X-ray plasma flow and turbulence in the colliding winds of WR140

We analyse $\textit{XMM-Newton}$ RGS spectra of Wolf-Rayet (WR) 140, an archetype long-period eccentric WR+O colliding wind binary. We evaluate the spectra of O and Fe emission lines and find that the plasmas emitting these lines have the largest approaching velocities with the largest velocity dispersions between phases 0.935 and 0.968 where the inferior conjunction of the O star occurs. This behaviour is the same as that of the Ne line-emission plasma presented in our previous paper. We perform diagnosis of electron number density $n_{\rm e}$ using He-like triplet lines of O and Ne-like Fe-L lines. The former results in a conservative upper limit of $n_{\rm e} \lesssim 10^{10}$-10$^{12}$ cm$^{-3}$ on the O line-emission site, while the latter can not impose any constraint on the Fe line-emission site because of statistical limitations. We calculate the line-of-sight velocity and its dispersion separately along the shock cone. By comparing the observed and calculated line-of-sight velocities, we update the distance of the Ne line-emission site from the stagnation point. By assuming radiative cooling of the Ne line-emission plasma using the observed temperature and the local stellar wind density, we estimate the line-emission site extends along the shock cone by at most $\pm$58 per cent (phase 0.816) of the distance from the stagnation point. In this framework, excess of the observed velocity dispersion over the calculated one is ascribed to turbulence in the hot-shocked plasma at earlier orbital phases of 0.816, 0.912, and 0.935, with the largest velocity dispersion of 340-630 km s$^{-1}$ at phase 0.912.


INTRODUCTION
A classical Wolf-Rayet (cWR) star is the final stage in the evolution of a massive star.It generally has a surface temperature of >30,000 K, luminosity of ∼ 10 6 L ⊙ , and large initial mass of >25 M ⊙ .A cWR star emits high-velocity stellar wind with a terminal speed of approximately 2000 km s −1 and large mass-loss rate of > 10 −5 M ⊙ yr −1 , producing a spectrum with broad emission lines.cWR stars are further classified into three broad subtypes according to their spectral characteristics: WN (primarily He and N emission lines), WC (no N and primarily He and C), and WO (O and WC emission lines).These subtypes are divided into subclasses according to their degree of ionisation.cWR stars explode as core-collapse supernovae, wherein the WN and WC stars become H-poor type-SN Ib and WO stars become type-SN Ic, the latter owing to the absence of an outer He layer.Prilutskii & Usov (1976) and Cherepashchuk (1976) first studied the production of X-ray emissions by the collision of dense stellar winds in massive binary stars (see also Cooke et al. 1978).They showed that the gas temperature reached ∼10 7 -10 8 K with X-ray luminosities of 10 33 -10 35 erg s −1 .Initial X-ray observations (Seward et al. 1979;Moffat et al. 1982;Caillault et al. 1985) showed that WR ★ E-mail: miyamoto-asuka@ed.tmu.ac.jp (AM) stars emit X-rays, irrespective of whether they belong to binaries, as described by Prilutskii & Usov (1976).Pollock (1987) conducted a uniform analysis of the 48 WR stars, which were observed with the Einstein X-ray Observatory.Their luminosities in the soft band (0.1-4 keV) were in the range from 10 32 to 10 34 erg s −1 .By incorporating the radio data, Pollock (1987) concluded that X-rays from the brightest group of the Einstein samples originated directly from the colliding stellar winds, as predicted by Prilutskii & Usov (1976), or from the Compton scattering of photosheric radiation by relativistic electrons accelerated by surface magnetic fields of up to a few hundred gauss, although de la Chevrotière et al. (2014) claimed that no significant global magnetic field existed.WR140 (HD193793), the target of this study, is a WR+ O binary composed of WC7pd and O5.5fc stars (Fahed et al. 2011), orbiting each other with a period of just under 8 years.Both stars expel highvelocity stellar winds, and their collision creates shocks that heat and compress the hot plasma, which then emits X-rays.WR140 is among the brightest massive binaries observed by Einstein and has been detected since the earliest stages of X-ray astronomy by Uhuru (Forman et al. 1978), HEAO-1 (Wood et al. 1984) and EXOSAT (Williams et al. 1990).
Detailed X-ray spectrometry became possible with later X-ray astronomy satellites (Koyama et al. 1990(Koyama et al. , 1994;;Zhekov & Skinner 2000;Pollock et al. 2005;De Becker et al. 2011;Sugawara et al. 2015;Pollock et al. 2021).Koyama et al. (1990) measured the X-ray spectrum of WR140 using the Ginga observatory.They determined the X-ray flux of 2-6 keV to be 1.5 × 10 −11 erg s −1 cm −2 , which results in a luminosity of 4.1×10 33 erg s −1 by assuming a distance of 1518 pc (Thomas et al. 2021).Koyama et al. (1994) observed WR140 using ASCA at the phase when the WR star was nearly in front of the O star.They found that the X-ray spectrum was heavily absorbed by  H ≃ 3 × 10 22 cm −2 .A series of X-ray observations of up to ∼10 keV across the periastron passage were performed using XMM-Newton (De Becker et al. 2011) and Suzaku (Sugawara et al. 2015).The researchers detected an increase in line-of-sight absorption as the stars approached the periastron passage.Sugawara et al. (2015) measured maximum plasma temperatures of 3.0-3.5 keV (35-41 MK) over a phase interval of 2.904-3.000.
In our first study (Miyamoto et al. 2022, hereafter referred to as Paper I), we analysed the data from WR140 observed using the reflection grating spectrometer (RGS; den Herder et al. 2001) onboard XMM-Newton (Jansen et al. 2001) over a period of 8 years and measured the plasma temperature, line-of-sight velocity, and velocity dispersion of the Ne emission lines at different orbital phases.We calculated the shape of the shock cone based on the balance of ram pressure between the stellar winds and evaluated the location of the Ne line-emission site on the shock cone by comparing the ratio of the expected line-of-sight velocity to the expected velocity dispersion with that of the observed value.We also constrained the electron number densities using the intensity ratio of He-like triplets of Ne at different orbital phases.
In this study, we aim to advance the understanding of the nature of shock cone plasma in WR140.The remainder of this paper is organised as follows: In Section 2, we describe the data used in this study and the data reduction method.In Section 3, we explain the data analysis methods adopted to derive the line-of-sight velocities and redtheir dispersions of O and Fe emission lines.These emission lines show a similar velocity trend to that of the Ne emission lines presented in Paper I. We also attempt to constrain the densities using the intensity ratios of these line components.In Section 4, we calculate the line-of-sight velocity and its dispersion (separately, not their ratio) of the plasma flowing in the shock cone, whose geometry was obtained in Paper I, from which the location of the Ne line-emission site is updated from Paper I. Additionally, the location of the O lineemission site is determined.We evaluate spatial extent of the Ne and O line-emission sites along the shock cone.For the first time, we report that excess of the observed line-of-sight velocity dispersion can be explained by turbulence in the X-ray plasma flow, using spatial extent of the Ne line-emission site evaluated from the temperature of the Ne line-emission plasma and its cooling time.Finally, in Section 5, we summarise the results of this study.
In this paper, all errors quoted are at the 90 per cent confidence level unless otherwise mentioned.

