Research in Astron. Astrophys. 201x Vol. X No. XX, 000–000http://www.raa-journal.org http://www.iop.org/journals/raa

Research inAstronomy andAstrophysics

Electronic content near lunar surface using dual-frequency VLBItracking data in single lunar orbiter mission ∗

Zhen Wang1,2, Na Wang1 and Jin-Song Ping2

1 Key Laboratory of Radio Astronomy, Xinjiang Astronomical Observatory,Chinese Academy ofSciences, Urumqi 830011, China; wangzh@xao.ac.cn

2 Key Laboratory of Lunar and Deep Space Exploration, National Astronomical Observatories,Chinese Academy of Sciences, Beijing 100012, China; jsping@bao.ac.cn

Received 2014 June 30; accepted 2014 September 6

Abstract In Vstar VLBI tracking observation of the Japanese lunar mission SELENE,there were opportunities of lunar grazing occultation when Vstar was very close to thelimb of the Moon. This kind of chance made it possible to probe the thin plasma layerabove the moon surface as a meaningful by-products of VLBI, by using the radio oc-cultation method with coherent radio waves of the S/X band. The dual-frequency mea-surements were carried out at Earth-based VLBI stations. In the line-of-sight directionbetween the satellite and the ground VLBI tracking station, the effects of the terrestrialionosphere, the interplanetary plasma and the thin lunar ionosphere mixed together in thecombined dual-frequency Doppler and phase observables. To separate the variation of theionospheric total electron content (TEC) near the surface of the moon from the mixedsignal, the influences of the terrestrial ionosphere and interplanetary plasma have beenremoved by using the short time trend extrapolation method. The lunar TEC is estimatedfrom the dual-frequency observation for Vstar from UT 22:18 to UT 22:20 on June 28,2008 at several tracking stations. The TEC results obtained at VLBI sites are identicalto each others, however, they are not as remarkable as the result obtained at Usuda deepspace tracking station.

Key words: planets and satellites: atmospheres — occultations — detection

1 INTRODUCTION

Predecessors in lunar ionosphere field have already done a large amount of interesting research works,among which a result suggested the existence of the lunar ionosphere. In the 1960s, refraction of radiowaves transmitted from radio stars was observed during lunar occultation event (Andrew et al. 1964).Under certain condition of the solar wind plasma and cosmic ray, number density of photoelectronat the height of few hundred meters on the lunar dayside hemisphere was estimated at the order of104 cm−3 (Walbridge 1973). Using the single satellite radio occultation technique and assuming thecase of ionosphere spherically symmetric distribution around the Moon, Soviet lunar missions of Luna19 and Luna 22 detected the peak of ionization density as large as 500 − 1000 cm−3 at the height of5–10 km above the lunar surface on the sunlit side of the Moon. And the electron number densitiesgradually decreased at a height of 10 km or higher and at 5 km or lower (Vasil’Ev et al. 1974; Vyshlov

∗ Supported by the national key basic research and development plan (Grant No. 2015CB857101).

2 Zhen Wang et al.

1976; Vyshlov et al. 1976; Vyshlov & Savich 1979). Savich (1976) argued that the remnant magneticfields might have shielded the solar wind to allow the accumulation of plasma around the Moon.

Considering the lunar surface is covered by a thick layer of dust, the charged dust particles on thelunar surface can be greatly accelerated by the electric field near the lunar surface and escaped fromthe surface of the Moon, then formed the wispy floated clouds (Stubbs et al. 2011). Various resultshave been obtained and suggested by different researchers till now. Imamura et al. (2012) suggestedthat electron density of the order of 100cm−3 were detected below 30 km altitude with solar zenithangles of less than 60◦ . The extremely high electron density of 500 − 1000 cm−3 on the surface of theMoon is possibly attributed to human errors in early data processing and analysis (Daily et al. 1977).Without considering the photoelectron sheath layer and solar wind, there cannot be an ionospheric layeraround the Moon (Bauer 1996). The density of the ionosphere distributed in the range from 0 to 100km height was believed to be an order of 1 cm−3 by Stern (1999). There are mainly three kinds ofgeneration mechanisms of the thin lunar ionosphere: 1) the solar ultraviolet radiation and cosmic rays;2) the remnant magnetic field of the Moon; 3) charged dust particles from lunar surface regolith. Upuntill now, the lunar ionosphere, which has the sporadic, tenuous and asymmetric distribution in thevicinity of the lunar surface, has always been a particularly intriguing and controversial subject.

