Testing Comptonization as the origin of the continuum in nonmagnetic Cataclysmic Variables. The photon index of X-ray emission

U Gem has a WD with mass ($M_{WD}$) of $1.07\pm 0.08\ M_{\odot}$ (Ritter & Kolb, 2003). It appears to be at most slowly rotating ($v\sin i\lesssim 100$ km s^-1), which corresponds to 20% of the break-up velocity (Lewin & van der Klis, 2006). The secondary star has a mass $M_{2}$ of $0.39\pm 0.02\ M_{\odot}$ (Ritter & Kolb, 2003) and spectral type M4 V (Harrison et al., 2000). The system is located at $100\pm 4$ pc of distance; it has an orbital period of 4.246 h (Harrison et al., 2004) and an inclination $i$ of $69\pm 2^{\circ}$ (Ritter & Kolb, 2003). Dips in the X-ray light curves have been observed during quiescence (Szkody et al., 1996, 2002), and during normal (Long et al., 1996) and anomalously outbursts (of $\sim$45 days) (Mason et al., 1988) as well. The X-ray dips in U Gem are less deep in quiescence than in outburst. The morphology of the dips changes from cycle to cycle, related to changes in the absorbing material. In U Gem both soft and hard X-ray fluxes are higher during outburst than in quiescence by a factor of $\sim$10–100 (see Lewin & van der Klis, 2006, and references therein).

Güver et al. (2006) studied the spectral emission of U Gem in both quiescence and outburst states, using the same XMM-Newton, Chandra HETG/ACIS, and RXTE PCA observations present in our sample. They fitted the quiescence spectra with both cemekl (or cvmkl) and mkcflow cooling flow models, finding a maximal temperature $kT_{\rm{max}}$ in the $\sim 15-38$ keV range. They report, for the first time, properties of the hard X-ray emission of this source in outburst. In this state, an extra X-ray non-termal component is needed, in addition to a simple mekal-based multi-temperature component, to obtain an acceptable spectral fit. Though deviations from the continuum are still noticeable, this extra component was better described by a power law rather than other models (such as thermal bremsstrahlung, see Table 4 and Fig. 3 and 4 therein). The authors report $kT_{\rm{max}}=9.49\pm 4.1$ keV and $18.44\pm 10.5$ keV for the cemekl component in the Chandra HETG/ACIS HEG and MEG spectra, respectively; and a power-law component with photon index $\Gamma$ of $0.54\pm 0.16$ and $0.64\pm 0.06$, respectively. Analyzing the 3-20 keV PCA spectra throughout the 2004 outburst the authors demonstrated evidence of a transient hard X-ray component – since in 9 out of 23 spectra the power-law component was not required. They suggested that this component is driven by a mechanism temporarily present during outburst, which could be either reflection of X-ray coming from either the optically thick plasma or from an optically thick boundary layer, as well from a transient magnetosphere present during outburst (see Güver et al., 2006, and reference therein). On the other hand, they noticed that spectral features expected by the reflection scenario such as the K_α fluorescent lines are either very weak or not observed during the outburst state in U Gem. It is important to stress, however, that reflection scenario is not the only one capable to explain the K_α fluorescent line production (see, e.g., Maiolino et al., 2019).

Mukai et al. (2003) showed that the Chandra spectrum of the DN U Gem (as well as SS Cyg and V603 Aql) can be described by the multi-temperature bremsstrahlung cooling-flow model mkcflow with $kT_{\rm{max}}=20$ keV. Byckling et al. (2010) fitted the XMM-Newton U Gem spectrum in quiescence also using the mkcflow model and found a maximum temperature $kT_{\rm{max}}=25.82^{+1.98}_{-1.43}$ keV and an equivalent width of the Fe 6.4 keV line (EW6.4) of $60^{+33}_{-32}$ eV. Using, on the other hand, a single temperature optically thin plasma model (mekal) they found $kT=0.78^{+0.03}_{-0.01}$ keV and EW6.4 of $50^{+25}_{-24}$ eV. Xu et al. (2016) analyzed the spectra of 41 CVs observed with Suzaku. They used the single temperature model apec to fit the 2–10 keV continuum and 3 Gaussian components (at 6.4 keV, 6.7 keV, and 7.0 keV) to fit the Fe emission lines of U Gem in quiescence. They found a plasma temperature $kT=16.5^{+4.49}_{-3.31}$ keV; and EW 6.4 $=43^{+16}_{-11}$ eV, EW6.7 $=258^{+22}_{-21}$ eV, and EW 7.0 $=178^{+11}_{-11}$ eV.

