11institutetext: Department of Physics and Astronomy, University of Turku,
Finland
11email<EMAIL_ADDRESS>22institutetext: Leibniz-Institut für
Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
22email<EMAIL_ADDRESS>33institutetext: Institut für Theoretische Physik,
IV, Ruhr-Universität Bochum, 44780 Bochum, Germany
33email<EMAIL_ADDRESS>44institutetext: Bay Area Environmental Research
Institute, NASA Research Park, Moffett Field, CA, USA 55institutetext: LESIA –
Observatoire de Paris, Univ. PSL, CNRS, Sorbonne Univ., Univ. de Paris, 5
place Jules Janssen, F- 92190 Meudon, France 66institutetext: University of
Minnesota, Minneapolis, MN, USA 77institutetext: European Space Agency (ESA),
European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ,
Noordwijk, The Netherlands 88institutetext: Institut für Experimentelle und
Angewandte Physik, Universität Kiel, 24118, Kiel, Germany

# Connecting solar flare hard X-ray spectra to in situ electron spectra

A comparison of RHESSI and STEREO/SEPT observations

N. Dresing 1177 A. Warmuth 22 F. Effenberger 3344 K.-L. Klein 55 S. Musset
6677 L. Glesener 66 M. Brüdern 88

###### Abstract

Aims. We aim to constrain the acceleration, injection, and transport processes
of flare-accelerated energetic electrons by comparing their characteristics at
the Sun with those injected into interplanetary space.

Methods. We have identified 17 energetic electron events well-observed with
the SEPT instrument aboard STEREO which show a clear association with a hard
X-ray (HXR) flare observed with the RHESSI spacecraft. We compare the spectral
indices of the RHESSI HXR spectra with those of the interplanetary electrons.
Because of the frequent double-power-law shape of the in situ electron
spectra, we paid special attention to the choice of the spectral index used
for comparison.

Results.  The time difference between the electron onsets and the associated
type III and microwave bursts suggests that the electron events are detected
at 1 AU with apparent delays ranging from 9 to 41 minutes. While the parent
solar activity is clearly impulsive, also showing a high correlation with
extreme ultraviolet jets, most of the studied events occur in temporal
coincidence with coronal mass ejections (CMEs). In spite of the observed onset
delays and presence of CMEs in the low corona, we find a significant
correlation of about 0.8 between the spectral indices of the HXR flare and the
in situ electrons. The correlations increase if only events with significant
anisotropy are considered. This suggests that transport effects can alter the
injected spectra leading to a strongly reduced imprint of the flare
acceleration.

Conclusions. We conclude that interplanetary transport effects must be taken
into account when inferring the initial acceleration of solar energetic
electron events. Although our results suggest a clear imprint of flare
acceleration for the analyzed event sample, a secondary acceleration might be
present which could account for the observed delays. However, the limited and
variable pitch-angle coverage of SEPT could also be the reason for the
observed delays.

###### Key Words.:

– Sun –

##  1 Introduction

In solar flares, energy that is stored in nonpotential coronal magnetic fields
is released impulsively, presumably triggered by magnetic reconnection. In
response, the solar atmosphere emits electromagnetic radiation over the whole
wavelength range from radio to gamma rays (e.g., Fletcher et al., 2011).
Analyses of this emission recorded by remote-sensing instruments have revealed
key insights into the physics of solar flares. In particular, the observation
of nonthermal bremsstrahlung in the hard X-ray (HXR) range has shown that
electrons are efficiently accelerated in flares and carry a significant
fraction of the energy released (cf. Holman et al., 2011; Warmuth & Mann,
2020). While nonthermal HXRs are primarily produced by electrons that
precipitate into deeper layers of the solar atmosphere, electrons can also
propagate upward through the corona and into interplanetary space. This is
revealed by type III radio bursts, which are rapidly drifting structures
observed in dynamic radio spectra (cf. White et al., 2011; Reid & Ratcliffe,
2014). They are generated by escaping electron beams that excite Langmuir
turbulence in the ambient plasma, which is subsequently converted to
electromagnetic radiation.

Such interplanetary electron beams can be detected in situ by particle
instruments on spacecraft. However, one common feature of solar electron
events has challenged our understanding of the parent acceleration process for
decades, which is a frequently observed delay of 10-20 minutes between the
occurrence of the solar counterpart, for example flare or radio type III
burst, and the inferred injection time of the electrons based on their
observed onset times at the spacecraft (e.g., Haggerty & Roelof, 2002; Kahler
et al., 2007). These delays were often interpreted as an indication of a
different acceleration process, for instance a coronal or CME-driven shock
(e.g., Haggerty et al., 2003; Kahler et al., 2007). However, also scenarios
where flare-accelerated electrons are re-accelerated or energized by ongoing
reconnection in the solar corona, possibly driven by the uplifting CME, are
under discussion (Maia & Pick, 2004). Furthermore, magnetic trapping might
also be involved in delayed onsets and for the acceleration of electrons to
higher energies (e.g., Dresing et al., 2018; Li et al., 2020).

However, not all solar energetic electron events show such a delay and some
case studies even reported different behavior at different energies, that is a
prompt and a delayed component, within a single event (Krucker et al., 1999;
Wang et al., 2006a; Li et al., 2020). This suggests that some electron events
detected in situ may indeed be of the same particle distribution as the HXR
producing electrons, or at least still carry imprints of the flare
acceleration. It is therefore tempting to compare the energy spectra of the
HXR flare with the one of the in situ electrons. Depending on which
approximation is used to invert the nonthermal HXR spectrum, the expected
relation of the photon spectral index $\gamma$ with the in situ electron
spectral index $\delta$ is either $\delta=\gamma_{thick}+1$ for the thick-
target model or $\delta=\gamma_{thin}-1$ for the thin-target model (cf. Brown,
1971; Holman et al., 2011). When analyzing 16 impulsive and non-delayed
electron events observed by Wind/3DP (Lin et al., 1995) and their HXR
counterpart detected by the RHESSI spacecraft (Lin et al., 2002), Krucker et
al. (2007) found a good linear correlation between the spectral indices of
0.83. However, the value pairs were neither consistent with the thin nor with
the thick-target model but were all lying in between. Another sample of 15
events studied by Krucker et al. (2007), which was characterized by larger
onset delays of $>8$ minutes, showed no clear correlation and a shift of the
points toward the thin-target solution, which led Petrosian (2016) to conclude
that the electrons of these events may have experienced a further acceleration
after their initial energization in the flare. An additional argument for the
close association of HXR-producing and escaping electrons has recently been
provided by Xia et al. (2021) who reported on two events showing consistent
energy cutoffs in the two populations.

The spectra of electrons observed in situ can often show spectral breaks or
transitions that can relate to transport processes both near the original
acceleration site and in interplanetary space (e.g., Kontar & Reid, 2009;
Strauss et al., 2020). Dresing et al. (2020) studied the spectra of 781
electron events observed with the Solar Electron and Proton Telescope (SEPT,
Müller-Mellin et al., 2008) aboard the two STEREO spacecraft and found double
power-law shapes in 56% of the events. In this paper, we use this electron
event list as a starting point and investigate the relation between the
energetic electron population precipitating onto the Sun as constrained by
RHESSI, and the interplanetary electrons detected in situ with the SEPT
instruments on board of the two STEREO spacecraft. We put a particular focus
on the timing and spectral relation between both populations.

Figure 1: Time evolution of the X-ray and radio emission associated with the
electron event on 2011 Mar 24. From bottom to top: time profiles of the GOES
soft X-ray flux, of the RHESSI 25–50 keV count rates (corrected for
instrumental effects), and of the radio flux at microwave frequencies, and
dynamic spectra in the meter-wave and decameter-hectometer-wave radio range.
The interval used for the computation of the RHESSI spectrum shown in Fig. 3
is indicated by the pair of red lines in the two bottom panels. Figure 2:
Solar energetic electron observations by SEPT aboard STEREO B on 2011 Mar 24.
The top panel shows the electron intensity in all available energy channels of
one viewing direction with pre-event background subtraction, the second panel
shows the 65-75 keV intensity in the four viewing directions of SEPT, and the
third panel displays the corresponding pitch-angles based in the central
pointing direction of the four telescopes.

##  2 Observations and data selection

Event selection started with a list of Solar Energetic Electron (SEE) events
observed with the SEPT instruments on board of the two STEREO spacecraft
compiled by Dresing et al. (2020) and available
online111http://www2.physik.uni-
kiel.de/stereo/downloads/sept_electron_events.pdf. The version of the list
used in this study covers the time from 2007 to 2018 and includes in total 925
SEE events, 557 at STEREO A and 368 at STEREO B. In the next step, the RHESSI
flare list222https://hesperia.gsfc.nasa.gov/rhessi3/data-access/rhessi-
data/flare-list/index.html was searched for solar flares that had a start time
within a one-hour window before the observed onset of the SEE event at the
STEREO spacecraft. This yielded 64 SEE event candidates covered by SEPT as
well as RHESSI. The low percentage of SEPT events recorded by RHESSI results
from the fact that the STEREO spacecraft were magnetically not well-connected
to the Earth-facing side of the Sun during the years of solar maximum, when
the majority of interplanetary electron events was observed. This was
especially the case for STEREO A flying ahead of Earth leading its magnetic
connection quickly to the backside of the Sun as seen from Earth. Therefore,
all except the first two events in 2007 were detected by STEREO B only.

