Lit Review Cassini Mission

7/31/2019 Lit Review Cassini Mission

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Saturns Magnetosphere

Luqiong Meng - 00513623

Project Code: SPAT-Dougherty-1

Supervisor: M. K. DoughertyAssessor: R. J. Forsyth

October 11, 2010

Abstract

A literature review on the background research and present un-derstanding on Saturn, Saturns dynamic magnetosphere and theinvolvement of its moons. The physics and interaction between thebow shock and magnetopause were discussed in greater detail asit presented an opportunity for further research. The theoreticalmethod for determining the position of the boundaries, and the geo-metric shape of the bow shock and magnetopause was also explored.Data from Cassini and pre-Cassini era were examined for identifica-tion of boundary crossing positions, and to understand the bimodaldistribution magnetopauses boundary position.

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Contents

1 Introduction 3

2 Background Reading 4

2.1 Saturns Rings . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Saturns Moons . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 The Bow Shock and Magnetosheath . . . . . . . . . . 52.3.2 The Magnetopause . . . . . . . . . . . . . . . . . . . 62.3.3 The Magnetotail . . . . . . . . . . . . . . . . . . . . 8

3 Geometric Distribution of Saturns Bow Shock and Mag-

netopause 10

3.1 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . 103.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Conclusion 13

Bibliography 14

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3

1 Introduction

Many groundbreaking discoveries have been made since Cassini entered theorbit of Saturn in June of 2004. It has given us the opportunity to closelystudy its rings, moons and its dynamic magnetosphere in more detail thanever before. The mission has been extended for another seven years - CassiniSolstice Mission, for further investigations of Saturns magnetosphere, Ti-tan and Enceladus as well as other icy moons.

Among the 12 instruments that are equipped on the Cassini orbiter, thefrequently used equipments for the analysis of magnetosphere are the Tech-nique Magnetometer (MAG) is for direct sensing of strength and direction

of magnetic field of Saturn and the Cassini Plasma Spectrometer (CAPS)for measuring the energy and charge particles that the instrument encoun-ters.

Figure 1: Artist impression of the Cassini Orbiter during the Saturn Orbit

Insertion (SOI). SOI is approx. 90min long and it offers the opportunity toclosely observe Saturn and its rings at high resolution. Source: NASA

The study of Saturns magnetosphere will provide us with a deeper under-


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4 2. BACKGROUND READING

standing of the planets interior and how it interacts with the solar wind,

and how the properties observed differ to that of Earth.

2 Background Reading

2.1 Saturns Rings

The Jovian planet has the most extensive planetary ring system - seven ma-jor divisions of rings that consist mostly of icy particles and dust. Amongst

Saturns rings, there are multiple gaps. The Keeler Gap lies within the ARing, and is caused by the moon Daphnis orbit. Whilst other gaps remainunexplained, many gaps are due to orbital resonances of Saturns moons.The moon Enceladus orbits within the E Ring, outermost ring in Saturnsmain ring cluster, and is believed to be a source of icy particles for the ring.

2.2 Saturns Moons

Saturn has 53 moons that are officially named. The most notable and exten-sively researched is Titan, due to its thick complex atmospheric conditionsand the absence of intrinsic magnetic field. Titan orbits mostly within themagnetosphere, along with the absence of significant dipole moment [Nesset al., 1982; Backes et al., 2005], the Kronian magnetospheric plasma hasdirect access to the upper Titan atmosphere.

One of Saturns icy moons, Enceladus (orbits at radius of 3.95Rs [Jia etal., 2010]), has gained particular interest in the scientific world due to itsplasma torus is mainly composed of water group ions [Richardson et al.,1998]. The study from the data that was collected by the Cassini flybys

in 2005 and 2008 has confirmed that the water plum is asymmetric, withextensive emanating jets from the south pole [Waite et al., 2006; Hansenet al., 2006]. As expected, the study [Kivelson et al., 2006] confirmed thatEnceladus is indeed the main source of plasma in E ring, and the massloading affects the surrounding plasma in the magnetosphere .


