A
The Astrophysical Journal, 679:1522Y1530, 2008 June 1 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
X-RAY SPECTROSCOPIC SIGNATURES OF THE EXTENDED CORONA OF FK COMAE Jeremy J. Drake,1 Sun Mi Chung,1 Vinay Kashyap,1 Heidi Korhonen,2 Adriaan Van Ballegooijen,1 and Detlef Elstner3 Received 2005 July 4; accepted 2008 January 8
ABSTRACT High-resolution Chandra X-ray spectra and surface Doppler images obtained from optical spectra of the rapidly rotating giant FK Com have been analyzed in order to investigate links between coronal and surface magnetic structures. Net redshifts were detected at the 3 level in the light of Ne k12.13 amounting to 140 km s1. Smaller shifts of 60 km s1 at the 2 level are seen in the X-ray spectrum as a whole, while the observed position of O viii k18.97, the second strongest line in the spectrum after Ne x, is also consistent with its rest wavelength. There is no statistical difference between redshifts during the first and second halves of the observation. Spectral line widths are most consistent with thermal broadening combined with rotational broadening at a scale height of 1R?, although they are also statistically consistent with surface rotational broadening. We interpret the results as indicative of hot plasma predominantly residing in extended structures centered at phase ¼ 0:75 with a size similar to that of the star itself. The contemporaneous Doppler images of the surface of FK Com reveal active longitudes at phases 0:6 and 0.9. We speculate that extended coronal structures correspond to magnetic fields joining the two active longitudes, which theoretical models predict are of opposite magnetic polarity. Such structures are supported by coronal potential field extrapolations of typical theoretical model surface magnetic field distributions. This study was based on a relatively short 40 ks Chandra observation. A much longer observation of FK Com with the HETGS, combined with contemporaneous Zeeman-Doppler imaging, would be of great value for constraining magnetospheric structure and dynamo models of rapidly rotating stars. Subject headingg s: stars: activity — stars: coronae — stars: individual ( FK Comae) — stars: late-type — X-rays: stars Online material: color figures
Chandra High Energy Transmission Grating (HETG) spectrum of Algol caused by the orbital motion of Algol B and found evidence for the presence of excess line broadening amounting to approximately 150 km s1 above that expected from thermal motion and surface rotation. Chung et al. (2004) inferred that a significant component of the corona at temperatures less than 107 K has a scale height of order the stellar radius. More recently, Hussain et al. (2005, 2007) have found evidence for rotationally modulated Doppler shifts in Chandra Low Energy Transmission Grating ( LETG) spectra of AB Dor that they attribute to active regions seen in Zeeman-Doppler imaging and coronal magnetic field extrapolations. Analysis of Chandra HETG spectra of AB Dor by Drake et al. (2008) found that rotational broadening was less than expected from a uniform corona covering the surface and implied a pole-dominated corona. These results represent the first direct spectroscopic evidence that the dominant coronal activity on rapidly rotating active stars is associated with the dark polar spots commonly seen in photospheric Doppler images (e.g., Strassmeier 2002). FK Com presents another rare case of a star with a large projected equatorial velocity (v sin i 160 km s1; Huenemoerder et al. 1993; Korhonen et al. 2000) that is accessible to Chandra grating spectroscopy. It is the eponymous prototype of the small group of FK Comae stars that appear to be single, rapidly rotating, late-type giants thought to have evolved from a coalesced binary (Bopp & Stencel 1981). Based on the similarity of its H line profile to the shape and phase variability seen in cataclysmic variables and T Tauri stars, Kjurkchieva & Marchev (2005) speculate that FK Com has a disk illuminated by a ‘‘low-mass hot secondary orbiting the disk,’’ although the line is more plausibly related to corotating circumstellar material (Welty et al. 1993;
1. INTRODUCTION Several papers in recent years have succeeded in demonstrating the capability of Chandra diffraction grating spectra to infer spatial properties of the hot coronae of late-type stars through rotationally driven Doppler shifts and broadening (Brickhouse et al. 2001; Chung et al. 2004; Hussain et al. 2005, 2007; Ishibashi et al. 2006; Huenemoerder et al. 2006; Drake et al. 2008). This progress is important because purely photometric means of investigating coronal structure, such as eclipse mapping or rotational modulation, are fraught with ambiguities in disentangling intrinsic source variations from variations of purely geometric origin. Unfortunately, with a resolving power of k/ k 1000 the Chandra grating spectrometers have a limited sensitivity to Doppler shifts—even velocities as high as 100 km s1 correspond to shifts or broadening of only a fraction of the instrumental profile width. Projected equatorial rotation velocities of late-type stars are typically an order of magnitude lower, even in the case of quite young and active stars. Existing studies have therefore concentrated on nearby stars with large projected rotation velocities of v sin i k 100 km s1. Brickhouse et al. (2001) observed Doppler shifts in the X-ray line profiles of the eclipsing W UMaYtype contact binary 44i Boo with an orbital phase that indicated that at least half of the emission was localized at high latitude in the primary star. Chung et al. (2004) detected Doppler shifts in the 1
Smithsonian Astrophysical Observatory, MS-3, 60 Garden Street, Cambridge, MA 02138;
[email protected]. 2 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D -85748 Garching bei Muenchen, Germany;
[email protected]. 3 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D -14482 Potsdam, Germany; elstner@ aip.de.
