X-RAY AND ULTRAVIOLET SPECTROSCOPY OF GALACTIC DIFFUSE HOT GAS ALONG THE LARGE MAGELLANIC CLOUD X-3 SIGHT LINE

We observed the emission of the hot diffuse gas toward off-fields of the LMC X-3 sight line once during the science working group (SWG) program and twice during the AO1 program (Table 1), using the CCD camera XIS (Koyama et al. 2007) on board Suzaku (Mitsuda et al. 2007). To obtain the diffuse gas emission as close as to the LMC X-3 sight line along which the X-ray O vii absorption line has been detected (see Section 2.2) but with a minimized confusion by stray lights from the point source, and to average out the possible spatial gradient of the diffuse emission intensity, we observed two fields that are in nearly opposite directions from LMC X-3 and ∼30' away from it, as illustrated in Figure 2. With this configuration and the roll angle of the XIS field of view, we estimate that stray lights from LMC X-3 contribute no more than 6% to the observed X-ray emission in 0.3–1.0 keV energy range during our observations. The XIS was set to the normal clocking mode and the data format was either 3 × 3 or 5 × 5, and the spaced-raw charge injection (SCI) was not applied to any of the data during the observations.

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We used processed data version 1.0.1.1 for the SWG observation and version 2.0.6.13 for the two AO1 observations. We adopted the standard data selection criteria to obtain the good time intervals (GTIs), i.e., excluding exposures when the Suzaku's line of sight is elevated above the Earth rim by less than 10° and exposures with the "cut-off rigidity" less than 6 GV (refer to Smith et al. 2007 for further information). We checked the column density of the Sun-lit atmosphere during the selected GTIs, and found that it is always below 1.0 ×  10¹⁵ cm⁻², which is the criterion for no significant neutral oxygen emission from the Earth's atmosphere (Smith et al. 2007). We also converted the pulse-height-analysis (PHA) channels of X-ray events to pulse-invariant (PI) ones by using the xispi script (version 2006-5-16 for SWG and version 2007-05-30 for AO1 observations).

We created X-ray images in 0.3–2.0 keV energy range for the three observations, and found three discrete X-ray sources in the SWG data. To obtain the "true" diffuse emission, we removed those events within circular regions centered at the sources with a radius of 1' for the two faint sources and 3' for the bright one. Modeling these discrete sources, we estimated the contamination of their stray lines to the diffuse emission to be less than 5% in 0.3–2.0 keV energy band.

In the last step, we excluded those events severely affected by the solar activity. The diffuse X-ray emission below 1 keV could be contaminated by X-ray emission of the solar-wind charge exchange (SWCX) if the proton flux exceeds 3 × 10⁸ s⁻¹ cm⁻² in the wind (Mitsuda et al. 2008). The probability of such contamination increases if the shortest Earth-to-magnetopause (ETM) distance is ≲10 Earth radius (R_E) (Fujimoto et al. 2007). Here, the magnetopause is defined as the lowest position along the line of sight where geomagnetic field is open to interplanetary space. We used solar-wind data obtained with the Solar Wind Electron, Proton, and Alpha Monitor (SWEPAM) aboard the Advanced Composition Explorer (ACE).⁶ We found that there are some time intervals with proton flux exceeding the above limit during the SWG and the first AO1 observations. We thus subdivided the observations and constructed X-ray spectra for various flux levels, and found that, for the SWG observation, the spectra are consistent with each other, while for the first AO1 observation the O vii and O viii intensities are enhanced in the high flux subsets. We then calculated the ETM distance, and found that during the SWG observation it is always longer than 5R_E when the magnetic field is open to the Sun direction and that it becomes as short as 1.4R_E when the magnetic field is open to anti-Sun direction during which solar-wind particles cannot penetrate. In contrast, during the first AO1 observation the ETM distance varies significantly and some times becomes shorter than 3R_E even when the magnetic field is open to the Sun direction. We further sorted the first AO1 data according to this distance and the solar-wind flux, and decided to use only those time intervals with the proton flux <3 × 10⁸ s⁻¹ cm⁻² or the ETM distance >3R_E, during which spectra of the SWG and the AO1 data are all consistent.

We estimated the non-X-ray-background from the night Earth database using the method described in Tawa et al. (2008). We found that for XIS1, the count rate discrepancy between the database and our observations is about 5% above 10 keV, which indicates the background uncertain level. Since the non-X-ray-background is only 10% of the diffuse emission for the energies below 1 keV, this uncertainty is negligible.

