Interchange reconnection as the source of the fast solar wind within coronal holes

The fast solar wind that fills the heliosphere originates from deep within regions of open magnetic field on the Sun called ‘coronal holes’. The energy source responsible for accelerating the plasma is widely debated; however, there is evidence that it is ultimately magnetic in nature, with candidate mechanisms including wave heating1,2 and interchange reconnection3–5. The coronal magnetic field near the solar surface is structured on scales associated with ‘supergranulation’ convection cells, whereby descending flows create intense fields. The energy density in these ‘network’ magnetic field bundles is a candidate energy source for the wind. Here we report measurements of fast solar wind streams from the Parker Solar Probe (PSP) spacecraft6 that provide strong evidence for the interchange reconnection mechanism. We show that the supergranulation structure at the coronal base remains imprinted in the near-Sun solar wind, resulting in asymmetric patches of magnetic ‘switchbacks’7,8 and bursty wind streams with power-law-like energetic ion spectra to beyond 100 keV. Computer simulations of interchange reconnection support key features of the observations, including the ion spectra. Important characteristics of interchange reconnection in the low corona are inferred from the data, including that the reconnection is collisionless and that the energy release rate is sufficient to power the fast wind. In this scenario, magnetic reconnection is continuous and the wind is driven by both the resulting plasma pressure and the radial Alfvénic flow bursts.

corona (interchange reconnection) is the driver of these bursts 9,[21][22][23] .Interchange reconnection in the weakly collisional corona is expected to be bursty rather than steady [24][25][26][27] .The energetic ions and enhanced pressure in these bursts are also signatures of reconnection [28][29][30] .The data suggest that it is a continuous process in the source regions of open flux.Figure 3c  To establish that interchange reconnection is the source of the bursty flows, we use the measurements and established principles of reconnection to deduce the basic characteristics in the low corona.The strength of the reconnecting magnetic field is a key parameter.As the field strength at the base of the corona has substantial variation, we estimate the amplitude of the reconnecting magnetic field by projecting the measured magnetic field at the PSP back to the solar surface.The R −2 fall-off of the radial magnetic field with heliospheric distance R is valid in the solar wind, but fails closer to the Sun.Thus, we use a combination of the R −2 behaviour at large R with a fall-off derived from a surface-averaged PFSS model below 2.5 R s (Extended Data Fig. 1).The resulting projection of the 600-nT magnetic field at 13.4 R s to the low corona is 4.5 G, which is consistent with the PFSS data in Fig. 2. Plasma density at the base of the corona is not measured directly.However, the characteristic amplitude of the bursty flows at PSP are around 300 km s −1 .Because the flows during bursty reconnection are Alfvénic, we can estimate the density knowing the magnetic field strength.The resulting density is around 10 9 cm −3 , a reasonable value for the low corona 31 .ions in a extend in energy to greater than 85 keV as suprathermal tails on the proton particle distribution in b. c, Red arcs mark the solar wind radial velocity (V R ) microstream structure that is organized in Carrington longitude at angular scales associated with supergranulation convection and the photospheric network magnetic field (Fig. 2).These microstreams become shorter in duration as the spacecraft accelerates through perihelion near the centre of this figure and sweeps more rapidly through Carrington longitude.
The thermal alpha particle abundance (A He , blue trace in c) is similarly modulated by the microstream structure.The alpha particle abundance is frozen-in at the base of the corona.d, Reversals of the radial magnetic field (B R ), so-called 'switchbacks', are organized by the microstreams and are linked to the radial flow bursts by the Alfvénicity condition.e, Photospheric footpoints from a PFSS model instantiation indicate two distinct coronal hole sources well separated in Carrington longitude (Lon), shown in Fig. 2 (and as dotted lines in Fig. 1e).

