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Absorption and reflection of radio waves in the Martian ionosphere
ARTICLE IN PRESS
Planetary and Space Science 55 (2007) 864–870 www.elsevier.com/locate/pss
Absorption and reflection of radio waves in the Martian ionosphere E. Nielsena,, D.D. Morganb, D.L. Kirchnerb, J. Plautc, G. Picardid a
Max Planck Institute for Solar System Research, 37191 Katlenburg-Lindau, Germany Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA c Jet Propulsion Laboratory, Pasadena, CA 91109, USA d Infocom Department, ‘‘La Sapienza’’ University of Rome, 00184 Rome, Italy
b
Received 13 July 2006; received in revised form 11 October 2006; accepted 11 October 2006 Available online 1 December 2006
Abstract Radio wave absorption in the Martian ionosphere has been predicted and tested against MARSIS radar observations. Models of the ionosphere densities and of absorption in a CO2 neutral atmosphere were used. The appearance of ground reflections in the MARSIS observations is shown to be consistent with predictions of reflection and absorption of radio waves in the ionosphere. It is concluded that the secondary density maximum, known to be typically present below the primary density peak, contributes considerably to the absorption and thus to the appearance of ground reflections. It is the first time predicted radio wave absorption in a CO2 planetary atmosphere has been tested against actual observations. r 2006 Elsevier Ltd. All rights reserved. Keywords: Mars; Ionosphere; Radio wave absorption; Top-side sounder
1. Introduction The low frequency radar Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on board the ESA mission Mars Express (MEX) is used primarily both to sound the ionosphere plasma and to sound the ground, surface and subsurface, for essentially water deposits in both liquid and frozen forms. The lowest altitude of the spacecraft is 300 km well above the altitude of the electron density maximum in the ionosphere. The altitude of the electron density maximum is typically 130 km. The ground sounding signal must therefore penetrate the ionosphere twice before detection. Thus, for a ground reflection to be detected the signal frequency must be larger than the maximum plasma frequency. If this condition is met, the ionosphere has two further effects on the signal: it will cause dispersion of the signal phases, and it will attenuate the signal amplitude. In this work we do not consider the signal dispersion. Instead, we will determine how the appearance of a ground reflected signal
Corresponding author. Tel.: +49 5556 979450.
E-mail address: [email protected] (E. Nielsen). 0032-0633/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2006.10.005
in the observations is controlled by reflection and absorption in the ionospheric plasma. Radio wave absorption in an atmosphere is controlled to a large extent by the collision frequency of thermal electrons with the neutral molecules. Since the major neutral atmospheric component on Mars is CO2 , which has a much larger scattering cross section for thermal electrons than does either oxygen or nitrogen, the absorption on Mars, for the same electron density and signal frequency, is much more severe than in Earth’s atmosphere.
2. Observations and analysis MARSIS can be operated either in a ground sounding mode or in the Active Ionosphere Sounder (AIS) mode. Here we use data obtained in the AIS mode. The radar operates between 0.1 and 5.4 MHz. A series of narrow near monochromatic signals are transmitted in sequence and for each frequency the time delays to echoes are measured. The echoes are either reflection from the ionosphere or from the ground. The observations are presented in a spectrogram displaying the intensity of the echo signal as a function of time delay (on the horizontal axis) and signal frequency
ARTICLE IN PRESS E. Nielsen et al. / Planetary and Space Science 55 (2007) 864–870
(on the vertical axis). An example of such a spectrogram is shown in Fig. 1. The virtual depth, which is half the delay time multiplied by the vacuum speed of light, is given on the top horizontal axis. The echo between 1.1 and 2.7 MHz is an ionospheric reflection. The later echoes at higher frequencies between 3.5 and 5.4 MHz are the signal reflected from the ground. It is typical for the ground reflection that when present it appears for all frequencies between a minimum frequency and the maximum frequency of the sounder. The distance to the target (the ground) is the same for all frequencies, and since all signals travel through the same ionosphere the delay times are only weakly increasing with decreasing frequency. This ground reflection is not always present in the spectrograms. The reason is that the radar signal may be either reflected before penetrating the ionosphere because the sounding frequency is less than the maximum plasma frequency, or be so severely attenuated that the signal drops below the receiver noise level. The primary electron density maximum in the Martian ionosphere is a Chapman layer controlled by solar radiation, which therefore varies in height and in intensity with solar zenith angle. It is to be expected that the minimum frequency for the ground reflection is to a large extent controlled by the solar zenith angle. We therefore display in Fig. 2 the appearance of ground reflections during one orbit by presenting the minimum frequency versus zenith angle. In this case the ground reflection appeared first for a zenith angle of 60 . For smaller zenith angles the denser ionosphere probably caused attenuation sufficient to reduce the received signal below noise level.
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Fig. 2. Data for orbit 2029. The minimum frequency for ground reflections is decreasing as the solar zenith angle increases, associated with a weakening of the solar radiation induced primary electron density layer.