Radio Science experiment in the Japanese lunar mission, Selenological and Engineering Explorer(SELENE or Kaguya), obtained abundant information on lunar ionosphere, and provided a new oppor-tunity to detect the morphology and the evolution of the lunar ionosphere, including the radial densitydistribution, and the effects of diffraction and refraction. At the same time, regional VLBI method wasalso applied to precisely measure the orbit information (Namiki et al. 2009). The raw tracking date ofthe VLBI observable during the SELENE satellite occultation period can be used to retrieve the lunarionospheric parameters. In the following section, the methods and results are presented and discussed.

2 EXPERIMENT SETTING UP

SELENE lunar mission was successfully launched on September 14, 2007, from the Tanegashima SpaceCenter(Hanada et al. 2010). It consists of three spacecrafts: the three-axis stabilized main orbiter, the re-lay subsatellite (Rstar), and the VLBI subsatellite (Vstar), with orbital periods of 120, 240 and 153 min-utes, respectively. These three spacecrafts all flied near the polar orbits. The main orbiter had an averagealtitude of 100 km around the moon. The altitudes of Rstar and Vstar varied from 120 km to 2395 km andfrom 129 km to 792 km, respectively. In SELENE mission, the VLBI observation (Iwata et al. 2001)used the VLBI Exploration of Radio Astronomy (VERA) network, which consisted of four Japanesetelescopes located at Mizusawa (MZ), Iriki (IR), Ishigaki (IS) and Ogasawara (OG)(Kobayashi et al.2003), and used four additional international telescopes located in Urumqi (UR, China), Shanghai(SH,China), Wettzell (WZ, Germany) and Hobart (HO, Australia)(Schluter et al. 2002). The baselines rangesfrom 796 km (SH-IS) to 12247 km (HO-WZ) (Liu et al. 2010). VLBI observation for Rstar was in orbitfrom October 9, 2007 to February 12, 2009, and Vstar from October 12, 2007 to June 29, 2009.

The two sub-satellites form an octagonal prism of 1m × 1m × 0.65m covered by solar cell panelsat the sides, and weigh approximately 45 kg. They were both spin-stabilized. The middle-gain S- andX-band dipole cluster antennas onboard the two satellites were used to receiver/transmit the carrierwaves from/to the earth. The dipole clusters were installed on the top panel of the satellite aligned withthe spin axis, and the X-band dipole cluster was connected to the top of S-band dipole clusters (Iwataet al. 2001). The geometric center of the middle-gain antennas was on the axis of the satellite. For eachside of the satellite pillar, pieces of collar and skirt were used to balance the solar pressure effects.Nevertheless, nutation of the spin axis inevitably occurred with long-term periods. Such nutation couldreduce the lifetime of the satellite, and could add modulation to the radio signal according to the spin,when antenna phase center did not co-incident with geometric center and the geometric axis did not co-incident with spin axis. To reduce the nutation, a circular tube with half-filling mercury was added insidethe satellite as a nutation dumper. The spin frequency was found of ∼ 0.18 Hz for two sub-satellites.The phase of the transmitted radio signal changed by a few tens degrees with spin frequency and itsharmonics. The effect of phase changes can be reduced by taking an average from long-term sampling

Lunar Ionosphere 3

Fig. 1 S- and X-band transmitter for Vstar. Two S-band and one X-band carrier signals areall synchronized from a same Crystal oscillator.

data. The narrow band phase tracking of the signal from the satellite enable us to perfectly remove suchphase changes. The block diagram of the S- and X-band transmitter onboard Vstar is shown in Figure 1.Two frequency signals at S-band and one at X-band were generated from a same crystal oscillator onVstar, so that they were all synchronized and coherent.

