Effect of an ICME on SKR]Effect of an interplanetary coronal mass ejection
on Saturn's radio emission

The Saturn  Kilometric  Radiation (SKR)  was  observed  for  the  first  time
during the flyby of Saturn by the Voyager spacecraft in 1980. These radio
emissions, in the range of a few kHz to 1 MHz, are emitted by electrons
travelling around auroral magnetic field lines. Their study is useful to
understand the variability of a magnetosphere and its coupling with the solar
wind. Previous studies have shown a strong correlation between the solar wind
[id=R1]dynamic pressure and the SKR intensity. However, up to now, the effect of an
Interplanetary Coronal Mass Ejection (ICME) has never been examined in detail,
due to the lack of SKR observations at the time when an ICME can be tracked and
its different parts be clearly identified. In this study, we take advantage of a
large ICME that reached Saturn mid-November 2014 [Witasse et al., 2017].
At that time, the Cassini spacecraft was fortunately travelling within the solar
wind for a few days, and provided a very accurate timing of the ICME structure. A
survey of the Cassini data for the same period indicated a significant increase in
the SKR emissions, showing a good correlation after the passage of the ICME shock
with a delay of $\sim$13 hours and after the magnetic cloud passage with a delay of
25-42 hours. [id=BC]In between, a smaller SKR burst could be correlated with a proton
flux peak occurring during the passage of the ejecta of the ICME.

§ KEYWORDS:
Saturn, Cassini, SKR emission, Interplanetary
Coronal Mass Ejection, solar wind

§ INTRODUCTION

The Saturn Kilometric Radiation (SKR) was observed for the first time by
[Kaiser et al., 1980] during the flyby of Saturn in January 1980, with the
Voyager/PRA (Planetary Radio Astronomy) instrument [Warwick et al., 1977]. The
SKR radio emission is a low frequency non-thermal radio emission observed between
a few kHz to about 1 MHz. It is emitted through the Cyclotron Maser Instability [id=BC](CMI)
[Wu and Lee, 1979, Lamy et al., 2010] triggered by accelerated electrons travelling
around auroral field lines [Lamy et al., 2009]. SKR is thus directly related to
magnetospheric dynamical activity.

The analysis of Voyager PRA data showed a strong correlation between the
[id=R1]solar windSolar Wind [id=R1]dynamic pressure and SKR emitted flux
[Desch, 1982, Desch and Rucker, 1983]. Desch, 1983 even showed
[id=R1]that the SKR disappeared while Saturn passed through the tail of
the Jovian magnetosphere. Thanks to the Cassini RPWS (Radio and Plasma
Waves Science) experiment [Gurnett et al., 2004] we have quasi-continuous
observations of the SKR from early 2004 to the end of mission in October
2017. The radio data have the potential to be used as a remote proxy for
both upstream driving and magnetospheric dynamics, and many studies have
sought to explore the role of the solar wind perturbations in stimulating
auroral and radio phenomena. Corotating interaction region (CIR) compressions
in the solar wind have been found to intensify the SKR bursts and occasionally
to disrupt their regular phasing [Badman et al., 2008, Kurth et al., 2016]. Dynamic
magnetotail reconnection events have also been shown to correlate well with
intensifications and low frequency extensions (LFEs) of the SKR
[Bunce et al., 2005, Jackman et al., 2005, Jackman et al., 2009, Reed et al., 2018].

[id=BC]The Although the link between enhanced solar wind
[id=BC]parameters dynamic pressure and intense [id=BC]planetary auroral activity SKR
has been known for many years [id=BC]at Saturn
[id=BC]<cit.> ,
[id=BC]and has also been studied in the context of Jupiter [Prangé et al., 2004, Hess et al., 2012, Kita et al., 2019]
or Uranus [Lamy et al., 2012], using modelled solar wind parameters when in-situ observations were not
available. [id=BC]In the case of Saturn, the solar wind dynamic pressure has been identified as
the main driver of enhanced SKR activity [Kaiser et al., 1980, Rucker, 1984]. [id=BC]The the
effect of Interplanetary Coronal Mass Ejections (ICME) [id=BC](see, e.g., Zurbuchen and Richardson, 2006
for detailed descriptions of ICME properties) on SKR activity has never been
described in detail, due to the lack of SKR observations at the time when an ICME
impact can be clearly identified. In this study, we take advantage of a large ICME
that reached Saturn in November 2014 [Witasse et al., 2017]. The solar wind
feature was tracked from the Sun up to Voyager 2 as well as simulated with the
WSA-ENLIL+Cone model. A [id=R1]snapshot still of this model at Saturn is shown
in Figure <ref>. One of the major challenges for interpreting
remote sensing observations is the lack of an upstream monitor to provide context
for the observations and a quantitative measure of the solar wind driving conditions.
However, for this rare example, the Cassini spacecraft was situated upstream of
the bow shock, sampling the solar wind for a few days. Thus, it has been possible
to use in situ data from the Cassini magnetometer (MAG) [Dougherty et al., 2004]
and energetic particle instrument (MIMI) [Krimigis et al., 2004] to provide
accurate timing for the ICME arrival. The ICME impacted Cassini on November 12th,
2014. A survey of the RPWS data for the same period indicated a significant
increase in the SKR emissions. This article reports on the correlation between
this solar wind disturbance and SKR emissions.

[id=R1]Solar Still of the solar wind velocity in the ecliptic
plane from a WSA‐ENLIL + Cone model simulation showing the ICME propagation
at Saturn. The ICME is marked as a black [id=R1]contourbubble on the right side
before Saturn. Time is given in the format YYYY-MM-DDThh. The full simulation
is available at [Witasse et al., 2017] and <http://ccmc.gsfc.nasa.gov>
under run ID

§ DATA AND TRAJECTORIES

In this study, we use several datasets from various instruments: radio frequency
data from the High Frequency Receiver (HFR) of Cassini/RPWS
[Gurnett et al., 2004]; magnetic field data from the Cassini/MAG (Magnetometer)
[Dougherty et al., 2004]; and particle [id=R1]observations distribution function moments from
Cassini/MIMI (Magnetosphere Imaging Instrument) [Krimigis et al., 2004]. The
trajectory data is provided by the CDPP (Centre de Données de la Physique des
Plasmas) through their AMDA (Automated Multi-Dataset Analysis) and 3Dview tools
[Génot et al., 2017, Génot et al., 2021].

The Cassini/RPWS/HFR instrument [id=R1]records is recording radio electric
signals from 3.5 kHz to 16 MHz, using three electric antennas. This instrument allows
[id=R1]for reconstruction of to reconstruct the absolute flux density and
polarization of the observed radio waves Cecconi and Zarka, 2005. In this study, we
make use of two datasets from HFR: (a) the Cassini/RPWS/HFR Level 3e (N3e) dataset
[Cecconi et al., 2017], i.e., the “Circular Polarization
Mode” goniopolarimetric inversion as described in section 2.1.3.2 of
Cecconi and Zarka, 2005) ; and (b) the Cassini/RPWS/HFR SKR dataset
[Lamy et al., 2009] as described in Lamy et al., 2008.

The Cassini/MIMI instrument is designed for energetic neutral and charged particle
detection. MIMI consists of three sensors of which we use the Low Energy
Magnetospheric Measurement System (LEMMS) sensor [Krimigis et al., 2004]. LEMMS is
a charged particle telescope with two units separated by 180$^{\circ}$ in pointing
that use solid state detectors and coincidence logic to determine the type of
particle (electron or ion) and its energy, as well as magnetic deflection to
better separate ions from low energy ($\leq$800 keV) electrons
[Roussos et al., 2018].

In this study, we use data from the electron channels E4 with energy between 0.8
and 4.7 MeV, with a [id=BC]1-hr 1 h average window and non-background subtracted.
channel shows MeV electron with a background level modulated by penetrating GCRs
(Galactic Cosmic Rays).
It was used to identify the Forbush decrease as a clear identification of the ICME
<cit.>. [id=BC]In addition, we use the proton channel P2 with
energy 2.3 to 4.5 MeV from the calibrated Cassini/MIMI-LEMMS dataset [id=BC]The LEMMS
data are available at NASA/PDS [Vandegriff J., 2018].

