The European Space Agency's spacecraft ROSETTA has reached its final destination, comet 67P/Churyumov-Gerasimenko. Whilst orbiting in the close vicinity of the nucleus the ROSETTA magnetometers detected a new type of low-frequency wave possibly generated by a cross-field current instability due to freshly ionized cometary water group particles. During separation, descent and landing of the lander PHILAE on comet 67P/Churyumov-Gerasimenko, we used the unique opportunity to perform combined measurements with the magnetometers onboard ROSETTA (RPCMAG) and its lander PHILAE (ROMAP). New details about the spatial distribution of wave properties along the connection line of the ROSETTA orbiter and the lander PHILAE are revealed. An estimation of the observed amplitude, phase and wavelength distribution will be presented as well as the measured dispersion relation, characterizing the new type of low-frequency waves. The propagation direction and polarization features will be discussed using the results of a minimum variance analysis. Thoughts about the size of the wave source will complete our study.

After a 10-year flight the ROSETTA spacecraft

Nevertheless the orbiter magnetometer RPCMAG observed magnetic, low-frequency
waves with frequencies around 30–50 mHz and relative amplitudes up to about

In the months after arrival at 67P/C-G, ROSETTA operated under different
conditions and at various distances to the comet. Thus, a comprehensive
insight into the frequency and amplitude characteristics of these waves may
be gained. No information, however, could be retrieved on the wavelengths,
velocities and the dispersion relation as only single-point observations were
available. This situation changed during separation, descent (and rebound)
and landing (SDL) of the ROSETTA lander PHILAE on 12 November 2014. During
the 1.5 days of joint operations of the orbiter magnetometer RPCMAG

In this paper we will give a short overview of the ROSETTA mission and the
plasma instrumentation in Sect. 2. Section 3 includes the temporal and
spatial evolution of wave properties and thus extends the findings presented
in

As all measurements and analysis techniques are affected by certain errors a systematic error estimation is given in Sect. 6 in order to be able to draw the right conclusions in Sect. 7.

ESA's comet chaser mission ROSETTA

As not only observations in close vicinity of the target body but also
measurements on the surface of 67P/C-G were intended to be conducted, the
ROSETTA mission was designed to comprise two spacecraft: an orbiter observing
the comet in varying distances between a few kilometres up to a few hundred
kilometres, and the Lander PHILAE, performing measurements on the surface of
67P/C-G. PHILAE was successfully separated from the orbiter on 12 November
2014 at 08:35 UTC and performed its final landing at 17:31 UTC

As ROSETTA is supposed to investigate plasma-physical properties in the
surroundings and on the surface of 67P/C-G, it is equipped with two plasma
packages, each of which containing a magnetometer experiment. The ROSETTA
Plasma Consortium (RPC)

The RPCMAG instrument, as part of RPC, is comprised of two triaxial fluxgate
magnetometer sensors (FGM)

The low-frequency waves, being the object of this study, occur in a frequency
range (

The ROMAP magnetometer

The magnetometer is designed to be a low power consuming instrument which
also generates only a small amount of telemetry packages. Therefore, RPCMAG
has been allowed to operate almost continuously since spring 2014 while
ROSETTA was still at about 1 million km away from the target comet. Thus,
measurements spanning 1 year are available in order to study the new wave
phenomena. All magnetic field observations described in this work are
presented in the Cometary-centered Solar EQuatorial-coordinate
system (CSEQ). Here the

Using the RPCMAG instrument we started to detect low-frequency waves at the
beginning of August 2014 at a distance of

Magnetic field measurements made by RPCMAG on 8 January 2015,
22:00–22:15 UTC, as an example for the detection of low-frequency waves.
Large-amplitude waves with a frequency of 28 mHz are clearly visible.
The spacecraft position at that time was (0.2,

In order to systematically investigate the temporal and spatial evolution of
the wave activity, the energy density in the 10–100 mHz band has been
calculated by integrating the power spectral density for almost 9000 hourly
intervals. As a result Fig.

As expected, measurements sampled from the solar wind over the time period
of May–August 2014 (violet part) revealed very low and featureless energy
density levels. However, the onset of wave activity at

Over the following months, between November 2014 and April 2015, ROSETTA
moved again to larger distances (green part). However, as seen in
Fig.

The energy density of the observed waves in dependence of the radial distance between ROSETTA and 67P/C-G for 1 year of observations. Time segments are colour-coded.

At 12 November 2014 – the day of landing – we had the unique opportunity of operating the two ROSETTA magnetometers in parallel at different locations. Thus, we use the descent phase of PHILAE to collect magnetic field data with both instruments, compare the waves detected with both sensors and analyse the relative wave phase shifts in order to estimate wavelength and wave velocity.