SS Cyg belongs to the U Gem type of DN. The system has a WD with mass $M_{WD}$ of $1.19\pm 0.02\ M_{\odot}$, a secondary star with mass $M_{2}$ of $0.704\pm 0.002\ M_{\odot}$ (Friend et al., 1990) and K5/5 spectral type (Ritter & Kolb, 2003). The binary system is located at $166\pm 12$ pc (Harrison et al., 1999, 2004), has an inclination angle $i$ of $37\pm 5^{\circ}$ (Ritter & Kolb, 2003) and a period of 6.603 h (Harrison et al., 2004). This source is one of the DNe broadly studied in outbursts, as it shows an optical outburst every $\sim$ 50 days, in which $m_{V}$ changes from 12th to 8th magnitude (Mauche & Robinson, 2001; Lewin & van der Klis, 2006, see for example, Figure 10.1 therein). They claim that the system shows a reflection component in the quiescence and outburst states, with larger contribution in the outburst (Done & Osborne, 1997; Lewin & van der Klis, 2006, and references therein). Mukai et al. (2003) found a maximum plasma temperature $kT_{\rm{max}}$ of 80 keV using fits of the Chandra spectrum of this source in quiescence and the multi-temperature mkcflow model.

Okada et al. (2008) analyzed the two Chandra/HETG observations present in our sample. They constrained the power law index and the temperature of the boundary layer in the framework of the cemekl model.

Ishida et al. (2009) presented a Suzaku XIS and HXD-PIN analysis of this source observed, in November 2005, in the quiescence and outburst states. Using the multi-temperature thin plasma model cvmekal (model in XSPEC), they found a maximum temperature of the plasma $kT_{\rm{max}}$ of $20.4_{-2.6}^{+4.0}$ (stat) $\pm~{}3.0$ (sys) keV in quiescence, and of $6.0_{-0.2}^{+1.3}$ keV in outburst.

Byckling et al. (2010) fitted a SUZAKU XIS spectrum of SS Cyg in quiescence using the optically thin plasma model mekal and the cooling model mkcflow (including photoelectric absorption and partial covering as well). As a result they obtained a plasma temperature of $10.44_{-0.17}^{+0.16}$ keV and a maximum temperature of the plasma $kT_{\rm{max}}$ of $41.99_{-0.76}^{+1.20}$ keV, respectively. In their fits EW6.4 is equal to $75^{+9}_{-4}$ eV and $73^{+6}_{-7}$ eV, respectively. Xu et al. (2016), using Suzaku data (during an outburst) and the single temperature model apec, fit the 2–10 keV continuum including 3 Gaussian components of the iron emission lines, (at 6.4 keV, 6.7 keV, and 7.0 keV). As a result they estimated a plasma temperature $kT=8.15_{-0.91}^{+1.23}$ keV; and EW6.4 $=67_{-10}^{+11}$ eV, EW6.7 $=415_{-30}^{+41}$ eV, and EW7.0 $=48^{+15}_{-11}$ eV.

VW Hyi is a well-studied source. It is located at $54\pm 0.1$ pc (see Nakaniwa et al., 2019, and references therein) and belongs to the SU UMa sub-group of DNe (Warner, 1987), which undergoes both normal DN outbursts and super-outbursts (Godon & Sion, 2005). The $M_{WD}$ was estimated as $0.63\pm 0.15\ M_{\odot}$ (Schoembs & Vogt, 1981)²²2A gravitational redshift determination done by Sion et al. (1997) yielded $M_{WD}=0.86^{+0.18}_{-0.32}\ M_{\odot}$. The secondary star has a mass $M_{2}$ of $0.11\pm 0.02\ M_{\odot}$ (Schoembs & Vogt, 1981) and it is a M6V star (Godon & Sion, 2005). The binary system has an inclination angle $i$ of $60\pm 10^{\circ}$ (Schoembs & Vogt, 1981), and an orbital period of 0.074271 days ($\sim$1.783 h, which lies below the CV period gap; Ritter & Kolb, 2003). VW Hyi shows super-humps (which are variations in the light curves at a period of a few per cent longer than the orbital period) with a period of 0.07714 days ($\sim$1.85 h). VW Hyi lies along a line of sight with a very low interstellar absorption, $N_{H}$ $\approx 6\times 10^{17}$ atoms cm^-2 (Polidan et al., 1990). This low interstellar absorption allows us to observe this system in almost all wavelength ranges.

