2. Age and distance
Basis for the determination of the age and distance of the new SNR is the law of radioactive chain-decay 44Ti Sc Ca, for which we have
with the definitions: f photon flux density, d distance, Y mass yield of the element A, m its atomic mass, its mean life time and t the age. For the 44Ti decay chain , so that we can neglect and the second exponential term of Eq. 1. The data available suggest 90 yrs, which we adopt for the following. This value is also close to the result of (87.7 1.7) yrs recently published by Ahmad et al. (1998). f is the flux of the 1.157 MeV line which has been measured by Iyudin et al. (1998) to (3.80.7)10-5 photons cm-2 s-1. Apart from the statistical error a systematic error should be added, which is estimated to 20%.
2.1. 44Ti and X-ray data
The range of d, t and Y of Eq. 1 can be constrained by introducing the X-results. The angular radius = 1o is related to d and t by = / d , with v the mean expansion velocity of the SNR. By substituting d or t of Eq. 1 by v a quantitative relation between and t or and d can be derived with v as a parameter. An estimate of v can be obtained from the X-ray spectra. The analysis of the ROSAT X-ray spectra is affected by the presence of the low energy emission of the Vela SNR, which is aggravated by the large size of RX J0852.0-4622. But an archival ROSAT PSPC pointing observation centred on the southeastern limb of the Vela SNR with an exposure of 11000 s happens to contain the northern limb section of RX J0852.0-4622. The number of counts is sufficient to extract a small section of the limb as well as a small section of the Vela SNR offset by just 10 arcmin to create both uniform source and background spectra. Limiting the analysis to these small regions, each 10 arcmin 10 arcmin in size, reduces the impact of any spectral and spatial non-uniformity across the source and the background. Fits to the residual northern limb spectrum were performed with a two component, optically thin thermal emission equilibrium model (Raymond-Smith model) with kT = 0.21 keV, kT = 4.7 keV and an absorption column density of N = 2.31021 cm-2. We note that the data can be fit equally well ( 1) with a straight power law with index = and absorption column density N = 1.21020 cm-2. The spectrum of the rest of the SNR can be obtained only from the ROSAT all-sky survey data and because of the relatively low exposure the spatial region selected for analysis needs to be large which increases the uncertainty in assessing the background level from the Vela SNR. For the full remnant excluding the bright northern limb an acceptable fit with 1 is obtained with a two temperature model with kT = 0.14 keV, kT = 2.5 keV and N = 4.01021 cm-2.
The matter density of the shock-wave heated SNR plasma can be derived from the observed X-ray flux via the relation = . is the cooling function for the best-fit values of kT; is the electron number density and is the number density of the un-shocked matter, intitially uniformly distributed in a sphere. Furthermore, a factor of four has been used for the density jump at the shock. The low and high temperature components are associated with densities of = 0.6d cm-3 and = 0.06d cm-3, respectively, with d2 measured in units of 200 pc. Despite the acceptable spectral fit the value of and the column density are quite uncertain, as the low temperature component could be significantly affected by the Vela SNR radiation, which is, however, not the case for .
As usual for thermal SNRs two components with different temperatures are needed for equilibrium models to fit the observed spectrum. If the plasma is far from ionization equilibrium the low temperature component appears as an artifact because of the under-ionization. The time-scale to reach ionization equilibrium is about 1012 s cm-3/ne, with ne the electron density of the radiating plasma in units of cm-3. With t = 680 yrs and the densities given above 1.5109 s cm n1010 s cm-3, which demonstrates that RX J0852.0-4622 departs significantly from ionization equilibrium. Clearly the high temperatures observed are closer to the real electron temperature. But even the high temperatures may underestimate the average temperature of the electrons and ions if the electrons are heated mainly by Coulomb collisons with the ions, which occurs on a timescale similar to that of reaching ionization equlibrium.