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Fig. 1.—Chandra HETG spectrum of FK Com, showing both HEG and MEG traces, binned at 0.0025 and 0.005 8 intervals, respectively. Prominent lines are labeled; lines that were used in our analyses are labeled with a larger font.
Huenemoerder et al. 1993). Current estimates for the spectral type of FK Com range from G2 III to G7 III, and its rotation period is 2.4 day (e.g., Bopp & Rucinski 1981; Walter & Basri 1982; Korhonen et al. 2000). Significant surface spot activity on FK Com was first inferred from periodic photometric variability (Chugainov 1966; Bopp & Rucinski 1981) and later in more detail by extensive photometry and Doppler imaging, which revealed spots mainly at high latitudes (Piskunov et al. 1994; Korhonen et al. 1999, 2000, 2001, 2004, 2007; Ola´h et al. 2006; Panov & Dimitrov 2007). A remarkable discovery is the detection of two permanent active longitudes that are 180 apart and the associated ‘‘flip flop’’ behavior. During a flip-flop event, the dominant part of the spot activity abruptly shifts from one active longitude to the other (Jetsu et al. 1991, 1993), with a cyclic period of about 6.4 yr (Korhonen et al. 2002). This flip-flop phenomenon has now been identified in eight other stars, including the Sun (Elstner & Korhonen 2005). Ultraviolet spectroscopy of transition region and coronal forbidden lines of rapidly rotating giants such as FK Com reveals evidence for rotational broadening in excess of that expected from surface rotation by factors of 2 (Ayres et al. 2003; Redfield et al. 2003). An analysis by Ayres et al. (2006) of Far-Ultraviolet Spectroscopic Explorer (FUSE ) observations of FK Com suggests that C iii k977 and O vi k1031 (formed at temperatures 3 ; 104 and 3 ; 10 5 K, respectively) are broadened to full-width halfmaxima in excess of 500 km s1, corresponding to at least twice the projected surface equatorial rotation velocity. In this paper, we apply techniques used to analyze Doppler shifts and broadening of the X-ray spectra of Algol and AB Dor by Chung et al. (2004) and Drake et al. (2008), respectively, to the Chandra HETG spectra of FK Com. We compare results to expectations based on the likely locations of active regions as revealed by contemporaneous visible-light Doppler images of the
surface of FK Com. The X-ray light curves and spectra presented here were first analyzed by Buzasi et al. (2003), who performed a differential emission measure analysis and estimated the abundances of prominent elements. Gondoin et al. (2002) present similar results based on XMM-Newton observations. 2. OBSERVATIONS 2.1. X-Ray Spectra FK Com was observed by the Chandra HETG and ACIS-S, on 2000 March 27 between UT 04:40 and UT 16:46, for a net exposure time of 41,400 s. Here we analyze the products of standard CIAO 3.1 processing, and in particular the Medium Energy Grating (MEG) spectrum. The measurement of spectral lines and subsequent computations were performed using the IDL Package for Interactive Analysis of Line Emission ( PINTofALE).4 The HETG spectra are illustrated in Figure 1, while a light curve obtained from the dispersed source events (spectral orders 1Y3) is shown in Figure 2. Buzasi et al. (2003) discussed the X-ray light curve; it exhibits the quick rise and exponential decay typical of a flare. This flare is apparently still in the rise phase at the start of the observation and peaks at 2.5 ks, with a decay beginning at about 7 ks into the observation. The decay lasts for most of the duration of the observation. The analysis that follows addressed the observation as a whole and also in specific time intervals illustrated in Figure 2. As pointed out by Buzasi et al. (2003), the HETG spectrum is characterized by H-like and He-like lines of Si, Ne, and O, together with lines from highly ionized species of iron, such as Fe xxiv, Fe xxv, and Fe xxvi, indicating the presence of very 4
PINTofALE is freely available from http:// hea -www.harvard.edu / PINTofALE.