Ground reflections occurred for all zenith angles larger than 60 up to 100 . These observations are reproduced in the following using model calculations. Nielsen et al. (2006) found that the main electron density peak is well approximated by a Chapman layer up to an altitude of 180–200 km, and exponentially decreasing with altitude above that height. The density profile (Eqs. (1)–(3)) is controlled by zenith angle and solar ionizing flux intensity (F ¼ F10:7 cm flux) (see for example summary in Nielsen, 2001 and references therein), N e ðhÞ ¼ N o 1 h hmax h hmax 1 Chðx; yÞ exp exp , 2 H H ð1Þ where N o is the subsolar maximum density, hmax the subsolar altitude of maximum density, H the neutral scale height in the Chapman layer, y the solar zenith angle, h the altitude, and x ¼ ðRMars þ hÞ=H, N o ¼ 200n100:36 log F =120 ð103 el=cm3 Þ, 1 ðkmÞ, hmax ¼ 120 þ 10 log Chðx; yÞ F H ¼ 10n exp 0:16 ln ðkmÞ. 100
Fig. 1. MARSIS Active Ionosphere Spectrogram displaying ionosphere (at low frequencies) and ground reflections (at high frequencies). The slant of the ground reflections towards higher delay time with decreasing frequency is caused by decreasing propagation speed as the frequency decreases. The ground reflection first appears at a minimum frequency of 3:2 MHz.
The plasma scale height above the Chapman layer is F H t ¼ 23n exp 0:55 ln ðkmÞ. 50
ð2Þ
(3)
Use of the Chapman function Chðy; xÞ takes into account that ionizing radiation extends past the terminator and allows analysis for zenith angles larger than 90 . In this analysis x ¼ 350 was used. In Fig. 3 there is an example of
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Fig. 3. Example of the primary density peak in the ionosphere model. At 5 MHz the signal passes through the layer and is attenuated by 11.8 dB in its way to and from the ground.
the model ionosphere for a zenith angle of 50 and a solar flux F10:7 ¼ 111 units. Neglecting the weak crustal magnetic fields the sounder signal propagating into the ionosphere is reflected where the signal frequency equals the plasma frequency qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f p ðkHzÞ ¼ 8:98 N e ðhÞ ðel=cm3 Þ. (4) The radar signal is attenuated by absorption in the ionosphere AðhÞ ¼ 4:61n104 N e ðhÞ
nðhÞ ðdB=kmÞ, o2 ðhÞ þ n2 ðhÞ
(5)
where o is the signal frequency (rad/s), and n ðs1 Þ the momentum-transfer electron-neutral collision frequency. The collision frequency is governed by the main molecular component in the Martian atmosphere, which is CO2 (Detrick et al., 1997). For the relatively cool Martian ionosphere the thermal mean energy is about 0.1 eV. Laboratory measurements in a CO2 gas of molecules show the collision frequency of such electrons to be close to 107 per molecule=s (Hake and Phelps, 1967). Multiplying the collision frequency per molecule by the CO2 concentration yields the altitude profile of the collision frequency, shown in Fig. 4. This profile is in very good agreement with Schunk and Nagy (2000). Note that these collision frequencies are nearly a factor of 100 larger than in Earth’s ionosphere. The reason is that the electron collision frequency with N2 molecules, the dominant molecule in Earth’s ionosphere, is much lower at
Fig. 4. Altitude profile of the electron momentum-transfer collision frequency in Mars’s CO2 atmosphere.
2 109 per molecule=s. This suggests that strong radio wave absorption is a striking aspect of the Martian ionosphere. The specific absorption (dB/km/electron) maximizes where the signal frequency equals the collision frequency; this occurs at altitudes of 80–90 km for the range of MARSIS AIS radar frequencies. Because the collision frequency increases with decreasing altitude the main contribution to the total absorption of a signal propagating through the ionosphere occurs below the peak density. The detailed density profile above the Chapman layer is of little importance in this respect. On the other hand additional electron densities below the density maximum could have an important contribution to the total absorption, even if these densities are relatively small. To illustrate the reflection and absorption properties of the ionosphere we calculate the absorption of radio waves of frequencies between 3 and 4 MHz (in steps of 0.2 MHz) in a Chapman layer for a solar flux of F10:7 ¼ 70. The result is shown in Fig. 5. The absorption is only calculated for signals that penetrate the ionosphere. At 3 MHz the signal is only penetrating the layer for zenith angles 464 and at 3.2 MHz for angles 453 , etc. Thus, a ground reflection can only occur at these frequencies at zenith angles larger than these limiting angles. For 3.8 and 4.0 MHz there is penetration of the layer at all zenith angles. However, the absorption is very large at small angles, approaching 40 dB at 4 MHz. If we assume that an ionospheric absorption larger than for example 20 dB will attenuate the signal below noise level, then a ground reflected signal will only occur for angles 442 . It appears that at lower frequencies the occurrence of ground reflection is limited by reflection in the layer, while at
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Fig. 5. Zenith angle variation of the absorption in a model ionosphere (for solar F107 flux of 70). Calculations are for 3.0, 3.2, 3.4, 3.6, 3.8, and 4.0 MHz. The low frequency curves terminate at the smallest zenith angle where it is penetrate the ionosphere.
higher frequencies the occurrence of ground reflection is limited by absorption in the ionosphere. In a coordinate system with signal frequency versus zenith angle we can now determine the area in which ground reflection occurs, cross-hatched in Fig. 6. The top panel is for an ionospheric absorption limit of 20 dB, and the bottom panel for 10 dB. The border of the crosshatched area marks the zenith angles and frequencies limiting the appearance of ground reflections. Note that the limiting values below 3 MHz and for angles larger than 65 are identical in the two plots; they are controlled by reflections inside the layer. For larger frequencies and smaller angles the limiting values differ because they are controlled by ionospheric absorption. When the allowed absorption limit increases (here from 10 to 20 dB) the ground wave appearance at higher frequencies spreads towards lower zenith angles. This kind of plot is hereafter referred to as a ‘ground-reflection plot’. Before comparing these predictions with observations we must also take into account the separation between radar and target (the ground). The attenuation owing to this spatial separation is given by (T. Hagfors, private communication) A2 a2 Pr ¼ Pt 2 , 4h ða þ hÞ2 l2
(6)
where A is the effective antenna area (calculated for a halfwave dipole gain of 1.64), a the radius of the spherical
Fig. 6. Ground-reflection plots. The cross-hatched area is the region where ground reflections occur. The larger the allowed absorption in the ionosphere (20 dB in the top panel, and 10 dB in the bottom panel) the larger the cross-hatched area.