In the next step, the association between the selected RHESSI flares and the
SEPT events was ascertained by the geometric consideration of whether the
flare was occurring at the correct hemisphere so that a magnetic connection
was at least remotely possible, followed by the inspection of radio
spectrograms provided by the WAVES instrument on the Wind satellite (Bougeret
et al., 1995) and the SWAVES instruments on the two STEREO spacecraft
(Bougeret et al., 2008). Type III bursts showing close temporal association
with the RHESSI flare were taken as strong evidence for an actual association.
Some events had to be discarded due to issues with the RHESSI data, for
example missing observations of the impulsive flare peak due to RHESSI
nighttime. In this manner, we finally obtained 17 events, for which we then
compared the spectral characteristics of the in situ electrons with the HXR
photon spectra. Two events on 2007 Jan 24 were observed by both STEREO
spacecraft, which at that time were separated by only 0.5 degrees. However,
because the lowest energy channels were corrupted in early 2007 for STEREO B
data we only use the observations of STEREO A for these two events in our
correlation. Section A.1 in the appendix discusses the spectral variation
between the closely spaced spacecraft for these two events and its implication
for our study.

Table 1: Event list including the basic parameters of the correlated flare and SEE events. For details, see main text. HXR | GOES | flare |  |  |  | $E_{\mathrm{b}}$ |  | $\Delta t$ | $L$ |  $\Delta\Phi$, $\Delta\Theta$
---|---|---|---|---|---|---|---|---|---|---
peak time | class | location | $\gamma$ | $\delta_{1}$ | $\delta_{2}$ | [keV] | s/c | [min] | [AU] | [deg]
2007/01/24 00:31:24 | B5.1 | S05W61 | $3.2\pm 0.09$ | $3.0\pm 1.0$ | $3.8\pm 0.6$ | 79 | A | $42\pm 10$ | 2.37 | 1, 1
2007/01/24 00:31:24 | B5.1 | S05W61 | $3.2\pm 0.09$ | $2.7\pm 1.0$ | $3.6\pm 0.9$ | 107 | B | $43\pm 1$ | 2.49 | 1, 0
2007/01/24 05:16:09 | B6.8 | S05W64 | $4.1\pm 0.26$ | $3.6\pm 0.3$ | – | – | B | $37\pm 1$ | 2.09 | 3, 0
2007/01/24 05:16:09 | B6.8 | S05W64 | $4.1\pm 0.26$ | $3.2\pm 0.6$ | $3.9\pm 1.3$ | 98 | A | $42\pm 10$ | 2.37 | 4, 1
2009/12/22 04:56:10 | C7.2 | S28W47 | $2.7\pm 0.04$ | $2.0\pm 0.1$ | $3.0\pm 0.2$ | 122 | B | $31\pm 1$ | 1.75 | 35, 34
2010/02/08 03:12:24 | C6.2 | N22E00 | $3.4\pm 0.10$ | $2.4\pm 0.2$ | – | – | B | $34\pm 1$ | 1.92 | 7, 21
2010/11/12 03:53:41 | C1.0 | S21E02 | $3.7\pm 0.06$ | $3.6\pm 0.3$ | – | – | B | $37\pm 1$ | 2.04 | 29, 28
2010/11/12 08:01:54 | C1.5 | S23W01 | $3.9\pm 0.08$ | $2.9\pm 0.3$ | $4.5\pm 0.5$ | 118 | B | $36\pm 1$ | 2.04 | 27, 30
2010/11/17 04:36:44 | B7.8 | S34E21 | $4.3\pm 0.11$ | $1.6\pm 1.7$ | $3.4\pm 1.0$ | 69 | B | $47\pm 1$ | 2.6 | 10, 41
2011/03/24 17:04:34 | C9.1 | S15E41 | $4.1\pm 0.05$ | $2.9\pm 0.6$ | $5.1\pm 2.3$ | 195 | B | $40\pm 1$ | 2.21 | 14, 14
2012/01/12 00:51:58 | C1.5 | N21E20 | $4.9\pm 0.53$ | $4.4\pm 0.4$ | $6.4\pm 2.0$ | 87 | B | $29\pm 1$ | 1.64 | 30, 14
2012/03/25 00:27:54 | C3.0 | N20E26 | $3.4\pm 0.03$ | $2.7\pm 0.4$ | $4.0\pm 0.9$ | 110 | B | $50\pm 1$ | 2.83 | 23, 18
2012/04/16 00:26:14 | C1.8 | N13E89 | $4.9\pm 0.10$ | $4.8\pm 0.5$ | – | – | B | $39\pm 1$ | 2.21 | 10, 14
2012/05/07 03:21:58 | C2.7 | N13E67 | $4.4\pm 0.03$ | $2.9\pm 0.2$ | $4.9\pm 0.6$ | 106 | B | $61\pm 10$ | 3.45 | 15, 17
2012/06/27 12:36:00 | C3.4 | N15E64 | $3.7\pm 0.03$ | $2.4\pm 0.3$ | $4.9\pm 0.6$ | 90 | B | $29\pm 1$ | 1.64 | 1, 22
2012/06/28 02:12:24 | C2.6 | N17E56 | $4.3\pm 0.09$ | $2.8\pm 0.6$ | $3.7\pm 0.4$ | 90 | B | $32\pm 1$ | 1.81 | 20, 24
2012/07/01 07:14:44 | C5.4 | N16E11 | $4.3\pm 0.14$ | $3.6\pm 0.3$ | $5.5\pm 0.7$ | 104 | B | $31\pm 1$ | 1.7 | 54, 23
2014/03/19 16:26:14 | C3.3 | S12E81 | $5.9\pm 0.20$ | $3.1\pm 0.7$ | $4.0\pm 0.7$ | 101 | B | $35\pm 5$ | 1.98 | 23, 18
2014/06/09 17:05:04 | C8.8 | S19E90 | $3.5\pm 0.05$ | $2.6\pm 0.5$ | $4.0\pm 1.4$ | 90 | B | $43\pm 1$ | 2.43 | 28, 17

##  3 Analysis

Figures 1 and 2 show remote-sensing and in situ observations of an example
event in the analyzed sample occurring on 24 Mar 2011. We present the analysis
of both types of spectra in the following.

Figure 3: Left: Background-subtracted RHESSI photon flux spectrum (black) of
the flare of 2011 Mar 24 fitted with an isothermal component (red) and a
nonthermal photon power-law (blue). The spectrum was derived using all RHESSI
detectors except for number 2 and 3. For comparison, the pre-event background
(brown) is plotted as well. The fit results for emission measure EM,
temperature $T$, and spectral index $\gamma$ are indicated. Right: Background-
subtracted in situ electron spectrum of the 2011 Mar 24 event. The spectrum is
constructed by the peak intensities of each energy channel (marked by circles
in the top panel of Fig. 2). The line represents a broken-power law fit to the
data.

###  3.1 X-ray and radio observations

The time histories of X-ray and radio emission in Fig. 1 show a C9-class flare
preceded and followed by distinct minor events. During the rise phase of the
soft X-ray flux, bursts produced by nonthermal electrons are observed in hard
X-rays and microwaves (second and third panels from bottom). The hard X-ray
emission is bremsstrahlung produced by electrons of several tens of keV, the
microwave emission is gyrosynchrotron radiation from electrons of several tens
to hundreds of keV. The microwave data are from the Sagamore Hill (SGMR)
Station (USA) of the Radio Solar Telescope Network
(RSTN)333https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-
features/solar-radio/rstn-1-second/. The two top panels display dynamic
spectrograms in the (180-25) MHz range (SGMR444Data from
https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-
radio/rstn-spectral/) and the (13.6-1) MHz
range555https://cdaweb.gsfc.nasa.gov/pub/data/wind/waves/ (Wind/WAVES;
Bougeret et al., 1995). They show several groups of type III bursts, produced
by electron beams at a few tens of keV propagating outward from the low corona
along open magnetic field lines. The hard X-ray and microwave bursts in the
low solar atmosphere occur at the times of well-identified and rather strong
type III bursts. Besides at times of the main HXR and microwave emission there
are tiny events, which accompany the other type III bursts. But the event
clearly has one main episode of energetic electron acceleration in the low
corona, lasting a few minutes, and the type III bursts demonstrate that
simultaneously electrons escape along open field lines to the high corona and
the interplanetary space.

The event is in many respects representative of our data set. Firstly, the
electron events are accompanied by hard X-ray and microwave bursts and by
metric-to-hectometric type III bursts. Secondly, the microwave bursts of 14
out of 17 events show time profiles and flux density spectra typical of
gyrosynchrotron emission666We note that while it is in principle possible to
constrain the electron spectrum from the optically thin gyrosynchrotron
spectrum, a simple relationship between the two indices exists only in the
extremely relativistic case, which generally does not apply to solar microwave
bursts. In the case of the analyzed events, the microwave bursts are weak (a
few tens of sfu at most), only a few percent of the quiet-Sun background.
Although the nonthermal part can be identified, it is likely superposed on a
thermal bremsstrahlung component. Under these circumstances, the microwave
emission does not offer a valuable quantitative constraint of the electron
spectral index., which suggests that electrons are accelerated to energies
above 100 keV. In two other events the nonthermal microwave emission seems to
be plasma emission, in one event only thermal bremsstrahlung is observed. A
third general feature is the gyrosynchrotron emission that lasts from 10 s to
5 min, and the nonthermal HXR emission lasting from 30 s to 2 min, in temporal
coincidence with type III emission at m-$\lambda$. Finally, in most events
(13/17) several groups of type III bursts are observed, and only one is
accompanied by a clear HXR and microwave burst.

###  3.2 In situ observations of electrons

The top panel of Fig. 2 displays the intensity measured by SEPT in all energy
channels and the circles at the intensity maxima mark the peak intensities
used to construct the background-subtracted peak intensity spectrum, which is
shown in Fig. 3 (right). The second panel from top shows the intensity of
65-75 keV electrons in all four viewing directions of SEPT with the
corresponding pitch angles of the telescope center axes plotted below. We
note, that in case of anisotropic events (like shown in Fig. 2), we always use
the spectrum observed in the viewing direction measuring the highest
intensity. In case of isotropy, the Sun-facing telescope was used. A poor
pitch-angle coverage due to non-nominal magnetic field configurations can
seemingly reduce or even hide the real anisotropy of a particle beam. As in
such cases the center of the particle beam with the highest electron
intensities is not well observed, this can potentially also affect the
determined spectrum and spectral shape (see also section 3.5).