The source shows a very low mass accretion rate during quiescence, $\dot{M}\approx 10^{-11}\ M_{\odot}$ yr^-1, emitting significantly in UV (between 35–47%; see Godon & Sion, 2005, and references therein). The first X-ray observations of VW Hyi in quiescence were done in 1984 with EXOSAT (van der Woerd & Heise, 1987), in which persistent hard (1–6 keV) and soft (0.04–1.5 keV) X-ray fluxes were observed. In the spectral analysis, an equally best fit was pointed out either using a power-law or a thermal bremsstrahlung model ($kT>5$ keV) without interstellar absorption ($N_{H}<10^{21}$ atoms cm^-2).

Belloni et al. (1991) fitted the spectrum of VW Hyi observed in quiescence by ROSAT using the optically-thin thermal plasma model Raymond-Smith with a single temperature (Raymond & Smith, 1977). They found a temperature of $2.17\pm 0.15$ keV for zero interstellar absorption (when absorption was included and significantly different temperature and flux were not found). Hasenkopf & Eracleous (2002) analyzed the spectrum of VW Hyi observed with ASCA, and using two- and multiple temperature thermal plasma models revealed that the resulting temperatures lie mostly between 4 and 10 keV.

Pandel et al. (2003, 2005) analyzed a XMM-Newton/EPIC spectrum of VW Hyi in quiescence (the same observation analyzed in this paper). They modeled the spectrum with cooling flow models – i.e., with multi-temperature thin thermal plasma models (cemekl, cevmkl and mkcflow) – and obtained a maximum temperature $kT_{\rm{max}}$ between 6 and 8 keV. Pandel et al. (2003) attempted to fit the EPIC spectra with one or two single-temperature mekal components (as commonly used to fit DNe spectra), but obtained a satisfactory fit only when three components of their model were used.

Nakaniwa et al. (2019) have also analysed the same XMM-Newton/EPIC observation present in our sample along with 3 more SUZAKU/XIS observations in quiescence. They report that all 0.2-10 keV spectra are moderately well fitted by the cevmkl and vmcflow cooling flow models, with a maximal temperature of 5-9 keV. Namely, for the XMM-Newton observation, they obtained a plasma temperature $kT_{\rm{max}}$ of $5.32_{-0.22}^{+0.23}$ keV and $6.95_{-0.19}^{+0.20}$ keV with the cevmkl and vmcflow models, respectively.

Xu et al. (2016), using Suzaku data and the single temperature model apec to analyze the 2–10 keV continuum, and 3 Gaussian components (at 6.4 keV, 6.7 keV, and 7.0 keV) fit the Fe emission lines, found in VW Hyi (in the quiescence state). They found a plasma temperature $kT$ of $5.79^{+4.71}_{-2.14}$ keV; and for the emission Fe lines they estimated EW6.4 = 0.01 eV (upper limit), EW6.7 = $1392^{+152}_{-172}$ eV, and EW7.0 = $42^{+58}_{-42}$ eV.

