Proton Temperature and Density Variations in Linear Magnetic Holes in the Solar Wind

Linear magnetic holes (LMHs) are pressure-balanced structures characterized by reduced magnetic pressure and compensatory thermal pressure enhancements, driven by proton temperature and/or density variations. Here we systematically investigate the relative contributions of the proton temperature and density to the thermal pressure by examining LMH characteristics separately in high-speed and low-speed solar wind streams. Using Solar Orbiter data (2020-2024), we analyze 348 LMHs (∼4.5-5.0 day^-1; 256 in low-speed and 92 in high-speed streams) identified via a combined partial variance of increments and minimum variance analysis method. Based on their thermal pressure contributions, the selected LMHs are classified into four types: temperature-dominant (T-LMHs), density-dominant (N-LMHs), temperature-and-density-enhanced (TN-LMHs), and background-like (BG-LMHs). We find that in low-speed streams, BG-LMHs are the most common (39%), followed by T-LMHs (25%). In high-speed streams, TN-LMHs are the most frequent (32%). For the first time, we introduce magnetic variance rate (MVR, the normalized temporal gradient of magnetic strength) to quantify phase steepness and a thermal dominance coefficient (TDC, the difference between normalized temperature and density perturbations) to assess the temperature contribution. The results reveal a statistically significant correlation between MVR and TDC exclusively in T-LMHs within low-speed streams (Spearman’s r = 0.4056, P = 0.0009), while other types and high-speed streams show no correlation (r < 0.23, P > 0.14). This selective correlation supports the role of ponderomotive forces—generated by steepening of nonlinear Alfvén waves—in heating T-LMHs, particularly in compressible low-speed wind environments. These results provide the first observational evidence linking phase-steepening dynamics to thermal enhancements in LMHs.