The data have been studied during a 30-day interval (2014-11-06 00:00:00 to
2014-12-06 00:00:00), [id=R1]that includes the predicted including on the prediction ICME
arrival times at Saturn (see next sections). Figure <ref>
[id=R1]shows is showing an overview of the magnetospheric configuration,
using 3DView [Génot et al., 2017], and a dynamic magnetospheric model
[Kanani et al., 2010] implemented in this tool. The input [id=R1]solar
windSolar Wind dynamic pressure is based on an MHD simulation
propagation of OMNI data [Tao et al., 2005], and is described in the next section
(and Figure <ref>). Figure <ref> shows the Cassini trajectory
together with two [id=BC]models modeled[id=BC]: a magnetopause [id=BC]model
[Arridge et al., 2006] and [id=BC]a bowshock [id=BC]model [Went et al., 2011],
using a typical [id=R1]solar wind ram pressure of 0.05 nPa[id=CJ], which
corresponds to an average solar wind dynamic pressure, intermediate between compressed and
rarefied conditions. Those
figures illustrate the geometrical configuration involved in this study: The
Cassini spacecraft [id=R1]is outside of comes out of the Kronian magnetosphere
at the beginning of the interval, on the Northern dawn side; it then travels in the
[id=R1]solar wind Solar Wind, while moving along the morning flank of the
magnetosphere; it reenters the equatorial magnetosphere in the late morning local
time at the end of the interval.

Cassini trajectory with Saturn's Magnetopause model
[Kanani et al., 2010]. Snapshots from 3Dview, at 00:00 on days 2014-11-10,
2014-11-13, 2014-11-19 and 2014-12-05, from (a) to (d) respectively. On panel
(d) a marker shows the modeled reentry into the magnetosphere.

Overview of the Cassini spacecraft trajectory on KSO (Kronian
Solar Orbital) coordinates, as [id=CJ]provided propided by AMDA. The radial
distance $R$ is displayed as a function of $x_\textrm{KSO}$, for the Cassini
trajectory and models of the [id=CJ]magnetopause magnetosphere and bowshock.
[id=CJ]The modelled boundaries have been computed with a solar wind dynamic
pressure of 0.05 nPa. We expect this value to have increased significantly during the
ICME passage, which might explain why the boundary positions shown here don't necessarily
reflect the observed position of the boundaries. The pink and green dots along the trajectory
are the location of Cassini at the labelled dates, the green location being the starting

§ OBSERVATIONS AND MODELS

Figure <ref> [id=R1]shows is showing the radio electric and the
in-situ particle and magnetic field observations for the selected 30 days.
The flux density and circular polarization degree spectrograms, and the SKR integrated
flux time series are showing an intense SKR activity episode, including LFEs,
from Nov. 11th to 29th, 2014:

* Before Nov. 11th, 12:00: The SKR is present with moderate
intensity, as expected for observations from early morning local time

* From Nov. 11th, 12:00 to Nov. 15th 00:00: A more intense
SKR episode is observed, with a pair of intense outburst accompanied with
LFEs on Nov. 13th at 12:00 and 19:30 (see Figure <ref>).
The LFE event is clear on the Integrated SKR Power panel, since the dashed
line (wide-band integration, 10 kHz to 1 MHz) is significantly higher than
the [id=CJ]solid plain line (medium-band integration, 100 to 400 kHz). This is also visible
on the upper panel, where strong continuous emissions are observed between 10
and 100 kHz.

* From Nov. 15th to Nov. 20th: An SKR dropout is observed,
with an isolated burst around Nov. 17th 00:00.

* From Nov. 20th to Nov. 24th: Another intense SKR
episode is observed with strong and long lasting LFEs.

* From Nov. 24th to Nov. 29th: The LFE component is going on,
with moderate intensity SKR bursts.

* From Nov. 29th to Dec. 1st: The SKR is dropping out and
resumes to expected levels at the end of the interval.

* From Nov. 29th to the end of the studied interval: A
periodic very low frequency signal ($\sim$5 kHz) is observed, and mostly
visible on the polarization panel. This feature corresponds to the 5 kHz
Saturn narrow-band emission, so called n-SMR [Louarn et al., 2007] or
n-SKR [Wang et al., 2010].

The SKR dropouts observed in the morning sector of the magnetosphere is unusual,
since this is the main activity LT sector of SKR
[Galopeau et al., 1995, Lamy et al., 2009].
Furthermore, one must keep in mind that the SKR modulation at or close to the
planetary rotation period makes it difficult to accurately determine the actual
onset of SKR events. The n-SMR feature observed at the end of the interval is
typical of energetic magnetospheric events, as described in
[id=R1]detail details in Louarn et al., 2007. Their Figure 1 shows similar
LFEs followed by n-SMR pulsed emissions. The in-situ data (magnetic field
and particle) displays several characteristic signatures which will be described
in section <ref>.

The variability of the emitted SKR power [Lamy et al., 2008]
is presented on Figure <ref>. The average usual SKR emitted power
is of the order of $10^6$ W/sr to $10^7$ W/sr, and we observe SKR average
power raising up to $10^7$ W/sr, with peaks to $10^8$ W/sr (i.e., one order of
magnitude higher than regular levels). SKR emitted power [id=R1]drops is dropping
down to $10^5$ W/sr and even down to undetectable levels on day Nov. 18th, 2014,
and on the last two days of Nov. 2014.

The from top to bottom: Radio electric flux density spectrogram;
Radio electric circular polarization degree spectrogram; SKR integrated flux
(plain line: 100-400 kHz range; dotted line: 10-1000 kHz range), with a 2
hours running average; energetic particle fluxes for electrons (magenta line)
[id=BC]and protons (green line) in units of $cm^{-2}sr^{-1}s^{-1}keV^{-1}$; and
magnetic field components in RTN coordinate system ($B_r$ in blue, $B_t$ in
orange, $B_n$ in red, and $|B|$ in black). The tags (capital letters from A to
S) correspond to events described in Table <ref>. Times
are given in the format

Right Handed polarized emitted SKR power integrated on 100-400 kHz
(plain line) and 10-1000kHz (dashed line), as measured by Cassini/RPWS/HFR.
The data has been averaged over 15 minutes.

Comparison of the solar wind modeled parameters from the two
selected propagation models. From top to bottom: (a) the SKR RH emitted
power density integrated over 100-400 kHz and smoothed to a temporal
resolution of 6000 seconds; (b) to (e) the modelled solar wind density (in
cm$^{-3}$), temperature (in eV), radial velocity (in km/s) and dynamic
pressure (in nPa), as provided by the ENLIL code at CCMC (black) and
1D-MHD code at CDPP (grey); (f) and (g) the modelled (ENLIL) and measured
(Cassini/Mag) solar wind magnetic field in RTN cooordinates ($B_r$ in
red; $B_t$ in blue; $B_n$ in grey; $B$ magnitude in black). The vertical
lines and the capital letter markers are the same as in Figure
<ref> and described in Table <ref>. Times are
given in the format YYYY-MM-DD.

The propagated [id=R1]solar wind Solar Wind data available in AMDA are presented in Figure
<ref>. This Figure shows the modeled [id=R1]solar wind Solar Wind [id=BC]density, temperature, radial velocity and dynamic pressure (panels (b) to (e)) dynamic pressure (top
panel), using the 1D MHD model developed by Tao et al., 2005. Setting a
threshold to 0.1 nPa, AMDA provides us with four time intervals of enhanced
dynamic pressure, with peak values at about 0.15 nPa. The four intervals are
shown in Table <ref>. The model is however not well
constrained [id=BC]since the simulation is run with input parameters
measured at Earth, which in Solar conjunction with Saturn at this time. as we can see on the lower panel of Figure <ref>,
since Saturn is in Solar conjunction from Earth. [id=BC]This model shall thus
only be used as an rough indication of the solar wind conditions.

ID     Start Time     End Time

1      2014-11-10 17:55     2014-11-10 19:25

2      2014-11-11 20:55     2014-11-12 17:25

3      2014-11-28 06:05     2014-11-28 09:05

4      2014-11-28 12:35     2014-11-28 18:35

AMDA derived dynamic pressure peaks ($>$ 0.1 nPa) as modeled by
Tao et al., 2005. Times are given in the format YYYY-MM-DD hh:mm

Propagated [id=R1]solarSolar wind data available at CCMC (Community Coordinated Modeling
Center) are also presented in Figure <ref>. The simulation uses ENLIL, a
3D MHD modeling code [Odstrcil, 2003]. The simulation run used here is
[Available at:
[Witasse et al., 2017]. [id=BC]The Figure presents the same solar wind
parameters, as for the 1D-MHD model presented in the previous paragraph, as well
as the modelled magnetic field components. The Figure shows a clear enhancement
of dynamic pressure from Nov. 15th to Nov. 17th, with a peak value around 0.2 nPa.
The ENLIL data also shows another similar event starting at the end of the
time interval, on Dec 4th.