target ð¼ Rmars Þ, l the signal wave length, and h the spacecraft altitude. The reflectivity of the target has been set to unity. The range attenuation in dB is Ar ¼ 10:0n log
Pr . Pt
(7)
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For a radius of 3398 km and an altitude of 300 km, Ar ¼ 94:2 dB at 3 MHz. For a total measurable attenuation of 120 dB, this allows for maximum 25.8 dB ionospheric absorption for that spacecraft altitude. In Fig. 7 the observations shown in Fig. 2 are displayed in a ground-reflection plot representative of that orbit (2029). Between 70 and 80 there is a ledge where the minimum frequency tends to remain constant for increasing angle. This is an instrumental effect: the radar has a dip in radiated power between 2:7 and 2.9 MHz. The minimum frequency is overestimated to its value on the high frequency side of this dip. The real minimum frequency eventually reappears on the low frequency side of the dip at a corresponding higher zenith angle. Apart from this ledge, for large zenith angles (470 ) there is good agreement between prediction and observation. This means that reflection and absorption at these high zenith angles are well described by the model. However, below 70 the maximum allowed absorption is clearly overestimated: the data points are located inside the crosshatched area rather than on the limiting border. These data points were obtained for spacecraft altitudes between 293 and 358 km. The corresponding range attenuation leads to maximum ionosphere attenuation (in the primary density layer—for which these calculations were made) between 26.0 and 24.1 dB. Note, two cross-hatched areas are shown: one for each of these limiting absorptions. The solid-line cross-hatched area corresponds to 24.1 dB, and the dashedand solid-line cross-hatched to 26.0 dB. These limiting
values are clearly too large and extend the cross-hatched area toward zenith angles that are much smaller than the observed ones. In addition to absorption in the primary layer there must be a further factor in the ionosphere causing absorption. Adding a zenith-angle-independent absorption of 18 dB to the calculated absorption in the primary layer brings the observations into much better agreement with the prediction, in Fig. 8. The zenith-angledependent component of the absorption is the absorption calculated for the primary layer. For that component the limiting values of absorption are 8.0–6.1 dB for the given spacecraft altitude variation. This shows that a major contribution to the total absorption comes from a source other than the primary ionospheric layer. As expected the limiting border at large zenith angles is not much affected by this additional absorption component. The MARSIS radar is a top-side sounder, which measures the electron density profile from high altitudes down to the altitude of the maximum electron density. At altitudes below the altitude of maximum density the density profile is not accessible to sounder observations. So far in the calculations we have assumed that the bottom-side ionosphere was governed by the Chapman layer fitted to the observations above the density maximum. The analysis so far suggests that this is not a valid assumption. The additional absorption required to fit the measurements to observations must arise owing to electron densities in this region which are larger than predicted by the bottom-side Chapman layer. Since the collision
Fig. 7. The same data points as in Fig. 2 are plotted in a ground-reflection plot. There is good agreement at low frequencies, while at high frequencies the maximum allowed ionosphere absorption (adjusted for spacecraft altitude is between 26.0 and 24.1 dB) is too large.
Fig. 8. Arbitrarily adding 18 dB to the calculated absorption brings also the data at large frequencies in good agreement with the observed data.
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frequency increases downwards from the primary density maximum, even small density increases in this region may contribute significantly to the total absorption. The Martian ionosphere has been extensively observed using the radio occultation technique, which allows the whole density profile to be determined (from 60 to 300 km) (Kliore, 1992). These observations show that typically there is a secondary layer a few tens of kilometers below the density maximum of the primary layer. The extra absorption implied by our analysis is likely to take place in this secondary layer with a typical peak altitude at about 110 km and a peak density about half the primary maximum (Kliore, 1992; Rishbeth and Mendillo, 2004). We now insert a secondary layer in the model calculations with a peak altitude at 110 km, a scale height of 10 km, and adjust the peak density to a good fit between calculations and observations, in Fig. 9. With the secondary layer included the calculated absorption increases. The absorption limits of 26.0 and 24.1 dB, derived considering the spacecraft altitude variation, lead now to a similar good fit of calculations and observations as in Fig. 8. More recently Paetzold et al. (2005) reported a sporadic third layer in the ionosphere of Mars. This layer could appear with a peak density altitude between 65 and 110 km, and a mean density maximum of 8 103 el=cm3 . Instead of the secondary layer we now insert in the calculation a layer at 90 km altitude with peak density of 6 103 el=cm3 and a scale height of 10 km. This layer yields a good fit of the data to observations similar to that given by the secondary layer. The result is similar to Fig. 9.
Fig. 9. Introducing the secondary ionosphere layer observed at Mars (Kliore, 1992), brings the observations in good agreement with the calculated total absorption in the ionosphere.