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2.3. MAGNETOSPHERE 5

2.3 Magnetosphere

2.3.1 The Bow Shock and Magnetosheath

The ionised solar plasma pervades interplanetary space, it controls the sizeof the magnetosphere and the dynamics of its boundaries. Due to the super-sonic speed of solar wind, magnetic field around Saturn deflects the solarplasma around the planet forming magnetosonic shock wave known as abow shock. The bow shock slows the solar wind to subsonic speed so itflows around the magnetosphere in streamline shape. The shock wave isformed in a collionless plasma, where by definition means that the colli-sions between the constituent particles happen so infrequently that they do

not play an important role [Kivelson and Russell, Intro. Space, 1995], andhence making this process irreversible as the state of the medium throughwhich the shock travelled is changed.

Figure 2: A diagrammatic representation of the structure of Saturns magneto-sphere. Featuring the bow shock, magnetosheath, magnetopause and the lobes.Source: NASA

Magnetosheath shown in Figure 2 is the transitory region of space betweenthe magnetopause and the bow shock. According to [Alexandrova and Sauret al., 2008], the Saturns magnetosheath contains shocked and decelerated


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Figure 3: The spectrographs show the magnetic strength and the orientationmeasured by VHM during inbound pass of the SOI orbit. The horizontal axisshows the spacecraft event time (SCET). Also shown are the spacecraft distancefrom Saturn center (range) in Saturn radii (RS); the latitude with respect toSaturns equatorial plane; and the spacecrafts local time with respect to Saturn(SLT) in decimal hours. Bow shock crossings are labeled, and examples of up-stream wave intervals are shown in the bottom panel. Source: Achilleos at el.,2006

the above condition for r will give us the estimated radius,

r 6

2B2

0

0v2, (2.2)

where B0 is the magnetic field strength of planet at r = 0. It has beenmeasured that the magnetic field strength at Saturns equator is 21T[Belenkaya et al., 2006]. As demonstrated on Figure 4, the magnetopauseis closed, i.e. the component of B normal to the boundary is zero.

The statistical techniques for Jupiter were used to analyse the empiricalshape of the magnetopause in [Achilleos et al., 2008], whereby the distri-bution of standoff distance of the magnetopause is a sum of two normaldistributions. The results from Achilleos et al. strongly suggest that theinternal mass loading and loss from the magnetospheric disk could be the


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8 2. BACKGROUND READING

Figure 4: A simple sketch of the magnetosphere in the noon-midnight meridian.Source: W. J. Hughes, Introduction to Space Physics, 1995

underlying reason for this bimodal distribution of magnetopause. As dis-cussed in Section 2.2, the plasma in the magnetopause is mainly ejected byEnceladus.

2.3.3 The Magnetotail

On the nightside of the magnetosphere stretches out into a magnetotail,where the reservoir of energy and plasma are situated.The two magnetotaillobes connects magnetically to polar region, shown in Figure 5. By assumingthat the magnetic flux is conserved between the polar gap and tail lobes,an estimated distance for the radius of the tail can be calculated [ Kivelsonand Russell, 1995] as below,

RT

RS =4B0BT

1

2

sin , (2.3)

where RT and BT are the radius and magnetic field strength of the tail lobe,RS is the radium of Saturn, B0 is the equatorial field strength and is thecolatitude of the equatorward edge of the polar cap.


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Intuitively, one would think that as the incident solar wind pressure in-creases, the flaring tail of magnetopause would decrease to make the tailmore streamline [Arridge et al., 2006]. However the observations showedthe contrary [e.g., Shue et al., 1997], the magnetopause flaring increaseswith the solar wind pressure.

A rare phenomenon occurs when frozen-in-flux criterion breaks down atthe magnetotails, whereby the opposing lobes comes together to reconnect,and hence the energy stored in the magnetic field is broken off as a plas-moid, this process is shown in Figure 5. the magnetic reconnection couldhappen. The condition for flux to be frozen into the field is when the mag-

netic Reynolds number Rm 0uL [Kivelson and Russell, 1995]. Hencewhen Rm >> 1, the magnetotail swells forming an obstacle that is causingbigger resistance to the solar wind, the plasmoid is pinched off carryingaway the reserved energy - process also known as substorm [Mitchell etal., 2005].

Figure 5: A diagram showing the formation of a plasmoid in the magnetotail.Source: D. P. Stern, 2006, A Brief History of Magnetospheric Physics during the

Space Age.


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103. GEOMETRIC DISTRIBUTION OF SATURNS BOW SHOCK AND

MAGNETOPAUSE

3 Geometric Distribution of Saturns Bow

Shock and Magnetopause

Extensive amount of research has been done on the geometric shape andsize of Saturns magnetopause. However the geometric distribution of thebow shock boundary is still not greatly understood, and hence it is an areathat could be explored further.