Observations
We analyse 10 datasets obtained at different orbital phases using the RGS (den Herder et al. 2001) onboard XMM-Newton (Jansen et al. 2001), covering a period of just over 8 years, from May 2008 to June 2016.The data all had individual exposure times of more than 18 ks.The orbital parameters adopted in this study are those used in Monnier et al. (2011) and are summarised in Table 1 of Paper I.
The most recent parameters are provided in Thomas et al. (2021); however, for consistency with Paper I, we continue to employ those of Monnier et al. (2011) in this paper.The apparent binary orbit projected onto the celestial sphere is sketched in Monnier et al. (2011).The observation logs are summarised in Table 2 of Paper I.

Data reduction
As explained in Paper I, we extract the spectra of the first and second orders of RGS1 and RGS2 from the event files and create response files according to the standard data reduction method using the HEAsoft (version 6.27.2 1 ) program provided by NASA's GSFC and the SAS (version 19.1.0 2 ) provided by ESA. Figure 2 in Paper I shows the positions of the O star relative to the WR star, where the 10 RGS observations are made together with their RGS spectra.As Paper I, we analyse only the datasets at the orbital phases K (0.816), A (0.912), L (0.935), B (0.968), and D (0.987) where the O star is in front of the WR star, showing X-ray spectra with sufficient statistical quality.An inferior conjunction of the O star occurs between phases L (0.935) and B (0.968).

O vii and O viii K𝛼 lines
Similar to the Ne lines in Paper I, we evaluate the line-of-sight velocity of K lines of O vii,viii and their dispersion.We perform spectral fitting by adopting a bvvapec*tbabs model using the energy bands of K lines of O vii,viii (0.55-0.59 keV and 0.635-0.670keV).The bvvapec model describes a velocity-broadened emission spectrum from an optically thin thermal plasma in collisional ionisation equilibrium, similar to the bvapec used in Paper I.Although bvvapec can change the abundance of elements with odd atomic numbers, all abundances that are not variable in bvapec are fixed at the solar abundances (Anders & Grevesse 1989).Consequently, the bvvapec model used in this study is identical to that used in Paper I, and we adopt the parameters shown in Table 4 of Paper I as the best-fit parameters of full energy-band fits.
To evaluate the O vii,viii lines, we set the temperature, O abundance, line-of-sight velocity and its dispersion, emission measure of the bvvapec model, and hydrogen column density of the tbabs model as free parameters and fix the abundances other than O at the values obtained with the full energy-band fit (Table 4 in Paper I).The results are summarised in Table 1 and Fig. 1 (left).The line-of-sight velocity ranges from −700 to −1200 km s −1 and its velocity dispersion ranges from 400-800 km s −1 .In general, this is the same as that of the Ne emission line reported in Paper I.

Fe xvii, Fe xviii, and Fe xx L lines
Spectral fitting is performed by adopting bvvapec*tbabs using the data for the energy bands of Fe xvii,xviii,xx emission lines.We set the temperature, Fe abundance, line-of-sight velocity and its dispersion, emission measure of the bvvapec model, and hydrogen column density of the tbabs model as free parameters and fix the abundances of the other elements at the values obtained with the full energy-band  Black and green colours are used for the first-order spectra of RGS1 and RGS2, respectively, while the red and blue colours are used for their second-order spectra, respectively.The best-fitting bvvapec*tbabs models are overlaid as histograms, whose parameters are summarised in Tables 1 and 2.
fit (Table 4 in

Summary of the line-of-sight velocity and its dispersion
We plot the line-of-sight velocity and its dispersion of the Ne, O, and Fe lines as functions of the orbital phase, as displayed in Fig. 2.
Here, we use the results of Ne from Table 5 reported in Paper I. The line-of-sight velocities are blue-shifted at these five phases where the the observer views the collision from within the shock cone.If these plasmas flow along the shock cone, the line-of-sight speed should be the largest and the velocity dispersion should be the smallest when the observer is closest to the axis of symmetry of the shock cone.The trends shown in Fig. 2 follow this expectation well, as the inferior conjunction of the O star occurs between phases B (0.968) and L (0.935).The O and Fe lines follow a trend similar to that of the Ne lines, reinforcing the results of Ne lines reported in Paper I. Note that we neglect the effect of the Coriolis force, which is not sufficiently strong to affect the axial symmetry of the shock cone at the phases before periastron passage (see APPENDIX A for the effect of the Coriolis force on the shape of the shock cone).

