Planetary foreshock radio emissions Zdenka Kuncic and Iver H. Cairns Centre for Wave Physics and Theoretical Physics Group, School of Physics, University of Sydney, Sydney, New South Wales, Australia Received 2 December 2004; revised 23 February 2005; accepted 21 April 2005; published 28 July 2005. [1] The electron foreshock regions upstream of Earth’s bow shock and upstream of traveling interplanetary shocks are known to be propitious sites for a variety of energetic particle and plasma wave phenomena, including radio emissions. A quantitative theoretical model has been developed for radio emissions associated with the terrestrial foreshock and for type II radio bursts associated with interplanetary shocks. Here, we generalize this model and apply it to other planetary foreshocks. We present predictions for the levels of planetary foreshock radio emissions and compare these with observations by past and present space missions. One key result is that Mercury can be a strong source of foreshock radio emissions, and this prediction may be testable with the anticipated BepiColombo space mission. Although the terrestrial foreshock radio emissions are the most detectable with existing instruments, our results predict that they are the second strongest in absolute terms, following the Jovian foreshock emissions. Indeed, we predict that the radio instrument on board Ulysses should have detected Jovian foreshock radio emissions, and we suggest that there is some evidence in the data to support this. We also suggest that Cassini was potentially capable of detecting foreshock emissions from Venus during its gravity-assist flybys and may possibly be capable of detecting foreshock emissions from Saturn under favorable solar wind conditions. Citation: Kuncic, Z., and I. H. Cairns (2005), Planetary foreshock radio emissions, J. Geophys. Res., 110, A07107, doi:10.1029/2004JA010953. 1. Introduction [2] Energetic particle and plasma wave activity have been detected by spacecraft in the upstream vicinity of the supersonic and superalfve ´nic bow shocks of all the planets visited to date in our solar system: Mercury [ Fairfield and Behannon, 1976], Venus [Strangeway, 1991], Earth [Scarf et al., 1971; Filbert and Kellogg, 1979; Anderson et al., 1981; Etcheto and Faucheux, 1984; Fuselier and Gurnett, 1984], Mars [Trotignon et al., 2000], Jupiter [Scarf et al., 1979], Saturn [Behannon et al., 1985], Uranus [Gurnett et al., 1986], and Neptune [Gurnett et al., 1989]. [3] Observations of Earth’s foreshock, in particular, also clearly reveal bursty radio emissions near the local electron plasma frequency, f R M p , and near 2f R M p [Gurnett, 1975; Hoang et al., 1981; Cairns, 1986; Lacombe et al., 1988; Reiner et al., 1997; Kasaba et al., 2000]. While it is possible that these radio emissions are intrinsically unique to the terrestrial foreshock, the association of similar radio emissions (solar type II bursts) and Langmuir waves with interplanetary foreshocks, as well as the detection of Langmuir-like waves in virtually all of the planetary foreshocks, strongly suggest that common underlying physical processes are operating in all planetary (and interplanetary) foreshocks [see, e.g., Boshuizen et al., 2004]. Radio emissions are therefore likely to be a charac- teristic property of all planetary foreshocks. We investigate this possibility here using a new theoretical model for fundamental (f R M p ) and second harmonic (2f R M p ) radio emissions developed for the terrestrial foreshock and inter- planetary foreshocks [Knock et al., 2001; Kuncic et al., 2002; Knock et al., 2003; Kuncic et al., 2004]. [4] In section 2, we generalize the existing theoretical model to take into account the variation in solar wind conditions with heliocentric distance and differences in bow shock geometry and obstacle size. We present our theoretical results in section 3. In section 4, we use our results to assess the detectability of planetary foreshock radio emissions by various spacecraft instruments. Our conclusions are presented in section 5. 2. Outline of Model [5] Here, we generalize a theoretical model for terrestrial foreshock radio emissions [Kuncic et al., 2002, 2004] and type II radio bursts from the foreshock regions of travelling interplanetary shocks [Knock et al. , 2001, 2003]. The model is based on four underlying physical components: (1) numerical calculation of electron foreshock beam distributions using the guiding center approximation, magnetic mirror reflection, and Liouville’s theorem [e.g., Cairns, 1987; Fitzenreiter et al., 1990; see also Knock et al., 2001; Kuncic et al., 2004]; (2) use of Stochastic Growth Theory (SGT) to predict the energy flow from electron JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, A07107, doi:10.1029/2004JA010953, 2005 Copyright 2005 by the American Geophysical Union. 0148-0227/05/2004JA010953 A07107 1 of 12
Transcript
Planetary foreshock radio emissions
Zdenka Kuncic and Iver H. CairnsCentre for Wave Physics and Theoretical Physics Group, School of Physics, University of Sydney, Sydney,New South Wales, Australia
Received 2 December 2004; revised 23 February 2005; accepted 21 April 2005; published 28 July 2005.
[1] The electron foreshock regions upstream of Earth’s bow shock and upstream oftraveling interplanetary shocks are known to be propitious sites for a variety of energeticparticle and plasma wave phenomena, including radio emissions. A quantitativetheoretical model has been developed for radio emissions associated with the terrestrialforeshock and for type II radio bursts associated with interplanetary shocks. Here, wegeneralize this model and apply it to other planetary foreshocks. We present predictionsfor the levels of planetary foreshock radio emissions and compare these with observationsby past and present space missions. One key result is that Mercury can be a strong sourceof foreshock radio emissions, and this prediction may be testable with the anticipatedBepiColombo space mission. Although the terrestrial foreshock radio emissions are themost detectable with existing instruments, our results predict that they are the secondstrongest in absolute terms, following the Jovian foreshock emissions. Indeed, we predictthat the radio instrument on board Ulysses should have detected Jovian foreshock radioemissions, and we suggest that there is some evidence in the data to support this. Wealso suggest that Cassini was potentially capable of detecting foreshock emissions fromVenus during its gravity-assist flybys and may possibly be capable of detecting foreshockemissions from Saturn under favorable solar wind conditions.
Citation: Kuncic, Z., and I. H. Cairns (2005), Planetary foreshock radio emissions, J. Geophys. Res., 110, A07107,
doi:10.1029/2004JA010953.
