DAVID R. CIARDI Department of Astronomy, University of Florida, Gainesville, FL 32611; ciardi=astro.uñ.edu

Transcription

1 THE ASTROPHYSICAL JOURNAL, 530:904È915, 2000 February 20 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. INFRARED SPECTROSCOPY OF THE SECONDARY STAR IN ST LEONIS MINORIS: IMPLICATIONS FOR EVOLUTION AND HIGH-/LOW-STATE BEHAVIOR IN CATACLYSMIC VARIABLES STEVE B. HOWELL Wyoming Infrared Observatory and Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, and Astrophysics Group, Planetary Science Institute, Tucson, AZ 85705; howell=psi.edu DAVID R. CIARDI Department of Astronomy, University of Florida, Gainesville, FL 32611; ciardi=astro.uñ.edu V. S. DHILLON Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK; vik.dhillon=shefðeld.ac.uk AND WARREN SKIDMORE Wyoming Infrared Observatory and Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071; skidmore=tana.uwyo.edu Received 1999 January 5; accepted 1999 September 30 ABSTRACT We present time-resolved K-band spectra of the polar ST LMi obtained during a time of zero mass transfer. Analysis of these Ðrst ever phase-resolved observations of an uncontaminated cataclysmic variable (CV) secondary star show no evidence for ellipsoidal variations, a ects due to gravity darkening, or irradiation of the L1 point. The data indicate instead that the secondary star has a phase-dependent temperature including the existence of a localized cooler region centered near orbital phase 0.8. We examine a few possible explanations for such phenomena and conclude that the most likely cause is due to starspot activity. The location of the critical Roche surface calculated with respect to the physical stellar surface of the secondary star is shown to change during the lifetime of a cataclysmic variable and thereby e ect its evolution. Previous suggestions of low-state behavior being caused by a starspot placed at L1 are shown not to work. However, an active chromosphere on the secondary star is both consistent with the current observations and may naturally explain high-/low-state behavior in CVs. Subject headings: binaries: general È infrared: stars È stars: activity È stars: chromospheres È stars: individual (ST Leonis Minoris) È stars: low-mass, brown dwarfs 1. INTRODUCTION Polars are a subclass of cataclysmic variables (CVs) that each contain a white dwarf (WD) primary and a low-mass red secondary star that Ðlls its Roche lobe and loses mass from the inner Lagrangian point (the L1 point). The white dwarf in a polar possesses a high magnetic Ðeld with a strength of typically 10È80 MG, but three polars have recently been discovered with Ðelds of 100È250 MG. Unlike nonmagnetic CVs, in which the transferred material forms an accretion disk around the primary, the high magnetic Ðeld of the primary causes the material Ñowing from the L1 point to eventually be funneled in an accretion stream onto the WD surface, impacting the WD directly within a relatively small area (D0.05R ) called the accretion region (Sirk & Howell 1998). The material WD leaving the L1 point has a ballistic trajectory in the binary orbital plane and follows that path until the magnetic Ðeld energy is sufficient to disrupt it. The point of this disruption is called the coupling region and occurs when the magnetic energy density, B2/8n, exceeds the kinetic energy density, ov2, at which point the accretion stream is lifted out of the orbital plane and falls onto the WD at one or both of its magnetic poles. Polars are reviewed in detail in Warner (1995, pp. 307È366). The star ST LMi is a fairly typical magnetic interacting binary system, classiðed as a polar, with V \ 15È17 (Downes, Webbink, & Shara 1997), an orbital period of 1.90 hr, a binary inclination of 56, a 0.76 M white dwarf, and an assumed 0.17 M secondary (Shahbaz _ & Wood 1996, here- _ after SW96). 904 Polars have been observed at many wavelengths from the X-ray to the infrared (Cropper 1990), with the UVÈIR bandpasses in each polar generally dominated by strong line emission and a rising blue continuum due to emission from the accreted material, the white dwarf, and the 100,000 K or hotter accretion region. Cyclotron emission, caused by the interaction of electrons with the WD magnetic Ðeld at or near the accretion poles, can also be quite prominent in the spectra of polars. Cyclotron emission manifests itself as broad asymmetric continuum humps underlying the polar spectrum, visible only when the magnetic pole is in view. The wavelength at which these humps appear in a spectrum is dependent on the strength of the primaryïs magnetic Ðeld (Ferrario, Bailet, & Wickramasinghe 1993). Thus, observations in search of the secondary star, even those performed in the IR region, are usually incapable of providing an uncontaminated view of the binary components. Spectral signatures from the faint, low-mass red secondary star are Ðlled in, greatly modiðed, and generally rendered completely invisible by emission from the various accretion processes. This lack of direct observation of the secondary star is true not only for polars but also for other CV types, as the line and continuum emission from the accretion stream and disk are often the dominant Ñux sources from X-ray to IR wavelengths (Ciardi et al. 1998b). Polars, however, do o er a unique opportunity to observe the secondary star directly as the mass transfer to the WD primary becomes very low or even turns o at times. During these so-called low states, direct observations

