3. The data and its interpretation
In Fig. 1 we show the predictions for the relative abundances of the V isotopes to be expected based on the standard Leaky Box propagation model (Lukasiak et al., 1994, 1997a), along with the combined measurements of the V isotopic composition from the Voyager (Lukasiak et al., 1997a) and ISEE spacecraft (Leske, 1993). This model assumes no decay of the K-capture isotopes. The ionisation losses in the interstellar medium are included in the calculation. The value of the characteristic time for escape from the confinement volume is tuned to fit accurately the B/C ratio below 1 GeV/nuc. Using this ratio as a reference gives the other calculated secondary to primary ratios for nuclei with mass number 10 to 15 to the same accuracy as the B/C ratio can be measured (Webber & Soutoul 1989). The values of isotopic abundance ratios of mainly secondary isotopes in the iron group are very weakly dependent on the value of this characteristic time for escape taken within reasonable limits: a change of the characteristic time for escape (a free parameter of the calculation) resulting in a change of 20% of the calculated B/C ratio results in a corresponding change of about 2% of the 51V /49V ratio. This and other isotopic ratios do depend on the cross sections - mainly from 56Fe which have been measured to an accuracy of a few percent (Webber, Kish and Schrier, 1990a) and the secondary production as a function of energy from Mn and Cr which can be calculated from the parametric formula (Webber, Kish and Schrier, 1990b). The ratios of the V isotopes are of course, very sensitive to the K-capture decay of 51Cr and 49V but not on the density of the medium where attachment and other catastrophic losses are taking place. The Voyager and ISEE measurements in combination and individually (see original references) clearly show both an enhancement of 51V and a depletion of 49V relative to the predictions, as is expected if some decay has occurred. In Fig. 2 we show the predicted and observed isotopic fractions of V. In Fig. 3 we show the 51V/49V ratio as a function of energy - in effect the combined effects of 49V depletion and 51V enhancement. We note that the predicted ratio of these isotopes assuming no K-capture decay is almost constant with both energy and modulation level at a value of 0.21. (The solar modulation levels are = 480 MV for Voyager and = 700 MV for ISEE-3). The ratio of 51V/49V measured by Voyager is somewhat larger than that of ISEE-3 but both of the observed ratios are much larger than the predicted value of 0.21. We believe this provides convincing evidence that this decay has indeed occurred in interstellar space. This conclusion is not affected by the uncertainties or the abundances at the cosmic rays source. The abundances of isobars 49(Ti) and 51(V) at the cosmic ray source, taken solar (and decayed) are a small fration ( 3%) of the spallogenic yield.
The question of what this evidence for decay means in terms of possible interstellar re-acceleration and/or interplanetary energy loss is somewhat more difficult to answer, however. The base 51V/49V ratio in Fig. 3 is calculated using the standard numerical diffusion-convection model for interplanetary modulation (Goldstein, Fisk and Ramaty, 1970), in which the effective average interplanetary energy loss is 240 MeV/nuc for the Voyager measurement and 350 MeV/nuc for the ISEE measurement as a result of the different modulation levels. No attachment is assumed. We now calculate the expected ratios assuming that radiative attachment occurs and that the attachment energy is the same as the current interstellar energy. The average measurements energy are 210 and 300 MeV/nuc for the Voyager and ISEE-3 instruments. The predicted ratios are now larger (but still smaller than the data) since some decay ( 10-20%) is expected to occur even at the current interstellar energies for Voyager and ISEE. These predictions, shown as the dashed curves in Fig. 3, are now split because of the different interstellar energies of the two measurements. To match more closely the observed and predicted ratios we must assume that either; 1) There has been some energy gain between attachment and the current energy of these isotopes in interstellar space or 2) interplanetary energy loss is less than that assumed in the standard modulation models. The dotted curve in Fig. 3 shows the prediction if attachment takes place at an interstellar energy 100 MeV/nuc below that of the observations. This curve represents the observations quite well.
Only radiative attachment has been considered here. Non-radiative attachment (the so called Brinkman-Kramers cross section on heavy ions) has not been calculated theoretically. Measurements suggest that this cross section is 1% of the radiative one down to 300 MeV/nuc (interstellar energy) in a medium with interstellar composition (Raisbeck et al. 1978, Crawford 1979).
© European Southern Observatory (ESO) 1998
Online publication: July 27, 1998