The two propagation models are predicting [id=BC]similar
solar wind parameters values and trends (density, temperature and radial velocity)
up to $\sim$Nov. 21st, with the noticeable exception of the dynamic pressure,
which is showing different peak times depending on the model, as well as rather
different overall variation all along the studied interval. The modelled magnetic
field doesn't reproduce the observed ICME structure. [id=CJ]During the
interval when Cassini exited into the solar wind (19 days, from labels A to S of
figure <ref> and Table <ref>), it was possible to
directly sample the interplanetary magnetic field. We can use this to compare
against model predictions for the broader interval. [id=BC]The two models
are predicting different arrival times of the ICME. [id=R1]The model
developed by  and available from the CDPP The
model from CDPP is about 5 days [id=R1]earlier
early compared to the ENLIL simulation run output from CCMC. Due to the solar
system orbital configuration, the ENLIL simulation run should be more accurate.
[id=OW]Indeed, the ENLIL simulation predicts the arrival of the ICME at
12:00 UT on 15 November, about 2.5 days after the real hit. This is a rather
accurate estimation given the distance of Saturn with respect to the Sun and
the limitations of the simulation at these distances [Witasse et al., 2017].

§ ICME EVENT

In order to correlate and interpret the variations of the SKR emissions, it
is necessary to [id=R1]characterise draw a picture of the ICME event. This ICME erupted from the
Solar Active Region 12192 on 14 October 2014 at $\sim$18:30 UT as seen by the
SOlar and Heliospheric Observatory (SOHO), the Project for On Board Autonomy 2
(PROBA-2), the Solar Dynamics Observatory (SDO), and the Solar
TErrestrial RElations Observatory Ahead (STEREO-A) missions. [id=R1]On its transit
to the outer solar system, the ICME encountered Venus, STEREO-A, Mars, comet
67P/Churyumov-Gerasimenko, Saturn, In its way towards the outer
solar system hit STEREO-A, Venus, Mars, comet 67P/Churyumov-Gerasimenko,
Saturn, and possibly New Horizons on its way to Pluto and Voyager-2 at the
heliosheath as discussed in detail by Witasse et al., 2017.
The propagation of this event was also modelled with two different solar wind
simulations[id=R1]: , such as [id=BC](i) the CDPP Propagation Tool, and [id=BC](ii)  the Wang-Sheeley-Arge
(WSA)-ENLIL + Cone model. For this [id=BC]latter latest case and based on the Graduated
Cylindrical Shell (GCS) fit performed to the coronagraph observations from
STEREO-A and SOHO, the CME was injected into the simulation using [id=R1]as inputs
[id=R1]of 1015 km/s [id=R1]for of radial speed, 150$^{\circ}$ [id=R1]for of
longitude, 12$^{\circ}$ [id=R1]for of latitude
and a full width of 116$^{\circ}$. For the ICME propagation out to Saturn, a
medium resolution (2$^{\circ}$) simulation was performed on a HEEQ spherical
grid of 1920${\times}$60${\times}$180 (r, $\theta$, $\phi$) [id=R1]size, with a range
of 0.1 to 10.1 AU in radius (r), -60$^{\circ}$ to +60$^{\circ}$ in latitude
($\theta$), and -180$^{\circ}$ to 180$^{\circ}$ in longitude ($\phi$). In
addition to the CME of this study, the simulation also included 138 CMEs with
speeds above 500 km/s and full angular widths above 50$^{\circ}$. [id=R1]This was
necessary in order to get the most accurate estimation of the arrival time of the ICME
to Saturn since most CMEs merge with the background solar wind at largest distances
[id=CJ]<cit.>. Figure
<ref> shows a [id=R1]snapshot still of the propagation of this ICME
just before its arrival at Saturn (the ICME is outlined in black), and Figure
<ref> shows the derived solar wind density, velocity and temperature
profiles obtained from the simulation at Saturn. The ICME arrived at Saturn
approximately one month after its ejection at the Sun as observed by Cassini,
which was immersed in the solar wind at this time.

Although there were no in-situ [id=R1]plasma measurements of the ICME
and the background
solar wind speeds, values of 500 and 400 km/s respectively can be estimated
from Witasse et al., 2017. This estimation is consistent with the modelled
[id=R1]solar wind Solar Wind velocity presented on Figure <ref>.

Table <ref>
gives a summary of the timing of the different regions of the ICME at Cassini
as well as the corresponding SKR enhancements. [id=R2]In particular, the
shock of the CME is seen as a significant increase of the interplanetary magnetic
field strength from 0.3 nT to 1.2 nT. It is followed by the sheath/ejecta, where a
clear rotation of the $B_y $component is seen. After that, there is the magnetic
cloud that is clearly identified with a rotation of the magnetic field $B_z$
component, with the addition that this event has a “magnetic bottle” structure
which is identified as the region where the magnetic field strength is at its
largest value (1.6-2 nT). [id=CJ]The internal structure of a magnetic bottle is comprised
of helical, twisted magnetic field lines, which present as a local intensification
of the field strength when traversed by a spacecraft.

Event                          Tag      ICME                  SKR                   2lDelay (hr)

Magnetosheath (outwards)         A      2c|2014-11-11 09:00     –

B     –                     2014-11-11 12:00      –

Shock arrival                    C     2014-11-12 22:50       –                    –

Sheath/ejecta                    D     2014-11-13 11:30       –                    –

E     –                     2014-11-13 11:40      12.8     from C

F     –                     2014-11-14 03:00      15.5     from D

G     –                     2014-11-15 02:00      38.5     from D

[id=BC]Proton injection (start)         [id=BC]H     [id=BC]2014-11-15 09:30       [id=BC]–     [id=BC]–

[id=BC]Proton injection (end)           [id=BC]I     [id=BC]2014-11-16 10:30       [id=BC]–     [id=BC]–

[id=BC]H J     –                     2014-11-16 12:00      [id=BC]– 26.5     [id=BC]– from H

Magnetic cloud start             [id=BC]J K     2014-11-16 19:30       –                    –

[id=BC]K L     –                     2014-11-17 11:00      [id=BC]– 24.5     [id=BC]– from I

Magnetic bottle (start)          [id=BC]L M     2014-11-18 06:10       –                    –

[id=BC]M N     –                     2014-11-19 07:20      25.2     from [id=BC]L M

Magnetic bottle (end)            [id=BC]N O     2014-11-22 01:30       –                    –

P     –                     2014-11-23 20:10      42.7     from [id=BC]N O

Magnetic cloud end/sheath        Q     2014-11-26 19:30       –                    –

R     –                     2014-11-28 19:00      47.5     from Q

Magnetosheath (inwards)          S     2c|2014-11-30 08:40      –

Timings of the major signatures of the ICME and SKR. The first
column are the tags shown on Figure <ref>. Times are given in the
format YYYY-MM-DD hh:mm

Zoomed-in version of Figure <ref>, from Nov. 10th
00:00 SCET to Nov. 15th, 12:00 SCET. The panel description is the
same as for Figure <ref>. Times are given in the format
YYYY-MM-DD, and hh:mm.

Zoomed-in version of Figure <ref>, from Nov. 18th
00:00 SCET to Nov. 24th 10:00 SCET. The panel description is the
same as for Figure <ref>. Times are given in the format
YYYY-MM-DD, and hh:mm.

It is noticeable that the enhanced activity of the SKR starts with the [id=R1]arrival
of the first event in the ENLIL simulation first ENLIL simulation run event, during the
enhanced [id=R1]solar wind Solar Wind density event, before
the peak dynamic pressure. The isolated SKR burst emission on Nov. 17th (during
phase (c)) corresponds to the peak of dynamic pressure predicted by the ENLIL
simulation run. The rise of SKR activity [id=R1]at the end of the interval also
[id=R1]corresponds correspond [id=R1]to a period of enhanced density and dynamic
pressure in the ENLIL simulation to the ENLIL enhanced density (and dynamic pressure).

