© ESO, 2010

1. Introduction

The Vela complex is one of the most interesting regions in the galactic plane. The observable flux from the Vela region ranges from radio to TeV energies. It consists of many objects, including the Gum nebula, the Vela supernova remnant (SNR) and Vela Jr. SNR (SNR RX J0852.0-4622 superposed on Vela), the binary system γ² Velorum, the IRAS Vela Shell, an OB-association, ζ Pup, etc. Some of them are shown in Fig. 2. Because of the distances to these objects it is possible that some of them can intersect not only in projection, but also physically. We propose a scenario of joint evolutionary interaction of the Vela SNR, the binary system γ² Velorum, the IRAS Vela Shell, the Vela OB2-association, and the Gum nebula.

2. A hydrodynamical model of the Vela SNR evolution

2.1. Vela SNR properties and peculiarities. NE-SW asymmetry

The Vela SNR is one of the closest supernova remnants to us. Different estimates of the distance to the Vela SNR suffer from a large uncertainty: from 250 ± 30 pc (Cha et al. 1999) to 350 pc (Dubner et al. 1998 and references therein). Hubble Space telescope parallax observations of the Vela pulsar give the distance to the pulsar of ${\mathit{D}}_{\mathrm{Vela}}\mathrm{=}\mathrm{29}{\mathrm{4}}_{-50}^{\mathrm{+}\mathrm{76}}$ pc (Caraveo et al. 2001), and the best estimate is from the VLBI parallax measure (Dodson et al. 2003): ${\mathit{D}}_{\mathrm{Vela}}\mathrm{=}\mathrm{28}{\mathrm{7}}_{-17}^{\mathrm{+}\mathrm{19}}\mathrm{pc}\mathit{.}$(1)Similarly uncertain are the estimates of the Vela SNR age, which range from a few thousand years (Stothers 1980) to t_SNR ≃ 2.9 × 10⁴ yr (Aschenbach et al. 1995). The most commonly cited estimate is t_SNR = t_pulsar ≃ 1.14 × 10⁴ yr, where t_pulsar is the age of the Vela pulsar (Reichley et al. 1970). The total 0.1−2.4 keV X-ray luminosity from Vela SNR in erg/s is (Lu & Aschenbach 2000) ${\mathit{L}}_{\mathrm{x}\mathit{,}\hspace{0.17em}\mathrm{tot}}\mathrm{=}\mathrm{3.0}\mathrm{\times }{\mathrm{10}}^{\mathrm{35}}{\left[\frac{{\mathit{D}}_{\mathrm{vela}}}{\mathrm{290}\hspace{0.17em}\mathrm{pc}}\right]}^{\mathrm{2}}\mathrm{erg}\mathrm{/}\mathrm{s}\mathit{.}$(2)The main peculiarity of Vela SNR is the difference in the X-ray brightness and radius of its south-west (SW) and north-east (NE) parts. The ROSAT All-Sky Survey image (Fig. 1) of the Vela SNR reveals a shell with a diameter of about 8° (Aschenbach et al. 1995), which implies a mean linear diameter of ${\mathit{d}}_{\mathrm{Vela}}\mathrm{\simeq }\mathrm{40}\left[\frac{{\mathit{D}}_{\mathrm{Vela}}}{\mathrm{290}\mathrm{pc}}\right]\mathrm{pc}\mathit{.}$(3)The SW part of the shell appears to have a radius larger by a factor of ${\mathit{R}}_{\mathrm{SW}}\mathrm{\simeq }\mathrm{1.3}{\mathit{R}}_{\mathrm{NE}}$(4)than the NE part.

Fig. 1 ROSAT All-Sky Survey image (0.1–2.4 KeV) of the Vela SNR (Aschenbach et al. 1995). A–F are extended features outside the boundary of the remnant (“bullets”). Light blue to white contrast represents a contrast in surface brightness of a factor of 500 (Aschenbach et al. 1995). Blue curves show the NE and SW hemispheres of the Vela SNR. The yellow curve shows the contour of the SWB of γ2 Velorum.

Apart from the difference of the radii, the spatially-resolved spectroscopic analysis by Lu & Aschenbach (2000) shows that the SW part of the shell appears to be hotter than the NE one. The shell is bright only on the NE side, while the SW side appears to be dim and is apparently more extended (see Fig. 1). The boundary between the bright and the dim part of shell is quite sharp (Lu & Aschenbach 2000). The change in the properties of the shell at different sides indicates that the characteristics of the ISM in the NE part differ from those in the SW part. The sharpness of the boundary shows that the change in the ISM properties is abrupt rather than gradual.

Lu & Aschenbach (2000) estimate the contrast change of the two faint regions, each 1.5° × 1.5°, in the NE and SW parts, to be a factor of ≃11 in brightness and ~6 in emission measure. Assuming the same estimate for the emission measure contrast change for the entire NE and SW parts of the SNR and taking into account the difference of the radii of the two parts of the SNR, one can find that the luminosity of the NE part L_x,NE is a factor of ~3.7 higher than the luminosity L_x,SW of the SW part.

Apart from the difference in the overall luminosity and temperature, the characteristics of the X-ray emission from the NE and SW parts of the SNR also reveal a difference in the column density of the absorbing material along the line of sight (Lu & Aschenbach 2000). The absorption column densities N_H range from 5.0 × 10¹⁹ cm^-2 in the NE part to 6.0 × 10²⁰ cm^-2 in the SW part.

Finally, the Vela SNR is peculiar in still another aspect: the main shock of the SNR is not observed. Instead, the bulk of the X-ray emission is distributed all over the SNR volume. Such an observational appearance can be caused by the SNR expanding into a highly inhomogeneous (“cloudy”) medium. In this case, the main shock advances through a low-density interstellar medium (ISM), leaving behind denser clouds, which are subsequently heated and partially evaporated by thermal conductivity and transmitted shocks. This results in the appearance of a distributed emission throughout the entire volume of the SNR, instead of from a thin shell at the interface of the main shock with the low-density ISM. The main X-ray emitters in the remnant are the two (cool and hot) phases (components) of heated cloud matter (Lu & Aschenbach 2000; Miceli et al. 2005, 2006).