SS Aur belongs to the U Gem type of DNe with high mass accretion rates $\dot{M}$. The binary system is located at $167^{+10}_{-09}$ pc (Harrison et al., 2004) and has an inclination angle $i$ of $38\pm 16^{\circ}$. The system has an orbital period of 0.1828(1) days (which is equivalent to 4.387 h) (Shafter & Harkness, 1986; Byckling et al., 2010; Harrison et al., 2004). The system hosts a WD with a mass $M_{WD}$ of $1.08\pm 0.40\ M_{\odot}$, and a secondary star of $\sim$M1 V type (Harrison et al., 2000) with a mass $M_{2}$ of $0.39\pm 0.02\ M_{\odot}$ (Ritter & Kolb, 2003, and references therein). Byckling et al. (2010) fitted a SUZAKU XIS spectrum of SS Aur in quiescence using both the optically thin plasma model mekal and the cooling model mkcflow (including photoelectric absorption and partial covering as well). They obtained a plasma temperature of $6.35\pm 0.40$ keV and a maximum temperature of the plasma $kT_{\rm{max}}$ of $23.47_{-3.02}^{+4.01}$ keV, respectively. In these fittings EW6.4 is equal to $73^{+37}_{-36}$ eV and $86^{+52}_{-53}$ eV, respectively. Xu et al. (2016), using Suzaku data and the single temperature model apec in the 2–10 keV continuum and 3 Gaussian (the Fe emission lines) components (at 6.4 keV, 6.7 keV, and 7.0 keV) found that SS Aur, in the quiescence state, has the best fit parameters of a plasma temperature of $8.48^{+5.34}_{-2.61}$ keV; and EW6.4 = $47^{+60}_{-29}$ eV, EW6.7 = 325${}^{+90}_{-65}$ eV, and EW7.0 = $169^{+57}_{-49}$ eV.

We analyzed in total four XMM-Newton EPIC-pn public observations, one observation of each source. See Table 1 for a log of the observations. All XMM-Newton observations were taken with the sources in the quiescence state.

VW Hyi, U Gem and SS Aur were observed with the pn camera operating in Imaging mode, while SS Cyg was observed with the pn camera in Timing mode. All light curves and spectra were extracted through the Science Analysis Software (SAS) version 14.0.0. We strictly followed the recommendations for the pn camera in each mode of observation (timing and imaging, respectively). Following Guainazzi (2016), we considered the 0.3$-$15.0 keV spectral energy range for observations taken in Imaging mode, and the 0.7$-$10.0 keV range for the observation taken in Timing mode.

We checked spectral variability extracting two light curves for each source. The two light curve energy ranges were selected accordingly to the observational mode: from 0.3 to 4.0 keV and 4.0 to 15 keV for observations taken in Imaging mode; and from 0.7 to 4.0 keV and 4.0 to 10.0 keV for observation taken in Timing mode. We computed ratios between the light curves in the two energy bands (hardness ratio, HR). The HR of SS Aur showed a time interval of increased noise in the end of the exposure, which was discarded in the spectral extraction. For all other observations, a count rate variability was not associated with a significant change in the HR or with noise increase. We used therefore the total EPIC-pn exposure time in the spectral extraction of these observations.

Standard filters were applied during data screening through the evselect task. We considered only single and doubles events (using pattern $\leq 4$). FLAG==0 was used to discard regions of the detector (like border pixels and columns with higher offset) for which the pattern type and the total energy is known with significantly lower precision.

The observation of SS Cyg is taken in Timing mode and prior 23rd of May 2012, period in which almost all EPIC-pn exposures are unexpectedly affected by X-ray loading (XRL) – which occurs when source counts contaminates the offset map taken prior the exposure. Because of this we applied the XRL correction to this observation.

In all spectral extraction, the background region was selected from a region away from the source. The distribution matrix (rmf) and the ancillary (arf) files were created through the rmfgen and arfgen tasks. The final spectra were rebinned in order to have at least 25 counts for each background-subtracted channel.

We used all 8 grating Chandra public observations of our nmCV sample presented to the preparation time of this paper, see Table 1 for a log of the observations. VW Hyi was observed only once during an outburst, while SS Cyg and U Gem were observed four and three times, respectively, in both outburst and quiescence states. SS Aur does not have public observations available in the archive. SS Cyg, U Gem and VW Hyi were observed once in LETG/HRC-S mode, while SS Cyg and U Gem were observed 3 and 2 times in HETG/ACIS-S mode, respectively. Following the standard procedure³³3https://cxc.harvard.edu/ciao/threads/gspec.html, we used CIAO v4.11 and the corresponding calibration files to reprocess the data. The spectra of each observation were generated with the Chandra_repro script. We combined the first order spectra together and adopted a minimum signal-to-noise value of 10 to group the spectra. We also extracted for each observation two light curves in 0.4-4 keV and 4-10 keV bands, and checked for variability. Significant changes in the HR were not observed and therefore we used the total exposure time in the spectral extraction. The reprocessed spectrum of VW Hyi did not show a spectral component at energies greater than 0.5 keV. Therefore, we did not consider this spectrum in our final spectral analysis.