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Vol. 679 TABLE 1 Parameters of FK Comae Used in Surface Doppler Imaging and X-Ray Analyses Parameter
Adopted Value
Teff (unspotted) ................. logg .................................. Radius .............................. Period ............................... v sin i................................. Inclination ........................ Microturbulence ............... Macroturbulence ..............
5000 K 3.5 8.7 R 2.4002466 day 159 km s1 60 1.0 km s1 2.0 km s1
phases of the Chandra observation start and stop (0.9 and 1.1, respectively) in Figure 4. Fig. 2.—Observed X-ray light curve of FK Com derived from dispersed HEG and MEG events. The top axis shows the rotational phase computed with the ephemeris HJD ¼ 2;439;252:895 þ (2:4002466 0:0000056)E of 1993 and 1994, and the bottom axis shows the elapsed time in days since the start of the observation.
high-temperature coronal material. Their differential emission measure distribution ‘‘shows a distinct low-state bump from logT ¼ 7:2 to logT ¼ 7:7, superimposed on which appears to be the flare contribution, which rises from logT ¼ 7:7 to peak around logT ¼ 8:0, and for which the peak emission is about 4 times the maximum quiescent DEM level.’’ 2.2. Doppler Imaging of the Stellar Surface To understand the results of the X-ray observations discussed here in the context of the surface activity of FK Com, we have investigated Doppler images that correspond approximately to the time of the observation (2000 March). A detailed description of the observations and methods used for the surface maps is given in Korhonen et al. (2006); a short description is also presented in Korhonen et al. (2004). Here we only describe the Doppler imaging analysis in brief. Observations were obtained between 2000 March 29 and 2000 May 5 at the Kitt Peak National Observatory in Arizona, using the 0.9 m coude´ feed telescope. The F3KB CCD detector was employed, together with grating A, camera 5, and the long collimator. This configuration gave the resolving power k /k ¼ 27;000. Using spectra spanning more than a month is quite unusual in Doppler imaging, as the surface structures often change on much shorter timescales. In this case, using observations with such a long timespan is justified, as the light curve of FK Com is very stable during the year 2000 (see Korhonen et al. 2002). Inversions of spectra and photometry to produce surface Doppler images were accomplished with the code INVERS7, based on the Tikhonov regularization inversion method (e.g., Piskunov et al. 1990). It was written by N. Piskunov and subsequently modified by T. Hackman ( Hackman et al. 2001). The relevant stellar parameters adopted for both surface Doppler imaging and X-ray analysis are listed in Table 1; further details concerning the selection of these parameters and the Doppler imaging and related model calculations can be found in Korhonen et al. (1999, 2000). Rotational phases were calculated using the Jetsu et al. (1993, 1994) ephemeris obtained from 25 years of photometrical observations, HJD ¼ 2;439;252:895 þ (2:4002466 0:0000056) E. The derived surface temperature maps for FK Com for the epoch 2000 March are illustrated in pseudo-Mercator projection in Figure 3. We also illustrate spherical maps for the approximate
3. X-RAY ANALYSIS 3.1. Doppler Shifts In earlier work (Chung et al. 2004), we developed a crosscorrelation method to search for velocity shifts in Chandra spectra, whereby observed spectra are Doppler-shifted by different velocities, and compared at each step with model or reference spectra. The advantage of this method is that the whole spectrum is used at once, rather than just the limited signal of individual spectral lines. Uncertainties in the derived Doppler shifts are determined using a Monte Carlo method, whereby the observed spectrum is resampled assuming Poisson errors and the analysis is repeated a sufficient number of times to obtain a well-sampled distribution (typically 100). We refer the reader to the earlier work for a more complete description of this method. We applied the cross-correlation analysis to spectra integrated over the entire observation and to the individual segments (i1 and i2) illustrated in Figure 2. These intervals were chosen to have equal exposure times and include data from both the MEG and the High Energy Grating ( HEG). The segment that falls on the first half of the observation includes most of the flare emission, while the second segment includes mostly quiescent emission. For a reference standard we employed a synthetic spectrum computed based on the differential emission measure ( DEM ) as a function of temperature and abundances, obtained by Buzasi et al. (2003). We note that the Buzasi et al. (2003) results are similar to those obtained from a 2001 January XMM-Newton observation by Gondoin et al. (2002). The spectrum synthesis was performed using the PINTofALE suite, employing spectral line emissivities from the APED database (Smith et al. 2001 and references therein) and the ionization equilibrium of Mazzotta et al. (1998).
