In situ and distant observations of the ultraviolet footprint of the moon Callisto by the Juno spacecraft

UV maps

The full mapping of the UV auroral emission above the poles of Jupiter is achieved by co-adding consecutive Juno-UVS measurements obtained between 68 and 210 nm. Each measurement consists of a 30-s scan of the auroral emissions, which corresponds to at least one spin of the Juno spacecraft. False shade maps spotlight the photon quantity recorded between 145 and 165 nm, which is a diagnostic of the depth of the auroral emission and the electron attribute vitality. This outcomes from the truth that photons are preferentially absorbed at wavelengths shorter than 140 nm by methane, situated deeper within the Jovian environment. The UV photons measured by Juno-UVS are mapped onto Jupiter’s latitude/longitude grid, assuming they’re emitted at 900 km-altitude above Jupiter’s 1 bar-level, which corresponds to the imply altitude of the moon-UV induced aurora⁷². The UV brightnesses had been calculated utilizing the tactic offered by ref. ⁷³. This consists first in integrating the photons recorded between 115–118 nm and 125–165 nm. The latter is then multiplied by 1.82 to extrapolate the brightness over the entire H₂ and Lyman-α emissions, i.e. within the 75–198 nm vary, utilizing a H₂ artificial spectrum from ref. ⁷⁴. This artificial spectrum was simulated by accounting for the Lyman, Werner and Rydberg band programs of H₂, assuming 300 Okay for the rotational and vibration H₂ temperatures, and excited by a mono-energetic electron beam of 100 eV. The spectrum was simulated as non-absorbed by the Jovian stratospheric hydrocarbons, and self-absorption was not accounted for.

Rotation charge

Consecutive spin-by-spin photos from the Juno-UVS instrument are used to derive the rotation charge of the recognized spots. In every body, the spot longitude ϕ_SIII and latitude λ_SIII are retrieved utilizing a polar grid superimposed on the UVS observations. The location of the spot is then magnetically back-traced onto the orbital airplane of Callisto. By investigating consecutive measurements, the equatorial longitude evolution of the spot as a perform of time may be deduced and in contrast with Callisto’s angular velocity within the S_III reference body. This latter is discovered utilizing Callisto’s synodic interval ({P}_{{Syn}}^{{Cal}}=({P}_{{Jup}}occasions {P}_{{Cal}})/({P}_{{Cal}}-{P}_{{Jup}})=10.177,h) after which derived utilizing dλ/dt = 360°/P_syn^Cal = (0.0098 area deg .{s}^{-1}.)

Estimate of the electron density at Callisto

Using the longitude separation of the Callisto TEB and MAW spots recognized and easy geometric issues, an estimate of the plasma density close to Callisto may be made.

We first show that if there isn’t any plasma dense sufficient to decelerate the propagation of Alfvén waves, the TEB and MAW spots (if current) ought to virtually be superimposed. More exactly, the equatorial longitude separation (varDelta lambda) is calculated as:

with ({omega }_{{Callisto}}=0.0098 area deg.{s}^{-1}) the rotation charge of Callisto, and (varDelta t={t}_{{TEB}}-{t}_{{MAW}}). The journey occasions ({t}_{{TEB}}) and ({t}_{{MAW}}) related to the propagation of Alfvén waves between Callisto and the TEB and MAW spots within the northern hemisphere are given by:

with L_N and L_S the size of the magnetic subject traces from Callisto to Jupiter within the Northern and Southern hemisphere, respectively, c the pace of sunshine in vacuum and (v=sqrt{frac{2E}{{m}_{e}}}) the classical electron pace. The size of the magnetic subject traces are decided utilizing the JRM33 + KK2005 magnetic subject mannequin (see ref. ⁷⁵ and “Magnetic mapping” in Methods).

In the current case, Callisto is situated at jovigraphic latitude ({theta }_{{S}_{{III}}}=-0.24^circ) and at an equatorial longitude ({lambda }_{{III}}=306.93^circ). The attribute vitality of the electron is taken as (E={m}_{e}{v}^{2}/2=10) keV. Therefore, the equatorial longitudes for northern TEB and MAW spots needs to be λ_TEB = 306.17° and λ_MAW = 306.86°, respectively. Therefore, the separation between the MAW and TEB spots is Δλ = 0.69° within the case the place there isn’t any plasma within the equatorial airplane of the magnetosphere.