He-like triplet of Oxygen
As explained in Paper I §3.4,and §4.2.1, the intensity ratio of the Helike triplet lines from the heavy elements is sensitive to the plasma density.Following the analysis method of Ne reported in Paper I, we attempt to constrain the plasma electron number density  e with a He-like triplet of O.We use the energy band of the He-like triplet of O vii (0.55-0.59 keV; see Fig. 1 left).As a continuum, we adopt the model composed of bvvapec multiplied by tbabs.We append three velocityshifted gaussians (zgauss) on this continuum to represent  , , and  components of O vii, and, instead, fix the O abundance of the bvvapec model to 0. The other parameters, including  H of the tbabs   1 and 2, respectively) plotted as a function of the orbital phase.At all phases, the line-of-sight velocity is negative (blue-shifted), implying that the plasma emitting these lines is approaching the earth.Both  los and  los seem to take their minimum values between phase L (0.935) and B (0.968), where the inferior conjunction of the O star occurs.
model, are obtained using the full energy band fit (Paper I, Table 4).We fixed the centroid energies of the  , , and  components at their rest-frame energies (0.5610 keV, 0.5687 keV, and 0.5740 keV, respectively), and their velocity shift is realized with the common redshift parameter of the zgauss models, which is  los (= ) shown in Table 1.The energy width  [keV] of the forbidden line is linked to  los [km s −1 ] of bvvapec listed in Table 1 through  f =( los /) f , where  f is the forbidden-line central energy. i and  r are scaled with  f according to their line central energies.
Even with these constraints, as reported in Paper I §3.4,we evaluate the uncertainty of the line parameters associated with  los manually.We adopt the errors of  los determined by the K lines of O vii and O viii (Table 1).First, we perform spectral fitting at the best-fit  los value.We then repeat the same fit at the maximum/minimum values of the confidence interval to obtain the errors in the line parameters.The same procedure is performed for all five phases.The resulting intensities of the triplet components are summarised in Table 3.
In parallel to the analysis of the spectra, as reported in Paper I §4.2.1, we calculate the intensities of  , , and  of O vii using the plasma code SPEX version 3.06.013developed by SRON4 (Kaastra et al. 1996) as a function of the electron number density  e and plot the ratio of  / and /.We assume that the plasma is in collisional Table 3. Best-fit parameters of the He-like triplet of O using the model comprised of bvvapec and three zgauss components, which represent a resonance line, intercombination lines, and a forbidden line.Instead, the O abundance of bvvapec is set to zero, and the other parameters of bvvapec and tbabs are set to the best-fit values obtained from fitting with O vii and O viii lines (Table 1).The model parameter redshift  los / is not constrained very well solely with the He-like line.Hence, the fitting is performed with  los fixed at its best-fit value and at the minimum and maximum values of the confidence interval separately.The line centroid energies  f ,  i , and  r are fixed at the rest-frame energies of the He-like triplet (0.561, 0.569, and 0.574 keV, respectively) and effectively set free to vary with the common value of the redshift ( los /). f is fixed at  f = (  obs /)  f , and  i and  r are linked to  f with their line energy ratios ( i / f and  r / f , respectively) As a result, the free parameters of the fitting is the intensities of the lines.

12.34
Table 4. Electron number density  e obtained with the He-like triplet of O.We obtain only the upper limits at phases K (0.816), A (0.912), and L (0.935) (Fig. 3) and no constraint on the other two phases.Note that the EUV excitation overwhelms the collisional excitation effect at phase L (0.935) (Table 5); hence, its upper limit is extremely conservative.
Phase  e (cm  4.However, these upper limits may be conservative depending on the degree of photoionisation effect due to the EUV light from the O star, which is evaluated in the next subsection.

EUV radiation effect on the O and Ne line-emission site densities
Using the electron number densities  e obtained in the previous subsection (Table 4), we calculate the rates of collisional excitation  e    and photoexcitation Γ   from the 3 S level to 3 P of oxygen using eqs.( 19) and ( 20) in Paper I, respectively, together with the ratios of the latter to the former: The results are summarised in Table 5.Note that we use the distances to the line-emission sites calculated later in §4.1.2(Table 7).For oxygen, because only the upper limits of  e are determined (Table 4), the rates of collisional excitation are the upper limits, and only the lower limits are determined for the UV excitation fractions.At phases K (0.816) and A (0.912), we have lower limits of a few per cents.In contrast, at phase L (0.935), the high fraction of EUV excitation implies that the enhancement of the intercombination lines  is realised with the EUV radiation from the O star.Hence, the upper limit of  e is very conservative compared to those at phases K (0.816) and A (0.912).
The density upper limit of the O-line emission site is consistent with that of Ne at phase A (0.912), whereas this is smaller than the allowable range of the Ne line emission site density (0.47-2.83×10 12 cm −3 , Paper I) at phase K (0.816).However, the emission sites of these two elements should be different in position along the shock cone.The emissivity of the He-like K line of O peaks at a temperature of 0.18 keV (≃2 MK), whereas that of the Ne peaks at  = 0.33 keV (≃4 MK, Mewe et al. 1985).It has been debated whether clumps in the plasma develop or deteriorate along the shock cone.In fact, Stevens et al. (1992) pointed out that plasma clumps can develop spontaneously after the plasma experiences shock owing to plasma instability.In contrast, dense clumps that may exist in the pre-shock stellar wind may be rapidly destroyed after entering the collision shock (Pittard 2007).We require a much higher quality spectrum of oxygen K emission lines to form a clear conclusion on the density profile along the shock cone.
Using the updated distance to the Ne line-emission sites to be presented in Table 7, the effect of EUV radiation on the Ne lineemission site densities is updated and also summarized in Table 5.Because the line-emission sites are more distant than those reported in Paper I, the photoexcitation probabilities are lower than those shown in Table 10 of Paper I. This effect appears most remarkably at phase K (0.816), where the contribution of the photoionisation effect becomes ≲10 per cent of the collisional excitation (Table 5).We believe that the Ne line-emission site density 0.47-2.83×10 12cm −3 (Paper I) is more plausible.

