Dependence of the neutron monitor count rate and time delay distribution on the rigidity spectrum of primary cosmic rays

Neutron monitors are the premier instruments for precisely tracking time variations in the Galactic cosmic ray flux at GeV-range energies above the geomagnetic cutoff at the location of measurement. Recently, a new capability has been developed to record and analyze the neutron time delay distribution (related to neutron multiplicity) to infer variations in the cosmic ray spectrum as well. In particular, we can determine the leader fraction L, defined as the fraction of neutrons that did not follow a previous neutron detection in the same tube from the same atmospheric secondary particle, from time delay histograms. Using data taken during 2000-2007 by a ship-borne neutron monitor latitude survey, we observe strong dependences of the count rate and L on the geomagnetic cutoff. We have modeled this dependence using Monte Carlo simulations of cosmic ray interactions in the atmosphere and in the neutron monitor. We present new yield functions for the count rate of a neutron monitor at sea level. The simulation results show a variation of L with geomagnetic cutoff as observed by the latitude survey, confirming that these changes in L can be attributed to changes in the cosmic ray spectrum arriving at Earth's atmosphere. We also observe a variation in L with time at a fixed cutoff, which reflects the evolution of the cosmic ray spectrum with the sunspot cycle, known as solar modulation.