by Sulkanen, Brasure, and Patterson (1981) that the radius determined in this manner varies weakly with the assumed mass ratio. For Lanning 10, we find R(D)=0.9+/-0.05 in units of the distance from the white dwarf to the inner Lagrangian point. The disk nearly spans the Roche lobe of the white dwarf. Inviscid accretion disk models (Flannery 1975; Lubow and Shu 1975) predict disk radii which are much smaller than this, while viscous disk models (Paczynski 1977) are consistent with the large disk radius we observe.

The surface brightness in the disk appears to fall steeply with radius. In Figure 3 we show the observed light curve (from the data of Fig. 1) and two synthetic light curves for disk models with different surface brightness distributions. The models assume q=1, R(D)=0.9, and inclinations chosen to give the observed eclipse depth.

Fig. 3.--Synthetic light curves for two power-law disk models are compared with the observed light curve. The model parameters are q=1, R(D)=0.9, i=72.7, alpha=-1.1; and q=1, R(D)=0.9, i=71.3, alpha=-1.4 for the broad and narrow light curves, respectively.

The R^(-1.1) and R^(-1.4) disk models shown produce eclipses which are broader and narrower, respectively, than the observed eclipse. The best fit is obtained with the power-law exponent alpha=-1.25+/-0.05. Although this is steeper than the R^(-3/4) dependence of the temperature in an optically thick steady-state accretion disk, bolometric corrections will cause the surface brightness to fall off faster than the temperature.

The bright spot, caused by the impact of material in the gas stream with material in the disk, produces the asymmetric wings of the eclipse wings of the eclipse profile. A reasonable fit to the asymmetric profile was achieved by adding a bright spot (four additional parameters) to the disk model. The spot is weak, contributing about 10% of the total light from the disk, and its parameters were not well determined. The absence of sharp jumps in the light curve requires that the spot extend to at least 20% of the dimensions of the disk.

The eclipse simulation does not explicitly include emission from the red dwarf, which contributes a fraction of the light remaining at mid-eclipse. We investigated the effect of the red dwarf by adding a constant source to our light curve simulation. The eclipse of the disk light must then be made deeper by increasing the inclination, but the resulting light curves become too wide and flat-bottomed to fit the observations. We estimate that the red dwarf contributes less than 10% of the light at mid-eclipse.

IV. SPECTROSCOPIC OBSERVATIONS

Spectroscopic observations of Lanning 10 were conducted on 7 nights during a 3 month period in early 1980, in advance of the eclipse discovery. A Varo-Reticon detector and pulse-counting data system designed by S. Shectman and G. Yanik were used on the coudé spectrograph of the Mount Wilson 2.5m telescope. the device is described by Mochnacki and Schommer (1979). Two Reticon arrays acquired simultaneous spectra of the object and of an adjacent region of the sky. A tungsten lamp spectrum was used to flatten the instrumental response, while argon arc spectra defined the wavelength scale for each array. Some 180 counts from the continuum of Lanning 10 were accumulated in each 1.2 A resolution element during 1800 s exposures. The night sky continuum contributed from 10% to 30% of the total signal. Several weak night sky emission lines were accurately removed by the sky subtraction procedure.

The spectra cover a 500 A range centered on the H-alpha emission line. A grand sum of 24 spectra of Lanning 10 is shown in Figure 4a. The individual spectra were rebinned to a heliocentric log-wavelength scale (32.7 km/sec per bin) before summing. The continuum has been flattened by polynomial division. The broad H-alpha emission line is formed in the accretion disk around the white dwarf, although the line profile does not show the double-peaked structure characteristic of an edge-on accretion disk. The wings of the H-alpha emission profile extend to at least 1600 km/sec. He I 6678 A emission is present but weak (1.2 A equivalent width).

Fig. 4.--(a) Summed spectrum of Lanning 10 near H-alpha. The orbital motion of the white dwarf and red dwarf were removed in (b) and (c), respectively, by shifting the individual spectra before summing. Emission line profiles of H-alpha and He I 6678 sharpen in (b), while an absorption feature (Ca I 6494 + Fe I 6496) appears in (c). The spectrum of the G0 V radial velocity standard star HD 112299 is shown in (d) for comparison.

The spectra were also summed in moving frames described by is the binary phase. In Figure 4b, the radial velocity variation of the H-alpha emission line (K=240 km/sec, phi(zero)=0.0) is removed. This sharpens up the H-alpha profile and brings He I 6678 more clearly into view. To search for lines from the red dwarf, the spectra were summed with fiducial phase phi(zero)=0.5 and several values for K. A weak absorption feature (0.4 A equivalent width_ is detected at 6595 A in Figure 4c. This blend of Ca I 6494 and Fe I 6496 is prominent in the spectra of the G and K type stars we used for radial velocity standards. The spectrum of HD 112299 is shown in Figure 4d for comparison. The line is sharpest in Lanning 10 for K=190 km/sec, but the data do not permit a more serious attempt to determine the velocity semiamplitude K(R) of the red dwarf's orbital motion.

Radial velocities measured for the centroid and the wings of the H-alpha emission line are given in Table 3. The centroid velocities were obtained by cross-correlating the individual spectra with a Gaussian template (464 km/sec FWHM). The wing velocities were obtained in the manner of Schneider and Young (1980) by matching up the counts in two Gaussian bandpasses (808 km/sec FWHM) separated by a fixed velocity (2060 km/sec). The velocities are corrected for a 16 km/sec instrumental offset determined from observations of six radial velocity standards (Heard and Fehrenbach 1972).

The centroid velocities displayed in Figure 5 as a function of binary phase clearly show the systematic variation appropriate for the white dwarf.