2.2. A hydrodynamical model of the Vela SNR

Despite extensive investigations, there is no common agreement about the evolutionary status of the Vela SNR. In early studies, a distance of 500 pc was assumed, which corresponds to a rather large size of 70 pc in diameter. Together with this assumption, the absence of the X-ray limb-brightening effect and of the clear signature of the high-speed shock in the SNR suggested a radiative stage of the Vela SNR evolution. The appearance of filament structures in optic and radio waves as well as 100 km s^-1 absorption lines in the spectra of background stars additionally supported this scenario (see, e.g. Gvaramadze (1999) and references therein). But recent observational data strongly support the hypothesis of the Vela SNR being in the adiabatic stage. New results for the distance place the Vela SNR at D ≈ 290 pc, implying that the mean radius of the Vela SNR is R ≈ 20 pc, and the dynamics of bullets (ejecta fragments) outside the SNR boundary suggest the expansion of the SNR in the low-density ISM. The presence of the Vela pulsar indicates that the Vela SN progenitor was of M_ini ≤ 25   M_⊙. For M_ini = 11−25   M_⊙ presupernova masses are M_fin = 10.6−16.6   M_⊙ and masses of the ejecta M_ej = 9−15   M_⊙. (Limongi & Chieffi 2006; Eldridge & Tout 2004; Kasen & Woosley et al. 2009). Therefore, the interaction (merger) of the massive SN ejecta with a velocity of over 1000 km s^-1 with the red supergiant (RSG) shell occurs in the adiabatic regime, and the Vela SNR with a radius of 20 pc and an age of about 10 000 years should be in the adiabatic stage of evolution with characteristic velocities of about mR_SNR/t_SNR ≈  1000 km s^-1 (m ≤ 1 in the free expansion case and m = 0,4 in the adiabatic one) without forming a thin dense radiative shell. Another observational confirmation of the absence of the 100 km s^-1 shell follows from the studies of absorption lines in the spectra of background stars (Cha & Sembach 2000), where all stars in the Vela SNR direction at distances smaller than 350 pc do not show evidences of a 100 km s^-1 absorption line. The maximum broadening corresponds to <50 km s^-1. Only stars with distances exceeding 500 pc show 100 km s^-1 features. Radio and optical shells (shell-like filaments) can be naturally explained by the emission of filamentary structures, exited by the SNR shock (akin to the Cyg Loop case, where filaments coexist with the main fast adiabatic shock).

The hydrodynamical model of the Vela SNR evolution cannot be described directly by the Sedov solution (Sedov 1959), because the expansion proceeds in a cloudy rather than homogeneous ISM. Instead, to describe the Vela SNR evolution one can use the White & Long solution, which describes the evolution of a supernova remnant expanding into a cloudy ISM (White & Long 1991).

As explained above, the observed asymmetry of the Vela SNR is most probably due to the difference in the properties of the ISM on different sides of the remnant, in particular, by the different densities of clouds or different density contrast between the clouds and the IC medium. Below we assume that before the SN explosion the average number density (concentration) and, therefore, volume filling factor of clouds in NE part was larger than that in the SW part. This naturally explains the smaller radius and the lower temperature of the NE part of the remnant. Once more, interaction of shock wave with clouds results in numerous filamentary structures of disrupted cloud material, visible in radio band, and the radio image of the Vela SNR really shows more numerous shell structures in the NE part than in SW one (Bock et al. 1998). The NE-SW asymmetry proposed here can also explain a pulsar wind nebula (PWN) displacement to the SW according to the pulsar position. Namely, the reverse shock from more dense NE part reaches and destroys PWN earlier (Blondin et al. 2001; LaMassa et al. 2008)

The conjecture that the densities on the two sides of the SNR are different is supported also by the dynamics of the shrapnel (bullets) – high-velocity clumps of the SN ejecta with an overabundance of heavy elements (Aschenbach et al. 1995; Miceli et al. 2008; LaMassa et al. 2008; Yamaguchi & Katsuda 2009). X-ray spectra of shrapnel argue a low density of the ISM around the Vela SNR, whereas a difference in the distances traveled by the protruding shrapnel on the NE (shrapnel pieces A-D/D’) and on SW (shrapnel pieces E and F) sides of the SNR, as it is illustrated for the shrapnel pieces D and E shown in Fig. 1, is consistent with a corresponding difference in mean ambient density, assuming that each shrapnel piece has approximately the same density and initial velocity.

The solution for the shock radius r_s of the remnant as a function of the age t has the form (White & Long 1991) ${\mathit{r}}_{\mathrm{s}}\mathrm{=}{\left[\frac{\mathrm{25}\mathrm{(}\mathit{\gamma }\mathrm{+}\mathrm{1}\mathrm{)}\mathit{KE}}{\mathrm{16}\mathit{\pi }{\mathit{\rho }}_{\mathrm{ic}}}\right]}^{\mathrm{1}\mathit{/}\mathrm{5}}{\mathit{t}}^{\mathrm{2}\mathit{/}\mathrm{5}}\mathit{,}$(5)where E is the explosion energy, ρ_ic is the density of the intercloud medium and γ = 5/3 is the adiabatic index. The solution (5) differs from the standard Sedov solution without evaporating clouds by a different choice of a phenomenological constant K.

The constant K depends on two parameters: on the ratio C of the fraction of the ISM mass initially contained in clouds and evaporated behind the shock wave to the ISM mass in the intercloud medium $\mathit{C}\mathrm{=}\frac{⟨{\mathit{\rho }}_{\mathrm{c}}⟩}{{\mathit{\rho }}_{\mathrm{ic}}}\mathit{,}$(6)where ⟨ρ_c⟩ is the volume-averaged density of the clouds, and on the ratio of the cloud evaporation time scale t_ev to the SNR age t$\mathit{\tau }\mathrm{=}{\mathit{t}}_{\mathrm{ev}}\mathit{/}\mathit{t}\mathit{.}$(7)To express the dependence of K on these two parameters we can use a simple analytical approximation $\frac{\mathit{K}}{{\mathit{K}}_{\mathrm{S}}}\mathrm{\simeq }{\left(\mathrm{1}\mathrm{+}\frac{\mathit{C}}{\mathrm{1}\mathrm{+}\mathit{\tau }}\right)}^{-1}\mathit{,}$(8)and K/K_S ~ C^-1 for C ≪ 1,τ ≫ 1, where K_S = 1.528 is the value of constant K for the Sedov solution (when C = 0). From Eq. (5) follows the value of the shock velocity ${\mathit{V}}_{\mathrm{s}}\mathrm{=}\frac{\mathrm{2}}{\mathrm{5}}\frac{{\mathit{r}}_{\mathrm{s}}}{\mathit{t}}\mathrm{=}{\left[\frac{\mathrm{(}\mathit{\gamma }\mathrm{+}\mathrm{1}\mathrm{)}\mathit{KE}}{\mathrm{4}\mathit{\pi }{\mathit{\rho }}_{\mathrm{ic}}{\mathit{r}}_{\mathrm{s}}^{\mathrm{3}}}\right]}^{\mathrm{1}\mathit{/}\mathrm{2}}\mathit{,}$(9)which allows to calculate the temperature at the shock ${\mathit{T}}_{\mathrm{S}}\mathrm{=}\frac{\mathrm{2}\mathrm{(}\mathit{\gamma }\mathrm{-}\mathrm{1}\mathrm{)}}{\mathrm{(}\mathit{\gamma }\mathrm{+}\mathrm{1}{\mathrm{)}}^{\mathrm{2}}}\frac{\mathit{\mu }{\mathit{m}}_{\mathrm{H}}}{\mathit{k}}{\mathit{V}}_{\mathrm{s}}^{\mathrm{2}}$(10)(here μ = 16/27 is the average mass per particle in hydrogen mass units m_H for helium/hydrogen abundance ratio n_He = (1/12)n_H and k is the Boltzmann constant) for the White & Long (1991) solution.

The dynamics of expansion of the SNR is fully characterized by a set of four parameters: the explosion energy E, the preshock intercloud ISM density ρ_ic, the cloud/intercloud density ratio C and the evaporation time/SNR age ratio τ. The values of these parameters can be derived from the set of the observed characteristics of Vela SNR, such as the shock radii, characteristics of the X-ray radiation for the both NE and SW parts, etc.