On 12 November 2014 at 08:35 UTC PHILAE separated from ROSETTA. This
occurred at a distance of

Temporal evolution of the distance between ROSETTA and PHILAE and also between PHILAE and 67P/C-G (centre) during the descent to 67P/C-G on 12 November 2014. The shown trajectories have been generated using the latest nominal kernels being available.

Projection of the two spacecraft trajectories in the

Figure

A closer look at the direction of the shown imaginary lines connecting the
two spacecraft reveals that these lines are approximately parallel over
the time of descent. This important geometrical feature will be considered
later during the estimation of the projected wavelength and the determination
of the wave direction. In this context also the mean background field
measured by RPCMAG shall be taken into account. It can be calculated by
averaging the measured field over certain time intervals. From the
background field point of view the descent phase can be split into three
major time intervals showing three different field configurations:

During SDL the orbiter magnetometer RPCMAG was permanently operating at 20 Hz sampling rate whereas the lander magnetometer ROMAP was operated at 1 Hz sampling rate. Due to this operational constraint the RPCMAG data had to be undersampled to an effective sample rate of 1 Hz in order to be directly comparable with ROMAP data. This reduction is done by just picking out every 20th raw vector and resampling the data in order to be aligned to the ROMAP time tags.

To eliminate the effects imposed by internal spacecraft disturbance sources to the magnetic field data, a 1st order
Butterworth-bandpass filter

It should be noted that the lander attitude, i.e. the orientation of the
Lander frame, in which the ROMAP data were measured, was primarily unknown
during descent and landing as it could not be linked to any celestial
coordinate system of reference. However, correlating RPCMAG and ROMAP data
and rotating the ROMAP data to the RPCMAG system using a fit algorithm for
minimizing the deviation of both datasets as described by

Camera experiment onboard ROSETTA

and CONSERTCOmet Nucleus Sounding ExpeRimenT onboard ROSETTA & PHILAE

Science and Operation Navigation Center, Toulouse,France

An example of 10 min parallel measurements of RPCMAG & ROMAP data
during the PHILAE descent. Waves with frequencies of

Figure

Waves with frequencies of

Correlation coefficients

The magnetic field data of the 10 min time interval presented in
Fig.

A rough estimate of the correlation length

Predominantly high correlation coefficients between the waves observed with RPCMAG and ROMAP in all the visited areas allow us to draw conclusions about the plasma environment. Collective plasma oscillations occur on length-scales larger than the maximum orbiter-lander distance. Therefore, the wavelength of the observed waves must be also much larger than the maximum distance between orbiter and lander and thus any spatial aliasing effects do not play any role – otherwise the correlation coefficients (and the required time shift to obtain max. correlation) would show a significant spatial variation. Hence, we conclude from the correlation analysis that the wavelengths have to be larger than 18 km.

The frequency of the waves is one key characterization parameter, as it reflects the processes that the plasma undergo. For a dynamic frequency analysis within the complete descent and landing phase the magnetic field data have to be treated in a special way. As mentioned previously, first order Butterworth bandpasses with 10 and 100 mHz corner frequencies have been applied twice (forward and backward in time in order to avoid phase shifts). Furthermore the complete time series are split into chunks of 1200 s intervals which are shifted forward by 60 s in each step. Each of these intervals is cut into 300 s wide windows which is shifted by only half window widths, namely 150 s, in order to achieve a reasonable overlap and to perform a statistical significant frequency analysis. Thus, each 1200 s interval is divided into seven smaller intervals of 300 s, which are used to obtain averaged spectral information by summing up the individual results of the single windows. The chosen interval lengths turned out to be a suitable compromise between the low frequencies to be analysed and the fewer data points available during SDL.

For the proper assessment of the estimated frequencies three different types
of frequencies are determined from the datasets: first ROMAP and RPCMAG time
series are investigated separately and the two individual frequencies of the
maximum wave power are calculated using dynamic power spectral analyses
during the mentioned intervals above. In addition a cross-spectral analysis
is executed using both datasets together and the frequencies of the maximum
cross power is determined as well. The three resulting histograms of the
calculated frequency distributions are presented in Fig.

Normalized histograms (using 32 bins) of the most prominent
frequencies for measurements by RPCMAG (green) and ROMAP (red). The
flywheel signature of PHILAE at

Further information about the occurring frequencies of max cross-power is
provided in Fig.

Nevertheless the plot reveals an interesting pattern. There seems to be a trend showing that lower frequencies appear at larger ROSETTA-PHILAE distances. However, as these measurement were made at different times, a purely temporal dependency – or a dependency of any other changing plasma entity – could be causing this finding as well.

Profile of the most significant wave frequency (including gray error bars) versus the orbiter-lander distance. The frequency at which the cross-spectral density of RPCMAG and ROMAP measurements reaches its maximum value is plotted against the distance between ROSETTA and PHILAE during descent.