Fig. 3.—Surface Doppler image of FK Com in pseudo-Mercator projection for 2000 March, corresponding to the epoch of the Chandra observation. The gray scale represents the surface temperature variation, as indicated by the sidebar.
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Fig. 4.—Surface Doppler images for rotational phases 0.9 (left) and 1.1 (right), corresponding approximately to the start and end of the Chandra HETG observation. The gray scale corresponds to the surface temperature variations as illustrated in the pseudo-Mercator projection in Fig. 3.
The results of the Doppler shift cross-correlation analysis are summarized in Table 2. The net Doppler shift obtained for the integrated observation was 68 31 km s1 for the MEG spectrum. We were unable to obtain a net Doppler shift for the HEG spectrum alone because of the lack of signal. We also analyzed the HEG + MEG spectra simultaneously and obtained a redshift of 55 28 km s1. Corresponding shifts measured from HEG + MEG spectra for the two intervals, i1 and i2, were 54 30 km s1 and 94 40 km s1, respectively. Since FK Com experienced a significant flaring episode during the Chandra observation, it is possible that lines formed at different temperatures could arise predominantly from different areas of the stellar surface. In this case, it is interesting to examine individual lines for Doppler shifts. Unfortunately, the somewhat sparse photon count in the FK Com data precludes a detailed analysis for all but two lines, Ne x k12.13 and O viii k18.96. Visual inspection of the Ne x k12.13 line indeed revealed some indication of a redward shift compared to its expected location; this shift was not as apparent in O viii at longer wavelengths. We applied the cross-correlation technique to these lines individually. In the case of Ne x, this involved analysis of HEG and MEG lines both individually and combined for the interval i1 þ i2, and combined for i1 and i2 separately. For O viii, there was insufficient signal to treat i1 and i2 separately, and we analyzed only the full observation interval i1 þ i2. The results can be found in Table 2. TABLE 2 FK Comae Doppler Shifts for Data Integrated across All Wavelengths, Individual Emission Lines of Ne x and O viii, and Data Split into Equal Exposure Times Velocity ( km s1) Time Interval
Spectral Feature
i1 + i2 .................. i1 + i2 .................. i1 + i2 .................. i1 .......................... i2 .......................... i1 .......................... i2 ..........................
k2Y25 Ne x k12.13 O viii k18.97 k2Y25 k2Y25 Ne x k12.13 Ne x k12.13
MEG
HEG
68 31 ... 115 44 157 46 25 60 ... ... ... ... ... ... ... ... ...
MEG + HEG 55 142 ... 54 94 98 139
28 35 30 40 41 54
The Ne x k12.13 line exhibits the largest shift of approximately 140 km s1. The measurements for the MEG and HEG spectra lie at slightly more than the 2 and 3 significance levels, respectively. In contrast, O viii k18.96 does not exhibit a significant redward shift. In the case of Ne x, the observed shifts are most likely associated with rotation rather than plasma flows; we address this in x 4. The observed HEG and MEG Ne x k12.13 lines are compared with synthetic spectra computed for redshifts of 0 and 140 km s1 in Figure 5. 3.2. Line Broadening FK Com has a projected equatorial rotation velocity of v sin i 160 km s1 (Huenemoerder et al. 1993; Korhonen et al. 2000) and, in principle, is one of the best candidates for the study of coronal extent and morphology through spin-driven Doppler broadening. If coronal lines are indeed broadened to 600 km s1, as the report of Ayres et al. (2004) suggests, this should be easily detected in the Chandra spectra. In order to investigate line broadening, we analyzed the two ‘‘bright’’ individual spectral lines that contained sufficient signal to be measurable; these were the H-like Ly doublets Ne x k12.13 and O viii k18.97. We also investigated the fast Fourier transform method developed by Drake et al. (2008) in their study of HETG spectra of AB Dor, applied to the full wavelength range of the MEG spectrum. However, this proved to be insufficiently sensitive because of the dominance of low counts in the vast majority of spectral bins. The individual line analysis technique uses as its basis synthetic line profiles computed for different projected rotation velocities assuming uniform surface emission. Full account is taken of thermal broadening, which is computed element by element; for this we again employed the DEM of Buzasi et al. (2003). We carried out the line-broadening analysis relative to the evolved star Vel, which has a very low projected rotation velocity of v sin i ¼ 6 km s1 (de Medeiros & Mayor 1995). This differential analysis eliminates uncertainties arising from calibration of the instrument line response function. Synthetic line profiles were calculated for Vel based on the DEM of Garcia-Alvarez et al. (2006). Spectral line widths were measured using the PINTofALE FITLINES program (Kashyap & Drake 2000) by fitting a function of the form F(k) ¼ a/f1 þ ½(k k 0 )/ 2 g , where a is the
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Fig. 6.—FK Com line widths for observed and synthetic line profiles, relative to Vel. Synthetic line profiles for FK Com were computed for different coronal scale heights; since the projected rotation velocity of Vel is only 6 km s1, rotational broadening is completely negligible. [See the electronic edition of the Journal for a color version of this figure.]
