Rings beyond the giant planets
Bruno Sicardy, Maryame El Moutamid, Alice C. Quillen, Paul M. Schenk, Mark R. Showalter, Kevin Walsh
77Rings beyond the giant planets
BRUNO SICARDY, MARYAME EL MOUTAMID, ALICE C. QUILLEN,PAUL M. SCHENK, MARK R. SHOWALTER, AND KEVIN WALSH
Until 2013, only the giant planets were known to host ringsystems. In June 2013, a stellar occulation revealed the pres-ence of narrow and dense rings around Chariklo, a smallCentaur object that orbits between Saturn and Uranus.Meanwhile, the Cassini spacecraft revealed evidence for thepossible past presence of rings around the Saturnian satel-lites Rhea and Iapetus. Mars and Pluto are expected to havetenuous dusty rings, though they have so far evaded detec-tion. More remotely, transit events observed around a starin 2007 may have revealed for the first time exoplanetaryrings around a giant planet orbiting that star.So, evidence is building to show that rings are more com-mon features in the universe than previously thought. Sev-eral interesting issues arise from the discovery (or suspicion)of the new ring systems described in this chapter. One ofthem is to assess how universal is the physics governingrings, in spite of large differences in size, age and origin.In other words, do rings obey some common, fundamentalprocesses, or are their similarities just apparent and stem-ming from very different mechanisms? Another interestingquestion is what those ring systems tell us about the origin,evolution and physical properties of the bodies they encircle.As such, rings may be of precious help to better understandthe formation of satellites and planets, not only in our ownsolar system, but also among extrasolar worlds. We will re-turn to those considerations in the concluding remarks ofthis chapter, after reviewing recent ring system discoveries.
In June 2013, narrow, sharply confined dense rings were dis-covered around the small Centaur object (10199) Chariklo.This asteroid-like object became the first body of the solarsystem, other than the giant planets, known to possess rings.Meanwhile, those rings resemble some of the sharply definedfeatures observed around Saturn or Uranus (Figs. 7.1-7.3),suggesting some common dynamics.Centaurs are small objects (diameters less than about250 km) with perihelion beyond Jupiter’s orbit (5.2 AU)and semi-major axis inside of Neptune (30.0 AU). They wereoriginally Trans-Neptunian Objects (TNO’s) that have been scattered by gravitational tugs from Neptune or Uranus(Gladman et al., 2008).Chariklo was discovered in February 1997 (Scotti, 1997)and is the largest Centaur known to date, with a diameterof about 240 km. Its very low geometric albedo (about 4%,see Table 7.1) makes it one of the darkest objects of the so-lar system. It moves close to a 4:3 mean-motion resonancewith Uranus, its main perturber. Dynamical studies indicatethat Chariklo has been captured in its present orbital con-figuration some 10 Myr ago, and that the half-life time ofits unstable current orbit is about 10 Myr (Horner et al.,2004), a very short timescale compared to the age of thesolar system.Year-scale photometric (Belskaya et al., 2010) and spec-troscopic (Guilbert-Lepoutre, 2011) variations of Chariklowere tentatively attributed to transient periods of cometaryactivity. As discussed below, those variations can be nat-urally explained by the presence of a flat, partially icyring system observed at various aspect angles, so that nocometary activity is necessary to explain this behavior. Ac-tually, we will see that no dust or gas production has beendetected so far around Chariklo.Meanwhile, Chiron (another Centaur similar in size toChariklo) is also surrounded by narrowly confined materialwhose interpretation is still debated. This shows that ma-terial around Centaurs or other small bodies may be morecommon than previously thought.In the following sub-sections, the term “Chariklo” willapply to the central body only, while “Chariklo’s system”will denote the entire set Chariklo plus its rings.
Chariklo’s rings were discovered during a stellar occulta-tion, which occurs when an object passes in front of a star,blocking its flux for some seconds (Fig. 7.2). Such an eventwas monitored on June 3, 2013 from various sites in Brazil,Uruguay, Argentina and Chile, see Fig. 7.1 and Braga-Ribaset al. (2014). This was the first successful Chariklo occulta-tion ever observed. This event was one of a number aimed atcharacterizing the sizes, shapes and surroundings of TNO’sand Centaurs (Assafin et al., 2012; Camargo et al., 2014),and monitoring Pluto’s atmosphere (Assafin et al., 2010).In the case of Chariklo, a further incentive was the searchfor surrounding (possibly cometary) material, as both sharpand diffuse secondary events were detected in 1993 and 19941 a r X i v : . [ a s t r o - ph . E P ] A p r Sicardy & at al.