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To address whether the rate of energy release is sufficient to drive, the wind we estimate the reconnection inflow rate V r .A lower limit follows from the fact that the flow bursts are nearly continuous.We define the reconnection time as t r = L B /V r , the time required for open field lines to traverse the characteristic scale length L B of the surface magnetic field, which is around 10° or 6 × 10 4 km.A second time is the time t b ≈ R PSP /V R for the reconnection bursts to reach the spacecraft at R PSP .In the limit t r >> t b , the outflows from the reconnection site would quickly pass by the spacecraft and there would be no high-speed flows until the spacecraft connected to another reconnection site.When t r ≤ t b , the spacecraft would measure bursty flows as the spacecraft crossed the entire supergranulation scale.The observations show the latter because bursty flows are measured during the entire crossing of the supergranulation scale.Observations suggest that t r ≤ t b or V r ≈ L B V R /R PSP is ≈3 km s −1 or around 0.01 of the local Alfvén speed, a low value if reconnection is collisionless, [32][33][34] but comparable to the magnetohydrodynamic (MHD) prediction 35 .With ambient temperatures of around 100 eV, the reconnection electric field is therefore around three orders of magnitude above the Dreicer runaway field.In this regime, collisions are too weak to limit electron acceleration, and collisionless processes dominate.The rate of magnetic energy release from interchange reconnection is given by V r B 2 /4π ≈ 5 × 10 5 ergs cm −2 s −1 using B = 4.5 G and V r = 3 km s −1 .This is comparable to that required to drive the high-speed wind, which is around 10 5 -10 6 ergs cm −2 s −1 .
Thus through the PSP observations, the Solar Dynamics Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) surface magnetic field measurements and well-known characteristics of magnetic reconnection, we have established that interchange reconnection is sufficient to drive both the ambient base solar wind flow through the radial pressure drop and the microstream bursts that lie on top of this flow.Further tests of the reconnection scenario concern the structuring of the flow bursts and the production of energetic protons and alphas.A key observation reported in the E06 data 9 and illustrated in the schematic in Fig. 3c is the temporal asymmetry in the bursts: large-amplitude bursts onset sharply and decrease gradually across the burst period and the time sequence then repeats.Data from a particle-in-cell (PIC) simulation is presented in Fig. 3b (Methods).A cut across the simulation outflow exhaust reveals high-speed bursts on newly reconnected field lines in the exhaust adjacent to the magnetic separatrix, whereas, on field lines in the exhaust interior, the fastest flow bursts have already passed the location of the cut, so the measured flows are weaker (Fig. 3a).Our simulations support the hypothesis that the bursts observed by the PSP correspond to crossings of interchange reconnection exhausts.Dispersion signatures are well documented in the cusp of the Earth's magnetosphere as a result of reconnection at the terrestrial magnetopause 36 .Reconnection between the closed magnetic flux of the Earth and 'open' flux in the solar wind is an analogue of coronal interchange reconnection.
Finally, the spectrum of energetic protons and alphas has been calculated from the interchange reconnection simulations.The simulation includes fully stripped alpha particles that are 5% by number, similar to the solar atmosphere 16 .Energy flux spectra of both species are shown in Fig. 4a.Data is taken from the outflow exhaust and includes only plasma that has undergone acceleration.Protons and alphas exhibit an energetic, non-thermal power-law distribution with spectral indices of around −8 for both species.As shown in Fig. 4b, in the spectrum of the differential energy flux of particles during the time 04:00-19:00 on 20 November 2021 (from Fig. 1), there are also energetic protons and alphas with energies beyond 100 keV.The spectra are again rather soft, having spectral indices of around −9, consistent with the simulation data.The energy in the simulation is normalized to the free parameter m i V A 2 .By equating the energy minimum of the proton power law in the simulation (approximately 5 m i V A 2 ) to that of the PSP measurements (approximately 7 keV), we find that the coronal value of m i V A 2 is around 1.4 keV, compared with around 0.9 keV from the 300 km s −1 estimate for V A based on the amplitude of the bursty flows measured at 13.4 R s .That the two values of m i V A 2 are close indicates that the Alfvén speed in the corona where reconnection is taking place is in the range of 300-400 km s −1 .
The picture that emerges is that reconnection directly heats the ambient coronal plasma sufficiently to drive the bulk outflow [37][38][39] and at the same time produces the turbulent velocity bursts that ride this outflow [24][25][26][27] .Extended Data Fig. 2 shows the strong heating of protons from the simulation in Fig. 3a,b.Of course, a fraction of the magnetic energy released during reconnection can take the form of Alfvén waves 1,2 or other magnetic structures 5 that can be dissipated , which is an arbitrary parameter 35 .
The units in the ordinate direction are arbitrary, although the reduced height of the alpha flux reflects the 5% number density of alphas.Both fluxes peak and then roll over into distinct soft power laws with slopes of −8.6 and −7.7 for the protons and alphas, respectively, with the alpha spectrum shifted to higher energy than that of the protons.The spectral indices of the energetic ions depend on the magnitude of the ambient guide (out-of-plane) magnetic field with stronger guide fields producing softer spectra.The data are from a simulation with a guide field of 0.55 of the reconnecting magnetic field.b, The proton (blue) and alpha (red) energy fluxes from PSP measurements during the time interval 04:00:00-19:00:00 on 20 November 2021 from Fig. 1.As in the simulations, the spectra peak and roll over into power-law-like suprathermal tails with a similar slope of −9 for the protons.Thus, the power-law slopes from the simulation and the observational data are very close.The alpha measurement does not extend to high enough energy to characterize any power-law behaviour.Finally, we can use the low energy bound of the power-law distribution from the simulation (approximately 5 m i V A 2 ) and observations (approximately 7 keV) to establish that the value of m i V A 2 at the coronal reconnection site is around 1.4 keV.
This is comparable with around 0.9 keV from the 300 km s −1 estimate for V A based on the amplitude of the bursty flows measured by the PSP at 13.4 R s .