The X-ray temperatures which have been produced by shock wave heating can be used to estimate the velocity of the shock wave: ; is the proton mass and µ is the mean molecular weight, which is 0.6 for a fully ionized plasma of cosmic abundances. Again, this relation is for a density jump of a factor of four at the shock. Discarding the low temperature components as argued above the X-ray temperatures stretch from 1.8 keV kT2 9.2 keV including 1- errors. The mean kT2, which is consistent at the same significance level with both the radiation from the bulk of the SNR and its northern limb section, taking the thermal option, is kT2 = 4.4 keV. The corresponding best estimates of the minimal and maximal shock velocities using the relation above are 1940 km s-1, 1240 km s-1 and 2800 km s-1, respectively. The current shock velocity is related to the mean expansion velocity v by the past temporal evolution of the SNR. With the limited observations available we are forced to rely on what is known about historical remnants. The compilation of Strom (1994) provides both maximal internal shock velocity and mean expansion velocity and the ratio is 1.5 for the Crab Nebula and Cas A, 2.5 for SN 1006 and 3.5 for the Kepler and Tycho SNRs. For a purely adiabatic expansion in a uniform medium of constant matter density (the Sedov description) = 2.5. As Strom has pointed out the observed maximal internal velocities may not be strictly related to but they provide a reasonable estimate. More recently measurements of the expansion rate in the X-ray band have become available by comparing images obtained with the EINSTEIN and ROSAT observatories or even just the ROSAT images taken at different epochs. Both Koralesky et al. (1998) and Vink et al. (1998) have found an expansion rate of Cas A of 0.002% yr-1 which corresponds to a factor of 1.55 for the ratio of mean expansion rate over current expansion rate. Hughes (1996) has found a similar value for the Tycho SNR. In each of these cases, however, the current expansion velocities, using reasonable distance estimates, are significantly larger than the X-ray spectra and temperatures indicate. Therefore a factor of 1.5 for is a very conservative lower limit to estimate v from X-ray spectra.
For a worst case estimate we define a velocity range for RX J0852.0-4622 applying factors of 1.5, 2.5, 3.5 to the minimal, best-estimate and maximal , respectively, which leads to a best-estimate expansion velocity = 5000 km s-1 bracketed by a minimal expansion velocity of = 2000 km s-1 and a maximal expansion velocity = 10000 km s-1; the values have been rounded off slightly. Since we don't know whether the X-ray temperatures are associated with either the blast wave heated ambient medium or the progenitor ejecta heated by reverse shocks, the expansion velocities derived may even be lower limits. Similarly, the values are too low if the electrons have not reached thermal equilibrium with the ions. For the discussion of the impact of the expansion velocity on age and distance we note that the 44Ti line appears to be broadened (Iyudin et al. 1998), the origin of which is unknown. In the most extreme case that the width is exclusively attributed to Doppler broadening the associated velocity is (153003700) km s-1 with an upper limit of = 19000 km s-1. We include for the sake of completeness, but we stress that the use of for constraining the type of progenitor is overinterpretating the -ray data and it is essentially misleading. Nevertheless, we add that Nagataki (1999) quotes expansion velocities 12000 km s-1 for sub-Chandrasekhar mass models of SNe Ia.
Fig. 2 shows the relation between and the age t of RX J0852.0-4622 parametrized by v. Despite the large uncertainty of v, t is determined to within 100 yrs for fixed using v of the X-ray data. For = 510-5 M and v = , t = 680 yrs and d = 200 pc (c.f. Fig. 3). Age and distance are rather insensitive to the exact value of the 44Ti -ray line flux. A total error of the flux of 40%, which is the sum of the statistical error and the systematic error, broadens the range of t by 40 yrs and that of d by 10 pc. If RX J0852.0-4622 is expanding as fast as indicates the age would be as low as 500 yrs. Model calculations provide a range for , which runs for symmetric core-collapse supernovae from 1.410-5 M to 2.310-4 M, depending on progenitor mass (Woosley & Weaver 1995, Thielemann et al. 1996). Within this range () is within (500 yrs, 400 pc) and (950 yrs, 80 pc). Nagataki et al. (1998) have pointed out that could be much higher in an axisymmetric collapse-driven supernova. For example, in their model with the highest degree of asymmetry they obtain = 5.110-4 for = 0.07 M. This value of would allow an age of up to 1000 yrs. For type Ia supernovae we find 7.910-6 M 4.710-5 M for carbon deflagration models (Nomoto et al. 1984, Iwamoto et al. 1999), which do not significantly differ from the core-collapse SNe, and accordingly the range for () is not affected. Values of as high as 210-3 M are obtained in He-detonation models (Woosley & Weaver 1994). This would allow () to lie between (850 yrs, 500 pc) and (1100 yrs, 100 pc). In summary, for any given by current models the upper limit of the distance of RX J0852.0-4622 is 500 pc and 1100 years for the age.