Table 7.1.
Chariklo main body physical parameters
Semi-major axis, period a a a b,c R equiv = 119 ± b p V = 0 . ± . b P C = 7 . ± .
036 hMass d ∼ kgSurface composition e ∼
60% amorphous carbon ∼
30% silicates, ∼
10% organics a Desmars (2015); Desmars et al. (2015). b Fornasier et al. (2014). c The radius of a spherical body that presents the sameapparent surface area as the actual body. d Order of magnitude estimate, using R equiv above and assuming an icy body. e Duffard et al. (2014a).
Figure 7.1
The discovery of Chariklo’s rings during the June 3,2013 stellar occultation. The dotted lines show the trajectoriesof the star in the plane of the sky relative to Chariklo, as seenfrom eight stations in Brazil, Argentina and Chile (the arrowindicates the direction of motion). The occultation by the mainbody was observed along the three black segments - or“chords” - near the center of the plot. Beside these detections,secondary events were observed somewhere inside the black,thick intervals, most of them unresolved in time. Some segmentsare longer because of the longer integration time used at thecorresponding stations, hence their larger uncertainties inposition. The two gray segments along the Bosque Alegre andCerro Tololo chords correspond to dead-times (due to imagereadouts) during acquisition, leading to non detections of thering, but still providing constraints on the ring location. Therings were not detected at Cerro Burek due to a largeintegration time at low signal-to-noise ratio. The size, shape andorientation of the inner, denser ring (C1R) is obtained thoughan elliptical fit to the black and gray segments, weighted withtheir respective uncertainties. The outer, fainter ring (C2R) wasresolved only in the best-sampled light curve of the Danishtelescope at La Silla (Fig. 7.2). Its orbit has been reconstructedassuming that C1R and C2R are concentric. Adapted fromBraga-Ribas et al. (2014). during stellar occultations by its sibling Chiron (Elliot et al.,1995; Bus et al., 1996), see below.Narrow secondary events were indeed detected during theJune 2013 event (Figs. 7.1 and 7.2), but it became rapidly clear that they could not be interpreted as collimated, ra-dial cometary jets ejected from Chariklo’s surface becausetheir geometries were mutually inconsistent with that inter-pretation. Instead, the ring interpretation was the simplest,although surprising, explanation for all the observed sec-ondary events. All the detections were in fact consistent withthe presence of two rings: an inner, denser ring, 2013C1R(C1R for short), orbiting at some 390 km from Chariklo’scenter, 15 km inside another, more tenuous outer ring, C2R(Fig. 7.1, Table 7.2). There were several arguments in favorof the ring interpretation drawn from those observations: • Although most of the stations appearing in Fig. 7.1 didnot resolve the rings, their equivalent widths W e (whichmeasure the amount of material contained in the rings, seeChapter 4) were essentially the same for all events. Suchcoincidence is hard to reconcile with a set of independentcometary jets going in different directions. • A flat ring system offers a natural explanation forChariklo’s long-term photometric variations (see Belskayaet al. 2010 and Fig. 7.4). Those variations merely reflectthe changing ring aspect as Chariklo and Earth revolvearound the Sun. • The ring interpretation also offers a simple explanation forthe appearance and disappearance of the 2.2 µ m water iceband in Chariklo’s spectra (Guilbert-Lepoutre 2011 andFig. 7.5). Again, the changing ring geometry causes thedisappearance and reappearance of the ice band, showingby the same token that the rings do contain water ice.Another occultation observed on April 29, 2014 fully con-firmed the ring interpretation drawn from the June 2013 dis-covery, and revealed finer structures in the main ring C1R,see Fig. 7.3 and the associated discussion. Other occulta-tions revealed either the main body only or the rings alone,but with lower signal-to-noise ratios or insufficient resolu-tion to reveal ring sub-structures (B´erard et al. 2016 andLeiva et al. 2016, in preparation). The secondary events shown around Chariklo in Fig. 7.1constrain the apparent shape, size and orientation of the ings beyond the giant planets Table 7.2.