We have analyzed 6 RXTE observations of three nmCVs: one of U Gem, one of SS Aur, and four of SS Cyg. SS Aur and SS Cyg Obs. ID 50012-01-01 were observed in quiescence. All other observations were taken with the source in outburst state. See Table 1 for a log of the observations.

All PCA data was analyzed following the standard procedure. Only low resolution (16 s) light curves were produced together with spectra in the 2–60 kev band. For each observation, spectra and light curves were derived using standard RXTE/FTOOLS. Briefly, the data reduction consists of the source $+$ background production, with subsequent subtraction of the PCA background estimated through the pcabackest tool. The PCA response matrix was built with pcarsp, and a systematic errors (off 0.04%) were added to each individual spectrum.

HEXTE 20–200 keV spectrum extraction (Rothschild et al., 1998) is done using comparison, for each cluster, the spectra from two separate background fields that are sampled alternately during observations. This capability allowed us, for example, in discarding data from cluster B for SS Cyg, since one of the background regions for this cluster (and for that sky position) is contaminated by the nearby source IGR J21485$+$4306. HEXTE background lines (Rothschild et al., 1998) were also treated and removed from the final spectrum. Spectra and response matrices were produced following the well-known procedures (see, e.g., D’Amico et al., 2001).

In all spectra, an addition of a photo-electric absorption ($N_{H}$) and/or a blackbody component (e.g., bbody or bbodyrad model) did not improve the fit performed in the $\sim~{}0.3-15/0.4-10$ keV energy range of XMM-Newton.

The spectrum of U Gem showed three iron emission lines, with centroid energies of: $6.394_{-0.013}^{+0.013}$ keV (at 2.5 sigma of the He-like K_α line), $6.68_{-0.04}^{+0.04}$ keV (compatible with He-like Fe K_α line) and $6.972^{+0.023}_{-0.019}$ keV (at 1.2 $\sigma$ from the H-like Fe K_α line at 7.0 keV); and equivalent widths (EWs) of $53^{+41}_{-25}$ eV, $281^{+100}_{-49}$ eV and $167^{+53}_{-40}$ eV, respectively.

The spectra of SS Cyg and SS Aur showed two iron emission lines. In SS Cyg, the lines appear with centroid energies of $6.634_{-0.023}^{+0.026}$ keV (compatible with neutral Fe K_α line) and $6.966^{+0.030}_{-0.026}$ keV (at 1.1 $\sigma$ from the H-like Fe K_α line at 7.0 keV); and EWs of $186_{-27}^{+321}$ eV and $75^{+97}_{-20}$ eV, respectively.

In SS Aur, the lines appear with centroid energies of $6.67_{-0.03}^{+0.04}$ keV (compatible with He-like Fe K_α line) and $7.00_{-0.05}^{+0.05}$ keV (compatible with H-like Fe K_α line); with EWs of $528^{+388}_{-156}$ eV and $169^{+99}_{-89}$ eV, respectively.

The VW Hyi spectrum is the only one that showed one emission iron line. This line appears with a Gaussian centroid energy of $6.672^{+0.017}_{-0.015}$ keV (at 1.6 $\sigma$ from the He-like Fe K_α line); and it is very strong, with EW equal to $995_{-143}^{+152}$ eV, which is 2$-$20 times stronger than those observed in other sources.

Table 2 shows the best-fit parameters and fit quality found for each XMM-Newton observation, and Figure 2 shows the best spectral fits. The presence of the Fe Gaussian lines are evident in all fits. Without adding any model to account for the iron line emission, the best-fit gives a reduced $\chi^{2}_{\rm red}=\chi^{2}$/degree of freedom (d.o.f)) of 1.54 (801/521) for VW Hyi, 1.38 (1151/836) for SS Cyg, 1.97 (530/269) for U Gem and 1.11 (672/604) for SS Aur. When Gaussian components were added to the fit, it leads to a $\chi^{2}_{\rm{red}}$ of 1.30 (672/519) for VW Hyi, 1.01 (840/831) for SS Cyg, 1.15 (366/317) for U Gem and 0.93 (556/598) for SS Aur.

