In Situ Signature of Cyclotron Resonant Heating in the Solar Wind

The dissipation of magnetized turbulence is an important paradigm for describing heating and energy transfer in astrophysical environments such as the solar corona and wind; however, the specific collisionless processes behind dissipation and heating remain relatively unconstrained by measurements. Remote sensing observations have suggested the presence of strong temperature anisotropy in the solar corona consistent with cyclotron resonant heating. In the solar wind, in situ magnetic field measurements reveal the presence of cyclotron waves, while measured ion velocity distribution functions have hinted at the active presence of cyclotron resonance. Here, we present Parker Solar Probe observations that connect the presence of ion-cyclotron waves directly to signatures of resonant damping in observed proton-velocity distributions using the framework of quasilinear theory. We show that the quasilinear evolution of the observed distribution functions should absorb the observed cyclotron wave population with a heating rate of ${10}^{-14}\mathrm{W}/{\mathrm{m}}^3$, indicating significant heating of the solar wind.

Figure 1

(a) Magnetic field measurements from PSP-FIELDS. (b) Velocity measurements from PSP-SPANi. (c) Spectra of magnetic field data. Spectral indices at $-3/2$, $-4$ and $-2.7$ are shown. Wavelet coefficients for total power are shown as black ⋄. Wavelet coefficients filtered by left- and right-handed ${\sigma }_b$ are shown in red and blue ⋄.

Figure 2

(a) Interpolation of $f_p(\mathbf{v})$ from SPANi in the $v_{\perp }-v_{\parallel }$ plane, with the mean magnetic field pointing vertically. Points show SPANi measurement locations. Solid lines show $v_{\parallel \mathrm{th}}$, and a set of cyclotron resonant diffusion contours are plotted. (b) Drifting bi-Maxwellian fit to $f_p(\mathbf{v})$. (c) Hermite representation of $f_p(\mathbf{v})$. Integration of $f_p(\mathbf{v})$ in (a)–(c) over $v_{\perp }-v_{\parallel }$ is normalized to the QTN density. (d) Contours of $f_p(\mathbf{v})$ determined by interpolating the gyrotropic distribution along QL diffusion contours for parallel cyclotron resonance. (e),(f) Drifting bi-Maxwellian and the Hermite representations of $f_p(\mathbf{v})$ evaluated along cyclotron resonance contours.

Figure 3

(a) Differential volumetric heating rates (positive $\mathcal{H}$) as a function of resonant parallel velocity computed from observed cyclotron spectra and drifting bi-Maxwellian fit to ion-distribution functions. The total heating rate is the sum over $v_{\parallel }$. Solid lines show the average $v_{\parallel \mathrm{th}}$ for the interval ($49\mathrm{km}/\mathrm{s}$). (b) Measured heating rates for a Hermite function approximation. (c),(d) Corresponding cooling rates (negative $\mathcal{H}$). (e) Distribution of total $\mathcal{H}$ for bi-Maxwellian and Hermite representations; respective lines show median value of $\mathcal{H}$. The turbulent cascade rate estimated from third-order moments is shown in green.