We constructed instrumental response files (rmfs) and effective area (arf) by running the scripts xisrmfgen and xissimarfgen (version 2006-10-26; Ishisaki et al. 2007). To take into account the diffuse stray light effects, we used a 20'-radius flat field as the input emission in calculating the arf. We also included in the arf file the degradation of low energy efficiency due to the contamination on the XIS optical blocking filter.

In this work, we only used the spectra obtained with XIS1, which is a backside-illuminated CCD chip and is of high sensitivity at photon energies below 2 keV compared to the other three frontside-illuminated CCDs, XIS0 and XIS2-3 (Koyama et al. 2007). We grouped the spectra to an S/N of ⩾10 in each channel and used energy range of 0.4–3.0 keV in our analysis. This range is broad enough for constraining the continuum and also covers the H- and He-like emission lines of nitrogen, oxygen, neon, magnesium, and L transition of Fe xvii. The N vii, O vii, O viii, and Ne ix lines are clearly visible in the spectra (Figure 3).

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The observed diffuse X-ray emission is mainly from the Galactic gas, and confusion from the LMC is little. The targeted sight lines are well outside the main body of the LMC and is ∼5° away from the active star-forming 30 Doradus region (see Figure 1 in Wang et al. 2005). Toward these sight lines, there is no evidence for the presence of a large-scale halo; the hot halo gas producing the observed O vii and O viii emission could be at too high temperatures to be confined by the LMC. Furthermore, comparing to the AO1 pointings, the SWG pointing is ∼1° further away from the LMC (Figure 2). The consistent measurements between the observations (see Section 3.1) indicate a lack of a radial gradient that could be expected in any LMC emission contribution. We therefore conclude that the LMC contribution to the observed emission, if any, is negligible.

Chandra and FUSE observed LMC X-3 with exposures of ∼100 and 120 ks, respectively. Based on these observations, Wang et al. (2005) reported the detection of O vii, Ne ix, and O vi absorption lines along the sight line. For ease of reference, we list these detection in Table 2. A joint analysis of the detected O vii and Ne ix Kα absorption lines, together with the nondetection lines of O vii Kβ and O viii Kα, allowed for the measurements of the characteristic temperature, velocity dispersion, and oxygen column density of hot gas along the sight line with little confusion with extragalactic gas (Wang et al. 2005). We adopted the same co-added spectra and the corresponding calibration files as obtained in Wang et al. (2005). Because the Chandra observation was carried out with the high-resolution camera (HRC) that has very little energy resolution itself, the spectrum therefore needs to be fitted in a broad spectral range with an order-combined response file in order to take into account the grating-order overlapping (refer to Wang et al. 2005). To easily implement, we further extracted the first grating-order spectrum by doing the following. We first obtained a "global" best fit to the spectrum over the wavelength range of 2–30 Å, and then subtracted the spectral counts channel-by-channel by the difference of model-predicted counts based on the order-combined response file from those based on the first-order response file. We used the first-order spectrum in ranges of 12–22 and 24–29.5 Å, covering the L transition of the Fe xvii as well as the K transitions of the H- and He-like neon, oxygen, and nitrogen ions. To facilitate a joint analysis of the X-ray absorption and emission spectra with the O vi absorption line measurement, we re-wrote the FUSE spectral file produced with the CALFUSE pipeline in a format that can be read into the XSPEC. A Gaussian profile with a full width at half-maximum (FWHM) of 20 km s⁻¹ was used to mimic the instrumental response of the FUSE data.

Wang et al. (2005) argued that the observed absorption lines trace the Galactic gas rather than any intrinsic material associated with LMC X-3. Here, we recapitulate their argument in the following. LMC X-3 has a systematic velocity of ∼300 km s⁻¹. However, with the typical velocity resolution of ∼20 km s⁻¹ offered by FUSE, the centroid of the O vi absorption line was measured as 55 ± 11 km s⁻¹ (1σ error), which is >10σ smaller than the velocity of LMC X-3. The consistent measurements of this line in two observations with different source flux also indicate a Galactic origin. In measuring the absolute wavelength, current X-ray instruments cannot offer a significantly better resolution than that systematic velocity, but Chandra grating observations can provide a relative wavelength measurement as accurate as several tens kilometer per second. Wang et al. found that the velocity shifts of the O vii, the low ionization O i Kα lines, and the wavelength interval between these two lines are consistent with those observed toward a Galactic source 4U 1820–303 and two extragalactic sources Mrk 421 and PKS 2155–304; the lines along the latter three sight lines are believed to have a Galactic origin. If the absorptions are associated with the LMC X-3 as in a photo-ionized wind scenario, the line width and velocity shift are expected to be on the order of the escaping velocity of the system (∼10³ km s⁻¹), which is inconsistent with the narrowness and rest-frame velocity of the observed O vii and O vi lines. They then attributed the observed absorptions to the Galactic gas, which is also assumed in this work.