These signals of sub-satellite were received at the ground VLBI station shown in Figure 2. TheVLBI system here is composed of the following parts: the front end of the telescope consists of alow-noise amplifier (LNA), a down-converter and a first local oscillator that convert the received radiowave of S/X-bands into an intermediate frequency (IF) signal of frequency of several hundred MHz,the back end of the telescope consists of a down-converter and a second local oscillator that convert theIF signal into a video-band signal with a frequency of a few tens of KHz, the digitized narrow bandrecorder system of ”IP-VLBI” / SRTP-station was used in the experiment. Four video-band signalswere simultaneously sampled at a rate of 200 kHz with 6 bit quantization by an analog-to-digital (A/D)converter in the SRTP-station (Ping et al. 2000; Hanada et al. 2010). The output data from the A/Dconverter were recorded on hard disks with integer values ranging from –32 to 31. All the referencefrequency and time signals, such as those for the down-converter and A/D sampler, were provided by anultra stable Hydrogen maser clock at each ground VLBI station.

In SELENE radio science experiments, scheduled radio occultation observations were made byUsuda deep space tracking station (Imamura et al. 2010). The final results were released in SELENEdatabase archive, as seen review from http://l2db.selene.darts.isas.jaxa.jp/index.html.en. VLBI multi-bits sampling raw data recorded at single site can be used to retrieve the lunar ionospheric informationas a by-products during the occultation periods.

3 PRINCIPLE OF TEC ESTIMATION BY DUAL FREQUENCY METHOD

Ground-based radio occultation observation, which is a common technique to explore the planetaryatmosphere and ionosphere, has advantages of high precision, high resolution, free from ground weather,and economical. When the ground-based antenna tracks an orbiter near the target planet of grazingoccultation, the radio wave from the orbiter pass through the atmosphere of ionosphere and troposphereif exist, and is affected by refraction and propagation delay. Researchers can study the characteristics ofthe atmosphere by using the radio wave signal data obtained at the tracking station. Lunar mission canuse this method also.

Figure 3 shows the concept of single orbiter radio occultation mode. In the case of Vstar, it wassometimes occulted by the ionosphere above the lunar surface and was observed from a ground VLBI

4 Zhen Wang et al.

Fig. 2 Receiver system of the ground station.

tracking station. In the observed phase shift of radio signals from Vstar, contributions from the terrestrialionosphere, the interplanetary plasma, and the lunar ionosphere along the radio signal path between thesatellite and the ground antenna were involved. The refraction of the terrestrial neutral atmosphere,including the troposphere and stratosphere, was one of the large error sources here. Together with theinstrumental error, these large errors can be removed using geometry-free dual-frequency combinationanalysis method. The influence of the terrestrial troposphere, the receiver noise and the undeterminedconstant errors were almost identical in the Vstar dual frequencies radio signals, since two signals almostshared same the propagation path. The components of the phase shift introduced by the interplanetaryplasma and by the terrestrial ionosphere were removed by using the combined phases of the signals fromVstar just before and/or after the occultation event. The phase shift caused by the terrestrial ionospherecould be a hundred times or more larger than that by the lunar ionosphere, but with small variationduring radio occultation period. It was necessary to observe for 50 ∼ 100 seconds before or afterthe occultation to estimate and remove the influence of the interplanetary plasma and the terrestrialionosphere. Usually the phase shifts introduced by the terrestrial ionosphere during the occultation wereusually not exactly the same as those 50 ∼ 100 seconds before the occultation. Thus, the componentof the terrestrial ionosphere could not be perfectly removed from the total phase shift using a samesimple value. In order to eliminate the component of the terrestrial ionosphere, considering a linearvariation during ∼ 110 seconds of occultation, efficient extrapolation algorithm was used based on thetime sequence of phase shifts. Then, the total electron content profiles in the ionosphere of the Moonwere obtained. This method was also used by Imamura et al. (2010).

The Vstar in SELENE mission transmitted three carrier signals of S-band and one of X-band, whichwere named S8/S9/X2. They were time synchronized and phase coherent with different frequencies. Thenominal carrier frequencies transmitted before launch were set by Equation (1) (Iwata et al. 2001),

fi = Ci · (f0 + ∆f0); f0 = 69.31255297(MHz) (1)

where, ∆f0 was the drift of the crystal oscillator, and Ci were the scale factors, which were 32, 33and 122 for the S8, S9 and X2 band, respectively. The TEC of the ionosphere can be estimated fromthe phase information of the radio waves recorded by a single ground station. As a kind of dispersionmedia, the ionospheric delay along the signal pass is inversely proportional to the square of the radiowave frequency. Linear combinations of the phases in two coherent frequencies allow us to extract theionospheric contributions.

