MNRAS 000, 1–7 (2017) Preprint 8 July 2018 Compiled using MNRAS LATEX style file v3.0 Solar wind magnetic field background spectrum from fluid to kinetic scales Roberto Bruno1⋆, Daniele Telloni2, Danilo DeIure3 and Ermanno Pietropaolo3 1National Institute for Astrophysics, Institute for Space Astrophysics and Planetology, Via del Fosso del Cavaliere 100, 00133 Roma, Italy 2National Institute for Astrophysics, Astrophysical Observatory of Torino, Via Osservatorio 20, 10025 Pino Torinese, Italy 3University of L’Aquila, Department of Physical and Chemical Sciences, L’Aquila, Italy 8 July 2018 ABSTRACT The solar wind is highly structured in fast and slow flows. These two dynamical regimes remarkably differ not only for the average values of magnetic field and plasma param- eters but also for the type of fluctuations they transport. Fast wind is characterized by large amplitude, incompressible fluctuations, mainly Alfv´enic, slow wind is generally populated by smaller amplitude and less Alfv´enic fluctuations, mainly compressive. The typical corotating fast stream is characterized by a stream interface, a fast wind region and a slower rarefaction region formed by the trailing expansion edge of the stream. Moving between these two regions, from faster to slower wind, we observe the following behavior: a) the power level of magnetic fluctuations within the inertial range largely decreases, keeping the typical Kolmogorov scaling; b) at proton scales, for about one decade right beyond the high frequency break, the spectral index becomes flatter and flatter towards a value around -2.7; c) at higher frequencies, before the elec- tron scales, the spectral index remains around -2.7 and, based on suitable observations available for 4 corotating streams, the power level does not change, irrespective of the flow speed. All these spectral features, characteristic of high speed streams, suggest the existence of a sort of magnetic field background spectrum. This spectrum would be common to both faster and slower wind but, any time the observer would cross the inner part of a fluxtube channeling the faster wind into the interplanetary space, a turbulent and large amplitude Alfv´enic spectrum would be superposed to it. Key words: (Sun:) solar wind – turbulence – waves – Sun: heliosphere – magnetic fields – plasmas 1 INTRODUCTION slows down and becomes cooler. This region was firstly named rarefaction region by Hundhausen (1972). Interest- Typical corotating high speed streams (HSS’ hereafter), i.e. ing enough, these two portions of the stream are separated those streams coming from the equatorial extension of po- by a very narrow region across which Alfv´enicity changes arXiv:1708.01145v1 [astro-ph.SR] 3 Aug 2017 lar coronal holes, are characterized by different regions. abruptly, from high to low (Bruno & Telloni 2015). Most Within these regions, extending on daily scales, field and of the time, the rarefaction region is followed by the helio- plasma parameters assume different average values and fluc- spheric current sheet crossing characterized by low Alfv´enic- tuations have a different character. The first region is the ity, low temperature but higher field and plasma compress- stream interface (SI), located between fast and slow stream, ibility. Thus, moving from fast to slow wind one observes a right where the dynamical interaction between the two flows different turbulence, not only relatively to its power level but is stronger (Schwenn and Marsch 1990; Bruno and Carbone also to its Alfv´enic character although the spectral slope at 2016). The SI is characterized by high level of pressure, both fluid scales clearly shows a persistent Kolmogorov-like scal- kinetic and magnetic, high temperature and low Alfv´enicity. ing. In addition, besides the above-cited differences within This region is followed by the trailing edge (TE), which is the fluid regime, there are also clear differences at proton characterized by the highest wind speed and temperature, kinetic scales. Bruno et al. (2014), investigating the behav- the lowest compressibility, and the highest level of Alfv´enic- ior of the spectral slope at proton scales, up to frequencies ity. The TE is then followed by a wind which progressively of a few Hz, beyond the high-frequency break separating fluid from kinetic scales, recorded a remarkable variability of the spectral index (Smith et al. 2006; Sahraoui et al. 2010) ⋆ Contact e-mail: [email protected] © 2017 The Authors 2 R. Bruno et al. within the following frequency decade or so. The steepest Table 1. Time intervals referring to the 4 high-speed streams spectra corresponded to the trailing edges of fast streams observed with CLUSTER and THEMIS, along with the corre- while the flattest ones were found within the subsequent sponding average wind speed. slow wind regions. The same authors found an