Fe xvii L lines
The intensities of some Fe-L lines are sensitive to the electron number density of the plasma.For Fe xvii (Ne-like Fe), the density-sensitive lines are 0.7242 keV (17.10 Å) and 0.7263 keV (17.05 Å) (Mauche et al. 2001), with an intensity of 17.05 Å stronger and that of 17.10 Å weaker as the electron number density increases.In addition to these two lines, a density-insensitive line at 0.7382 keV (16.78 Å) is also observed, as shown in Fig. 1, although the energy resolution of the RGS is not high enough to fully resolve them.
We attempt to evaluate  e using the ratios (17.05Å)/(16.78Å) and (17.10Å)/(16.78Å) (Mauche et al. 2001).Spectral fitting is performed using the energy bands of the Fe xvii lines (0.70-0.77keV).In contrast to the case of O (Section 3.2.1),as Fe contributes not only to the line emission but also continuum emission, we are not able to set the Fe abundance equal to 0. Instead, we remove these three emission lines from the bvvapec model and added three velocity-shifted Gaussian (zgauss) to the fitting model.As in the analysis of O vii, the line central energies are set free to vary using the redshift parameter  los that is common among the three lines.The line widths are constrained to vary in proportion to the line central energies.
We calculate the ratios (17.05Å)/(16.78Å) and (17.10Å)/(16.78Å) with the intensities derived and compare them with the theoretical curves as a function of the electron number density  e (Mauche et al. 2001).However, the intensity ratios are not constrained at all; the theoretical ratios (17.05Å)/(16.78Å) and (17.10Å)/(16.78Å) vary in the range from 1.1 to 1.5 and from 0.0 to 0.9, respectively, as a function of  e (Mauche et al. 2001, Figure 2), whereas the observed ratios at phase L (0.935), which have the best statistics among the five data sets, ranged from 0.89 to 2.79 and from 0.00 to 1.21, respectively.This is because the line separations are comparable to the energy resolution of the RGS.Consequently, we are unable to make any meaningful constraints on  e with the Fe xvii lines.

Line-of-sight velocity and its dispersion along the shock cone
In Paper I, we argued that the ratio of the observed line-of-sight velocity and its dispersion (| los |/ los ) provides a reliable estimate of the line-emission site as long as the plasma flow is laminar, because in this case, | los |/ los is a monotonically increasing function of the distance from the stagnation point and its value is uniquely determined by the shock cone geometry, which is calculated based on the ram pressure balance between the stellar winds from the two stars.However, if the plasma flow includes a turbulent component, the observed  los (=  obs ) would be enhanced, as expressed in Equation ( 23) in Paper I. In addition, if the line-emission sites extend spatially along the shock cone, the variation of  los within the sites further enhances  obs (this possibility is not considered in Paper I).Thus, the ratio | los |/ los tends to underestimate the distance of the line-emission site from the stagnation point.However, the observed  los , that is, the net plasma velocity on a macro scale, is not affected by the turbulence by definition, and we believe that  los is a more reliable tool for deriving the line-emission sites than | los |/ los .Accordingly, in this Section 4.1, we first calculate  los and  los separately along the shock cone.

Initial velocity at the stagnation point
To calculate  los and  los along the shock cone, we must calculate the initial velocity of the plasma flow at the stagnation point.At the stagnation point, the macroscopic velocity is zero because the stellar winds makes head-on collision.In such a case, the plasma is expected to flow out at the speed of sound.Thus, we calculate the speed of sound based on the fact that the plasma temperature is 3.5 keV (41 MK) at the stagnation point (Sugawara et al. 2015).
Under the assumption that the abundance of WR stars is He:C = 5:2 (Hillier & Miller 1999) and those of the O star are H:He = 10:1, the mean molecular weights  wr and  o of each stellar wind, including the electrons, are calculated to be  wr = 1.52 and  o = 0.61.Here we assume that the stellar winds from the WR and O stars become admixed after passing through the shock surface.First, we derive the particle number density  rw and  o of each stellar wind at the stagnation point from  = 4 2 ()() and the stellar wind velocity formula where we set =1 not only for the O star but also for WR star.This is acceptable in our case, because the shock cone is formed far away from the WR star, and hence the WR wind velocity there is nearly insensitive to the choice of  (Sugawara et al. 2015).Usov (1992) stated that the acceleration of winds is almost negligible beyond 3-5 times the radius of the star, and according to Sugawara et al. (2015), the braking of the stellar wind of the WR star owing to the EUV radiation from the O star can be ignored because the temperature of the hot component does not decrease until phase D (0.987).Table 6 summarises the distances of the stagnation point from the two stars and the stellar wind parameters at each phase.The mean molecular weight  of the plasma in the shock cone is calculated using the following equation: which results in  =0.88, independent of the orbital phase.As =5/3,  B =3.5 keV (= 41 MK, Sugawara et al. 2015), and  H = 1.67 ×10 −24 g, the speed of sound  s is: which is adopted as the plasma outflow velocity at the stagnation point.
Thus far, we have assumed that the winds from the WR and O stars become admixed immediately after they experience the shock.However, some previous studies claim that it takes some time for the winds to mix (e.g.Usov 1992;Stevens et al. 1992).In this case, the two winds have different sound velocities at the stagnation point.According to Equation (3), with  =  wr and  o , they are 610 and 960 km s −1 , respectively, which differ from the values obtained using Equation (3) only by 20-30 per cent.In Section 4.4, we show that this difference barely affects characterisation of the nature of the plasma flow.