As described by

Amplitudes of magnetic fields observed by RPCMAG (green) and ROMAP (red) at the most significant frequencies plotted versus the orbiter-lander distance. The amplitudes represent the mean of all three components.

For a detailed amplitude analysis the time series of RPCMAG and ROMAP data
have been analysed in the frequency domain
(Fig.

The ratio of the ROMAP/RPCMAG magnetic field
amplitudes (from Fig.

It can be seen that both instruments detect the same variations in the
signals. Especially the common temporal variations registered at about 11 km
distance prove spatial coherence of the observed plasma dynamics. This is
consistent with the estimated coherence length of 48 km. In addition we know
from the long-term observations that the “singing of the comet” commenced
at 100 km distance from the comet. Therefore, we regard an area of

Furthermore, it should be mentioned that the ROMAP signals were slightly
larger for larger orbiter-lander distances compared with the RPCMAG
amplitudes. This is exhibited even clearer in Fig.

The relative phase shift of the waves measured at different locations is a key parameter for the estimation of the wavelength. This phase shift is calculated at the local frequency of maximum cross-power, derived from a cross-spectral analysis. The algorithm has been applied to all data available during the SDL segments using the parameters and thresholds mentioned above.

From the theoretical point of view the phase shift is identical for
corresponding component-pairs

The phase shift between signals of RPCMAG and ROMAP (blue), taken at the frequency at which the maximum cross-spectral density occurs, versus the orbiter-lander distance. The red line represents the linear fit.

As a result of this phase analysis the relative phase shift

Due to the lack of scientifically usable data for the times where orbiter and
lander were still connected (i.e. at 0 km distance) and where the ROMAP boom
was still in its stowed positions, statements about phase shifts can only be
made for ROSETTA/PHILAE distances between 3 and 14 km. From
Fig.

It has to be noted for the following estimation of the wavenumber and
wavelength that these entities have to be regarded as projected wavenumber

Thus, we get a projected wavenumber

Normalized histogram (bin size: 40 km) of the estimated wavelengths, projected on the orbiter-lander connecting line.

A more detailed wavelength study can be performed using not only the global
estimated phase gradient

The estimated wavelengths, projected on the orbiter-lander connecting line, are plotted versus the orbiter-lander distance.

The larger wavelengths and smaller wavenumbers, being exhibited at
larger distances are related to lower frequencies at larger distances as can
be seen in Fig.

The combination of frequencies and wavelengths (respectively angular
frequencies and wavenumber) in a common diagram, as exhibited in the plot of
the calculated dispersion relation in Fig.

The phase velocity

Derived dispersion relation (blue) including a linear fit (red). For the calculation the projected wavelength on the orbiter-lander connecting line and the related angular frequencies at which the maximum cross-power occurs have been used.

Using the minimum- and
maximum-variance analysis (MVA) additional wave properties have been obtained
to complete the knowledge of the “singing comet” waves

From the two columns of Fig.

The temporal behaviour of the maximum variance directions (not shown here), however, does not exhibit any striking feature, neither for ROMAP nor for the RPCMAG measurements.

Distribution of

The angle distribution of minimum variance directions, representing the wave
propagation directions, can be obtained from Fig.

Distribution of

From these findings we calculate (0.68, 0.44, 0.34) as the average minimum
variance direction in the CSEQ-System. Only eigenvalue ratios of

This means that the main wave propagating direction during the descent points
approximately in the diagonal in space direction from

Furthermore the propagation direction can be compared with the mean direction
of the background magnetic field. From the three major magnetic field
configurations stated in the “joint observations section” we calculate the
mean directions of the magnetic field as

The polarization analysis yields that elliptical or more complex modes are
prevailing for all transversal waves showing a significant propagation
direction defined by

As completion of the parameter discussion an error estimation shall be given finally. We are concentrating on wave properties only, therefore neither instrument offsets nor the s/c bias fields play any role. The influences of the orbiter reaction wheels have been eliminated, the disturbance of the lander fly wheels was recognized but does not influence the analyses as it is outside the frequency band of interest. Amplitudes and frequencies have been derived by the means of power spectral density analyses using moving time windows and averaging over sub-windows as described above. Thus, we have seven degrees of freedom in our spectral calculations, which is for sure not ideal, but a suitable compromise, in order to get a reasonable frequency resolution under the given circumstances.

The crucial point is the phase and wavelength calculation. For this the
relative timing of both magnetometer datasets has to be precise. With our
knowledge of the data handling onboard ROSETTA and PHILAE, we know that the
timing accuracy is better than

Furthermore, a conservative guess of the relative position error of 100 m would cause an additional uncertainty in wavelength of 1 % at 10 km distance.