In the FUSE spectra of LMC X-3, Hutchings et al. (2003) and Wang et al. (2005) also found an O vi emission line whose velocity centroid varies as a function of the binary phase. This phase dependency could be explained if the emission arises from the companion star illuminated by the X-ray primary. The similar X-ray O vii emission has not been observed. The lines of our interests in this work are all very narrow (with an FWHM of ∼10² km s⁻¹) and their measurements depend on the local continuum. The observed emission line is very broad (with a half-width of ∼10³ km s⁻¹) and therefore will not affect our measurements herein presented.

The SXB emission is a composite of various components. Chiefly among them are the diffuse hot gas associated with the large-scale Galactic disk/halo, the Local Hot Bubble (LHB), the SWCX, and the extragalactic (primarily from unresolved active galactic nuclei (AGNs)) and the Galactic (mainly unresolved stars) discrete sources. Recent X-ray shadowing experiments with Suzaku and XMM-Newton indicate that the combined contribution from the LHB and the SWCX can be described with an emitting plasma at a temperature of ∼1.2 ×  10⁶ K with an EM of 0.0075 cm⁻⁶ pc (Smith et al. 2007; Galeazzi et al. 2007; Henley et al. 2007), which is equivalent to the line intensities of 3.5 and 0.04 LU for O vii triplet and O viii, respectively. The contribution from unresolved stellar sources is expected to be negligible at high galactic latitudes (|b|>30°; Kuntz & Snowden 2001) and is not considered further in this work. The extragalactic emission contribution can be approximated as a power law (PL) with an index of ∼1.4 and a normalization of ∼10.9 photons cm⁻² kev⁻¹ s⁻¹ sr⁻¹ at 1 keV (e.g., Hickox & Markevitch 2006; see Section 4.2 for further discussion).

We decompose the SXB emission in the LMC X-3 off-fields by jointly fitting the three Suzaku emission spectra. We first fit the spectra with an XSPEC model combination of mekal_LHB + wabs(powerlaw_exg + vmekal_disk). We fix the cool gas absorption (wabs) to be N^c_H = 3.8 × 10²⁰ cm⁻², derived from the neutral absorption edge study (Page et al. 2003). We assume the Galactic diffuse hot gas (as denoted by vmekal_disk) to be isothermal, let the abundances of nitrogen, neon, and iron be fitting parameters, and fix the abundance ratios between other metal elements and oxygen to the solar values. We also fix the LHB component to the values mentioned above (but see Section 4.1 for further discussion) and allow the normalization of the extragalactic PL component (powerlaw_exg) to vary in the fit (accounting for the cosmic variance). This simple model combination fits the emission data well. The fitting parameters are consistent among the three observations except for slightly higher nitrogen abundance and PL normalization values for the SWG data. The discrepancy in the nitrogen abundance is probably due to the calibration uncertainty of the XIS1 for the SWG observation taken at early stage (see Section 3.2), while the high PL normalization is likely caused by the residual contamination (the wing of the point-spread function) of the relatively bright field source that cannot be completely excluded from the SWG data (Section 2.1). We then link all fitting parameters among three observations except for nitrogen abundance, the PL index, and PL normalization, which are linked within the two AO1 observations but are allowed to vary between AO1 and SWG ones. The fit is acceptable with χ²/dof = 194/179 (Figure 3). The fitting parameters are presented in the first row of Table 3. By setting the abundances of nitrogen, oxygen, and neon in the Galactic disk component to be zero, and using Gaussian profiles to fit the N vii, O vii, O viii and Ne ix lines at 0.50, 0.56, 0.65, and 0.91 keV, we measure the intrinsic (cool-gas-absorption-corrected) emission line intensities of the diffuse hot gas (Table 2).

Assuming the intervening gas to be isothermal and adopting the interstellar medium (ISM) metal abundances from Wilms et al. (2000), Wang et al. (2005) constrained the gas temperature, velocity dispersion, and O vii (or equivalent hydrogen) column density, by jointly analyzing the detected O vii and Ne ix Kα absorption lines with the nondetections of O vii Kβ and O viii Kα lines. Following the same procedure, we have re-fitted the spectrum reduced in Section 2.2 and obtained nearly identical results to those obtained by Wang et al. (the second row in Table 3), except for the equivalent hydrogen column density N_H due to the different oxygen abundance adopted here. In order to compare with the Suzaku result on the relative abundance of N/O, we further included the nondetected N vi and N vii Kα absorption lines in our fit (Figure 4 and Table 2). The fit gives a 95% upper limit, N/O < 2.2, which is consistent with the value constrained from the Suzaku AO1 data, but is lower than that inferred from the SWG data. We therefore attribute the apparent super-solar nitrogen abundance observed in the SWG data to the instrumental calibration uncertainty.