2 IR SPECTROSCOPY OF SECONDARY IN ST LMi 905 TABLE MAY 28 TIME-RESOLVED IR SPECTROSCOPY OF ST LMI HJD Integration Mid-Exposure Orbital Phase Time Number (2,450,596.0]) Mid-Exposure (s) can be made of the secondary star, revealing an almost completely uncontaminated look at its spectral appearance. The reason for CV low states is not well understood (see 4.3), and there is certainly no predictive ability at this time; thus, direct spectral views are very rare. Until now, there have been no phase-resolved spectral observations of the low-mass secondary star in a short-period CV during a time of no mass transfer. However, during a serendipitous episode near the top of the world, luck and experience combined to allow us a rare view of a naked CV secondary star. For the last few years, we have had a program in place to obtain IR spectroscopy of a variety of CV subtypes, including polars (Dhillon et al. 1997, 2000; Ciardi et al. 1998a, 1998b). During one of our program runs, we observed the star ST LMi in a state of zero mass transfer, thereby allowing an uncontaminated view of the secondary star. Preliminary analysis of our IR spectral observations were presented in Ciardi et al. (1998a). In this paper, we present a detailed analysis of the orbitally resolved spectroscopy obtained in the K band (centered at 2.2 km) for the polar ST LMi. We Ðnd that the secondary shows spectral modulation that is wholly unexpected and inconsistent with ellipsoidal variations, gravity darkening, or irradiation. In order to postulate a cause for the unusual spectral appearance, we present a brief discussion of several possible explanations, including starspots and the evolutionary e ect of the location of the critical Roche surface with respect to the stellar atmosphere of the secondary star. 2. OBSERVATIONS Time-resolved K-band spectroscopy of ST LMi was obtained in 1997 May with the 3.8 m United Kingdom Infrared Telescope (UKIRT). The observations covered the wavelength range from 1.85 to 2.47 km with the spectral regions shortward of 1.95 km and longward of 2.45 km being unusable because of telluric absorption. During our observations of ST LMi, the star had V and K magnitudes of D17.5 and 14, respectively (Ciardi et al. 1998a). Our time-resolved spectroscopy resulted in 12 Ðnal binned spectra, each covering (including readout overhead) slightly less than 0.1 in orbital phase, i.e., about 9.5 minutes each. A summary of our observations is given in Table 1, where all reported binary orbital phases have been determined from our sodium line radial velocity measurements, as discussed below. Our radial velocity solutions for ST LMi (i.e., orbital period, K amplitude, and systemic velocity) are in good agreement with those presented in SW96. The K-band spectroscopy was acquired with the UKIRT Cooled Grating Spectrometer (CGS4) equipped with a 256 ] 256 InSb array. The observations utilized a 75 line mm~1 grating, a 150 mm focal length, and a 1A.22 slit width. To optimize the spectral sampling and remove bad pixels, the detector array was mechanically shifted by 2 pixels in 0.5 pixel steps in the dispersion direction, as is commonly done. In addition, each spectrum is composed of four telescope nod positions in order to provide accurate sky subtraction. Thus, each phase-resolved spectrum presented here is a summation of 16 integrations, each of 30 s, giving a total exposure time of 480 s. This instrument setup provides a pixel resolution of D175 km s~1, giving our spectra an e ective Ðnal velocity resolution (2 pixels) of 350 km s~1. Sky subtraction was performed by nodding the telescope between two positions on the sky separated by D20A. Flat Ðelds and argon arc lamps were observed just prior to the target observations. Telluric correction was performed in FIG.1a FIG. 1.ÈTwelve time-resolved K-band spectra of ST LMi. The y-axis is relative Ñux (in mjy), and each spectrum is vertically o set by 0.98 mjy from the spectrum directly below. Note the changing spectral appearance with orbital phase. FIG.1b

3 906 HOWELL ET AL. Vol. 530 the standard way via observations of the F star BS 4412 (F7 V) and were obtained close in time and airmass to ST LMi. Any stellar features present in the BS 4412 spectrum were masked out, and all the ST LMi spectra were then divided by it. We Ñux calibrated our spectra in the usual fashion using BS 4412 and assuming that it radiates as a blackbody. Figure 1 presents the twelve Ðnal phase-binned spectra for ST LMi. The spectra are labeled with their orbital phase that runs from the top to the bottom in both Figures 1a and 1b, and the y-axis is in mjy. Each phase-resolved spectrum has a signal-to-noise ratio (S/N) of D35 in the continuum. The continuum Ñux levels are well determined as the night of observation was photometric as evidenced by frequent measurement of the proðle and count rate of the guide stars used for the observations as well as the standard stars taken at approximately 30 minute intervals. All of our observations were guided and obtained using the UKIRT tip-tilt secondary. The seeing was usually near 0A.4 (with only two excursions to near 0A.8, each for less than 1 integration time) and was determined by using the visible light TV guider images and an established relation between the visible image seeing and that in the K band. We also made frequent cross-cuts of the spectra themselves using available UKIRT/CGS4 software at the telescope. The very good seeing and the use of a parallactic angle slit width of 1A.22 assured that slit losses were unlikely. Additionally, we have spectral coverage (see Table 1) for greater than 1 orbit, and the one-third period of overlap yields consistent results when phased together (see Figs. 2 and 3 below). Our manner of observation and the resultant overlapping phase information both give us conðdence that our reported Ñuxes, while possibly only relative, are precise. Apparent features in the spectra blueward of 1.95 km and redward of 2.45 km are not believed to be due to incomplete removal of telluric features during data reduction. The spectral features that are present in our time-resolved observations consist of absorptions due to the Na I doublet at and km, 12CO bandheads at , , , and km, and the two very broad water absorption bands extending away from km in both directions. Note that these water bands are from the secondary star itself and are not telluric in origin. 