###  3.3 Analysis of photon and electron spectra

For the associated HXR bursts, the peak time of the nonthermal emission was
determined from RHESSI lightcurves by using the highest energy range in which
a flare signature was observed. In most cases, this was in the range of 25-50
keV. In all cases, the used lightcurves showed a more impulsive behavior as
seen in the 6-12 keV band, which is always dominated by thermal emission for
medium to large flares. In all events, the duration of the nonthermal peak was
around 30 sec. A RHESSI count spectrum was then obtained by integrating over a
30 sec time interval centered at this HXR peak time as marked by the vertical
lines in Fig. 1, using a combination of all detectors that were well-
functioning according to the RHESSI detector health database. Inspecting the
background-subtracted spectra, we found the nonthermal part to be consistent
with a single power-law in all events. The spectra were then fitted with the
combination of an isothermal plasma component, a broken power-law with a fixed
slope of -1.5 below the break that reproduces the nonthermal component
(Emslie, 2003). A photospheric albedo component was taken into account using
the standard RHESSI OSPEX spectral analysis
package777https://hesperia.gsfc.nasa.gov/ssw/packages/spex/doc/ospex_explanation.htm
(based on Kontar et al. (2006)), assuming an isotropic electron distribution,
which is more consistent with observations than a strongly beamed distribution
(cf. Kontar & Brown, 2006). We have additionally performed the spectral
fitting without an albedo component and found only small differences of the
spectral indices (smaller than 0.1) and conclude that the albedo component
does not influence our results.

The nonthermal emission is thus characterized by the spectral index $\gamma$
above the break. The upper energy limit of the fit range was determined by the
counting statistics, which implied that several events could only be fitted up
to 30 keV (the limit was 60 keV on average). Since photons of a given energy
are mainly produced by electrons of about twice this energy, we do have an
energy overlap with SEPT even in these cases. The resulting spectrum and
corresponding fits for the example event on 24 Mar 2011 are shown in Fig. 3
(left). Additionally, we also performed thick-target fits to the spectra,
which we use to determine the number of accelerated electrons (see Sect. 3.6).
Using the resulting spectral indices from these thick-target fits in our
correlation analysis (not shown) does not change the correlation but as it
involves extra model assumptions, we decided not to use these values. We
furthermore refrained from using fits applying the thin-target model since we
see no evidence for thin-target emission, as discussed in Section 3.5.

Figure 4: Left: Histogram of the time delay $\Delta t$ between the nonthermal
HXR flare peak and the onset of the SEE event at STEREO. The black histogram
refers to all events, while the green one shows the distribution for the
events that are potentially associated with CMEs. The dotted lines indicate
the median of the distributions. Middle: Histogram of the longitude separation
$\Delta\Phi$ between the flare location and the extrapolated footpoint of the
magnetic field line connecting STEREO to the Sun. Right: Correlation plot of
the time delay $\Delta t$ and the longitude separation $\Delta\Phi$. The
colors denote the degree of anisotropy of the in situ electrons. $C$ indicates
the linear correlation coefficient.

The right-hand side shows the corresponding spectrum of the in situ electron
event and a broken-power law fit. For each event, the electron observations of
SEPT were corrected from potential contamination due to ions or higher energy
electrons as described in Dresing et al. (2020). To determine the spectrum of
the event we use the peak intensities observed individually in each available
energy channel (marked by the circles in the top panel of Fig. 2) after a pre-
event background subtraction has been applied. We then fit each spectrum with
single- and double-power law functions and chose the better fit based on the
reduced chi square of the fits. The fits take into account the uncertainties
of the peak intensities caused by counting statistics as well as the energy
bin widths representing an uncertainty in energy. The uncertainties of the fit
parameters were determined using 95%-confidence intervals. For details see
Dresing et al. (2020) and Strauss et al. (2020). We note that determining
electron fluence spectra with STEREO/SEPT data is complicated due to the issue
of ion contamination that is usually more dominant during the later phase of
the events. Determining reliable fluence values and, especially,
uncertainties, which are required by the fit, is difficult. We therefore
decided not to present an analysis of the in situ fluence spectra here but
comment on potential differences between the peak flux and the fluence spectra
in Section 4.2.

Table 1 shows the basic parameters for all 19 flare and SEE events, including
the HXR peak time (as detected at the spacecraft), GOES class, flare location,
HXR photon spectral index $\gamma$, in situ electron spectral indices
$\delta_{1}$ and $\delta_{2}$888If $\delta_{2}$ and $E_{b}$ are missing, a
single power law fit was used, spectral break energy $E_{\mathrm{b}}$, which
STEREO spacecraft detected the SEE event, the time delay $\Delta t$ between
the nonthermal HXR flare peak (corrected for light travel time) and the onset
of the SEE event at STEREO, propagation path length $L$ of 55-85 keV electrons
corresponding to $\Delta t$ (see section 3.4), and the longitude and
latitudinal separations $\Delta\Phi$ and $\Delta\Theta$ between the flare
location and the ballistically extrapolated footpoint of the magnetic field
line connecting the spacecraft to the Sun.

###  3.4 Timing and magnetic connectivity

The onset times of the SEPT electron events were determined using the
3$\sigma$ method, which can only be considered as an upper limit for the real
onset time. An earlier onset could be masked by the background noise of the
detector (Laitinen et al., 2010). Furthermore, especially in the case of more
gradual intensity increases, which can also be caused by non-nominal magnetic
field orientations resulting in a poor pitch-angle coverage at the SEPT
instrument, the 3$\sigma$ method can yield onset times that are too late.
Larger time averaging is often used to overcome these issues, and the time
averaging applied for each event has been used as a measure for the
uncertainty of the onset time (Dresing et al., 2020). This uncertainty has
been propagated to $\Delta t$ in table 1 in cases when higher averaging was
used. Otherwise, the uncertainty represents the time resolution of the
STEREO/SEPT data of 1 minute. The time delays $\Delta t$ in our sample, which
range from 29 to 61 minutes, with a median of $\Delta t$ = 37 minutes, are the
delays between the HXR peak time at the Sun and the detection of the $55-85$
keV electron onset. Assuming that the in situ measured electrons were injected
at the time of the HXR peak, $\Delta t$ represents the propagation time of the
first arriving particles. A scatter-free propagation along a nominal Parker
spiral would take about 20 minutes at these energies. Comparing $\Delta t$
with this nominal and scatter-free propagation time we find that all events in
our sample arrive delayed.

The events with medium to large anisotropy at their onset (see Table 3), where
the spacecraft was likely well-connected to the electron source, have delays
between 29 and 40 minutes. While these delays are among the shorter ones in
our sample, they still exceed expectation for scatter-free propagation by 9-20
minutes.

Therefore, our event sample does not seems to contain any true prompt events
as defined by Krucker et al. (2007) with a delay between the flare and the
inferred injection time of the in situ measured electrons of $<8$ minutes.
There can be several reasons for the observed delays. On the one hand, it
could be due to instrumental effects leading to a delayed onset determination
as described above. Furthermore, we note, that the pitch-angle coverage was
not ideal in the majority of the events, which could cause apparent onset
delays especially if the electron beam was very narrow during the early phase
of the event. In this case, the delay would not represent a physical process
related to the acceleration, injection, or transport of the particles. On the
other hand, the actual propagation path of the electrons could be longer than
the nominal Parker spiral, either due to large-scale distortions of the field
or due to pitch-angle scattering. Field-line random walk caused by footpoint
motion tied to the solar convection or by the turbulent solar wind evolution
can cause significant lengthening of the actual path that particles need to
follow along the magnetic field. Recent studies find that the effective field
line length can be up to twice as long as the nominal Parker connection (see,
e.g., Laitinen et al., 2016; Laitinen & Dalla, 2019; Chhiber et al., 2020),
which can cause equivalent delays in the observed particle onsets. Assuming
that such effects or scattering cause the delays, i.e. the electrons were
injected at the flare peak time, the column $L$ in the table provides the path
lengths corresponding to $\Delta t$ for 55-85 keV electrons. Finally, an
actually delayed injection of the electrons at the Sun can not be ruled out a
priori. Different effects or a mixture of them being dominant for different
events in our sample are, of course, also possible.

Figure 4 shows histograms of $\Delta t$ and the longitudinal separations
$\Delta\Phi$. Despite the partially significant delays, the majority of the
events is magnetically well-connected in longitude to STEREO, with
$\Delta\Phi$ between 0.5 and 54 degrees (median: 15 degrees). There is no
correlation between onset delay and longitude separation (see Fig. 4 right).
We also do not find any correlation with the latitudinal separation
$\Delta\Theta$ (listed in Table 1). Furthermore, the degree of anisotropy
(marked by the color in the right panel) does not correlate with the onset
delays suggesting that interplanetary pitch-angle scattering is not the main
reason for the observed delays. The green histograms in Fig. 4 denote those
events associated with CMEs that are located close to the flaring region and
have heights below one solar radius at the time of the flare (see appendix A).
They may therefore potentially influence the injection and coronal propagation
of the electrons. While the events associated with these CMEs are not
outstanding in other parameters of our analysis they seem to be among those
events showing larger separation angles (middle panel of Fig. 4) suggesting
that the CME may be involved in enlarging the injection region. The fact that
many of the analyzed events are observed in different magnetic polarity
sectors than that of the flaring active region at the Sun (see Table 3) could
furthermore suggest an injection that covers a wider angular range even across
the neutral line. Such a scenario was also suggested by Kallenrode (1993) who,
however, reported that a current sheet crossing can also lead to a decrease in
SEP intensities. On the other hand, pitch-angle scattering in the IP medium
may also be involved in filling both sides of the heliospheric current sheet
with the electron population. The majority of our events are also accompanied
by coronal EUV jets (see appendix A) but no particular connection with the
time delay or separation angle was found.