As a final result we therefore obtain an assured value for projected wavelength in the order of about 300 km, derived from the joint RPCMAG/ROMAP measurements. This clearly proves the assumption made earlier that the considered region of observation is small in relation to the occurring wavelengths.

The considered phase error of

A final remark on the variability of the obtained parameters shall be made
here. During the considered descent and landing phase of PHILAE, which lasted
about 9 h, the comet performed a 3/4-rotation. From long-term measurements
it is known that, e.g. the outgassing rate, and also the particle
density, is modulated not only with the comet rotation period but also with
the half period of 6.2 h

The limitations originated in the equipment available has to be considered as
well. We have only two spacecraft at our disposal. Both are permanently
moving, one is approaching a rotating comet with unknown properties. This
situation complicates the interpretation of those results, which have to be
derived from joint measurements, i.e. phase shifts, wavelengths and
velocities. Hence the distinction between spatial and temporal effects stays
ambiguous for these parameters. For proper determination of the real
wavelength methods like the wave-telescope

With the ROSETTA mission we were able to perform long-term magnetic field
measurements during the long approach phase to 67P/C-G, and at 67P/C-G during
landing of PHILAE. During SDL we had the unique opportunity to conduct a joint
measurement with two magnetometers, RPCMAG and ROMAP, at different, varying
locations. These joint measurements confirm the detection of low-frequency
waves with frequencies around

The joint measurements also allowed to calculate the mean projected
wavenumber (

According to the general antenna theory

The dominating wave propagation direction can be found roughly along the
diagonal in space direction from the CSEQ (

It has been demonstrated in Fig.

The comprehensive wave analysis presented in our work took advantage of the availability of the unique two point measurements during SDL, which were required to reveal the obtained wave properties.

We are heading to the end of the successful ROSETTA mission in September 2016, where final RPCMAG observations will be made along the planned and controlled descent of the ROSETTA orbiter down to 67P/C-G.

The data used have been publictaed in the Planetary Science Archive (PSA)
provided by ESA and the Planetary Data System (PDS) operated by NASA. PSA is
accessible via:

Used RPCMAG data can be found in the so called calibrated Prelanding-dataset:

RO-SS-RPCMAG-3-PRL-CALIBRATED-V6.0: Glassmeier, K.-H., Richter, I., Koenders, C., Goetz, C., Eichelberger, H., and Cupido, E.: ROSETTA RPCMAG PRELANDING PHASE (PRL) CALIBRATED DATA RECORD V6.0, RO-SS-RPCMAG-3-PRL-CALIBRATED-V6.0, ESA Planetary Science Archive and NASA Planetary Data System, 2016.

Used ROMAP data have been submitted to PSA but are still under review. They will be acessilbe in three different datasets:

RL-C-ROMAP-3-SDL-MAG-V1.0: Auster, H. U., Apathy, I., Berghofer, G., Remizov, A., and Roll, R.: ROSETTA-LANDER 67P ROMAP 3 SDL MAG V1.0, ESA Planetary Science Archive and NASA Planetary Data System, 2015.

RL-C-ROMAP-3-RBD-MAG-V1.0: Auster, H. U., Apathy, I., Berghofer, G., Remizov, A., and Roll, R.: ROSETTA-LANDER 67P ROMAP 3 RBD MAG V1.0, ESA Planetary Science Archive and NASA Planetary Data System, 2015.

RL-C-ROMAP-3-FSS-MAG-V1.0: Auster, H. U., Apathy, I., Berghofer, G., Remizov, A., and Roll, R.: ROSETTA-LANDER 67P ROMAP 3 FSS MAG V1.0, ESA Planetary Science Archive and NASA Planetary Data System, 2015.

The RPCMAG and ROMAP data will be made available through the PSA archive of ESA and the PDS archive of NASA. Rosetta is a European Space Agency (ESA) mission with contributions from its member states and the National Aeronautics and Space Administration (NASA). The work on RPCMAG and ROMAP was financially supported by the German Ministerium für Wirtschaft und Energie and the Deutsches Zentrum für Luft- und Raumfahrt under contract 50QP 1401. We thank the European taxpayers for the kind support of our space research. All computations concerning the s/c position and orientation have been calculated with use of the SPICE software developed by NASA's NAIF team. We thank K. C. Hansen for providing two values for the gas production rate which were extracted from a plot of a talk given at the ROSETTA SWT meeting at ESAC in December 2015. Portions of this research were performed at the Jet Propulsion Laboratory, California Institute of Technology under contract with NASA. We are indebted to the whole Rosetta Mission Team, SGS, and RMOC for their outstanding efforts making this mission possible. We express our sincere gratitude to the referees of this paper who contributed significantly to the finishing touch of this publication. The topical editor, E. Roussos, thanks W.-H. Ip and one anonymous referee for help in evaluating this paper.