The phase information of the received signal is denoted by Equation (2),

Φi = 2πfiτtotal + 2π · 40.3c

· TEC

fi+ Φspin

i + Φconst.i (2)

Lunar Ionosphere 5

Fig. 3 The concept of occultation.

where, i represents the channel of the recorded coherent signal (S8, S9 and X2); fi is the correspondingfrequency; τtotal includes common delays in the S/X band, such as the geometric delay, the troposphericdelay, clock offset, instrumental delay and so on; c is the light velocity; Φspin

i is the phase caused by thesatellite spin; and Φconst.

i is the mutual phase difference, which is a constant or varies slowly in a fewtens of minutes.

In SELENE mission, Rstar and Vstar were spin stabilized satellites, and for each of them the direc-tion of the spin axis was almost perpendicular to the lunar orbital plane. However, the spin axis slightlyswayed due to satellite nutation, and it could modulate the radio signal with the frequency of the spin andthe harmonic frequencies. Additionally, the main lobe of the S-band dipole cluster was in the directionperpendicular to the axis, and the effects of the interference from the top panel and the collars of satel-lite were detected. These effects, however, were not significant for the X-band dipole cluster antennabecause it was higher from the top panel. Following the satellite motion, periodic signals due to the spinand the nutation with higher frequency harmonics might appear in the receiving phase and Doppler. Theobserved time series of signal phase show the modulations with a period of ∼ 5.35 seconds due to thespin of Vstar.

Based on the relation between the TEC and the phase differences of S8 and X2, the TEC is describedby Equation (3),

∆Φ = ΦS8 −32122

· ΦX2 = 2π · 40.3c

· TEC

fi· ( 1

32− 32

1222 ) + ∆Φspin + ∆Φconst. (3)

where, ∆Φ is the corresponding phase differences between ΦS8 and ΦX2 . The term of ΦS8 − 32122 ·ΦX2

contains the phase difference between the initial phase and the phase caused by instrumental delays

6 Zhen Wang et al.

Fig. 4 The phase extraction process flows .

onboard the satellite and of ground instruments. The TEC can’t be derived from Equation (3), directly.The change of TEC from t = 0 to t = t can be derived by Equation (4),

∆TEC =32 · f0

1222−322

1222

· 12π

· c

40.3· π

180· [∆Φ(t) − ∆Φ(0)]

≈ 0.00492 · [∆Φ(t) − ∆Φ(0)] (TECU)(4)

Lunar Ionosphere 7

Fig. 5 (a) The X2-band carrier signal; (b) Before cyclic correction, the 4096 phases averageinto one phase, 16 data in one interval unit of FFT ; (c) After cyclic correction, 16 datain one FFT unit; (d) Before cyclic correction in between two neighbored integrated timeintervals, the phases in 10 FFT units;(e) After cyclic correction, the phases in 10 FFT units;(f) After fitting a 2-order polynomial function, the standard deviation of the residual phasesof X2-band is 20.0016 degree for 0.02048 second integration. The ”cyclic correction” is thecorrection of integer ambiguity or of the cycle slips of the combined carrier phase. There aretwo kinds of phase cycle slips, 1) the possible phase slips between two neighbored integratedtime intervals; 2) the possible phase slips in a given integrated time.