Now contemplating that there’s a plasma dense sufficient to decelerate the propagation of Alfvén waves, then inside this plasma sheet (PS) the group velocity ({v}_{A}) of the Alfvén waves is:

with (B) the native magnetic subject energy, (rho) the native plasma mass density, and ({mu }_{0}) the vacuum permeability. Outside of the plasma sheet, the place the plasma density is low, we take into account the Alfvén pace to be the pace of sunshine (c). Therefore, the journey time t_TEB and t_MAW related to the propagation of the Alfvén waves from Callisto to the northern spots at the moment are:

with L_{S in PS}, L_{N in PS} the size of the northward and southward magnetic subject traces within the plasma sheet, L_{S out PS}, L_{N out PS} the size of the northward and southward magnetic subject traces exterior of the plasma sheet. L_N = L_{N in PS} + L_{N out PS} and L_S = L_{s in PS} + L_{S out PS} symbolize the entire size of the magnetic subject traces from Callisto to Jupiter’s northern and southern auroral areas, respectively. Note {that a} tilt (theta) of the Alfvén wings, relying on the Mach Alfvén quantity ({M}_{A}) as (theta ,={atan}({M}_{A})), exists and will increase ({L}_{{S; in; PS}}) and ({L}_{{N; in; PS}}). ({M}_{A}) is dependent upon the Alfvén pace ({v}_{A}) and subsequently on the plasma density (rho). An uncertainty issue (varDelta {L}) will subsequently be taken on the lengths ({L}_{{S; in; PS}}) and ({L}_{{N; in; PS}}), which will probably be propagated to calculate an uncertainty on the worth of (rho).

The main constraints are the place of the UV footprint and their related equatorial longitudes ({lambda }_{{III}}). In the current examine, ({lambda }_{{TEB; noticed}},=,303.05^circ,,{lambda }_{{MAW; noticed}},=,297.7^circ), subsequently (Delta {lambda }_{{noticed}},=,5.35^circ ,.)

Using these constraints and the earlier formalism, we estimate the plasma mass density as follows:

1. 1.

   We first assume the PS to be aligned with the centrifugal equator, i.e., at (theta=,3.1^circ) (within the ({lambda }_{{III}},=,204.2^circ) course) of the jovicentric equator. We then assume a plasma sheet top scale (H), which provides the values of ({L}_{{S; in; PS}},,{L}_{{S; out; PS}},,{L}_{{N; in; PS}}) and ({L}_{{N; out; PS}}).

2. 2.

   We assume a plasma density ({rho }_{0}) on the middle of the PS and we decide (rho)_i the density alongside the magnetic subject line within the PS utilizing the next density profile equation⁷⁶:

   $${rho }_{i}={rho }_{0} , exp left(-sqrt{frac{{({r}_{i}-{r}_{0})}^{2}+{{z}_{i}}^{2}}{H}}proper)$$

   (5)

   with ({r}_{0}) the equatorial diameter set to Callisto’s orbital distance, i.e., ({r}_{0}=26.33space {R}_{J},,{r}_{i}=sqrt{{{x}_{i}}^{2}+{{y}_{i}}^{2}}) the equatorial radial distance, ({z}_{i}) the altitude above the equator of the place of the measurement level (i), and H the plasma sheet scale top.

3. 3.

   We decide the Alfvén pace velocity ({v}_{A}), primarily based on the calculated ({rho }_{i}) and the magnetic subject amplitude ({B}_{i}) utilizing the JRM33 + KK2005 magnetic subject mannequin. From that, we get hold of the values of ({t}_{{TEB}},{t}_{{MAW}},{lambda }_{{TEB}},{lambda }_{{MAW}}) and subsequently (varDelta {lambda }_{{calculated}}).

4. 4.

   By making use of this technique on totally different values of ({rho }_{0}), we decrease (|varDelta {lambda }_{{calculated}}-varDelta {lambda }_{{noticed}}|).

5. 5.

   We then run the identical above calculations for various values of the size top (H) to reduce (|{lambda }_{{MAW; calculated}}-{lambda }_{{MAW; noticed}}; and; {lambda }_{{TEB; calculated}},-,{lambda }_{{TEB; noticed}}) .

