projects:jupiter:first [Fundamental Physics in Radio Astronomy]

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====== First successful interferometry ======

==== Data set ====

The data set L202279 was observed on 2014-01-24 in the time range 20:00-21:25 UTC using the stations CS002-007, DE601,602,603,604,605,FR606,SE607,UK608.

First diagnostic plots were made from the online correlations provided by the ILT. These have a low resolution of 1 sec and 1 subband (200 kHz), which is not sufficient for a proper analysis, but it can be used as a first-look and to find good time ranges for high-resolution correlations.

We have such plots for {{l202279_singstat.pdf|single stations}} and {{l202279_baselines.pdf|selected baselines}}. In these we see that there are indeed regions in time and frequency with emission from both hemispheres. 

For the first real calibration tests, we concentrate on one second of data near 20:16:10.5 UTC, which is at 971 sec offset from the beginning.

Here are 1000 sec around that time (only one baseline as overview, reduced frequency range):

{{:projects:jupiter:first_overview_1000sec.png?direct&1000}}

(Most plots here are displayed with reduced resolution. Click on them, maybe twice, for full size.)

The horizontal blue structures near 12 MHz are RFI, but the red ones just below 20 MHz are real.
The vertical green dashed lines indicate times with jumps in the integer-sample delay, white areas are missing data.


Here are 100 sec around that time:

{{:projects:jupiter:first_overview_100sec.png?direct&1000}}



Here are 10 sec around that time:

{{:projects:jupiter:first_overview_10sec.png?direct&1000}}


==== Calibration and integrated analysis ====

For the analysis we only use 1 sec with further reduced frequency range. Here we have a good overlap of signals from both hemispheres:

{{:projects:jupiter:first_overview_1sec.png?direct&1000}}

We correlate only the stations CS002,DE601,602,604,605,FR606,SE607,UK608, but not the other core stations (only short baselines) or DE603 (missing data).

FIXME: The calibration process will be described in detail at a later time. For the moment I just want to present some results. We use all these stations for an eigenvalue decomposition, but later exclude CS002,DE604,UK608 from the interferometry, because their parameters are inconsistent with the rest. This is most probably due to bad station calibration, which causes polarisation leakage of the order 1.

The eigenvalue decomposition is also used as basis for identifying good signals from either hemisphere:

{{:projects:jupiter:first_eigendecomp.png?direct&1000}}

Assuming that the northern and southern emission consist of only one unresolved component each, which may have a frequency-dependent position (as expected for electrons moving along a single field line for each hemisphere), we can first fit the mean S-N offset together with a linear drift with frequency. The following plot shows fits of such parameters for the 1-sec time and frequency range just shown:

{{:projects:jupiter:first_global_posfit.png?direct&1000}}

The left panel is for the group delay, which is given by the position plus frequency-derivative multiplied with mean frequency, which is not constrained very accurately. The middle panel is the position from the phases. This is much more precise, but it took some effort to solve for the lobe ambiguities, or in other words understand which peak in the dirty map is the real peak. The right panel is the difference of the two, corresponding to the frequency-derivative multiplied with the mean frequency.
The straight lines are results from a few individual baselines, the dark spot is a fit to all good baselines. The dotted circles are expectations as explained below. The agreement is far from perfect, but astonishingly good for this first attempt.



==== Expectation ====

This is based on the magnetic field model of Connerney et al. (2018). As a very first guess I follow the field lines from the actual position of Io (retarded for light time to the Earth) towards both poles. Once it reaches the point at which the local cyclotron frequency equals the mean frequency of the signal, I determine the position and its frequency derivative. The following plot shows Jupiter coloured according to the magnetic field strength at the surface. The points above the surface have cyclotron frequency equal to observing frequency. Green is foreground, red behind the planet and yellow foreground with an angle between field and line of sight in the range 50 to 80 deg. Io and its field line are shown in black. Note that no correction for the lag along Io's orbit or for the wobble of the plasma torus with Jupiter's rotation was applied.

{{:projects:jupiter:first_magmod.png?direct&700}}


==== Analysis resolved in time and frequency ====

Because the fit of the relative positions and shifts looks so plausible, I continued to try and determine positions as function of time and frequency. As origin for the absolute coordinates I used the middle between the signal from both hemispheres. In the Jupiter's N-S direction this is probably not too far from the centre of the planet, but in the E-W direction it is a very bad approximation.
Nevertheless, just as illustration, for a limited time range:

{{:projects:jupiter:first_posfits_abs.png?direct&1000}}

The upper panels show X, the lower Y coordinates, left is southern hemisphere, right is northern hemisphere. These values are dominated by the general offset between both hemispheres. We can also subtract the mean offset to make the motion with time/frequency more visible (note the different colour scale):

{{:projects:jupiter:first_posfits_motion.png?direct&1000}}

This is now dominated by the linear drift with frequency. Finally we also subtract the linear drift as function of frequency to show deviations from this overall effect (note the again different colour scale):

{{:projects:jupiter:first_posfits_resid.png?direct&1000}}

There are still significant residuals, but this does not necessarily mean that the motion really has strong non-linear components. It could also be that the southern (LH) signal is not really produced along one field line, but is a steady continuum along a range of field lines. There is then no reason to expect a simple shift with frequency. Because I only measure //relative// positions, this would also affect the apparent motion of the S-burst signals from the northern hemisphere. And then there are of course residual calibration errors, which may be related to polarisation leakage in the signals.

Very intriguing is evidence for a position gradient //across// the S-burst linear features. This can not be explained so easily by calibration problems, but it is too early to take this gradient very seriously. Luckily such effects can also be measured without a calibration of absolute position, so that we can study this potentially very interesting features also for individual hemispheres, and then potentially with stronger signals.
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