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higher in the coronal to further drive the bulk outflow 1,2,5,37 .However, the in situ data from reconnection in the Earth's magnetosphere 40 and at the heliospheric current sheet 41 show strong local plasma energization rather than wave generation.The time asymmetry that characterizes the bursty flows 9 and the spectral indices of the power-law distributions of energetic ions are in remarkably good agreement with the interchange reconnection simulation data, in which local plasma energization dominates waves and turbulence.Still, three-dimensional simulations with greater scale separation might show stronger magnetic turbulence.In either scenario, interchange reconnection is the likely energy drive mechanism of the fast solar wind.Recent remote-sensing measurements 42,43 also support the interchange magnetic reconnection scenario.We note that structured microstreams and magnetic switchbacks are present throughout the inner heliosphere measured by the PSP and that the primary difference between the slow and fast solar wind may lie in the magnetic topology of the underlying coronal hole.

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Potential field source surface modelling
To generate the footpoints shown in Figs.1e and 2, a PFSS model 16,17 was run using an Air Force Data Assimilative Photospheric Flux Transport-Global Oscillation Network Group (ADAPT-GONG) magnetogram [44][45][46] from 21 November 2022, with a source surface height set to the canonical value of 2.5 R S 19 by means of the open-source pfsspy 47 software.The footpoint mapping from the PSP down to the solar surface followed the methodology 48 comprising a ballistic heliosphere 49,50 and the PFSS domain from 2.5 R S down to the photosphere 51 .
The results for PSP E10 were distinct and compelling.As shown in Figs. 1 and 2, for 20-21 November, the PSP was rotating faster than the Sun and moving from left to right in the Carrington frame of reference shown in those plots.The footpoint mapping connected deep inside two mid-latitude negative polarity coronal holes of substantial area.This source mapping is uniquely well supported, compared with previous PSP encounters, owing to the comparison of the in situ data.First, the magnetic polarity measured by the PSP throughout the encounter is well explained by the PFSS current sheet geometry and coronal hole polarity.Second, the times when the PSP maps to the centre of these large coronal holes correspond to maxima in solar wind speed, and at the time the connection switches from one source to another in the model, there is a distinct dip in solar wind speed, clearly consistent with the traversal of overexpanded field lines at the coronal hole boundaries 52 .This correspondence is clearly shown in Fig. 1 where the transition between 'stream 1' and 'stream 2' marked in the bottom panel corresponds to the dip in solar wind speed (black trace, Fig. 1c).