Table 2 summarizes the outcomes. The finest end result offers MAW and TEB footprint equatorial longitudes ({lambda }_{{MAW; calculated}}=297.70^circ) and ({lambda }_{{TEB; calculated}}=303.05^circ .) This is obtained for a plasma sheet scale top (H=0.94,{R}_{J}), and a density ({rho }_{0}=3.6pm 0.5times {10}^{-27}) kg.cm^-3, which corresponds to a density at Callisto ({rho }_{{at; Callisto}}=2.3pm 0.3times {10}^{-27}) kg.cm^-3. Note that the uncertainties are primarily based on the lean angle of the Alfvén wings, which will increase the size of the magnetic subject line within the plasma sheet as (L={L}_{{in; PS}}occasions varDelta L) with (varDelta L=1/cos theta=1.14), with (theta={atan}({M}_{A})) for ({M}_{A}=0.55). We subsequently take the imply worth between the outcomes with (varDelta L=1) and (varDelta L=1.14)

Using the plasma distribution mannequin of ref. ⁷⁷, we estimate that at Callisto’s orbital distance and on the centrifugal equator, the plasma consists of 54.7% sulfur ions (9.9% S⁺, 35.1% S⁺⁺, 9.7% S⁺⁺⁺), 26.6% oxygen ions (21.6% O⁺, 5% O⁺⁺), 12.5 % protons H⁺, and 6.2% sodium ions Na⁺. Given this composition, we calculate that the common ion mass m_imply is 23.3 amu (3.87 × 10^-26 kg) and the common ion cost q_imply is + 1.6q_e. Based on these values, we estimate that the ion density on the middle of the present sheet and at Callisto, given by ({n}^{{ions}}=rho /{m}_{{imply}}), are ({n}_{0}^{{ions}}=0.094pm 0.012) cm^-3 and ({n}_{{at; Callisto}}^{{ions}}=0.060pm 0.008) cm^-3, respectively. We derive the related electron densities utilizing quasi-neutrality assumption, i.e., ({n}^{{electrons}}={q}_{{imply}}{n}^{{ions}}), resulting in ({n}_{0}^{{electrons}}=0.15pm 0.02) cm^-3 and ({n}_{{at; Callisto}}^{{electrons}}=0.095pm 0.012) cm^-3.

Electron vitality flux and attribute vitality

The downward electron vitality flux (mW.m^-2), i.e., the vitality flux precipitating into Jupiter’s environment and inducing aurora, is estimated from Juno-JADE-E measurements of electrons throughout the loss cone. The dimension of the loss cone on the measurement time is estimated by ({sin }^{-1}left({r}^{-3/2}proper)) the place r is the gap from the Juno spacecraft to the middle of Jupiter. Electron differential quantity flux (DNF, [cm^-2.s^-1.sr^-1.keV^-1]) throughout the loss cone is then transformed into vitality flux, EF, by:

the place the summation is carried out on the JADE-E vitality channels, with E and ΔE check with the geometric imply worth and the vitality width of every vitality channel, respectively. The attribute vitality of the downward electrons, EC, is derived utilizing:

with E and ΔE the geometric imply worth and the vitality width of every vitality channel, respectively.

Magnetic mapping

The footpaths of the Galilean moons and the Juno spacecraft are derived by an iterative follow-up of the magnetic subject line, with a relentless step dimension of (1/300,{R}_{J}simeq 240) km between the article of curiosity and Jupiter’s environment. The footpaths are computed at a 900-km altitude above the 1-bar stage, equivalent to the imply altitude of the moon-UV induced aurora⁷⁸. To be sure that the magnetic subject line mapping is as correct as potential, we use two totally different fashions relying on the radial distance of the article to be mapped and the course of the sector line tracing. To derive the footpaths of Io, Europa, Ganymede, and Juno above the auroral areas of Jupiter, i.e. for M < 20, we use the JRM33 + CON2020 mannequin, a mixture of an intrinsic and exterior magnetic subject mannequin primarily based on Juno-MAG knowledge. The footpath of Callisto and Juno M-Shell for M > 20 are inferred with the JRM33 + KK2005 mannequin, because it offers extra correct estimates of the magnetic subject parts close to the orbit of Callisto (Supplementary Fig. 7), within the center, and outer magnetosphere, i.e., r > 20 R_J⁷⁵. The moons’ footpaths are derived by contemplating solely magnetic subject fashions. Consequently, no impact of the propagation time of the waves and particles between the moons and Jupiter’s environment are taken under consideration on this calculation.