For the NE and SW shock radii R_NE ≃ 18 pc and R_SW ≃ 23 pc and SNR age t_Vela ≃ 1.14 × 10⁴ yr from Eq. (9) we obtain corresponding shock velocities ${\mathit{V}}_{\mathrm{NE}}\mathrm{=}\mathrm{0.4}{\mathit{R}}_{\mathrm{NE}}\mathit{/}{\mathit{t}}_{\mathrm{Vela}}\mathrm{\approx }\mathrm{6.0}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}\mathrm{cm}\mathrm{/}\mathrm{s}\mathit{,}$(11)${\mathit{V}}_{\mathrm{SW}}\mathrm{=}\mathrm{0.4}{\mathit{R}}_{\mathrm{SW}}\mathit{/}{\mathit{t}}_{\mathrm{Vela}}\mathrm{\approx }\mathrm{7.7}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}\mathrm{cm}\mathrm{/}\mathrm{s}\mathit{,}$(12)and from Eq. (10) shock temperatures ${\mathit{T}}_{\mathrm{S}}^{\mathrm{NE}}\mathrm{\approx }\mathrm{4.8}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}\hspace{0.17em}\mathrm{K}$, ${\mathit{T}}_{\mathrm{S}}^{\mathrm{SW}}\mathrm{\approx }\mathrm{7.8}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}\hspace{0.17em}\mathrm{K}$. Average (emission measure weighted) temperature of plasma inside the SNR is about twice as high (White & Long (1991)): $⟨{\mathit{T}}_{\mathrm{hot}}^{\mathrm{NE}}⟩\hspace{0.17em}\mathrm{\approx }\mathrm{1.9}{\mathit{T}}_{\mathrm{S}}^{\mathrm{NE}}\mathrm{\approx }\mathrm{9}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}\hspace{0.17em}\mathrm{K}\mathit{,}$(13)$⟨{\mathit{T}}_{\mathrm{hot}}^{\mathrm{SW}}⟩\hspace{0.17em}\mathrm{\approx }\mathrm{1.9}{\mathit{T}}_{\mathrm{S}}^{\mathrm{SW}}\mathrm{\approx }\mathrm{1.5}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}\hspace{0.17em}\mathrm{K}\mathit{.}$(14)According to the results of Lu & Aschenbach (2000) X-ray radiating plasma in both parts of the Vela SNR consists of two phases: a hot one (T ~ 0.5−1.2 keV) and a cool one (T ~ 0.09−0.25 keV), and the cool one dominates the X-ray luminosity of the SNR. The temperatures found above correspond to the hot component in the two-temperature Raymond-Smith thermal plasma model used in Lu & Aschenbach 2000). The hot evaporated gas component with the volume filling factor f_hot ≃ 1 dominates the shock dynamics, while the cool one with f_cool = 1 − f_hot ≪ 1 dominates in X-ray radiation. The role of the initial intercloud interstellar gas is negligible in both shock dynamics and X-ray radiation. It means that $\frac{{\mathit{C}}_{\mathrm{hot}}}{\mathrm{1}\mathrm{+}\mathit{\tau }}\mathrm{\gg }\mathrm{1}\mathit{,}$(15)where C_hot =  ⟨ ρ_c,hot ⟩ /ρ_ic, and hereafter we take τ ≪ 1 and use the approximation $\mathit{K}\mathit{/}{\mathit{K}}_{\mathrm{S}}\mathrm{=}{\mathit{C}}_{\mathrm{hot}}^{-1}$. In this case, Eq. (5) for shock radius is reduced to ${\mathit{r}}_{\mathrm{Vela}}\mathrm{=}{\left[\frac{\mathrm{25}\mathrm{(}\mathit{\gamma }\mathrm{+}\mathrm{1}\mathrm{)}{\mathit{K}}_{\mathrm{S}}\mathit{E}}{\mathrm{16}\mathit{\pi }{\mathit{m}}_{\mathrm{H}}{\mathit{n}}_{\mathrm{hot}}}\right]}^{\mathrm{1}\mathit{/}\mathrm{5}}{\mathit{t}}^{\mathrm{2}\mathit{/}\mathrm{5}}\mathit{,}$(16)where n_hot = ρ_c,hot/m_H is the nucleon number density of the hot component. As we can see, Eq. (16) is the Sedov solution, in which a mean density of intercloud plasma inside the remnant ρ_ic is replaced by the mean density of the evaporated clouds (of the dominant hot component ρ_c,hot in our case).

The nucleon number density of the hot component n_hot can be estimated from its X-ray radiation. The X-ray luminosity of the SNR is an integral over SNR volume for X-ray emissivity ϵ_X = n_en_HΛ_X(T) of plasma with temperature T, electron (hydrogen) number density n_e(n_H) and cooling function Λ_X(T) ${\mathit{L}}_{\mathrm{X}}\mathrm{=}{\mathrm{\int }}_{\mathrm{𝒱}}{\mathit{ϵ}}_{\mathrm{X}}\mathrm{d𝒱}\mathit{.}$(17)Within the model of White & Long (1991), L_X is estimated in erg/s as $\begin{array}{ccc}{\mathit{L}}_{\mathrm{X}}\mathrm{=}\mathrm{1.7}\mathrm{\times }{\mathrm{10}}^{\mathrm{34}}\mathit{Q}{\mathrm{\Lambda }}_{-22}{\left[\frac{{\mathit{n}}_{\mathrm{ic}}}{\mathrm{1}\mathrm{cm}-3}\right]}^{\mathrm{2}}{\left[\frac{{\mathit{r}}_{\mathrm{s}}}{\mathrm{1}\mathrm{pc}}\right]}^{\mathrm{3}}{\left[\mathrm{1}\mathrm{+}\frac{\mathit{C}}{\mathrm{1}\mathrm{+}\mathit{\tau }}\right]}^{\mathrm{2}}\mathit{,}& & \end{array}$(18)where n_ic = ρ_ic/m_H is the intercloud ISM nucleon number density (nucleon number density n = (4/3)n_H )), Λ_-22 is the cooling function in units 10^-22   erg   cm³   s^-1, Q is a number on the order of one and depends on C and τ (for C ≫ 1 and τ ≪ 1 Q ≃ 1).