Fig. 5.—Observed Ne x k12.13 lines as seen in HEG (top) and MEG (bottom) spectra compared with theoretical model profiles computed for a redshift of 140 km s1 and at rest. [See the electronic edition of the Journal for a color version of this figure.]
amplitude and is a characteristic line width. For a value of the exponent ¼ 2:5 in the denominator, this function has been found to be a good match to observed HETGS line profiles, which are not well matched by Gaussian profiles ( Drake 2004). FITLINES employs Levenberg-Marquardt minimization and a Monte Carlo sampling about the goodness of fit for error estimation. We list measured line widths for FK Com and Vel, together with corresponding differences in FK Com and Vel theoretical model profiles, in Table 3. The measured line widths are compared to those of Vel and to theoretical FK Com line profiles simulated assuming different coronal scale heights in Figure 6.
Here we define the scale height as the height above the stellar surface, expressed in units of the stellar radius, R?, such that surface rotation corresponds to a height of 0R?. Note that under this definition negative scale heights are possible and correspond to the case in which emission occurs more toward the poles than the equator, such that broadening is less than that induced by rotation of uniform surface emission. The individual observed line widths shown in Figure 6 have fairly large uncertainties compared with the differences between theoretical profiles corresponding to different coronal scale heights. It is therefore of interest to combine the different line measurements to increase the signal-to-noise ratio. This is not straightforward, since each line is sensitive to rotational broadening to a different extent and in a nonlinear fashion. We therefore adopted a Monte Carlo approach, in which we sampled the measured line width confidence interval (assumed Gaussian) and interpolated the implied scale height using the theoretical line widths computed as a function of scale height. This was done relative to Vel, in the sense that we compared observed line width differences relative to Vel with theoretical line width differences. This was done 100 times each for the O viii MEG and Ne x HEG and MEG lines listed in Table 3 to obtain the distributions of scale heights for each line. Finally, we computed the error-weighted mean of the different scale height distributions, and this is illustrated in Figure 6. Based on this error-weighted mean, we found the median scale height to occur at 0.15R?, with 1 and 3 upper limits of 0.94R? and 1.98R?, respectively. The lower 1 limit occurs at 1.15R?.
TABLE 3 Observed and Model Line Widths for FK Comae and Velorum FWHM (8) Model a
Observation Grating
Rest Wavelength (8)
FK Com
Vel
FK Com
Vel
FK Com Excess Relative to Velb
MEG........................ MEG........................ HEG ........................
12.13 18.97 12.13
0.026 0.005 0.026 0.015 0.015 0.012
0.020 0.001 0.019 0.003 0.015 0.002
0.023 0.028 0.017
0.020 0.024 0.013
0.003 0.003 0.005
a b
Model line widths include instrumental, thermal, and surface rotational broadening. Excess line widths refer to (wobs wmod ) FK Com (wobs wmod ) Vel , where wobs and wmod refer to observed and model line widths, respectively.