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From now on, we let the normalization of the extragalactic PL component and the N/O ratio for the SWG observation vary independently of those for the AO ones in our data analysis. We will not further discuss these values in the text but still list them in our resulting Table 3 for references.

The gas temperature inferred from the above absorption line fits is a factor of ∼2 lower than that constrained from the emission spectral analysis (Section 3.1 and Table 3). We note that the temperature would be even lower if a super-solar Ne/O value as indicated in the emission spectral analysis (Section 3.1) were adopted in our absorption line fits. This temperature inconsistency clearly indicates that the X-ray emitting/absorbing gas is not isothermal. In this case, the emission and absorption arise preferentially in different temperature ranges.

Motivated by the observed morphology of diffuse X-ray emission around the nearby disk galaxies, Yao & Wang (2007) constructed a nonisothermal model for the Galactic disk hot gas. In the following, we first briefly formalize this model and then constrain it using the obtained absorption and emission data along the LMC X-3 sight line.

Assuming that the hydrogen number density and temperature of the hot gas can be characterized as

$$\begin{equation} n = n_0 e^{-z/(h_{\rm n}\xi)} \qquad {\rm and\qquad } T = T_{\rm 0} e^{-z/(h_{\rm T}\xi)}, \end{equation} \tag{ 1 }$$

where z is the vertical distance away from the Galactic plane, n₀ and T₀ are the midplane values, and h_n and h_T are the scale heights, and ξ is the volume filling factor that is assumed to be 1 in this paper, we can derive

$$\begin{equation} n=n_{\rm 0}(T/T_{\rm 0})^\gamma, \end{equation} \tag{ 2 }$$

where γ = h_T/h_n. Therefore, the differential hydrogen column density distribution is also a PL function of T,

$$\begin{equation} dN_{\rm H} = n dL = \frac{N_{\rm H}\gamma }{T_{\rm 0}} (T/T_{\rm 0})^{\gamma -1} dT, \end{equation} \tag{ 3 }$$

and the corresponding ionic column density along a sight line with a Galactic latitude b can be expressed as

$$\begin{equation} N_{\rm i} = \frac{N_{\rm H} \gamma A_{\rm e} }{T_{\rm 0}} \int ^{T_{\rm 0}}_{T_{\rm min}} \left(\frac{T}{T_{\rm 0}} \right)^{\gamma -1} f_{\rm i}(T)\,dT, \end{equation} \tag{ 4 }$$

where N_H = n₀h_nξ/sin b, and A_e and f_i(T) are the element abundance and ionization fraction for the ion, and T_min = 10⁵ K is the minimum temperature assumed (line emission and absorption below this temperature are negligible; Figure 1).

Similarly, the emission intensity (from a single line or a continuum) is

$$\begin{equation} I = \frac{A_{\rm e}}{4\pi } \int _0^L \Lambda (T) n_e n\, dL = \frac{A_{\rm e}}{4\pi }\int ^{T_{\rm 0}}_{T_{\rm min}} \Lambda (T) \frac{dEM}{dT}dT, \end{equation} \tag{ 5 }$$

where Λ(T) is the corresponding emissivity of the hot gas. The differential EM is

$$\begin{equation} \frac{dEM}{dT} = \frac{1.2 N_{\rm H}^2 \gamma }{T_{\rm 0 }L} \left(\frac{T}{T_{\rm 0}} \right)^{2\gamma -1}, \end{equation} \tag{ 6 }$$

where the factor 1.2 accounts for the helium contribution to the electron density, and L = h_nξ/sin b is the effective path length of the hot gas.

Both the emission and absorption data can be used independently to constrain the parameters N_H, T₀, γ, and the relative element abundances (e.g., Ne/O; Equations 4 and 5). A simultaneous fit to the emission and absorption further allows for the estimate of the L parameter (Equation 6). We have revised our absorption line model developed in Yao & Wang (2005) and the thermal emission model cevmkl in XSPEC to facilitate the use of the ionic column density N_i and the EM as a PL function of T (Equations 4–6; Yao & Wang 2007).

