ON THE EXPANSION RATE, AGE, AND DISTANCE OF THE SUPERNOVA REMNANT G266.2−1.2 (Vela Jr.)

The expansion rate measured using Chandra data (0.42 ± 0.10 arcsec yr⁻¹) is about half the expansion rate obtained using XMM-Newton data (0.84 ± 0.23 arcsec yr⁻¹; Katsuda et al. 2008a). The two measurements are from similar time intervals (2003 to 2008 for Chandra and 2001 to 2007 for XMM-Newton) and from similar regions (i.e., bright portions of the northwestern rim). However, the regions used are not identically the same. It is possible that there is an azimuthal variation in the expansion rate along the northwestern rim of G266.2−1.2. Although the difference is not statistically significant, the expansion rates in regions A and B differ by a factor of 1.5 (Table 3). While there may not be significant differences in the expansion rates along the northeastern rim of SN 1006 (Katsuda et al. 2009), there do appear to be significant azimuthal variations in the expansion rates of Cas A (DeLaney & Rudnick 2003) and Kepler (Katsuda et al. 2008b). Furthermore, the variations reported for these latter two remnants could be as large as a factor of two or more.

If the angular radius θ = 086, then the fractional expansion rates $\dot{\theta }/\theta$ are 0.136 ± 0.042 kyr⁻¹ and 0.27 ± 0.07 kyr⁻¹ for Chandra and XMM-Newton, respectively.²¹ The fractional expansion rate provides a crude constraint on the age of the remnant. If the radius of the forward shock r_f∝t^m, where t is the age and m is the expansion parameter, and if m is a constant over the time interval of the expansion measurement, then $t = m \theta / \dot{\theta }$. While the value of m is unknown, it is most likely in the range from 0.4 (the Sedov–Taylor phase) to 1 (the free-expansion phase). In this case, the age of G266.2−1.2 is in the range ²² from 2.1 to 13 kyr (Chandra) or from 1.2 to 5.0 kyr (XMM-Newton), provided the expansion results for the northwestern rim are representative of the remnant as a whole.

To try to obtain better constraints on the age of G266.2−1.2, we used the hydrodynamic models of Truelove & McKee (1999). Since the physical conditions—the initial kinetic energy (E₀), mass (M_ej), and mass density distribution (ρ_ej∝v⁻ⁿt⁻³) of the ejecta, the ambient mass density distribution (ρ₀ = 1.42m_pn₀), and the evolutionary state (t/t_ch)—are unknown, a five-dimensional grid in E₀, M_ej, n, n₀, and t/t_ch was used with 81 values of E₀: 10⁴⁹, 10^49.05,..., 10⁵³ erg; 41 values of M_ej: 10⁰, 10^0.05,..., 10² M_☉; seven values of n: 6, 7, 8, 9, 10, 12, 14 (i.e., m = (n − 3)/n = 0.50,..., 0.79); 101 values of n₀: 10⁻⁵, 10^−4.95,..., 10⁰ cm⁻³; and 999 values of t/t_ch: 0.01, 0.02,..., 9.99. Note that the characteristic age t_ch = 6.18 (E₀/10⁵¹ erg)^−1/2(M_ej/10M_☉)^5/6(n₀/0.1 cm⁻³)^−1/3 kyr. Collectively, the grid includes 2.35 billion scenarios. Of course, most of the scenarios are improbable. We tried to make the range of values for each parameter large enough to bracket the expected value of the parameter. The following four criteria were used to determine which scenarios and, hence, which ages, are plausible.

One criteria is that the distance-independent fractional expansion rate (i.e., $v_{\rm f} / r_{\rm f} = \dot{\theta } / \theta$) must be compatible with the Chandra result (i.e., is in the range from 0.094 to 0.178 kyr⁻¹). Scenarios that did not satisfy this criteria were discarded.

Another criteria is that the forward shock speed must be greater than or equal to 1000 km s⁻¹. Such speeds are required (e.g., Equation (A5) of Allen et al. 2008) to accelerate electrons to energies high enough to produce X-ray synchrotron spectra with cut-off frequencies in excess of 10¹⁷ Hz (Pannuti et al. 2010).