###  3.5 Spectral correlations

The results of correlating the spectral indices of the HXR photons and the in
situ electron measurements are shown in Figures 5 and 6. As discussed above
several energy-dependent effects may alter the spectrum observed in situ
eventually leading to spectral breaks, which requires to make a choice between
the two different spectral indices. For the events in our sample this choice
is often not straightforward as breaks are often found below or around 100
keV, which is in between the mean locations of the two different spectral
breaks (60 keV and 120 keV) as reported for instance by, Krucker et al.
(2007); Dresing et al. (2020). We therefore start by using always the lower
($\delta_{1}$) or the upper spectral index ($\delta_{2}$) as observed by SEPT
in case of broken power-laws and compare these with the HXR spectral index
$\gamma$. The corresponding correlation plots are shown in figures 5 and 6.
Note that in case of single power-law shapes the same in situ spectral index
has been used in both plots. The panels on the left of the figures include all
17 events, while the ones on the right consider only the nine events that
showed a distinct anisotropy (medium to large; see appendix A and last column
of table 3).

Figure 5: Correlation plots of the HXR photon spectral index $\gamma$ observed
by RHESSI and the electron spectral index $\delta$ obtained from STEREO/SEPT,
plotted for all events (left) and only the events with distinct anisotropy of
the in situ electron flux (right). In the case of events with broken power-
laws, we use here the spectral index below the break, $\delta_{1}$. For three
events, we consider either $\delta_{1}$ (red), or $\delta_{2}$ (blue). The
dotted lines indicate linear fits to the data. The dashed lines indicate the
relationships between $\gamma$ and $\delta$ expected for thick and thin-target
bremsstrahlung, respectively. The fit parameters are indicated, as well as the
linear correlation coefficients $C$.

Figure 6: As in Fig. 5, but showing the correlation of the HXR photon spectral
index $\gamma$ with the electron spectral index $\delta_{2}$ (characterizing
the high-energy part of the SEE spectrum) instead of $\delta_{1}$ in the cases
of a broken power-law. We consider either all events including the three
special cases (red), or we omit these events (black).

Three events appear to behave differently as their spectral indices
$\delta_{1}$ and $\delta_{2}$ lie systematically below the rest of the
distributions (marked by colored points in figures 5 and 6). We suspect that
these three cases represent events showing a spectral break caused by
Langmuir-wave generation (expected to occur at lower energies than the break
due to pitch-angle scattering) while the rest of the broken-power-law events
corresponds to breaks caused by pitch-angle scattering (see appendix A.2 for
more discussion on these events). Fig. 7 helps to illustrate this. It shows a
broken power-law spectrum containing two breaks and therefore three different
spectral indices $\delta_{0}$, $\delta_{1}$ and $\delta_{2}$. The first break,
marked by $\mbox{E}_{\mbox{b\\_L}}$ is assumed to correspond to Langmuir-wave
generation and the second break ( $\mbox{E}_{\mbox{b\\_trans}}$) to pitch-
angle scattering during interplanetary transport, respectively. According to
the description above, the three special events would cover the spectral part
of $\delta_{0}$ and $\delta_{1}$ while the other events correspond to
$\delta_{1}$ and $\delta_{2}$ in this sketch. To correctly handle the spectral
indices of these three events we therefore have to treat their $\delta_{2}$
values as $\delta_{1}$ values. Their $\delta_{1}$ would correspond to
$\delta_{0}$ in the sketch (not covered by the other events) and the
$\delta_{2}$ range of the other events is not covered by these three events.
We therefore have to use the blue points instead of red points in Fig. 5 and
remove the $\delta_{2}$ values (red points) from the correlation in Fig. 6.

Figure 5 shows that $\gamma$ and $\delta_{1}$ are correlated. For the three
events discussed above, both spectral indices $\delta_{1}$ (red, suspected
wrong values) and $\delta_{2}$ (blue, suspected correct values) are included.
The differently colored legends represent the Pearson correlation coefficient
and linear fit results using either $\delta_{1}$ (red) or $\delta_{2}$ (blue)
of these three events. Similarly, for Fig. 6 the correlation in red
corresponds to using all $\delta_{2}$ values in the sample, and the one in
black excludes the three red points as discussed above assuming that these
events do not provide a corresponding $\delta_{2}$ observation. The
correlations in both plots improve significantly when treating the three
events as discussed. Although the correlations with the lower and higher in
situ spectral indices are very similar, the implications for the relation
between the photon and in situ spectral indices are very different: The value
pairs in Fig. 5 clearly align along the thin-target approximation, while the
points in Fig. 6 shift to the range between thick and thin-target lines with
some points even lying above the thick target model.

Taking the correlation of $\gamma$ and $\delta_{1}$ at face value, one could
conclude that the nonthermal photon spectrum is actually generated by thin-
target emission, and that indeed both the remote-sensing and the in situ
observations detect the same particle population. However, thin-target
emission is generally believed to dominate nonthermal flare spectra only in
those cases where the HXR footpoints are occulted by the solar limb (cf.
Krucker et al., 2008). The footpoints are the locations where accelerated
electrons are stopped collisionally in the denser chromosphere, and
consequently they emit thick-target radiation, which will usually dominate any
thin-target contribution from the corona. We have performed HXR imaging with
RHESSI for all flares in order to ascertain whether HXR footpoints are present
or could be potentially obscured. In 7 flares, footpoint pairs could be
unambiguously detected, while in another 7 events, only possible indications
for footpoints could be found due to the limited image fidelity caused by the
small number of nonthermal counts. In the rest of the events, nonthermal and
thermal sources were found to be contiguous. Only one flare was located so
close to the limb that an occultation of the footpoints is possible. We find
no systematic differences in the spectral correlations for the events with
clearly visible footpoints as compared to the other flares. We thus conclude
that the HXR spectrum is actually dominated by thick-target emission.

Table 2 summarizes the determined correlation coefficients between the photon
spectral index $\gamma$ and the two electron spectral indices $\delta_{1}$ and
$\delta_{2}$, also including further subsamples based on a rough anisotropy
classification of the events (see appendix A and last column of table 3). The
correlations clearly improve if only anisotropic events are taken into
account, however the number of events with large anisotropies is unfortunately
very low. We also investigated the quality of the correlations with respect to
the onset delay, the longitudinal, and latitudinal separation angles between
flare and spacecraft magnetic footpoint at the Sun as well as the presence of
CMEs or EUV jets but did not find any dependence on these parameters.

Table 2: Pearson correlation coefficients $C$ between photon spectral index
$\gamma$ and in situ electron spectral index $\delta$. Also given are the
uncertainties on $C$ based on a bootstrapping approach.

| all | medium & large | large
---|---|---|---
| events | anisotropy | anisotropy
no. of events | 17 | 9 | 4
$\gamma$ vs. $\delta_{1}$ | $0.50\pm 0.19$ | $0.69\pm 0.20$ | $0.61\pm 0.55$
$\gamma$ vs. $\delta_{2}$ | $0.49\pm 0.19$ | $0.27\pm 0.44$ | $0.28\pm 0.77$
$\gamma$ vs. $\delta_{1}$11$1$I | $0.80\pm 0.08$ | $0.86\pm 0.09$ | $0.96\pm 0.06$
$\gamma$ vs. $\delta_{2}$22$2$I | $0.79\pm 0.09$ | $0.88\pm 0.18$ | $1.0\pm 10^{-4}$
999 n situ electron spectral index $\delta_{2}$ has been used for the three
special events (see text). n situ electron spectral index $\delta_{2}$ has
been excluded for the three special events (see text).

Figure 7: Sketch illustrating a broken-power law spectrum with two breaks
$\mbox{E}_{\mbox{b\\_L}}$ and $\mbox{E}_{\mbox{b\\_trans}}$ forming three
spectral indices $\delta_{0}$, $\delta_{1}$ and $\delta_{2}$.

Figure 8: Correlation plots of the number of nonthermal electrons above 45 keV
in the flares derived from thick-target fits of HXR spectra and the number of
electrons escaping into interplanetary space, plotted for all events (left)
and only the events with distinct anisotropy of the in situ electron flux
(right).

###  3.6 Total number of escaping electrons

Figure 8 shows the total number of escaping electrons inferred from the in
situ observations ($>45$ keV and $<425$ keV) as a function of the number of
electrons $>45$ keV accelerated in the flare assuming thick-target emission
and integrating the derived peak flux over 30 seconds. The number of in situ
electrons has been determined by integrating the fluence spectrum of the
events observed in the telescope showing the highest intensity increase, which
was also used to construct the peak intensity spectrum. The fluence is the
integrated flux over the duration of the event, with the duration being
defined by the onset of the event and an individual end time. This end time
was determined for each energy channel individually by the time when the flux
decreased to $1/e$ of the peak flux. In the same manner as for the peak
intensity spectra, analyzed in this work, the pre-event background was
subtracted from the flux before calculating the fluence and the contamination
correction was applied (c.f. Section 3.3) assuming a constant contamination
over the duration of the event.