§ DISCUSSION

The SKR variability observed the month of Nov. 2014 is closely related to the
ICME events, with observed delays of $\sim$ 20h between SKR and [id=R1]solar
wind Solar Wind events.
We observe that the integrated power (over 100-400 kHz, i.e, the core of the
SKR band, as well as over the 10-1000 kHz, i.e., the extended SKR band) increase
by 1 order of magnitude. We also observe SKR dropouts at undetectable levels.
[id=BC]With the assumption of a direct control of the SKR intensity by
the solar wind dynamic pressure [Kaiser et al., 1980],
[id=BC]such Such low SKR level conditions are indicating significant
expansion of the Kronian magnetosphere (or, equivalently, a strong depletion of
the [id=R1]solar windSolar Wind). It is noticeable that
[id=R1]these trends are the increase, dropout and increase again
is very similar as the event presented in Figure 1 of Jackman et al., 2005.
[id=BC]Desch and Rucker, 1983 reported the disappearance of SKR when
Saturn is in Jupiter's magnetotail, hence in a depleted plasma environment.

The spacecraft is located on the dawn side of the magnetosphere ($\sim$0700 hr
LT) [id=CJ]throughout this interval. [id=CJ]It is expected due
to the location of radio sources and the hollow cone beaming pattern of the SKR
that radio emissions in the main SKR band should maximise around this viewing
location . Indeed, Figure <ref> displays
continuous SKR modulations around Nov. 11th 2014, as expected from this vantage
point.This local time sector should display
continuous SKR modulations, as
observed before Nov. 11th, 2014 on Figure <ref>, as described in
The SKR modulation breakouts, as well as SKR peaks
and dropouts are [id=BC]thus clearly [id=R1]related to
a specific set of events, responding to the dynamics, rather than an effect
of limited viewing due to spatial constraints.

The intensification in the main band of SKR is accompanied by an extension of
the emission to lower frequencies [id=CJ](LFE), similarly to what is observed in the case
of a CIR [id=CJ]compressions impacting the Kronian magnetosphere, as investigated in [id=R1]detail details by
Jackman et al., 2005. This strong, continuous extension of emission is
interpreted as a growth/expansion of the radio source to higher
altitudes along the field line, with the lower field strength correlated to
lower frequency emission (due to the [id=BC]CMI cyclotron maser instability generation

We observe an enhancement [id=BC]of SKR intensity after in-situ events
in the SKR $\sim$20 hours after in-situ events,
with delays ranging from $\sim$13 hr [id=R1]after at the shock arrival, to $\sim$25 hr
at the [id=BC]proton injection and [id=BC]start of the magnetic bottle [id=BC]start, and to $\sim$44 hr
near the end of the event. The uncertainty on the delays shall be evaluated
taking into account the SKR modulation at or close to the
planetary rotation period, i.e., $\sim$10.5 hr [Lamy, 2010]. [id=BC]Considering a
typical SKR burst duration of $\sim$5.2 hr (half the planetary rotation period), the uncertainty is asymmetric:
from about $-$5.2 hr (if the event occurs during the low SKR level modulation phase) to 0 hr (if the
event occurs during the high SKR level modulation phase). This
implies an asymmetric uncertainty from 0 (if the event occurs during the
high SKR level modulation phase) to $\sim$5.2 hr (1/2 of the modulation
period, if the event occurs during the low SKR level modulation phase).
[id=BC]This implies that delays can be overestimated by a few hours.
Our findings on delays between in-situ and radio events are fully consistent
with the study of Taubenschuss et al., 2006, where delays between [id=R1]solar
wind Solar Wind and SKR events have been derived using statistical methods. This previous
study identified delays ranging from $\sim$13 hr for dynamic pressure
enhancement, to $\sim$27 hr to $\sim$44 hr for magnetic field events.
[id=BC]The observed delays can be expressed in units of the average planetary
rotation period: 13 hr, 25 hr and 44 hr correspond respectively to 1.2, 2.4 and 4.2
planetary rotation periods with an uncertainty of $-$0.5/$+$0 planetary rotation. Jackman et al., 2005
reported delays of about 40 hours. Rucker, 1984 reported delays of
a few planetary rotation, with a maximum correlation at about 4 planetary rotations.
Interestingly, Figure 6 of Rucker, 1984 shows a superposed-epoch analysis of
SKR peaks with various solar wind parameters: a statistical delay of a few planetary
rotations is observed (the figure is too small to get a better estimate). This suggests
that the delay in the response of SKR to solar wind variability is always present. In the
general case, the SKR periodic variability makes it difficult to evaluate the delays.
However, since the event studied here triggers a drastic change in SKR properties, the
delay can be estimated directly.

[id=BC]Such long delays are still not understood. Jackman et al., 2013
reported substorm-like event in Saturn's magnetotail at a distance of $\sim$45
$R_s$. With the modelled solar wind velocity (400 to 500 km/s, see Figure
<ref>), the solar wind event is reaching this distance after a
few hours at most. The observed delays are thus inconsistent with a direct control
by the solar wind. The variability of SKR is modulated by several factors: an active
local sector [Galopeau et al., 1995], which location is driven by the the solar wind
velocity [Galopeau and Lecacheux, 2000] and the rotating magnetospheric plasma (see,
e.g., Lamy et al., 2013, which describes in detail the relation between the
magnetospheric plasma rotation (observed with an energetic neutral atoms imager) and
the auroral activity (observed at radio, infrared and ultraviolet spectral ranges).
As shown in that latter study, the dynamics and the transport of plasma in the
magnetosphere are key drivers of the auroral variability.

[id=BC]According to the CMI mechanism, several parameters can
play a role in the enhancement or damping of radio emissions: the growth rate is
related to the presence of free energy (unstable particle distribution functions,
such as energetic beams, loss cone or shell distributions), as well as a locally
depleted and magnetized cold plasma. SKR bursts and
dropouts are observed during the event studied here. This indicates a radical
reconfiguration of the magnetosphere, resulting in a change of the plasma
properties in the radio source regions (i.e., along the auroral magnetic field lines).
Understanding the magnetospheric response to intense solar wind events requires
global and dynamical modelling of Saturn's magnetosphere at scales of a few planetary

Thanks to the specific orbital configuration during the event, we have
been able to observe simultaneously the ICME in the [id=R1]solar wind Solar
Wind upstream
from Saturn, as well as the SKR response. This study is thus very
complementary to other studies <cit.>
using only modelled data to identify the event arrival times at Saturn.
The shock arrival time derived from the data is estimated to
2014-11-12 22:50. The 1D-MHD modelled data [Tao et al., 2005] predicts a
first dynamic pressure pulse starting at 2014-11-10 17:55, and a second,
longer one, at 2014-11-11 20:55. The ENLIL model [Odstrcil, 2003]
predicts a peaked solar wind density on 2014-11-11 and a peaked
dynamic pressure on 2014-11-15. In terms of time of arrival estimations,
our observational data seem to favor the 1D-MHD modelling available in
AMDA provides, compared to the ENLIL code available at CCMC.
[id=BC]However, it is clear that current solar wind modelling tools are
not providing solar wind parameters with sufficient timing accuracy for
detailed comparison with in-situ measurement at the distance of Saturn.

§ CONFLICT OF INTEREST STATEMENT

The authors declare that the research was conducted in the absence of any commercial
or financial relationships that could be construed as a potential conflict of interest.

§ AUTHOR CONTRIBUTIONS

BC performed writing, conceptualization, data gathering, figure editing.
OW, CMJ and BSC performed conceptualization, writing – reviewing and editing.
MLM provided CCMC data.

§ FUNDING

BC acknowledges support from Observatoire de Paris, CNRS/INSU (Centre National de
la Recherche Scientifique / Institut des Sciences de l'Univers) and CNES (Centre
National d'Etudes Spatiales). OW was supported by ESA (European Space Agency).
CMJ's work at DIAS was supported by the Science Foundation Ireland Grant 18/FRL/6199.
BSC acknowledges support through UK-STFC Ernest Rutherford Fellowship
ST/V004115/1 and STFC grants ST/S000429/1, ST/W00089X/1.