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3. Discussion The MARSIS radar is a low frequency top-side sounder orbiting above the main electron density layer in the Martian ionosphere. The radar operates at frequencies that cover and somewhat exceed the range of plasma frequencies in the ionosphere. The radar can therefore be used to sound both the ionosphere and the ground. A reflection from the ground is observed when the frequency is larger than the maximum plasma frequency and when the absorption in the ionosphere does not attenuate the radar signal below detection limit. For a given spacecraft altitude there is therefore an upper limit to the ionospheric absorption allowing a ground reflection to be observed. The absorption limit depends on the details of the ionospheric density profile as it varies with solar flux intensity and solar zenith angle. The purpose of this work is to account for the typically observed pattern of ground reflections considering reflection and absorption of radio waves in the ionosphere. This is the first time absorption calculations in the Martian ionosphere have been tested by observations. We have used a model of the main (primary) density peak, which approximates the layer with a Chapman layer both above (where MARSIS makes observations, and we know this is a good approximation) and below. The absorption calculations are based mainly on an electron-neutral collision frequency profile, which is set equal to the collision cross-section of thermal electrons with CO2 molecules times the CO2 density. It is noted that the collision frequencies at Mars are nearly a factor of 100 larger than at similar altitudes in Earth’s ionosphere, which makes Mars a strong radio wave absorber. An example of the results of such calculations is shown in Fig. 6. Ground reflections appear in the cross-hatched area. For high zenith angles, and for low frequencies, the cut-off is caused by reflection of the radio wave inside the density layer. At smaller zenith angles, and for higher frequencies, the cutoff is controlled by absorption in the layer. For larger allowed absorption the area of ground reflections extends further towards still smaller zenith angles. For a selected orbit (#2029) the minimum frequency for which ground reflections occurred was determined as a function of zenith angle. The data were compared to predictions for this orbit, in Fig. 7. Good agreement implies that the data points should be located on (clustering around) the border of the cross-hatched area. At low frequencies there is a good agreement. This means that reflections inside the primary layer are well described by the model. However, at higher frequencies the data points are located in the cross-hatched area, which means that there is stronger absorption occurring than is derived from the model. Increasing the calculated absorption by 18 dB brings the prediction into agreement with the data points. This agreement is shown in Fig. 8. We suggest that this additional absorption arises from a secondary layer known to exist below the primary density layer. Including a secondary layer with typical parameter
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values in addition to the primary layer confirms that such a configuration can account for the MARSIS observations. Note that a more recently observed sporadic layer may be present at still lower altitudes. We find that such a layer could also account for the observations. The secondary layer is thought to be the result of ionization by soft solar X-rays (Fox and Dalgarno, 1979). The sporadic third layer was suggested to be associated with ablation of meteorites in the atmosphere, therefore the sporadic occurrence (Paetzold et al., 2005). It is very likely that other causes for absorption may play a role. For example, Morgan et al. (2006) have found that intervals of ground reflection absorption lasting up to two weeks coincide in time with high fluxes of solar energetic particles in the 10 MeV range. These events are observed at solar zenith angles up to 113 , well into the night side of Mars. Occurrence of absorption on the nightside is thought to be due to the impinging particles having helical orbits of planetary-sized cyclotron radius, which are not clearly shadowed by the planet. Cosmic rays with energies affecting the ionosphere densities are channeled towards high latitudes on Earth due to the dipole magnetic field. During these absorption events on Mars, which has a weak and sporadic magnetic field, most of the planet appears to be affected. Hard Xrays emitted at the onset of solar flares would cause short lasting ð1 hÞ density increases on the dayside Mars ionosphere (e.g. Mendillo et al., 2006). Also local acceleration processes could play a role. Recently inverted-V events were reported on Mars (Lundin and et al., 2006). The observed variation of the minimum frequency of ground reflections are in very good agreement with the variation predicted by propagation in the primary layer. This follows from the good fit in Fig. 8, where only a constant increase in ionospheric absorption had to be included to obtain a match. It follows that the model for absorption calculations in the primary layer is realistic. The success of the absorption calculations together with the multiple possible sources inducing increases in the ionospheric electron densities, and thus causing absorption, suggests that it is time to monitor the radio wave absorption on Mars for the purpose of studying the occurrence and nature of these processes. A simple low noise monochromatic receiver placed on the surface of
Mars to record variations of the cosmic noise intensity as it changes owing to changing absorption would serve such a purpose (Nielsen, 1998).
Acknowledgments MARSIS was built and is jointly managed by the Italian Space Agency and NASA. Mars Express was built and is operated by the European Space Agency. The research at the University of Iowa was supported by NASA through contract 1224107 with the Jet Propulsion Laboratory.