1. Introduction
[2] Energetic particle and plasma wave activity havebeen detected by spacecraft in the upstream vicinity ofthe supersonic and superalfvenic bow shocks of all theplanets visited to date in our solar system: Mercury[Fairfield and Behannon, 1976], Venus [Strangeway,1991], Earth [Scarf et al., 1971; Filbert and Kellogg,1979; Anderson et al., 1981; Etcheto and Faucheux, 1984;Fuselier and Gurnett, 1984], Mars [Trotignon et al., 2000],Jupiter [Scarf et al., 1979], Saturn [Behannon et al., 1985],Uranus [Gurnett et al., 1986], and Neptune [Gurnett etal., 1989].[3] Observations of Earth’s foreshock, in particular, also
clearly reveal bursty radio emissions near the local electronplasma frequency, fRM p, and near 2fRM p [Gurnett, 1975;Hoang et al., 1981; Cairns, 1986; Lacombe et al., 1988;Reiner et al., 1997; Kasaba et al., 2000]. While it ispossible that these radio emissions are intrinsically uniqueto the terrestrial foreshock, the association of similarradio emissions (solar type II bursts) and Langmuir waveswith interplanetary foreshocks, as well as the detectionof Langmuir-like waves in virtually all of the planetaryforeshocks, strongly suggest that common underlyingphysical processes are operating in all planetary (andinterplanetary) foreshocks [see, e.g., Boshuizen et al.,
2004]. Radio emissions are therefore likely to be a charac-teristic property of all planetary foreshocks. We investigatethis possibility here using a new theoretical model forfundamental (fRM p) and second harmonic (2fRM p) radioemissions developed for the terrestrial foreshock and inter-planetary foreshocks [Knock et al., 2001; Kuncic et al.,2002; Knock et al., 2003; Kuncic et al., 2004].[4] In section 2, we generalize the existing theoretical
model to take into account the variation in solar windconditions with heliocentric distance and differences inbow shock geometry and obstacle size. We present ourtheoretical results in section 3. In section 4, we use ourresults to assess the detectability of planetary foreshockradio emissions by various spacecraft instruments. Ourconclusions are presented in section 5.
2. Outline of Model
[5] Here, we generalize a theoretical model for terrestrialforeshock radio emissions [Kuncic et al., 2002, 2004]and type II radio bursts from the foreshock regions oftravelling interplanetary shocks [Knock et al., 2001,2003]. The model is based on four underlying physicalcomponents: (1) numerical calculation of electron foreshockbeam distributions using the guiding center approximation,magnetic mirror reflection, and Liouville’s theorem [e.g.,Cairns, 1987; Fitzenreiter et al., 1990; see also Knock et al.,2001; Kuncic et al., 2004]; (2) use of Stochastic GrowthTheory (SGT) to predict the energy flow from electron
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beams to Langmuir waves [Robinson, 1992; Robinson andCairns, 1998]; (3) analytic estimates of volume emissivitiesfor fRM p and 2fRM p radiation generated by specific nonlinearLangmuir wave processes [e.g., Robinson and Cairns1998]; (4) estimation of radiation flux levels from summingtwo-dimensional (2-D) source planes along a 3-D shocksurface [Kuncic et al., 2004]. On the basis of preliminaryresults from a detailed comparison between our resultsfor terrestrial 2fRM p emission and Geotail observations(Z. Kuncic et al., manuscript in preparation, 2005), themodel is accurate to within a factor of 1–10 in the radioflux. In order to make this model generally applicable toplanetary foreshocks, it is necessary to consider the varia-tion in the solar wind properties with heliocentric distance,and to generalize the bow shock geometry to take intoaccount the different shapes and sizes of planetaryobstacles.
2.1. Heliocentric Variation of Solar Wind Parameters
[6] The relevant solar wind input parameters are thethermal electron and ion temperatures TRM e and TRMi
, theelectron number density nRM e, the bulk speed uRM sw ,the orientation qbu of the interplanetary magneticfield (IMF) B with respect to uRMsw
and the globalshock strength parameter uRM
sw/vRRMM A, wherevRRM
MA = B/ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim�nRMemRRMMp
pis the Alfven speed. The
thermal electron speed is vRM e = (kTRMe/mRRM
Me)1/2. In
addition, the background solar wind electrons are assumedto have a combined Gaussian–Kappa distribution withnumber densities nRMG and nk in the respective Gaussiancore and Kappa halo components, satisfying nRMG + nk =nRM e [see Kuncic et al., 2004, and references therein]. Therelative heliocentric variation in nRMG and nk, and in k, arespecified below.[7] The variation of these solar wind parameters with
heliocentric distance d needs to be specified in order tocalculate their values upstream from each planetary bowshock. We use TRM e(d) / d�0.6 as a representative electron
core temperature profile. This is based on observationstaken in the ecliptic plane by various spacecraft, ascompiled by Maksimovic et al. [2000] and summarized inFigure 1. Note that there is a paucity of TRMe
measurementsbeyond 5 AU, so we simply extrapolate this profile out tolarge heliocentric distances. The implications of a TRM e
profile that flattens in the vicinity of Uranus and Neptuneare discussed in section 4. For the ion temperature,we use TRM i(d) / d�0.6 for d ] 20 AU and TRM i(d) /d0.4 for d ] 20 AU (see Figure 1). This ion profile is basedon model fits to the solar wind proton temperature mea-sured by Voyager 2 [Isenberg et al., 2003; Richardson andSmith, 2003]. The increase in TRM i beyond 20 AU isbelieved to be due to interstellar pickup ions.[8] For the electron number density, we use nRM e(d) /
d�2 inferred from charge neutrality and mass continuity.The corresponding plasma frequency is fRM p ’ 9nRM e
1/2 Hz.We assume that the solar wind speed has an approximatelyconstant value of uRM sw ’ 400 RRMM km s�1. This impliesthat uRM sw /vRRMM A / nRM e
1/2 B�1 / d�1B�1. For a Parkerspiral magnetic field, B(d) / d�2 for d ] 1 AU andB(d)/ d�1 for d ^ 1 AU, implying that uRM sw/vRRMMA/ d ford ] 1 AU and is approximately constant for d ^ 1 AU. TheParker spiral model also implies tan qbu(d) / d.[9] For the ratio of Kappa-halo to Gaussian-core electron
number densities, we use nk/nRMG / d�0.25, which wasmeasured by Ulysses in the ecliptic plane within 5 AU[Gary et al., 1994]. For the heliocentric profile of k, we usethe relation k(d) = 3
2[1 �TRM e(d)/Tk(d)]
�1, where Tk is theelectron temperature in the Kappa component ofthe distribution function. This is approximately constantfor d ] 1 AU (as measured by Mariner 10), and varies asTk / d�0.38 for 1.2 ] d] 5.4 (as measured by Ulysses) [seeMaksimovic et al., 2000, and references therein]. Since thereare no available data for Tk beyond �5 AU, we extrapolatethis profile out to large heliocentric distances, which impliesa constant value of k ’ 2 at and beyond Jupiter.[10] Table 1 lists the solar wind parameters calculated at
each planet location with respect to their well-known typicalvalues at 1 AU. Unless otherwise indicated, we will usethese representative values in our calculations for eachplanetary foreshock.
