Paolo Desiati's activity

Cosmic rays arrival direction distribution has an energy-dependent large angular scale anisotropy with an amplitude of order 10^-3-10^-4. The first comprehensive study was was provided by a network of muon detectors sensitive to sub-TeV energies and located at different latitiudes (Nagashima et al., J. Geophys. Res., 103, 17, 429, 1998).

Relative Intensity Map

The observations revealed the evidence of a superposition of two different modulations in arrival direction. One with a sidereal variation identified with an extended deficit centered around 12 hours that seems to extend mostly across the northern hemisphere (the so-called loss cone). And one with a sidereal variation identified with a broad excess centered around 6 hours, with half opening angle of about 68$^{\circ}$ that comprises the direction of the heliotail, and extended across part of the northern and the southern hemispheres (the tail-in excess). The figure above shows the cosmic ray sidereal daily variation from the different telescopes (each with a different energy threshold scale) and directions.

Relative Intensity Map

The anisotropy features persist in the multi-TeV energy region, where small angular scale features seem to overlap to the smooth broad modulation. The Tibet ASγ array (Amenomori et al., Science, 314, 439, 2006) observed cosmic rays arrival direction distribution at different median energies in the multi-TeV region (see figure above). While the loss-cone deficitstructure seems to persists its global structure with increasing energy, the tail-in excess seems to break up in a few smaller scale structures.

The MILAGRO collaboration (Abdo et al., Phys. Rev. Lett., 101, 221101, 2008), using experimental analysis techniques used in γ ray searches, filtered out all anisotropy features wider than 30° and revealed two localized regions of multi-TeV (1-10 TeV) cosmia rays. The most significant region A (10σ) coincides with the direction of the heliotail (the black dot in the figure above).

A localized excess of multi-TeV cosmic rays is more likely produced by perturbations in their directional propagation, that occur nearby, with respect to their gyro-radius (70-700 AU in a 3 μG magnetic field for protons with energy of 1 and 10 TeV, respectively). Sub-TeV cosmic rays should hardly have small angular scale structures, even is local causes are responsible for thei origin. Scattering in magnetic field is more significant al low energy. It is likely that the broad tail-in excess at sub-TeV energies and the localized excess in the multi-TeV range, are manifestations of the same local phenomenology, which involves the heliotail.

Relative Intensity Map

The 11-year solar dynamo cycle generates magnetic field of opposite polarities. As the magnetic field is carried away by the ~ 450 km/sec solar wind, the reversed field regions are accumulated and compressed in the heliotail region. This is where magnetic reconnection is expected to occur. Turbulence is also expected to exis, which affects reconnection speed, i.e. the speed at which in-flowing magnetic field is annihilated by ohmic dissipation.

Relative Intensity Map

In the Sweet-Parker model of reconnection (Sweet P.A., Conf. Proc. IAU Symposium 6, Electromagnetic Phenomena in Cosmical Physics, 123, 1959; Parker E., J. Geophys. Rev., 62, 509, 1957) the outflow is limited within the width of transition zone Δ, which is determined by ohmic diffusivity (see top of figure on the left). In the Lazarian-Vishniac model of reconnection of weakly stochastic magnetic field (Lazarian A., Vishniac E.T., ApJ, 517, 700, 1999), the outflow is limited by the diffusion of magnetic field lines, which depend on turbulence (see center of figure above). Reconnection rate, as a consequence, is increased by the turbulence effect of many magnetic field lines. IN particular, reconnection speed is close to the turbulent velocity of the medium.

Relative Intensity Map

Magnetic reconnection regions are possible acceleration sites of cosmic rays. As a particle bounces back and forth between converging magnetic field lines, it gains energy through first order Fermi acceleration mechanism. The energy spectrum taht results from acceleration is expected to be steeper than the one from shock acceleration, but similar to that of diffuse cosmic rays. The maximum energy that protons can reach under this process depends on the magnetic field and the size of the acceleration region L_zone ~ 670 AU between the 11-year solar cycle magnetic field polarity reversals in the heliotail. This provides E_max ~ 50 TeV.

More detailed calculations should provide a more accurate estimations. We can predict that, unless some process of magnetic field amplification occurs in the turbulent heliotail, the acceleration of cosmic rays of energy much larger than 10 TeV is unlikely possible with magnetic reconnection. This is about the enrgy scale at which MILAGRO observed an apparent cut-off of the cosmic rays from the localized regions.

This study has still exploratory character. Detailed simulations are needed to derive the actual quantification of this phenomenology. Nevertheless the proposed scenario has more realistic grounds than the other models currently proposed to explain the MILAGRO localized excess regions of cosmic rays.

Paolo Desiati
(August 3^rd, 2010)

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