Chen & Gehrels (1999) have also used the X-ray temperature to derive age and distance, although in a slightly different manner. They use the temperature derived from the ROSAT data for the central region (Aschenbach 1998) which might not be representative for the current expansion velocity at the rim, why we prefer a somewhat higher velocity consistent with the apparently higher temperature observed at the limb. For the mean expansion velocity, which should be higher than the current expansion velocity by some factor, Chen & Gehrels derive a range of 2000-5000 km s-1, whereas we propose a range of 2000 km s-1 to 10000 km s-1 by comparison with observational data obtained for the historical remnants. For given velocity and our results agree with those obtained by Chen & Gehrels, but our estimates allow a wider range of age and distance.
2.2. 44Ti ionization
44Ti decays by electron capture, which means that lifetime depends on ionization stage, in particular to what extent the K shell is populated. The 44Ti lifetime of 90 yrs is the mean lifetime for two electrons in the K-shell irrespective of the number of electrons in the higher shells. For just one electron in the K-shell, the hydrogen-like state 44Ti+21, the lifetime is expected to be about twice as long, and for the fully ionized atom 44Ti+22 the lifetime is . Eq. 1 gives the decay rate for the ionic fraction Ti = 0 (full ionization), Ti = 0 (one electron in the K-shell) and Ti = 1. For Ti 1 Eq. 1 is modified by introducing the ionic fraction Ti with = 90 yrs and Ti with = 2 90 yrs; the impact of Ti has been neglected because of its comparatively low contribution to f. The solution for t of Eq. 1 for either the `ionization' or the `no-ionization' case is done with the same f. As before also d and t are not independent of each other but constrained by and v, which means that not only t but also d is to change for the `ionization' case compared to the `no-ionization' case. So the comparison is done with the same v but not with the same d. Furthermore v is constrained by the X-ray spectra and the impact of the uncertainty of v on d and t has been given in the previous section. If t = for = 1 and t = for 1 Eq. 2 describes the change of the age in terms of .
The ionization stage of 44Ti of GRO J0852-4642 is not yet known, but a case study is useful to demonstrate quantitatively the impact of the ionization on the estimate of t and d. If 44Ti would have been heated to around kT = 4.4 keV like the X-ray emitting plasma, e.g. by a reverse shock propagating in the ejecta and if 44Ti is in ionization equilibrium the ionic fractions can be extracted from literature. Titanium has not been tabulated so far but the distributions of the ionic fraction of calcium and iron are available, which are taken as case representative examples. Arnaud & Rothenflug (1985), for instance, computed = 0.086, = 0.339 and 57.5% of Ca completely ionized for log T = 7.8. Using Eq. 2 = 680 yrs increases to = 930 yrs as does d by the same factor of q. For iron, which has = 0.686 and = 0.269 at log T = 7.8, = 900 yrs, which is very close to the result obtained for Ca, despite a significantly different distribution of the ionic fractions. For higher temperatures, e.g. log T = 8.5, = 0, = 0.0465 and 95.4% of Ca is completely ionized. For this ionic fraction distribution q = 1 and t and d are unchanged although only 4.65% of the total decays radioactively. For even lower values of , i.e. a larger fraction of totally ionized 44Ti, or the age becomes even lower. Using the distribution of the ionic fractions of iron at log T = 8.5, q = 1.28. Clearly, the ionization of Ti has an impact but of moderate size. Values of t and d may be underestimated by some 30% when the ionization starts to affect the K-shell population and they may be even unchanged if only some 10% or less of the Ti has just one electron in the K-shell but is otherwise completely ionized.
Quite recently Mochizuki et al. (1999) have modelled the heating and ionization of 44Ti by the reverse shock in Cas-A, for which they report the possibility of a currently increased 44Ti activity. With respect to RX J0852.0-4622 / GRO J0852-4642 they find that the reverse shock does not heat the ejecta to sufficiently high temperatures to ionize 44Ti because of the low ambient matter density. Future X-ray spectroscopy measurements may answer the question of ionization. But independent of the outcome this section shows that even if ionization were significant it does not change the conclusion that RX J0852.0-4622 / GRO J0852-4642 is a young nearby SNR.