2.2. Generalized Bow Shock Geometry
[11] In the existing model for terrestrial and interplanetaryforeshock radio emissions, the shock is assumed to beparaboloidal and, in the case of Earth’s bow shock, anempirical fit is used to determine the standoff distance, aRM s
and shock curvature, parameterized by bRM s. Here, the bowshock geometry is generalized to a conic section, which ismore commonly used to fit bow shock measurements forthe nonterrestrial planets [see, e.g., Farris and Russell,1994]. We neglect orbital aberration effects, which shouldbe negligible for the bow shocks of all the planets, exceptperhaps Mercury, where the orbital aberration is �7� foruRM sw ’ 400 RRMM km s�1.[12] In polar (r, q) coordinates with the origin at the focus,
located at a distance aRM f from the bow shock nose, theconic bow shock geometry is given by
r ¼ L
1þ e cos q: ð1Þ
Figure 1. The heliocentric variation in Te (solid lines)measured by various spacecraft: Mariner 10 (M10), Voyager2 (V2), and Ulysses (Ul) [see Maksimovic et al., 2000]. Thedashed line is the Te(d) profile used in this work. The dottedline is the Ti(d) profile used here and is based on Voyager 2data [e.g., Isenberg et al., 2003].
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Here, r is the radial distance to all points on the shockfront,e is the eccentricity, L = (1 + e)aRM f is the semilatus rectum(i.e., the distance from the focus to the shockfront measuredperpendicular to the solar wind flow), and q is the solar-zenith angle (see Figure 2). This can be transformed intoa coordinate system (X, Y) that is centered on the planetand lies in the Sun-planet plane (i.e., analogous to theGSE coordinate system for Earth) by substituting (x0, y0) =(X � aRM s + aRM f, �Y ) into r =
locus of points (XRRMM s, YRRMM s) on a conic bow shock inGSE-equivalent coordinates:
eþ 1ð Þ XRRMM s � aRMs
� �2aRMf � e� 1ð Þ XRRMM s � aRMs
� �h iþ Y 2
RRMM s ¼ 0; ð2Þ
which converges to XRRMM s � aRMs+ bRM sYRRMM s
2 = 0 fora parabola (e = 1) when bRM s = 1/4aRM f. This is themodel commonly used for Earth’s bow shock [e.g.,Kuncic et al., 2004]. More generally, the shock curvatureconstant bRM s can be related to the other geometricparameters by
1
bRMs
¼ eþ 1ð Þ 2aRMf þ aRMs e� 1ð Þ� �
ð3Þ
and (2) then reduces to
Y 2RRMM s þ XRRMM s � aRMs
� � 1
bRMs
� e2 � 1
XRRMM s
� �¼ 0: ð4Þ
The parameters e, aRM s, bRM s thus uniquely define a bowshock geometry. Table 2 shows typical values of theseparameters for all the planetary bow shocks deduced frommodel fits of the general conic section (1) to measurementstaken by various spacecraft: Mariner 10 (Mercury: Leblancet al. [2003]); Pioneer Venus Orbiter (Venus: see Strangewayand Crawford [1995] and references therein); Wind and IMP8 (Earth: Cairns et al. [1996];Merka et al. [2003]); Phobos 2(Mars: Trotignon et al. [1993]); Voyagers 1 and 2, Pioneers10 and 11, Ulysses, and Galileo (Jupiter: Huddleston et al.[1998]); Voyager and Pioneer (Saturn: Slavin et al. [1983]);Voyager 2 (Uranus: Xue et al. [1996]; and Neptune: Cairnset al. [1991]).[13] To calculate the properties of the electron foreshock
region, we also need to define the bow shock geometry inforeshock coordinates (R, x), where R and x are parallel andperpendicular to the tangential IMF, respectively. We assumethe solar-planetary plane, where Z = 0, contains B anduRM sw , and the planet’s center of mass. The origin of theforeshock coordinate system is located at the tangent contactpoint (XRRMM t, YRM t) [see Kuncic et al., 2004]. Using thetransformations X(R, x) = XRRMM t � x sin qbu � R cos qbuand Y(R, x) = YRM t + x cos qbu � R sin qbu in (2), the locusof points on a conic bow shock in foreshock coordinates isdefined by G(RRRMM s, xRRMM s) = 0, where
G R; xð Þ ¼ XRRMM t � aRMs � x sin qbu � R cos qbu� �� 1
bRMs
� e2 � 1
XRRMM t � x sin qbu � R cos qbu� �� �
þ YRMt þ x cos qbu � R sin qbuð Þ2; ð5Þ
where (3) has been used.
Table 1. Solar Wind Parameters Calculated as a Function of Heliocentric Distance d at Each Planet Locationa
d (AU) TRM e, K TRM i, K nRM e, m�3 fRM p, kHz uRM sw /vRRMM A qbu nk/nRM G k
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[14] The tangent point (XRRMM t, YRM t) is obtained bysimultaneously solving G(R, x) = 0 and @G/@R = 0, bothevaluated at (R, x) = (0, 0). This gives
1� e2 � 1
cot2 qbu� �
X 2RRMM t
� zaRMs
e2 � 1ð Þ 1� e2 � 1
cot2 qbu� �
XRRMM t
þ aRMs
bRMs e2 � 1ð Þ 1� 1
4z2aRMsbRMs cot
2 qbu
� �¼ 0
YRRMM t ¼ e2 � 1
XRRMM t �1
2aRMsz
� �cot qbu; ð6Þ
where z = (e2 � 1) + 1/(aRM sbRM s). Similarly, the angle qbnbetween B and the normal to the bow shock at each point onits surface is calculated from the definition
tan qbn ¼ � @G=@x
@G=@R¼ c1 cot qbu � c2
c1 þ c2 cot qbu; ð7Þ
where c1 = YRRMM t + x cos qbu � R sin qbu and c2 =1/(2bRMs
) � (e2 � 1)(XRRMM t � x sin qbu � R cos qbu) + aRM s
(e2 � 1)/2. The local Alfven Mach number is then obtainedfrom MRMA = juRM sw � nj/vRRMM A = (uRM sw /vRRMM A)jcos (qbu + qbn)j and the Rankine-Hugoniot jump conditionsare then used to calculate the change in solar wind andshock parameters from upstream to downstream regions.All subsequent calculations involving electron reflectionand energization, foreshock trajectories and distributions,growth of Langmuir waves and conversion to electro-magnetic radiation remain the same as those described byKuncic et al. [2004].
3. Source Distributions and Flux Levels ofRadio Emissions
[15] Figure 3 shows the theoretical predictions for thesource regions of 2fRM p radio emission from the foreshocksof each planet. Specifically, the volume emissivity is plottedfor the plane Z = 0.[16] The fRM p and 2fRM p radio fluxes are also calculated at
an observer located a distance 2aRM s upstream from eachplanet along the Sun–planet line, as indicated by thesymbol O in each plot in Figure 3. These radio fluxes areplotted in Figure 4, and it is emphasized that the observer–planet distance varies significantly from one planet toanother. Figure 5, on the other hand, shows the radio fluxespredicted at a fixed observer location 0.1 RRMM AU up-stream from each planet, along the Sun–planet line.[17] As can be seen qualitatively in Figure 4, the fluxes
calculated at X = 2aRM s effectively scale out the dependenceof the radio emission on the physical size of the obstacleand on the shock geometry. Quantitatively, this can also beunderstood from the result that the radio flux is approxi-mately proportional to the square of the shock’s radius ofcurvature [Knock et al., 2003], and this dependence ispartially nullified by the inverse distance squared depen-dence (for distances sufficiently large that proximity effectsare negligible). Thus Figure 4 reflects mostly the depen-dence of the radio fluxes on heliocentric variations in solarwind parameters. The exceptions are for Venus, Earth, andMars, where the observer location X = 2aRM s is sufficiently
close to the source region that proximity effects are non-negligible (see Figure 3). Conversely, the radio fluxescalculated at a fixed, absolute distance of 0.1 AU fromeach planet, as shown in Figure 5, provide an indication ofthe intrinsic, rather than relative, strength of each planetaryforeshock source.