Following Krucker et al. (2007) we assume an electron beam that is emitted
into a cone with a width of $30^{\circ}$ to derive the total number of in situ
electrons, and we use cones of $15^{\circ}$ and $60^{\circ}$ to estimate the
uncertainties shown in Fig. 8. Propagating this cone along the nominal Parker
spiral to a distance of 1 AU results in a spherical cap over which the
electrons are spread at the spacecraft position. To infer the total number of
electrons of the event, the number of electrons detected in the small SEPT
instrument are therefore scaled to the area of this spherical surface. We
note, that this approach assumes a constant energetic electron density over
the cone angle, which is only a first-order approximation. Secondly, the
sectored measurements by SEPT show that the observed particle distribution at
the spacecraft is much more isotropic compared to the assumed cone, which is
expected in case of non-negligible particle scattering during interplanetary
transport. However, without proper transport simulations and multi-spacecraft
observations a more accurate approach demanding fewer assumptions to determine
the total number of in situ electrons is not feasible.

The left hand plot of Fig. 8 shows all events in our sample, while the right
hand figure shows only events with significant anisotropy. The legends provide
the results of linear fits and the Pearson correlation coefficients. A
reasonable correlation of 0.75 is found for all events, and a slightly lower
correlation of 0.6 for the anisotropic events. Although one would rather
expect a larger correlation for anisotropic events, i.e. in the case of less
pitch-angle scattering, an effect that can reduce the determined number of
escaping electrons, the anisotropic sample does indeed contain on average
higher numbers of escaping in situ electrons. In contrast to results by James
et al. (2017), who used data by ACE/EPAM (Gold et al., 1998) and determined a
fraction of 6 to 148% of escaping electrons compared to the HXR-producing
electrons our results confirm the findings by Krucker et al. (2007). We find
very small fractions of escaping electrons with mean ratios of only 0.18% for
all events and 0.24% for the anisotropic events. For comparison, Krucker et
al. (2007) found a ratio of 0.2%.

##  4 Discussion

###  4.1 Modification of electron spectra between the acceleration region and
the spacecraft

Transport processes in the flare and in interplanetary space can alter the
initial spectral distribution of nonthermal electrons. One such process that
causes energy loss is due to Coulomb collisions (cf. Brown, 1971) when
energetic electrons propagate through a background plasma. For the escaping
electrons, this effect is negligible in interplanetary space, but it can play
a role near the acceleration site. Reid & Kontar (2013) concluded that coulomb
collisions are negligible as an energy-loss process above an energy near 40
keV, which is in the relevant range for our analysis. However, because
collisional energy loss will lead to a progressive flattening of the electron
flux spectrum toward lower energies, it could thus potentially account for the
fact that the in situ spectra are harder than the ones inferred from HXR
observations (see Fig. 5). We have, therefore, considered a model of the
ambient electron density consisting of a 2.5-fold Newkirk model (Newkirk,
1961) in the lower corona, which then transitions to the Mann model (Mann et
al., 1999) that is more appropriate for the upper corona and IP space. We
inferred the electron density in the corona above the acceleration region from
the starting frequency of the type III bursts, as observed by the worldwide
e-Callisto network (www.e-callisto.org). We found the median start frequency
near 330 MHz. Under the usual assumption of harmonic plasma emission this
corresponds to an ambient electron density of $3.4\cdot 10^{8}$ cm-3 and an
acceleration region below 0.1 R⊙ above the photosphere. Taking this value,
integrating from this height to 1 AU, and computing the effect of the spectral
flattening according to Brown (1971), we find that Coulomb collisions have
indeed a negligible effect on the spectral index in the energy range we have
considered here, and thus cannot account for the spectral differences between
precipitating and escaping electrons.

While Coulomb collisions may be neglected in our analysis, other processes
such as the generation of Langmuir waves or pitch-angle scattering may cause
spectral changes both in the flare and in the interplanetary medium (as
discussed in Section 3.5). Kontar et al. (2014) showed for example that strong
pitch-angle scattering in coronal loops can potentially cause a flattening of
the HXR spectrum and lead to spectral breaks. However, several previous
studies have found significant correlations between the HXR and in situ
electron spectral index (e.g., Kallenrode et al., 1987; Dröge, 1996; Krucker
et al., 2007) and it was suggested that 1) both spectra belong to the same
accelerated population and 2) that transport effects do only play a minor role
in altering the spectra. Many of such past studies, which analyzed solar
energetic electron spectra have used instruments, which covered only energies
$\gtrsim 100$ keV and which lacked a fine energy resolution in the lower
energy part that is needed to resolve spectral breaks caused by interplanetary
transport processes, i.e. the generation of Langmuir turbulence and pitch-
angle scattering, as discussed in this manuscript. Furthermore, both of the
mentioned transport processes are dominant at lower or near-relativistic
energies (Dröge, 2003; Agueda et al., 2014) making it difficult to detect
these with instrumentation covering mainly $\gtrsim 100$ keV. Instruments such
as the Wind/3DP and STEREO/SEPT mainly measure near-relativistic electrons
where these spectral breaks occur. However, because of the slightly different
energy coverage and resolution of the Wind/3DP and STEREO/SEPT instruments
they are likely sensitive to different spectral breaks with 3DP usually
detecting the break caused by Langmuir-wave generation and SEPT the one by
pitch-angle scattering (see Krucker et al., 2009; Kontar & Reid, 2009; Dresing
et al., 2020; Strauss et al., 2020) so that the spectral index above the break
$\delta_{2}$ detected by 3DP is likely covered by the spectral index below the
break $\delta_{1}$ as seen in SEPT data. However, an unambiguous
identification of the type of the spectral break in a single event can be
difficult because of the overlapping energy ranges of these effects. Three
events in our sample showed a systematic shift with respect to the spectral
indices of the rest of the events suggesting that these were indeed events
covering the Langmuir wave-related spectral break different to the other
events. Therefore, these events have been re-categorized accordingly (see
section 3.5 and figures 5 and 6) leading to significantly improved
correlations.

###  4.2 The spectral correlation of HXR-producing and in situ electrons

We find correlations between the HXR spectral index and the one of the in situ
electron spectrum of about 0.8 for both sets of value pairs either using the
spectral index below or above the break (see Table 2), however when using
$\delta_{1}$ the points align along the thin-target solution (Fig. 5), while
they are shifted more toward the thick-target line (lying between thick and
thin-target lines) when using $\delta_{2}$ (Fig. 6). A preliminary analysis of
the corresponding SEPT fluence spectra showed overall no change for the
$\delta_{1}$ values, but the $\delta_{2}$ values showed a trend of shifting
toward softer spectral indices causing the data points to align more along the
thick-target solution or lying even above it in the correlation plot (not
shown). However, due to the issue of ion contamination these fluence spectra
suffer large uncertainties and are less reliable.

We assume that our value pairs using $\delta_{1}$ should be compared to the
values shown by Krucker et al. (2007) who compared HXR spectra observed by
RHESSI with Wind/3DP electron spectra above the break ($\delta_{2}$). They
found a similar correlation of about 0.8, however, their value pairs were
lying between the thick and thin target solutions. The alignment of our value
pairs using $\delta_{1}$ along the thin-target model is not expected since
imaging of nonthermal footpoints shows that in most events thick-target
emission has to be dominant. After excluding also the role of energy loss due
to Coulomb collisions (see Section 4.1) we therefore suspect that another
systematic effect causes this shift. Krucker et al. (2007) found only a good
correlation for non-delayed events suggesting that the delays, frequently
observed during solar energetic electron events (e.g., Haggerty & Roelof,
2002; Kahler et al., 2007), may be caused by another or an additional
acceleration process. This is different for the events studied in this work:
all of our events show delays of at least 9 minutes with respect to the flare.
However, as discussed in Section 3.4 instrumental effects and especially
nonideal pitch-angle coverage could often be the cause for apparent delays.

Although Krucker et al. (2007) found only a low correlation of 0.43 for their
delayed event sample, those value pairs did also show a shift toward the thin-
target line, i.e. toward harder in situ electron spectra like our
$\gamma-\delta_{1}$-value pairs. Petrosian (2016) suggested that a further
acceleration process acting on the flare-accelerated electron distribution
could be the reason for this shift. However, given the still significant
correlation coefficient for our value pairs we note that such a further
acceleration should either only be of minor importance or scale with the flare
itself, so that only a systematic shift of the spectral index is caused, and
the overall correlation is preserved. We note that Krucker et al. (2007) also
suggested the possibility of further acceleration in the flare due to trapping
in closed and shrinking field lines. This would, however, only affect the
downward moving electrons, which produce the HXR spectrum.

###  4.3 Anisotropic electron events and the number of escaping electrons

We find a clear improvement of our correlations when only taking into account
anisotropic events suggesting that pitch-angle scattering can lead to a
vanishing imprint of the acceleration. We note that the lack of anisotropy can
either be caused by strong scattering during interplanetary transport but also
due to poor pitch-angle coverage of SEPT caused by non-nominal magnetic field
configurations. See table 3, which lists the strength of the anisotropy for
each event and marks if poor pitch-angle coverage was present. Consequently,
even in the case of low scattering conditions, the limitations of the
measurement can lead to vanishing correlations, i.e. to a change of the
observed spectral indices. We note, that Wind/3DP does not suffer from such a
limitation because of its unique directional observations covering the
complete 4$\pi$ space, which is for example not the case for the ACE/EPAM
instrument (Gold et al., 1998). Although EPAM/LEMS provides eight different
sectors determined through the spacecraft’s spin, there exist magnetic field
directions that are perpendicular to the measurement plane of EPAM/LEMS
reducing the pitch-angle coverage to only one point in pitch-angle space for
all sectors.