§ ACKNOWLEDGMENTS

The authors thank the developers of: AMDA (Automated Multidataset Analysis Tool)
and 3Dview at CDPP (Centre de Données de la Physique des Plasmas); Autoplot at
University of Iowa; and TOPCAT (Tools for Operations on Catalogues and Tables) at
Bristol. Figures <ref>, <ref>, <ref> and
<ref> have been produced with
Autoplot [Faden et al., 2010]. The Cassini/RPWS data displayed on the figures have
been retrieved from PADC (Paris Astronomical Data Centre) using the das2
[Piker, 2017] interfaces of the MASER (Measurements, Analysis, and Simulation
of Emission in the Radio range) team [Cecconi et al., 2020]. The Cassini/MAG is
distributed by University of Iowa, also through a das2 interface. Figure
<ref> have produced with TOPCAT [Taylor, 2005], after
conversion of the ENLIL original tabular data into VOTable [Ochsenbein et al., 2019], and
transferring the other datasets from AMDA [Génot et al., 2010, Génot et al., 2021] using
SAMP (Simple Application Messaging Protocol) [Génot et al., 2014, Taylor et al., 2015].
The authors thank the two reviewers for their helpful comments, as well as
L. Lamy and V. Génot, who sent valuable comments based on the initial
manuscript version published on ArXiv.org.

§ DATA AVAILABILITY STATEMENT

The datasets analyzed for this study and their location have been described
the section <ref>. [id=BC]Appendix <ref>
presents material, which can be used to reproduce figures of this paper.

§ APPENDIX

§ SUPPLEMENTARY MATERIAL

The supplementary material for this paper [Cecconi et al., 2021] is available from <https://doi.org/10.25935/DZRB-P221>, and contains the following content.

§.§ Autoplot configuration files

Three Autoplot configuration files ( extension) are available:

*  to reproduce Figure <ref>.

*  to reproduce Figure <ref>.

*  to reproduce Figure <ref>.

*  to reproduce Figure <ref>.

§.§ 3Dview files

* : 3Dview [Génot et al., 2017] generated
movie, showing the Cassini trajectory during the studied interval. The
Cassini/MAG magnetic field vector is plotted along the trajectory, with a
rainbow color map for the magnetic field amplitude. The received SKR RH
integrated power time series (on the 10 to 1000 kHz band) is also plotted
along the trajectory, in the orbit plane, with a white-blue color map for
the power values. The magnetopause location is also displayed, using the
[Kanani et al., 2010] model, with the dynamic pressure input provided
by 3dview from [Tao et al., 2005].

* : 3Dview configuration file to reproduce

§.§ TOPCAT files

* : A TOPCAT session VOTable file containing
several tables: (i) the ENLIL solar wind parameters from the CCMC modelling
run; (ii) the 1D-MHD propagated solar wind parameters [Tao et al., 2005];
(iii) the SKR emitted power of its RH component, from the Cassini/RPWS/SKR
dataset [Lamy et al., 2009], with a temporal
resolution of 600 seconds; (iv) the same dataset with a resolution of
6000 seconds; and (v) the measured magnetic field [Dougherty et al., 2004],
with a 60 seconds temporal resolution. Datasets (ii) to (v) have been
transferred from AMDA to TOPCAT thanks to the SAMP protocol
[Génot et al., 2014, Taylor et al., 2015]. Upon loading this file
into TOPCAT, a set of predefined data selections and computed variables will
be available to the user.

* : The same content as in the previous item,
exported from TOPCAT using the FITS format option.

* : A STILTS script that can be used to reproduce
Figure <ref>.

* : Details on how to use these files.

[Arridge et al., 2006]
Arridge, C. S., Achilleos, N., Dougherty, M. K., Khurana, K. K., and Russell,
C. T. (2006).
Modeling the size and shape of Saturn's magnetopause with variable
dynamic pressure.
J. Geophys. Res. 111.

[Badman et al., 2008]
Badman, S., Cowley, S. W. H., Lamy, L., Cecconi, B., and Zarka, P. (2008).
Relationship between solar wind corotating interaction regions and
the phasing and intensity of Saturn kilometric radiation bursts.
Ann. Geophys. 26, 3641–3651.

[Bunce et al., 2005]
Bunce, E. J., Cowley, S. W. H., Wright, D. M., Coates, A. J., Dougherty, M. K.,
Krupp, N., et al. (2005).
In situ observations of a solar wind compression-induced hot plasma
injection in saturn's tail.
Geophysical Research Letters 32.

[Cecconi et al., 2017]
[Dataset] Cecconi, B., Lamy, L., and Zarka, P. (2017).
Cassini/RPWS/HFR N3e Data Collection, PADC/MASER.

[Cecconi et al., 2020]
Cecconi, B., Loh, A., Le Sidaner, P., Savalle, R., Bonnin, X., Nguyen, Q. N.,
et al. (2020).
MASER: A Science Ready Toolbox for Low Frequency Radio Astronomy.
Data Science Journal 19, 1062.

[Cecconi et al., 2021]
[Dataset] Cecconi, B., Witasse, O., Jackman, C., Sánchez-Cano, B., and
Mays, M. (2021).
Effect of an interplanetary coronal mass ejection on Saturn's radio
emission. Supplementary material (Version 1.0), PADC/MASER.

[Cecconi and Zarka, 2005]
Cecconi, B. and Zarka, P. (2005).
Direction finding and antenna calibration through analytical
inversion of radio measurements performed using a system of 2 or 3 electric
dipole antennas.
Radio Sci. 40, RS3003.

[Crary et al., 2005]
Crary, F. J., Clarke, J. T., Dougherty, M. K., Hanlon, P. G., Hansen, K. C.,
Steinberg, J. T., et al. (2005).
Solar wind dynamic pressure and electric field as the main factors
controlling Saturn's aurorae.
Letters to Nature 433, 1–3.

[Desch, 1982]
Desch, M. D. (1982).
Evidence for Solar Wind Control of Saturn Radio Emission.
J. Geophys. Res. 87, 4549–4554.

[Desch, 1983]
Desch, M. D. (1983).
Radio Emission Signature of Saturn Immersions in Jupiter's Magnetic
J. Geophys. Res. 88, 6904–6910.

[Desch and Rucker, 1983]
Desch, M. D. and Rucker, H. O. (1983).
The relationship between Saturn kilometric radiation and the solar
J. Geophys. Res. 88, 8999–9006.

[Dougherty et al., 2004]
Dougherty, M. K., Kellock, S., Southwood, D. J., Balogh, A., Smith, E. J.,
Tsurutani, B. T., et al. (2004).
The Cassini Magnetic Field Investigation.
Space Sci. Rev. 114, 331–383.

[Faden et al., 2010]
Faden, J., Weigel, R. S., Merka, J., and Friedel, R. H. W. (2010).
Autoplot: a browser for scientific data on the web.
Earth Sci. inform. 3, 41–49.

[Galopeau and Lecacheux, 2000]
Galopeau, P. and Lecacheux, A. (2000).
Variations of Saturn's radio rotation period measured at kilometer
J. Geophys. Res. 105, 13089–13102.
Publisher: American Geophysical Union

[Galopeau et al., 1995]
Galopeau, P., Zarka, P., and Le Quéau, D. (1995).
Source location of Saturn's kilometric radiation: The
Kelvin-Helmholtz instability hypothesis.
J. Geophys. Res. 100, 26397–26410.

[Génot et al., 2014]
Génot, V., André, N., Cecconi, B., Bouchemit, M., Budnik, E.,
Bourrel, N., et al. (2014).
Joining the yellow hub: Uses of the Simple Application Messaging
Protocol in Space Physics analysis tools.
Astronomy and Computing 7, 62–70.
2014A   C.....7...62G

[Génot et al., 2017]
Génot, V., Beigbeder, L., Popescu, D., Dufourg, N., Gangloff, M.,
Bouchemit, M., et al. (2017).
Science data visualization in planetary and heliospheric contexts
with 3DView.
Planetary and Space Science ,

[Génot et al., 2021]
Génot, V., Budnik, E., Jacquey, C., Bouchemit, M., Renard, B., Dufourg, N.,
et al. (2021).
Automated Multi-Dataset Analysis (AMDA): An on-line database and
analysis tool for heliospheric and planetary plasma data.
Planetary and Space Science 201, 105214.

[Génot et al., 2010]
Génot, V., Jacquey, C., Bouchemit, M., Gangloff, M., Fedorov, A., Lavraud,
B., et al. (2010).
Space Weather applications with CDPP/AMDA.
Adv. Space. Res. 45, 1145–1155.