References Detrick, D.L., Rosenberg, T.J., Fry, C.D., 1997. Analysis of the Martian atmosphere for riometry. Planet. Space Sci. 45, 289. Fox, L.J., Dalgarno, A., 1979. Ionization, luminosity, and heating of the upper atmosphere of Mars. J. Geophys. Res. 84, 7315. Hake Jr., R.D., Phelps, A.V., 1967. Momentum-transfer and inelasticcollision cross sections for electrons in O2 , CO, and CO2 . Phys. Rev. 158 (1), 70. Kliore, A.J., 1992. Radio occultation observations of the ionospheres of Mars and Venus, Venus and Mars: Atmospheres, Ionospheres, and Solar wind interactions. Geophysical Monograph 66, AGU. Lundin, R., et al., 2006. Plasma acceleration above Martian magnetic anomalies. Science 311, 980. Mendillo, M., Withers, P., Hinson, D., Rishbeth, H., Reinisch, B., 2006. Effects of solar flares on the ionosphere of Mars. Science 311, 1135–1138. Morgan, D.D., Gurnett, D.A., Kirchner, D.L., Huff, R.L., Brain, D.A., Boynton, W.V., Acun˜a, M.H., Plaut, J.J., Picardi, G., 2006. Solar control of radar wave absorption by the Martian ionosphere. Geophys. Res. Lett. 33, L13202, doi: 10.1029/2006GL026637. Nielsen, E., 1998. Mars riometer system. Proceedings of 32nd ESLAB Symposium on ‘Remote sensing methodology for Earth observations and planetary exploration’, ESTEC, Noordwijk, The Netherlands. Nielsen, E., 2001. Mars ionosphere and solar wind. MPAE-W-04-01-03. Nielsen, E., Gurnett, D.A., Kirchner, D.L., Huff, R.L., Orosei, R., Safaeinili, A., Plaut, J.J., Picardi, G., 2006. Observations of vertical reflections from the topside Martian ionosphere. Space Science Rev., in press. Paetzold, M., Teilman, S., Haeusler, B., Hinson, D., Schaa, R., Tyler, G.L., 2005. A Sporadic third layer in the ionosphere of Mars. Science 310, 837. Rishbeth, H., Mendillo, M., 2004. Ionospheric layers of Earth and Mars. Planet. Space Sci. 52, 849. Schunk, R.W., Nagy, A.F., 2000. Ionospheres. Cambridge University, New York.
Planetary and Space Science 55 (2007) 864–870 www.elsevier.com/locate/pss
Absorption and reflection of radio waves in the Martian ionosphere E. Nielsena,, D.D. Morganb, D.L. Kirchnerb, J. Plautc, G. Picardid a
Max Planck Institute for Solar System Research, 37191 Katlenburg-Lindau, Germany Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA c Jet Propulsion Laboratory, Pasadena, CA 91109, USA d Infocom Department, ‘‘La Sapienza’’ University of Rome, 00184 Rome, Italy
b
Received 13 July 2006; received in revised form 11 October 2006; accepted 11 October 2006 Available online 1 December 2006
Abstract Radio wave absorption in the Martian ionosphere has been predicted and tested against MARSIS radar observations. Models of the ionosphere densities and of absorption in a CO2 neutral atmosphere were used. The appearance of ground reflections in the MARSIS observations is shown to be consistent with predictions of reflection and absorption of radio waves in the ionosphere. It is concluded that the secondary density maximum, known to be typically present below the primary density peak, contributes considerably to the absorption and thus to the appearance of ground reflections. It is the first time predicted radio wave absorption in a CO2 planetary atmosphere has been tested against actual observations. r 2006 Elsevier Ltd. All rights reserved. Keywords: Mars; Ionosphere; Radio wave absorption; Top-side sounder
1. Introduction The low frequency radar Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on board the ESA mission Mars Express (MEX) is used primarily both to sound the ionosphere plasma and to sound the ground, surface and subsurface, for essentially water deposits in both liquid and frozen forms. The lowest altitude of the spacecraft is 300 km well above the altitude of the electron density maximum in the ionosphere. The altitude of the electron density maximum is typically 130 km. The ground sounding signal must therefore penetrate the ionosphere twice before detection. Thus, for a ground reflection to be detected the signal frequency must be larger than the maximum plasma frequency. If this condition is met, the ionosphere has two further effects on the signal: it will cause dispersion of the signal phases, and it will attenuate the signal amplitude. In this work we do not consider the signal dispersion. Instead, we will determine how the appearance of a ground reflected signal
Corresponding author. Tel.: +49 5556 979450.
E-mail address: [email protected] (E. Nielsen). 0032-0633/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2006.10.005
in the observations is controlled by reflection and absorption in the ionospheric plasma. Radio wave absorption in an atmosphere is controlled to a large extent by the collision frequency of thermal electrons with the neutral molecules. Since the major neutral atmospheric component on Mars is CO2 , which has a much larger scattering cross section for thermal electrons than does either oxygen or nitrogen, the absorption on Mars, for the same electron density and signal frequency, is much more severe than in Earth’s atmosphere.
2. Observations and analysis MARSIS can be operated either in a ground sounding mode or in the Active Ionosphere Sounder (AIS) mode. Here we use data obtained in the AIS mode. The radar operates between 0.1 and 5.4 MHz. A series of narrow near monochromatic signals are transmitted in sequence and for each frequency the time delays to echoes are measured. The echoes are either reflection from the ionosphere or from the ground. The observations are presented in a spectrogram displaying the intensity of the echo signal as a function of time delay (on the horizontal axis) and signal frequency
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(on the vertical axis). An example of such a spectrogram is shown in Fig. 1. The virtual depth, which is half the delay time multiplied by the vacuum speed of light, is given on the top horizontal axis. The echo between 1.1 and 2.7 MHz is an ionospheric reflection. The later echoes at higher frequencies between 3.5 and 5.4 MHz are the signal reflected from the ground. It is typical for the ground reflection that when present it appears for all frequencies between a minimum frequency and the maximum frequency of the sounder. The distance to the target (the ground) is the same for all frequencies, and since all signals travel through the same ionosphere the delay times are only weakly increasing with decreasing frequency. This ground reflection is not always present in the spectrograms. The reason is that the radar signal may be either reflected before penetrating the ionosphere because the sounding frequency is less than the maximum plasma frequency, or be so severely attenuated that the signal drops below the receiver noise level. The primary electron density maximum in the Martian ionosphere is a Chapman layer controlled by solar radiation, which therefore varies in height and in intensity with solar zenith angle. It is to be expected that the minimum frequency for the ground reflection is to a large extent controlled by the solar zenith angle. We therefore display in Fig. 2 the appearance of ground reflections during one orbit by presenting the minimum frequency versus zenith angle. In this case the ground reflection appeared first for a zenith angle of 60 . For smaller zenith angles the denser ionosphere probably caused attenuation sufficient to reduce the received signal below noise level.