A third criteria is that the inferred amount of thermal X-ray emission from the forward-shocked material cannot exceed observational constraints. The pshock model of XSPEC was used to describe this emission. The abundances were assumed to be solar and the temperature was set to 0.3 keV. While the temperature is unknown, it is expected to be at least this high since the electron temperatures measured for other X-ray synchrotron-emitting remnants are larger. Had a higher temperature been used, then more scenarios would have been discarded. The lower and upper limits on the pshock ionization timescale were set to zero and 1.2n₀t, respectively. The pshock normalization was set to 3.64 × 10⁻¹⁸(n₀/1 cm⁻³)²(r_f/1 cm) cm⁻⁵. This value is based upon the assumptions that the shock-heated gas fills one quarter of the volume inside the forward shock and that it has an electron-to-proton ratio of 1.2 (i.e., that the proton and electron densities are 4n₀ and 4.8n₀, respectively). The pshock emission is absorbed using the XSPEC model tbabs with n_H = 1.2 × 10²² atoms cm⁻². This absorption column density represents an upper limit for the remnant (Acero et al. 2013). Lower column densities would have resulted in more scenarios being discarded. The absorbed thermal X-ray spectrum was compared to the total ROSAT spectrum for a 086 radius cone along the line of sight through G266.2−1.2. This spectrum includes emission from both the G266.2−1.2 and Vela supernova remnants. As long as the absorbed emission model for a scenario does not exceed the ROSAT spectrum by more than 3σ at any point in the spectrum, the scenario is considered plausible. This constraint limits the ambient density to be below 0.4 cm⁻³.

The last criteria used is an energy constraint. The sum of the kinetic and thermal energies of the forward-shocked material plus the inferred energy of the cosmic-ray protons cannot exceed E₀, the initial kinetic energy of the ejecta. This constraint is less restrictive than it would have been if the computation also included the energies associated with the shocked and unshocked ejecta, with the other cosmic-ray particles, and with the magnetic field. The kinetic energy of the forward-shocked material is assumed to be given by $U_{\rm KE,f} = 3 \pi \rho _{0} r_{\rm f}^{3} v_{\rm f}^{2} / 8$ (i.e., =M_s(3v_f/4)²/2, where $M_{\rm s} = 4 \pi \rho _{0} r_{\rm f}^{3} / 3$). The thermal energy of the forward-shocked material is assumed to be given by the same expression (i.e., U_{kT, f} = ∑_i3N_ikT_i/2, where $N_{i} = 4 \pi \rho _{i} r_{\rm f}^{3} /(3 m_{i})$ and $kT_{i} = 3 m_{i} v_{\rm f}^{2} / 16$). The total energy in cosmic-ray protons is obtained by integrating the momentum-dependent energy over the power-law number-density distribution dn/dp = A(p/p₀)^−Γexp ((p₀ − p)/p_max) and by multiplying by one quarter of the total volume. Here, A = 3.5 × 10⁻⁸ cm⁻³ (GeV/c)⁻¹, p₀ = 1 GeV/c, Γ = 2.0, and p_max = 18 TeV/c. These parameters are based on a joint fit of an inverse Compton model to gamma-ray data and of a synchrotron model to radio and X-ray data (see Allen et al. 2011). The number density of protons is assumed to be one hundred times larger than the number density of electrons at p = 1 GeV/c. A larger proton-to-electron ratio would have lead to more scenarios being discarded. The integration is performed from p_min to 10p_max. The former quantity is the momentum at which there is a transition from a Maxwell–Boltzmann distribution to the power-law. Implicit in this calculation is the requirement that the number density of thermal protons must exceed the number density of nonthermal protons at thermal momenta. The energy constraint limits E₀ to be above 4 × 10⁴⁹ erg, n₀ to be above 3 × 10⁻⁴ cm⁻³, r_f to be less than 70 pc (i.e., d < 5 kpc), and v_f to be less than 10⁴ km s⁻¹.

Of the 2.35 billion scenarios considered, 57.4 million (2.45%) satisfy all four of our plausibility criteria. A histogram of the ages for the plausible scenarios is shown in Figure 6. The youngest plausible scenario has an age of 2.2 kyr. The oldest is 8.4 kyr. If the lowest 5% and highest 5% of the distribution are discarded, then the 90% confidence level interval for the age is from 2.4 to 5.1 kyr.

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This range is based upon the assumption that the models of Truelove & McKee (1999) are suitable for G266.2−1.2. Although Truelove & McKee (1999) only considered uniform ambient densities, it is possible to obtain a simple scaling factor between the age obtained using their model and the age expected if the ambient material has a mass density distribution ρ∝r^−s. At early times (i.e., those for which t < 0.5 t_ch), the effective value of m would be given by (n − 3)/(n − s), not (n − 3)/n (Truelove & McKee 1999). As a result, m, and hence the age, is larger by a factor of n/(n − s). Therefore, if the ambient material is from a steady wind (i.e., s = 2) and if n ⩾ 6, then the age is underestimated by no more than a factor of 1.5.

