Modeling the spectrum and composition of ultrahigh-energy cosmic rays with two populations of extragalactic sources
Saikat Das, Soebur Razzaque, Nayantara Gupta
Abstract
Abstract We fit the ultrahigh-energy cosmic-ray (UHECR, $$E\gtrsim 0.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>≳</mml:mo><mml:mn>0.1</mml:mn></mml:mrow></mml:math> EeV) spectrum and composition data from the Pierre Auger Observatory at energies $$E\gtrsim 5\cdot 10^{18}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>≳</mml:mo><mml:mn>5</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>18</mml:mn></mml:msup></mml:mrow></mml:math> eV, i.e., beyond the ankle using two populations of astrophysical sources. One population, accelerating dominantly protons ( $$^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>1</mml:mn></mml:msup></mml:math> H), extends up to the highest observed energies with maximum energy close to the GZK cutoff and injection spectral index near the Fermi acceleration model; while another population accelerates light-to-heavy nuclei ( $$^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>4</mml:mn></mml:msup></mml:math> He, $$^{14}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>14</mml:mn></mml:msup></mml:math> N, $$^{28}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>28</mml:mn></mml:msup></mml:math> Si, $$^{56}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>56</mml:mn></mml:msup></mml:math> Fe) with a relatively low rigidity cutoff and hard injection spectrum. A significant improvement in the combined fit is noted as we go from a one-population to two-population model. For the latter, we constrain the maximum allowed proton fraction at the highest-energy bin within 3.5 $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math> statistical significance. In the single-population model, low-luminosity gamma-ray bursts turn out to match the best-fit evolution parameter. In the two-population model, the active galactic nuclei is consistent with the best-fit redshift evolution parameter of the pure proton-emitting sources, while the tidal disruption events could be responsible for emitting heavier nuclei. We also compute expected cosmogenic neutrino flux in such a hybrid source population scenario and discuss possibilities to detect these neutrinos by upcoming detectors to shed light on the sources of UHECRs.