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Fig. 2. Data for orbit 2029. The minimum frequency for ground reflections is decreasing as the solar zenith angle increases, associated with a weakening of the solar radiation induced primary electron density layer.
Ground reflections occurred for all zenith angles larger than 60 up to 100 . These observations are reproduced in the following using model calculations. Nielsen et al. (2006) found that the main electron density peak is well approximated by a Chapman layer up to an altitude of 180–200 km, and exponentially decreasing with altitude above that height. The density profile (Eqs. (1)–(3)) is controlled by zenith angle and solar ionizing flux intensity (F ¼ F10:7 cm flux) (see for example summary in Nielsen, 2001 and references therein), N e ðhÞ ¼ N o 1 h hmax h hmax 1 Chðx; yÞ exp exp , 2 H H ð1Þ where N o is the subsolar maximum density, hmax the subsolar altitude of maximum density, H the neutral scale height in the Chapman layer, y the solar zenith angle, h the altitude, and x ¼ ðRMars þ hÞ=H, N o ¼ 200n100:36 log F =120 ð103 el=cm3 Þ, 1 ðkmÞ, hmax ¼ 120 þ 10 log Chðx; yÞ F H ¼ 10n exp 0:16 ln ðkmÞ. 100
Fig. 1. MARSIS Active Ionosphere Spectrogram displaying ionosphere (at low frequencies) and ground reflections (at high frequencies). The slant of the ground reflections towards higher delay time with decreasing frequency is caused by decreasing propagation speed as the frequency decreases. The ground reflection first appears at a minimum frequency of 3:2 MHz.
The plasma scale height above the Chapman layer is F H t ¼ 23n exp 0:55 ln ðkmÞ. 50
ð2Þ
(3)
Use of the Chapman function Chðy; xÞ takes into account that ionizing radiation extends past the terminator and allows analysis for zenith angles larger than 90 . In this analysis x ¼ 350 was used. In Fig. 3 there is an example of
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Fig. 3. Example of the primary density peak in the ionosphere model. At 5 MHz the signal passes through the layer and is attenuated by 11.8 dB in its way to and from the ground.
the model ionosphere for a zenith angle of 50 and a solar flux F10:7 ¼ 111 units. Neglecting the weak crustal magnetic fields the sounder signal propagating into the ionosphere is reflected where the signal frequency equals the plasma frequency qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f p ðkHzÞ ¼ 8:98 N e ðhÞ ðel=cm3 Þ. (4) The radar signal is attenuated by absorption in the ionosphere AðhÞ ¼ 4:61n104 N e ðhÞ
nðhÞ ðdB=kmÞ, o2 ðhÞ þ n2 ðhÞ
(5)
where o is the signal frequency (rad/s), and n ðs1 Þ the momentum-transfer electron-neutral collision frequency. The collision frequency is governed by the main molecular component in the Martian atmosphere, which is CO2 (Detrick et al., 1997). For the relatively cool Martian ionosphere the thermal mean energy is about 0.1 eV. Laboratory measurements in a CO2 gas of molecules show the collision frequency of such electrons to be close to 107 per molecule=s (Hake and Phelps, 1967). Multiplying the collision frequency per molecule by the CO2 concentration yields the altitude profile of the collision frequency, shown in Fig. 4. This profile is in very good agreement with Schunk and Nagy (2000). Note that these collision frequencies are nearly a factor of 100 larger than in Earth’s ionosphere. The reason is that the electron collision frequency with N2 molecules, the dominant molecule in Earth’s ionosphere, is much lower at
Fig. 4. Altitude profile of the electron momentum-transfer collision frequency in Mars’s CO2 atmosphere.
2 109 per molecule=s. This suggests that strong radio wave absorption is a striking aspect of the Martian ionosphere. The specific absorption (dB/km/electron) maximizes where the signal frequency equals the collision frequency; this occurs at altitudes of 80–90 km for the range of MARSIS AIS radar frequencies. Because the collision frequency increases with decreasing altitude the main contribution to the total absorption of a signal propagating through the ionosphere occurs below the peak density. The detailed density profile above the Chapman layer is of little importance in this respect. On the other hand additional electron densities below the density maximum could have an important contribution to the total absorption, even if these densities are relatively small. To illustrate the reflection and absorption properties of the ionosphere we calculate the absorption of radio waves of frequencies between 3 and 4 MHz (in steps of 0.2 MHz) in a Chapman layer for a solar flux of F10:7 ¼ 70. The result is shown in Fig. 5. The absorption is only calculated for signals that penetrate the ionosphere. At 3 MHz the signal is only penetrating the layer for zenith angles 464 and at 3.2 MHz for angles 453 , etc. Thus, a ground reflection can only occur at these frequencies at zenith angles larger than these limiting angles. For 3.8 and 4.0 MHz there is penetration of the layer at all zenith angles. However, the absorption is very large at small angles, approaching 40 dB at 4 MHz. If we assume that an ionospheric absorption larger than for example 20 dB will attenuate the signal below noise level, then a ground reflected signal will only occur for angles 442 . It appears that at lower frequencies the occurrence of ground reflection is limited by reflection in the layer, while at
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Fig. 5. Zenith angle variation of the absorption in a model ionosphere (for solar F107 flux of 70). Calculations are for 3.0, 3.2, 3.4, 3.6, 3.8, and 4.0 MHz. The low frequency curves terminate at the smallest zenith angle where it is penetrate the ionosphere.