Chariklo’s rings physical parameters
Radius a Radial width Normal optical depthRing C1R 390 . ± . . < W < . b average τ N ∼ . c Ring C2R 404 . ± . W ∼ τ N ∼ a . ± . < . a α p = 10 h 05 min ±
02 min, δ p = +41 ◦ ±
13’ (equatorial J2000)Visible reflectivity d ( I/F ) V = 0 . ± . d
20% water ice, 40-70% silicates, 10-30% tholins,small quantities of amorphous carbon a From Braga-Ribas et al. (2014), assuming circular rings. b Smallest and largest widths observed during the June 3, 2013and April 29, 2014 stellar occultations (Sicardy et al., 2014, and B´erard et al. 2016, in preparation). c With some someopaque parts, see text and Fig. 7.3. d Duffard et al. (2014a).
Time%(seconds%a-er%3%June%2013,%00:00:00.0%UTC)%% N o r m a li z e d % fl u x % o f % s t a r % + % C h a r i k l o % La Silla - ESO Danish 1.54 m Figure 7.2
Plot of the stellar flux vs. time, as observed fromthe Danish telescope at La Silla, during the June 3, 2013occultation. This is the best sampled at highest signal-to-noiseratio light curve among the various sites involved in thisobservation (Fig. 7.1). It shows a ∼ . main ring C1R projected in the sky plane (the case of themore tenuous, nearby ring C2R is considered in a secondstep, as mentioned in the caption of Fig. 7.1).The simplest model for ring C1R is that of an ellipse withone focus at Chariklo’s center of mass. However, we do notknow a priori the ring pole position, nor its apse orientation.Moreover, we do not have enough occulting chords acrossthe main body from the observation of June 2013 (nor fromother later ones, to date) to determine Chariklo’s center po-sition relative to the main ring (Fig. 7.1).Thus, one has to make the simpliflying assumption thatRing C1R is circular, with opening angle B and position an-gle P as seen from Earth. An elliptical fit to the secondaryevents of Fig. 7.1 then provides the center of the ellipse, itsapparent semi-major and semi-minor axes a (cid:48) and b (cid:48) (pro-jected in the sky plane) and its position angle. Note that inthe circular assumption, | sin( B ) | = b (cid:48) /a (cid:48) . The elliptical fit displayed in Fig. 7.1 allows two alterna-tive ring pole positions, depending on which part of the ringis “in front” the sky plane. This ambiguity can be solved byconsidering Chariklo’s photometric evolution over time. Thepole position adopted here (Table 7.2) predicts that the ringswere observed edge-on in 2008, in agreement with Chariklo’ssystem photometric behavior (Fig. 7.4). Conversely, the al-ternative solution predicts an edge-on configuration in 1994that is out of phase compared to the observed behavior.Moreover, the solution adopted here was confirmed duringanother Chariklo stellar occultation observed on April 29,2014 (B´erard et al. 2016, in preparation). Defining the ringpole direction as being parallel to the ring angular momen-tum, there is a further ambiguity since two opposite orbitalmotions are possible, that correspond to opposite values of B . We have arbitrarily chosen B >
From the June 3, 2013 discovery observations, no materialwas detected in the gap between C1R and C2R up to anormal optical depth of about 0.004 (Braga-Ribas et al.,2014). Those observations did not reveal structures insideC1R and C2R, due to insufficient time resolution (Fig. 7.2).However, data obtained at higher rate during another event(April 29, 2014) revealed a double-dip structure inside ringC1R, while no structure has been identified so far in theshallower C2R profiles (Fig. 7.3).The densest parts of C1R are consistent with opaque ma-terial concentrated at very sharp edges. The main smooth-
Sicardy & at al. F l u x Radius in ring plane (km) C1R C2R C1R C2R
June 3, 2013 Danish April 29, 2014 Springbok GiEerg April 29, 2014 SAAO
Figure 7.3
Chariklo’s ring radial profiles derived from theJune 3, 2013 stellar occultation (Danish telescope, top), theApril 29, 2014 combined event at Springbok and Gifbergstations (middle), and the same event at the South AfricanAstronomical Observatory (SAAO, bottom). The gray boxescorrespond to the zero stellar fluxes (complete stardisappearance), where its thickness represents photometricuncertainties, while unity corresponds to the full, unoccultedstellar flux. The horizontal axis is the distance to Chariklo’scenter, measured in the plane of the rings, using the orientationgiven in Table 7.2. This orientation is derived assuming that therings are circular, so that this plot cannot be used to assess orput upper limit on the ring eccentricities. The vertical dottedlines are the ring radii adopted in Table 7.2. Due to the differentacquisition rates and viewing geometries, the light curves haveradial samplings of 3.6, 1.0 and 0.57 km par data point in thetop, middle