Cosmic Ray Spectra and Metal Budget Regulated by the Galactic Wind

TL;DR

The paper addresses how advection by a Galactic wind shapes local cosmic ray spectra, showing that a wind profile with a maximum speed of $V_0 \approx 700~\mathrm{km\,s^{-1}}$ and a diffusion law $D(p)=D_0(\mathcal R/1\,\mathrm{GV})^{\delta}$ can reproduce the observed spectral hardening around a few hundred GV and softening near TV without modifying the diffusion index. A decelerating wind beyond a launching region yields a sharp spectral bump around ${\cal R}\sim\mathrm{TV}$, and an enhanced CR density at $z\sim3$–$5$ kpc produces a hard spectrum ($\sim$ index $2$) favorable for the Fermi bubbles' gamma-ray emission from $\pi^0$ decay. The work further links CR transport to galaxy evolution by analyzing gas circulation and metal budgets, finding that wind-driven outflows are needed to regulate disk metallicity while Be production from CR spallation is insufficient to sustain disk Be, implying a higher Be/O ratio in the halo as a fossil signature of past CR density. Overall, the study highlights wind advection as a crucial mechanism connecting CR physics with Galactic gas flows and chemical evolution, while outlining observational and theoretical questions about wind parameters and Be enrichment.

Abstract

We study the advection effect of the Galactic wind on the local cosmic ray spectra. The spectral hardening from a few hundred GV and softening from a few TV are reproduced by a velocity profile with a maximum velocity of $\sim 700~\mbox{km}~ \mbox{s}^{-1}$ without introducing a break in the power-law dependence of the diffusion coefficient. Additionally, we find that a hard CR spectrum below $\sim$ TV with an index of $\sim 2$ at an altitude $\sim 3$-$5$ kpc from the Galactic disk. This hard spectrum is favorable for the gamma-ray spectrum of the Fermi bubbles. With the obtained CR fluxes, we discuss the matter circulation in our Galaxy with the wind. While the wind has an essential role in maintaining the metal abundance in the disk, the production rate of Beryllium, which originates from CR spallation, is so low that the ratio Be/O in the halo should be larger than that in the disk gas.

Figures (10)

• Figure 1: The total Hydrogen density at $R=8.5$ kpc (upper) and wind velocity profile (lower) in our model. The red line in the upper panel is the wind density profile with the mass loss rate of $7.26\times 10^{-3}M_\odot \hbox{kpc}^{-2}\hbox{yr}^{-1}$ ($5.13 M_\odot \hbox{yr}^{-1}$) implied from the quasi-steady gas circulation. The dashed line in the lower panel is the test case with the constant velocity.
• Figure 2: CR C and B spectra at $z=0$ and $t=1$ Gyr (solid lines). The data points are from CALET 2020PhRvL.125y1102A2022PhRvL.129y1103A, AMS-02 2017PhRvL.119y1101A2018PhRvL.120b1101A, DAMPE DAMPEPhysRevLett.134.191001, and Voyager 2016ApJ...831...18C. The inset shows a zoom-up view around the spectral bump. The green and red dashed curves are contributions of $^{11}$B and $^{10}$B, respectively.
• Figure 3: CR proton spectrum at $z=0$ and $t=1$ Gyr (blue solid line). The data points are from CALET adriani22, AMS-02 aguilar15, DAMPE DAMPE, and Voyager 2016ApJ...831...18C. The inset shows a zoom-up view around the spectral bump. The green dashed curve is the model without the wind, and the orange dashed curve is the model with a constant wind velocity (see Figure \ref{['fig:profile']}).
• Figure 4: Diffusion (color scale) and advection (cyan lines) timescales of protons as a function of the altitude $z$. The blue dotted line is the highlighted diffusion timescale for $p=5\hbox{TeV}/c$. The magenta curves indicate the timescale of adiabatic energy change resulting from the acceleration/deceleration of the wind. The dashed curves correspond to the model with a constant wind velocity (see Figure \ref{['fig:profile']}).
• Figure 5: Effective disk thickness $H$ as a function of proton momentum. The solid line is our standard case, while the dashed is the model with a constant wind velocity (see Figure \ref{['fig:profile']}).