The anisotropy is also expected to influence the correlation between the
number of escaping electrons with the number of flare electrons as shown in
Fig. 8 because larger anisotropies imply weaker interplanetary scattering
conditions and therefore less dispersal of the injected population. However,
we do not find an improvement of the correlations when only taking into
account the anisotropic events. But poor pitch-angle coverage, which can lead
to the underestimation of the anisotropy as well as to an underestimation of
the total number of electrons, may again affect the results. Furthermore, the
strong assumptions, which have to be made to determine the number of escaping
electrons likely play an even larger role for the weak correlation. These
assumptions are i) the same size of the cone ($30^{\circ}$) filled with
electrons for each event, which is very likely not true due to varying
injection cone sizes, i.e. the angular width of open magnetic field lines. ii)
A constant distribution of electrons over the $30^{\circ}$ cone, which is only
a first-order approximation because of the observed presence of weak or
missing anisotropies depicting the presence of interplanetary scattering.
Furthermore, an angular-dependent injection function is possible. iii) A
nominal Parker field with a fixed Parker spiral length for all events, not
taking into account large-scale structures or field line meandering, which
will further introduce event to event variations leading to a vanishing
correlation. Nevertheless, our results confirm the findings by Krucker et al.
(2007) that only a very small fraction ($\sim 0.2$%) of accelerated electrons
are finally injected into interplanetary space when compared to the number of
the HXR producing electrons.

###  4.4 The timing of electron release in the corona

A simple picture of the relationship between electrons detected at 1 AU and
radio or X-ray emitting electrons in the solar atmosphere is a common short
acceleration and the release into magnetic structures in the corona and onto
open field lines to the heliosphere. This picture is supported by a number of
detailed timing studies of the start times of impulsive electron events (see
the discussion of the 2000/05/01 case in Klein, 2021). But in other events the
first electrons were reported to arrive later at the spacecraft than expected.
Instruments with limited pitch-angle coverage, such as the STEREO detectors,
might just miss the first arriving electrons, creating an apparent delay.
Linhua Wang and coworkers (Wang et al., 2006a, 2016) exploited the excellent
pitch-angle coverage of the Wind/3DP instrument in systematic analyses of the
onset time and the duration of release of electrons across the energy range
between a few keV and some tens or hundreds of keV. They found that electrons
detected with energies below 20 keV at the spacecraft were released since
earlier times and over longer durations than the electrons above about 30 keV.
Kontar & Reid (2009) ascribe such inferred earlier releases to the energy loss
of the Langmuir-wave generating (low-energy) electrons. As an alternative, or
an addition, our observations suggest a scenario where electron beams are
accelerated to different energies in several successive episodes: we find that
the solar counterparts of the electron events are in general groups of type
III bursts, discernible at frequencies above $\sim$1 MHz. As illustrated in
Fig. 1, the hard X-ray and microwave emissions, which are produced by
electrons at tens to hundreds of keV, accompany one of these groups of type
III bursts, but other groups occur before and afterward. Such additional type
III bursts without prominent microwave counterpart are observed in 13/17 of
our events. This is also shown by the timing of the microwave bursts and the
DH type III bursts (Table 3, cols. 2 and 4). Since type III bursts at 1 AU are
produced by electrons with energies below 20 keV (e.g., Ergun et al., 1998),
this timing implies that repeated episodes of impulsive electron acceleration
to relatively low energies (a few tens of keV) occur in the corona, and that
one such episode is also accompanied by the acceleration of near-relativistic
electrons. The low-energy electrons are hence accelerated over longer times
than those of higher energies that are seen through their hard X-ray and
microwave emission, consistent with Wang and coworkers. But the higher time
resolution offered by the radio and HXR analysis shows that the observations
cannot be ascribed to a single, time-extended acceleration episode of low-
energy electrons, and a different, shorter and delayed, episode at the higher
energies. The electron fluxes at 1 AU rather result from multiple injections
of electrons in the corona. Each release produces electrons up to a few tens
of keV that are able to emit type III bursts, but the near-relativistic
electrons are only accelerated during part of these acceleration episodes.
This particular interval actually consists of several successive events, too,
as seen by the multiple microwave peaks. Vlahos & Raoult (1995) argued indeed
that apparently individual type III bursts actually result from multiple
energy releases, and Chen et al. (2013) confirmed this idea by the Karl G.
Jansky Very Large Array (VLA) observations with high temporal and spectral
resolution.

###  4.5 Association with jets and CMEs

The association of the electron events in the present study with various types
of EUV activities, including jets and large-scale mass motions, is in line
with earlier studies on 3He-rich SEP events (Wang et al., 2006b; Pick et al.,
2006; Nitta et al., 2006, 2015). However, we do not find a unique association
with EUV jets. Y-M Wang and coworkers (Wang et al., 2006b; Pick et al., 2006)
used SoHO observations to identify EUV jets associated with 3He-rich SEP
events (13/21 events with suitable observations). They suggested that EUV
imaging with higher cadence would reveal more jets, and proposed a model where
the EUV jet was the signature of magnetic reconnection between closed and open
coronal magnetic field lines, which also led to the particle acceleration of
electrons and ions. But high-cadence EUV imaging from STEREO and especially
SDO used in the present work, as in Nitta et al. (2015), does not confirm the
expected systematic association between impulsive SEP events and coronal
plasma jets. In some events the eruptive coronal activity may hide the plasma
jet, but in some others jets are definitely not detected with SDO/AIA.
However, there are also events with a clear timing correspondence, within a
few minutes, of the electron acceleration in the corona revealed by hard X-ray
and microwave emission, and the plasma jet. There is no a priori reason to
exclude magnetic reconnection on the sole reason that no EUV jet is observed.
The association with type III bursts and the PFSS extrapolations show the
existence of open field lines in the parent active region. The scenario of
interchange reconnection (e.g., Shibata et al., 1994) as the origin of
impulsive electron events therefore remains attractive, although the
observations do not provide a unique simple picture where impulsive electron
events would be exclusively associated with EUV jets, rather than with
eruptive activity on larger scales.

The association of electron events with CMEs gives another hint to a more
diversified picture of the origin of impulsive particle events than the
historic two-class picture of either impulsive (flare-associated) or gradual
(CME-associated) SEP-events (Reames, 1999). CMEs are not an occasional
counterpart of the impulsive electron events studied here, but some white-
light signature is observed with virtually all our electron events. In the
only case where we did not identify a CME in the vicinity of the position
angle of the parent flare, 2007 Jan 24, a faint signature might be hidden by a
broad CME from a distinct active region. In the other events CMEs are seen in
the corona. Their morphologies range from jet-like, which on occasion (2010
Nov 17) are clearly the extension of an EUV jet to the higher corona, to
extended, as already reported by Wang et al. (2006b). The combination of
coronographic observations from SoHO and STEREO offered us the possibility to
have in most events one spacecraft, which saw the parent activity close to the
solar limb, so that the identification of a CME was much easier than in the
earlier SoHO observations. The enhanced cadence of the STEREO coronagraphs
also allows for a better timing identifications. In three out of 14 events
where adequate coronographic observations were available, the CME came from
previous erupting activity. They show that the CME is not a necessary
condition for the electrons to achieve near-relativistic energies. But in nine
cases the extrapolated height of the CME at the time of the hard X-ray and
microwave burst, i.e. at the time of acceleration of near-relativistic
electrons, was a few fractions of a solar radius above the photosphere. The
presence of these low-altitude CMEs seems to be associated with those events
at larger longitudinal separation angles (see Fig. 4). These CMEs might hence
play a role in widening the injection region, for example due to field-line
spreading or deflection in the corona, or to electron acceleration on open
field lines remote from the parent active region (e.g., Salas-Matamoros et
al., 2016).

##  5 Summary and conclusions

For 17 different solar flare events we correlated the HXR spectral
characteristics measured by RHESSI with the corresponding spectra of electron
events observed in situ with STEREO/SEPT. Most of the in situ electron events
show broken power-law spectra presumably caused by transport effects. At least
two processes during interplanetary transport have been identified that are
capable of causing such spectral breaks: i) the generation of Langmuir
turbulence and ii) pitch-angle scattering (see discussion above). However, the
range of the potential positions of these different breaks overlap at
$\sim$$100\text{\,}\mathrm{keV}$. This and the limited energy range and
resolution of energetic particle instruments are likely the reasons why
usually only a single break is identified in solar energetic electron spectra
(e.g., Lin et al., 1982; Reames et al., 1985; Krucker et al., 2009; Dresing et
al., 2020). It can therefore be not straightforward to identify which part of
the spectrum is least influenced by the above effects and best suited to infer
the acceleration spectrum.

We investigated the correlation of the HXR spectral index with both spectral
indices (in case of broken-power-law shapes) observed in the in situ spectra.
We find a good correlation of $\sim 0.8$ for both sets of value pairs with an
alignment along the thin-target solution, i.e. a shift toward harder in situ
electron spectral indices, when using the spectral index below the break
$\delta_{1}$ or a shift toward the thick-target solution when using
$\delta_{2}$. All of our events would fall into the class of delayed events as
defined by Krucker et al. (2007) who found only a low correlation of $\sim
0.4$ for these events. Although it cannot be ruled out that many of the
observed onset delays are only apparent delays caused by instrumental effects,
such as occasional poor pitch-angle coverage of STEREO/SEPT, the majority of
our events are accompanied not only by EUV jets but also by CMEs. While the
jets are likely a sign of interchange reconnection providing the flare-
accelerated electrons with a connection to open field lines, a potential role
of the CMEs in the acceleration process as suggested by Petrosian (2016),
which could also cause the observed delays, cannot be ruled out. However, we
do not find an effect of the CMEs on the correlation of the spectral indices.
Nevertheless, the CMEs could have perturbed the transport of electrons through
the lower corona, which might occasionally have caused a wider or shifted
injection into interplanetary space as suggested by the correlation of CMEs
with events observed at larger longitudinal separation angles.

We find clearly improving correlations when only considering events, which
show significant anisotropies in the in situ electron observations. This
suggests that transport effects such as pitch-angle scattering can reduce the
spectral imprint of the acceleration and need to be taken into account when
inferring the accelerated electron spectrum from spacecraft measurements.