and bottom panels, respectively. The best resolvedprofiles are eventually diffraction-limited at the Fresnel scalelimit (about 0.8 km). They show sharp edges and a W-shapedstructure in the main ring C1R, as well as a width variation forring C1R. ing effect of the April 29, 2014 profiles is Fresnel diffraction,which amounts to about 0.8 km when projected at the ring(the finite stellar diameter being negligible for that event).At this scale, one cannot resolve the edges, as the occulta-tion profiles are compatible with infinitely sharp boundaries(B´erard et al. 2016, in preparation).So far, only eight C1R profiles obtained in 2013 and 2014could provide an estimation the ring radial width W (pro-jected in the ring plane), the other profiles having insuffi-cient resolution to do so. The width W shows significantvariations between 4.8 and 7.1 km (Sicardy et al. 2014 andTable 7.2), with dynamical implications that are discussedlater.For the unresolved profiles, it is possible to estimate theequivalent width W e (1+2) = ( W · p N + W · p N ) of the ring edge-‐on (~2008) a b s o l u t e m a g n i t ud e ring discovery (June 2013) Chariklo discovery (Feb. 1997) Year Figure 7.4
The observed absolute magnitude of Chariklo’ssystem (gray squares) are fitted by a model (black line) thataccounts for both the ring and Chariklo contributions to thetotal observed flux (see Eq. 7.2). Adapted from Duffard et al.(2014a). global ring system C1R+C2R, where W i and p Ni denotethe physical width and normal opacitiy of each component,respectively. For a monolayer ring, W e is a measure of theamount of material contained along a radial cut of that ring.It can be viewed as the width of an opaque monolayer ringthat would block the same amount of light as the observedring (see Elliot et al. 1984 and Chapter 4).The fifteen or so C1R+C2R occultation profiles obtainedso far provide a consistent value close to W e (1+2) ∼ ∼ W e ∼ .
25 km (with dispersion ∼ .
05 km), with no significantazimuthal variations. Thus, the system C1R+C2R does notshow appreciable azimuthal variations in W e and C2R ap-pears to contain ∼
10 times less material than C1R.
The long-term photometric evolution of Chariklo’s systemis a natural consequence of the changing aspect of its rings.During the 63-years orbital period, the rings have an openingangle B to the Earth that varies between extreme values ofabout −
60 to +60 degrees. Using the size, width and radiusof Chariklo and its rings (Tables 7.1 and 7.2), it follows thatthe total apparent surface area of the rings at maximum B represents about 35% of Chariklo’s apparent surface area.For one of the possible ring pole positions previously dis-cussed, the rings had their maximum opening angle in 1997and were observed edge-on in 2008 (Fig. 7.4). The resultingchanging apparent ring geometry then satisfactorily repro-duces the shape and timing of Chariklo’s system absolutemagnitude, while excluding the alternative solution afore-mentioned.Elaborating on that, let us consider the photometric be-havior of a flat, circular ring of radius a , width W and open-ing angle B . The brightness of such a flat surface is measuredby its reflectivity I/F , where πF is is the incident solar flux ings beyond the giant planets density and I is the intensity emitted from the ring surface(remembering that the reflectivity of a perfect Lambert sur-face is I/F = 1). The flux densities F r and F C received fromthe main ring and Chariklo are respectively: F r ∝ ( I/F ) r S (cid:48) r and F C ∝ p C φ C ( α ) S (cid:48) C , (7.1)where S (cid:48) r = 2 πaW µ is the ring’s apparent surface area, with µ = | sin( B ) | , p C is Chariklo’s geometric albedo, α is thephase angle, φ C ( α ) is the phase function (with φ C (0) = 1 bydefinition), and S (cid:48) C = πR is Chariklo’s apparent surfacearea, where the equivalent radius R equiv , see Table 7.1.Defining H as the absolute magnitude of Chariklo’s sys-tem (main body plus rings), i.e. its magnitude at 1 AU fromEarth and Sun and at zero phase angle, and assuming thatChariklo’s absolute magnitude H C is essentially constantover time, we obtain:10 . H C − H ) = 1 + 2 aW µp C φ C ( α ) R (cid:18) IF (cid:19) r (7.2)Monitoring of H vs. time (as µ changes) provides ( I/F ) r ,once Chariklo’s photometric properties are known, as wellas the parameters a and W , derived from occultation data(Table 7.2).A more detailed modeling of the observed variations (Duf-fard et al. 2014a and Fig. 7.4) provides ( I/F ) r = 0 . ± . µ m. We note that the reflectivity of Saturn’s A ring,which has an optical depth comparable to that of ring C1R,is ( I/F ) ring A ∼ . α and β , which also have optical depths com-parable to that of C1R, have ( I/F ) α,β ∼ .