3.1. Earth
[18] In our previous paper [Kuncic et al., 2004], wepresented an extensive and detailed study of terrestrialforeshock radio emissions. The nominal results for Earth’sforeshock shown in Figures 3, 4, and 5 are presented herefor completeness and are also used to measure the relativeimportance of foreshock radio emissions predicted for theother planets.
3.2. Mercury
[19] In Figure 3, the 2fRM p source region predicted forMercury is shown for two different IMF orientations: qbu =130� and qbu = 90�. Results for two values of qbu are shownas there is some evidence from Mariner 10 observations thatthe IMF upstream from Mercury reconfigures itself onrelatively short timescales [Luhmann et al., 1998].[20] Our theoretical model predicts that 2fRM p emission
from the Hermean foreshock decreases strongly as the IMFapproaches a parallel orientation with respect to the Sun–Mercury line. Specifically, our model predicts that the mean2fRM p emissivity drops by a factor of �3 as qbu varies from90� to 130�. As the IMF approaches the Parker spiral anglefor Mercury, ’22� (or qbu ’ 158�, see Table 1), the quasi-perpendicular region of the bow shock moves down to theflanks, where the shock is weakest (i.e., MRMA is smallest),and fewer electrons are accelerated. This effect may beexacerbated if the �7� aberration of the Hermean bowshock from the Sun–Mercury line is taken into account.Consequently, our model predicts that negligible radioemission is generated when the IMF angle is close to itsParker spiral value (although we note that processes otherthan shock acceleration may energize particles under theseconditions). The relative strength of the Hermean foreshockradio emissions for the two different IMF orientations isalso indicated in Figures 4 and 5.[21] As is evident from Figure 3, the relative size of the
foreshock and strength of the 2fRM p emission predicted forMercury when qbu ’ 130� are quite different from thatpredicted for Earth (where qbu ’ 135�). In addition to itsrelatively eccentric bow shock shape, the actual physicalsize of Mercury’s foreshock is considerably smaller thanEarth’s. On the other hand, our model predicts that theaverage 2fRM p emissivity in the Hermean foreshock can besubstantially stronger than that in the terrestrial foreshock if,as some observations indicate [Luhmann et al., 1998], theIMF at Mercury is indeed capable of reconfiguring itself toqbu ’ 90�.[22] The predicted increase of the Hermean 2fRM p emis-
sivity relative to Earth is due to the highly sensitivedependence of the nonlinear conversion efficiency on TRM e,which is largest for the innermost planet (see Table 1).Specifically, the theory predicts a 2fRM p nonlinear conver-sion efficiency that increases (approximately) exponentiallywith TRM e, and the emissivity is directly proportional to theconversion efficiency (see Kuncic et al. [2004] for details).
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As shown in Figure 4, the total 2fRM p flux at X = 2aRM s ispredicted to be �5 times higher for Mercury compared tothat for Earth. Similarly, the predicted fRMp radio flux is upto 40 times higher. According to our theoretical model, thefRM p emissivity is less dependent on TRM e than the 2fRM p
emissivity but more strongly dependent on the spatialvelocity gradients of backstreaming electron beams in theforeshock, and such gradients are largest for Mercury, whichhas the smallest physical size. On the other hand, Figure 5suggests that in absolute terms, Mercury’s foreshock emis-sions are intrinsically much weaker than those of Earth,Jupiter, and Saturn but are comparable to those of Venus.[23] In summary, our model predicts that despite the small
physical sizes of the obstacle and bow shock, Mercury’sforeshock can be a strong local source of both 2fRM p andfRM p radio emissions. We discuss the implications of theseresults for future space missions in section 4.2.1 below.
3.3. Venus and Mars
[24] The average volume emissivity predicted forVenus’s 2fRM p foreshock radio emission is comparable tothat predicted for Earth. Indeed, the fluxes of both fRM p
and 2fRM p radio emissions at O are also comparable (seeFigure 4). This is consistent with the similarity betweenother plasma wave phenomena observed upstream ofEarth’s and Venus’ bow shocks [e.g., Strangeway andCrawford, 1995]. On the other hand, Figure 5 indicatesthat the intrinsic strength of Venus’s foreshock radio emis-sions, as measured by a fixed observer positioned 0,1 AUfrom the planet, is substantially less than the terrestrialemissions. Thus our results suggest that the smaller physicalsizes of Venus’s bow shock and foreshock, with respect toEarth, override the similarity in planet size and the higherupstream values of TRM e and nRM e favorable for strong radioemissions (see Tables 1 and 2 and Figure 3).
[25] In the case of the Martian foreshock, the average2fRM p volume emissivity for Mars is comparable to that ofEarth and Venus, despite the slightly lower upstream valuesof TRM e and nRM e (this is because the model assumes that thevolume emissivity depends on the spatial gradients of thebeam free energy, which are relatively larger in the case ofMars’ smaller foreshock). As indicated in Figure 4, how-ever, the predicted 2fRM p radio flux immediately upstreamof Mars is significantly lower than that of Venus and Earth.This implies that the effects of a substantially smallerphysical size are not completely scaled out at X = 2aRM s,and indeed, the absolute radio fluxes plotted in Figure 5further suggest that the Martian foreshock radio emissions,while present, are intrinsically the weakest of all the innerplanets owing to an overall smaller source volume.[26] The predicted fRM p radio fluxes immediately up-
stream of Venus’ and Mars’ bow shocks are similar to thatfor Earth (see Figure 4). This is because the theoreticalmodel predicts that the fRM p emission is less sensitive to theupstream TRM e but more sensitive to the spatial gradients invelocity of the backstreaming electron beams. These gra-dients are more significant in the smaller foreshock of Marsand thus compensate for the effects of lower TRM e toproduce fRM p emission at levels comparable to those ofVenus and Earth.[27] Interestingly, Phobos-2 observations of the region
upstream of Mars’ bow shock indicated an abrupt dropin the levels of electron plasma waves in regions beyond�6 RRMM along the IMF [Trotignon et al., 2000]. Thiseffect has been attributed to the small physical size ofthe Martian bow shock, which may limit the electronenergization process. Our results, however, do not in-clude this effect and show backstreaming electron beamsand associated emissions reaching distances well beyond�6 RRMM along the IMF.