Analysis of the starting frequencies of the associated type III radio bursts
suggests that the acceleration height of most of our events was below 0.1 R⊙
above the photosphere. Furthermore, a detailed inspection of radio and
microwave observations suggests that the electron fluxes at 1 AU could result
from multiple injections of electrons in the corona as the majority of our
events is accompanied by groups of type III bursts. However, higher energy,
i.e. near-relativistic electrons are only accelerated during part of these
acceleration episodes as an indicated by the shorter hard X-ray and microwave
emission.

in situ measurements of solar energetic electrons will remain a key observable
to study acceleration, injection, and transport processes of SEP events.
Furthermore, as their propagation time from the Sun to Earth is significantly
shorter than that of associated solar energetic ions, one main application of
solar energetic electrons is space weather forecast as used for example in the
Relativistic Electron Alert System for Exploration (REleASE, Posner et al.,
2009). Electron event observations during the upcoming solar cycle taken by
new space missions such as Parker Solar Probe or Solar Orbiter open up new
opportunities to understand solar energetic electrons events. Much
advantageous over the study presented here, Solar Orbiter will allow to detect
the HXR flare and the in situ electrons at the same spacecraft, with the
Spectrometer/Telescope for Imaging X-rays (STIX; Krucker et al., 2020) and the
Energetic Particle Detector (EPD; Rodríguez-Pacheco et al., 2020).
Furthermore, both new space missions will take measurements at much smaller
radial distance than 1 AU allowing to tackle the effect of interplanetary
transport especially when combined with 1 AU baseline observations provided
for instance by, STEREO A, SOHO, ACE, and Wind. The new state-of-the art
instruments also provide energetic electron measurements over a wider energy
range with very fine energy resolution, which might finally allow to separate
the imprints of acceleration and transport in the energy spectra.

###### Acknowledgements.

The work of A. W. was supported by DLR under grant No. 50 QL 1701. F.E. and
N.D. acknowledge support from NASA grant NNX17AK25G and F.E. from DFG grant EF
98/4-1. N.D. acknowledges financial support by DLR under grant 50OC1702. We
thank the International Space Science Institute (ISSI) for hosting our team on
“Solar flare acceleration signatures and their connection to solar energetic
particles.” L.G. acknowledges the NASA DRIVE SolFER Science Center grant
80NSSC20K0627. This study has received funding from the European Union’s
Horizon 2020 research and innovation program under grant agreement No.
101004159 (SERPENTINE).

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##  Appendix A Additional information on the analyzed events

Table 3 provides additional information on the events under study. Column one
lists the HXR date and peak time. Columns 2 and 3 list the characteristics of
the associated microwave bursts: the start and end time, the highest frequency
where the nonthermal microwave signature was observed, and the type of the
predominant microwave emission, thermal (th), gyrosynchrotron (gs) or plasma
emission (p). Column 4 lists the start and end time of the decametric type III
burst, read from the dynamic spectra observed by Wind or STEREO near 10 MHz,
using data with 1 min integration. Column 5 indicates if the event was
associated with a type II radio burst and provides its start and end time.
Columns 6 and 7 provide the magnetic polarity of the associated active region
in the corona and locally at the spacecraft (indicated by column 8) during the
SEE event. The last column provides a rough classification for the strength of
the observed electron anisotropy during the early phase of the electron
events.
The polarity of the magnetic field in the corona was inferred from the
potential field source surface (PFSS) extrapolation of the SoHO/MDI
measurements in the photosphere. The method of Schrijver & DeRosa (2003)
implemented in the PFSS tool of the Solarsoft package was used. The polarity
in the Table is the one of the open field lines rooted in the flaring active
region. The in situ magnetic field polarity was determined by separating
between inward our outward pointing magnetic field vectors as measured by
STEREO/MAG (Acuña et al. 2008) during the time of each electron event. The
table shows, that the in situ electron events were often observed in opposite
polarity sectors than coronal polarity of the corresponding flare. We do,
however, not see any influence of the polarity on other parameters such as the
onset delays or the quality of the spectral correlations.
In two events (2009 Dec 22 and 2012 Apr 16) type II bursts were observed at
meter wavelengths, without counterpart in the Wind/WAVES spectrum below 14
MHz. Only the first was reported by NOAA/SWPC. On 2009 Dec 22 the type II
burst started with the intense microwave emission and HXR burst, and it lasted
a few minutes longer. DH type III bursts were observed by Wind/WAVES during
its entire duration. On 2012 Apr 16 the type II emission occurred during the
decay of the microwave and HXR burst. DH type III bursts accompanied the
microwave/HXR burst, but not the type II burst. No clear difference of the
energy spectra of the electrons was found when compared to the rest of the
events.
For the anisotropy classification, presented in the last column of table 3, we
first determined the anisotropies using the method described by Brüdern et al.
(2018), and categorized anisotropies $A<1$ as small, $1>A>2$ as medium, and
$A>2$ as large. Mixed classifications are provided for events with
anisotropies close to the limiting values of 1 or 2. The asterisks in the
anisotropy column mark events with limited or poor pitch-angle coverage, which
can lead to an underestimation of the anisotropy.

Table 3: Complementary radio, magnetic polarity and anisotropy information of
the analyzed event

HXR | Microwave burst | $\nu_{\rm max}$ | DH III | II | Magnetic polarity |  |
---|---|---|---|---|---|---|---
peak time | start - end | [GHz]/ | start-end |  | corona | in situ | s/c | anisotropy
|  | type |  |  |  |  |  |
2007/01/24 00:31:24 | 00:31:10-00:32:00 | 9/gs | 00:29-00:33 | – | neg | mixed | A | small/medium
2007/01/24 00:31:24 | – | – | – | – | neg | mixed | B | small
2007/01/24 05:16:09 | 05:15:50-05:16:30 | 5/gs | 05:12-05:19 | – | neg | mixed | B |  small**$*$L
2007/01/24 05:16:09 | – | – | – | – | neg | mixed | A | small/medium
2009/12/22 04:56:10 | 04:53:00-04:57:00 | 17/gs | 04:52-05:04 | 04:57-05:03 | pos | pos | B | large
2010/02/08 03:12:24 | 03:12:20–03:14:00 | 17/gs | 03:13-03:16 | – | neg | neg | B | small
2010/11/12 03:53:41 | 03:53:25–03:56:00 | 1/p | 03:45-03:54 | – | neg | neg | B |  small/medium**$*$L
2010/11/12 08:01:54 | 08:01:00–08:04:50 | 15/gs | 07:55-08:11 | – | neg | neg | B |  medium/large **$*$L
2010/11/17 04:36:44 | 04:36:30-04:37:10 | 3/gs | 04:31-04:37 | – | pos | neg | B |  small/medium **$*$L
2011/03/24 17:04:34 | 17:03:00-17:06:50 | 15/gs | 16:53-17:16 | – | pos | neg | B | large
2012/01/12 00:51:58 |  $\sim$00:49–00:53 | 5/gs | 00:49-00:53 | – | neg | pos | B |  small**$*$L
2012/03/25 00:27:54 | 00:27:05–00:28:30 | 9/gs | 00:22-00:28 | – | neg | neg | B |  small**$*$L
2012/04/16 00:26:14 |  $\sim$00:25-00:28 | 4/gs | 00:24-00:30 | 00:29-00:40 | uncertain | neg | B |  small/medium**$*$L
2012/05/07 03:21:58 | 03:21:00–03:26 | 17/gs | 03:20-03:29 | – | neg | neg | B |  medium**$*$L
2012/06/27 12:36:00 | 12:36:00–12:36:30 | 9/gs | 12:34-12:40 | – | neg | neg | B | medium/large
2012/06/28 02:12:24 | 02:12:00–02:13:30 | 2/p | 02:10-02:14 | – | neg | pos | B |  medium**$*$L
2012/07/01 07:14:44 | 07:14:40–07:14:50 | 9/gs | 07:09-07:25 | – | neg | pos | B | large
2014/03/19 16:26:14 | 16:29:00–16:32 | 15/th | 16:24-16:30 | – | uncertain | pos | B | large
2014/06/09 17:05:04 | 17:04:30–17:06:20 | 15/gs | 17:03-17:07 | – | uncertain | pos | B |  medium**$*$L

101010 imited or poor pitch-angle coverage in SEPT measurements due to non-
nominal magnetic field configuration.

Many of the analyzed flares were accompanied by coronal jets seen in EUV.
Table 4 summarizes the observations of these jets using EUV images. For the
first 4 events, EUV observations from the STEREO-A EUVI (Wuelser 2004) at 195
Å were used, because they provide the best available time cadence for these
dates, which are before the launch of the Solar Dynamic Observatory (SDO,
Pesnell et al. 2012) mission in 2010. However, the time cadence (5 minutes in
average) and spatial resolution are not sufficient to clearly confirm the
absence of jets, for instance during the first event. Despite these
instrumental limitations, jets and eruptions are still clearly found for the
other three events. For the later events, data from the Atmospheric Imaging
Assembly (AIA, Lemen et al. 2012) on board SDO was available. AIA has a
cadence of 12 second and provides images of the Sun in 7 EUV filters. The 304
Å filter was used to look for coronal jets within one hour of the X-ray peak
time of the flare, as jets are typically bright in this wavelength. In the 13
events observed in the SDO era, only two events are not associated with a
coronal jet. Most of the observed jets are observed at the time and location
of the flare, as reported in the third column of table 4. The events for which
no jet was found, or with a jet delayed or at a different location in the
active region than a flare, are not particularly associated with delayed SEP
electron events.