05 (Karkoschka,2001). Thus, Chariklo’s rings appear roughly three timesdarker than Saturn’s A ring, twice as bright as Uranus’ α and β rings, and about three times brighter than Chariklo’s sur-face. Note also that at maximum opening angle ( B ∼ ◦ ),the ring to Chariklo flux ratio is F r /F C ∼ The Chariklo system spectrum has been monitored since1997, and also shows long-term variations. In particular, thewater ice bands at 1.5 µ m and 2 µ m disappeared in 2007-08,while being prominent in 1997. The rings provide a naturalexplanation for that behavior: they contain water ice thatvanished out of view during the 2008 ring plane crossing(Fig. 7.4).By subtracting spectra when the rings are well openand spectra of Chariklo alone (edge-on geometry), one canobtain the spectrum of the rings alone, see Fig. 7.5. Itclearly shows the presence of water ice, with a robustlyderived abundance close to 20% (Duffard et al., 2014a).Other compounds must be present, but with far less con-strained abundances, with degeneracies between the variousspecies. Current estimates yield values of 40-70% silicates,10-30% tholins and a small amount of amorphous carbon.Conversely, Chariklo’s spectrum does not reveal any pres-ence of water, and is consistent with about 60% of amor-phous carbon, 30% of silicates and 10% of organics (Ibid.). Figure 7.5
Synthetic spectra of Chariklo alone (gray) and itsrings (black) derived from spectra of Chariklo’s system obtainedat different epochs, with various ring opening angles. Thispermits to disentangle the contributions from the main bodyand from the rings. Note the water ice bands around 1.5 µ m and2 µ m in the ring spectrum. Adapted from Duffard et al. (2014a). Of course, those spectra reveal surface properties, and maybe unrelated to the bulk compositions of the ring particlesand Chariklo’s interior. It particular, they do not precludethe existence of water ice inside Chariklo.
Chariklo has a rotation period near 7 hours and an equiva-lent radius close to 120 km (Table 7.1). Unfortunately, otherphysical properties like size, shape or density are poorly con-strained, while having important consequences on the ringdynamics, see the next subsection.Currently, no direct imaging system can resolve Chariklo’sdisk (it subtends less than 0.03 arcsec on the sky), and thereare not enough stellar occultations observed so far to pindown Chariklo’s size and shape (which can be done in prin-ciple at kilometric accuracy using that method). The occul-tation data currently available show that Chariklo cannotbe a spherical body. The observations are in fact consis-tent with either an oblate spheroid with equatorial and po-lar radii of 133 ×
125 km, respectively, or an ellipsoid withmain axes 167 × ×
86 km, with typical uncertainties of5 km on each dimension (Leiva et al. 2016, in preparation).Assuming a homogeneous body in hydrostatic equilibrium,this would imply densities of some 1-3 g cm − (Maclaurinspheroid case) or close to 0.8 g cm − (Jacobi ellipsoid case),with corresponding dynamical oblatenesses around 0.07 and0.20, respectively. Taken together, the two cases consideredhere imply a Chariklo mass in the range 0 . − × kg.It should be remembered, however, that an irregular shapecannot be currently discarded, and that the hydrostaticand homogeneous hypotheses may be invalid. Clearly, moremulti-chord occultations are needed to build a correct modelfor Chariklo’s size and shape. Sicardy & at al.