Line-of-sight velocity and its dispersion
Using the initial velocity of the plasma outflow described in the previous section, we calculate the plasma flow velocity  along the shock cone and transform it into | los | and  los as functions of the  coordinate in Fig. 4. We then compare the calculated and observed  los to update the locations of the line emission sites.To derive  los and  los from the flow velocity , we utilise the shape of the shock cone that is determined based on the ram-pressure balance of stellar winds in Paper I (Usov 1992;Cantó et al. 1996;Pittard & Stevens 1997).We consider the coordinate system shown in Fig. 4. In this flow configuration, the momentum of the plasma at an arbitrary point  on the shock cone increases by receiving the tangential component of the momentum of the stellar winds into a small vector Δ along the shock cone.The mass increment rate  () and plasma velocity Dividing Equation (4) with Equation (5) yields the following recurrence equation for  (): By using the initial value of  (Section 4.1.1),we obtain the velocity  along the shock cone sequentially using Equation ( 6).Next, we calculate the line-of-sight velocity and its dispersion from the plasma flow velocity using Equations ( 15) and ( 17) in Paper I, respectively, by incorporating  () as, los (, , , , ) = Note that, for the angular averages, the shielding of part of the shock cone by the O star can be neglected because the solid angle of the O star is considerably smaller than the shock cone (Fig. 10 of Paper I).
Thus far, we have assumed that the plasma flow is laminar in our calculations of | los | and  los .Although the laminar flow does not have any velocity dispersion, the observed emission lines emanate from an annular region on the shock cone whose different parts are seen under different angles.As a result, we observe different  los values from different portions of the line-emission plasma, which provides non-zero values to the line-of-sight velocity dispersion  los , even in the case of laminar flow.The calculated  los value is purely geometrical in origin.This can be understood from the factor Δ/ √︁ Δ 2 + Δ 2 in Equation ( 8) (see Section 4.1.4 of Paper I).

Excess of the velocity dispersion and locations of the Ne and O line-emission sites
In this Section, we compare the observed line-of-sight velocities of the Ne and O emission lines with those calculated in the previous section to identify the locations of these line-emission sites.Figure 5 shows the profiles of | los | (middle panel) and  los (bottom panel) calculated using Equations ( 7) and ( 8).We also draw the horizontal lines representing the allowed ranges of The  coordinate of the Ne line-emission site determined with | los | (middle panels) is more distant from the stagnation point than that determined with | los |/ los (top panels) at earlier phases K (0.816), A (0.912), and L (0.935).Simultaneously, the allowed range of the observed  obs is larger than the theoretical  los .This implies that there is an additional factor that enhances the velocity dispersion above the calculated  los .Possible additional components for enhancing the velocity dispersion are summarised in Equation ( 23) of Paper I. In this equation,  lam is equal to  los [Equation ( 8)] in the present study.Furthermore, the velocity dispersion associated with the thermal motion of Ne x ( th ) is negligible (Paper I). ⊥ , originating from the divergence of the plasma while it flows along the shock cone, is expected to be small compared with  lam because the diverging angle of the plasma flow (≃ 2( − ) in Fig. 2 of Usov 1992, for example) must be smaller than the opening angle of the shock cone (=  in Fig. 2 of Usov 1992, for example).
In addition to  lam and  turb (the velocity dispersion of the turbulence) in (Paper I), we must newly take into consideration the spatial extent of the Ne line-emission site along the shock cone.If the extent is sufficiently large, the variation in | los | along the shock cone, which we denote hereafter as  vlos , may not be negligible.Consequently, Equation ( 23) given in Paper I can now be written as, In summary, the observed velocity-dispersion enhancement is attributed to the turbulence and/or to the variation in the line-of-sight velocity along the shock cone.In Sections 4.3 and 4.4, we consider these possibilities in detail.As described in Section 4.1, the locations of the line-emission sites should be measured using | los | rather than using | los |/ los because the observed  obs is now found larger than the calculated  los expected based on the laminar flow.Table 7 summarises the lineemission site locations, updated with | los | using the middle panels of Fig. 5.The distance  from the stagnation point for both the Ne and O line-emission sites range from 1 × 10 13 cm at phase D (0.987) to 13 × 10 13 cm at phase K (0.816).These locations correspond to the spatial centroids of the line-emission sites, and their spatial extents will be considered in Sections 4.3.
At later phases B (0.968) and D (0.987), the  coordinates from | los |/ los and | los | are consistent both for Ne and O, and the allowed ranges of the observed  los shown in the lower panel overlaps with the theoretical curve [except for O at phase D (0.987)].This implies that no significant turbulence is detected at these phases.

Spatial extent of the line-emission sites along the shock cone
In this Section, we explore the spatial extents of the Ne and O lineemission sites along the shock cone.Now that we know the location, the temperature, and the flow velocity of the O and Ne line-emission sites, and we can calculate the densities there from the local rampressure balance of the stellar winds, we can calculate the thermal energy that the line-emission plasmas possess, evaluate their cooling time, and finally obtain their spatial extent along the shock cone as a product of plasma flow velocity and cooling time.We do not intend to derive any strict solution of the shock cone plasma but just calculate radiative cooling of the plasma based on the observed quantities and elementary fluid mechanics.In this Section, the spatial extent of the Ne line-emission site at phase K (0.816), as an example, is discussed in detail.The results of Ne and O in all phases are summarised in Table 8 and 9.