3. SPECTRAL ANALYSIS Spectra of polars obtained during times of high mass transfer have a radically di erent appearance that those shown in Figure 1. Ciardi et al. (1998a) present a K-band spectrum of ST LMi obtained 6 months after the data discussed here, when mass transfer had resumed. At that time, ST LMi presented a typical polar infrared spectrum showing the strong emission lines due to Brc, Brd, Paa, and He I, possible cyclotron hump features, and no indication of any secondary star absorption features. In contrast, the spectra discussed here were obtained during a time of zero mass transfer (Ciardi et al. 1998a) and contain no contribution from accretion material (emission lines or continuum contamination) other than weak cyclotron continuum emission seen near orbital phase 0.9 (see 3.1). Additionally, any continuum Ñux contribution at 2.2 km from the WD primary can be, at most, only 2% (see Ciardi et al. 1998b), and even if the accretion region on the WD surface has remained hot after the cessation of mass transfer, its small emitting area precludes any interfering continuum contribution within the K spectral band. Thus, the data reported here represent the Ðrst-ever time-resolved spectra of an uncontaminated secondary star in a CV Absorption L ine Radial V elocities In Figure 1, it is quite clear that the spectral appearance of ST LMi changes with orbital phase and that the apparent e ective temperature sampled by each observation is not constant. For example, the deepening of the Na absorption and the increased water absorption (red and blue ends of the spectra dropping down) are clear indicators of cooler atmospheric regions on the stellar surface. To conðrm that the observed Na absorption line and CO absorption bands seen in our data do indeed originate from the secondary star, we have constructed radial velocity curves. The Na and the 12CO bands had their line Ñuxes measured in the usual manner using the SPLOT routines available in IRAF. The Na absorption line was well approximated by a Gaussian proðle, while the 12CO bands, which do not have an expected Gaussian proðle, were only marginally matched. Figure 2 shows the radial velocity curves obtained for Na and the bluest 12CO band. The remaining redward 12CO bands show similar but much noisier results. The top panel of Figure 2 shows the Na measurements, the middle panel the 12CO velocities, and the bottom panel combines both radial velocity measurements with our best-ðt orbital solution. While the 12CO measurements are noisier and appear slightly o set in phase from the Na measurements (because of the issue mentioned above), both absorption-line veloci- Radial Velocity (km/sec) Radial Velocity (km/sec) Radial Velocity (km/sec) Na I (22076A) CO (22935A) Na I 12CO Na I + 12CO (22935A) Phase FIG. 2.ÈRadial velocity curves for the Na and 12CO absorption lines. The phasing clearly indicates an origin of these lines at the secondary star. The bottom panel shows the observed RV data overplotted with our newly determined RV solution.

4 No. 2, 2000 IR SPECTROSCOPY OF SECONDARY IN ST LMi 907 ties are exactly in phase with a source located on the secondary star. The largest uncertainty in IR spectroscopic radial velocity solutions is the velocity resolution of the observations. For our data, we can estimate the 1 p velocity uncertainties in the usual manner of using ^1 the velocity resolution per pixel times the fractional pixel error 2 of the wavelength scale Ðt, here found to have a maximum value of 1/2 pixel. Using the Na absorption line measurements and a standard 1 p uncertainty of ^75 km s~1, we Ðnd a blue-to-red crossing ephemeris of T \ 2,450, ^ (D^0.1 in phase). From our 0 radial velocity solution, the K velocity amplitude for the absorption features is ^ km s~1 (a value of 329 ^ 6kms~1 was found by SW96), and our determined c velocity of 79.7 ^ 41.7 km s~1 is higher than the value of 3 ^ 4kms~1 given in SW96. We attribute the di erences between our K and c velocity solutions and those of SW96 obtained using 2 near-ir spectra to the fact that our data have poorer phase coverage, lower S/N, poorer velocity resolution (350 vs. 70 km s~1), the Na I doublet being unresolved in our data, and CO measurements of a molecular band rather than an atomic line. Even given our somewhat poorer determined values, we are conðdent that our results are consistent with those of SW96 and that the absorption features seen in our spectra indeed originate with the secondary star Orbital Modulation of Continuum Flux Time series observations, especially in the K-band continuum, of Roche-lobe Ðlling secondaries are generally modulated by ellipsoidal variations (Russell 1945) even when the overall emission is dominated by accretion e ects (e.g., Bailey et al. 1985; Ciardi et al. 1998b). The signature of such variations is a double humped cosine curve peaking at orbital phases 0.25 and 0.75, times when the secondary star presents its largest emitting area to the observer. The maximum amplitude for ellipsoidal variations is 0.25 mag and occurs when the orbital inclination of the binary is 90. Another e ect sometimes seen in close binaries, which contain nonspherical components, is that of von Zeipel gravity darkening. Simply stated, gravity darkening occurs when surface regions, which are farther from the axis of rotation of the secondary, have slightly cooler e ective temperatures and thus emit slightly less Ñux per unit area. Additionally, secondary stars in short-period interacting binaries are close to their collapsed companions (about a solar radius in the case of ST LMi) and often show irradiation e ects, i.e., heating of the atmosphere of the secondary star near the L1 point due to high-energy photons coming from accretion events on or near the primary. Irradiation is particularly prevalent in magnetic CVs, where there is no accretion disk to provide some shielding of the L1 point. Observationally irradiation manifests itself as a temperature (thus, continuum Ñux) increase seen at orbital phase 0.5 and, at times, narrow emission lines from the heated face of the secondary (e.g., Somers, Ringwald, & Naylor 1997). SW96 present strong evidence for irradiation of the secondary star in ST LMi during a time of high mass transfer, in the form of Ca II emission centered at the L1 point. In order to search for evidence of the above mentioned e ects, we have numerically convolved three continuum Ðlters with our time-resolved spectra to produce intermediate-band light curves. The positions of the continuum Ðlters were chosen to avoid the spectral features due to Na and 12CO, but only one of the Ðlters could avoid the continuum regions controlled by the two broad water absorption bands. The three rectangular Ðlters, each of FWHM 0.5 km, were centered at , , and km. The resulting light curves are presented in the bottom left panel of Figure 