4 RESULT OF OBSERVATION

This section describes the results from tracking data at two VLBI stations, Iriki and Ishigaki. The antennaeffective aperture of both stations is 20 m. The two stations are located at longitude and latitude E130◦6′,N31◦4′, E124◦0′, N24◦4′, respectively. One ingress ionospheric occultation event, which continuedfrom UT 22:18 to UT 22:20 on June 28, 2008 for 108 seconds, was found and retrieved from VLBIobservation database. Iriki and Ishigaki stations received the radio waves which passed 60-30 km and30-0 km above the lunar surface, for the periods from 22:18:00.021 to 22:18:55.006 (about 55 sec) andfrom 22:18:55.006 to 22:19:48.745 (53 sec), respectively. These data were processed and analyzed stepby step to extract the TEC of the lunar ionosphere along the signal paths. During the occultation period,

8 Zhen Wang et al.

Fig. 6 (a) The time series of differential phase, taken during an ingress occultation on June 28,2008, the phase information corresponds to the satellite hided into behind the moon as seenfrom the tracking station of Iriki; (b) The spectrum of removing satellite spin; (c) The phasevariation for S8/X2 after removal of spin; (d) The phase variation for S8/X2 after addition ofthe compensating trend.

the occultation tangential point projected on the surface of the Moon was at East longitude of ∼ E62.5◦, North latitude of ∼ N73.4◦, with solar zenith angle of ∼ 104◦ .

Phase shifts due to Doppler effect are extracted from radio waves in one-way link between Vstarand a VLBI station. The data processing flow diagram is given in Figure 4. The signals interceptedby the radio telescope in the VLBI station were recorded and stored in a hard disk as binary data. Weconverted it to decimal data for processing. The random noise is eliminated from the data at first. In the1st Fast Fourier Transform (1st FFT), we find the maximum power by the mass center method using65,536 sampling data as one interval unit of FFT. Then the reference frequency signal is constructedin each FFT unit. The frequency corresponding to the peak spectra is used for estimation of the phaserotation in later process. The band-pass filter is used in frequency domain to extract the signal in the1st inverse FFT. The target signal is compared with reference signal at frequency domain and rotated intime domain, then low-pass filtered at frequency domain. Then the 2nd FFT and the Low-pass filter areapplied to the target signal to get the low frequency signal in frequency domain. After the 2nd inverseFFT, the 4,096 phase data of the real part and the imaginary part are obtained separately for each interval.Every 4,096 data are accumulated and 16 data sets of real and imaginary parts are obtained in one FFTunit. After correction of phase slip in a FFT unit, the target signal phase time series is obtained. Theresults from the above processes for X2-band signal are illustrated in Figure 5 (a)-(f).

The total phase differences calculated from S8/X2-band, is shown in Figure 6 (a) using black dots,with the trend component and the residual phase using red circles and blue dots, respectively. The spectraof the phase difference and the spectra after removal of the effect due to the spin using a low pass filterare shown in the upper and the lower panels of Figure 6 (b), respectively. Then the phase variationsafter removal of the effect of the spin is obtained and shown in Figure 6 (c) using black dots, where thetrend is not compensated. Finally we get the phase variation including the compensated trend, and thatprocessed by Gaussian smoothing as shown in Figure 6 (d) using black line and red line, respectively.

Lunar Ionosphere 9

Fig. 7 The time series of column density variations.

Fig. 8 The electron column density profiles in the ionosphere of the moon.

In the conventional single-satellite occultation method, the additional influences caused by the ter-restrial ionosphere and the interplanetary plasma along the signal path could not be eliminated thor-oughly. We follow the idea in Imamura et al. (2010) and Imamura et al. (2012) that the total TECcontains the terrestrial ionosphere and the interplanetary plasma in the range from 60 to 30 km abovethe lunar surface, and that the terrestrial ionosphere and the interplanetary plasma along the signal pathare constant or linear varying during the time of occultation of about 110 seconds. These componentscan be removed from the TEC by means of linear fitting of the data obtained before and/or after theoccultation, which has not the effect of the lunar ionosphere. The TEC profile during 110 seconds oftotal occultation interval for 0 to 60 km above the lunar surface is shown in Figure 7 as a cyan line.