These revised models are then used to jointly fit the absorption and emission data. For the absorption data, the fit includes not only the significantly detected O vii and Ne ix Kα lines, but also the key nondetections of the O vii Kβ, Fe xvii L, and Kα transitions of O viii, Ne x, N vii, and N vi at 18.626, 15.010, 18.967, 12.134, 24.779, and 28.787 Å, respectively, which provide useful constraints on the physical and chemical properties of the absorbing gas. The revised cevmkl model is used to fit the Galactic disk component of the emission spectra (vmekal_disk in Section 3.1). The abundance ratios of N/O, Ne/O, and Fe/O, which are linked together between the absorption and emission models, are allowed to vary in our fit. This joint fit is satisfactory; the directly constrained model parameters are reported in the third row of Table 3. We then infer the temperature scale height as h_T = 1.4(0.2, 5.2) kpc and the gas density at the Galactic plane as n₀ = 1.4(0.3, 3.4) × 10⁻³ cm⁻³. The confidence contours of h_n, T₀, and N_H versus γ are plotted in Figure 5.

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From the nonisothermal Galactic disk model constrained with the X-ray emission and absorption data, we estimate the total O vi contained in the diffuse hot gas as N_O VI ∼ 3.4 × 10¹⁴ cm⁻², which is consistent with that inferred from the observed O vi λ1031.96 line absorption (Figure 6; see also Wang et al. 2005; Section 2.2). Including the O vi line in our joint analysis tightens the constraints on the model parameters (the forth row of Table 3), especially on the temperature distribution.

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The biggest uncertainty in modeling the SXB emission is the estimate of the contributions from the LHB and SWCX. Our understanding for both components is still very poor because it is very hard to decompose their contributions. The SWCX emission could in principle be estimated by tracing the solar-wind flux and the neutral atoms in the Earth's atmosphere and in the local ISM (e.g., Lallement et al. 2004). However, such an estimation is model dependent. For instance, for the line of sight with Galactic coordinates (l, b) = (27865, − 4530) observed on 2003 March 3, the O vii emission is estimated to be 0.83 and 3.7 LU by Koutroumpa et al. (2007) and Henley & Shelton (2008), respectively. Recent comparisons of the observed X-ray emission with models for the SWCX suggest that the foreground emission in the shadowing experiments can be mainly attributed to the SWCX and that the LHB emission is negligible (Koutroumpa et al. 2007; Rocks et al. 2007; but also see Shelton 2008). The total O vii intensity of the SXB toward a high Galactic latitude sight line (l, b = 272°, − 58°) is 2.7(2.0, 3.4) LU (1σ range), obtained from a recent Suzaku observation (Mitsuda et al. 2006). If emission from both the LHB and the SWCX is isotropic and independent of Galactic latitude, this value can be regarded as the upper limit of the combined contribution of these two components.

Our results are not qualitatively affected by above discussed uncertainties. To be more quantitative in assessing the effect, we allow EM of the LHB plus SWCX component to vary from 0 to 0.0113 cm⁻⁶ pc (Section 3.1), representing two extreme cases. The low boundary corresponds zero emission of the LHB and the SWCX components, whereas the high boundary corresponds to the 3σ upper limit of the observed O vii intensity (i.e., 4.8 LU) toward the high Galactic latitude sight line. We then re-perform our spectral analysis described in Sections 3.1 and 3.4. We find that new constrained gas temperature in modeling the emission data alone under the isothermal assumption is still about two times higher than that constrained from the absorption data (refer to the first and fifth rows in Table 3), which still necessitates the nonisothermal model developed in Section 3.3. The new results constrained in the joint analysis are also consistent with the old values, except for with a slightly broader uncertain range (refer to the forth and sixth rows in Table 3).

In modeling the emission spectra, we used a simple PL function to approximate the extragalactic contribution (Section 3.1). Recent Chandra and XMM-Newton deep surveys for the cosmic SXB have resolved ≳80% of the background emission at 1–8 keV into extragalactic discrete sources (e.g., Hickox & Markevitch 2006). Optically bright sources tend to be spectrally hard while faint sources tend to be spectrally soft (e.g., Mushotzky et al. 2000). To examine the goodness of our approximation, we replace the simple PL with a broken PL and fix the break energy at 1 keV to model the extragalactic component in our joint analysis described in Section 3.3. We obtain the photon indices as 1.7(1.3, 2.0) and 1.4(1.3, 1.5) below and above 1 keV, respectively, and find that the parameters of the Galactic hot gas are barely affected (the seventh row of Table 3).