In addition to the emission iron lines in the $\sim$ 6.4 - 7.0 keV energy range, we observed in all spectra another strong and broad residual excess peaked at $\sim$ 1.01 keV, with Gaussian centroid in the $\sim$ 0.96 - 1.02 keV energy range (see the Gaussian₀ component in Table 2). These centroid energies are compatible with resonance lines emitted by Ne X, Fe XVII or Fe XXI ions. Table 3 summarizes these possible emission lines.

We determined the range of physical parameters given by the compTT model:

• •

  The temperature $kT_{s}$ of the seed photons ranges from 0.056 to 0.174 keV.

• •

  The electron temperature, $kT_{e}$ of the Comptonization cloud ranges from 5.99 to 8.72 keV.

• •

  The optical depth $\tau$ of the Comptonization cloud ranges from 2.65 to 4.73.

The residual broad excess around 1 keV observed in all XMM-Newton spectra was also observed in three out of five HETG/ACIS Chandra spectra analysed in this paper. This feature and the narrow emission lines (narrow excesses $\gtrsim 2\sigma$) present in the Chandra spectra were modeled by simple Gaussian components. U Gem has one HETG/ACIS observation in quiescence and one in outburst state, whereas SS Cyg was observed once in quiescence and twice in outburst state.

Fitting the continuum with only one compTT component without adding any component to account for the emission lines, the best-fit gives a $\chi^{2}_{\rm red}$ of 1.85 (131/71) and 2.57 (321/125) for U Gem Obs. ID 647 and 3767, respectively; and 1.24 (589/478), 2.5 (421/168), and 1.57 (143/91) for SS Cyg Obs. ID 646, 648, and 2307, respectively. When Gaussian components were added to the fit, it leads to a $\chi^{2}_{red}$ of 1.03 (67/65) and 1.01 (114/113) for U Gem Obs. ID 647 and 3767, respectively; and 0.97 (453/467), 0.80 (121/151), and 0.64 (52/81) for SS Cyg Obs. ID 646, 648, and 2307, respectively.

Table 4 and 5 show the best-fit parameters and fit quality for each spectrum of U Gem and SS Cyg, respectively. Figures 3$-$4 show spectral fits.

In U Gem, the values of the temperature kT_e and $\tau$ parameters, agree at 90$\%$ confidence level, in the two observations: $\tau$ is $\sim$ 5, and kT_e is equal to $5.0_{-0.5}^{+0.5}$ keV and $6_{-2}^{+5}$ keV in Obs. 647 (in quiescence) and 3767 (in outburst), respectively. On the other hand, a value of the temperature kT_s of the seed photons in Obs. 3767 ($0.66_{-0.10}^{+0.12}$ keV) appears $\sim$ 8 times greater than the temperature in Obs. 647 ($0.66_{-0.10}^{+0.12}$ keV). For the two observations, the total model led to $\chi^{2}_{red}$ of 1.0 (see Table 4).

In SS Cyg, independently of the source state, the best-fits were found in general by a compTT component with kT_s of 0.10 keV, kT_e of $\sim$ 5 keV, and $\tau$ of $\sim$ 6. It is important to stress that initially all parameters were considered as a free one, however, the electron temperature kT_e appears not well constrained by the fits – it either assumed values greater than the upper limit given by the Chandra effective energy band (8 keV), or lower than the minimum value acceptable by the Comptonization model (5 keV, see Hua & Titarchuk (1995)). Therefore, this parameter was kept fixed in the three fits. The spectrum of Obs. 648 is the only one which shows a very low seed photon temperature kT_s of $0.020_{-0.003}^{+0.004}$ keV – the presence of many lines in the soft energy band of this spectrum may affect the value of this parameter. We obtained a $\chi^{2}_{red}$ of $\sim$ 1.0 for the fit to Obs. 646, and lower than 1.0 for Obs. 648 and 2307 (see Table 5).