3. The three intermediate-band light curves show a single-peaked modulation centered near phase 0.8È0.9. There is no evidence for two humps per orbit as would be the case for ellipsoidal variations, no uneven minima (at phases 0.5 and 0.0) as expected for gravity darkening, nor any modulation centered at phase 0.5 as expected from irradiation. Ellipsoidal variations were observed in ST LMi during high-state J, H, and K observations by Bailey et al. (1985; see their Fig. 4). ST LMiÏs light curve at that time consisted of an uneven double-humped modulation with a 0.8 mag amplitude peak near phase 0.9 and a 0.2 mag hump at phase Both peaks were sinusoidal in shape and each covered a total of D0.35 in phase. The higher amplitude peak was attributed, with the help of polarization measurements, to cyclotron emission from the self-eclipsing primary accreting pole, while the smaller amplitude peak (and presumably its twin at phase 0.75 hidden by the cyclotron emission) was attributed to ellipsoidal variations from the Roche-lobeÈ Temperature (K) Line Flux Cont. Flux (mjy) Effective Temperature H2O Band Strength Continuum Flux A 22750A 23400A Phase Line Flux Line Flux Line Flux Na I CO (22935A) Band Strength CO (23227A) Band Strength Phase FIG. 3.ÈSecondary star temperature (in K), spectral absorption feature line Ñuxes (in mjy), and the K-band continuum value (in mjy), all plotted as a function of orbital phase. Note that all indicators point toward a localized cooler region on the secondary star, centered at phase 0.8. The error bar shown in the temperature plot represents the typical uncertainty of each measurement. See text for details.

5 908 HOWELL ET AL. Vol. 530 Ðlling secondary star. The location and amplitude of the hump at phase 0.25 was conðrmed in all three IR bandpasses presented by Bailey et al. and was consistent in shape and strength with the expected 0.2 mag ellipsoidal variations. Our continuum light curves show that during the time of zero mass transfer some residual cyclotron emission remains near phase 0.9 (K. Beuermann 1999, private communication) but with only 1 of the amplitude seen by Bailey et al. (1985). On the other 3 hand, if ellipsoidal variations were still present, their expected amplitude should remain constant at 0.2 mag and the hump at phase 0.25 would be obvious. For example, in the km light curve shown in Figure 3, the modulation at phase 0.25 due to ellipsoidal variations would produce a sine-like hump with a peak value of 3.0 mjy. Instead, our data show no evidence at all for any modulation of amplitude greater than D0.05 mjy at phase We are forced to conclude that ellipsoidal variations, which should dominate our continuum light curve, are simply not present Orbital Modulation of Spectral Features Taking the Ñux at km as a Ðducial continuum point in our spectra and measuring the amount of absorbed Ñux blueward to 2.0 km and redward to 2.4 km, we can provide an estimate of the variation in absorption strength of the two water bands. The middle left panel in Figure 3 shows our results for the H O absorption bands; the top 2 curve in the panel is the blueward absorption band where a more negative line Ñux is indicative of a stronger absorption feature. Although noisy, the water features show their greatest absorption strength near phase 0.8. Orbitally resolved measurements of the absorption Ñux of Na I and the 12CO bands are also shown in Figure 3 (right panels). The line Ñuxes are in mjy and are accurate to ^5% for the Na lines and about 10% for the CO bands. We again see that the greatest absorption strength occurs near orbital phase 0.8. This increase at phase 0.8 also occurs in measurements of the equivalent widths of these lines and in the two far-red 12CO bands, the latter being far noisier. Increased absorption strengths in Na I, 12CO, and H O 2 indicate an origin in a cooler temperature region on the secondary star (Leggett et al. 1996). To illustrate and conðrm the position of maximum absorption in the Na I line, we have constructed a Doppler map (Marsh & Horne 1988), presented in Figure 4. Despite the somewhat poor velocity resolution of our Doppler map, Figure 4 clearly shows that the Na I absorption is associated with the secondary star. The trailed spectrogram has a K velocity amplitude of approximately 330 km s~1, consistent 2 with the value derived by SW96 and our radial velocity curves presented in Figure 2. The maximum absorption is seen not to be centered on the secondary star but appears to be slightly displaced toward the leading edge. The resolution of this Doppler map is too poor to yield an accurate value for this displacement, and the Doppler map on its own could not convincingly locate the o set position of the maximum Na I absorption. However, examination of the map in Figure 4 shows that the velocity position of maximum Na I absorption is consistent with the conclusions drawn from the orbitally resolved measurements of the Na I absorption strength shown in Figures 2 and 3. The distribution of Na I absorption in velocity space in our data is radically di erent from that seen by SW96. FIG. 4.ÈUpper panel: Trailed spectrum of the Na I absorption line; bright levels indicate greater absorption strength. L ower panel: Resulting Doppler map, indicating that the position of maximum absorption is on one side of the secondary star, corresponding to an orbital phase of about 0.8. The position of the secondary Roche lobe, the white dwarf, the binary center of mass, and the ballistic trajectory of the mass transfer stream are shown. During a high state of ST LMi, they show that the Na I 8194 A absorption line is produced uniformly all over the secondary star. It is difficult to compare these two results directly, as the mass transfer state of the star was completely di erent and the formation region for the Na I j8194 doublet is near the top of the stellar photosphere while that for the Na I 2.2 km line measured here is generally lower in the atmosphere (Mihalas 1978) Secondary Star T emperature As part of our IR spectroscopy program at UKIRT, we have obtained spectra of single K and M main-sequence stars to use as templates and calibration tools in our work on the secondaries in CVs (see Dhillon et al. 2000). This library of late-type dwarfs consists of stars of luminosity