Most of the analyzed flares were accompanied by coronal mass ejections (CMEs).
Table 4 summarizes the observations using the coronagraphs aboard SoHO
(LASCO/C2, Brueckner et al. 1995) or STEREO (SECCHI/COR1, Howard et al. 2008).
In order to avoid spurious associations due to projection effects, we
restricted the sample to events where the parent active region was within 30∘
of the limb. The third column displays the central meridian distance (CMD) for
the chosen spacecraft. The fifth column gives the time of first appearance in
the field of view of the coronograph, together with the estimated heliocentric
distance as identified in the images111111Movies provided by JHelioviewer or
https://cdaw.gsfc.nasa.gov/stereo/daily_movies/. Whenever possible a rough
estimate of the speed in the plane of the sky is also provided, as well as the
height of the CME front at the time of the HXR peak, which is inferred from
linear back projection. Column six provides comments for specific events.

CMEs are found during all events where adequate coronographic observations are
available. The relationship with the flare and electron events is not always
clear, however. The 2007 Jan 24 events are not related with the partial halo
CME observed at the time of the flare. Since the CME appeared in LASCO images
at the east limb before the west limb, it likely originated from a region in
the eastern solar hemisphere. No active region was on the eastern solar disk
this day, but a candidate crossed the east limb three days later. We therefore
conclude that the partial halo CME was a backside event. In three cases the
CME was already high above the solar limb at the time of the flare (2012 Apr
16 and Jun 27, 2014 Mar 19). The starting frequencies of the type III bursts
associated with these events show that the electron acceleration must have
occurred at lower height. In nine events the extrapolated height of the CME
front at the time of the HXR burst is within 1 R⊙ above the photosphere, so
that its early rise may have been related with the electron acceleration as
traced by the HXR and radio emissions. The CMEs are in general not large, and
some are reminiscent of jets.

Table 4: Jets and CMEs possibly related with the electron events and flares.

| EUV jet | Coronal mass ejection
---|---|---
HXR peak time | Instr | First/ | Instrument/ | Height-time evolution | Comment
|  | Distance | CMD [deg] | (first/$r_{0}$/$V$/$r$(HXR)) |
(1) | (2) | (3) | (4) | (5) | (6)
2007/01/24 00:31 | STA | -/- [1] [2] | SoHO W61 | 01:32/2.3 R⊙/-/- | E backside
2007/01/24 05:16 | STA | 05:15/$<5^{\prime\prime}$ | SoHO W64 | 06:06/2.5 R⊙/ -/- | E backside
2009/12/22 04:56 | STA | 04:55/$<5^{\prime\prime}$ | STB W114 | 05:11/1.7 R⊙/470/1.0 R⊙ |
2010/02/08 03:12 | STA | 03:20/$<5^{\prime\prime}$ [3] | STB W71 | 03:41/1.6 R⊙/200/1.1 R⊙ | jet
2010/11/12 03:53 | AIA | 04:05/$<5^{\prime\prime}$ [4] | STA W86 | 03:55/1.7 R⊙/580/1.6 R⊙ | faint diffuse
2010/11/12 08:02 | AIA | 08:55/$10^{\prime\prime}$ | STA W83 | 08:05/? R⊙/700/1.4 R⊙ | faint diffuse
2010/11/17 04:37 | AIA | flare/$<5^{\prime\prime}$ | STA E105 | 04:45/1.8 R⊙/930/1.2 R⊙ | jet
2011/03/24 17:05 | AIA | flare/$<5^{\prime\prime}$ | CMD $>30^{\circ}$ |  |
2012/01/12 00:52 | AIA | 01:12/$<5^{\prime\prime}$ [3] [4] | STB W92 | 01:01/1.7R⊙/520/1.3 R⊙ |
2012/03/25 00:28 | AIA | -/- [1] | STB W93 | 00:26/1.9R⊙/860/1.7 R⊙ |
2012/04/16 00:26 | AIA | -/- [1] | SoHO E89 | 00:36/3.5 R⊙/$\sim 490$/3.1 R⊙ | narrow
2012/05/07 03:22 | AIA | -/$<5^{\prime\prime}$ [2] [4] | CMD $>30^{\circ}$ |  |
2012/06/27 12:36 | AIA | flare/$20^{\prime\prime}$ | SoHO E64 | 12:10/3.2 R⊙/$\sim 760$/4.3 R⊙ | pre-existing
2012/06/28 03:22 | AIA | flare/$<5^{\prime\prime}$ [2] | CMD $>30^{\circ}$ |  |
2012/07/01 07:15 | AIA | flare/$<5^{\prime\prime}$ | STB W105 | 07:25/2.2R⊙ /700/1.6 R⊙ |
2014/03/19 16:26 | AIA | flare/$15^{\prime\prime}$ | SoHO E81 | 15:24/4 R⊙/- /- | pre-existing
2014/06/09 17:05 | AIA | 17:20/$50^{\prime\prime}$ | SoHO E90 | 17:24/2.8 R⊙/$\sim 680$/1.7 R⊙ |

121212 Columns: (1) Date (see Table 1), (2)-(3): EUV jet (instrument (2),
start time/distance from HXR emission site (3), ); (4)-(6): CME (instrument
and central meridian distance of the flare (4), first detection/heliocentric
distance/ speed in the plane of the sky (km s-1)/extrapolated heliocentric
distance at the HXR peak) (5), comment (6) Comments in column (3): $[1]$ jet
not detected in the data; $[2]$ numerous jets in this active regions over a
few hours; $[3]$ possible filament eruption; $[4]$ faint ejection.

###  A.1 Implications of the spectral variation in the two multi-spacecraft
events of 24 Jan 2007

Two events on 24 Jan 2007 were observed by both STEREO spacecraft when they
were still separated by less than one degree in longitude and latitude. As
expected the peak intensities and onset times are very similar as detected by
the two observers. However, both events were observed during changing magnetic
field conditions leading to variable and partly nonoptimal pitch-angle
coverage of the SEPT instruments. The pitch-angle coverage was always better
at STEREO A, which might be the reason for the slightly larger anisotropies
compared to STEREO B. For the first event, the determined spectral indices of
the peak spectra are similar at the two spacecraft but for the second event
STEREO B only observes a single power law while STEREO A detects a broken
power law. Although the spectral values observed at the two spacecraft agree
within their uncertainties for the two events this illustrates how the
magnetic field configuration and variation can not only influence onset
determinations but also the determined spectra. It is expected that the most
reliable spectra are those where the instruments detect the electron
population propagating anti-sunward along the magnetic field, i.e. at pitch
angle 0 or 180 (depending on the magnetic field polarity). If these directions
are not covered by the instrument or if strong scattering has led to a
vanished anisotropy, the determined spectra may carry systematic changes.
Unfortunately, periods of non-ideal pitch-angle coverage occur regularly in
SEPT measurements so that several of the analyzed events may be subject to
this limitation.

###  A.2 The events on 17 Nov 2010, 28 June 2012, and 19 Mar 2014

An important issue discussed in this manuscript is that it is not
straightforward to choose the appropriate spectral index out of the usually
observed double power law spectrum for a comparison with its solar
counterpart. Observations of near-relativistic electrons usually show only one
spectral break or transition (e.g., using Wind/3DP (Krucker et al. 2007) or
STEREO/SEPT (Dresing et al. 2020)). However, due to the limited overall energy
range and energy resolution of these instruments their ability to resolve
which of the different effects caused the spectral break or if an overlap of
effects determines the spectral shape is also limited. The correlation with
the solar counterpart spectral index may even help here: When correlating the
photon spectral index $\gamma$ with both the lower $\delta_{1}$ and upper
$\delta_{1}$ spectral indices of the in situ electron spectra (Fig. 5 & 6) we
find that three events (17 Nov 2010, 28 June 2012, and 19 Mar 2014) do not fit
the rest of the distributions. As described in section 3 we suspect that these
three events show a spectral transition, which can rather be attributed to
Langmuir-wave generation while the spectral transitions of the rest of the
events are likely caused by pitch-angle scattering (Dresing et al. 2020;
Strauss et al. 2020). Indeed, when treating these three events accordingly in
the correlation plots (Fig. 5 & 6) the overall correlations increase
significantly. One of these three events (17 Nov 2010) is indeed the event
with the lowest break energy in our whole sample ($E_{b}=69$ keV), which
supports the assumption that this break can be attributed to Langmuir-wave
generation, which is expected to yield a break around 60 keV (Krucker et al.
2009). The break energies of the other two special events (90 and 101 keV) are
rather low with respect to the mean spectral break value of 120 keV found by
Dresing et al. (2020), which was attributed to pitch-angle scattering, however
many other events analyzed here show similar low break energies. The two
latter events are both anisotropic. While the pitch-angle coverage during the
28 June 2012 event is not optimal, likely leading to an underestimation of the
anisotropy, the pitch-angle coverage during the 19 Mar 2014 event is ideal and
shows a very strong anisotropy (not shown). Consultation of the STEREO level3
Interplanetary Coronal Mass Ejection (ICME) list131313https://stereo-
ssc.nascom.nasa.gov/data/ins_data/impact/level3/STEREO_Level3_ICME.pdf reveals
that STEREO B was embedded inside an ICME when the 19 Mar event occurred. The
usually very quiet magnetic field conditions inside ICMEs may have contributed
to very weak scattering conditions during this event and consequently high
anisotropy. The pitch-angle distribution during the 28 June event is peculiar
as the highest intensities are observed in SEPT’s north and ani-sun sectors,
suggesting that also during this event, the spacecraft was embedded inside a
non-nominal magnetic field configuration. However, an ICME passage is only
reported for about six hours after the event onset. The solar origin of this
electron event is, however, not doubted given the good temporal correlation
with the flare and the associated type III radio burst, and the notable
anisotropy. In spite of the peculiarities of these two latter events, they are
otherwise not outstanding when comparing their characteristics such as peak
intensities or energies, strength of the anisotropy, onset delays or radio
features with the rest of our sample. The reason why the spectral break due to
Langmuir-wave generation is dominant in the spectra of these events, is
therefore not conclusively understood.