higher frequencies the occurrence of ground reflection is limited by absorption in the ionosphere. In a coordinate system with signal frequency versus zenith angle we can now determine the area in which ground reflection occurs, cross-hatched in Fig. 6. The top panel is for an ionospheric absorption limit of 20 dB, and the bottom panel for 10 dB. The border of the crosshatched area marks the zenith angles and frequencies limiting the appearance of ground reflections. Note that the limiting values below 3 MHz and for angles larger than 65 are identical in the two plots; they are controlled by reflections inside the layer. For larger frequencies and smaller angles the limiting values differ because they are controlled by ionospheric absorption. When the allowed absorption limit increases (here from 10 to 20 dB) the ground wave appearance at higher frequencies spreads towards lower zenith angles. This kind of plot is hereafter referred to as a ‘ground-reflection plot’. Before comparing these predictions with observations we must also take into account the separation between radar and target (the ground). The attenuation owing to this spatial separation is given by (T. Hagfors, private communication) A2 a2 Pr ¼ Pt 2 , 4h ða þ hÞ2 l2
(6)
where A is the effective antenna area (calculated for a halfwave dipole gain of 1.64), a the radius of the spherical
Fig. 6. Ground-reflection plots. The cross-hatched area is the region where ground reflections occur. The larger the allowed absorption in the ionosphere (20 dB in the top panel, and 10 dB in the bottom panel) the larger the cross-hatched area.
target ð¼ Rmars Þ, l the signal wave length, and h the spacecraft altitude. The reflectivity of the target has been set to unity. The range attenuation in dB is Ar ¼ 10:0n log
Pr . Pt
(7)
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For a radius of 3398 km and an altitude of 300 km, Ar ¼ 94:2 dB at 3 MHz. For a total measurable attenuation of 120 dB, this allows for maximum 25.8 dB ionospheric absorption for that spacecraft altitude. In Fig. 7 the observations shown in Fig. 2 are displayed in a ground-reflection plot representative of that orbit (2029). Between 70 and 80 there is a ledge where the minimum frequency tends to remain constant for increasing angle. This is an instrumental effect: the radar has a dip in radiated power between 2:7 and 2.9 MHz. The minimum frequency is overestimated to its value on the high frequency side of this dip. The real minimum frequency eventually reappears on the low frequency side of the dip at a corresponding higher zenith angle. Apart from this ledge, for large zenith angles (470 ) there is good agreement between prediction and observation. This means that reflection and absorption at these high zenith angles are well described by the model. However, below 70 the maximum allowed absorption is clearly overestimated: the data points are located inside the crosshatched area rather than on the limiting border. These data points were obtained for spacecraft altitudes between 293 and 358 km. The corresponding range attenuation leads to maximum ionosphere attenuation (in the primary density layer—for which these calculations were made) between 26.0 and 24.1 dB. Note, two cross-hatched areas are shown: one for each of these limiting absorptions. The solid-line cross-hatched area corresponds to 24.1 dB, and the dashedand solid-line cross-hatched to 26.0 dB. These limiting
values are clearly too large and extend the cross-hatched area toward zenith angles that are much smaller than the observed ones. In addition to absorption in the primary layer there must be a further factor in the ionosphere causing absorption. Adding a zenith-angle-independent absorption of 18 dB to the calculated absorption in the primary layer brings the observations into much better agreement with the prediction, in Fig. 8. The zenith-angledependent component of the absorption is the absorption calculated for the primary layer. For that component the limiting values of absorption are 8.0–6.1 dB for the given spacecraft altitude variation. This shows that a major contribution to the total absorption comes from a source other than the primary ionospheric layer. As expected the limiting border at large zenith angles is not much affected by this additional absorption component. The MARSIS radar is a top-side sounder, which measures the electron density profile from high altitudes down to the altitude of the maximum electron density. At altitudes below the altitude of maximum density the density profile is not accessible to sounder observations. So far in the calculations we have assumed that the bottom-side ionosphere was governed by the Chapman layer fitted to the observations above the density maximum. The analysis so far suggests that this is not a valid assumption. The additional absorption required to fit the measurements to observations must arise owing to electron densities in this region which are larger than predicted by the bottom-side Chapman layer. Since the collision
Fig. 7. The same data points as in Fig. 2 are plotted in a ground-reflection plot. There is good agreement at low frequencies, while at high frequencies the maximum allowed ionosphere absorption (adjusted for spacecraft altitude is between 26.0 and 24.1 dB) is too large.
Fig. 8. Arbitrarily adding 18 dB to the calculated absorption brings also the data at large frequencies in good agreement with the observed data.
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frequency increases downwards from the primary density maximum, even small density increases in this region may contribute significantly to the total absorption. The Martian ionosphere has been extensively observed using the radio occultation technique, which allows the whole density profile to be determined (from 60 to 300 km) (Kliore, 1992). These observations show that typically there is a secondary layer a few tens of kilometers below the density maximum of the primary layer. The extra absorption implied by our analysis is likely to take place in this secondary layer with a typical peak altitude at about 110 km and a peak density about half the primary maximum (Kliore, 1992; Rishbeth and Mendillo, 2004). We now insert a secondary layer in the model calculations with a peak altitude at 110 km, a scale height of 10 km, and adjust the peak density to a good fit between calculations and observations, in Fig. 9. With the secondary layer included the calculated absorption increases. The absorption limits of 26.0 and 24.1 dB, derived considering the spacecraft altitude variation, lead now to a similar good fit of calculations and observations as in Fig. 8. More recently Paetzold et al. (2005) reported a sporadic third layer in the ionosphere of Mars. This layer could appear with a peak density altitude between 65 and 110 km, and a mean density maximum of 8 103 el=cm3 . Instead of the secondary layer we now insert in the calculation a layer at 90 km altitude with peak density of 6 103 el=cm3 and a scale height of 10 km. This layer yields a good fit of the data to observations similar to that given by the secondary layer. The result is similar to Fig. 9.
