The cosmic-ray proton spectrum measured near Earth is usually decomposed into a smooth Galactic background plus the contributions of discrete, recent supernova remnants (SNRs) within about 1 kpc of the Sun. Under a three-dimensional convection-diffusion model with burst-like injection, Thoudam (2006) found that the background plus all known nearby SNRs underpredicts the observed local proton flux below about 100 GeV, and inferred a 'missing' source with characteristic age of order 10510^{5} yr at a distance of order 0.10.1 kpc that has never been detected in radio or X-ray surveys; the same source predicts a dipole anisotropy of order 5×10−35\times10^{-3}, above the measured ∼10−3\sim10^{-3} level. Two decades of follow-up work — injection-history studies; precision measurements by Voyager 1, AMS-02, CALET and DAMPE; Local-Bubble diffusion models — have left the problem open: no 10510^{5}-yr remnant at ∼0.1\sim0.1 kpc has been either identified or quantitatively excluded, the decomposition of the sub-TeV proton spectrum between discrete nearby sources and a smooth background with modified local diffusion remains contested, and the predicted-versus-measured anisotropy tension is explicitly acknowledged as unresolved in current literature.

Background

Galactic cosmic rays (CRs) are relativistic charged particles, mostly protons, arriving at Earth almost isotropically. The near-equality between the power supernovae supply to the Galaxy and the power needed to maintain the Galactic CR energy density argues that most CRs up to PeV energies are accelerated at the shock waves of supernova remnants (SNRs) by diffusive shock acceleration, a first-order Fermi process in which particles gain energy by repeatedly crossing the shock. After escaping a remnant, CRs wander through the magnetized interstellar medium (ISM) in a process well described as diffusion, with an energy-dependent diffusion coefficient D(E)D(E); in the solar neighborhood a standard parametrization is D(E)=D0(1+E/E0)αD(E)=D_{0}(1+E/E_{0})^{\alpha} with α≈0.6\alpha\approx0.6 and D(10 GeV)≈1028 cm2 s−1D(10\,\mathrm{GeV})\approx10^{28}\,\mathrm{cm^{2}\,s^{-1}}, constrained mainly by the observed ratio of secondary to primary nuclei (for example boron to carbon). Below a few tens of GeV the spectrum measured near Earth is further reshaped by solar modulation — energy losses and geomagnetic cutoffs imposed by the solar wind — while the Voyager 1 spacecraft has directly measured the unmodulated local interstellar spectrum (LIS) outside the heliosphere.

Because diffusion is slow, only supernova explosions within roughly 1.5 kpc of the Sun contribute appreciable time-dependent variations to the local proton flux; more distant sources blend into a quasi-stationary background. Thoudam (2006) constructed the local CR proton spectrum from GeV to 100 TeV by separating these components: a continuous source distribution in space and time for the distant background, and a discrete space-time treatment for the known nearby SNRs (among them Vela, Monogem, Geminga and the Cygnus Loop), assuming burst-like, effectively instantaneous injection at explosion time t=0t=0. He found that the background plus the known nearby remnants underpredicts the observed proton flux below about 100 GeV, and that the deficit is repaired only by one additional, unidentified 'missing' source of characteristic age t∼105t\sim10^{5} yr at a distance r∼0.09r\sim0.09–0.10.1 kpc. Such an old, very close remnant would be faint in radio and X-rays — its electrons would no longer be energetic enough for strong synchrotron emission — while still a strong local proton source, and would subtend tens of degrees on the sky; whether it can hide at present survey sensitivities is an open observational question. The claim also implies a dipole anisotropy (a tiny dipolar asymmetry in the CR arrival directions) of order 5×10−35\times10^{-3}, whereas air-shower experiments such as the High-Altitude Water Cherenkov Observatory (HAWC), a ground-based detector of the particle cascades that TeV cosmic rays produce in the atmosphere, measure dipole amplitudes of (0.5–1)×10−3(0.5\text{–}1)\times10^{-3} at TeV energies.

Modern data sharpen the question. The Alpha Magnetic Spectrometer (AMS-02) on the International Space Station measured the proton spectrum precisely up to a rigidity (momentum per unit charge) of 1.8 TV and found a hardening above about 300 GV; the DArk Matter Particle Explorer (DAMPE) measured protons to 100 TeV and the Calorimetric Electron Telescope (CALET) to about 10 TeV, finding a softening or bump at roughly 10 TeV; Voyager 1 fixed the low-energy LIS. The Sun sits inside the Local Bubble, a hot, low-density cavity carved by recent supernovae, in which CR diffusion may be locally suppressed; and radioactive 60Fe{}^{60}\mathrm{Fe} deposits in deep-sea crusts, together with 60Fe{}^{60}\mathrm{Fe} in cosmic rays, record supernova activity within a few hundred parsecs during the last few million years — though at Myr rather than 10510^{5}-yr ages. Whether the local proton spectrum requires discrete, 10510^{5}-yr-scale nearby sources, or is fully explained by a smooth background with modified local propagation, is the unresolved issue that this problem addresses.

Problem Statement

Determine the discrete nearby-source content of the local cosmic-ray proton spectrum in the solar neighborhood, and in particular the status of the predicted missing old, close supernova remnant. The question has three jointly necessary parts, all anchored to the measured local proton spectrum from the Voyager 1 local interstellar spectrum up to about 100 TeV (AMS-02, CALET, DAMPE):

(1) Spectrum decomposition. Quantify the contribution of discrete nearby supernova remnants relative to the smooth Galactic background. Specifically, does the flux below about 100 GeV require, in addition to the background and the known nearby SNRs, at least one source with characteristic age t∼105t\sim10^{5} yr at distance r∼0.1r\sim0.1 kpc, as found by Thoudam (2006) under burst-like injection with an α=0.6\alpha=0.6 diffusion coefficient — and does this requirement survive realistic energy-dependent escape of CRs from the remnant, alternative diffusion-coefficient behaviors, and locally modified diffusion inside the Local Bubble?

(2) Source existence. Does such an old (∼105\sim10^{5} yr), very nearby (∼0.1\sim0.1 kpc) supernova remnant exist? This means either the identification of a candidate object in modern radio, X-ray and gamma-ray survey data, with distance and age estimates placing it in the required range, or a quantitative demonstration that all-sky survey sensitivities and completeness exclude a remnant of that age and distance energetic enough to supply the required proton flux.

(3) Anisotropy consistency. Is the dipole anisotropy induced by the required nearby-source contribution consistent with the measured large-scale anisotropy, given the uncertainties in the local magnetic field, heliospheric effects and local diffusion? The predictions to be reconciled with the measured dipole are the energy-independent geometric estimate ξ∼5×10−3\xi\sim5\times10^{-3} tied to the sub-100 GeV missing-source claim (Thoudam 2006) and, at TeV energies, the model dipole of (1.1–6)×10−3(1.1\text{–}6)\times10^{-3} at 1-100 TeV versus the measured amplitudes of (0.5–1)×10−3(0.5\text{–}1)\times10^{-3} (Bhadra et al. 2025; HAWC).

A complete answer provides a quantified, data-consistent decomposition of the local proton spectrum into background plus discrete nearby components across roughly 1 GeV to 100 TeV, together with, for any source found to be required, either its observational identification or a demonstrated exclusion, and an assessment of the resulting anisotropy.

References

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