3.4. Outer Planets
[28] The Jovian foreshock region, shown in Figure 3, isthe largest sized source region for 2fRM p and fRM p emissions,
Figure 4. Total fluxes (RMW RMm�2) of 2fp planetary
foreshock radio emission calculated at an observer Olocated a distance 2as upstream from each planet along theSun–planet line, where as is the bow shock standoffdistance, listed in Table 2. The radio fluxes are calculatedfor the nominal solar wind conditions listed in Table 1,except for the case of Mercury, where the fluxes arecalculated for qbu = 90� and 130� (lower values). Trianglesand squares correspond to fp and 2fp radio fluxes,respectively.
Figure 5. Planetary foreshock radio fluxes calculated at afixed observer location 0.1 AU upstream of each planet,along the Sun–planet line, for the nominal solar windconditions listed in Table 1, except for Mercury, where wehave used qbu = 90� and 130� (lower values). Triangles andsquares correspond to fp and 2fp radio fluxes, respectively.
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owing to the large physical sizes of the obstacle, bow shock,and foreshock. It is not, however, immediately obviouswhether the larger physical size can compensate for thedecreases in volume emissivity caused by the heliocentricdeclines in TRM e and nRM e. The results in Figure 4 predictthat the 2fRM p radio flux at an observer O located a distanceaRM s upstream of the Jovian bow shock is almost threeorders of magnitude lower than that for Earth, while thepredicted fRM p radio flux is comparable to that for Earth.This suggests that the Jovian foreshock, despite its largevolume, is not as strong a source of radio emissions asEarth’s foreshock is at an observer distance scaled for theshock’s size. Since the fluxes calculated at X = 2aRM s
effectively scale out the effects of obstacle size and shockgeometry, the relatively low levels of Jovian foreshockfluxes at O can be attributed to the heliocentric decline inTRM e and nRM e. In absolute terms, however, the Jovianforeshock is predicted to be the most powerful source ofradio emissions, as indicated by the fluxes calculated at afixed location 0.1 AU, as plotted in Figure 5. Thus we canconclude that the physical size of Jupiter’s foreshock sourcevolume is indeed sufficiently large to compensate for thelower upstream values of TRM e and nRM e and produceintrinsically strong radio emissions.[29] A similar conclusion applies to the remaining outer
planets. The foreshock source region predicted for Saturn(c.f. Figure 3) also has a large volume, but the radio fluxesat O (which are approximately scale-free) are significantlylower than those for Jupiter (c.f. Figure 4), owing to thelower values of TRM e and nRM e. When the absolute fluxes arecalculated (Figure 5), on the other hand, the Saturnianforeshock radio emissions are predicted to be the thirdstrongest, after Jupiter’s and Earth’s. The foreshock sourceregions predicted for Uranus and Neptune are both verysimilar, owing to the similarity in physical size and bowshock geometry of these outer planets. The upstream(approximately scale-free) radio fluxes at O (Figure 4) areslightly lower for Neptune than for Uranus, and this is dueto the heliospheric decline in TRM e and nRM e. The absolute2fRM p radio fluxes calculated at X = 0.1 AU are the weakestof all the planetary foreshock 2fRMp fluxes predicted here.[30] An interesting prediction evident in Figure 5 is that
the fRM p radio fluxes should become increasingly compara-ble with and then exceed the 2fRM p flux as the heliocentricdistance increases. Indeed, for Neptune, our results predictthat the fRM p source should be an order of magnitudestronger than the 2fRM p source. This effect can be attributedto the dependence of the nonlinear processes producing theradio emission on the ratio TRM i/TRM e, which in turndepends on the assumed heliocentric variation of TRM i andTRM e. Thus we expect our results for Uranus and Neptunewill change if the TRM e profile at large heliocentric distancesactually increases, rather than continues to decrease mono-tonically, as is currently assumed (see Figure 1).[31] Finally, note that the 2fRM p foreshock source regions
of all the outer planets are distinctly wider in the directionperpendicular to the IMF than those of the inner planets (c.f.Figure 3). This effect can be understood as follows. As TRM e
decreases with heliospheric distance, there are fewer back-streaming electrons with very high parallel speeds, andan increasing fraction of backstreaming electrons withparallel speeds comparable to the perpendicular drift speed
vRRMM d = uRM sw sin qbu (which also slightly increases withheliospheric distance because the Parker spiral angleapproaches 90�). The fraction of backstreaming electronsthat can drift deeper into the foreshock thus increases withincreasing heliocentric distance, thereby increasingly bias-ing the source regions deeper in the foreshock.
4. Detectability of Radio Emissions
[32] The potential detectability of planetary foreshockradio emissions can be assessed by first calculating thepredicted radio fluxes at appropriate observer locations andthen comparing these fluxes to specific instrument sensitiv-ity thresholds. From the analysis in the previous section, wecan conclude that in absolute terms, and under nominalsolar wind conditions, the predicted trend in intrinsicstrength of foreshock emissions is (from strongest to weak-est): Jupiter, Earth, Saturn, Venus, Mercury, Mars, Uranus,Neptune. However, this is based on the total radio fluxescalculated at a fixed observer positioned at 0.1 AU fromeach planet. More generally, the flux increases as anobserver moves arbitrarily close to the source region. Thusin this section, we examine how close an observer (orspacecraft) would have to approach each planet in orderfor the predicted radio fluxes to reach sufficiently highlevels to be detectable by spacecraft instruments.[33] We emphasize that the predicted radio fluxes can
vary substantially with changes in solar wind conditions andthat the results presented here are for nominal conditions,except for Mercury, where we have used qbu = 90�. Theinfluence of variable solar wind conditions on terrestrialforeshock radio emissions was studied by Kuncic et al.[2004]. It was found that 2fRM p radio emission is particularlysensitive to TRM e and qbu, while fRM p emission is sensitive tothe ratio TRM i/TRM e. Similar trends are expected for radioemissions from other planetary foreshocks. Furthermore, acomparison of our results for terrestrial foreshock emissionsagainst Geotail data (Z. Kuncic et al., manuscript in prep-aration, 2005) suggests that our model may be underesti-mating the actual 2fRM p radio flux by as much as a factor of10. Thus our assessment of the detectability of planetaryforeshock radio emissions is likely to be a conservative one.On the other hand, we do not include thermal noise levels orcontinuum emission when calculating the detection thresh-olds. These effects will make it more difficult to unambig-uously identify fRM p and 2fRM p emission signatures in realinstrument data.