2.3. Explosion energy E0
The Sedov relation , which has been adopted for describing the adiabatic expansion of an SNR of radius R in a homogenous medium of matter density , has been used quite often in the past to estimate the explosion energy E0 associated with the supernova (Winkler & Clark 1974, Pfeffermann et al. 1991). The limitations of this approach are well known. The X-ray spectra provide , from which v is derived, the X-ray flux is proportional to via (cf. Sect. 2.2) and the X-ray image shows the angular extent . With the Sedov relation is not yet uniquely determined but can then be expressed as a function of a single variable, for instance t. Since for RX J0852.0-4622 t can be related to via Eq. (1), is a function of . In contrast to the relation , is constrained because of the limited range of , at least towards the higher end. Fig. 4 shows for various v, because v is not uniquely determined by the X-ray spectra.
For the reference values of = 510-5 M and v = = 5000 km s-1, = 2.61049, which is a factor of about 40 less than the canonical = 1051 erg. With v = 5000 km s-1 this value can not be reached with a realistic ; even a value of = 1050 erg is hardly consistent with reasonable values at v = 5000 km s-1. It is interesting to note that a similarly low value of , i.e. 4.41049 erg s-1 have been derived by Willingale et al. (1996) for the SNR of SN 1006, with which RX J0852.0-4622 shares a number of other similarities like the X-ray appearance and the ratio of radio to X-ray surface brightness (Aschenbach 1998). For the reference value of d = 200 pc the total swept-up mass of RX J0852.0-4622 is less than one solar mass, which means that the slow-down of the remnant expansion may not be dominated by , so that the applicability of the Sedov relation may be questioned. The radial evolution depends then on the details of the explosion rather than just on . For instance, most of the kinetic energy of the SN may be in matter which does not radiate in X-rays.
could be raised by increasing . The slow down could have occurred at times when regions of higher density might have been passed by the shock wave, e.g. if the progenitor star had produced a strong stellar wind. For a mass loss rate of 10-5 Myr-1 and a wind velocity of 1000 km s-1 the wind number density would exceed 104 cm-3 within a radius of about 61015 cm and X-rays would have been emitted from this region. Lower wind velocities like those typical of red supergiants would increase the size accordingly. The emission region would expand to a measurable size over the 700 yrs but both radiative cooling and adiabatic expansion are likely to have reduced the flux below the detection limit. Nevertheless, we point out that the ROSAT image shows weak but enhanced emission from the central 15´ diameter region (c.f. Fig. 1).
For higher values of v, e.g. for v = = 10000 km s-1 and = 510-5M, = 2.91050 erg is relatively close to the canonical E0, but the swept-up, X-ray radiating mass is still just 1 M. Basically, because of the low and the maximal value of d consistent with the swept-up, X-ray radiating mass never exceeds a few solar masses.
In summary, E0 is not very sensitive to (c.f. Fig. 4) but instead to the mean expansion velocity v. Taking the full range of v indicated by the X-ray spectra it follows that 1049 erg E0 31050 erg for a Sedov-type expansion.
The energy budget made of E0 and the kinetic and thermal energy observed can be used to constrain the mass of the progenitor. The total energy Ex of the X-ray radiating mass, i.e. the sum of the kinetic energy and the thermal energy, amounts to Ex = 41048 erg s- 1 with in units of 1000 km s-1. Since the maximum velocity of the ejecta should not exceed the uniform expansion velocity v , which for the adiabatic case is 2.5, a lower limit of the ejecta mass Mej is with Mej in M and E in 1051 erg. For v = = 5000 km s-1 4 M, i.e. a massive progenitor is required for E = 1, whereas a low mass progenitor with M 0.9 M is consistent with the data for v = = 10000 km s-1. A more massive progenitor is required if the bulk of the ejecta mass is moving at significantly lower velocities.