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4. DISCUSSION 4.1. X-Ray Doppler Shifts and Line Broadening The cross-correlation Doppler analysis shows the FK Com spectrum to be redshifted by an average of 60 km s1 for the period of the observation, based on results for the entire 2Y25 8 spectrum. The redshift is, however, most pronounced in the light of Ne x k12.13—the only line for which sufficient signal is present to investigate wavelength shifts in both intervals, i1 and i2, separately. The shift observed in Ne x amounts to 140 km s1 for both intervals combined. In contrast, the next brightest line, O viii k18.97, exhibits no statistically significant deviation from its rest wavelength, although the 2 upper limit is consistent with the shift found for Ne x. There is also no statistically significant evidence for a change in redshift between intervals i1 (flare dominated) and i2 (tail of flare decay and relative quiescence), although both Ne x and the combined HEG + MEG spectra provide some indication that larger shifts might be present in the second interval than the first. These two results are, of course, not independent, since the Ne x line contributes some part to the combined 2Y25 8 spectra. The lack of a significant change in the observed shift is interesting because it implies that the location of the flaring source is similar to that which dominates the quiescent emission, at least for the hotter lines. The lack of a significant shift in O viii might appear puzzling; formally, the result is consistent with that for the spectrum as a whole, although it deviates from the Ne x result by 2 . The presence of systematic velocity shifts points either to plasma flows at least partially along the line of sight or to an asymmetric distribution of plasma on the star, resulting in net rotation-driven shifts. The former seems unlikely, since it would imply net downward flows of the hot plasma that dominates the X-ray spectrum, whereas the opposite would be expected, cooler plasma condensing and collapsing under gravity, with upflows of heated plasma. We therefore interpret the net redshifts as betraying the presence of a preponderance of the emitting plasma on the receding hemisphere. In this scenario, differences between Ne x and O viii shifts could be caused by different distributions of cooler and hotter plasma; cooler P3 ; 106 K plasma would appear to be more uniformly distributed on the star based on the indication of a smaller O viii redshift. One of the initial aims of this study was to investigate the possible connection between surface spot distributions—presumed to correspond to areas of enhanced magnetic activity (e.g., Korhonen et al. 2004 and references therein)—and coronal activity. Since we cover only a small part of the rotation phase, any estimate of the location of the X-rayYbright plasma on the receding hemisphere based on the observed velocity shift depends to a large extent on the coronal scale height. The principal surface feature of FK Com revealed by the Doppler images is a high-latitude (65 ) dark spot located at phase ¼ 0:6. During the Chandra observation, this spot would have had a line-of-sight radial velocity varying from 65Y0 km s1 during the observation. Since we do find some evidence for a redshift in the range of about 100 km s1 during the second interval, i2, when the dark spot has no net radial velocity, it seems unlikely that the dominant, localized hot plasma responsible for the redshifted X-rays is directly associated with this region alone. Instead, the relatively constant redshift during the observation implies that the emission is centered at phase 0.75Y0.8, where equatorial surface velocities are 150 km s1. Plasma located at the most active latitudes of 65 inferred from Doppler imaging would imply a coronal scale height of 1R?. In this scenario, a
Fig. 7.—Coronal scale height of FK Com in units of the stellar radius, R?, based on the combined data from all the measured lines in both HEG and MEG spectra, as realized by a Monte Carlo sampling of the FK Com line widths relative to Vel. The vertical lines indicate the 1 and 3 upper limits. Surface rotation corresponds to R? ¼ 0. [See the electronic edition of the Journal for a color version of this figure.]
plausible magnetic field configuration might be loops joining the darker surface regions between phases ¼ 0:6 and 1. Further clues can be obtained from the observed line widths. While the rather poor signal-to-noise ratio for individual lines renders their widths statistically compatible with no rotational broadening (Fig. 6), taken together they are more consistent with surface rotation or a width of 300 km s1 (Fig. 7). The firm 3 upper limit corresponds to a scale height of 2R?, or a width of 900 km s1. In considering these widths, however, it must be kept in mind that the net redshifts imply that we are seeing emission that is dominated by one hemisphere of the star; line widths then reflect broadening predominantly from only half of the star, and the corresponding coronal scale heights required to produce this effect are essentially twice that for the case of uniform surface coverage. We conclude, tentatively, that the line width and centroid information support a picture in which the X-ray emission from FK Com during the Chandra observation originates predominantly from phases in the range ¼ 0:5Y1, the same phase range that optical surface Doppler imaging reveals to be most spotted, with a scale height of order the stellar radius. 