Unfortunately, we do not know the X-ray luminosity of the hot component of Vela SNR with satisfactory accuracy. Therefore, we use the more accurate data about the emission measure of the hot plasma for the calculation of the nucleon number density of the hot component. According to the observation of Lu & Aschenbach (2000), the mean value of the emission measure A of ϕ_pixel × ϕ_pixel = 8.75′ × 8.75′ pixel $\mathit{A}\mathrm{=}{\mathrm{10}}^{-14}{\mathrm{\int }}_{\mathrm{pixel}}{\mathit{n}}_{\mathrm{e}}{\mathit{n}}_{\mathrm{H}}\mathrm{d𝒱}\mathit{/}\mathrm{4}\mathit{\pi }{\mathit{D}}_{\mathrm{Vela}}^{\mathrm{2}}$(19)of the hot plasma in NE region is ${\mathit{A}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{(}\mathrm{5}\mathrm{-}\mathrm{7}\mathrm{)}\mathrm{\times }{\mathrm{10}}^{-4}\mathrm{cm}{}^{-5}$. Meanwhile, from Eq. (19) and conditions n_en_H = 0.66n², it follows that $\mathit{n}{\mathit{f}}^{\mathrm{1}\mathit{/}\mathrm{2}}\mathrm{=}\mathrm{1.5}{\mathit{A}}^{\mathrm{1}\mathit{/}\mathrm{2}}{\left[\frac{{\mathit{R}}_{\mathrm{Vela}}}{\mathrm{20}\mathrm{pc}}\right]}^{\mathrm{-}\mathrm{1}\mathit{/}\mathrm{2}}\hspace{0.17em}{\mathrm{cm}}^{-3}$(20)and, taking into account that ${\mathit{f}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{1}$, ${\mathit{n}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{4.0}\mathrm{\times }{\mathrm{10}}^{-2}\mathrm{cm}-3.$(21)Now, from Eq. (16), we can find nucleon number density of hot component in SW part of Vela SNR ${\mathit{n}}_{\mathrm{hot}}^{\mathrm{SW}}\mathrm{=}{\mathit{n}}_{\mathrm{hot}}^{\mathrm{NE}}{\left[\frac{{\mathit{R}}_{\mathrm{NE}}}{{\mathit{R}}_{\mathrm{SW}}}\right]}^{\mathrm{5}}\mathrm{\simeq }\mathrm{1}\mathrm{\times }{\mathrm{10}}^{-2}\mathrm{cm}-3$(22)and the energy of the Vela SNR explosion $\mathit{E}\mathrm{=}\frac{\mathrm{16}\mathit{\pi }{\mathit{m}}_{\mathrm{H}}}{\mathrm{25}\mathrm{(}\mathit{\gamma }\mathrm{+}\mathrm{1}\mathrm{)}{\mathit{K}}_{\mathrm{S}}}\frac{{\mathit{R}}_{\mathrm{NE}}^{\mathrm{5}}}{{\mathit{t}}_{\mathrm{Vela}}^{\mathrm{2}}}{\mathit{n}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{1.4}\mathrm{\times }{\mathrm{10}}^{\mathrm{50}}\mathrm{erg}\mathit{.}$(23)The cool component of the X-ray radiating plasma in the Vela SNR does not influence the shock dynamics, but dominates in the X-ray luminosity. The mean value of the emission measure A and the temperature of the cool plasma in the NE region is ${\mathit{A}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{(}\mathrm{3}\mathrm{-}\mathrm{5}\mathrm{)}\mathrm{\times }{\mathrm{10}}^{-3}\mathrm{cm}{}^{-5}$, ${\mathit{T}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.1}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}\mathrm{K}$ and in the SW region ${\mathit{A}}_{\mathrm{cool}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{(}\mathrm{4}\mathrm{-}\mathrm{6}\mathrm{)}\mathrm{\times }{\mathrm{10}}^{-4}\mathrm{cm}{}^{-5}$, ${\mathit{T}}_{\mathrm{cool}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.17}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}\mathrm{K}$ (Lu & Aschenbach 2000). From Eq. (20) for the NE part of the Vela SNR follows $\mathrm{(}{\mathit{n}}_{\mathrm{cool}}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{1}\mathit{/}\mathrm{2}}{\mathrm{)}}^{\mathrm{NE}}\mathrm{=}\mathrm{1.6}\mathrm{(}{\mathit{A}}_{\mathrm{cool}}^{\mathrm{NE}}{\mathrm{)}}^{\mathrm{1}\mathit{/}\mathrm{2}}\mathrm{cm}-3\mathrm{\simeq }\mathrm{1.0}\mathrm{\times }{\mathrm{10}}^{-1}\mathrm{cm}-3.$(24)The filling factors of hot and cool plasma in the NE part can be estimated from the equality of the pressure P ∝ nT of both components: (n_coolT_cool)^NE ≃ (n_hotT_hot)^NE$\frac{{\mathit{f}}_{\mathrm{cool}}^{\mathrm{NE}}}{{\mathit{f}}_{\mathrm{hot}}^{\mathrm{NE}}}\mathrm{=}\frac{{\mathit{f}}_{\mathrm{cool}}^{\mathrm{NE}}}{\mathrm{1}\mathrm{-}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{NE}}}\mathrm{=}{\left[\frac{{\mathit{T}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{(}{\mathit{n}}_{\mathrm{cool}}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{1}\mathit{/}\mathrm{2}}{\mathrm{)}}^{\mathrm{NE}}}{{\mathit{T}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{(}{\mathit{n}}_{\mathrm{hot}}{\mathit{f}}_{\mathrm{hot}}^{\mathrm{1}\mathit{/}\mathrm{2}}{\mathrm{)}}^{\mathrm{NE}}}\right]}^{\mathrm{2}}\mathrm{\simeq }\mathrm{8}\mathrm{\times }{\mathrm{10}}^{-2}$(25)or ${\mathit{f}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.07}$, ${\mathit{f}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.93}$. And, finally, from Eq. (20) follow nucleon number densities ${\mathit{n}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.38}\mathrm{cm}{}^{-3}$, ${\mathit{n}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.04}\mathrm{cm}{}^{-3}$.

Similarly, for the SW part of the Vela SNR $\mathrm{(}{\mathit{n}}_{\mathrm{cool}}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{1}\mathit{/}\mathrm{2}}{\mathrm{)}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{3.1}\mathrm{\times }{\mathrm{10}}^{-2}\mathrm{cm}{-3}^{}$, ${\mathit{f}}_{\mathrm{cool}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.09}$, ${\mathit{f}}_{\mathrm{hot}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.91}$, and ${\mathit{n}}_{\mathrm{cool}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.10}\mathrm{cm}{}^{-3}$, ${\mathit{n}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.01}\mathrm{cm}{}^{-3}$.

Table 1 gives a summary of the parameters of the NE and SW parts of the SNR derived from the X-ray data.

As a test for the self-consistency of our model we can calculate the predicted X-ray luminosities of different parts/components of Vela SNR in erg/s, using Eq. (17): ${\mathit{L}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{=}\frac{\mathrm{2}}{\mathrm{3}}\mathit{\pi }{\mathit{R}}_{\mathrm{NE}}^{\mathrm{3}}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\left(}{\mathit{n}}_{\mathrm{e}}{\mathit{n}}_{\mathrm{H}}{\mathrm{\Lambda }}_{\mathit{X}}\mathrm{\right(}\mathit{T}\mathrm{)}{\mathrm{)}}_{\mathrm{cool}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{2.2}\mathrm{\times }{\mathrm{10}}^{\mathrm{35}}{\mathrm{\Lambda }}_{-22}\mathit{,}$(26)where we use the approximation validated by White & Long (1991) Λ_-22(T) = 1. Similarly, ${\mathit{L}}_{\mathrm{hot}}^{\mathrm{NE}}\mathrm{\simeq }\mathrm{0.4}\mathrm{\times }{\mathrm{10}}^{\mathrm{35}}{\mathrm{\Lambda }}_{-22}\hspace{0.17em}\mathrm{erg}\hspace{0.17em}\mathrm{s}-1\mathit{,}$(27)${\mathit{L}}_{\mathrm{cool}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.6}\mathrm{\times }{\mathrm{10}}^{\mathrm{35}}{\mathrm{\Lambda }}_{-22}\hspace{0.17em}\mathrm{erg}\hspace{0.17em}\mathrm{s}-1\mathit{,}$(28)${\mathit{L}}_{\mathrm{hot}}^{\mathrm{SW}}\mathrm{\simeq }\mathrm{0.06}\mathrm{\times }{\mathrm{10}}^{\mathrm{35}}{\mathrm{\Lambda }}_{-22}\hspace{0.17em}\mathrm{erg}\hspace{0.17em}\mathrm{s}-1.$(29)The total model luminosity L_X,   tot ≃ 3.2 × 10³⁵Λ_-22   erg   s^-1 is close to the observed one of Eq. (2)

3. Interaction of the Vela SNR and the γ² Velorum stellar wind bubble

Estimates of the physical parameters of the Vela SNR derived in the previous section show that it is evolving in the inhomogeneous medium whose density changes in a step-like manner. In this section we explore the possibility that this step-like change of the ISM parameters can be related to the presence of the boundary of the stellar wind bubble (SWB) around a Wolf-Rayet (WR) star in the γ² Velorum system, which is situated in the vicinity of the Vela SNR.