Thermal energy and cooling rate of the line-emission plasma
| los | and  los of the Ne line-emission plasma are determined primarily by the Ne x K line, because it is more intense and narrower than Ne ix (Fig. 3 of Paper I).We therefore first explore the temperature of the plasma that radiates Ne x K based on atomic data.We refer to Mewe et al. (1985) for the so-called 'cooling coefficient' of the Ne x K line Λ Ne x () (photons cm 3 s −1 ).We then multiply this by the square of the plasma particle number density  2 () to obtain the emissivity  Ne x () (photons cm −3 s −1 ).For the density (), we utilise the fact that the post-shock plasma flow in the shock cone is Table 8.Values of the parameters used in the calculation to obtain the spatial extent of the Ne and O line-emission sites along the shock cone.( Ne/O ) is the particle number density at the Ne or O line-emission site under the assumption of isobaric plasma flow,  wr,ring is the angle between the WR wind orientation and the tangent of the shock cone at the Ne or O line-emission site (=  wr in Fig. 4),  1 is the ram-pressure of the WR wind at the Ne or O line-emission site,  Ne/O, loc is the particle number density at the Ne or O line-emission site under the assumption of a local pressure balance with the WR wind,  Fe is the emissivity due to iron emission lines (including that of Si and S lines for O),  brems is the emissivity of the thermal bremsstrahlung,  is the cooling time of the Ne and O line-emission plasma,  Ne/O is the local plasma flow velocity at the Ne or O line-emission site [equation ( 6)],  ring is the spatial extent of the Ne or O line-emission site along the shock cone, and  ring is the distance of the Ne or O line-emission site from the stagnation point along the shock cone.

Phase
( Ne/O )  wr,ring   The values of  los for Ne and O at all phases are summarised in Table 9.They are of order 10-100 km s −1 .We remark that temperature range Δ = 0.32 keV is evaluated from the profile of  Ne x () (Fig. 6).To determine the real tem-perature range,  Ne x () should be further multiplied by the plasma volume.Since the plasma flow that cools along the shock cone has a larger volume at lower temperatures, the resultant temperature range is smaller than that shown in Fig. 6 as the lower bound of  Ne x () has a sharp cutoff owing of the recombination from Ne x to Ne ix.Strictly speaking, the temperature range Δ = 0.32 keV should be regarded as the upper limit.
Finally, for evaluating  ring of O K lines, we have took into account the plasma cooling not only by the Fe lines but also by Si and S lines in a similar manner to Equation (B7), because the temperature of the O vii,viii line-emission site is lower (∼0.2 keV).At such temperatures, Si and S cooling work in addition to Fe (Gehrels & Williams 1993).

Evaluation of the turbulent velocity
In this section, we consider the origin of the excess velocity dispersion detected in Section 4.2.As already discussed there, the excess is expressed with Equation (9) as where  obs is summarized in Table 5 of Paper I for Ne and Table 1 for O.  los is found in Fig. 5. Magnitudes of the quantities that appear in Equation ( 11) are summarized in Table 9.
√︃  2 turb +  2 vlos is of order 100 km s −1 , whereas  vlos is in general smaller than this.Consequently, we believe that the observed excess of the velocity dispersion that cannot be explained with the  los distribution should be attributed to turbulence.The turbulence velocity dispersion, which is listed in Table 9, is detected at the three early phases K (0.816), A (0.912), and L (0.935) for Ne, whereas only the upper limit is obtained at the latter two phases: B (0.968) and D (0.987).A similar tendency is also found for O, where turbulence is significantly detected at phases K (0.816) and A (0.912), whereas at the later phases,  turb is an upper limit, except for the last phase D (0.987).The resultant  turb values of O are summarised in Table 9.The magnitude of  turb is generally in the order of 100 km s −1 for both Ne and O.
Note that the two earlier orbital phases in which we detect a statistically significant  turb coincide with the phases where extraordinarily high plasma density of up to ∼10 12 cm −3 is detected with the He-like triplet of Ne ix K line (Paper I).Such a high density may be a result of turbulence.
Fig. 8 shows the plots of  turb listed in Table 9 as functions of the  coordinate measured from the stagnation point. turb appears to increase with the distance from the stagnation point.This may indicate growing turbulence in the hot-shocked plasma as it flows along the shock cone.However, as shown in this figure, this trend is not statistically significant.Future studies on high accuracy measurements are required to conclude whether this trend is real or not.
Finally, as predicted in Section 4.1.1,we examine the possible uncertainty of the theoretical curves | los | and  los associated with the uncertainty of the initial velocity at the stagnation point.Our claim of turbulence detection is entirely based on the calculated profiles of  los and | los |.Hence, if their uncertainty is too large, we would not be able detect the turbulence.We calculate | los | and  los using the initial speeds (=  s ) = 610 and 960 km s −1 ,which are the values of pure WR star wind and pure O star wind, respectively.Fig. 9 shows these results together with the case of the initial speeds = 800 km s −1 at phase A (0.912), for example.The three  los curves (lower panel) converge at the right end of the  coordinate, whereas the upper panel curves | los | differ slightly, even at the right end of .However, the difference is approximately 6 per cent at full amplitude.Hence, we conclude that the difference in the initial speed seldom affects the characterisation of the plasma flow.

Limitation of our approach and prospect for future study
In Section 4.3, we have derived the spatial extent of the Ne and O line-emission sites based on the simple radiative cooling calculation.We employ the observed plasma temperatures.The densities are calculated from the stellar wind parameters.The radiative cooling efficiency relies on atomic physics.Although these evaluations are accurate enough for the order-of-magnitude estimation we made on the spatial extent, there remain some uncertainties.Usov (1992), for example, presented a "stratified" shock cone plasma model in which the stellar winds keep flowing along their own stream lines even after experiencing the shock (see Fig. 3 of Usov 1992).In such a case, the plasma cooling should be considered for each stream line independently, and the resultant temperature distribution is a superposition of the temperature distributions along the stream lines.Nevertheless, we believe our discussion on the spatial extent of the plasma and the turbulence made an important step forward for understand-  ing the physical state of the colliding stellar wind plasma, since the evaluations are mades based on the simple but clear assumptions.
Our final goal is to understand the physical state of the colliding wind shock plasma, namely to derive distribution of physical quantities, such as the temperature, the density and the velocity of the plasma along the shock cone.For this to be realized, obviously we need full simulation of the wind collision from the theoretical side.From the observational side, on the other hand, we can achieve our purpose if we can do what we did for the Ne K emission lines to other abundant metals such as O, Mg, Si, S and Fe.This can be done with the Resolve instrument (X-ray micro-calorimeter, Kelley 2022;Ishisaki et al. 2022) onboard the XRISM observatory (Tashiro et al. 2020) launched in 2023 September.