4.2. Coronal Structure of Rapidly Rotating Giants The above picture is supported in general by other observations of rapidly rotating evolved stars. We note some other relevant studies below. Gondoin et al. (2002) concluded that flaring activity seen during two 2001 January observations of FK Com by XMM-Newton ‘‘were partly grouped within a large compact region of about 30 extent in longitude reminiscent of a large photospheric spot.’’ If correct, this would present a scenario similar to that outlined above, in which we see emission dominated by one hemisphere. However, it is not clear to us how the longitude of flares in the XMM-Newton observation could be constrained, since no Doppler shift, or other spatial information, appears to be present in the data. More detailed and stringent constraints on line widths and shifts can, at least in principle, be obtained from FUSE and Hubble Space Telescope (HST ) UV-FUV spectrometers that provide much greater resolving powers than can be achieved at X-ray wavelengths. As noted in x 1, Ayres et al. (2006) found O vi k1031 and
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C iii k977 broadening in excess of 500 km s1 based on FUSE spectra. Such broadening corresponds to a scale height of 1R? if it results from rotation alone—similar to that found here based on X-ray lines formed at much hotter temperatures. Interestingly, Ayres et al. (2006) also compared observed FUV Doppler shifts with photospheric Doppler images and concluded that the O vi and C iii lines could not originate directly above the dark surface spots present during the observation, similar to our conclusions here. An earlier study of these and other transition region (T 105 K) lines in rapidly rotating Hertzsprung gap giants by Ayres et al. (1998) also found evidence for suprarotational broadening corresponding to scale heights of 1R?. These authors pointed out that such a scale height is an order of magnitude larger than the thermal scale height for a T 105 K plasma and proposed an explanation based on the unusually long filling times of extended loop structures: the extended loop-filling timescale leads to significant cooling of evaporated material during the filling phase, which then leaves warm plasma well above its thermal scale height. They noted the possibility of centrifugal trapping of warm plasma in extended loops near the corotation radius, as has been argued for the rapidly rotating young dwarfs typified by AB Dor (e.g., Robinson & Collier Cameron 1986; Collier Cameron & Robinson 1989; Ferreira & Jardine 1995; Jardine et al. 2001 and references therein). Similar excess broadening was measured in C iii k977 and O vi k1032 by Dupree et al. (2005) from FUSE spectra of 31 Com (v sin i ¼ 67 km s1; de Medeiros & Mayor 1999). However, they also detected signatures of outflow in the same lines and suggested that they are formed in an extended windlike atmosphere, rather than in a magnetically confined plasma. Coronal forbidden lines of Fe ( Fe xviii k974, Fe xix k1118, and Fe xxi k1354) that are formed at temperatures similar to the Ne x lines studied here complete a consistent picture, showing broadening similar to the cooler transition region lines in rapidly rotating giants corresponding to scale heights of 1R? (Ayres et al. 2003; Redfield et al. 2003). Other evidence from Chandra spectra of rapidly rotating evolved stars also supports the general scenario of coronal scale heights comparable to the stellar radius. Chung et al. (2004) found evidence for excess broadening in the X-ray lines of Algol, which originate from the K2 subgiant (Algol B). Photoexcitation of the intercombination lines of He-like O by the radiation field of Algol A also failed to exhibit the phase dependence that would be expected from a compact corona. Finally, we note that Audard et al. (2004) detected line broadening in excess of the instrumental profile in Chandra spectra of the active single giant YY Men (v sin i ¼ 45 km s1; Piskunov et al. 1990). While these authors found the measured line widths reasonably consistent with thermal broadening in the extremely hot (up to 108 K) corona of this star, they also suggest that some contribution from rotational broadening due to X-rayYemitting material high above the surface could be present as well. While only preliminary at present, the line of evidence suggests that coronal structure on rapidly rotating giants is likely more extended relative to the stellar radius than that on similarly rotating dwarfs, as might be expected from their respective surface gravities. Of particular note is the recent comparison of the coronal model found for the K0 dwarf AB Dor by extrapolation of the surface magnetic field distribution found from ZeemanDoppler imaging by Hussain et al. (2007). Those models indicate that the X-rayYemitting corona is likely somewhat less extended than that for FK Com, with a maximum height of 0.3Y0.4R?.