Chariklo’s tidal disruptive forces must be strong enoughto prevent the accretion of ring particles into small satel-lites. To be disrupted, a particle at distance a from Charikloshould have a density ρ of the order of, or lower than acritical density ρ crit (Tiscareno et al., 2013): ρ < ρ crit = 4 πρ C γ (cid:18) R equat a (cid:19) , (7.3)where ρ C and R equat are Chariklo’s density and equato-rial radius, while γ is a dimensionless parameter that de-scribes the structure of the disrupted particles. For instance, γ = 4 π/ γ ∼ γ ∼ R equat ∼
150 km (see above). More-over, values of γ ∼ a ∼
400 km, we obtain ρ crit ∼ . ρ C . For an expected icybody like Chariklo, we can assume ρ C ∼ − . Thissuggests that the ring particles should be rather underdense( < ∼ . − ) to prevent accretion. Such densities are ac-tually typical of what is observed in the outer regions ofSaturn’s A ring (Tiscareno, 2013). As previously noted, how-ever, while water ice is clearly identified in Chariklo’s rings(Fig. 7.5), other compounds must be present, like silicatesor tholins. This would make Chariklo’s ring quite different,in terms of composition, from those of Saturn, which are ba-sically pure water ice (see Chapter 3 by Cuzzi et al. ). Verylittle is known about the physical properties of individualring particles in general (including those of Saturn’s rings).In that context, it remains to be seen if particles partlycomposed of silicates or tholins may have densities as low as0.5 g cm − , for instance if they are porous or fluffly. More-over, the criterion proposed in Eq. 7.3 might miss some ofthe physics at work and be too crude for a firm claim thatChariklo’s ring particles must be underdense. Although hugely different in terms of size and mass,Chariklo’s rings share a local velocity field similar to thoseof Saturn or Uranus. Using a typical mass M C ∼ kgfor Chariklo (see above), we obtain a ring orbital meanmotion of n ∼ (cid:112) GM C /a ∼ − s − at a ∼
400 km,where G is the gravitational constant. This is comparableto the orbital motions in Uranus’ rings and the outer partof Saturn’s rings. Consequently, the local Keplerian shears, dv/da = − n/ v is the orbital velocity), are alsocomparable. In other words, a particle in Chariklo’s ringsesssentially “sees” the same local velocity field as a particlein Saturn’s and Uranus’ rings. In fact, the mere requirement that the rings must resideinside the Roche zone imposes the value of n , and thus of dv/da . In effect, combining Eq. 7.3 and n = (cid:112) GM C /a , weobtain n ∼ (cid:112) γGρ crit /
3. So, the velocity field surroundingthe ring particles depends only on their physical properties,i.e. γ and ρ crit , whatever the central body mass or the ringdimension are.In the same vein, we see that the ring thickness h onlydepends on the particle physical properties, and not on themacroscopic ring parameters. A dense collisional ring tendsto adjust itself so that its Toomre’s stability parameter Q stays near unity: Q = v rms nπG Σ ∼ hn πG Σ ∼ , (7.4)where Σ is the ring surface density, v rms is the ring particlevelocity dispersion and h is the ring thickness, h ∼ v rms /n .As Chariklo’s main ring is densely packed with particles,Σ ∼ ρ crit R , where R is the radius of the largest particles.So, h ∼ (3 π ) /γQR ∼ a few times R from the estimation of γ given before, and from Q ∼
1. In the case of Saturn’s rings, R ∼ h ∼
10 m (Colwell et al., 2009). We donot know the size distribution in Chariklo’s rings, but if itis similar to that in Saturn’s rings, they should also have athickness of h ∼
10 m.