3.1. Physical characteristics of the γ² Velorum binary system

γ² Velorum is a WC8+O8-8.5III binary system. The WR component in this binary system is the closest to Earth WR star (WR11). The estimates of the distance to γ² Velorum have evolved over the years and are still controversial. An early estimate of the distance based on HIPPARCOS parallax was $\mathrm{25}{\mathrm{8}}_{-31}^{\mathrm{+}\mathrm{41}}$ pc (Schaerer et al. 1997). It was recently revised by several scientific groups. Millour et al. (2007) give an interferometric estimate of the distance $\mathrm{36}{\mathrm{8}}_{-13}^{\mathrm{+}\mathrm{38}}$ pc. North et al. (2007) estimate the distance to γ² Velorum to be $\mathrm{33}{\mathrm{6}}_{-7}^{\mathrm{+}\mathrm{8}}\mathrm{pc}$ based on the orbital solution for the γ² Velorum binary obtained from the interferometric data. Finally, a revision of the analysis of HIPPARCOS data gives a distance of $\mathrm{33}{\mathrm{4}}_{-32}^{\mathrm{+}\mathrm{40}}\mathrm{pc}$van Leeuwen (2007). Therefore, in the following we take the distance to γ² Velorum to be D_γ²Vel ≃ 330pc.

The current mass estimate of the WR star is M_WR = 9.0 ± 0.6   M_⊙ (North et al. 2007). The mass of the O star is M_O = (28.5 ± 1.1)   M_⊙ (North et al. 2007). The γ² Velorum system is an important source from the viewpoint of nuclear gamma-ray astronomy. Because it is the nearest WR star, this is the only source that can potentially be detected as a point source of 1.8 MeV gamma-ray line emission from the radioactive ²⁶Al with current generation instruments. Previous observations by COMPTEL put an upper limit at the level of 1.1 × 10^-5 γ cm^-2s^-1 on the line flux from the source (Oberlack et al. 2000), which is, apparently, below the typical predictions of the models for stars with the initial mass M_ini ~ 60   M_⊙. One should note, however, that modeling of ²⁶Al production suffers from uncertainties of the nuclear reaction cross-sections, stellar parameters (such as rotation and metallicity), etc. (Limongi & Chieffi 2006; Palacios et al. 2005).

The estimate of the initial mass of the WR star, M_ini ~ (57 ± 15)   M_⊙, is obtained from the evolutionary models of isolated rather than binary stars (Schaerer et al. 1997). It is possible that within a binary system, the mass transfer between the companions can change the stellar structure of both components, so that, for example, stars with initial masses as low as 20M_⊙ can become WR stars in binary systems (Vanbeveren 1991). Modeling the binary evolution of γ² Velorum leads to a lower limit on the initial mass of the WR star: M_WR,i ≥ 38   M_⊙ in (Vanbeveren et al. 1998) and M_WR,i ≃ 35   M_⊙, M_O,i ≃ 31.5   M_⊙ in (Eldridge 2009).

3.2. The stellar wind bubble around γ² Velorum

WR stars are expected to be surrounded by the multi-parsec scale bubbles blown by the strong stellar wind inside a photoionized HII region. The size of the HII region and bubble depends on the (time-dependent) joint action of the photon luminosity in the Lyman continuum L_LyC and the mass-loss rate of the star, Ṁ_w, on its age, t, on the wind velocity v_w and on the density of the ambient medium into which the bubble expands, ρ₀. Qualitatively, the relation between the bubble radius R_bub and the above parameters can be found using the analytical calculation of Weaver et al. (1977)${\mathit{R}}_{\mathrm{bub}}\mathrm{=}\mathit{\kappa }{\left(\frac{\mathrm{1}}{\mathrm{2}}\mathit{Ṁ}\mathrm{w}{\mathit{v}}_{\mathrm{w}}^{\mathrm{2}}\right)}^{\mathrm{1}\mathit{/}\mathrm{5}}{\mathit{\rho }}_{\mathrm{0}}^{\mathrm{-}\mathrm{1}\mathit{/}\mathrm{5}}{\mathit{t}}^{\mathrm{3}\mathit{/}\mathrm{5}}\mathit{,}$(30)where κ is a numerical coefficient which, in the simple case considered by Weaver et al. (1977) was κ = [125/(154π)]^1/5, while in a realistic case it can be found from numerical modeling based on a stellar evolution model. For example, a numerical model considered by Arthur (2007), which studied the evolution of a star with initial mass 40   M_⊙ in a medium of density n₀ = 15 cm^-3, predicts the final radius of the shock in the ambient interstellar medium R_sh ≃ 36 pc at the end of WR phase before SN explosion. Using the Eq. (30) one can re-scale the numerical simulations for the particular values of ISM density to find that for the typical value n₀ = 0.1 cm^-3 in the ISM the radius of the SWB can reach 100 pc. Meanwhile, as we will see later, γ² Velorum system was born in a molecular cloud and its bubble should be considerably smaller.

3.3. Overlap between the Vela SNR and γ² Velorum bubble

Comparing the distances of Vela SNR (~290 pc) and γ² Velorum system (~330 pc) and taking into account the proximity of the two objects on the sky, one can notice that if the SWB around the γ² Velorum system has indeed a radius of 30−70 pc (≥5° on the sky), the Vela SNR, which itself has a size of ~40 pc, is expected to physically intersect with the γ² Velorum bubble. In view of this geometrical argument it is natural to ascribe the observed step-like change in the parameters of the ISM at the location of the Vela SNR to the boundary of the SWB of γ² Velorum.

The hypothesis of intersection between the Vela SNR and γ² Velorum SWB is further supported by the simple geometrical form of the boundary between the bright and the dim part of the SNR shell. Indeed, the boundary roughly follows the contour of an ellipse whose major axis is perpendicular to the direction from the center of Vela SNR toward the γ² Velorum, so that the minor axis is aligned with the direction toward γ² Velorum, see Fig. 1. The projected distance between the Vela SNR and γ² Velorum is D ^′ = 5.2°. Assuming the distances D_Vela ≃ 290pc and D_γ²Vel ≃ 330pc one finds that the physical distance between the two objects is ${\mathit{R}}_{{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}\mathrm{=}{\mathit{D}}_{\mathrm{Vela}\mathrm{-}{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}\mathrm{\simeq }\mathrm{44}\mathrm{pc}\mathrm{.}\mathit{,}$(31)which we adopt as an estimate for the radius of the SWB around γ² Velorum.

