Alpha-to-proton Temperature Ratio Distributions Using Parker Solar Probe Measurements

The distributions of the temperature excess of alphas to protons (ε) were studied using Parker Solar Probe measurements for Encounters 2 through 14. The distributions were mapped based on heliographic distance, Coulomb number, plasma β, and Alfvén Mach number (M A ). The importance of collisional effects in the thermalization of solar wind is observed for a wide range of Coulomb numbers. The distributions correlate better with N β and NM A than just N. Furthermore, evidence was found for a narrow region immediately above the Alfvén surface (1 < M A < 2) where ε has values much higher than the mass ratio.


Introduction
Understanding the mechanisms behind coronal heating is still one of the most important open problems in solar physics.NASA's 2018-launched Parker Solar Probe (PSP) has as one of its science objectives the study of the flow of energy heating the corona and accelerating the solar wind (Fox et al. 2016).That is enabled by PSP's remarkable proximity to the Sun during perihelia (with the closest ones reaching below 10 R s ), including various crossings of the Alfvén, sonic, and β = 1 surfaces, for increasingly more extended periods as the mission progresses and the PSP perihelia get closer to the Sun due to Venus's fly-by gravity assists (Chhiber et al. 2019).
The scientific question of particular importance is understanding the alpha particle preferential heating with respect to protons.In the solar wind, especially at distances closer to the Sun, the ratio of alpha temperature T α to proton temperature T p is often significantly higher than 1.Recent models suggest that there is a zone between ∼0.1 R s and the Alfvén surface where this ratio is particularly enhanced, on the order of the ion-to-proton mass ratio and above (Kasper et al. 2013).This suggests that the physical processes driving the preferential heating are highly active at these distances and reduce their prevalence around the Alfvén surface and larger distances.As the solar wind evolves, the temperature ratio gradually decays to close to unity (Kasper et al. 2017;Kasper & Klein 2019).The drivers of this gradual thermalization are thought to be Coulomb collisions (Hernández et al. 1987).Various theories have been presented to explain the driving of preferential heating, such as resonant wave heating (Cranmer 2000), velocity filtration (Scudder 1992), stochastic heating by low-frequency Alfvénic turbulence (Chandran et al. 2010), and others.Some of the processes might be at play simultaneously.Resolving the physical processes driving the preferential heating is of the highest importance.
Experimentally, the preferential heating has been observed by many spacecraft.Many observations are from near-Earth solar wind where the preferential heating has been observed by spacecraft such as Prognoz 1 (Bosqued et al. 1977), Prognoz 7 (Yermolaev &Stupin 1990), andWind (Kasper et al. 2008).However, the new PSP data enable a critical turning point in our understanding of preferential heating.For the first time, it is possible to measure preferential ion heating in the low heliosphere and inside the Alfvén surface.The current study focuses on experimentally resolving the profile of the alpha-toproton temperature ratio as a function of solar distance and its dependence on various plasma parameters.

Methodology
PSP is equipped with four instrument suites and in our study we use two of those: FIELDS, measuring magnetic and electric fields including plasma waves and radio emissions (Bale et al. 2016), and Solar Wind Electrons Alphas and Protons (SWEAP), measuring electron and ion distribution functions and corresponding moments (Kasper et al. 2016).For magnetic field data, a 1 minute data cadence is used.As for the SWEAP suite, the used data for ion temperatures, velocity, and density are retrieved from the Solar Probe ANalyzer-Ions (SPAN-I) instrument.The original cadence is about two measurements per second.The data are averaged to a 1 minute resolution and all derived quantities are calculated in this cadence.Finally, a spike removal treatment was applied.In total, 23 million data points are used in the following analysis.
The analysis uses data from PSP Encounters 2 through 16 for distances up to 40 Gm, where the data quality is reliable.We use all the data from the perihelion and up to distances where SPAN-I data exist consistently for any particular encounter.Starting with Encounter 8, PSP has crossed into the sub-Alfvénic region at perihelia (Kasper et al. 2021).The data quality flags provided with the data sets were used to discard data that might have issues.For FIELDS, only data with quality flag 0 (good) is used.As for SPAN-I, all data with quality flag bits indicating potential faults (e.g., counter overflow, no targeted sweep, overdeflection) was removed.
The preferential heating can be characterized by the quantity ε, the alpha-to-proton temperature ratio excess, defined as in Kasper et al. (2017): The Astrophysical Journal Letters, 964:L2 (5pp), 2024 March 20 https://doi.org/10.3847/2041-8213/ad2ded Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
The ε value of zero corresponds to alpha and protons having equal temperatures.