4.1. Predicted Radio Fluxes
[34] Figure 6 shows the variation in the fRM p and2fRM p fluxes within 200 RRM p upstream and downstreamfrom each planet, analogous to a spacecraft flyby. The1/XRRMM obs
2 decline in radio fluxes is clearly evident in thewings of the profiles for each planet. The slight differencesin the profiles in Figure 6 are due to the foreshock locationalong the Sun–planet line varying with each planet, and theforeshock being almost symmetric about the Sun–planetline for Mercury and the outer planets but not for Venus,Earth, and Mars. The sharp peak in the 2fRM p flux profilefor Earth is a resolution effect; in principle, we could expectsimilar sharp peaks in all the profiles, mimicking direct, insitu measurements at a localized source point.
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[35] As the terrestrial foreshock 2fRM p radio emissionshave been detected by a variety of different spacecraftwithin 200 RRRMME, Figure 6 suggests that the foreshocksof virtually all the planets should produce 2fRM p emissiondetectable by similar spacecraft instruments within a finitedistance of the source. For Mercury, in particular, thepredicted 2fRM p flux within 100 RRMM is comparable to thatof Earth within 200 RRRMME. For Venus, a spacecraft wouldhave to approach within 50 RRM
V in order to detect 2fRM p
foreshock radio emissions at a level comparable to thatwithin 200 RRRMM E of Earth. For Mars, a spacecraft flybywould have to be closer still, within 30 Martian radii. ForJupiter and Saturn, a spacecraft would have to approachwithin �10 RRM p to measure radio fluxes at a levelcomparable to the terrestrial 2fRM p flux at 200 RRRMME. ForUranus and Neptune, the predicted radio fluxes are toolow to be comparable to the terrestrial emissions within200 RRRMM E (although technically, the flux can be infinitelylarge if the observer location coincides with a source point).The detectability of these predicted emissions by specificspacecraft instruments is discussed next.
4.2. Comparison With Instrument Thresholds
[36] Figure 7 shows the sensitivity thresholds of plasmawave and radio instruments on board past and presentspace missions. We now describe how these thresholds arecalculated.[37] To compare the predicted radio flux levels (in RRMMW
m�2) with noise thresholds of various spacecraft plasma andradio instruments, it is necessary to first convert the spectralvoltage Vf collected by an antenna (in RRMM V Hz�1/2) to thespectral field Ef (in RRMM V m�1 RRMM Hz�1/2) in the plasma,as follows:
Ef ¼Vf
LRRMMa
CRRMMa
CRRMMa þ CRRMMb
!�1
: ð8Þ
Here, LRRMM a is the antenna length, and CRRMM a and CRRMM b
are the effective antenna and base capacitances [Manning,2000]. The conversion to a total flux is then obtained bydividing Ef
2 by the effective impedance and multiplying bythe bandwidth Df:
F ¼ e� E2f Df n c; ð9Þ
where n is the refractive index. In the following calculations,we use n = 0.05 for f = fRM p and n = 0.866 for f = 2fRM p. Forcases where the effective capacitance due to antenna–plasma coupling was not found in the literature, we assumeERRMM f ’ Vf /LRRMM a. In some cases, the instrument noiselevel is given directly in the literature as Ef.4.2.1. Mercury[38] A key result of our theoretical work is the prediction
of strong foreshock radio emissions from Mercury when theIMF orientation is close to perpendicular with respect to thesolar wind velocity. This potentially provides a definitivetest for our model, as well as a key observational issue forspacecraft missions.[39] Unfortunately, there were no electric field instru-
ments on board Mariner 10, which made flybys ofMercury (and Venus) during 1974–1975. (The Hermeanbow shock wave phenomena reported by Fairfield andBehannon [1976] were deduced by a power spectrumanalysis of Mariner 10’s magnetic field data.) Similarly,the MESSENGER spacecraft, launched in March 2004,will not have a radio and plasma wave instrument. Thusthe comparison of our theoretical predictions for Mercuryagainst spacecraft data will have to wait until the Bepi-Colombo mission. The plasma wave investigation plannedfor this mission will include electric field measurements,with an anticipated sensitivity of�10�18 RRMM V2m�2Hz�1
at several 10 RRMMs kHz (H. Matsumoto, private communi-cation, 2005). This will be sufficient to detect our predicted
Figure 6. Predicted planetary foreshock radio fluxes calculated at observer locations within 200 Rp
upstream and downstream of each planet, along the Sun–Planet line in the ecliptic plane. The solid anddashed lines represent 2fp and fp fluxes, respectively.
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2fRM p emissions, but the spacecraft will not be ready forlaunch before 2012, with first observations in 2016.4.2.2. Venus[40] The scientific payload of the Pioneer Venus Orbiter,
which arrived at Venus in December 1978, included anelectric field detector (OEFD). The signals were processedwith a four-channel spectrum analyzer with a 30% band-width and a nominal noise level of Ef
2 ’ 3 � 10�13 RRMM V2
m�2 Hz�1 at 30 kHz [Scarf et al., 1980]. From (9), thiscorresponds to a flux threshold of F ’ 4 � 10�13 RRMM Wm�2, which is well above the peak radio flux levelspredicted by our model for fRM p emission, as indicated inFigure 6. Note that even with improved sensitivity andhigher resolution, the instrument would have been incapableof detecting 2fRM p emission, since the highest frequencybandpass channel was at 30 kHz, which approximatelycorresponds to the local upstream electron plasma frequencyat Venus (see Table 1).[41] A flyby of Venus was also made by Galileo in 1990.
The Plasma Wave Subsystem (PWS) instrument on thisspacecraft included a 6 m dipole antenna capable ofmeasuring electric fields down to a noise level of Ef ’15 RRMM nV m�1 Hz�1/2 at f ’ 10 kHz, and a widebandreceiver with a spectral resolution Df ’ 197 Hz in the50 RRMM Hz � 80 RRMM
kHz passband [Gurnett et al.,1992]. Assuming the noise level is approximately thesame at f ’ fRM p ’ 36 kHz and f ’ 2fRM p upstream fromVenus, this corresponds to flux sensitivities of F ’ 6 �10�18 RRMM W m�2 for fRM p emission, and F ’ 1 �10�16 RRMM W m�2 for 2fRM p emission. A comparisonwith the theoretical predictions in Figure 6 indicates that thePWSwas potentially capable of detecting both fRM p and 2fRM p
emission within �20 RRMV. Galileo’s closest approach was
within a few RRMVof Venus, but its trajectory was somewhatunusual: it approached Venus from the downstream region,and skimmed the bow shock, crossing it several times in thequasi-parallel, low MRMA regions. This may explain why nodetections of 2fRM p emissions were reported.[42] Two flybys of Venus were also made by Cassini in
1998 and 1999, which is equipped with a Radio and PlasmaWave Science (RPWS) instrument consisting of three elec-tric field antennas and a wideband receiver (WBR) with apassband 0.8–75 kHz appropriate for Venusian fRM p and2fRM p emissions, with spectral resolution Df ’ 109 Hz[Gurnett et al., 2004]. The in-flight noise level [see Gurnettet al., 2004, Figure 24] is Ef
2 ’ 3 � 10�17 RRMM V2 m�2
Hz�1 in the range of frequencies considered here (seeGurnett et al. [2004] and Zarka et al. [2004] for informationon effective antenna length and capacitance). Using (9), thisimplies WBR flux limits of F ’ 4 � 10�19 RRMM W m�2 forf ’ fRM p, and F ’ 8 � 10�18 RRMM W m�2 for f ’ 2fRM p.According to Figure 6, our results predict that the CassiniRPWS/WBR was capable of detecting Venusian fRM p
emission within ’40 RRMV and 2fRM p emission within�20 RRM V . Although no such detections have beenreported in the literature, this prediction clearly warrantsfurther scrutiny of the data. Finally, although the VenusExpress mission is scheduled for launch in late 2005, itwill not be equipped with a plasma wave instrument.4.2.3. Earth[43] Multiple spacecraft have detected terrestrial 2fRM p
and, to a lesser extent, fRM p radio emission. Here, wecompare our theoretical results against observations byISEE-3 and Wind. A comparison of our results againstobservations by ISEE-1 and Geotail has been presentedelsewhere [Kuncic et al., 2002], and a more detailed
Figure 7. Radio flux sensitivity thresholds for various plasma and radio instruments on past and presentspace missions. Solid and dotted lines correspond to noise levels for 2fp and fp emission, respectively,where fp is the local value of the solar wind electron plasma frequency upstream of the planet targeted byeach mission. In the case of Voyager, the PWS noise levels are a lower limit estimated at Jupiter; in thecase of Galileo, the PWS noise levels are approximately relevant for observations at both Venus andJupiter; in the case of Cassini, the WBR noise levels refer to observations at both Jupiter and Saturn (seetext for details).