CONCLUSION
We analyse the high-resolution X-ray spectra of the WR+O binary WR140 observed using the RGS onboard XMM-Newton from May 2008 to June 2016.High-quality spectra are obtained when the O star is in front of the WR star.Following the analysis method for the Ne K emission lines reported in Paper I, we find that the line-of-sight velocity of O vii,viii ranges from −700 to −1200 km s −1 , and its dispersion ranges from 400 to 800 km s −1 , respectively, and those of Fe xvii,xviii,xx from −800 to −1400 km s −1 , and from 500 to 1100 km s −1 , respectively.These values are approximately the same as those obtained for the Ne emission lines.From the O, Fe, and Ne emission lines, we confirm that the observed | los | and  obs are largest and smallest, respectively, between phases B (0.968) and L (0.935), where the inferior conjunction of the O star occurs.This behaviour of the observed velocities is consistent with the picture in which the colliding wind plasma flows along the shock cone.
We perform a density diagnosis using the intensity ratios of the He-like triplet components of O.However, we have imposed only upper limits of  e ≲10 10 -10 12 cm −3 due to statistical limitations and uncertainty of the amount of EUV radiation from the O star.We also attempt to estimate  e using the intensity ratios 17.10 Å, 17.05 Å and 16.78 Å of Fe xvii (Mauche et al. 2001).However, we are not able to obtain any constraints owing to poor statistics and weakness of the lines.
We adopt  los as a more reliable measure of the locations of line emission regions than | los |/ los .We calculate  los using the plasma flow velocity  [Equations ( 5) and ( 6)].As a result, we find that the location of the Ne line-emission site measured with | los | is more distant from the stagnation point than that with | los |/ los at the earlier orbital phases K (0.816), A (0.912), and L (0.935), and the observed velocity dispersion  obs is larger than the calculated  los at these phases.We update the distance of the Ne line-emission sites using | los | to be from 1×10 13 cm [phase D (0.987)] to 13×10 13 cm [phase K (0.816)] (Table 7).The values of the newly measured O lineemission sites are similar.Based on the observed temperatures, the densities calculated from the stellar wind parameters, and the atomic physics for the radiative cooling efficiency, we have found that the Ne and O line-emission regions extend along the shock cone by up to ±58 per cent (Ne lines at phase K(0.816) of the distance from the stagnation point along the shock cone.The variation of | los | within this 'ring' is, however, considerably smaller than  obs .This implies that the excess observed velocity dispersion

√︃
2 obs −  2 los contains the turbulence component.We find that the maximum turbulent velocity dispersion  turb of Ne is 340-630 km s −1 at phase A (0.912).A similar maximum  turb of 400-660 km s −1 is also obtained for O at phase K (0.816) (Table 9).At the later phases B (0.968) and D (0.987), we obtain no excess of the velocity dispersion from Ne.A similar trend is observed for the O lines.
Based on the plot of  turb versus the distance from the stagnation point  (Fig. 8), we suggest that the turbulence in the hot-shocked plasma increases as the plasma flows along the shock cone.Because of statistical limitations, however, future high quality measurements must be conducted before drawing a conclusion whether this trend is real or not.
Table A1.Transverse velocity of the shock cone plasma  cor gained by the Coriolis force. and  represent the distance between the WR star and the O star and its time derivative, respectively. orb and  orb are the angular and orbital velocities of the O star, respectively. cor is the acceleration by the Coriolis force, and  cor =  cor  esc is the transverse velocity of the shock cone plasma gained by the Coriolis force over time when the plasma moves over a distance of 10.

Phase
orb  orb  cor  cor (=  cor  esc ) (km s −1 ) (10 13 cm) (10 −8 s −1 ) (km s −1 ) (10 −5 km s −2 ) (km s where  e,⊙ and  p,⊙ are the electron and proton densities, respectively, at the solar abundance (Allen 1973) Here  wr and  o are the elevation angles of the Ne line-emission site viewed from the centers of the WR and O stars (see Fig. 4).These angles and the mixture fractions  wr and  o are listed in Table B1.
In the same way as Equation (B8),  e and  Fe are expressed as With Λ Fe,⊙ (),  Fe,Allen ,  e and  Fe being obtained here from Equations (B19) and (B20) and with  Ne,loc from Equation (B3), we can calculate  Fe () using Equation (B7); the results are summarised in Table 8.  Fe ( Ne ) at phase K (0.816) is 4.6 × 10 −8 erg cm −3 s −1 .
Table B1.Values of the parameters used in the calculation to obtain the spatial extent of the Ne and O line-emission sites along the shock cone. wr/o is the elevation angles of the Ne/O line-emission site viewed from the centers of the WR/O star (see Fig. 4

Figure 1 .
Figure 1.Spectra of phase A (0.912) around the energy bins of O vii, viii K (left) and Fe xvii,xviii,xx lines (right).Black and green colours are used for the first-order spectra of RGS1 and RGS2, respectively, while the red and blue colours are used for their second-order spectra, respectively.The best-fitting bvvapec*tbabs models are overlaid as histograms, whose parameters are summarised in Tables1 and 2.
Paper I).The energy bands used are 0.70-0.77keV (Fe xvii), 0.81-0.90keV (Fe xviii), and 0.93-1.00keV (Fe xx).The results are summarised in Table 2 and Fig. 1 (right).The line-of-sight velocity ranges −from 800 to 1400 km s −1 and its dispersion ranges from 500 to 1100 km s −1 .These are the same as those measured with the O lines (Section 3.1.1)and Ne lines (Paper I).