The remnant was most likely produced by a core collapse supernova.²³ (1) There are reports of an X-ray emitting compact central object (Aschenbach 1998; Slane et al. 2001; Pavlov et al. 2001). (2) There is no evidence of thermal X-ray emission, which suggests that G266.2−1.2 is expanding into the rarefied environment of a stellar wind-blown bubble (Slane et al. 2001; Lee et al. 2013). (3) There is a molecular cloud (the Vela Molecular Ridge) and a group of massive stars (i.e., Vel OB1; Eggen 1982) with which the remnant may be associated. Yet, if G266.2−1.2 is the remnant of a Type Ia supernova, instead of a core collapse event, then Dwarkadas & Chevalier (1998) suggest the ejected material may have an exponential mass density distribution ρ_ej∝e^−vt⁻³ instead of a power-law distribution ρ_ej∝v⁻ⁿt⁻³. Although Truelove & McKee (1999) did not consider models with exponential ejecta profiles, Dwarkadas & Chevalier (1998) note that Type Ia remnants have been modeled using a power law with n = 7. If the sample of plausible scenarios is limited to the subset with n = 7 and with M_ej = 1.4 M_☉, then the 90% confidence level interval for the age is from 2.4 to 4.5 kyr with no scenario having an age less than 2.2 kyr or more than 6.1 kyr.

For these reasons, the age of G266.2−1.2 is expected to be between 2.4 and 5.1 kyr whether or not it was produced by a core collapse supernova. In no case is the remnant expected to be younger than 2.2 kyr, which contradicts most of the previous age estimates. These estimates are reviewed hereafter.

The first estimate published was that of Aschenbach (1998), who argues that G266.2−1.2 is less than or about 1.5 kyr old. This result is based upon the high temperature that is obtained when the ROSAT PSPC data are fitted with a thermal emission model. However, subsequent observations with the ASCA GIS (Tsunemi et al. 2000), which had better spectral resolution, reveal that the X-ray flux is dominated by synchrotron radiation and show no evidence of thermal emission (Slane et al. 2001).

Several age estimates are based upon evidence of emission associated with the decay of ⁴⁴Ti. Iyudin et al. (1998) report an emission line at 1.16 MeV in COMPTEL data and obtain an age of about 0.68 kyr. Chen & Gehrels (1999) and Aschenbach et al. (1999) expand upon this work and find ages between 0.6 and 1.1 kyr and less than 1.1 kyr, respectively. Tsunemi et al. (2000) report the detection of a 4.1 ± 0.2 keV X-ray emission line from the northwestern rim with ASCA. They attribute this line to ⁴⁴Ca produced by the decay of ⁴⁴Ti. Based upon the 1.16 MeV line flux, they estimate an age between 0.6 and 1.0 kyr. Slane et al. (2001) reexamined the ASCA data. While they find a hint of a 4 keV line in the SIS0 data for a region in the northwest, they find no such evidence in the SIS1 data for the same region. Iyudin et al. (2005) report a line feature at 4.45 ± 0.05 keV in XMM-Newton spectra for the northwestern, western, and southern rims. Hiraga et al. (2009) find no evidence of a 4 keV emission line in Suzaku data. Their upper limits on the line flux are well below the line fluxes reported by Tsunemi et al. (2000), Iyudin et al. (2005), and Bamba et al. (2005a). Their limits are also below the X-ray line flux inferred from the gamma-ray line flux of Iyudin et al. (1998). Furthermore, there is some concern about the statistical significance of the 1.16 MeV line in the COMPTEL data (Schönfelder et al. 2000) and there is no evidence of 67.9 and 78.4 keV lines in the INTEGRAL data (Renaud et al. 2006). Since the evidence of X-ray and gamma-ray emission lines associated with the decay of ⁴⁴Ti is questionable, claims of their detections do not provide a compelling reason to doubt the age range inferred from the measurement of the expansion rate.

Following suggestions that G266.2−1.2 is young, Burgess & Zuber (2000) searched for evidence of a geophysical signature of the supernova that produced it. They report that South Pole ice core samples exhibit temporal spikes in the abundance of nitrate and that these spikes may be associated with historic supernovae. Their Figure 1 shows spikes that could be associated with the Kepler, Tycho, and AD 1181 supernovae. It also shows a spike that occurred in AD 1320 ± 20. If this spike is associated with G266.2−1.2, then the age of the spike would be consistent with ages inferred from the reports of ⁴⁴Ti line emission. However, they note that it is not clear that the ionizing radiation from supernovae significantly affects the terrestrial nitrate abundance. For example, there is no spike associated with Cas A. Unfortunately, the results presented in their figure do not go back far enough to determine whether or not there are spikes associated with the Crab and SN 1006 supernovae.