3.1 Theoretical Models

Currently there are two models for the geometric shape and position of bowshock. The first was constructed by Slavin et al. [1985] using pre-Cassinidata, and the second model was constructed by Hendricks et al. [2005].

Theoretically the shape of a shock wave due to a point object is givenby the Mach cone [ Masters et al., 2008], this is when the abrupt pressuredifference between the solar wind and the magnetosphere forming a shockwave that roughly takes in the shape of a cone. The flaring angle of the

shock wave is dependent on the Mach number M. As the Mach numberincreases, so does the strength of the shock wave formed, and hence theMach cone becomes increasingly narrow and vice versa.

In the study Masters et al., an axially symmetric conic section about thethe solar wind flow direction was used to model the shape of bow shock.The general equation of a conic section is given in the equation below,

r =

L

1 + cos

, (3.1)

where r is the distance from the focus of the conic section to a point on theshock surface, L is the size parameter, is the eccentricity and the focusposition and is the corresponding polar coordinate angle with respect tothe axis of symmetry [Masters et al., 2008].


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3.2. OBSERVATIONS 11

Since the location of magnetopause is determined by the pressure differ-

ent across the boundary, an increase in solar wind pressure will compressthe magnetosheath, and in turn the boundary of magnetopause will re-trieve [Petrinec and Russell, 1993]. The bow shock is expected to behavein a similar manner as the the geometric shape of the bow shock is a directconsequence of magnetopause.

By making the assumptions detailed in Section 3.1 of Masters et al. andafter pressure correction, a new model of conic section was obtained with being (1.05 0.09) which emphasises the hyperbolic nature of the ob-served bow shock. The new best fit conic section takes in the form of below(variables same as Equation 3.1),

r =

L

1 + 1.05cos

. (3.2)

Combining this with the power law gives us a rough estimate of the bowshock position,

RSN = 12.3PSW1

4.3 =L

2.05, (3.3)

where RSN is the same value as r in (3.2), and PSW is the pressure of thesolar wind.

3.2 Observations

Using the method above described in Masters et al., it was found that thenew hyperbolic conic section model fits well. As can be seen from Figure6, the best fit conic section to the crossing distribution after correction isshown in red line which is much better fit than without correction (Figure7 on Masters et al. 2008). The size parameter of the average shock locationshown in Figure 6 is (512)RS, which implies that the average shock standoffdistance is (251)RS. These crossing positions implies that the bow shocklies in between the distance of 18RS to 46RS.

It was shown that the Slavin et al. has a bigger flare, significant differ-ences arised between the this and the new model by Masters et al. model isclearly due to the lack of local time coverage in the pre-Cassini era. Basedon this particular research paper, it is believed that the magnetosphere is


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123. GEOMETRIC DISTRIBUTION OF SATURNS BOW SHOCK AND

MAGNETOPAUSE

Figure 6: Left: The positions of the bow shock crossings used in the construc-tion of the model after the correction for solar wind dynamic pressure variationprojected into the aberrated x-r plane compared to the optimised conic section.Right: A comparison between the locations of the bow shock predicted by thenew empirical model and Slavin et al. model and Hendricks et al. 2005 model.Source: Masters et al. 2008

more compressible than previously predicted by Arridge et al. 2006. Forfuture investigation, it was advised to taken into account of the inertialstresses in the magnetodisc current sheet. With this in mind, further in-vestigation on the distribution of bow shock crossings and how it moves inrelation to the magnetopause would be the right direction to gain a insight-ful understanding of Saturns magnetosphere.


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4 Conclusion

A substantial amount of background reading and research has been done tounderstand the different parts of magnetosphere and its boundaries, suchas the mass loading effect of Enceladus and frozen-in-flux phenomenon thatexcretes energetic plasmoid, all of which will be a solid foundation for myfuture research.

The new empirical model for the Saturns bow shock by Masters et al.[2008] provides a good guideline for the methodology to be used and im-provements to be done. The dynamic environment of the magnetospherewill provide us with more phenomenons and new discoveries. As more data

sample will be available from the extended Cassini mission, the empiricalbow shock model will be constantly revised and a construction of the prob-ably distribution (like the one for magnetopause in Joy et al. [2002]) of theposition of bow shock would provide us with a better understanding of theinteraction between the magnetopause and bow shock.