In this work, we have assumed the emitting/absorbing gas to be optically thin, i.e., we have neglected the resonant scattering effect of the hot gas. To qualitatively assess the validity of our assumption, we assume the hot gas density to be uniform for easy analysis. The observed O vii emission line consists of unresolved triplet transitions, resonance, forbidden, and intercombination lines at 21.60, 22.10, and 21.80 Å, respectively. Since the oscillation strength is essentially zero for the latter two transitions, we consider the "scattering" only for the resonant line. The absorbed resonant photons should be re-emitted isotropically; half of these re-emitted photons are expected to favor the observing direction. Taking all these into account, we obtain the observed line intensity as

$$\begin{equation} I = (1 - f) I_0 + 0.5fI_0 \left(1 + \frac{ 1 - e^{-\tau } }{\tau } \right), \end{equation} \tag{ 7 }$$

where τ is the (max) absorption optical depth at center wavelength of the resonant transition, and I₀ is the "intrinsic" (without the scattering) line intensity. Here, f is the resonant transition fraction of the O vii triple, which is a function of gas temperature. Taking the (max) temperature at the Galactic plane T₀ ∼ 3 × 10⁶ K (Table 3), which favors more to the resonant transition and gives f = 0.65, we get I ≳ 0.675I₀ for any value of τ. This indicates that the observed intensity should not be different from the intrinsic value by a factor larger than 1.5. In reality, the "background" gas cloud also scatters the photons emitted by the "foreground" cloud to the observing direction. If this effect is further considered, the difference should largely disappear. Therefore we conclude that the resonance scattering should not significantly affect our results, although a more detailed modeling needs to be performed to account for a more realistic geometry of the hot gas distribution.

Our analysis indicates that the gas responsible for the observed X-ray absorption/emission along the LMC X-3 sight line has a path length about a few kpc and is consistent with the Galactic disk in origin. This result has important implications for understanding the structure and origin of hot gas around our Galaxy. As described in Section 1, high ionization X-ray absorption lines with zero velocity shift have been observed along many extragalactic sight lines, and the O vii emission lines are also detected at various high Galactic latitudes. Several scenarios have been proposed for the origin of the emitting/absorbing gas, including the intergalactic medium (IGM) of the Local Group, the large-scale Galactic halo, and the thick Galactic gaseous disk (see Yao & Wang (2007) for a review). These scenarios cannot be distinguished kinematically because of the limited spectral resolution of current X-ray instruments. So, currently the most direct information about the location of the gas comes from differential analysis of the X-ray absorption lines toward sources at different distances. Wang et al. (2005) find that the O vii absorption along the sight line toward LMC X-3, at a distance of ∼50 kpc, is comparable to those observed toward AGN sight lines. Therefore, if the LMC X-3 sight line is representative, one can then conclude that the bulk of the X-ray absorption around the Galaxy is within ∼50 kpc. A similar conclusion has been reached based on the estimate of the total baryonic matter contained in the O vii-bearing gas, and on the angular distribution of the O vii absorption (Fang et al. 2006; Bregman & Lloyd-Davies 2007). A comparison of a Galactic sight line (4U 1957+11) with two extragalactic sight lines toward LMC X-3 and Mrk 421 further indicates that there is no significant O vii absorption in the extended Galactic halo beyond a few kpc (Yao et al. 2008), which is consistent with the conclusion drawn in this work.

The O vii emission from the hot gas beyond LMC X-3 is not expected to be important either. Yao et al. (2008) obtained a 95% upper limit to the O vii absorption beyond LMC X-3 as N_O VII < 3.7 × 10¹⁵ cm⁻². Assuming this much of O vii uniformly distributed in a region with an extension scale of l, we calculate its emission as I_O VII < 0.025/(A_O 0.1l_100 kpc) LU for the entire temperature range from 10⁵ to 10⁷ K, where A_O 0.1 is the oxygen abundance in unit of 10% solar value and l_100 kpc is in unit of 100 kpc. In contrast, the inferred O vii intensity of the Galactic disk diffuse gas is 5.0 LU (Section 3.1 and Table 2).

We have shown that the X-ray emission and absorption as well as the far-UV O vi absorption along the sight line toward LMC X-3 can be explained by the presence of a thick Galactic hot gaseous disk. A similar explanation holds for the sight line toward Mrk 421, for which another joint X-ray absorption/emission and UV absorption has been carried out (the X-ray emission is, however, mostly based on the RASS broadband measurements; Yao & Wang 2007). The characteristic scale height of the disk is also consistent with the Ne ix column density distribution in the Galaxy (Yao & Wang 2005). The gas in the disk is shown to have a normal metal abundance (Wang et al. 2005; Yao & Wang 2006) and is clearly due to the heating by mechanical energy feedback from stars in the Galaxy (e.g., Ferrière (1998)). Such an interpretation is also supported by the X-ray emission observations of nearby disk galaxies like our own. The diffuse X-ray emission has been routinely observed in many late-type normal star-forming spirals and is confined to a region around galaxies with vertical extent no more than a few kpc (e.g., Wang et al. 2001, 2003; Tüllmann et al. 2006a, 2006b). Both the intensity and the spatial extent appear to be scaled with galactic star-formation rate (e.g., Tüllmann et al. 2006b). Therefore, we conclude that the X-ray emitting/absorbing and O vi-absorbing gas, as studied in this paper, arises primarily from the stellar feedback in the Galactic disk.