The M-Shell parameter is outlined as the gap between Jupiter’s middle and the minimal of the magnetic subject energy alongside the sector line. This latter is computed by an iterative tracing of the magnetic subject traces till the minimal of the magnetic subject energy is reached.

We emphasize that the usage of the JRM33 (13^th-order) mannequin to explain Jupiter’s inner magnetic subject constitutes a serious step ahead within the unambiguous identification of the Callisto footprint reported on this examine. Indeed, such a mannequin permits far more exact and detailed estimates of Jupiter’s magnetic subject than was beforehand potential with the VIP4 (4^th-order) inner magnetic subject mannequin⁷⁹ used within the earlier tentative detections of the Callisto auroral footprint.

Cyclotron Maser Instability and progress charge calculation

Amplification of radio waves can happen via the Cyclotron Maser Instability (CMI) underneath totally different circumstances: (i) the plasma must be tenuous and magnetized to satisfy ({f}_{{pe}}ll {f}_{{ce}}) with f_pe = (frac{1}{2pi }{(frac{{n}_{e}{q}^{2}}{{varepsilon }_{0}{m}_{e}})}^{0.5}) the electron plasma frequency and f_ce = (frac{1}{2pi }(frac{{qB}}{{m}_{e}})) the electron cyclotron frequency, (ii) the presence of scorching, weakly relativistic and unstable electrons usually embedded inside a chilly, distinguished, electron inhabitants. The CMI amplifies waves close to the electron cyclotron gyrofrequency ({omega }_{{ce}}=2,pi {f}_{{ce}}) alongside the resonance equation (omega=frac{{omega }_{{ce}}}{varGamma }+{okay}_{}{v}_{}) the place ω = 2πf is the wave angular frequency, ({varGamma }^{-1}=sqrt{1-frac{{v}^{2}}{{c}^{2}}}) is the Lorentz issue and okay_|| and v_|| are the projection of the wave vector okay and the electron velocity v onto the course of the native magnetic subject. In the (v_⊥, v_||) part area, the resonance equation transposes into the equation of a circle outlined by its middle ({v}_{0}=frac{{okay}_{}{c}^{2}}{{omega }_{{ce}}}) and its radius ({v}_{r}=sqrt{{v}_{.}^{2}-{2c}^{2}Delta omega }) with (Delta omega=(omega -{omega }_{{ce}})/{omega }_{{ce}}).

Waves are amplified every time the wave progress charge computed from the EDF (F) alongside the resonance circle is optimistic. The analytical expression of the expansion charge outcomes from the right-handed extraordinary (RX) mode dispersion equation. The latter is dependent upon the plasma properties^11,80:

the place ({F}_{h}) represents the normalized electron distribution, ({epsilon }_{h}=frac{{omega }_{{ph}}}{{omega }_{{ce}}}) and ({epsilon }_{c}=frac{{omega }_{{computer}}}{{omega }_{{ce}}}) with ({omega }_{{ph}},,{omega }_{{computer}}) the plasma frequency of the cold and hot electrons, respectively.

This equation implies that the CMI free vitality supply lies within the EDF portion the place (frac{partial {F}_{h}}{partial {v}_{perp }}) is optimistic. The progress charge is the integral of the perpendicular gradient of the recent EDF (frac{partial {F}_{h}}{partial {v}_{perp }}) alongside the CMI resonance circle within the velocity area.

To derive the anticipated depth of the amplified wave ({S}_{{Radio}}), we supposed a homogeneous supply of latitudinal extent ({L}_{C}) with a relentless progress charge (gamma). We assumed that the CMI mechanism amplifies galactic noise of depth ({S}_{{Source}}left(proper.{10}^{-19}{W}.{m}^{-2}.H{z}^{-1}) at 10 MHz⁸¹). The achieve (frac{{S}_{{Radio}}}{{S}_{{Source}}}) is then given by: (frac{{S}_{{Radio}}}{{S}_{{Source}}}=exp (frac{4pi {f}_{{ce}}gamma {L}_{C}}{{v}_{g}})).

For the sake of simplicity, we used the worth of the group velocity ({v}_{g}=0.1c)⁸².