Erratum: A new model for the Heliosphere's 'IBEX Ribbon' (Astrophysical Journal Letters (2017) 812 (L9) DOI: 10.1088/2041-8205/812/1/l9)

In Giacalone & Jokipii (2017, hereafter GJ17), it was noted that our numerical simulations revealed a double-humped structure within the modeled IBEX ribbon. We believe that this is an artifact of an unreported assumption used in our numerical model that was used to increase the computational speed of the calculation. The magnetic field was assumed constant over a very small fraction of the particle gyroperiod. This assumption was not reported in our original Letter. In this Erratum, we report results from a much smaller, but otherwise similar, calculation to the one presented in GJ17, which does not make this assumption, and more accurately solves for the equations of motion of the particles. We find that the double-humped pitch-angle distribution feature is not present in this case. Note also that this is briefly discussed in Zirnstein et al. (2020). Although we now conclude that the double-humped feature is not real, we find that the assumption used in our prior numerical calculations does not effect the other conclusions in GJ17. In particular, unchanged is the general conclusion that the IBEX ribbon is a region of enhanced particle intensity caused by the trapping of charged particles magnetically mirrored within turbulent fluctuations in interstellar magnetic field. We do not repeat the calculations presented in GJ17 in this Erratum. As noted above, the unreported assumption that we used had the effect of significantly reducing the computation time. Without this assumption, the calculations require considerably more computational resources than we currently have available. Thus, in order to show the importance of this assumption, we consider a much smaller problem, but with otherwise similar physics. We solve the equations of motion of charged particles experiencing the Lorentz force due to a magnetic field composed of a uniform background magnetic field, that points in the positive z-direction, and a turbulent component, which has a zero mean and a functional form that is given in GJ17. This is similar to our approach in GJ17, but here we use different parameters in order to reduce the computational resources. For instance, in this problem, we assume that the turbulent coherence length and maximum wavelength are a factor of 10 times smaller compared to that used in GJ17. Each charged particle is initially placed at (0, 0, z), where z is chosen randomly between -5 au<z<?5 au. The initial velocity vector of each particle is (v sin a0, 0, v cosa0), where a0 is the initial pitch angle. The cosine of the pitch angle, µ0, is given by cos[p 2 - tan-1(z 10 au)]. The initial pitch angle of each particle depends on where it placed along z. This is similar to the situation described in GJ17 in which there is a point source of fast neutral hydrogen atoms (in this case 10 au away from the line on which they are released in the direction normal to it), which move radially away from the source at speed V?=?440 km s-1, and become pickup ions once they are ionized through a charge exchange. Each particle is followed forward in time until it reaches a time chosen from an exponential distribution with a mean time, 10 au/V, representing the loss of particles associated with charge exchange (as discussed in GJ17). We compute pitch-angle distributions at various locations along z by binning the pitch angle along the particle trajectories, and these are discussed below. The numerical method used here is the same as that in GJ17 except that we use the correct numerical algorithm and do not assume the field is constant over any fraction of the particles’ orbit. The method, known as the Burlirsh–Stoer method, uses an adjustable time step based on an evaluation of the normalized “truncation” error (see Press et al. 1986), which we take to be 10-7. Note that we also perform a simulation in which we used the same approximation made in GJ17 in order to demonstrate its effect on the results for this problem. Figure 1(a) shows the distribution of the pitch cosine at the location z?=?0. This corresponds to the location in which particles are initially released with a pitch cosine of zero, relative to the average magnetic field. In the GJ17 study, this would correspond to the center of the IBEX ribbon. The red curve is the case of the more accurate numerical solution, discussed above, while the black curve is for the case in which we use the (incorrect) assumption that was used in our GJ17 study. We note that for the case of the more accurate numerical solution, the double-humped pitch-angle distribution is not present. We thus conclude that this feature is a (Figure Presented).