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comparison between our results and Geotail data in partic-ular will be forthcoming (Z. Kuncic et al., manuscript inpreparation, 2005).[44] ISEE-3 was in Earth orbit at �235RRRMME
during1978–1981. The spectral field sensitivity of the longelectric dipole antenna associated with the Plasma WaveInvestigation (PWI) on this spacecraft was Ef ’ 6 �10�9 RRMM V m�1 Hz�1/2 at f ’ fRM p ’ 25 kHz, and Ef ’3 � 10�9 RRMM V m�1 Hz�1/2 at f ’ 2fRM p, and theanalyzer bandwidth was Df ’ 0.15 f [Scarf et al., 1978].From (9), this corresponds to flux thresholds of F ’ 2 �10�17 RRMM W m�2, and F ’ 2 � 10�16 RRMM W m�2 atf ’ fRM p and f ’ 2fRM p, respectively. According to ourtheoretical results in Figure 6, the ISEE-3 PWI should nothave been capable of detecting fRM p or 2fRM p radio emissionunder normal solar wind conditions from its location inorbit around Earth. Indeed, terrestrial foreshock radioemission has only been detected by the ISEE-3 SBH radioexperiment [Hoang et al., 1981; Lacombe et al., 1988]. Forthe Df ’ 3 kHz radiometer bandpass on SBH, the spectralvoltage sensitivity was Vf ’ 5 RRMM nV Hz�1/2 [Knoll etal., 1978]. This implies Ef ’ 0.06 RRMM nV m�1 Hz�1/2
for the LRRMM a ’ 90 m antenna (no information about theeffective capacitance was reported by Knoll et al. [1978]).This gives radio flux thresholds of F ’ 1 � 10�21 RRMM
W m�2 at f = fRM p ’ 25 kHz, and F ’ 2 � 10�20 RRMM Wm�2 at f = 2fRM p. According to Figure 6, our results concurwith the positive detection of terrestrial foreshock radioemission by the ISEE-3 SBH radio receiver.[45] The Wind WAVES experiment is capable of detect-
ing terrestrial foreshock radio emissions with either itsThermal Noise Receiver (TNR) or its radio receiverRAD1. Both instruments have similar sensitivities (Vf ’7 RRMM nV Hz�1), but the TNR has slightly better spectralresolution (Df/f ’ 4.4%); the effective total capacitanceis CRRMM a/(CRRMM a + CRRMM b) ’ 0.86 for the LRRMM a ’ 50 melectric dipole antenna [Bougeret et al., 1995]. From (8), thisimplies a spectral field sensitivity of Ef ’ 0.16 RRMM nV m�1
Hz�1/2. Using (9), this converts to total flux thresholds of F’4 � 10�21 RRMM W m�2 for f’ fRM p ’ 25 kHz, and F ’ 1 �10�19 RRMMW m�2 for f ’ 2fRM p. Our theoretical resultsshown in Figure 6 suggest that the Wind TNR is not onlyreadily capable of detecting 2fRM p emission within200RRRMME of Earth but is also sufficiently sensitive toobtain a high signal-to-noise detection of fRM p radioemission, which is usually more difficult to detect be-cause of confusion with electrostatic waves at f ’ fRM p.4.2.4. Mars[46] The Phobos-2 spacecraft crossed the Martian bow
shock several times during its 2-month mission in early1989. The Plasma Wave System (PWS) observed intenseelectrostatic wave oscillations at the local electron plasmafrequency, typically around 15–20 kHz, down to levels ofEf � 1 mRRMM V m�1 Hz�1/2 [Trotignon et al., 2000].Although the full details of this instrument are unavailable(see Grard et al. [1989] for a description), we can estimatethe fRM p and 2fRM p radio flux limits using the observationalEf limit above and an arbitrary spectral resolution of Df ’1 kHz. This gives F ’ 1 � 10�13 RRMM W m�2 for f ’fRM p, and F ’ 2 � 10�12 RRMM W m�2 for f ’ 2fRM p .Clearly, from Figure 6, we would not expect any foreshockradio emissions to have been detected by the Phobos-2
PWS, unless the combined instrument sensitivity andspectral resolution were at least four orders of magnitudebetter than we have crudely estimated.4.2.5. Outer Planets[47] The first plasma and radio wave survey of the outer
planets was made by the Plasma Wave System (PWS) onboard the two Voyager spacecraft, which encounteredJupiter in 1979, Saturn in 1980–1981, Uranus in 1986,and Neptune in 1989. The spectrum analyzer on the PWSwas built with an electric field sensitivity threshold thatdecreases slightly with frequency, ranging from 1.7 m RRMM
V m�1 at 10 Hz to 0.3 m RRMM V m�1 at 56 kHz [Scarf andGurnett, 1997]. Since the predicted fRM p and 2fRM p emis-sions from the outer planets are in the range 1–10 kHz (seeTable 1), the lower limit of E 0.3 m RRMM V m�1 for theelectric field threshold can be used in (9) to obtain equiv-alent minimum radio flux thresholds of F 1 � 10�17 RRMM
W m�2 for fRM p emission, and F 2 � 10�16 RRMM W m�2
for 2fRM p emission. These values are indicated in Figure 7,and a comparison with Figure 6 immediately indicates thatthe predicted flux levels of both fRM p and 2fRM p foreshockemissions for almost the outer planets fall below thethreshold for detectability by Voyager’s PWS. The excep-tion is for Jupiter, where our results predict a marginaldetection of fRM p emission within a few RRRM MJ
of theforeshock.[48] Jupiter’s space plasma environment has been exten-
sively studied by the dedicated spacecraft missions Ulyssesand Galileo. The Ulysses Unified Radio and Plasma wave(URAP) experiment included a Radio Astronomy Receiver(RAR) with a spectral voltage sensitivity Vf ’ 30 RRMM nVHz�1/2 at 10 RRMM kHz [Stone et al., 1992], which isapproximately equal to the local 2fRM p frequency upstreamof Jupiter (see Table 1). For the 72.5 RRMM m antenna and0.75 RRMM kHz bandwidth, this is equivalent to a fluxsensitivity of F ’ 3 � 10�19 RRMM W m�2 (no informationwas found in the literature on effective antenna capaci-tance). Our results for Jupiter in Figure 6 indicate that theJovian 2fRM p foreshock radio emission should have beendetectable by the Ulysses RAR within �50 RRRM MJ
of thebow shock. Although no such detection has been reported inthe literature, there does appear to be some tentativeevidence in the URAP data (available at urap.gsfc.nasa.gov/www/data_access.html) indicating that Jovian 2fRM p