Only rough estimations of the ring mass and angular mo-mentum can be made at the present stage. As argued inthe previous subsection, the local kinematic conditions inthe ring C1R should be close to those prevailing in Saturn’srings. Assuming a surface density Σ ∼ − forC1R (typical of Saturn’s ring densest parts, Colwell et al.2009), and considering the quantities in Table 7.2, we ob-tain a ring mass estimate M r ∼ kg, equivalent to anicy body of radius ∼ M r /M C ∼ − , and is largerthan, but still comparable to the corresponding fraction inthe case of Saturn’s rings, M r /M S ∼ − (Cuzzi et al.,2009).Another method can be used to estimate C1R’s mass.Its physical width W varies from about 5.5 to 7.1 km (Ta-ble 7.2). This suggests that C1R may behave like some ofthe Uranian rings (French et al., 1991), i.e. a set of nestedelliptical streamlines locked into a common precession rateregime, against the differential precession (stemming fromthe central body’s oblateness) that should destroy this con-figuration.In those models, the narrow ring is globally described byan ellipse with mean semi-major axis a and mean eccen-tricity e , while its inner and outer edges are described byaligned ellipses with semi-major axes a inn and a out , and ec-centricities e inn and e out , respectively. To first order in e ,the width of the ring then varies with true anomaly f as W = ∆ a [1 − q e cos( f )], where q e = e + a∂e/∂a is a di-mensionless parameter that depends on both the eccentric-ity and its gradient across the ring, ∂e/∂a = ∆ e/ ∆ a , with∆ e = e out − e inn and ∆ a = a out − a inn . ings beyond the giant planets One mechanism proposed by Goldreich and Tremaine(1979b,a) to lock the streamlines into a rigid precessionregime is self-gravity. In essence, the mass of the inner half ofthe ring increases the precession rate of the outer half, andvice-versa, thus maintaining the alignment. This requiresa ratio M r /M C of the order of ( e/ ∆ e )(∆ a/a ) J ( R C /a ) ,where J is the dynamical oblateness of the central body.Elaborating on that basis, Pan and Wu (2016) estimate aC1R mass of a few 10 kg, comparable to the estimate al-ready given before. This reinforces the notion that the ringC1R is comparable, both in terms of surface density anddynamical behavior, to some of the dense and narrow ringsof Saturn or Uranus.Those estimates must be considered with caution, though,first because neither e nor q e are currently known. The oc-cultation data are not yet accurate and numerous enough toprovide detailed ring orbital solutions and edge models.Secondly, only variations of width W with respect to the inertial mean longitude λ have been derived right now, whilevariations vs. true anomaly f should be determined to testrigid precession models. This will be possibe only when thering apsidal precession rate ˙ (cid:36) ∼ . R c /a ) J n is deter-mined. An expected value of J is ∼ Ω C R C / GM C , assum-ing a homogeneous body, where Ω C = 2 π/P C is Chariklo’sspin rate. From Table 7.1, one obtains J ∼ .
08 and˙ (cid:36) ∼ − s − , so that the ring apse should precess overa period of a couple of months only. This is much shorterthan the eleven months or so separating the June 2013 andApril 2014 occultations from which values of W are derived(Table 7.2). Consequently, it is not yet possible to compareconsistently those observations and obtain a coherent plotof W vs. f .Finally, we do not know yet if the observed width varia-tion is caused by a m =1 azimuthal wavenumber, or by somehigher (free or forced) wavenumbers which would require arevision of the mass estimation made above.More generally, the physics at work in dense narrow ringsmay be more complex than the purely self-gravitating mod-els evoked so far. In particular, viscous effects due to in-terparticle collisions near sharp ring edges resonantly per-turbed by (yet to be discovered) shepherd satellites maysignificantly increase the mass estimation quoted above, seeChiang and Goldreich (2000) and Mosqueira and Estrada(2002). Those models predict enhanced ring surface densi-ties at some 100-500 m from the edges, consistent with thedouble-dip structures observed in α and (cid:15) Uranus’ rings oc-cultation profiles (French et al., 1991), and interestingly, inthe C1R profile too (Fig. 7.3).Finally, approximating Chariklo as a homogeneoussphere of radius R equiv , the ratio of the ring an-gular momentum to that of Chariklo is H r /H C ∼ ( M r /M C ) P C √ Gρ C (cid:112) a/R equiv . From Tables 7.1 and 7.2,we obtain H r /H C ∼ − . Applying the same calculationto Saturn’s rings, where we assume that the rings are uni-formly spread between ∼ H r /H S ∼ − (using M r /M S ∼ − , see above).This is smaller than, but still comparable to the fraction H r /H C . In any case, we see that very small fractions of Chariklo’s mass and angular momentum are stored in therings, a noteworthy result when it comes to discussing therings’ origin. Rings C1R and C2R are both sharply confined, see Fig. 7.3.If unperturbed, they should spread out on a timescale of(Goldreich and Tremaine, 1979b): t ν ∼ W ν , (7.5)where ν is the kinematic viscosity associated with particlecollisions. A typical value of ν is ∼ nh , where h is thering thickness. Taking W ∼ t ν ∼ /h years, where h is expressed in meters. Assumingagain h ∼
