Measuring Changes in the Atmospheric Neutrino Rate over Gigayear Timescales

Measuring the cosmic ray flux over timescales comparable to the age of the Solar System, $\sim 4.5\mathrm{Gyr}$, could provide a new window on the history of the Earth, the Solar System, and even our Galaxy. We present a technique to indirectly measure the rate of cosmic rays as a function of time using the imprints of atmospheric neutrinos in “paleo-detectors,” natural minerals that record damage tracks from nuclear recoils. Minerals commonly found on Earth are $\lesssim 1\mathrm{Gyr}$ old, providing the ability to look back across cosmic ray history on timescales of the same order as the age of the Solar System. Given a collection of differently aged samples dated with reasonable accuracy, this technique is particularly well-suited to measuring historical changes in the cosmic ray flux at Earth and is broadly applicable in astrophysics and geophysics.

Figure 1

Differential distribution of the number of recoils per unit target mass and unit time ($n$) with respect to the recoil track length ($x$) for a halite paleo-detector (modeled as ${}^{23}\mathrm{Na}$ and ${}^{31}\mathrm{P}$; see text). In addition to the signal induced by interactions of atmospheric neutrinos (solid green), we also show the spectrum of background tracks induced by interactions of radiogenic neutrons (dashed orange) and the track length spectrum from spontaneous fission daughters (purple dash-dotted) assuming a ${}^{238}\mathrm{U}$ concentration of 0.01 ppb by weight, consistent with previous work on paleo-detectors [15]. See the text for a discussion of these backgrounds. Note that there are two virtually background-free track length regions: $2\mu \mathrm{m}\le x\le 20\mu \mathrm{m}$ and $50\mu \mathrm{m}\le x\le 1\mathrm{mm}$. Only recoils with $A>4$ are included; lighter nuclei are not expected to give rise to visible tracks.

Figure 2

The average recoil rate one would infer from samples as a function of their age for three different scenarios: constant atmospheric neutrino flux (green), linearly decreasing flux with a 50% drop over 1 Gyr (orange), and constant flux with a transient event where the flux is elevated by 100% for 100 Myr (purple). Error bands represent the $1\sigma$ error one would obtain on the average recoil rate from a sample of a given age, assuming that the age of samples can be determined with relative uncertainty of 5% and its mass with 1% uncertainty.