Obergaulinger et al. (2014) performed a hydrodynamic analysis assuming that G266.2−1.2 is expanding into an environment with several molecular clouds that have a variety of masses and densities. While they note that they cannot eliminate the possibility that the remnant is a few thousand years old, they favor an age of about 0.8 kyr. Unfortunately, it's not clear that their assumptions are applicable to G266.2−1.2. For example, there's no clear evidence that the remnant is expanding into a medium with a large density gradient. In their simulated images, the X-ray emission from the rim of the remnant is irregularly shaped and clumpy, unlike the observations, which show an outer edge that follows a nearly circular arc in the northwest (Figures 1 and 2). Furthermore, the X-ray emission in their model is entirely thermal, whereas the X-ray emission from the remnant is dominated by nonthermal emission, at least above about 1 keV. In fact, the conditions of their model (i.e., a downstream shock-heated plasma with n = 1 cm⁻³ and kT = 1 keV) are incompatible with the limits obtained from the ROSAT data. If kT = 1 keV, then the downstream density cannot be larger than 0.4 cm⁻³. For these reasons, the results of their analysis may not be accurate for G266.2−1.2.

Bamba et al. (2005a) infer an age between 0.42 and 1.4 kyr using a novel technique. This technique is based upon a simple hydrodynamic model and upon a relationship between the age and the quantity ν_roll/l², where ν_roll and l are the roll-off frequency and downstream scale length of X-ray synchrotron radiation, respectively (Bamba et al. 2005b). At present, there is too little data to evaluate its reliability.

Of the previously published ages, 17.5 kyr (Telezhinsky 2009) is unique in that it is larger than the ages inferred from the Chandra data. Telezhinsky suggests that G266.2−1.2 entered the radiative phase 1.5 kyr ago. As a result, a significant fraction of the thermal energy of the shock-heated gas has been lost. Therefore, it's possible to have a large ambient density (n₀ = 1.5 cm⁻³) without the thermal X-ray emission being higher than observational constraints. The large density means that the TeV gamma-ray emission can be described primarily in terms of the photons produced by neutral-pion decay instead of inverse Compton scattering. However, it's not clear that this model is consistent with the detection of thin, X-ray–synchrotron-dominated filaments. These filaments, which are thought to be associated with the forward shock, have synchrotron cut-off frequencies in excess of 10¹⁷ Hz (Pannuti et al. 2010). Using Telezhinsky's magnetic field strength of 67 μG, the corresponding electron cut-off energy is greater than 10 TeV. Yet, if particle acceleration at the forward shock ended 1.5 kyr ago (Telezhinsky 2009), then electrons with energies in excess of 1 TeV would have lost their energy via synchrotron radiation. The synchrotron spectrum would have a cut-off frequency of about 10¹⁵ Hz and would not detectable at X-ray energies. Another concern is that the model may violate energy conservation. For example, the amount of energy transferred to the bulk kinetic motion and to the random thermal motion of the forward-shocked material (even if some of this energy has been lost via radiation) may be expressed as $U_{\rm f} \equiv U_{\rm KE,f} + U_{kT,{\rm f}} = 3 \pi \rho _{0} r_{\rm f}^{3} v_{\rm f}^{2} / 4 = 1.96 \times 10^{53} (n_{0}/1\, {\rm cm}^{-3}) (\theta / 1^{\circ })^{3} (\dot{\theta } / 1 {\rm \,arcsec}\, {\rm yr}^{-1})^{2} (d / 1\, {\rm kpc})^{5} {\rm erg}$. Using Telezhinsky's values of n₀ (1.5 cm⁻³) and d (0.6 kpc) and our values of θ (086) and $\dot{\theta }$ (0.42 arcsec yr⁻¹), yields U_f = 2.57 × 10⁵¹ erg. Although this computation excludes all other forms of energy, the value of U_f is still much larger than Telezhinsky's initial kinetic energy of 2 × 10⁵⁰ erg.

In summary, a wide range of ages have been inferred for G266.2−1.2 using a variety of different evidence. Of these reports, we argue that the most reliable are those based upon the measurement of the expansion rate of the remnant. The biggest concern with this technique is that the expansion rate in the northwest may not be representative of the remnant as a whole. If the Chandra results are accurate and representative, then G266.2−1.2 is between 2.4 and 5.1 kyr old.