PSP/SWEAP data analysis
We use proton and alpha particle measurements from the Solar Wind Electrons Alphas and Protons (SWEAP) instrument suite 11 on PSP.The proton spectrum in Fig. 4 is taken from the Solar Probe Analyzer (SPAN-Ion) SF00 data product, averaged over the time range from 20 November 2021 at 04:00:00 to 20 November 2021 at 19:00:00 and summed over all look directions.We work in units of energy flux as opposed to number flux or distribution function as it results in a spectrum spanning fewer orders of magnitude at high energy, facilitating the comparison between SPAN-Ion and Integrated Science Investigation of the Sun (ISOIS)/Epi-Lo data, as well as being the quantity most directly related to the SPAN-Ion measurements.The power law for the protons is fit to the four highest energy SPAN data points and the ISOIS data points.The alpha spectrum is obtained in the same way from SPAN-Ion's sf01 data product, except that a small amount (around 1%) of contaminant protons leaking in from the sf00 channel are accounted for and subtracted.The large shift to higher energy of the alphas relative to the protons during this interval means that the contaminant protons have no impact on the power law part of the spectrum or its exponent, and only affect the lowest energy data points.

Estimation of the reconnection magnetic field
The strength of the magnetic field that drives interchange reconnection will control the rate of magnetic energy release and the spectra of energetic particles produced.Although the SDO/HMI observations make known the structure of the magnetic field in the low corona, these measurements do not show the strength of the magnetic field that is actually undergoing reconnection because there is substantial variation of the field strength along the surface.To estimate the strength of the magnetic field driving the flow bursts measured by the PSP, we project the measured magnetic field at the PSP and project this magnetic field down to the solar surface.The radial magnetic field B R at the perihelion of E10, as shown in Fig. 1, is around 600 nT.Direct measurements of the radial profile of B R over the first five PSP orbits have established an R −2 scaling for the field 45 , consistent with the conservation of the radial magnetic flux.However, deviations from this scaling are expected close to the Sun.Specifically, because closed flux occupies a substantial fraction of the solar surface, the open flux will be compressed into a reduced fraction of the solar surface, which will lead to greater compression of the magnetic field near the solar surface.A rough estimate of the increased magnetic field compression can be obtained by averaging the radial magnetic field obtained from the PFSS model during the E10 perihelion.The radial dependence of this averaged field is shown in Extended Data Fig. 1.The magnetic field compression from 2.5 R s , the outer boundary of the PFSS grid, down to just above the solar surface is around 26, which is well above the compression of around 6.25 from the R −2 dependence.Thus, we assume that the R −2 describes the radial dependence from R = 13.4R s to 2.5 R s and take the compression of 26 from 2.5 R s to just above the solar surface.The projection of the 600-nT field down to the solar surface is around 4.5 G, which is in reasonable agreement with the strength of the solar surface magnetic field shown in Fig. 2.