radio emission may have been detected by the RAR duringa bow shock crossing in mid-February 1992 in whichJupiter’s intense magnetospheric low-frequency continuumemission was substantially suppressed (R. MacDowell,private communication, 2004). It is emphasized that confu-sion with escaping continuum radiation can be a majorproblem for identifying Jovian fRM p and 2fRM p radiation. Afull analysis of this Ulysses RAR data, and a more detailedcomparison with our theoretical calculations is deferred tofuture work.[49] The flux sensitivities of the Galileo PWS, calculated
in section 4.2.2, are F ’ 6 � 10�18 RRMM W m�2 forfRM p emission, and F ’ 1 � 10�16 RRMM W m�2 for2fRM p emission. According to Figure 6, our theoreticalresults predict that Jovian foreshock radio emissions shouldnot have been detectable by the Galileo PWS, except possiblyemission at fRM p within a few RRRM MJ
of the foreshock. Nosuch detections have been reported in the literature.
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[50] The first encounter with Saturn since Voyager hasrecently been made by the Cassini spacecraft, whichalso made a flyby of Jupiter in 2000–2001. Both thehigh-frequency receiver (HFR) and the wideband receiver(WBR) include passbands appropriate for Jovian and Sat-urnian fRM p and 2fRM p emission, which fall in the range 1–10 kHz (see Table 1). However, the 0.8–75 kHz WBRpassband has better spectral resolution (with Df ’ 109 Hz)than the 3.5–16 kHz HFR passband, which has Df/f ’ 10%.The WBR is thus potentially more capable of detectingJovian and Saturnian narrowband foreshock radio emis-sions. The in-flight noise level [see Gurnett et al., 2004,Figure 24] is Ef
2 ’ 1 � 10�16 RRMMV2 m�2 Hz�1 at f ’
5 kHz and Ef2’ 5� 10�17 RRMM V2m�2Hz�1 at f’ 10 kHz.
Using (9), this implies WBR flux limits of F ’ 1 �10�18 RRMMWm�2 at f’ 5 kHz, F’ 1� 10�17 RRMMWm�2
at f ’ 10 kHz. These estimates are relevant for both theJovian and Saturnian foreshock emissions. Our theoreticalresults in Figure 6 indicate that during Cassini’s Jupiterflyby, the WBR was potentially capable of detecting fRMp
emission, and of marginally detecting 2fRM p emission, butonly within the immediate vicinity of the foreshocksource region. Unfortunately, Cassini’s closest approachto Jupiter was �135 RRRM MJ
, and our results indicate that itwould have been out of range to detect 2fRM p emission andunlikely to have detected fRM p emission. Indeed, no suchdetections have been reported, even during periods when theintense low-frequency continuum was not present [see, e.g.,Zarka et al., 2004]. Similarly, our results predict that theSaturnian foreshock radio emissions are probably too weakto be detected by the Cassini WBR, except under unusualcircumstances. A caveat to this conclusion is that theheliocentric profile TRMe
/ d�0.6 assumed here may actuallybe flatter at or beyond Saturn, in which case the 2fRM p fluxeswould be higher than have been predicted here.
5. Conclusion
[51] We have presented a generalized theoretical modelfor the production of radio emissions within the foreshockregions upstream from planetary bow shocks, by directanalogy with an existing model we developed for terrestrialforeshock radio emissions. This model fully takes intoconsideration the effects of heliospheric variation in solarwind parameters, as well as the dependence on variations inobstacle size and bow shock geometry. We have presentedresults showing the predicted 2fRM p foreshock source regionfor each of the planets and the predicted fRM p and 2fRM p
radio fluxes at a distance equal to the standoff distance fromthe bow shock nose. These estimates approximately scaleout the dependence of the emission on shock size andgeometry. We have also calculated the radio fluxes at afixed, absolute observer location, 0.1 AU upstream fromeach planet, as well as heliocentric profiles of the predictedradio fluxes within 200 planetary radii of each planet,analogous to a spacecraft flyby.[52] One key theoretical prediction resulting from this
work is that Mercury’s foreshock can be a particularlystrong local source of radio emissions. This can be attrib-uted to the high upstream electron temperature, whichstrongly influences the theoretically calculated 2fRM p radioemissivity. This prediction will be testable with the forth-
coming space mission BepiColombo. Our results alsosuggest that Jovian foreshock radio emissions are intrinsi-cally the strongest of all planetary foreshock emissions andshould have been potentially detectable by the radio instru-ments on Ulysses. We are following up unpublished datathat suggests such a detection was in fact made by theUlysses RAR instrument. The second intrinsically strongestsource of radio emissions is the terrestrial foreshock. Ourmodel predicts that all the other planetary foreshocks shouldalso produce finite and potentially significant levels of fRM p
and 2fRM p emissions, with fRM p emission dominating beyondSaturn.[53] Finally, our results indicate that the lack of direct
observational evidence for nonterrestrial (and non-Jovian)foreshock radio emissions may be attributed, at least in part,to the inadequate sensitivity and spectral resolution ofspacecraft instruments, rather than to the intrinsic weaknessof the emission itself. This certainly appears to be the casefor foreshock radio emissions from all the inner planets.Another problem is separation of foreshock radiation frommagnetospheric continuum radiation, particularly for Jupiterand the outer planets.
[54] Acknowledgments. This research was funded by the AustralianResearch Council. The authors thank the referees for valuable commentsthat helped to improve the paper.[55] Shadia Rifai Habbal thanks Jan Merka and Yasumasa Kasaba for
their assistance in evaluating this paper.
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�����������������������I. H. Cairns and Z. Kuncic, School of Physics, University of Sydney,
