PHOTOIONIZED FEATURES IN THE X-RAY SPECTRUM OF EX HYDRAE

EX Hydrae (EX Hya) belongs to a sub-class of magnetic cataclysmic variables (CVs), known as intermediate polars (IPs), wherein the white dwarf (WD) magnetic field (≈0.1–10 MG) channels material from the inner edge of the truncated accretion disk through the accretion curtains and accretion columns to spots near the magnetic poles (Rosen et al. 1988). In this model, the channeled material reaches supersonic velocities in the pre-shock flow ($v_{\rm ff}= (2GM_{\rm WD}/R_{\rm WD})^{1/2} \simeq 6000 \rm \;km \;s^{-1}$, where $v_{\rm {ff}}$ is the free-fall velocity for a WD of mass M_WD = 0.79 M_☉ and radius R_WD = 7.1 × 10⁸ cm) before passing through a strong stand-off shock near the WD surface. At the shock, the kinetic energy is converted into thermal energy, heating the gas to temperatures of ∼20 keV (Fujimoto & Ishida 1997; Brunschweiger et al. 2009). Below the shock, in the post-shock flow, the cooling material radiates its thermal and residual gravitational energy through free–free, bound–bound, and free–bound radiation, which is primarily detected in X-rays.

The nature of the observed X-ray spectrum depends primarily on the specific accretion rate (i.e., the accretion rate per unit area). The small spot size and hence high specific accretion rate of magnetic CVs impose a conical geometry that does not allow the X-ray photons to escape without further interaction. Thus, the observed spectrum is dominated by emission lines formed in a region photoionized by the radiation field from the shocked region. In contrast, the boundary layer at the inner edge of the accretion disk of non-magnetic CVs covers a relatively large area and therefore the specific accretion rate is low, allowing X-rays to escape freely. Mukai et al. (2003) observed this "binomial" distribution in moderately exposed (∼100 ks) observations obtained with Chandra using the High Energy Transmission Grating (HETG) and generally found that the X-ray spectra of magnetic CVs are compatible with photoionized emission while those of non-magnetic CVs are consistent with a collisionally ionized, cooling gas (modeled as a cooling-flow in X-ray spectral fitting packages such as XSPEC⁶). Interestingly, EX Hya was the "exception" of the distribution: its X-ray spectrum was well fit with a cooling-flow model. This can be explained if EX Hya has a tall shock (Allan et al. 1998), a lower accretion rate, and/or larger accretion spots than other IPs, and therefore a low specific accretion rate, leading to a dominant collisionally ionized, cooling spectrum.

We have obtained a deeper observation of EX Hya with Chandra in order to study a number of accretion-related phenomena. In this paper, we present new results from this observation discussed in Section 2. In Section 3, we present an analysis of the line profiles that require a broad component, and a photoionization model to explain it. Discussion and conclusions are presented in Section 4.

EX Hya was observed with Chandra using the HETG in combination with the ACIS-S for 496 ks. The observation was obtained in four segments (ObsIDs 7449: start time 2007 May 13 22:15:35 UT, exposure time 130.65 ks; 7452: start time 2007 May 17 03:12:38 UT, exposure time 49.17 ks; 7450: start time 2007 May 18 21:56:57 UT, exposure time 162.73 ks; and 7451: start time 2007 May 21 14:15:08 UT, exposure time 153.07 ks). We extracted High-Energy Grating (HEG) and Medium-Energy Grating (MEG) ± first-order spectra and Ancillary Response Matrices (ARFs) using the CIAO⁷ script fullgarf, while Response Matrix Functions (RMFs) were extracted using the mkgrmf script. We combined ARFs and spectra from each segment using the add_grating_spectra script. For Si xiv λ6.18 and Mg xii λ8.42, fits were performed using the HEG and MEG ± first-order data, whereas for Fe xvii λ16.78 and O viii λ18.97 we used only MEG ± first-order data, due to the rapid decay of the HEG effective area for λ ≳ 17 Å (Chandra Proposer's Observatory Guide v11.0, POG).

3.1. Line Profiles Analysis

In order to test models of the cooling of the post-shock gas (e.g., Aizu 1973; Canalle et al. 2005), we measured the fluxes of the strong emission lines observed in the HETG spectrum using a Gaussian to represent each emission line and a first-order polynomial to represent the nearby continuum. We found that some of the strong emission lines were poorly fit with such a model, and acceptable fits, in particular for O viii λ18.97, Fe xvii λ16.78, Mg xii λ8.42, and Si xiv λ6.18, could be obtained by adding a second Gaussian to represent the broad-line wings. All the parameters were free to vary, and their limits were determined to 90% confidence. Figure 1 shows these emission lines together with the best-fit models. Central wavelength, full width half maximum (FWHM), and observed flux of the narrow and broad components are listed in Table 1.