6 No. 2, 2000 IR SPECTROSCOPY OF SECONDARY IN ST LMi 909 class V, with spectral types from K2 to M6. Later type stars and other luminosity classes are available in the work by Leggett et al. (1996). The twelve phase-resolved ST LMi spectra available to us here were matched against each of the library spectra, providing a best-ðt temperature at each orbital phase. Our template library provides e ective temperature information in steps of about ^100 K, and each ST LMi spectrum was better Ðtted by one template star compared with the others. We note here that none of the single main-sequence star spectra matched the ST LMi secondary star in both the strengths of the absorption lines and overall continuum shape. Some of the template Ðts were better at Ðtting the line depths, while others were better at Ðtting the overall continuum shape. The Ðtting of the lines is less certain because of the fact that the single star templates are not fast rotators, they may have metallicity di erences, and the continuum S/N in each phased ST LMi spectrum is low enough to make proðle matching uncertain. We thus opted to use a best overall Ðt, which averaged the line and continuum e ects but with more weight given to the continuum Ðtting. This Ðtting procedure produced a best guess of the e ective temperature observed at each phase but does not imply ideal matches of main-sequence spectral types with the secondary in ST LMi. For example, the Ca I triplet (2.2614, , and km) is present in early M stars but weakens greatly by M6 V (Dhillon et al. 2000, and our template stars). We Ðnd no indication of this line in any of our ST LMi spectra, and its absence in our data may be caused by its weakness and subsequent loss due to rotational broadening or it could be due to temperature or metallicity e ects in the secondary star. The assignment of a single speciðc main-sequence spectral type to the secondary star in ST LMi is not possible, nor does it appear to be meaningful. However, we can assign a best-ðt temperature to each spectrum by matching the overall continuum shape, the water absorption bands, and the strength of the Na I line with our template spectra. In doing this, we make the assumption that, if composition and e ective log g are constant, then the spectral changes observed must be due to changes in the e ective temperature of the secondary star. The top left panel of Figure 3 presents the results of our temperature Ðtting procedure. The secondary star shows clear temperature variations from 3100 to 2600 K throughout the orbit and conðrms our premise from the above discussion that the secondary star appears to have a localized cooler region, centered near orbital phase 0.8. We Ðnd that the ST LMi spectra are the Ñattest ÏÏ during the phase interval 0.9È0.2, indicating phases of hottest temperature (3100 K), while the phase interval 0.6È0.9 has the strongest water band and other absorptions and thus yields the coolest temperature Ðts (2600 K). Our temperature error in the Ðts is believed to be about ^100 K based on the temperature steps provided by the library stars. When the secondary star temperature is found to be lowest, we would expect to see a decrease in the continuum Ñux, yet precisely the opposite occurs. As indicated above, we attribute the rise in the continuum at phase 0.9 to residual cyclotron emission. Let us examine how such emission might e ect the K band measurements presented here and whether it could be the cause of the apparent temperature decrease seen during these same phases. Cyclotron emission is caused by radiating electrons caught near the magnetic pole of the primary star. The electrons radiate at various harmonics with usually only a few percent of the total energy coming out at the fundamental (Warner 1995, pp. 321È323). These harmonics occur at speciðc wavelengths in the spectrum depending on the magnetic Ðeld strength of the primary star with some additional dependence on its mass and radius. Cyclotron emission, or humps ÏÏ as they are called, have just this appearance: a broad (500È1000 A or more) asymmetric hump whose edge can modulate the shape of the spectral continuum by 5%È15%. The apparent wavelength of peak emission and the shape and height of the humps can change with the total amount of radiating material as there is a direct relation between the proðle of the Maxwellian distribution of the electrons and that of the cyclotron humps. For ST LMi, Ferrario et al. (1993) obtained high-state K-band spectra and determined the location of the cyclotron emission based on their spectra and a model for cyclotron emission. Using a magnetic pole strength of 12 MG for ST LMi, Ferrario et al. calculated that the Ðfth harmonic cyclotron hump peak occurs at a wavelength 1.90 km, with a minimum near the middle of the K band. In order to see how the presence of such cyclotron emission, near phase 0.9 in our observations, might e ect the determination of line strengths and secondary star temperature Ðts, we have modeled the situation in Figure 5. A cyclotron hump model was created from the data and cyclotron model shown in Ferrario et al. (1993) when ST LMi was observed in a high state. Points in the wavelength range of 1.8 km \j\2.4 km were extracted from their Figure 2, and a spline function was Ðtted to those points. The cyclotron hump model was then normalized such that its median value was unity. A 2600 K NextGen stellar atmosphere model (Hauschildt, Allard, & Baron 1999) has been normalized such that its median value was unity as well. The normalized high-state cyclotron model was then scaled down by 30% and added to the normalized stellar atmosphere model. By so doing, we have increased the model atmosphere continuum Ñux by a factor of 1.5, exactly as seen in our continuum Ñux plot of Figure 3. This model exercise was able to increase the observed continuum Ñux in a physically realistic manner without drastically a ecting the observed spectral shape (i.e., temperature indicator) and line proðles. Thus, we believe that the rise in continuum Ñux FIG. 5.ÈModel spectrum for ST LMi near phase 0.9 showing the addition of a cyclotron hump and the lack of its e ect on the spectral shape. See text for details.