Before discussing the O vi-bearing gas location, let us look at the O vi emission properties first. In Section 3.4, we have shown that the observed O vi absorption can be predicted from the X-ray-data-constrained nonisothermal gas model and have then used the O vi λ1031.96 absorption line to further constrain our spectral model. With the fitted model parameters, we can estimate the intrinsic O vi emission intensity of the diffuse hot gas toward LMC X-3, and then compare it with observations. The best-fit model gives 186 LU in total for the O vi doublet λλ1032 and 1038. Taking all the 90% boundaries that favor more O vi emission, we obtain a firm upper limit of 1612 LU.

There is no direct measurement of the O vi emission within 1° of the LMC X-3 sight line. Within ∼5°, some observations show measurable O vi λ1032 emission as 2.1–5.7 × 10³ LU, while other observations only yield upper limit even with longer exposures (Otte & Dixon 2006; Dixon et al. 2006; Dixon & Sankrit 2008). Since the O vi emission could vary by a factor of >2.3 at an angular scale as small as 25' (Dixon et al. 2006), it is nearly impossible to reliably estimate the O vi emission toward LMC X-3 sight line based on the few existing nearby samples. However, if there were a measurable O vi emission toward the LMC X-3 sight line (but see below), it must be in order of several thousand LU, as typically observed at high galactic latitudes, which is significantly larger than that predicted in the O vii-bearing gas and therefore unlikely arises from the diffuse hot gas.

Where is the O vi-bearing gas then? To answer this question, it is important to compare the spatial distributions of the O vi absorption and emission. In this work, we find that most of the O vi absorption can arise from the diffuse gas along a vertical scale of ∼3 kpc around the Galactic plane. Figure 7 shows the density and column density distributions of O vi and O vii as a function of the vertical distance, predicted from our constrained nonisothermal disk model. While compared to O vii, O vi is distributed in a relative narrow region, which is mainly due to the sensitive dependence of O vi population on temperature (Figure 1), about 80% of the O vi column still spreads over as large as 1 (from 2.7 to 3.7) kpc. Observationally, O vi absorption has been detected toward essentially all sight lines, and the characteristic scale height of the O vi column densities is similar to that constrained in this work (e.g., Savage et al. 2003). It has been suggested that O vi could largely arise at interfaces between hot and cool ISMs. However, for Mrk 421 sight line, Savage et al. (2005) counted the number of cool gas velocity components and found that the interfaces can only account for at most 50% of O vi absorption, leaving a bulk of the O vi to other origins. In contrast, the O vi emission is measured toward only ∼30% of the surveyed sky (Otte & Dixon 2006; Dixon & Sankrit 2008). These results clearly indicate that the "commonly" observed O vi-absorbing gas in the kpc scale is not primarily responsible for the detected O vi emission. We propose that the low-temperature regime of the kpc-scale diffuse gas could contain a significant or even dominant fraction of the observed O vi absorption, as indicated in this work, and that the conductive interfaces between hot and cool gases, though could be another reservoir of O vi ion, are mainly responsible for the observed O vi emission. This picture not only explains the spatial distribution of the O vi absorption, but also naturally explains the sight-line-to-sight-line O vi variation in both absorption and emission. For LMC X-3 sight line in particular, since all the observed O vi can be attributed to the diffuse gas, the O vi emission is not expected to be strong.

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If hot gas toward the LMC X-3 sight line represents reasonably well the hot ISM of the Galactic disk as a whole, we can then use our nonisothermal gas model to estimate the total radiative energy loss rate of the gas, and compare it to the expected energy input from supernova (SN) explosions. It has long been observed that in the low L_x/L_B (L_B is the blue luminosity) early-type galaxies, X-ray radiative energy loss rate of the diffuse hot gas is far less than the expected SN energy input (e.g., Canizares et al. 1987; Brown & Bregman 2000). However, all the previous studies were based on imaging observations in which decomposing different emission components is a complicated task (e.g., Li et al. 2007) and could make the inferred properties of the "true" diffuse hot gas very uncertain. So far the LMC X-3 sight line is the only sight line along which the high-resolution X-ray emission/absorption and far-UV absorption measurements with a minimal confusion are available, which allow us to tightly constrain the thermal and chemical properties as well as the global spatial distribution of the Galactic diffuse hot gas, as presented in this work. It is thus worthwhile re-examining the radiative power of the Galactic hot gas based on these characterizations.