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14 BIBLIOGRAPHY

Bibliography

Arridge C.S, N. Achilleos, M. K. Dougherty, K. K. Khurana, and C. T.Russell (2006), Modeling the size and shape of Saturns magnetopausewith variable dynamic pressure, J. Geophys. Res. VOL. 111, A11227,doi:10.1029/2005JA011574

Acua, M. H., and N. F. Ness (1980), The magnetic field of Saturn:Pioneer 11 observations, Science, 207, 444446, doi:10.1126/science.207.4429.444.

Alexandrova. O and J. Saur (2008), Alfven vortices in Saturnsmagnetosheath: Cassini observations, GEOPHYSICAL RESEARCHLETTERS, VOL. 35, L15102, doi:10.1029/2008GL034411

Backes, H. et al. 2005 Titans magnetic field signature during the firstCassini encounter. Science 308, 992995, doi:10.1126/science.1109763.

Belenkaya, E.S.; Alexeev, I.I.; Kalagaev, V.V.; Blohhina, M.S.(2006). Definition of Saturns magnetospheric model parame-ters for the Pioneer 11 flyby. Annales Geophysicae 24: 114556.doi:10.5194/angeo-24-1145-2006.

Farris, M. H., C. T. Russell, M. F. Thomsen, and J. T. Gosling(1992), ISEE-1 and -2 observations of the high beta shock, J. Geo-phys. Res., 97, 19,121.

Hansen, C. J., L. Esposito, A. I. F. Stewart, J. Colwell, A. Hendrix,W. Pryor, D. Shemansky, and R. West (2006), Enceladus water vaporplume, Science, 311, 14221425, doi:10.1126/science.1121254.

Jia, Y.D, C. T. Russell, K. K. Khurana, J. S. Leisner, Y. J.

Ma, and M. K. Dougherty, Time-varying magnetospheric environmentnear Enceladus as seen by the Cassini magnetometer, Geophys. Res.Lett. 37 L09203 (2010).

Joy, S. P., M. G. Kivelson, R. J. Walker, K. K. Khurana, C. T.


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magnetopause and bow shock locations, J. Geophys. Res., 107(A10),1309, doi:10.1029/ 2001JA009146.

Master, A., N. Achilleos, M. K. Dougherty, J. A. Slavin, G. B. Hospo-darsky, C. S. Arridge, and A. J. Coates (2008), An empirical model ofSaturns bow shock: Cassini observations of shock location and shape,J. Geophys. Res., VOL. 113, A10210, doi:10.1029/2008JA013276.

Kivelson, M. G., Russel, C. T., (1995), Introduction to SpacePhysics, Cambridge University Press, ISBN 0-521-45104-3.

Mitchell,D. G., P. C. Brandt, E. C. Roelof, J. Dandouras, S. M.Krimigis, B. H. Mauk, C. P. Paranicas, N. Krupp, D. C. Hamilton,W. S. Kurth, P. Zarka, M. K. Dougherty, E. J. Bunce, and D. E.Shemansky, (2005), Energetic ion acceleration in Saturns magnetotail:Substorms at Saturn?, Geophys. Res. Lett., 32 20.

Ness, N. F., Acuna, M. H., Behannon, K. W. & Neubauer, F.M. 1982 The induced magnetosphere of Titan. J. Geophys. Res. 87,13691381, doi:10.1029/JA087iA03p01369.

Petrinec, S. M., and C. T. Russell (1993), External and internalinfluences on the size of the dayside terrestrial magnetosphere,Geophys. Res. Lett., 20, 339.

Richardson, J. D., A. Eviatar, M. A. McGrath, and V. M. Vasyli?nas(1998), OH in Saturns magnetosphere: Observations and implications,J. Geophys. Res., 103, 20,24520,256, doi:10.1029/98JE01127.

Slavin, J. A., E. J. Smith, J. R. Spreiter, and S. S. Stahara(1985), Solar wind flow about the outer planets: Gas dynamicmodeling of Jupiter and Saturn bow shocks, J. Geophys. Res., 90,

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Waite, J. H., et al. (2006), Cassini Ion and Neutral Mass Spec-trometer: Enceladus plume composition and structure, Science, 311,14191422, doi:10.1126/science.1121290.

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