7 910 HOWELL ET AL. Vol. 530 centered at phase 0.9 is unrelated to the secondary star and that the observed temperature changes of the secondary star are real. We therefore conclude that the secondary star in ST LMi, during this time of zero mass transfer, shows evidence for temperature change as a function of orbital phase, with an apparent localized cool region centered near phase 0.8. If we were to naively assign main-sequence spectral types to our measured temperatures at any single phase, we would see that the secondary star in ST LMi covers the range from M3 V to M6 V. The standard method of spectral type assignment in CVs (based solely on an empirical P orb -M2 relation) would predict the secondary to be M5 V. Taking the observed range in spectral type at face value, one would estimate an orbital period for ST LMi of 3.6 hr (for the M3 V choice) or 1.6 hr (for the M6 V choice), while the true period is 1.9 hr. Based on these results, we caution the reader concerning the use of main-sequence spectral type relationships for CV secondaries or the use of a single (e.g., eclipse) spectrum to provide detailed information about the secondary star (cf. Smith & Dhillon 1998). For a discussion of the proper massèradiusèorbital period relations for a secondary star in a CV, see Howell, Rappaport, & Nelson (2000). 4. DISCUSSION The data analysis above reveals that the secondary star in ST LMi presents phase-resolved properties, which we are hard pressed to understand. Simple arguments would lead us to believe that for a CV secondary star observations of the IR continuum and spectral variations, which are uncontaminated by accretion emission, should reveal the presence of ellipsoidal variations, possibly irradiation e ects and gravity darkening, or some combination of all three. However, we apparently Ðnd no evidence for any of these phenomena in our data. Instead, we have determined that the secondary star in ST LMi appears to be of nonconstant temperature with a localized cooler region centered near orbital phase 0.8. We can make no mistake about its location; the radial velocity curves of the Na I and 12CO absorptions provide an unambiguous tracer of the orbital motion. Given this situation, let us explore a few possible explanations, which may help in the interpretation of our data von ZeipelÏs T heorem Let us brieñy examine von ZeipelÏs theorem (von Zeipel 1924) to see if this could be the cause for our spectral appearance. The emergent Ñux from a stellar photosphere varies proportionally to the value of the local surface gravity. Therefore, for a rotating star in hydrostatic equilibrium, equipotential surfaces are also isothermal, isobaric, and isopycnic and the outward Ñux at any of these surfaces is dependent on the temperature gradient. Thus, the emitted Ñux (PT 4) is proportional to the value of the local e ective surface gravity. This e ect is referred to as gravity darkening.1 In general, gravity darkening is rarely of a magnitude, which will compete with or exceed ellipsoidal e ects, that are expected to be present in IR observations of CV secondaries. This is due to the fact that CV secondaries 1 As with a number of astronomical concepts, gravity darkening evolved based on optical observations, and clearly the darkening or brightening of a surface region depends on the bandpass of the observation. (approximate spectral types KÈM) all have convective envelopes for which gravity darkening is, at best, one-third the level present in radiative envelope stars such as W UMa systems. However, since we Ðnd no evidence for ellipsoidal variations in our ST LMi observations, we explore here the possibility that what we do see could be caused by gravity darkening. While we believe this is unlikely, given the fully convective nature of the secondary star in ST LMi, we feel that for completeness we should rigorously test the hypothesis. It can be shown (Kopal 1978, pp. 191È197, 322È331), which for typical CVs of any orbital period, the ratio of the three radii of the critical Roche lobe surface (R1, the distance from the center of mass to either side of the secondary star; R2, to the L1 point; and R3, to the back of the star) have almost constant ratios R1/R2 \ 0.66 and R1/ R3 \ This fact means that for a Roche lobe Ðlling secondary, the e ect of gravity darkening can be approximated by three di erent temperature regions on its surface. If we assign a temperature of 3000 K at R1 for the secondary under consideration here, we would expect cooler temperatures of 2750 and 2400 K at R3 (back) and R2 (L1 point), respectively, if the secondary star had a radiative envelope. This type of surface structure would produce a double, but uneven, humped light curve with predictable phases of maximum light. The maximum Ñux modulation, which could be expected because of gravity darkening at phases 0.0 and 0.5 for a fully convective secondary, is therefore of order *F \ 0.4. Other than a single broad hump 3È5 times this level (because of cyclotron emission), there is no evidence in our continuum light curve data (Fig. 3) for any modulations of this amplitude or phasing. Thus, we conclude that our observed modulations can not be reconciled with being caused by gravity darkening Stellar Activity: Starspots One of the Ðrst thoughts that comes to mind when dealing with a rapidly rotating late-type star with an apparent localized cool region is that of starspot activity. Shortperiod CVs contain secondary stars of mass [0.3 M _, which are fully convective in their structures (Howell, Rappaport, & Politano 1997). Single main-sequence stars of this approximate mass are typically slow rotators and inactive. However, similar mass main-sequence M stars with rapid rotation are found to be sources of high stellar activity, including Ñares, magnetic loops, and starspots. M stars, which rotate rapidly (the fastest of which are in dme-dme binaries such as CM Dra or YY Gem with rotation periods of order 1È2 days, or possibly faster rotators [\1 day] such as very young K and M stars in the Pleiades), are observed to show all the indicators of active chromospheres, i.e., Na, Ca, and H emission lines in the optical spectral region (formed at 7000È10,000 K regions in the chromosphere) and, for the middle to late M types, probable zebra ÏÏ surfaces. The latter term relates to the fact that their surfaces are so saturated with starspots that observationally Ñux modulations due to spotted and unspotted regions cannot be easily di erentiated since the regions are homogenized (E. Guinan 1999, private communication). Active M stars such as the dme pair CM Dra, show optical emission lines from their active chromospheres, but photometrically their light curves are modulated very little, only about 1% because of surface spots. This is in sharp