The energy loss rate of the hot gas can be expressed as

$$\begin{equation} \frac{d^2U}{dsdt} = 2\times \int _0^\infty 1.2n^2\Lambda (T)\, dz, \end{equation} \tag{ 8 }$$

where the factor 2 accounts for the two sides of the Galactic disk. With our model (Equation 1), we can re-write Equation (8) as

$$\begin{equation} \frac{d^2U}{dtds} = 2\times \int ^{T_0}_{T_{\rm{min}}} 1.2n_0^2 \left(\frac{T}{T_0}\right)^{2\gamma -1}\Lambda (T) (-h_{\rm T}) d\left(\frac{T}{T_0}\right). \end{equation} \tag{ 9 }$$

Assuming the solar abundances, plugging in the best-fit n₀, T₀, γ, and h_T values (Section 3.3), and taking the emissivity Λ(T) from the atomic database ATOMDB⁷, we obtain the local surface emissivity of the hot gas as 3.1 and 16.1 × 10³⁶ erg s⁻¹ kpc⁻² in 0.1–10 and 0.01–10 keV bands, respectively. Including the additional O vi emission of ∼3000 LU from the interface component, the total radiative energy loss rate is ∼3 ×  10³⁷ erg s⁻¹ kpc⁻².

The radiative cooling of the Galactic disk hot gas only accounts for less than 10% of the expected energy input of the stellar feedback. At Sun's galactocentric radius, the SN rate is 19 and 2.6 Myr⁻¹ kpc⁻² for type II and type Ia, respectively (Ferrière 1998). If on average each type II SN progenitor releases 2 ×  10⁵⁰ erg of energy before it explodes and each SN explosion releases 10⁵¹ erg (Ferrière 1998; Leitherer et al. 1992), the total energy input is then 8 × 10³⁸ erg s⁻¹ kpc⁻², which is about 20 times higher than our estimated gas cooling rate. The "missing" energy could be either emitted in other wavelength bands (e.g., infrared) or have been consumed in driving other Galactic activities (e.g., galaxy-size out flows).

Obviously, such an estimation is model dependent. Shelton et al. (2007) recently concluded that ∼70% of the SN energy input could be radiated away by the Galactic hot gas. In their model, they required the observed O vi emission to be co-spatial with the O vi absorption and assumed both the O vi-bearing and the hotter O vii-bearing gas to be isobaric. This requirement results in that most of the O vi-bearing gas is confined within a region of <100 pc in size, which favors to produce about 10 times more thermal emission in the energy range of 0.01–0.1 keV than our model. In contrast, we constrain our model with X-ray O vii and O viii emission and absorption, and find that most of the O vi absorption could arise from the kpc-scale diffuse gas. In our model, because of large extent of the diffuse gas (therefore a low density), its emitting power is at most as much as that of the observed/expected O vi emission lines, which presumably arise from the interfaces between the hot and cool ISMs (Section 4.5). The scale size of the O vii- and O vi-bearing gas derived in this work and utilized in our estimation is consistent with that obtained in the recent O vi absorption surveys (Savage et al. 2003; Bowen et al. 2008).

In our analysis, we find that, while the relative abundance of Fe/O is about the solar value, the Ne/O is about two times higher (Table 3). This overabundance of neon, if true, is consistent with the interpretation of about 50% of oxygen and iron being depleted into dust grains. However, because this overabundance is mainly derived from the emission data in which decomposing various components is still very uncertain, the depletion interpretation therefore may not be unique. For instance, Henley & Shelton (2008) suggest that the SWCX could also produce apparent nonsolar abundance ratio. Furthermore, our understanding of the chemical abundances in the solar system is still poor. For example, the oxygen value has recently been revised downward by ∼35% (Asplund et al. 2005), but this revision is still under debate (Antia & Basu 2006). The abundance pattern in the ISM is also suggested to be slightly different from that in the solar system (Wilms et al. 2000). So it is more useful to list the number density ratio of Ne/O derived in this work, which is 0.25(0.19, 0.33). We prefer to defer the interpretation of the apparent overabundance of neon until a better understanding of both the SWCX and the solar chemical abundances is reached.