10 Zhen Wang et al.

According to the statistical results of SELENE mission, the lunar ionosphere higher than 30 km abovelunar surface is too thin to be considered. We assume that above 30 km, the interplanetary plasma playskey role of lunar ionosphere, and truncate the lunar ionosphere at 30 km. This is a fixed point for fittingthe interplanetary plasma and terrestrial ionospheric effects. The fixed point which is about 30 km abovethe surface of the moon at 55 seconds of the horizontal axis is indicated by a red dot. The TEC estimatedvariation from 0 to 60 km is shown in Figure 7 as a magenta line for 110 seconds. Linear fitting of theTEC for the range higher than 30 km, which corresponds to the time from 0 to 55 seconds, is shownin Figure 7 using a blue line. Green line is the simple extended line of blue line for the interplanetaryplasma and terrestrial ionospheric TEC below 30 km. The green line is slightly different from the trendof the TEC for lower than 30 km as shown in Figure 7 from 55 to 110 seconds. At last, the TEC in thelunar ionosphere is obtained from the data for about 53 seconds by subtracted green line from cyan line,as shown in Figure 7 using a black line. The trend by subtracted green line from magenta line is alsoshown in Figure 7 using a red line. The S8 and X2-band residual phases for 0.02 seconds integration af-ter a polynomial fitting of the second degree is 13.3 and 20.0 degrees, respectively, which corresponds toabout 0.19 and 0.28 degrees in RMS for 100 seconds integration, respectively. The error in the differencephase of S8/X2-band for 100 seconds integration in RMS is obtained according to Equation (5),√

Integration timeOccultation time interval ×

√RMS1

2 + RMS22

=√

0.02100 ×

√13.32 + (20 × 32

122 )2 ≈ 0.2◦ (5)

where, RMS1 and RMS2 are corresponded to the Root Mean Square for Integration time. The reso-lution of the total phase is 0.2 degrees, and the theoretical resolution of TEC becomes 0.001 TECUcorresponding to this phase resolution. This means that the VLBI observation has a sensitivity betterthan ∼ 1014/m2 for the TEC in the range from 0 to 30 km above the lunar surface.

In Figure 8, the vertical profile of the TEC along the signal path is converted from the time seriesdata. Vertical axis here is the height of the tangential point of occultation path near the Moon surface.The TEC variation observed at Iriki VLBI station is shown by the black line, its trend is shown by the redline. For comparison, the TEC observed at Ishigaki VLBI station, which was estimated using the samemethod above, is also shown by the blue line with the trend of the green line. As seen from Figure 8, thedifference between the results of lunar ionosphere from Iriki and Ishigaki are less than 20% concerningthe TEC trend. However, these results are about 30% or ∼ 0.01TECU weaker than the result observedat Usuda station, released in SELENE database archive and than the results given by Ando et al. (2012).

5 DISCUSSION AND CONCLUSION

Some cases of lunar occultation data were found in a large amount of VLBI tracking data of SELENEmission. We applied the Vstar occultation data to retrieve the lunar ionosphere as a useful by-product.The differential carrier phases of the coherent S/X band signals have been used to calculate the lunarionospheric electron contents. In data analysis, we removed the contribution from the terrestrial iono-sphere, and derived the effect of lunar ionosphere from VLBI data. Observations at different ground sitesof ∼ 1000km apart gave identical results. The independent observations and data processing methodsenhanced the reliability of the results.

Usuda tracking station, obtained a TEC of ∼ 0.03TECU at bottom layer for the same event, theTEC results have been released in SELENE data archive. This result is ∼ 30% higher than multi-sites re-sults obtained in this paper. This may indicate that the Moon has a weaker thin ionosphere than estimatedbefore. There were only a few cases of occultation in SELENE VLBI observations. We are trying to usemore data for this kind of study to compare the results of different sites. This kind of difference shouldbe studied in detail in future missions. The method developed here can also be implemented in the studyof the planetary ionosphere. The relatively weaker lunar surface ionosphere is still an open question. Itwill need other independent technique, like active and/or passive radar observation on the lunar surfacewith kilometer wavelength in the future exploration missions, to explore the lunar ionospheric density.

Lunar Ionosphere 11

Acknowledgements The authors thank to the SELENE Project for conducting these VLBI experimentsand producing the data for the community. The data used in this paper is under a cooperation framebetween NAOJ/NINS and XAO/CAS. The authors are grateful for discussions with Prof. NobuyukiKawano on data analysis, and thank Prof. Qinghui Liu for fruitful assistance on this work, and thank todiscuss with Prof. K. Matsumoto for the attitude of the Vstar in orbit.

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