The LETG/HRC spectra of SS Cyg and U Gem were not successfully described by only one thermal Comptonization component. Moreover, a presence of many lines in the 0.07-2 keV energy band makes a problem to satisfactory fit the data. For example, a good fit in terms of $\chi^{2}$-statistic ($\chi^{2}_{red}<2$) is obtained when the soft energy band (E $<$ 2.5 keV in SS Cyg and E $<$ 1.5 keV in U Gem, respectively) is not taken into account. In this case, fitting SS Cyg and U Gem spectra with a thermal compTB component (Farinelli et al., 2008) and two Gaussian components – with centroid energies at 1.86 and 2.005 keV – led to $\chi^{2}_{red}$ of 1.34 (16/12) and 1.33 (47.9/36), correspondingly.

The broad residual excess peaked around $\sim$ 1 keV, observed in all XMM-Newton Epic-pn spectra, was also observed in the Chandra spectra of U Gem Obs. ID 3767 in outburst, and SS Cyg Obs. ID 648 and 2307 (in outburst). This broad excess could be an emission from Fe XVII, Fe XXI, or Ne X ions (see Table 3). However, the fit of this feature with a Gaussian component led to lower centroid energies. In U Gem Obs. ID 3767, the Gaussian line energy is frozen at 1.0 keV, with $\sigma$ equal to $0.24_{-0.06}^{+0.07}$ keV (see Table 4). In SS Cyg Obs. ID 648 and 2307, it is equal to $0.87_{-0.04}^{+0.03}$ keV and $0.93_{-0.05}^{+0.04}$ keV, respectively; with $\sigma$ equal to $0.15_{-0.02}^{+0.03}$ keV and $0.10_{-0.03}^{+0.04}$ keV, respectively (see Table 5). Table 6 summarizes the possible resonance narrow emission lines observed in the Chandra HETG/ACIS spectra. In U Gem (see Table 4), the spectrum of Obs. ID 647 shows two emission lines, with centroid energies at $6.63_{-0.07}^{+0.08}$ keV (compatible with He-like K_α Fe line at 6.7 keV) and $2.006^{+0.004}_{-0.001}$ keV (compatible with Si XIV, at 2.007 keV). The spectrum Obs. ID 3767 shows three emission lines, with centroid energies at $6.68_{-0.02}^{+0.02}$ keV (compatible with He-like K_α Fe line), $2.004_{-0.005}^{+0.001}$ keV (at 3$\sigma$ of Si XIV line), and $1.86_{-0.01}^{+0.01}$ keV (compatible with Si XIII, at 1.865 keV).

In SS Cyg (see Table 5), the spectrum of Obs. 646 shows only the three iron lines in the 6.4-7.0 keV energy range: at $6.39_{-0.01}^{+0.01}$ keV (compatible with neutral K_α Fe line), $6.67^{+0.01}_{-0.02}$ keV (at 3$\sigma$ of the He-like K_α Fe line), and $6.97_{-0.03}^{+0.01}$ (at 3$\sigma$ of the H-like K_α Fe line). The spectrum of Obs. 648 shows in total six emission lines, with centroid energies at: $0.87_{-0.04}^{+0.03}$ keV (compatible with emission from either Ca XVIII, Fe XVII, Ni XIX, or Ni XVIII; see Table 6), $1.346_{-0.004}^{+0.004}$ keV (compatible with emission from Mg XI at 1.343, and 1.5$\sigma$ from the 1.352 keV line), $1.473_{-0.005}^{+0.004}$ (compatible with emission from Mg XII, at 1.473), $1.859_{-0.004}^{+0.003}$ keV (at 2 sigma of Si XIII emission), $2.005_{-0.004}^{+0.003}$ keV (compatible with Si XIV emission), and $6.65_{-0.04}^{+0.03}$ keV (at 1.7 $\sigma$ from the He-like K_α Fe line). The spectrum of Obs. 2307 shows in total four emission lines, with centroid energies at: $0.93_{-0.05}^{+0.04}$ keV (compatible with Ca XVIII, Ni XIX, and Ne IX), $1.472_{-0.007}^{+0.008}$ keV(compatible with Mg XII), $1.857_{-0.005}^{+0.005}$ keV (at 1.6 $\sigma$ from the Si XIII line), and $6.61_{-0.01}^{+0.01}$ keV ( at 1.7 $\sigma$ from the Fe XXII K_α line at 6.627 keV), see Table 6.