Fig. 9. Introducing the secondary ionosphere layer observed at Mars (Kliore, 1992), brings the observations in good agreement with the calculated total absorption in the ionosphere.
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3. Discussion The MARSIS radar is a low frequency top-side sounder orbiting above the main electron density layer in the Martian ionosphere. The radar operates at frequencies that cover and somewhat exceed the range of plasma frequencies in the ionosphere. The radar can therefore be used to sound both the ionosphere and the ground. A reflection from the ground is observed when the frequency is larger than the maximum plasma frequency and when the absorption in the ionosphere does not attenuate the radar signal below detection limit. For a given spacecraft altitude there is therefore an upper limit to the ionospheric absorption allowing a ground reflection to be observed. The absorption limit depends on the details of the ionospheric density profile as it varies with solar flux intensity and solar zenith angle. The purpose of this work is to account for the typically observed pattern of ground reflections considering reflection and absorption of radio waves in the ionosphere. This is the first time absorption calculations in the Martian ionosphere have been tested by observations. We have used a model of the main (primary) density peak, which approximates the layer with a Chapman layer both above (where MARSIS makes observations, and we know this is a good approximation) and below. The absorption calculations are based mainly on an electron-neutral collision frequency profile, which is set equal to the collision cross-section of thermal electrons with CO2 molecules times the CO2 density. It is noted that the collision frequencies at Mars are nearly a factor of 100 larger than at similar altitudes in Earth’s ionosphere, which makes Mars a strong radio wave absorber. An example of the results of such calculations is shown in Fig. 6. Ground reflections appear in the cross-hatched area. For high zenith angles, and for low frequencies, the cut-off is caused by reflection of the radio wave inside the density layer. At smaller zenith angles, and for higher frequencies, the cutoff is controlled by absorption in the layer. For larger allowed absorption the area of ground reflections extends further towards still smaller zenith angles. For a selected orbit (#2029) the minimum frequency for which ground reflections occurred was determined as a function of zenith angle. The data were compared to predictions for this orbit, in Fig. 7. Good agreement implies that the data points should be located on (clustering around) the border of the cross-hatched area. At low frequencies there is a good agreement. This means that reflections inside the primary layer are well described by the model. However, at higher frequencies the data points are located in the cross-hatched area, which means that there is stronger absorption occurring than is derived from the model. Increasing the calculated absorption by 18 dB brings the prediction into agreement with the data points. This agreement is shown in Fig. 8. We suggest that this additional absorption arises from a secondary layer known to exist below the primary density layer. Including a secondary layer with typical parameter
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values in addition to the primary layer confirms that such a configuration can account for the MARSIS observations. Note that a more recently observed sporadic layer may be present at still lower altitudes. We find that such a layer could also account for the observations. The secondary layer is thought to be the result of ionization by soft solar X-rays (Fox and Dalgarno, 1979). The sporadic third layer was suggested to be associated with ablation of meteorites in the atmosphere, therefore the sporadic occurrence (Paetzold et al., 2005). It is very likely that other causes for absorption may play a role. For example, Morgan et al. (2006) have found that intervals of ground reflection absorption lasting up to two weeks coincide in time with high fluxes of solar energetic particles in the 10 MeV range. These events are observed at solar zenith angles up to 113 , well into the night side of Mars. Occurrence of absorption on the nightside is thought to be due to the impinging particles having helical orbits of planetary-sized cyclotron radius, which are not clearly shadowed by the planet. Cosmic rays with energies affecting the ionosphere densities are channeled towards high latitudes on Earth due to the dipole magnetic field. During these absorption events on Mars, which has a weak and sporadic magnetic field, most of the planet appears to be affected. Hard Xrays emitted at the onset of solar flares would cause short lasting ð1 hÞ density increases on the dayside Mars ionosphere (e.g. Mendillo et al., 2006). Also local acceleration processes could play a role. Recently inverted-V events were reported on Mars (Lundin and et al., 2006). The observed variation of the minimum frequency of ground reflections are in very good agreement with the variation predicted by propagation in the primary layer. This follows from the good fit in Fig. 8, where only a constant increase in ionospheric absorption had to be included to obtain a match. It follows that the model for absorption calculations in the primary layer is realistic. The success of the absorption calculations together with the multiple possible sources inducing increases in the ionospheric electron densities, and thus causing absorption, suggests that it is time to monitor the radio wave absorption on Mars for the purpose of studying the occurrence and nature of these processes. A simple low noise monochromatic receiver placed on the surface of
Mars to record variations of the cosmic noise intensity as it changes owing to changing absorption would serve such a purpose (Nielsen, 1998).
Acknowledgments MARSIS was built and is jointly managed by the Italian Space Agency and NASA. Mars Express was built and is operated by the European Space Agency. The research at the University of Iowa was supported by NASA through contract 1224107 with the Jet Propulsion Laboratory.
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