Figure 2 .
Figure 2. Line-of-sight velocity ( los ) and its dispersion ( los ) of Ne ix, x (Table 5 of Paper I), O vii, viii and Fe xvii, xviii, xx (Tables1 and 2, respectively) plotted as a function of the orbital phase.At all phases, the line-of-sight velocity is negative (blue-shifted), implying that the plasma emitting these lines is approaching the earth.Both  los and  los seem to take their minimum values between phase L (0.935) and B (0.968), where the inferior conjunction of the O star occurs.

Figure 3 .
Figure 3. Density diagnosis of the plasma with the intensity ratio of the He-like triplet of O vii at phases K (0.816), A (0.912), and L (0.935).The red and blue curves represent  / and /, respectively.The vertical axis is the intensity ratio and the horizontal axis is the electron number density.The blue boxes represent the observed ratio / in the vertical axis and the resultant density upper limits in the horizontal axis.Since the allowed range of the observed  / ratio is wider than the theoretical range shown in the vertical axis, we cannot pose any constraint on the density from the  / ratio.The electron number density at phases B (0.968) and D (0.987) could not be constrained with this method.

Figure 4 .
Figure 4. Scheme of calculating the plasma flow velocity along the shock cone.The -axis is the line connecting the centres of the WR and O stars, and the stagnation point is at the origin.Note that  =

Figure 5 .
Figure 5. | los |/ los (upper panel), the line-of-sight velocity | los | (middle panel) and its dispersion  los (lower panel) as a function of the  coordinate.The theoretical curves (blue) are based on our numerical calculations based on Paper I and Equations (7) and (8).The cyan and orange hatches indicate the locations of the K line-emission site of Ne and O, respectively, which are obtained by intersecting the allowed ranges of the observed | los |/ los and | los | with the theoretical curves.The vertical dashed lines of the lower panels ( los ) indicate the locations of line-emission sites determined from the middle panel | los |.The allowed ranges of the velocity dispersion are larger than the theoretical ones at the locations of the line-emission sites at earlier phases K (0.816) and A (0.912) for both Ne and O.

Figure 7 .
Figure 7.  los estimated with the spatial extent of the Ne line-emission plasma  ring using the theoretical curve of  los (same as the middle panel of Fig. 5) at phase K(0.816).The Ne line-emission plasma has the width ±58 per cent of  ring from the centre of gravity of the line-emission site.

Figure 8 .
Figure 8. Turbulence velocity dispersion  turb as a function of .

Figure 9 .
Figure 9.Comparison of the profiles of the line-of-sight velocity | los | (the upper panel) and its dispersion  los (the lower panel) at phase A (0.912) with initial speeds (=  s ) = 610 km s −1 (orange, pure WR star composition), 800 km s −1 (blue, averaged composition of the WR-and O stars) and 960 km s −1 (black, pure O star composition).

Table 1 .
Best-fit parameters of the K lines of O vii, viii with the bvvapec and tbabs models [see Fig. 1 (left) for the plot].Hydrogen column density  H and abundances other than O are fixed at the best-fit parameters in the full energy band (Table4in Paper I).The parameters ,  O ,  los (redshift of centroid energies of emission lines),  obs (broadening of emission lines), and the emission measure (EM) are allowed to vary.

Table 2 .
Best-fit parameters of the lines of Fe xvii, xviii, xx with the bvvapec and tbabs models [see Fig. 1(right) for the plot].Parameters of abundances other than Fe and  H are fixed at best-fit parameters in the 0.325-5.35keVband(Table4inPaperI).The other parameters are treared the same as in Table1.
equilibrium and use the CIE model.We use the resonance line  to help constrain the density if either  or  is weak.By comparing the SPEX curves with the intensity ratios derived from the fitting in Table3, we are potentially able to determine the electron number density  e .The results obtained under the assumption of pure collisional excitation are shown in Fig.3.Based on this figure, the upper limits of  e are obtained at phases K (0.816), A (0.912), and L (0.935), which are summarised in Table ionisation

Table 5 .
Rates of collisional excitation and photo-excitation from the 3 S level to 3 P, and the ratio of the latter to the former.For Ne, we recalculate the values using the updated line-emission site locations, to be presented in Section 4.1.2.Phase e    ( e ) (s −1 ) Γ   ( r ,    ) (s −1 ) fraction (percent)

Table 6 .
Stagnation point distance from each star and the densities and velocities of the pre-shock stellar winds from the two stars at the stagntion point.Notably the wind velocity of the WR star reaches its terminal velocity 2860 km s −1 at the stagnation point.
where  wr,o and  wr,o are the stellar wind velocity and angle between the stellar wind vector and vector Δ, respectively; and ΔΩ wr,o is the solid angle subtended by the annulus containing the vector Δ over each star, expressed as ΔΩ wr,o () = Ω wr,o () −Ω wr,o ( −Δ), where Ω wr,o () = 2(1 − cos  wr,o ). wr,o is the mass-loss rate of each star.The effect of gravity can be ignored here as the escape velocity of the O star's wind at the stagnation point is less than 1/10 of the terminal velocity of the O star's wind  ∞,o . () is expressed as follows: | los |/ los , | los |, and  los measure using the Ne ix, x and O vii, viii lines and determine the ranges  from | los |/ los and | los |.The vertical lines in the  los panels are identical to those in the | los | panels.The theoretical curve and data of Ne in the | los |/ los panel are taken from Paper I.
A similar analysis of the Fe lines do not yield restrictive results; hence, hereafter, we concentrate on the Ne and O data.

Table 9 .
Magnitude of the velocity dispersion components derived from the calculated spatial extent of the Ne or O line-emission region.|Δ los | is the range of | los | within the  ring in Table 8 and  los is the dispersion of | los | (= |Δ los |/2). turb is the dispersion of the turbulence velocity.