Zoom In Zoom Out Reset image size

Table 1. Line Fit Parameters

Linea	Narrow Component				Broad Component
	λb	FWHMc			λb	FWHMc
	(Å)	$\rm (km \;s^{-1})$	Fluxd		(Å)	$\rm (km \;s^{-1})$	Fluxd
O viii λ18.97	18.972+0.006−0.006	315+34−25	7.13+0.4−0.3		18.972+0.011−0.011	1922+230−162	2.77+0.3−0.3
Fe xvii λ16.78	16.777+0.024−0.012	117+42−50	2.75+0.18−0.15		16.783+0.019−0.018	1963+1247−511	0.55+0.19−0.21
Mg xii λ8.42	8.422+0.006−0.006	360+41−34	1.08+0.09−0.08		8.424+0.006−0.006	1329+176−108	0.53+0.10−0.09
Si xiv λ6.18	6.183+0.006−0.006	410+23−57	1.09+0.03−0.10		6.185+0.006−0.006	1297+69−78	0.84+0.03−0.05

Notes. ^aO viii and Fe xvii were fit using only the MEG arm; Mg xii and Si xiv were fit using both the HEG and MEG arms. ^bAbsolute wavelength accuracy: $\rm HEG=0.006$ Å, $\rm MEG=0.011$ Å. Relative wavelength accuracy: $\rm HEG=0.0010$ Å, $\rm MEG=0.0020$ Å (Chandra POG). ^cFWHM ≈2.3548σ. ^dUnits of 10⁻⁴ photons cm⁻² s⁻¹.

Download table as:  ASCIITypeset image

An instrumental origin for these broad emission lines seems unlikely. First, the broad component is detected in four spectral orders simultaneously (HEG and MEG ± 1), whereas any broadening in the dispersion direction of a diffraction arm should not affect the dispersion in another arm. Second, as shown in Figure 2, a comparison with a similarly deeply exposed observation of the pre-main-sequence star TW Hya (exposure time: 489 ks; Brickhouse et al. 2010) with the same instrument configuration does not show similar broad features.

Zoom In Zoom Out Reset image size

The statistical significance of the presence of a broad component in the line profiles was assessed by fitting 10,000 Monte Carlo realizations of the spectra in the neighborhood of each line, using a model consisting of a continuum plus a single Gaussian, with the same exposure time, RMFs, and ARFs as our observation, following the method described in Protassov et al. (2002) and Reeves et al. (2003). We fit the simulated spectra using two models: a continuum plus (1) a single Gaussian (with a total of four free parameters, resulting in: χ²(O viii) = 503.70; χ²(Mg xii) = 1671.69; χ²(Si xiv) = 868.04; and χ²(Fe xvii) = 162.72) and (2) two Gaussians (with a total of seven free parameters, resulting in: χ²(O viii) = 398.60; χ²(Mg xii) = 1577.30; χ²(Si xiv) = 772.40; and χ²(Fe xvii) = 141.77). The difference in χ² between the fit of the double- and single-Gaussian models to the data was computed for each spectrum in order to test if the broad component could be produced purely by random, Poisson noise. We found that only 1–10 in 10,000 of the randomly generated single-Gaussian spectra could produce a similar decrease in χ² when compared to the observed data, after the addition of a broad emission line (see Table 1 and Figure 3). The null hypothesis probability that the broad component could arise purely from Poisson noise is ≲0.1%; thus, the broad components are detected at 99.9% confidence.

Zoom In Zoom Out Reset image size

3.2. The Photoionization Model

Our photoionization models (A–D) yield fluxes for O viii in good agreement with the observed value, but the predicted Fe xvii, Mg xii, and Si xiv fluxes are smaller by a factor of 2–30. Although our simple model is not accurate in the prediction of all the observed fluxes, it is appropriate in the sense that it shows that very small spots require higher pre-shock densities than those observed by Mauche et al. (2001, 2003) for the post-shock flow, and very large accretion spots give small ionization parameters that cannot produce the observed flux. Furthermore, comparison of the free-fall velocity with the FWHM indicates that the accretion column must not be too far from the limb of the WD as seen from Earth. The model predicts that the Doppler width ($v \approx 2000 \rm \;km \;s^{-1}$) of the ionized material is smaller than the ${\sim }6000 \rm \;km \;s^{-1}$ free-fall velocity, which would be seen if the columns were observed face-on. The smaller observed line width suggests that the accreting poles remain in the vicinity of the WD limb as seen from Earth, as supported by the small spin-phase radial velocity variations observed by Hoogerwerf et al. (2005) and the small equivalent width ($\rm EW\sim 36$ eV) of the Fe Kα line: George & Fabian (1991) calculated that such an EW would be observed if the angle between the line of sight and the reflecting surface is roughly 80°, i.e., the accreting poles are close to the limb.