[Gurnett et al., 2004]
Gurnett, D. A., Kurth, W. S., Kirchner, D. L., Hospodarsky, G. B., Averkamp,
T. F., Zarka, P., et al. (2004).
The Cassini Radio and Plasma Wave Investigation.
Space Sci. Rev. 114, 395–463.

[Hanlon et al., 2004]
Hanlon, P. G., Dougherty, M. K., Forsyth, R. J., Owens, M. J.,
Hansen, K. C., Tóth, G., et al. (2004).
On the evolution of the solar wind between 1 and 5 AU at the time of
the Cassini Jupiter flyby: Multispacecraft observations of interplanetary
coronal mass ejections including the formation of a merged interaction
Journal of Geophysical Research (Space Physics) 109, A09S03.

[Hess et al., 2012]
Hess, S. L. G., Echer, E., and Zarka, P. (2012).
Solar wind pressure effects on Jupiter decametric radio emissions
independent of Io.
Planetary and Space Science 70, 114–125.

[Jackman et al., 2005]
Jackman, C., Achilleos, N., Bunce, E., Cecconi, B., Clarke, J., Cowley, S.
W. H., et al. (2005).
Interplanetary conditions and magnetospheric dynamics during the
Cassini orbit insertion fly-through of Saturn's magnetosphere.
J. Geophys. Res. 110, A10212.

[Jackman et al., 2009]
Jackman, C., Lamy, L., Freeman, P., Zarka, P., Cecconi, B., Kurth, W. S.,
et al. (2009).
On the character and distribution of lower-frequency radio emissions
at Saturn and their relationship to substorm-like events.
J. Geophys. Res. 114.

[Jackman et al., 2013]
Jackman, C. M., Achilleos, N., Cowley, S. W. H., Bunce, E. J., Radioti, A.,
Grodent, D., et al. (2013).
Auroral counterpart of magnetic field dipolarizations in Saturn's
Planetary and Space Science 82-83, 34–42.

[Kaiser et al., 1980]
Kaiser, M. L., Desch, M., Warwick, J., and Pearce, J. (1980).
Voyager Detection of Nonthermal Radio Emission from Saturn.
Science 209, 1238–1240.

[Kanani et al., 2010]
Kanani, S. J., Arridge, C. S., Jones, G. H., Fazakerley, A. N.,
McAndrews, H. J., Sergis, N., et al. (2010).
A new form of Saturn's magnetopause using a dynamic pressure balance
model, based on in situ, multi-instrument Cassini measurements.
Journal of Geophysical Research (Space Physics) 115, A06207.

[Kita et al., 2019]
Kita, H., Kimura, T., Tao, C., Tsuchiya, F., Murakami, G., Yamazaki, A., et al.
Jovian UV Aurora's Response to the Solar Wind: Hisaki EXCEED and
Juno Observations.
Journal of Geophysical Research (Space Physics) 124,

[Krimigis et al., 2004]
Krimigis, S. M., Mitchell, D. G., Hamilton, D. C., Livi, S., Dandouras, I.,
Jaskulek, S., et al. (2004).
Magnetosphere Imaging Iinstrument (MIMI) on the Cassini Mission to
Space Sci. Rev. 114, 233–329.

[Kurth et al., 2016]
Kurth, W. S., Hospodarsky, G. B., Gurnett, D. A., Lamy, L., Dougherty, M. K.,
Nichols, J., et al. (2016).
Saturn kilometric radiation intensities during the Saturn auroral
campaign of 2013.
Icarus 263, 2–9.

[Lamy, 2010]
Lamy, L. (2010).
VARIABILITY OF SOUTHERN AND NORTHERN SKR PERIODICITIES.
PRE 7 , 39–5010.1553/PRE7s39

[Lamy et al., 2009]
Lamy, L., Cecconi, B., Prangé, R., Zarka, P., Nichols, J., and Clarke, J.
An auroral oval at the footprint of Saturn's radiosources, colocated
with the UV aurorae.
J. Geophys. Res. 114, A10212.

[Lamy et al., 2009]
[Dataset] Lamy, L., Cecconi, B., and Zarka, P. (2009b).
Cassini/RPWS/HFR SKR Data Collection, PADC/MASER.

[Lamy et al., 2012]
Lamy, L., Prangé, R., Hansen, K. C., Clarke, J. T., Zarka, P., Cecconi, B.,
et al. (2012).
Earth-based detection of Uranus' aurorae.
Geophys. Res. Lett. 39.

[Lamy et al., 2013]
Lamy, L., Prangé, R., Pryor, W., Gustin, J., Badman, S. V., Melin, H.,
et al. (2013).
Multispectral simultaneous diagnosis of Saturn's aurorae throughout
a planetary rotation.
Journal of Geophysical Research (Space Physics) 118,

[Lamy et al., 2018]
Lamy, L., Prangé, R., Tao, C., Kim, T., Badman, S. V., Zarka, P., et al.
Saturn's Northern Aurorae at Solstice From HST Observations
Coordinated With Cassini's Grand Finale.
Geophys. Res. Lett. 45, 1–20.

[Lamy et al., 2010]
Lamy, L., Schippers, P., Zarka, P., Cecconi, B., Arridge, C., Dougherty, M.,
et al. (2010).
Properties of Saturn kilometric radiation measured within its source
Geophys. Res. Lett. 37.

[Lamy et al., 2008]
Lamy, L., Zarka, P., Cecconi, B., Prangé, R., Kurth, W. S., and Gurnett, D.
Saturn Kilometric Radiation: average and statistical properties.
J. Geophys. Res. 113.

[Louarn et al., 2007]
Louarn, P., Kurth, W. S., Gurnett, D., Hospodarsky, G., Persoon, A., cecconi,
B., et al. (2007).
Observation of similar radio signatures at Saturn and Jupiter:
implications for the magnetospheric dynamics.
Geophys. Res. Lett. 34.

[Ochsenbein et al., 2019]
Ochsenbein, F., Williams, R., Davenhall, C., Demleitner, M., Donaldson, T.,
Durand, D., et al. (2019).
VOTable Format Definition.
IVOA Recommendation 10.25504/FAIRsharing.g2ChgH

[Odstrcil, 2003]
Odstrcil, D. (2003).
Modeling 3-d solar wind structure.
Advances in Space Research 32, 497–506.
Heliosphere at Solar Maximum

[Palmerio et al., 2021]
Palmerio, E., Nieves-Chinchilla, T., Kilpua, E. K. J., Barnes, D., Zhukov,
A. N., Jian, L. K., et al. (2021).
Magnetic Structure and Propagation of Two Interacting CMEs from the
Sun to Saturn.
J. geophys. Res. Space Physics in press, 1–45.

[Piker, 2017]
Piker, C. W. (2017).
Das2: Interface control document.
Zenodo 10.5281/zenodo.3588535

[Prangé et al., 2004]
Prangé, R., Pallier, L., Hansen, K. C., Howard, R. A., Vourlidas, A.,
Courtin, R., et al. (2004).
An interplanetary shock traced by planetary auroral storms from the
Sun to Saturn.
Nat. Bur. Std. 432, 78–81.

[Reed et al., 2018]
Reed, J. J., Jackman, C. M., Lamy, L., Kurth, W. S., and Whiter,
D. K. (2018).
Low-Frequency Extensions of the Saturn Kilometric Radiation as a
Proxy for Magnetospheric Dynamics.
Journal of Geophysical Research (Space Physics) 123, 443–463.

[Roussos et al., 2018]
Roussos, E., Jackman, C., Thomsen, M., Kurth, W., Badman, S., Paranicas, C.,
et al. (2018).
Solar Energetic Particles (SEP) and Galactic Cosmic Rays (GCR) as
tracers of solar wind conditions near Saturn: Event lists and applications.
Icarus 300, 47–71.

[Rucker, 1984]
Rucker, H. O. (1984).
EXTERNAL CONTROL OF SATURN KILOMETRIC RADIATION: VOYAGER 1 AND 2
Planetary Radio Emissions 1 1, 143–160

[Tao et al., 2005]
Tao, C., Kataoka, R., Fukunishi, H., Takahashi, Y., and Yokoyama, T. (2005).
Magnetic field variations in the Jovian magnetotail induced by solar
wind dynamic pressure enhancements.
J. Geophys. Res. 110, A11208.