empirical re- lationship between the power associated to the inertial range and the spectral slope observed within this narrow region # Year Time interval s/c hVi −1 which allowed to estimate that this slope approaches the DoY:hh km s Kolmogorov scaling within the slowest wind and reaches a 1 2007 72:06 - 73:09 CLUSTER-1 671 limiting value of roughly 4.4 within the fast wind. In addi- 74:15 - 75:18 CLUSTER-1 612 tion, Bruno et al. (2014) suggested the possible role played 79:09 - 80:12 CLUSTER-1 296 also by Alfv´enicity in this spectral dependence. Recent the- 2 2011 36:18 - 37:01 THEMIS-C 580 oretical results seem to move in this direction attributing a 37:18 - 38:01 THEMIS-C 527 relevant role to Alfv´enic imbalance within the inertial range 39:08 - 39:21 THEMIS-C 422 (Voitenko & De Keyser 2016). 40:18 - 41:01 THEMIS-C 323 The location of the frequency break and the nature of the fluctuations within this restricted frequency range 3 2011 149:15 - 150:00 THEMIS-C 680 was addressed by several authors within the recent lit- 152:15 - 153:00 THEMIS-C 514 153:15 - 154:00 THEMIS-C 447 erature on this topic (see reviews by Alexandrova et al. 154:15 - 155:00 THEMIS-C 399 (2013); Bruno and Carbone (2016)). Although turbulence phenomenology would limit the role played by parallel 4 2011 174:15 - 175:00 THEMIS-B 605 wavevectors k k, Bruno & Trenchi (2014) firstly found that 178:15 - 179:02 THEMIS-C 408 the cyclotron resonant wavenumber showed the best agree- 179:15 - 180:00 THEMIS-B 389 ment with the location of the break compared to results obtained for the ion inertial length and the Larmor ra- dius. Successively, Chen et al. (2014) found similar results of the spectral power density adopted in order to collapse all k but did not consider a possible role of k because it was the spectra on top of each other to highlight a remarkable not consistent with the observed anisotropy of turbulence similarity in the spectra. The main difference with the (Horbury et al. 2008). Thus, this problem is still open and analysis by Bruno et al. (2014) is that these authors did these observations expect to have a theoretical explanation. not apply any normalization and the collapsing of the Telloni et al. (2015) analysed the nature of the magnetic spectra within the high frequency range came out naturally. fluctuations within this limited frequency range beyond the Moreover, another major difference was in the choice of the spectral break and found that their character was com- intervals. In Alexandrova et al. (2009) most of the intervals patible with left-hand, outward propagating ion cyclotron belonged to compressive regions while, in our analysis, they waves and right-hand kinetic Alfv´en waves, confirming pre- were avoided since we aimed to show the spectral evolution vious findings by authors like He et al. (2011, 2012a,b); from fast to slow wind within typical corotating HSS. Podesta and Gary (2011). Thus, the main goal of the present work is that of In particular, Bruno & Telloni (2015) found that these checking whether the results highlighted in Figure 4 by two populations of fluctuations experienced a different fate Bruno et al. (2014) are fortuitous or represent the canon- within different regions of the velocity stream. Both fluctu- ical situation within corotating HSS. ations become indeed weaker and weaker when analysing slower and slower wind, and the left-handed population would be the first one to disappear. Another interesting fea- 2 DATA ANALYSIS AND RESULTS ture of the analysed spectra, which stimulated the present work, was represented by the results shown in Figure 4 of In order to perform this kind of analysis it is necessary to Bruno et al. (2014). Those spectra refer to different time in- have observations covering a wide range of time scales. Since tervals chosen along the speed profile, from fast to slow wind. we aim to study the magnetic field power density spectrum The low frequency range and the high frequency range were between fluid and proton kinetic scales we need to cover obtained by Fourier transforming WIND data from the flux- time scales ranging from several tens of minutes to tens of gate magnetometer and THEMIS-C data from the searchcoil hertz. Such a wide dynamical range is generally covered by magnetometer, respectively. While within the inertial range two different kind of magnetometers, one for the low fre- the power density level greatly differs from fast to slow wind, quency or DC field and another one for the high frequency as expected, no evident differences can be observed within or AC field. Two common kinds of magnetometers adopted the high frequency range above 1Hz, all the spectra col- onboard magnetospheric and heliospheric s/c are flux-gate lapse on top to each other showing a spectral slope that and the search-coil instruments for DC and AC field, re- Bruno et al.