The measured expansion rate, even when coupled with the hydrodynamic simulations, does not provide a significant constraint on the distance. For example, Figure 7 shows that the range from 0.7 to 3.2 kpc encompasses 90% of the 57.4 million scenarios that satisfy the plausibility criteria described in Section 3.1. The full range of distances for these scenarios is from 0.3 to 4.5 kpc. Hereafter, we review other inferences about the distance.

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If, as expected, the remnant was produced by a core collapse supernova, then it is likely that it is part of the Vela Molecular Ridge. This material is concentrated into two groups (Murphy & May 1991), one at a distance of 0.7 ± 0.2 kpc (Liseau et al. 1992) and the other at a distance of about 2 kpc. In particular, the progenitor of G266.2−1.2 may have been a member of either the Vel OB1 or Vel OB2 ²⁴ associations, which are at distances of about 0.8 and 1.8 kpc, respectively (Eggen 1982). Duncan & Green (2000) report that a distance of 1–2 kpc, instead of a distance much less than 1 kpc, yields a diameter that is more compatible with the diameters of remnants that have similar radio surface brightnesses (see their Figure 6).

Reynoso et al. (2006) use the column density n_H toward the central compact object CXOU J085201.4–461753, as measured by Becker & Aschenbach (2002), to infer a distance of 2.4 ± 0.4 kpc. However, Acero et al. (2013) show that most of the column density along this line of sight (and toward the remnant) is associated with the Vela Molecular Ridge. Therefore, the compact object (and G266.2−1.2) can be no further than 0.9 kpc. This limit is consistent with the results of Kim et al. (2012), who suggest that the remnant may be a source of far-ultraviolet emission, in which case it is closer than 1 kpc.

Since the values of n_H associated with G266.2−1.2 are significantly larger than the values associated with the Vela supernova remnant (Slane et al. 2001), the remnant must lie beyond Vela (d_Vela = 0.29 ± 0.02 kpc; Dodson et al. 2003). A more restrictive lower limit can be obtained from the properties of the X-ray synchrotron emission in the northwest. Since the synchrotron cut-off frequency exceeds 10¹⁷ Hz (Pannuti et al. 2010), the shock speed must be larger than about 1000 km s⁻¹ (Allen et al. 2008), which implies that the distance $d = v_{\rm f} / \dot{\theta } > 0.5$ kpc.

Conversely, Aschenbach (2013) argues that the remnant is closer, perhaps much closer, than 0.5 kpc. This argument hinges upon the assumption that the gamma-ray emission is dominated by neutral-pion decay.²⁵ Yet, Berezhko et al. (2009) could not make such a model work if the remnant is nearby. Furthermore, if the Fermi spectrum of Tanaka et al. (2011) includes emission from both G266.2−1.2 and PSR J0855−4644, particularly at the lower end of their spectrum, then an inverse Compton scattering model may provide a better description of the gamma-ray emission from G266.2−1.2 (e.g., Katsuda et al. 2008a; Lee et al. 2013).

Early estimates of the distance, based upon evidence of line emission associated with the decay of ⁴⁴Ti, also suggest the source is nearby (e.g., d = 0.2 kpc, Iyudin et al. 1998; d = 0.1–0.3 kpc, Chen & Gehrels 1999; and d < 0.5 kpc, Aschenbach et al. 1999). However, as described in Section 3.1, this evidence is questionable.

In summary, the preponderance of the distance results suggests that G266.2−1.2 is between about 0.5 and 1 kpc from Earth. Hereafter, we assume the remnant is at a distance of 0.7 ± 0.2 kpc. Note that this assumption does not significantly affect the constraints on the age. Table 4 lists sample hydrodynamic properties for G266.2−1.2, assuming it is at a distance of either 0.5, 0.7, or 0.9 kpc. These properties include the initial kinetic energy, E₀, the mass, M_ej, and the power-law index, n, of the ejected material, the ambient density, n₀, the age, t, the radius, r_f, and speed, v_f, of the forward shock, the expansion parameter, m, the mass of the material swept up by the forward shock, M_s, and the amount of kinetic energy that has been transferred to this material, U_{KE, f}. The values in the table, which are based upon the results of the hydrodynamic study described in Section 3.1, are only meant to be representative. The values for each property can vary substantially from the listed values for individual scenarios. The value of n was arbitrarily chosen to be nine. As a result, the value of m = 2/3. The value of E₀ was arbitrarily chosen to be 10⁵¹ erg, except for the case with d = 0.5 kpc. At the closer distance, which is at the low end of the distribution in Figure 7, none of the scenarios with E₀ = 10⁵¹ erg (or with E₀ > 10⁵¹ erg) satisfied all of the plausibility criteria.