8 No. 2, 2000 IR SPECTROSCOPY OF SECONDARY IN ST LMi 911 contrast to modulations of up to 50% or more for stars, such as those of the RS CVn class, that contain KV stars that have large, localized spotted regions on their surfaces (E. Guinan 1999, private communication). M stars later than M5 V are not well observed, particularly in the IR spectral region; thus, the details of their level and modulation of chromospheric activity are poorly known. Apparently, the only published IR spectrum of an active M star is that by Short & Doyle (1998), who present a J-band (1.2 km) spectrum of the dme star AU Mic. This star shows emission lines in the optical region indicative of chromospheric activity yet has Pab ( km) in absorption. Short & Doyle discuss the fact that Pab will be in absorption even when other (optical) lines of hydrogen are in emission, but that Pab can quickly become an emission line if there is increased chromospheric pressure, i.e., if the temperature structure in the stellar atmosphere is such that the base of the chromosphere is hot enough to form Paschen lines. In other words, the spectral line behavior is simply reñecting the fact that the Balmer transitions come from the upper photosphere and lower chromosphere regions of a typical stellar atmosphere, while the Paschen lines are formed deeper in the photosphere (e.g., Figs. 7È32 of Mihalas 1978), an astrophysical example of the Boltzmann equation in action. The behavior of chromospheric activity in very late type main-sequence stars is currently not well understood. Extreme rapid rotation (as in CV secondaries) may cause the stellar interior to become so chaotic that organized magnetic Ðeld structures may not be possible. At some rate of rotation (perhaps less than 1 rotation day~1; E. Guinan 1999, private communication), the chromosphere becomes saturated with activity and further increasing the rotation rate will cause no additional increase in amount of stellar activity. Additionally, the very cool L stars may not be capable of producing chromospheres at all or may have atmospheric structures, which are di erent from other main-sequence stars (Allard et al. 1997). Theoretical work has shown that if the mass-loss rate can be kept at a very high level a radiative core can be maintained within the secondary star even when its mass falls below 0.3 M _ (S. Rappaport 1998, private communication). This high rate of mass transfer is unlikely to occur over the long term in CVs, but short-duration periods of very high mass transfer (such as in the ER UMa stars) may fall into this category. We note that there are no known low-mass stars that have rotation rates as fast as those of the secondaries in short period CVs. Thus, we have no prototypes to use as guides for what type of atmospheric activity these stars may produce or the timescales on which this activity may change. Given the above discussion, the fact that the secondary star in ST LMi is a fast rotator, and the likely possibility that starspot activity may be responsible for the complex temperature structure seen in our data, we would expect the spectra of the secondary star to show other indicators of stellar activity as well. We therefore examined our data to see if Paa or any of the Brackett series lines are present. Because of their weakness in such a cool stellar atmosphere, and the relatively low S/N of the spectra, rotational broadening may disallow their detection unless they were strongly in emission. We Ðnd no indication of their presence in any of our spectra. We note here, however, that Ciardi et al. (1998a) present an optical spectrum of ST LMi taken only 7 days after our K band observations. The optical spectrum shows that the Hb and Hc absorption lines contain weak emission cores, similar to that seen in active M stars. Ciardi et al. attributed this emission to the possible restarting of mass transfer; however, we entertain here the idea that the H lines, observed during a time of no spectral contamination by mass transfer, may have been revealing an active chromosphere on the late-type secondary star in ST LMi Critical Roche Surface We have shown above that secondary star irradiation, ellipsoidal variations, and gravity darkening are nonexistent in our observations of ST LMi. The idea of stellar activity (i.e., an active chromosphere with starspots) seems promising as an explanation of the variable temperature structure. Therefore, in this section we will examine how the atmospheric structure of the secondary star in a CV will be e ected by the location of the critical Roche surface. Cataclysmic variables evolve from longer to shorter orbital period during their lifetime. Such evolution and its consequences on the secondary star are discussed in Howell et al. (1997) and Howell et al. (2000). For our purposes here, we will examine four stages within the evolution of a CV, di erentiated by their rate of evolution. These four stages were chosen based on the work of Howell et al. (1997; see their Fig. 2) and relate directly to the four di erent evolutionary rates, which occur in the secondary star radius, dr /dt. Table 2 details the parameters used and calculated sec within this section for the four stages under consideration. Stage 1 is from initial contact (i.e., start of mass transfer) to an orbital period of near 3 hr (the top edge of the period gap where the secondary star begins to develop deep convective zones and eventually becomes fully convective when its mass drops to [0.3 M ); stage 2 is from 3 to 1.75 hr (and _ includes CVs, which form in the period gap); stage 3 is from 1.75 hr to the orbital period minimum; and stage 4 is from the period minimum to the end of the CVs evolution during which time the orbital period increases and the secondary star is degenerate. For each of the evolutionary stages, we assign mean values of M0, temperature, mass, radius, and log g (see Table 2; Howell et al. 1997). Roche (1849a, 1849b, 1873) developed the mathematical formulation of the properties of equipotential surfaces, but the results were generally not applied to stars until early in the 1900s. Eddington (1926) and later Chandrasekhar (1933) showed that the external shapes of distorted stars in close binaries were well approximated by constant gravity or Roche surfaces for stars modeled as polytropes. We are most familiar with the equipotential surfaces for close binary components, which Ðnally merge together at one point (the L1 point) and have a Ðgure-eight shape. The secondary star in a semidetached binary Ðlls its critical Roche surface and transfers matter to the primary star. Less discussed is that within this critical Roche lobe of the secondary other equipotential surfaces can be examined where each is successively smaller and more spherical than the previous surface (Kopal 1978, pp. 312È322). Thus, a secondary star, which shrinks inside its critical Roche surface2 during periods of low to zero mass transfer, could appear spherical in shape and show no ellipsoidal e ects. 2 We will see below that it does not have to be the actual stellar surface (q \ 2) that Ðlls the Roche Lobe during mass transfer or that shrinks within 3 it during low states.