[Taubenschuss et al., 2006]
Taubenschuss, U., Rucker, H. O., Kurth, W. S., Cecconi, B., Zarka, P.,
Dougherty, M. K., et al. (2006).
Linear prediction studies for the solar wind and saturn kilometric
Annales Geophysicae 24, 3139–3150.

[Taylor, 2005]
Taylor, M. B. (2005).
TOPCAT & STIL: Starlink Table/VOTable Processing Software.
ASP Conference Series 346, 29–33

[Taylor et al., 2015]
Taylor, M. B., Boch, T., and Taylor, J. (2015).
SAMP, the Simple Application Messaging Protocol: Letting
applications talk to each other.
Astronomy and Computing 11, 81–90.
2015A   C....11...81T

[Vandegriff J., 2018]
[Dataset] Vandegriff J., M. J., Kusterer M.B. (2018).
CASSINI SATURN MIMI LEMMS CALIBRATED DATA ARCHIVE,
CO-S-MIMI-4-LEMMS-CALIB-V1.0, NASA Planetary Data System.

[Wang et al., 2010]
Wang, Z., Gurnett, D., Fischer, G., Ye, S.-Y., Kurth, W. S., Mitchell, D.,
et al. (2010).
Cassini observations of narrowband radio emissions in Saturn's
J. Geophys. Res. 115.

[Warwick et al., 1977]
Warwick, J., Pearce, J., Peltzer, D., and Riddle, A. (1977).
Planetary radio astronomy experiment for Voyager missions.
Space Sci. Rev. 21, 309.

[Went et al., 2011]
Went, D. R., Hospodarsky, G. B., Masters, A., Hansen, K. C., and Dougherty,
M. K. (2011).
A new semiempirical model of Saturn.
J. Geophys. Res. Space Physics 116, 1–9.

[Witasse et al., 2017]
Witasse, O., Sánchez-Cano, B., Mays, M. L., Kajdič, P., Opgenoorth,
H., Elliott, H. A., et al. (2017).
Interplanetary coronal mass ejection observed at STEREO-A, Mars,
comet 67P/Churyumov-Gerasimenko, Saturn, and New Horizons en route to Pluto:
Comparison of its Forbush decreases at 1.4, 3.1, and 9.9 AU.
Journal of Geophysical Research (Space Physics) 122,

[Wu and Lee, 1979]
Wu, C. and Lee, L. (1979).
A theory of the terrestrial kilometric radiation.
Astrophys. J. 230, 621–626.

[Zurbuchen and Richardson, 2006]
Zurbuchen, T. H. and Richardson, I. G. (2006).
In-Situ Solar Wind And Magnetic Field Signatures of Interplanetary
Coronal Mass Ejections.
Space Sci. Rev. 123, 31–43.


# Differentiable and Learnable Robot Models

Franziska<EMAIL_ADDRESS>
Facebook AI Research, Menlo Park, USA Austin Wang*<EMAIL_ADDRESS>
Facebook AI Research, Menlo Park, USA Giovanni Sutanto<EMAIL_ADDRESS>
Intrinsic Innovation LLC. Yixin Lin<EMAIL_ADDRESS>
Facebook AI Research, Menlo Park, USA Paarth Shah
<EMAIL_ADDRESS>
Oxford Robotics Institute Equal contribution The contribution was made while
Giovanni Sutanto was working as an intern at Facebook AI Research in Fall
2019.

###### Abstract

Building differentiable simulations of physical processes has recently
received an increasing amount of attention. Specifically, some efforts develop
differentiable robotic physics engines motivated by the computational benefits
of merging rigid body simulations with modern differentiable machine learning
libraries. Here, we present a library that focuses on the ability to combine
data driven methods with analytical rigid body computations. More concretely,
our library _Differentiable Robot Models_ implements both _differentiable_ and
_learnable_ models of the kinematics and dynamics of robots in Pytorch. The
source-code is available at
https://github.com/facebookresearch/differentiable-robot-model.

Keywords: Differentiable simulations, Robotics

##  1 Introduction

Building or learning differentiable simulations of robots and their
environments comes with several potential benefits: Massive potential for
parallelization (Freeman et al., 2021); enabling principled hybrid modeling
via analytical models and data-driven neural networks (Heiden et al., 2021;
Sutanto et al., 2020) and generally enabling the development of model-based
reinforcement learning. The high potential of differentiable simulators has
created a lot of interest and progress in developing differentiable physics
engines and rigid body simulations that are differentiable (Freeman et al.,
2021; Heiden et al., 2021; Werling et al., 2021; de Avila Belbute-Peres et
al., 2018; Geilinger et al., 2020; Giftthaler et al., 2017; Hu et al., 2019;
Qiao et al., 2020); some of them through analytical gradients (Carpentier et
al., 2015–2021, 2019; Carpentier and Mansard, 2018; de Avila Belbute-Peres et
al., 2018).

In this context, we introduce our library for _differentiable robot models_
which implements analytical _differentiable_ and _learnable_ robot models in
PyTorch (Paszke et al., 2019). In contrast to existing libraries, our library
differs in two ways from existing libraries: 1) our library focuses on
differentiable robot models (instead of full simulations with environment
modeling), and provides differentiable kinematic and dynamic representations.
These robot models can then, for instance, be used for control of the modeled
robots in either simulation or on hardware (Bhardwaj et al., 2021; Bechtle et
al., 2020). 2) Our library provides differentiable analytical rigid body
simulations that can selectively make rigid bodies _learnable_. When a rigid
body becomes _learnable_ , we can either identify its physical constants (such
as mass) from data, or learn flexible representations (such as neural
networks) for the parameters of the rigid body from data. Our learnable robot
models are implemented as general torch modules, and thus can be easily used
within typical deep learning pipelines.

##  2 Library Overview: Differentiable and Learnable Robot Models

Figure 1: Overview: (left) Conceptual illustration of library (right)
officially supported robots

Our Differentiable Robot Model library parses URDFs and creates fully
differentiable models. More precisely, the library constructs analytical
kinematics and dynamics computations as a computation graph via PyTorch
(Paszke et al., 2019) for the robot described in a given URDF (see Figure 1).
Our library can be used on any URDF that describes a kinematic tree, and we
created and tested specifically the following robots: Kuka iiwa, Franka Panda,
Fetch arm and the Allegro Hand. We see at least four primary use cases for the
library:

  * •

Given a complete and accurate URDF (all kinematic and dynamic parameters are
accurately specified): The library can be utilized as ground truth model
within model-based RL algorithms or trajectory optimization settings (Bhardwaj
et al., 2021; Bechtle et al., 2020) and enables batching and leveraging of GPU
resources.

  * •

Given an incomplete URDF or the goal is to study learning algorithms: We can
learn any unknown parameters of the robot from observations by harnessing the
power of automatic differentiation. For instance, it is possible to identify
the dynamics parameters of the analytical dynamics model and compare to
learning other dynamics representations with varying degrees of structure
(Sutanto et al., 2020).

  * •

Because this library implements the analytical (ground truth) models of robots
within a modern deep learning framework, it can support the pursuit of finding
the ”convolutional neural network” of robot motion.

  * •

Finally, this library can be utilized as a teaching tool that allows to teach
core robotics concepts such as kinematics in the context of modern deep
learning frameworks.

The library works with any properly written URDF file that describes a
kinematic tree. We officially support several robot models which are shown in
Figure 1. Our algorithms are carefully tested on these robots to ensure that
computations within our framework are identical to that of a commercial
physics engine such as Bullet (Coumans and Bai, 2016). Our library
implementation is based on spatial vector notation and implements kinematics,
such as forward kinematics and Jacobian computations, as well as rigid body
dynamics following Featherstone’s book (Featherstone, 2014). Specifically, to
compute the various components of the robot equations of motions, it
implements the Recursive Newton Euler (RNEA) Algorithm (inverse dynamics), the
Composite Rigid Body Algorithm (CRBA) (inertia matrix computation), and the
Articulated Body Algorithm (ABA) (forward dynamics).

##  3 API Design and Workflow

Our library follows the standard PyTorch API design, such that instantiating a
robot model is as simple as a standard _torch.nn.Module_. This design also
allows for easy integration with neural-network based modules in PyTorch.