We can decide which models are more adequate using additional arguments. First, the height of the shock should be larger than ≈0.015 R_WD to account for the observed modulation in the X-ray light curves (Allan et al. 1998; Hoogerwerf et al. 2006), but less than ∼2 R_WD to account for T_e ∼ 20 keV at the shock. Second, the predicted densities should be less than the values derived by Mauche et al. (2001, 2003) from the Fe xvii and Fe xxii line ratios. Third, a significant optical depth for electron scattering implies modulations (pulse fraction ≳10%) in the light curves in the 6–8 keV range, which were observed in Ginga data by Rosen et al. (1991). Allan et al. (1998), however, found only an upper limit of 4% for the pulse fraction in the light curve in the 6–8 keV range observed with ASCA. Moreover, as detailed by Rosen (1992), the favorable lines of sight to detect a high energy modulation due to electron scattering would also imply significant photoelectric absorption in the pre-shock material, which will extinguish the low-energy flux and manifest itself as flat-bottomed X-ray curves.

Based on the above conditions, we discard models C and D because: (1) their densities are higher than those obtained by Mauche et al. (2001, 2003) line ratios; (2) the combination of high densities and small accretion spot size implies significant optical depth for electron scattering (see Table 2), predicting flat-bottomed soft X-rays light curves, which are not observed (Hoogerwerf et al. 2006; Allan et al. 1998); and (3) model D implies a small shock height, such that the collisionally ionized lines in the post-shock flow will form even closer to the WD. Such emission would not show the observed sinusoidal modulation in the light curves (Allan et al. 1998), but would show the presence of two spikes (observed in the Mg xi light curve, but not in the more highly ionized Mg xii; Hoogerwerf et al. 2006).

Models A and B are both acceptable because: (1) their densities agree with values obtained from observations (Mauche et al. 2001, 2003); and (2) the optical depth for electron scattering in Models A and B is low and its contribution to the high energy light curve modulation and absorption is small, in agreement with the absence of ∼100% pulse fraction in the low-energy light curves and upper limit of 4% in the pulse fraction of the light curves in the 6–8 keV range observed by Allan et al. (1998).

Summarizing, we detect for the first time in X-rays a broad component in the emission-line profiles of EX Hya and suggest that its origin is related to photoionization of a region in the pre-shock flow by radiation emitted in the post-shock cooling flow. Such an origin conforms with that of the broad optical, UV, and FUV emission lines observed in EX Hya (Hellier et al. 1987; Greeley et al. 1997; Mauche 1999; Belle et al. 2003): lines whose widths, fluxes, and radial velocities vary predominately on the WD spin phase, which are interpreted as arising in the pre-shock flow. Even more satisfying, in two cases—O vi λλ1032, 1038 in the FUV (Mauche 1999) and N v λλ1239, 1243 in the UV (Belle et al. 2003)—narrow components that rotate with the WD are observed in the predominately broad emission lines. In fact, the most obvious difference between the O vi and N v emission lines in the FUV and UV wavebands and the O viii λ18.97, Fe xvii λ16.78, Mg xii λ8.42, and Si xiv λ6.18 emission lines in the X-ray waveband is the relative strength of the narrow and broad components. Although rather simple, our photoionization model for the origin of the broad component of the X-ray emission lines yields appropriate values for the height of the shock and the size of the accretion spot. Altogether, our observational findings and the results from our model agree with a scenario where the geometry imposed by the specific accretion rate allows most of the photons from collisional excitation to escape freely, and a small fraction of those photons to photoionize the pre-shock gas. In this regard, the X-ray spectrum from EX Hya manifests both features of the "binomial" distribution found by Mukai et al. (2003).

We thank the anonymous referee for useful comments which help to improve the final manuscript. We acknowledge support from NASA to the Smithsonian Astrophysical Observatory (SAO) under Chandra GO7- 8026X for G.J.M.L. C.W.M.'s contribution to this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. N.S.B. is supported by NASA Contract NAS8-03060 to SAO for the Chandra X-ray Center.

Facilities: CXO - Chandra X-ray Observatory satellite