Fig. 5--The equivalent width and centroid radial velocity of the H-alpha emission line in Lanning 10 as a function line of orbital phase. Open symbols denote measurements of low weight. The single horizontal error bar indicates the integration time. The fitted sine curve has K=240 km/sec , gamma=-61 km/sec, and phi(zero)=0.07. Note that spectroscopic conjunction occurs well after the eclipse.

A circular orbit of the form

was fit by least squares to the centroid and to the wing velocities. The best-fit parameter values, their 1 sigma errors, and the rm error of the fit are listed at the foot of Table 3. Both sets of velocities gave 240 km/sec for the value of K(em). The small difference in the gamma velocity for the centroid and the wings reflects a slight asymmetry in the emission profile which may be seen in Figure 4. The fiducial phase phi(zero) of gamma velocity crossing occurs significantly later than the eclipse phase 0.0. Both the centroid and wing velocities show this effect. The emission line thus appears to lag behind the expected motion of the white dwarf. Uncertainty in the eclipse ephemeris (0.004 phases at the time of the spectroscopic observations) is too small to account for the discrepancy.

Enhanced line emission associated with the bright spot could cause the observed phase lag in the centroid velocities. The phase lag in the wing velocities indicates that a brightness asymmetry is also present in the high velocity material close to the white dwarf. This asymmetry might be caused by the magnetic field of the white dwarf if the white dwarf rotates synchronously with the binary orbit.

A disk asymmetry producing the phase lag can make the observed value of K(em) different from the white dwarf velocity amplitude K(W). The sinusoidal shape of the observed radial velocity curve suggests that the effective velocity may be represented by a vector sum of the white dwarf velocity and a perturbation velocity coused by the brightness asymmetry. The observed radial velocity at phases 0.0 and 0.5 implies that the amplitude of the perturbation is at least 100 km/sec. If the perturbation velocity is directed toward the white dwarf along the line between the stars, then the value of K(W) is 217 km/sec instead of 240 km/sec. Bright spot emission is visible in several systems as a distinct component (the S-wave component) in the emission line profile. The S-wave in U Gem attains its maximum radia velocity just after spectroscopic conjunction (Smak 1976). If the same is true of the velocity perturbation in Lanning 10, the K(W) remains greater than 217 km/sec. The uncertain nature of these corrections leaves some doubt as to the true value of K(W) for Lanning 10.

V. THE DYNAMICAL STATE OF LANNING 10

The prospect of obtaining masses for the stars in eclipsing cataclysmic systems make them important for studies of the evolutionary history of cataclysmic variables. Lanning 10 promises to be especially valuable in this regard since lines from both the disk and the red dwarf are detected. With the present data, we cannot follow the orbital motion of the red dwarf, and so we cannot propose a unique dynamical model for the system. However, our observations place constraints which already show that the dynamical state of Lanning 10 is unusual.

The first constraint comes from the emission line profiles. The broad emission profile results from motion of the accreting gas, and so the largest velocity in the profile must not exceed the Keplerian velocity at the surface of the accreting object. For Lanning 10 we require

where m(W) and r(W) are the mass and radius of the white dwarf. The white dwarf mass-radius relationship (Hamada and Salpeter 1961) transfers this inequality into a lower limit on the mass of the white dwarf:

From the binary period and emission-line radial velocity amplitude, we compute the mass function

Finally, as discussed in Section III, the eclipse light curve supplies a relation between q and i which is given to good approximation by equations (2) and (3) with ΔΦ=0.07. This relation entails the lower limit q>0.1 below which the red dwarf is too small to produce the observed eclipse width at any inclination.

The above considerations limit our attention to a family of models which may be parameterized by the mass ratio q. Details of some representative models are collected in Table 4. These results are not sensitive to uncertainty in the q-i relationship from the eclipse. The masses change by on 6% when the eclipse width is changed by 25%. The largest source of uncertainty lies in K(W), so we include results for two values of K(W) in Table 4.

We first assume that K(W)=240 km/sec, the nominal value given by our spectroscopic observations. The results in Table 4 then show that for q<1.25 the accreting object is too massive to be a white dwarf. This possibility will not be considered further here. Models with q<4 require the red dwarf to be considerably denser than a main-sequence star. The red dwarf star attains main-sequence structure for q near 4, and for q>4 the white dwarf mass violates equation (5).

The conventional picture of a cataclysmic binary as a white dwarf plus a red dwarf near the main sequence thus leads us to a model with a large mass ratio. Mass transfer is unstable on a dynamical or Kelvin-hemholtz time scale when the accreting star is less massive than its companion (Paczynski 1971). Although the lifetime of systems in the unstable state is only about 10E-3 that of systems evolving on a nuclear or gravitational radiation time scale, increased accretion luminosity would render them visible at larger distances.

We next consider a smaller value of K(W), since the opposite assumption produces even more exotic models than the ones we have just considered. For K(W)=200 km/sec, Table 4 shows that the white dwarf mass is below the Chandrasekhar limit for q>0.92, while main-sequence structure for the secondary is possible for q near 1.4. A mass ratio above unity is still favored. The conventional model, with a white dwarf plus a late-type main-sequence star, permits a mass ratio less than unity only for K(W)<180 km/sec.

The dynamical state of Lanning 10 promises to be interesting. Further clarification will come with a direct determination of q by either a radial velocity study of the absorption lines or by analysis of the eclipse of the emission lines from the disk. Work on both of these fronts will be reported in a future paper.

REFERENCES

Young. P., and Schneider, D. P. 1980, Ap. J., 238, 955.

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