Another approach to constrain the progenitor and the supervova type has been taken by Chen & Gehrels (1999). They have used the shock wave velocity indicated by the X-ray temperature observed in the central region of the SNR and used this as the current expansion velocity. By comparison of this velocity with that predicted by SN explosion models and their subsequent evolution into an ambient medium of constant matter density, they conclude that the likely progenitor of the SNR was a massive star of 15 M with a type II explosion, solely based on the relatively low value of the current expansion velocity v inferred from the X-ray temperature. Lower mass progenitors like those leading to a SN of type Ia are supposed to have significantly higher ejecta velocities and according to Chen & Gehrels an ambient matter density 500 cm-3 is required to decelerate the explosion wave from initially 11000 km s-1 to the current value of 1300 km s-1, using the relation v t (Chen & Gehrels, 1999). If we use the standard Sedov-Taylor relation of v t instead, i.e. the asymptotic limit of the evolution into a uniform medium of constant matter density, a much lower ambient density of 1.4 cm-3 is sufficient to reduce the ejecta speed from 11000 km s-1 to v = 3900 km s-1 (the upper limit of v estimated by Chen & Gehrels) in 1000 years for an ejecta mass of one solar mass and E0 = 1051 erg. Although this ambient density still exceeds the observed value by a factor of 30 it is not unreasonable in comparison with other SNRs and ISM densities. Different ejecta mass, explosion energy and non constant density distributions, in particular, might reduce the required matter density further. In contrast to Chen & Gehrels we are therefore very reluctant to rule out a SNIa for RX J0852.0-4622 based on just the X-ray temperature.
2.4. 44Ti, 26Al and the supernova type
After the discovery of its X-ray emission in early 1996 it was attempted to identify RX J0852.0-4622 as a source contributing to the 1.8 MeV 26Al -ray line emission from the Vela region, which had been mapped with the COMPTEL instrument (Oberlack et al. 1994, Diehl et al. 1995). Because of its identifaction as an SNR and because of its apparently low distance RX J0852.0-4622 was considered a good candidate to provide a measurable amount of the 26Al -ray line emission. 1.8 MeV -ray lines are emitted in the radioactive decay of 26Al, which is processed and released in supernovae but in other sources as well. The 1.8 Mev Vela source appears to be extended with a significant peak at about lII = 267.4o, bII = -0.7o. Oberlack (1997) has used the ROSAT X-ray map of the Vela region to model the 1.8 Mev -ray map, taking into account the full size of the Vela SNR, the Vela SNR explosion fragments (Aschenbach et al. 1995), RX J0852.0-4622 and other potential sources. He found two "COMPTEL point-like" sources which could contribute significantly to the -ray peak, which are the Vela SNR fragment D/D´ and RX J0852.0-4622. The peak position and the center position of RX J0852.0-4622 agree within the 2- localization accuracy of COMPTEL, and the 1.8 Mev point source flux is f = (2.20.5)10-5 photons cm-2 s-1 out of the total Vela flux of f = (2.90.6)10-5 photons cm-2 s-1. Recently, Diehl et al. (1999) reported a 2- upper limit of 210-5 photons cm-2 s-1 for a contribution of RX J0852.0-4622 to the overall Vela emisson. This result is not really in conflict with the result of Oberlack, which we are going to use in the present paper. As we show below most of the our conclusions do not depend on the precise value of f anyway. If f is to be attributed to a single SNR with a representative yield of = 510-5 M it follows from Eq. (1) that the distance of the source would be (160 20) pc using a mean lifetime of = 1.07106 yrs. Because this excitingly low distance for an SNR was not supported by any other measurements at that time and because of other competing 26Al sources like the Vela SNR fragment D/D´ the results were not published.
But after the discovery of the emission, which immediately implies a low age because of its short lifetime and a correspondingly low distance because of the X-ray angular diameter, the situation has changed and both the 44Ti and the 26Al flux may indeed come from a single supernova now visible as the RX J0852.0-4622 SNR. Because of the uncertainty of the amount of f actually to be attributed to RX J0852.0-4622 we discuss two cases in the following chapters: a.) f is entirely from RX J0852.0-4622; b.) f is not entirely associated with RX J0852.0-4622 but then the COMPTEL data provide a firm upper limit of f = 3.510-5 photons cm-2 s-1, which is the total flux observed for the entire Vela region.
Eq. 1 can be used to compute the age of RX J0852.0-4622 by using the fluxes of just the two radionuclides, making use of :
Interestingly, the age determination does not require knowledge of the distance, and it depends only on the ratio of the mass yields of the two elements considered, which might be useful for further searches for young SNRs. For f = f and = 1, = (750 25) yrs. This age agrees remarkably well with the age t = = 680 yrs which has been derived from the 44Ti data and the X-ray measurements, and it appears to support the identification of RX J0852.0-4622 being the source of both the 44Ti and the 26Al emission. Furthermore the value of is not very sensitive to the precise value of ; even if only one fifth of , e.g., is actually associated with RX J0852.0-4622, is reduced by just 145 yrs.