Particle-in-cell simulations
Our estimate of the rate of interchange reconnection based on projections of the PSP observations back to the low corona suggest that reconnection there is deeply in the collisionless regime.To explore the structure of the interchange reconnection exhaust and the resulting energetic proton and alpha spectra measured at the PSP, we use the PIC model p3d (ref.53).The MHD model is not adequate to explore the particle energization documented in the PSP data.We limit the calculations to a two-dimensional system with an initial magnetic geometry that leads to reconnection between open and closed flux low in the corona 3,54 .Because of constraints on the domain size possible with the PIC model, there is no gravity in the simulations, so the model does not describe the complete dynamics of the solar wind drive mechanism.In addition, line-tied boundary conditions are not imposed at the nominal coronal surface.Thus, the model is not a complete description of interchange reconnection in the low corona, but will provide information on the dynamics of collisionless reconnection, the structure of the outflow exhaust, the bulk heating and the spectra of accelerated particles.We include alpha particles (5% by number) so that the spectra of protons and alphas can be compared.
The initial state for the simulation consists of a band of vertical flux (field strength B 0 in the negative radial direction) with a low plasma density (0.1 n 0 ) and an adjacent region with higher density that is a cylindrical equilibrium.The detailed initial state has been described previously 23 , so the governing equations are not repeated here.The peak magnetic field of the cylindrical equilibrium is 0.76 B 0 with a peak density of n 0 .The temperatures are uniform with T e = T p = T a = 0.06 m p V A0 2 with V A0 the Alfvén speed based on B 0 , n 0 and the proton mass m p .Thus, in the initial state, the plasma pressure is small compared with the magnetic pressure, as expected in the corona.The guide field B z is non-zero everywhere with a profile that balances the pressure and tension forces.The strength of the guide field can be varied by choosing its value in the region of vertical flux.Its value does not substantially affect the overall structure and dynamics of reconnection shown in Fig. 3.However, because a strong guide field weakens the Fermi drive mechanism for particle energy gain, the guide field controls the power-law index of energetic protons and alphas.The energy fluxes shown in Fig. 4 were from a simulation with a guide field of 0.55 B 0 .Simulations with a weaker (stronger) guide field produced harder (softer) spectra.
The results of the simulation are presented in normalized units: times to the Alfvén transit time across the domain of scale length L, L/V A0 , plasma fluxes to n 0 V A0 and energies to m p V A0 2 .The domain dimensions in the x and y directions are equal.The mass ratio m p /m e = 25 is artificial as is the velocity of light (20 V A0 ) and the proton inertial scale d p = L/163.84.As has been established in earlier papers, the results are not sensitive to these values 33,34 .The radius of the cylindrical magnetic field is 60 d p and the grid scales are 0.02 d p in both space directions, with around 400 particles per cell.3b.The temperature is normalized to m p V A0 2 , which, as discussed in the main text is in the range of 0.9 keV to 1.6 keV.Thus, since the magnetic energy released per particle during reconnection is around m p V A0 2 , a large fraction of the released magnetic energy is goes into the heating and energization of the ambient plasma very close to the magnetic energy release site.The energy going into turbulent magnetic fields that is injected upward into the corona and is available to further heat the ambient plasma remains to be explored.
is a schematic that shows open flux reconnecting with closed flux regions in the low corona.In this figure the open flux migrates to the left, reconnecting with successive regions of closed flux, with the consequence that the bursty outflow from interchange reconnection fills all of the open flux, as seen in the data.

Fig. 1 |
Fig.1| Time series measurements of the solar wind plasma and magnetic field through the November 2021 solar encounter.a,b, Hot solar wind ions in a extend in energy to greater than 85 keV as suprathermal tails on the proton particle distribution in b. c, Red arcs mark the solar wind radial velocity (V R ) microstream structure that is organized in Carrington longitude at angular scales associated with supergranulation convection and the photospheric network magnetic field (Fig.2).These microstreams become shorter in duration as the spacecraft accelerates through perihelion near the centre of this figure and sweeps more rapidly through Carrington longitude.

Fig. 2 |Fig. 3 |Fig. 4 |
Fig. 2 | Solar wind during PSP Encounter 10 emerges from two coronal holes.a, An extreme ultraviolet (193 Å) map of the corona shows cooler regions (darker pixels) associated with open magnetic field within two separate, near-equatorial coronal holes.A PFSS model maps the interplanetary magnetic field from the PSP spacecraft to footpoints (white diamonds) within the coronal holes.b, The magnetic field and velocity microstream profile within the first coronal hole: the upper panel shows minimum (blue) and maximum (red) radial speed versus longitude, and the second panel shows the vertical magnetic field along the footpoints extending from the photosphere to 30 Mm from magnetogram measurements and a PFSS model that accounts for the motion of the spacecraft.The bottom panel is a map of the magnetic field polarity just above the photosphere, again from the PFSS model.c, The corresponding structure within the second coronal hole.These data indicate that the radial magnetic field is organized into mixed radial polarity intervals on the same scales as the velocity microstreams observed by PSP.

Extended Data Fig. 1 |Extended Data Fig. 2 |
Magnitude of the radial magnetic field from PFSS.The magnitude of the radial component of the magnetic field is modelled by the PFSS implementation, constrained by magnetograms at the photospheric footpoints and the open boundary condition at 2.5 R S .This field magnitude is consistent with the field measured at Parker Solar Probe and is used to estimate the Alfvén speed at the reconnection site.Proton temperature in the plane of reconnection with overlying magnetic field lines.The proton temperature is shown from the same simulation and the same time as the vertical flux shown in Fig.