Almost all observations showed a low count rate ($<1$ cts/s) in the energy band $>25$ keV of the PCA spectra. The same, or no counts, were observed in the 40-150 keV of the HEXTE spectra. Therefore, except for Obs. ID 50012-01-01-00 of SS Cyg, we performed the spectral analysis considering only the PCA spectra with energy range up to 25 keV.

Because RXTE Obs. ID 50012-01-01-00 of SS Cyg is simultaneous to Chandra Obs. ID 646, we have analysed the 0.4-8 keV HETG/ACIS Chandra spectral band together with the 8-60 keV PCA and 60-150 keV HEXTE energy band of RXTE.

The spectrum of U Gem Obs. ID 80011-01-02-00, SS Aur Obs. ID 30026-03-01-00, and SS Cyg Obs. ID 10040-01-01-000 were well described, in the $\sim$ 5–25 keV energy band, by only one compTT component. On the other hand, the other three spectra of SS Cyg (Obs. ID 50012-01-01-00, 10040-01-01-001, and 10040-01-01-00) required a second spectral component. For all these three observations, we fit a model consisting of (1) a blackbody (bbody) plus a Comptonization (compTT) component or (2) a sum of two Comptonization (compTT) components.

In general, taking into account the $\chi^{2}$-statistic and the range of physical parameters, the best fits were found for the second case – that is, when two compTT components were used to describe the total spectra. Namely, the best-fits were found when both the electron temperature $kT_{e}$ and the optical depth $\tau$ of the compTT model were tied between the two components. Figure 5 shows the the geometry of our Comptonization model. We definitely establish that there is a disk which supplies the seed photons for the transition layer (Compton cloud). While red lines indicate the trajectories of the photons which illuminate the transition layer coming from the white dwarf (WD) surface. As a result the emergent X-ray spectrum formed in the transition layer as a result of up-scatering of the seed photons of the disk and WD surface off hot electrons of the Compton cloud.

In order to assess the statistical significance of the second compTT component, we computed the probability of chance improvement of the $\chi^{2}$ by means of an F-test. It is worth stressing that the F-test to be used in this case is not the one that uses the $\Delta\chi^{2}$ as test statistics (let us call it independent F-test, or I-F-test for short). Indeed, in order to correctly use the I-F-test, the $\chi^{2}$ variables must be linearly independent. In our case the two components share some parameters, therefore are not independent by construction, and therefore we must use another test statistics: the dependent F-test (D-F-test for short). This test statistics is defined in terms of the ratio between the normalized $\chi^{2}$ (see, eg, Barlow, 1989; Press et al., 1992), and has been already successfully used for the assessment of the statistical significance of multiplicative components (that, too, are dependent components by construction) by Orlandini et al. (2012) and Iyer et al. (2015) among others.

The probability of chance improvement of the $\chi^{2}$ by adding the second compTT component, evaluated by means of a D-F-test, is equal to 3$\times 10^{-8}$ in SS Cyg Obs 50012-01-01-00, 0.07 in Obs. 10040-01-01-001, and 0.02 in Obs. 10040-01-01-00.

From these values we see that the second compTT component is statistically significant (equivalent to 5.4$\sigma$ for a one-tailed test) only for the 50012-01-01-00 SS Cyg observation. This does not mean that this component is not present also in the other two RXTE observations, but only that the SNR in those two latter observations does not allow its detection above a confidence level of about 2$\sigma$.

Table 7 shows the best-fit parameters and fit quality for each source and observation. Figure 6 shows the spectral fits to U Gem and SS Aur. Figure 7 shows the spectral fits to the three observations of SS Cyg in outburst. It is important to stress that these three observations are consecutive. Figure 8 shows the spectral fit to the 0.4$-$150 keV simultaneous Chandra/RXTE spectra of SS Cyg in quiescence. Finally, Figure 9 shows the photon index $\Gamma$ as a function of the best-fit electron temperatures kT_e of the TL for all sources analyzed using our nmCV sample.

Because of the low energy resolution of PCA, the emission iron lines expected in the $\sim$6.4$-$7.0 keV energy range are not well resolved. Therefore, only one Gaussian component is required to account for the excesses in this energy range. Table 8 shows the line energy found for each observation, wherein for the simultaneous Chandra/RXTE spectra we exceptionally show the three iron emission lines observed by HETG/ACIS Chandra.