Some interesting conclusions can be drawn about the type of the supernova by making use of model produced values of (. The core-collapse models of Woosley & Weaver (1995) give 0.1 4.1 for progenitor masses between 11 M and 40 M for initial solar metallicity, excluding their models with M. This leads to = (540-880) yrs 30 yrs. Fig. 5 shows the () - plane of the core-collapse model data (S-sequence of solar metallicity) of Woosley & Weaver (1995); pairs of () with greater than the values cut by the line of fixed v are not consistent with f. Fig. 5 demonstrates that the models of Woosley & Weaver (1995) are consistent with relatively low expansion velocities, most of them with 5000 km s-1, which fits nicely the expansion velocity estimated from the X-ray temperature. For increasingly lower metallicity, of the Woosley & Weaver computations decreases and eventually the data of all the Z = 0 models are above the v = 5000 km s-1 cut, except the models for which 10-8 M. We note that the data of the models S18A, S19A and S25A describing the explosion of the progenitor with a mass of 18 M, 19 M and 25 M, respectively, are closest to the v = 5000 km s-1 line. This appears to be in rather good agreement with the conclusion which has been derived from the energy balance described in Sect. 2.3.
The core-collapse models of Thielemann et al. (1996) for masses between 13 M and 25 M show similar values of but significantly lower values of because only the yields of the explosively produced elements are given (Thielemann, private communication, 1999). Therefore is to be treated as lower limit, and the applicability to RX J0852.0-4622 remains unanswered at this stage.
Interestingly, Woosley & Weaver (1995) have also calculated the yields of models with very little output of , from which the supernova power is being drawn after a possible plateau phase. Models with a small yield of , which may explain the sub-luminous supernovae after the early phase, also have low but relatively high values of , which is produced predominantly in the upper envelope by ordinary burning. The yields predicted by Woosley & Weaver for solar metallicity are shown in Fig. 5 as well. Clearly, the ratio of is very high and it is too high to be consistent with the observations. Given the low value of , is simply too large. Such large values have to be checked against f. f requires a minimal d for a given , which in turn requires a maximal t to be consistent with . Minimal d and maximal t define a minimal expansion velocity for the angular diameter not to exceed . Fig. 5 shows that the Woosley & Weaver models require very large values of v Such high mean expansion velocities after some 700 yrs are unlikely and it is evident that these models cannot explain the RX J0852.0-4622 measurements primarily because they are inconsistent with the upper limit of the 26Al flux. Furthermore, the models of Woosley & Weaver show a signficant gap for , which covers the range 310-8 M 10-5 M. This gap might be artificial and further model calculations are required to check, whether the fall-back of matter towards the center of the explosion chokes the production of the high-Z elements to the extent shown by the current explosion models. Models with somewhat lower values of both and would be consistent with the observations, and a lower value of might mean a low value of as well, which allows for a sub-luminous supernova although the connection between low Y and low kinetic energy and luminosity is not yet well established.
Models for type Ia supernovae predict a much higher ratio of (); Iwamoto et al. (1999) predict 16 470 and the sub-Chandrasekhar models of Woosley & Weaver have 280 930. These values correspond to a relatively large t (Eq. 3) and a low d with = , which results in a relatively low value of the mean expansion velocity, i.e. 50 km s-1 275 km s-1 for the models of Iwamoto et al. and 180 km s-1 1060 km s-1 for the models of Woosley & Weaver. These values are well below the lower limit velocity of = 1240 km s-1 and are therefore inconsistent with the X-ray temperature measurements. It appears that the type Ia model predictions are in serious conflict with the measurements, thus excluding type Ia models from explaining RX J0852.0-4622. But this conclusion hinges on the assumption that = is actually associated with RX J0852.0-4622. If only a minor fraction of 1% of is due to RX J0852.0-4622, also type Ia models may be reconsidered. For this case d and t are given in Sect. 2.1.
© European Southern Observatory (ESO) 1999
Online publication: October 14, 1999