3.4. Estimate of the total mass of the stellar wind bubble of γ² Velorum

Within the geometrical model discussed above, the observed difference in the absorption column density N_H between the NE and SW parts of the Vela SNR can be used to estimate the total mass of the ISM swept up by the stellar wind of γ² Velorum over the entire lifetime of the SWB. Taking the difference between the measured N_H values in the NE part and SW parts (Lu & Aschenbach 2000) $\mathrm{\Delta }{\mathit{N}}_{\mathrm{H}}\mathrm{=}{\mathit{N}}_{\mathrm{H}\mathit{,}\mathrm{SW}}\mathrm{-}{\mathit{N}}_{\mathrm{H}\mathit{,}\mathrm{NE}}\mathrm{\simeq }\mathrm{5.5}\mathrm{\times }{\mathrm{10}}^{\mathrm{20}}\mathrm{cm}-2$(32)one can find the total mass of the γ² Velorum SWB: $\mathit{M}\mathrm{\simeq }\mathrm{4}\mathit{\pi }{\mathit{R}}_{{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}^{\mathrm{2}}\mathrm{\Delta }{\mathit{N}}_{\mathrm{H}}\mathrm{\times }\frac{\mathrm{4}}{\mathrm{3}}{\mathit{m}}_{\mathrm{H}}\mathrm{\simeq }\mathrm{1.3}\mathrm{\times }{\mathrm{10}}^{\mathrm{5}} {\mathit{M}}_{\mathrm{\odot }}{\left[\frac{{\mathit{R}}_{{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}}{\mathrm{44} \mathrm{pc}}\right]}^{\mathrm{2}}\mathit{.}$(33)Assuming that the bubble has expanded into a homogeneous ISM over the entire expansion history, one would estimate the ISM density around γ² Velorum as

${\mathit{n}}_{\mathrm{ISM}}\mathrm{=}\frac{\mathit{M}}{\mathrm{(}\mathrm{4}\mathit{/}\mathrm{3}\mathrm{)}\mathit{\pi }{\mathit{R}}_{{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}^{\mathrm{3}}{\mathit{m}}_{\mathrm{H}}}\mathrm{\simeq }\mathrm{12}{\left[\frac{{\mathit{R}}_{{\mathit{\gamma }}^{\mathrm{2}}\mathrm{Vel}}}{\mathrm{44}\mathrm{pc}}\right]}^{-1}\mathrm{cm}-3.$(34)One could notice that this estimate of the density of the ISM is much higher than the estimates of both the intercloud and of the volume-averaged cloud density around Vela SNR (Table 1). We come back to the discussion of the origin of this discrepancy below.

4. The γ² Velorum system and the IRAS Vela shell

The angular size of the γ² Velorum SWB, found from our interpretation of the asymmetry of the Vela SNR, i.e., from the ratio of R_γ²Vel ≃ 44pc and the distance 330pc as ≃7.6° coincides with the angular size of a large circular arc like structure, centered on (l,b) = (263°, −7°) with the radius R_IVS ≃ 7.5°, which is visible in the infrared band, known as the “IRAS Vela shell” (IVS) (Sahu 1992). This structure surrounds the Vela OB2 association including γ² Velorum and ζ Puppis. A recent study of the spatial distribution of the neutral hydrogen and radio continuum emission at 1420 MHz of the IVS by Testori et al. (2006) provides a new estimate of the coordinates of the centroid of IVS from the observed IR emission (l,b) = (259.9°, −8.3°) and the radius of the neutral hydrogen shell in the SW sector between position angles ~162° and ~265°R_IVS ≃ 5.7°. Testori et al. (2006) also estimate the mass of ionized and atomic components of the shell, assuming a distance of 400 pc: M_IVS ≃ 9.1 × 10⁴   M_⊙ (or M_IVS ≃ 6.0 × 10⁴   M_⊙ for our distance 330pc). It is expected that the amount of molecular gas in the IVS is about ~10⁵   M_⊙(Rajagopal & Srinivasan 1998).

A possible interpretation of the IVS as a boundary of the SWB of γ² Velorum was discussed by Oberlack et al. (2000) and Testori et al. (2006).

Adopting this interpretation, one can find that the estimates of the parameters of the SWB of γ² Velorum  derived above from the analysis of X-ray data on the Vela SNR, agree well with those found from the analysis of the IVS data. In particular, adopting an estimate of the distance toward γ² Velorum for the center of the IVS, one finds the radius ${\mathit{R}}_{\mathrm{IVS}}\mathrm{~}\mathrm{44}\left[\frac{{\mathit{D}}_{\mathrm{Velorum}}}{\mathrm{330}\mathrm{pc}}\right]\mathrm{pc}$(35)and the total mass of the shell ${\mathit{M}}_{\mathrm{IVS}}\mathrm{~}\mathrm{1}\mathrm{\times }{\mathrm{10}}^{\mathrm{5}}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}$(36)comparable to the estimates found in Eqs. (31) and (33), respectively.

4.1. Implications for the models of the Wolf-Rayet star

The initial mass of the WR11 star M_ini is equal the sum of the current mass of the star M_WR = 9.0   M_⊙ and the mass which was blown by the wind: ${\mathit{M}}_{\mathrm{ini}}\mathrm{=}{\mathit{M}}_{\mathrm{WR}}\mathrm{+}\mathrm{\Delta }{\mathit{M}}_{\mathrm{MSS}}\mathrm{+}\mathrm{\Delta }{\mathit{M}}_{\mathrm{(}\mathrm{RSGS}\mathit{/}\mathrm{LBVS}\mathrm{)}}\mathrm{+}⟨\mathit{Ṁ}\mathrm{WR}⟩{\mathit{t}}_{\mathrm{WR}}\mathit{,}$(37)where Ṁ_WR is the mass loss rate and t_WR is the time interval of the WR wind. The sum in the above equation includes mass loss via different types of winds ejected by the star at different stages of stellar evolution: the main sequence stage (MSS) wind, the red supergiant stage (RSGS) (for stars with initial mass M_ini ≤ 40   M_⊙) or the luminous blue variable stage (LBVS) (for M_ini ≥ 40   M_⊙) wind, and the continuing WR wind. Numerical calculations from Freyer et al. (2003), Freyer et al. (2006), van Marle et al. (2005), Arthur (2007), van Marle et al. (2007), Perez-Rendon et al. (2009) show that the MSS and RSGS/LBVS dominate the mass loss with typical values of mass loss before WR stage (21−26)   M_⊙ for M_ini ~ (30−60)   M_⊙. Meanwhile, the WR stage dominates in the kinetic energy of the wind, injected into the wind bubble.