9 912 HOWELL ET AL. Vol. 530 TABLE 2 PARAMETERS USED AND CALCULATED FOR CRITICAL ROCHE SURFACE LOCATION Parameter Stage 1 Stage 2 Stage 3 Stage 4 Orbital period (hr)... Contact to D3 3 to to P min Post P min Mean M0 (g s~1) ] ] ] ] 1014 dr/dt (R _ yr~1)... [2.5 ] 10~9 [4.6 ] 10~11 [6.3 ] 10~11 ]6.0 ] 10~12 Mean temp sec (K) Mean mass sec (M _ ) Mean radius sec (R _ ) v T (cm s~1) ] ] ] ] 105 q h (hr) log g (cm s~2) l (km) o M0 (g cm~3) ] 10~ ] 10~8 3.9 ] 10~8 2.2 ] 10~8 Phot o (g cm~3)... 10~9 10~7 10~5 10~4 Low chrom o (g cm~3)... 10~11 10~9 10~7 10~6 B crit (G) ,463 Upper photosphere to Critical Roche Surface Location... Lower photosphere lower chromosphere Upper chromosphere Upper chromosphere In Figure 6, we have calculated the radii of the four equipotentials, which deðne the Roche lobe for one member of a binary star. Figure 6 uses the parameters of the ST LMi binary and shows the four radii for the critical Roche surface (which forms the secondary star Roche lobe equipotential surface). The lines are labeled as to which of the four radii they correspond to where R2 and R3 are in the x-direction (the line connecting the two stars) and X is in toward the L1 point. The horizontal dotted line was calculated from equation (4) in Howell et al. (2000) and represents the radius assigned to a spherical Roche Lobe having the same volume as the actual egg-shaped one. This radius is usually taken as the radius of the secondary star. Using the information given in Figure 6, we note that a 10% shrinkage ÏÏ of the secondary star within its critical Roche lobe by would still produce 0.1 mag ellipsoidal variations. At least a 20% decrease would be needed in order to produce small enough variations so as to go unobserved here. For the secondary in ST LMi, a 10% shrinkage Radius X 10 5 (km) R3 (X out ) R2 (X in ) R1 (Y) R4 (Z) Radius of Roche Lobe % of Roche Lobe FIG. 6.ÈThe four Roche equipotential surfaces that deðne the critical Roche surface for the secondary star in ST LMi. The R2 value at x \ 0 deðnes the location of the L1 point. The dotted line is the radius of an equivalent volume sphere and is generally taken as the radius of the secondary star Roche lobe. amounts to a physical distance of 14 ] 103 km. While it is hard to imagine that a star could change its physical radius by this amount, or more, on short timescales such as those observed for high- and low-state transitions (a few weeks to months), we note that this distance is only 2È3 times the height of the suns chromosphere and about equal in size to the chromosphere in an active M star. Therefore, if we could show that it is the chromosphere, and not the q \ 2 photo- 3 sphere, that actually Ðlls the critical Roche lobe and is the source of the transferred material, we may be able to account for the lack of ellipsoidal variations seen in ST LMi during a low state and provide a possible mechanism, which could explain CV high and low states. Using the mass transfer rate for a given CV (Howell et al. 1997) as an indicator of the total amount of material leaving the secondary star per unit time, we can calculate the mean density of the material, which must be transferred to the primary and determine from where within the stellar atmosphere of the secondary it must be removed. The general properties used in this section to determine the values calculated in Table 2 are taken to be approximately equal to those of equal mass main-sequence stars. At present, there are no detailed models of CV secondaries or their atmospheric structure, thus we have no better estimates to use. Material transferred through the L1 point does not simply come from the region near L1: it migrates from the entire critical Roche equipotential of the secondary star. This is the surface we call the Roche lobe and one that encompasses the entire star. Let us start our calculation by determining the timescale needed to empty one scale height worth of material from the Roche lobe. This emptying out of a Roche lobe scale height will occur on a dynamic timescale and is given approximately by the radius of the secondary star (i.e., the radius of the Roche lobe) divided by the thermal velocity of the gas (v /R ). With the assumption of a Boltzmann distribution for T pure sec hydrogen gas within the secondary star atmosphere, the thermal velocity, v, is simply (3kT /m)1@2, and the calculated Roche lobe sweep-out T times (q ) are of order a few hours (Table 2). In order h to determine the mean density of material being swept from the Roche surface, we must determine the height of this material within the atmosphere of the secondary star.