Results and Discussion
First, we analyze ε as a function of solar distance.The result is shown in Figure 1.Distances farther away from the Sun are probed in every Encounter, while distances closer to the Sun are probed only in later Encounters.The normalization is done in two ways for each column (distance bin) and shown in separate figures.In Figure 1(a), bins are normalized to the total number of counts in the column.That means that each column shows the probability distribution of ε, and the figure shows the evolution of the probability distribution of ε with distance.In Figure 1(b), bins are normalized to the number of counts of the highest peak of the column.This figure makes it easier to compare the evolution of the shape of εʼs probability distribution with distance.Similar pairs of figures using both ways of normalization are also shown for other parameter dependencies later.Figure 1 shows that the correlation between ε and R is not very good, and other parameters should order better the ε evolution.It is, however, interesting to note that for distances below about 30 R S , ò shows a quite clear tendency to increase with the proximity to the Sun.
The ε(R) histograms in Figure 1 are given in a 26 × 26 grid.This bin number was chosen to ensure that, in each column, every bin has an average number of data points higher than 5000, i.e., that the average number of data points per bin in each column is higher than the square root of the total number of data points.This was chosen as a reasonable benchmark for the significance of a bin.This same principle and value will be used for choosing the number of bins for the remaining histograms.
One parameter that we expect can better order the ε evolution is the Coulomb number, defined as in Hernández et al. (1987): where w αp is in km s −1 and n p in cm −3 .It is well established that Coulomb collisions drive the thermalization of ε throughout the solar wind (Feldman et al. 1974;Hernández et al. 1987;Vocks & Marsch 2002).A clear relation between the two is known from measurements from spacecraft such as Wind (Kasper et al. 2008), and more recently PSP (Mostafavi et al. 2024).Figure 2 shows the  2 The Astrophysical Journal Letters, 964:L2 (5pp), 2024 March 20 correlation between ε and the Coulomb number N. The correlation for N is much better than for R, but some scattering and discontinuity are still present.
To find other quantities that correlate better with ε, we analyze encounters with significant enhancements or spikes in ε (such as Encounters 2 or 5, respectively).Figure 3 shows Encounter 5 data with a large variation in temperature ratio, including a significant spike in the afternoon of 2020 June 8.It appears to be a crossing of the heliospheric current sheet (HCS), indicated by the inversions of B r /|B| and the Strahl electron pitch angle.It is seen that the plasma β and M A are well inversely correlated with ε, as a gradual increase in both quantities with the approach of the HCS happens simultaneously with a decrease in T α /T p , and when the temperature ratio peaks during the crossing, both β and M A show a sudden drop.Based on the previous, we introduce new quantities, NM A and Nβ, and Figures 4(b The figures show a better correlation than simply to the Coulomb number (Figure 2).These new quantities agree with the standard Coulomb number values at the position of the Alfvén surface (M A =1) and the β = 1 surface, respectively.The position of these surfaces changes significantly throughout the solar cycle and with heliographic distance.These new quantities are also sensitive to crossings of ICMEs, HCS, and other structures with different thermal and magnetic properties of plasmas.The reason why the new quantities show better correlation is not clear and more studies are required.
Another important observation is the location of regions where ε reaches peak values significantly higher than the mass ratio.Figure 5(a) shows that the region of highest ε values is observed in the range 1 < M A < 2, corresponding to distances immediately above the Alfvén surface.This same region is also localized roughly where 0.1 < β < 0.3.This suggests that the Alfvén surface may be a critical region where the highest values of ε are generated.Still, more studies are required to confirm this result, particularly from the following encounters.

Conclusions
This work identifies some of the most significant dependencies of the alpha-to-proton temperature ratio in the solar wind.A good correlation is found with the Coulomb number N, consistent with earlier studies.However, quantities NM A and Nβ show an even better correlation.There is no good physical explanation for why there should be a better correlation with these quantities.Still, they show a good correlation also when crossing plasmas with different thermal and magnetic properties, such as the HCS.
We present evidence that there is a region where the alphato-proton temperature ratio is significantly higher than expected by the theory.In the regions of the lowest Coulomb number, ε is of the order of the alpha-to-proton mass ratio, as expected by theory within the preferential heating zone.In regions of high Coulomb number, plasma tends toward thermalization (ε ∼ 0).However, in the region located at distances where 1 < M A < 2, i.e., immediately above the Alfvén surface, the alpha-to-proton temperature ratio is significantly higher than the mass ratio, which is a result that is not predicted by theory.

Figure 1 .
Figure 1.Distribution of excess alpha-to-proton temperature ratio as a function of heliographic distance.

Figure 2 .
Figure 2. Distribution of excess alpha-to-proton temperature ratio as a function of Coulomb number.
) and (d) show ε as a function of the new quantities.The ε distributions as a function of NM A and Nβ are shown in 4(b) and (d).

Figure 3 .
Figure 3. Encounter 5 featuring a crossing of the heliospheric current sheet (HCS).(a) The ratio between radial component and magnitude of the magnetic field; (b) the total magnitude of the magnetic field; (c) differential energy flux pitch angle distribution of electrons in the energy channel 391.4 eV; (d) proton temperature; (e) alpha particle temperature; (f) plasma β; (g) M A : Alfvén Mach number; (h) alpha-to-proton temperature ratio; (i) proton velocity (black) and alpha velocity (green); (j) Alfvén velocity (green) and proton-alpha velocity difference (black).

Figure 5 .
Figure 5. Distribution of excess alpha-to-proton temperature ratio as a function of Alfvén Mach number and plasma beta.

Figure 4 .
Figure 4. Distribution of excess alpha-to-proton temperature ratio as a function of NM A and Nβ.