For the γ² Velorum binary one can calculate the total stellar wind mass loss ΔM ≃ 29   M_⊙ as the difference between the initial and contemporary masses of stars in binary systems, which are M_WR,ini ≃ 35   M_⊙, M_O,ini ≃ 31.5   M_⊙ and M_WR ≃ 9.0   M_⊙, M_O ≃ 28.5   M_⊙ respectively, according to Eldridge (2009). This includes the mass-loss rate from the slow red supergiant stage wind ΔM_RSGS ≃ 19   M_⊙ (Freyer et al. 2006). Therefore, the remaining 10M_⊙ of the hot intercloud gas in the γ² Velorum SWB correspond to fast MSS and WR winds. Clumps, created by the interaction of the fast WR wind and the slow RSG wind, together with ISM clouds (Gum nebula interior, see below), survived the passage through the expanded IVS, are the main sources of X-ray emitting plasma in SW part of Vela SNR. As follows from Table 1, the lower limit on the total mass of gas in clumps and clouds inside the SWB is ${\mathit{M}}_{\mathrm{cl}}^{\mathrm{SWB}}\mathrm{=}{\mathit{M}}_{\mathrm{hot}}^{\mathrm{SWB}}\left[\frac{{\mathit{n}}_{\mathrm{hot}}^{\mathrm{SW}}}{{\mathit{n}}_{\mathrm{ic}}^{\mathrm{SWB}}}{\mathit{f}}_{\mathrm{hot}}^{\mathrm{SW}}\mathrm{+}\frac{{\mathit{n}}_{\mathrm{cool}}^{\mathrm{SW}}}{{\mathit{n}}_{\mathrm{ic}}^{\mathrm{SWB}}}{\mathit{f}}_{\mathrm{cool}}^{\mathrm{SW}}\right]\mathrm{=}\mathrm{256}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}\mathit{.}$(38)Let us estimate the energy budget of IVS. Assuming that the IVS is a boundary of the SWB of γ² Velorum we can estimate its kinetic energy, assuming an expansion velocity V_exp ≃ 13km   s^-1 (Testori et al. 2006) ${\mathit{E}}_{\mathrm{kin}}^{\mathrm{IVS}}\mathrm{\simeq }\frac{\mathrm{1}}{\mathrm{2}}{\mathit{M}}_{\mathrm{IVS}}{\mathit{V}}_{\exp }^{\mathrm{2}}\mathrm{\simeq }\mathrm{2}\mathrm{\times }{\mathrm{10}}^{\mathrm{50}}\hspace{0.17em}\mathrm{erg}\mathrm{.}$(39)

Thermal energy inside of the SWB of γ² Velorum is limited by conditions of strong Vela SNR shock and the dominance of the mean density of evaporated clouds in postshock plasma.

Strong shock condition means that the ratio of pressures inside the remnant and bubble and equivalently the ratio of energy densities should be high $\mathit{E}{\mathit{R}}_{\mathrm{SW}}^{-3}\mathit{/}{\mathit{E}}_{\mathrm{th}}^{\mathrm{SWB}}{\mathit{R}}_{\mathrm{IVS}}^{-3}\mathrm{\gg }\mathrm{1}$ or ${\mathit{E}}_{\mathrm{th}}^{\mathrm{SWB}}\mathrm{\ll }\mathit{E}{\left[\frac{{\mathit{R}}_{\mathrm{IVS}}}{{\mathit{R}}_{\mathrm{SW}}}\right]}^{\mathrm{3}}\mathrm{~}\mathrm{1}\mathrm{\times }{\mathrm{10}}^{\mathrm{51}}\hspace{0.17em}\mathrm{erg}\mathit{.}$(40)The dominance of evaporated cloud material in the postshock region ${\mathit{C}}_{\mathrm{hot}}^{\mathrm{SW}}\mathrm{=}{\mathit{n}}_{\mathrm{c}\mathit{,}\mathrm{hot}}^{\mathrm{SW}}\mathit{/}{\mathit{n}}_{\mathrm{ic}}^{\mathrm{SWB}}\mathrm{\gg }\mathrm{1}$ means that ${\mathit{n}}_{\mathrm{ic}}^{\mathrm{SWB}}\mathrm{\le }\mathrm{0.1}{\mathit{n}}_{\mathrm{hot}}^{\mathrm{SW}}$ and we take hereafter ${\mathit{n}}_{\mathrm{ic}}^{\mathrm{SWB}}\mathrm{\simeq }{\mathrm{10}}^{-3}\mathrm{cm}{}^{-3}$ (i.e. C = 10) and ${\mathit{T}}_{\mathrm{ic}}^{\mathrm{SWB}}\mathrm{\simeq }\mathrm{3}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}\mathrm{K}$ as reasonable parameters of the hot (intercloud) gas inside the SWB enclosed in the IVS. The total mass and thermal energy of this hot gas inside γ² Velorum is ${\mathit{M}}_{\mathrm{hot}}^{\mathrm{SWB}}\mathrm{\simeq }\mathrm{10}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}$ and ${\mathit{E}}_{\mathrm{hot}}^{\mathrm{SWB}}\mathrm{\simeq }\mathrm{1}\mathrm{\times }{\mathrm{10}}^{\mathrm{49}}\hspace{0.17em}\mathrm{erg}\hspace{0.17em}\mathrm{s}$. Meanwhile, the thermal energy of clumps and clouds with a reasonable value of temperature T_cl ≤ 10⁴K is only ${\mathit{E}}_{\mathrm{cl}}^{\mathrm{SWB}}\mathrm{\le }\mathrm{1}\mathrm{\times }{\mathrm{10}}^{\mathrm{48}}\hspace{0.17em}\mathrm{erg}$.

To summarize, in our hydrodynamical model of IVS the total (thermal and kinetic) energy of the γ² Velorum SWB is ${\mathit{E}}_{\mathrm{SWB}}\mathrm{=}{\mathit{E}}_{\mathrm{kin}}^{\mathrm{IVS}}\mathrm{+}{\mathit{E}}_{\mathrm{hot}}^{\mathrm{SWB}}\mathrm{+}{\mathit{E}}_{\mathrm{cl}}^{\mathrm{SWB}}\mathrm{\simeq }\mathrm{2}\mathrm{\times }{\mathrm{10}}^{\mathrm{50}}\mathrm{erg}$(41)with evident dominance of kinetic energy of the massive (~10⁵   M_⊙) IVS in the total sum. Inside the SWB we predict about 10   M_⊙ of hot intercloud gas and about 260   M_⊙ of immersed warm/cool clumps/clouds (in case of their complete evaporation inside Vela SNR). It is worth noting that temperature and density of plasma inside IVS are not well restricted by observations, and here we use approximate values, which are consistent with the adopted limits.

We can compare these estimates with the results of numerical simulations of stellar wind bubbles around WR stars. Numerical simulations of the evolution of a star with an initial mass M_ini = 35   M_⊙, as proposed by Eldridge (2009) for WR11, were made by Freyer et al. (2006) for an environment with a density of n₀ = 20cm^-3 and a temperature of T₀ = 200K. They show that at the end of the calculations (before the SN explosion) the hot gas bubble has a mean radius of 34pc and shell-like HII and HI regions of the swept up ambient gas extend out to a distance of 43−44pc, the total mass is 1.5 × 10⁵   M_⊙, the kinetic energy is 4.9 × 10⁴⁹   erg, the thermal energy of the hot gas is 1.1 × 10⁵⁰   erg, of the warm gas 4.3 × 10⁴⁹   erg, i.e., the radius, total mass and total energy (kinetic and thermal, 2 × 10⁵⁰   erg) are surprisingly close to our estimate for γ² Velorum. Nevertheless, two important differences should be clarified for γ² Velorum namely, the kinetic energy dominance and the low density of the ISM.

4.2. Density of the interstellar medium and interaction with the Gum nebula

The three estimates for the “typical” ISM density derived above provide widely different values. The estimate based on the dynamics of expansion of Vela SNR suggests a low value for the ISM density n_ISM ≤ 0.01 cm^-3, while the estimate based on the total mass of the SWB around γ² Velorum (n_ISM ~ 16 cm^-3) and the estimate based on the dynamics of expansion of the SWB (n_ISM ~ 20 cm^-3) suggest a much higher density. This points to the fact that the distribution of the ISM in the direction of the Vela region, in the distance range ~300−400 pc, is highly inhomogeneous. This is, in principle, not surprising, because the region is known to contain several stellar formations with different properties.

