The Comparison of Total Electron Content Between Radio and Thompson Scattering

Abstract

The total electron content (TEC) of the solar corona in June 2002 is calculated by three observational techniques and the results are compared. The first technique is solar rotational tomography (SRT) applied to a 14-day time series of LASCO-C2 polarized brightness images, and the other two techniques use the Cassini spacecraft radio beacon for Doppler tracking (phase delay) and ranging (group delay). While the Doppler-tracking technique has an arbitrary zero-point, it is otherwise found that the three methods produce consistent estimates of the TEC to within established uncertainties, providing an independent check on the calibrations. The verification of the accuracy of the Doppler-tracking technique enables a significant improvement to the use of spacecraft data sets in studying the heliosphere: the density component to Faraday rotation can be separated from the magnetic-field component as variable structures cross, such as coronal mass ejections and magnetohydrodynamic waves. Furthermore, we show that the unique frequency-time variable characteristics of the hydrodynamic components of waves can be studied. Based on this work, future Faraday rotation studies of variable solar phenomena will isolate the electron density changes from the magnetic-field contribution. This capability will enable advanced research into variable heliospheric magnetic fields.

Appendix

The full ranging and Doppler-tracking data comparison is provided here. When ranging data were unavailable, the Doppler-tracking data are presented as well. We performed an initial wavelet analysis on the Doppler-tracking data; however, more resources need to be provided to reprocess the raw data to increasing the resolution for a more complete analysis.

The observation made on 21 June is particularly interesting for a future article, after reprocessing. At an offset around 1.8 $R_{\mathrm {s}}$ at the beginning of the time frame (below the LASCO C2 FOV), these data illustrate fluctuations or structures stronger than any of the other data sets. Overall, they vary more strongly by a factor of 1.5 than the streamer observation on 20 June and by an order of magnitude larger than the following observation on 22 June. The large discontinuity around 1600 UT appears to be valid at the current time resolution (100 s), but reprocessing is necessary to eliminate the possibility that it is due to an engineering reconfiguration error in the experiment. Jensen and Russell (2008) demonstrated that reasonable estimates for the parallel magnetic-field require good estimates for the density at the point of closest approach. While Jensen and Russell (2008) extrapolated Solar–Terrestrial Environment Laboratory (STELab) interplanetary scintillation (IPS) density data inward, white-light data are equally appropriate (Xiong et al. 2013a).

The top plots of Figures 5 – 16 show the Doppler TEC (red) in comparison to the ranging TEC (blue), shifted as discussed in Section 2.2. In Figures 5a and 16a of the set the X-band offset frequencies were not used in the TEC calculation because the incorrect ephemerides were used for downconverting the X-band on 14 June, which introduced an artificial drift that required specialized processing. Furthermore, X-band data were not collected on 26 June because the radio science receiver was unavailable. These days were processed by reverting to Equation (11) and assuming that the spacecraft ephemerides were accurate enough for removing the first term from the residual frequency offsets. The ranging data for these time periods support this assumption. On 18 June through 21 June, ranging data were not collected; as a result, the $\mathrm{TEC}_{\mathrm{ini}}$ was left at zero. None of the time periods plotted were continuously observed. The adjustment in TEC initial under this condition can be seen best on 17 June. While conducting script tests, there were multiple gaps in the observations, and when they were adjusted to the median range value for the time period, the gaps between 19:00 and 21:00 UT are therefore particularly obvious. When no ranging data were available for the time period of interest, the last value for TEC was used as the TEC initial following the gap.

Figure 5

14 June, $21~R_{\mathrm{s}}$, drop in the lowest frequency is indicative of the negative slope of the TEC; ionospheric TEC dominates ranging, as shown by the quadratic polynomial structure. Zero is in the red region, and the time step is 100 s.

Figure 6

16 June, $14.5~R_{\mathrm{s}}$, the higher frequencies show a semiperiodic fluctuation beginning at 0.003 Hz that increases with time to 0.0047 around 20,000 s later (note that zero has different colors).

Figure 7

17 June, $11.3~R_{\mathrm{s}}$, the higher frequencies show a semiperiodic fluctuation at a fixed frequency around 0.0047 Hz throughout the time (3000 and 10000 s, respectively). A secondary fluctuation may also be present around 0.0035 Hz (note that zero has different colors).

Figure 8

18 June, $8.1~R_{\mathrm{s}}$, the higher frequency semiperiodic fluctuations continue to be present around 0.0047 Hz. Another appears to be present around 0.004 Hz. The increasing complexity in the higher frequency fluctuations is resolved better; they appear to have a frequency structure that varies with time at the limit of detectability. Note that zero is orange in the left wavelet figure and blue in the right.

Figure 9

19 June, $5.6~R_{\mathrm{s}}$, the regularity of the 0.004 Hz region waves appears to be adjusted while the overall spectrum is similar to that on 18 June.

Figure 10

20 June, $2.8~R_{\mathrm{s}}$, the high-frequency structure has extended into lower frequencies (0.004 Hz). Another wave appears to be present around 0.0035 Hz.

Figure 11

21 June, $1.8~R_{\mathrm{s}}$, the higher frequency (0.0047 Hz) complexity and strength appears to be reduced (insofar as the range of frequencies can be resolved with a 100 s sample rate). The 0.003 Hz waves dominate the spectra.

Figure 12

22 June, $4.4~R_{\mathrm{s}}$, the higher frequency strength is similar to 20 June, but its structure is simple. A lower frequency fluctuation around 0.0035 Hz appears to be present and increases in frequency with time (8000 s) to 0.0045 Hz.

Figure 13

23 June, $7.4~R_{\mathrm{s}}$, the higher frequency wave has more structure and extends to lower frequencies; two lower frequency waves around 0.004 and 0.003 Hz appear to be present simultaneously.

Figure 14

24 June, $9.9~R_{\mathrm{s}}$, the higher frequency wave continues to be structured; a lower frequency wave at 0.0033 Hz increases with time (9000 s) to 0.0045 Hz.

Figure 15

25 June, $13.1~R_{\mathrm{s}}$, the higher frequency wave is less structured; a lower frequency wave persists at around 0.0035 Hz.

Figure 16

26 June, $15.4~R_{\mathrm{s}}$, the higher frequency wave is similar to 25 June; the lower frequency wave appears to have a frequency of around 0.004 Hz.

The bottom plots of Figures 5 – 16 show the Mexican top-hat wavelet analysis of the form: $A (1 - x^{2}/a^{2}) \exp(-x^{2}/2 a^{2})$, where $A = 2/(3a)^{1/2}\pi^{1/4}$, and a is the width. The highest frequencies (dominated by the solar corona) show a distinct bursty wave behavior. Data from 16 June ($14.5~R_{\mathrm{s}}$, ingress), for example, show a series of bursts that increase in frequency with time. By 18 June ($8.1~R_{\mathrm{s}}$, ingress), the character of the higher frequency bursts increases in complexity, which persists until the day of conjunction on 21 June ($1.7~R_{\mathrm{s}}$, closest approach) and then resumes again on 22 June ($3.7~R_{\mathrm{s}}$, egress) and stops on 24 June ($9.9~R_{\mathrm{s}}$, egress). A better wave analysis can be performed with higher resolution TEC data, but this requires resources to archive and reprocess the raw data samples. Frequencies with the highest power ranged between 0.0047 and 0.003 Hz (3.5 to 5.5 min periods, wavelength depends on the local Alfven speed); we note that the greatest power in the solar helioseismology spherical harmonics resonances on the photosphere is around 5 min. Combined with the Faraday rotation data collected during the time period, the waves can be further analyzed with respect to the magnetic field.