###  3.1 Creating and Using a Differentiable Robot Model

Specifically, to initialize a differentiable robot model, all the user needs
is a path to a urdf:

⬇

1from differentiable_robot_model.robot_model import DifferentiableRobotModel

2

3urdf_path = "path/to/robot/urdf"

4robot = DifferentiableRobotModel(urdf_path)

This command will create a tree of rigid bodies, according to the structure
outlined in the URDF and initialize the rigid bodies with the kinematics and
dynamics parameters specified in the URDF. Once the robot model is loaded, a
user can then perform various operations, such as querying the robots
properties, or executing kinematic and dynamic computations:

⬇

1# Robot properties

2robot.get_joint_limits()

3robot.get_link_names()

4

5# Values to query the model with

6jpos = torch.rand(7), jvel = torch.rand(7), jacc_des = torch.rand(7)

7torques = torch.rand(7)

8ee_link_name = "iiwa_link_ee"

9

10# Robot kinematics and dynamics

11ee_pos, ee_quat = robot.compute_forward_kinematics(jpos, ee_link_name)

12J_lin, J_ang = robot.compute_endeffector_jacobian(jpos, ee_link_name)

13

14jacc = robot.compute_forward_dynamics(jpos, jvel, torques)

15torques_desired = robot.compute_inverse_dynamics(jpos, jvel, jacc_des)

Notably, these computations are fully differentiable, and changes in the
output can be propagated to the input. For example, we can compute inverse
kinematics by iteratively updating the joint position until the predicted end-
effector pose matches a desired pose.

###  3.2 Differentiable and Learnable Rigid Body

The key building block of the differentiable robot model is the differentiable
rigid body, similar to having layers as the key building block of neural
networks. The robot model is essentially a tree of connected rigid bodies
where the tree connections define how inputs/outputs/gradients are propagated.
Each rigid body has variables that capture the (local) kinematic and dynamic
state of the body. In some applications, it might be desirable to learn
parameters of the robot model. In that case, the user can make the parameters
of links learnable:

⬇

1from differentiable_robot_model.rigid_body_params import PositiveScalar

2

3# make a parameter of a link learnable

4robot_model.make_link_param_learnable(<link_name>, <param_name>, <module>)

5# for instance:

6robot_model.make_link_param_learnable("link_1", "mass", PositiveScalar())

While our library provides implementations for parametrizations (such as a
_PositiveScalar_ ”net”), users can specify their own flexible parametrizations
with a torch.nn.Module.

###  3.3 Learning Loop

Finally, to learn parameters from data, the user implements a typical learning
loop

⬇

1 """ generate training data via ground truth model """

2train_data = generate_sine_motion_forward_dynamics_data(gt_robot_model,
n_data=n_data, dt=1.0 / 250.0, freq=0.1)

3train_loader = DataLoader(dataset=train_data, batch_size=100, shuffle=False)

4

5""" optimize learnable params """

6optimizer = torch.optim.Adam(robot_model.parameters(), lr=1e-2)

7loss_fn = NMSELoss(train_data.var())

8for i in range(n_epochs):

9 losses = []

10 for batch_idx, batch_data in enumerate(train_loader):

11 q, qd, qdd, tau = batch_data

12 optimizer.zero_grad()

13 qdd_pred = robot_model.compute_forward_dynamics(

14 q=q, qd=qd, f=tau, include_gravity=True, use_damping=True)

15 loss = loss_fn(qdd_pred, qdd)

16 loss.backward()

17 optimizer.step()

###  3.4 Conclusion

We present our library on differentiable and learnable robot models, that
provides a flexible implementation of analytical rigid body simulations of
popular robots in Pytorch. Our library works for arbitrary kinematic trees,
but officially supports (with testing) a variety of robots (see Figure 1).
Finally, our library enables the user to selectively make rigid bodies
learnable, and explore the option of identifying parameters or more complex
models from data.

## References

  * Bechtle et al. (2020) Sarah Bechtle, Neha Das, and Franziska Meier.  Learning extended body schemas from visual keypoints for object manipulation.  _arXiv preprint arXiv:2011.03882_ , 2020.
  * Bhardwaj et al. (2021) Mohak Bhardwaj, Balakumar Sundaralingam, Arsalan Mousavian, Nathan D Ratliff, Dieter Fox, Fabio Ramos, and Byron Boots.  Storm: An integrated framework for fast joint-space model-predictive control for reactive manipulation.  In _5th Annual Conference on Robot Learning_ , 2021.
  * Carpentier and Mansard (2018) Justin Carpentier and Nicolas Mansard.  Analytical derivatives of rigid body dynamics algorithms.  In _Robotics: Science and Systems_ , 2018.
  * Carpentier et al. (2015–2021) Justin Carpentier, Florian Valenza, Nicolas Mansard, et al.  Pinocchio: fast forward and inverse dynamics for poly-articulated systems.  https://stack-of-tasks.github.io/pinocchio, 2015–2021.
  * Carpentier et al. (2019) Justin Carpentier, Guilhem Saurel, Gabriele Buondonno, Joseph Mirabel, Florent Lamiraux, Olivier Stasse, and Nicolas Mansard.  The pinocchio c++ library – a fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives.  In _IEEE International Symposium on System Integrations (SII)_ , 2019\.
  * Coumans and Bai (2016) Erwin Coumans and Yunfei Bai.  Pybullet, a python module for physics simulation for games, robotics and machine learning, 2016.
  * de Avila Belbute-Peres et al. (2018) Filipe de Avila Belbute-Peres, Kevin Smith, Kelsey Allen, Josh Tenenbaum, and J Zico Kolter.  End-to-end differentiable physics for learning and control.  _Advances in neural information processing systems_ , 31:7178–7189, 2018.
  * Featherstone (2014) Roy Featherstone.  _Rigid body dynamics algorithms_.  Springer, 2014.
  * Freeman et al. (2021) C. Daniel Freeman, Erik Frey, Anton Raichuk, Sertan Girgin, Igor Mordatch, and Olivier Bachem.  Brax - a differentiable physics engine for large scale rigid body simulation, 2021.  URL http://github.com/google/brax.
  * Geilinger et al. (2020) Moritz Geilinger, David Hahn, Jonas Zehnder, Moritz Bächer, Bernhard Thomaszewski, and Stelian Coros.  Add: analytically differentiable dynamics for multi-body systems with frictional contact.  _ACM Transactions on Graphics (TOG)_ , 39(6):1–15, 2020.
  * Giftthaler et al. (2017) Markus Giftthaler, Michael Neunert, Markus Stäuble, Marco Frigerio, Claudio Semini, and Jonas Buchli.  Automatic differentiation of rigid body dynamics for optimal control and estimation.  _Advanced Robotics_ , 31(22):1225–1237, 2017\.
  * Heiden et al. (2021) Eric Heiden, David Millard, Erwin Coumans, Yizhou Sheng, and Gaurav S Sukhatme.  NeuralSim: Augmenting differentiable simulators with neural networks.  In _Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)_ , 2021.  URL https://github.com/google-research/tiny-differentiable-simulator.
  * Hu et al. (2019) Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand.  Difftaichi: Differentiable programming for physical simulation.  _arXiv preprint arXiv:1910.00935_ , 2019.
  * Paszke et al. (2019) Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al.  Pytorch: An imperative style, high-performance deep learning library.  _Advances in neural information processing systems_ , 32:8026–8037, 2019.
  * Qiao et al. (2020) Yi-Ling Qiao, Junbang Liang, Vladlen Koltun, and Ming C Lin.  Scalable differentiable physics for learning and control.  _arXiv preprint arXiv:2007.02168_ , 2020.
  * Sutanto et al. (2020) Giovanni Sutanto, Austin Wang, Yixin Lin, Mustafa Mukadam, Gaurav Sukhatme, Akshara Rai, and Franziska Meier.  Encoding physical constraints in differentiable newton-euler algorithm.  In _Proceedings of the 2nd Conference on Learning for Dynamics and Control_ , volume 120 of _Proceedings of Machine Learning Research_ , pages 804–813. PMLR, 10–11 Jun 2020.  URL https://proceedings.mlr.press/v120/sutanto20a.html.
  * Werling et al. (2021) Keenon Werling, Dalton Omens, Jeongseok Lee, Ioannis Exarchos, and C Karen Liu.  Fast and feature-complete differentiable physics for articulated rigid bodies with contact.  _arXiv preprint arXiv:2103.16021_ , 2021.