First, γ² Velorum belongs to the γVel association, which is a subcluster of the OB-association Vela OB2 (Jeffries et al. 2008). The density of the ISM in the OB association soon after γ² Velorum’s formation is expected to have been much higher because of the presence of a parent molecular cloud. The initial expansion of the γ² Velorum bubble into a dense ${\mathrm{(}}^{}{\mathrm{10}}^{\mathrm{2}}\mathrm{-}{\mathrm{10}}^{\mathrm{3}} {\mathrm{cm}}^{-3}{\mathrm{)}}^{}$ molecular cloud (the progenitor of Vela OB2) can explain the large mass of the swept up ISM in a shell around the SWB. In this scenario, the stellar wind and the radiation of γ² Velorum destroyed the parent molecular cloud and swept up its gas. For some time the stellar wind of γ² Velorum was practically trapped inside a ~10⁵   M_⊙ cloud, and only when the energy accumulated in the SWB and HII region exceeded the gravitationally bound energy of the cloud (~10⁵⁰   erg   s for R_cl = 10pc cloud), the dense shell of swept-up cloud material began to be accelerated by the thermal pressure of the SWB and the HII region gas without considerable additional mass loading and counter pressure of hot rarefied gas of the ISM. At this evolutionary stage, the thermal energy of the system converts into the kinetic energy of the shell, resulting in the atypical dominance of the kinetic energy of the IVS in the total energy balance of the γ² Velorum SWB/HII region.

Fig. 2 Locations of the Vela SNR (Vela pulsar is shown as a cross), γ2 Velorum (shown as a circle), IRAS Vela Shell (IVS) bubble and Gum nebula (center is shown as a square) in Galactic coordinate system.

Next, both the Vela SNR and the γ² Velorum SWB could be interacting with a still larger scale SNR, known as the Gum nebula. This nebula is a very large region of the ionized gas about 36° in diameter, centered approximately at (l,b) = (258°, −2°) (Gum 1952), shown in Fig. 2. Brandt et al. (1971) explained the Gum nebula as a fossil Stromgren sphere of the Vela X supernova and estimated the distance to nebula to be ${\mathit{D}}_{\mathrm{Gum}}\mathrm{=}\mathrm{400}\mathrm{\pm }\mathrm{60}\mathrm{pc}\mathit{.}$(42)Reynolds (1976) suggested that the Gum nebula is an 1 Myr old SNR, which is now heated and ionized by the two very hot stars zeta Puppis and gamma Velorum within it. Later Woermann et al. (2001) showed that the Gum nebula can possibly be a SNR of the zeta Puppis companion. They showed that runaway O-star zeta Puppis was within <0.5 deg of the expansion center of the Gum nebula about 1.5 Myr ago, which is evidence of the relation between the SN explosion of the binary companion and the Gum nebula expansion. Assuming a distance of 400 pc the radius of Gum nebula is about ${\mathit{R}}_{\mathrm{Gum}}\mathrm{\simeq }\mathrm{124}\left[\frac{{\mathit{D}}_{\mathrm{Gum}}}{\mathrm{400}\mathrm{pc}}\right]\mathrm{pc}\mathit{.}$(43)This means that both the Vela SNR and γ² Velorum are situated inside the cavity formed by the expansion of the SNR associated to the Gum nebula.

The Gum nebula as a very old (0.9−2.0 Myr) SNR should be at the late radiative stage of evolution, which can be modeled with the solution of Cioffi et al. (1988) for the shock dynamics. Assuming the the current radius 124 pc, age ~1.5 Myr and the explosion energy of 10⁵¹E₅₁ erg, we can find out the density of the ISM in which the Gum nebula expands: ${\mathit{n}}_{\mathrm{ISM}}\mathrm{=}\mathrm{0.07}{\mathit{\varsigma }}^{\mathrm{-}\frac{\mathrm{5}}{\mathrm{36}}}{\left[\frac{\mathit{t}}{\mathrm{1.5}\mathrm{Myr}}\right]}^{\mathrm{-}\frac{\mathrm{7}}{\mathrm{6}}}{\left[\frac{{\mathit{D}}_{\mathrm{Gum}}}{\mathrm{400}\mathrm{pc}}\right]}^{\mathrm{-}\frac{\mathrm{35}}{\mathrm{9}}}{\mathit{E}}_{\mathrm{51}}^{\frac{\mathrm{17}}{\mathrm{72}}}\mathrm{cm}-3\mathit{,}$(44)where ζ is the metallicity factor, equal to 1 for solar abundances.

The estimate of the average density of the ISM around Gum nebula shows that actually the nebula expands into the medium with a much lower density than the one suggested by the estimate of the total mass of the SWB around γ² Velorum. This supports the hypothesis that the enhancement of the density of the ISM was locally present around the γ² Velorum system at moment of its birth, most probably because of an OB association.

5. Conclusions

We developed a model for the interaction of the Vela SNR and the γ² Velorum SWB, which explains the observed NE/SW asymmetry of the Vela SNR.

Adopting a model of the expansion of the Vela SNR into a “cloudy” ISM, we showed that the volume-averaged density of the shock-evaporated clouds in the NE part of the SNR has to be about four times higher than in the SW part. We noticed that a plausible explanation for the observed density contrast is that the Vela SNR exploded at the boundary of the SWB around a nearby Wolf-Rayet star in the γ² Velorum system, which is situated at approximately the same distance as the Vela SNR.

Within our model of the interaction of the Vela SNR and the γ² Velorum SWB, the difference of the spectral characteristics of the X-ray emission from the NE and SW parts of the remnant can be used for an estimate of the parameters of the γ² Velorum bubble. We showed that the measurement of the change of the column density of the neutral hydrogen gives an estimate of the total mass of the SWB, ~1 × 10⁵   M_⊙.

On the basis of modeling the dynamics of expansion of the bubble around γ² Velorum, we confirmed the initial mass of the Wolf-Rayet star in the γ² Velorum system suggested by Eldridge (2009) to be ≃35   M_⊙. This estimate is lower than the previous estimates used for the derivations of predictions of the flux of a γ-ray spectral line at 1.8 MeV, expected from the decays of ²⁶Al in this source. Taking into account the revised estimate of the initial mass of the Wolf-Rayet star, the ²⁶Al line flux flux from γ² Velorum is expected to be much below the COMPTEL limit.

Acknowledgments

We would like to thank the referee, John Dickel, for many useful comments and suggestions, which appreciably inproved the paper. I.S. acknowledges support from Erasmus Mundus, “External Cooperation Window”.

References

All Tables

All Figures

Fig. 1 ROSAT All-Sky Survey image (0.1–2.4 KeV) of the Vela SNR (Aschenbach et al. 1995). A–F are extended features outside the boundary of the remnant (“bullets”). Light blue to white contrast represents a contrast in surface brightness of a factor of 500 (Aschenbach et al. 1995). Blue curves show the NE and SW hemispheres of the Vela SNR. The yellow curve shows the contour of the SWB of γ2 Velorum.

In the text

	Fig. 2 Locations of the Vela SNR (Vela pulsar is shown as a cross), γ2 Velorum (shown as a circle), IRAS Vela Shell (IVS) bubble and Gum nebula (center is shown as a square) in Galactic coordinate system.
In the text