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Brickhouse et al. (2001) and Huenemoerder et al. (2006) also find evidence for a compact corona based on rotational modulation and line shifts of Chandra HETGS spectra of the contact binaries VW Cep (K0 V and G5 V) and 44i Boo (G0 V and G0V). 5. THEORETICAL FOOTNOTE Moss et al. (1995) showed that mean-field dynamos in rapidly rotating stars give rise to nonaxisymmetric modes and fields. Moss (2004, 2005) and Elstner & Korhonen (2005) have succeeded in modeling the characteristics of flip-flop activity behavior, first identified in FK Com, but now found in eight other stars, through a mixture of nonaxisymmetric dynamo modes and oscillating axisymmetric modes. The nonaxisymmetric dynamo modes have magnetic configurations that give rise to two starspots 180 apart, with opposite polarities. It therefore appears quite plausible that magnetic fields capable of trapping coronal plasma could join the two active longitudes. Such magnetic structures would be of a size similar to that of the star itself. In the case of FK Com, we speculate that such a structure is responsible for the net redshift we see, which appears to originate from plasma centered at phase 0:75. Following this this speculation, we have investigated the types of coronal structure that might be supported by the FK Com dynamo model of Elstner & Korhonen (2005) through potential field extrapolation of the model prediction of the surface magnetic field. We used the extrapolation method described by Hussain et al. (2002) with the electric currents set to zero (Clm ¼ 0). We chose a surface field map from the Elstner & Korhonen (2005) simulations that were qualitatively similar to the surface spot map shown in Figures 3 and 4, specifically, with one of the dominant latitude spots somewhat stronger than the other. The model predicts the radial field component at the stellar surface, and we computed the potential field for an assumed source surface radius of 1.8R?. The source surface radius is an unconstrained free parameter that defines the radius at which the open field dominates and is assumed to be radial. The value of 1.8R? was chosen by iteration, in order to ensure that the source surface radius was only slightly larger than the maximum closed loop heights. Significantly larger values do not change this closed loop height appreciably, but result in a population of loops that are not magnetically confined. In Figure 8 we show the resulting surface flux distribution and 100 randomly selected closed field lines illustrating the hot corona represented by a minimum magnetic pressure B 2 /8 > 2 dyne cm2. At a temperature of 107 K, this field would be capable of sustaining a plasma density of k109 cm3. While this coronal model is obviously very schematic and not directly applicable to FK Com, it does illustrate that reasonably extended coronal plasma can be sustained by its expected type of surface magnetic field distribution. The model confirms that the polar spots, being of opposite polarity, will harbor connecting loops that would tend to give rise to pole-dominated emission. However, the model also shows the connection of these polarized high-latitude regions to lower latitudes whose polarity is opposite to that of the dominant spot. These lower latitude fields would give rise to significant rotational broadening as appears to be seen in rapidly rotating active giants. 6. CONCLUSIONS A sensitive analysis of Chandra HETG spectra of FK Com has revealed redshifts of 140 km s1 in Ne x k12.13 and a strong indication of a smaller shift of 60 km s1 in the spectrum
No. 2, 2008
EXTENDED CORONA OF FK Com
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Fig. 8.—Potential field extrapolation of the surface magnetic field predicted by the flip-flop model of Elstner & Korhonen (2005) for an assumed source surface radius of 1.8R?. The field lines shown correspond to 100 randomly selected closed field lines that are capable of sustaining a hot corona, with a magnetic pressure B 2 /8 > 2 dyne cm2. [See the electronic edition of the Journal for a color version of this figure.]
analyzed as a whole. In contrast, no significant shifts are seen in O viii, although the 2 upper limit is consistent with the shift found for Ne x. There is no indication of any statistically significant change in redshift between the first and second halves of the observation. We suggest that the redshifted emission results from plasma residing predominantly in extended structures centered at phase ¼ 0:75 with a scale height similar to the stellar radius. This phase is midway between two dark active longitudes revealed in contemporaneous visible-light surface Doppler images. We speculate that the coronal structures revealed by Doppler shifts correspond to magnetic fields joining these two active longitudes, which theoretical models predict are of opposite magnetic polarity. A significant radial extent of X-rayYemitting plasma up to 1R? is consistent with the observed widths of Ne x and O viii lines. Such extended structures are qualitatively supported by coronal potential field extrapola-
tions of theoretical flip-flop dynamo model surface magnetic field distributions. The present study is limited in scope by the relatively short Chandra observation; more phase coverage and greater signal are required to provide more quantitative constraints on magnetospheric structure and dynamo models. A much longer observation of FK Com with the Chandra HETGS, combined with contemporaneous Zeeman-Doppler imaging would clearly be of great value. We thank the NASA AISRP for providing financial assistance for the development of the PINTofALE package. J. J. D., S. C., and V. K. were supported by NASA contract NAS8-39073 to the Chandra X-Ray Center during the course of this research. H. K. acknowledges the German Deutsche Forschungsgemeinschaft, DFG project grant KO 2320/1.
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