10 m, we obtain t ν ∼ a few thousand years. More-over, Poynting-Robertson (PR) differential drag also causesa spreading over a timescale of (Goldreich and Tremaine,1979b): t P R ∼ (cid:18) c f (cid:12) (cid:19) (cid:18) Wa (cid:19) ρτ R, (7.6)where c is the velocity of light, f (cid:12) is the solar flux den-sity at Chariklo, ρ the density of the particles and τ isthe optical depth. Taking ρ < ρ crit ∼ . − , as ex-plained before, and τ ∼
1, we obtain a typical value of t P R ∼ R meters years, i.e. a few million years for sub-cm particles. The effect of PR drag is even more drastic forsmaller grains, with a depletion time of only a few monthsfor micrometric particles. Even if very crude, these estima-tions show that Chariklo’s rings are either very young, orconfined by an active mechanism.It is remarkable that apparently similar ring confinementoccurs in systems so widely different (in terms of orbitalradii) as those of Saturn or Uranus, compared to Chariklo.In fact, looking at Chariklo’s rings’ optical depth profiles(Fig. 7.3), it is hard to distinguish them from their Uraniancousins, see French et al. (1991) and Chapter 4.A classical theory to confine ring material invokes thepresence of putative “shepherd satellites”. In its simplestversion, a shepherd of mass M s can exert a torque T m ontoa ring edge at a discrete m + 1 : m mean motion resonance(where the ring particle completes m + 1 revolutions whilethe satellite completes m revolutions, with m integer), seeGoldreich and Tremaine (1982): T m ∼ . m a n Σ (cid:18) M s M C (cid:19) . (7.7)As m increases, resonances overlap and the torque density(torque per unit interval of semi-major axis) is: dTda ∼ . a n Σ (cid:18) M s M C (cid:19) (cid:16) ax (cid:17) , (7.8)where x is the distance between the satellite and the ring.To prevent spreading, the satellite torque must balance theviscous torque T ν associated with inter-particle collisions. Ina Keplerian velocity field, it is: T ν = 3 πna ν Σ . (7.9) Sicardy & at al.
Making T m = T ν , and in the case of discrete resonances, theradius R s of a shepherd with density ρ s is: R s ∼ (cid:18) ρ C ρ s (cid:19) / (cid:18) hma (cid:19) / R C . (7.10)This yields radii of a few km for icy shepherds ( ρ s ∼ − ), taking m of a few times unity and h a few me-ters. Concerning the gap between C1R and C2R, it shouldbe opened in the overlapping resonance regime (Eq. 7.8),in which case, the radius of the satellite is (Goldreich andTremaine, 1982): R s R C ∼ (cid:18) ρ C ρ s (cid:19) / (cid:18) ha (cid:19) / (cid:18) W gap a (cid:19) / < ∼ W gap ∼ T m , thereaction from the latter induces a migration rate | ˙ a s | ∼ | T m | / ( anM s ), where a s is the shepherd’s semi-major axis.Considering that T m = T ν and using Toomre’s criterion ofEq. 7.4, one obtains: | ˙ a s | ∼ m (cid:18) ha (cid:19) (cid:18) hT orb (cid:19) , (7.12)where T orb is the orbital period. We may apply this for-mula to the shepherd satellites Cordelia and Ophelia whichconfine the Uranian (cid:15) ring. In this case, m ∼ T orb ∼
10 hours, a ∼ ,
000 km and h ∼
10 meters. Thisyields | ˙ a s | ∼ − . As the shepherds orbit at some1000-2000 km from the (cid:15) ring, this implies short recessiontimescales of some million years for those two satellites. Thisproblem is exacerbated for Chariklo, due to the smallness ofthe semi-major axis a (by more than two orders of magni-tudes) compared to the case of the giant planets. ApplyingEq. 7.12 to the Chariklo case actually provides recessiontimescales of some thousands of years only if one assumesagain h ∼
10 meters, and considering that T orb must againbe of the order of 10 hours.One possibility is that, for a so far unexplained reason,Chariklo’s ring particles are much smaller than those of Sat-urn or Uranus, resulting in a much smaller value of h , andthus, much longer recession timescales for the shepherds.The shepherding physics may also be more complex thanassumed here. For instance, the viscous torque (7.9) can besignificantly reduced due to the local reversal of the vis-cous angular momentum flux, caused by the satellite itself(Goldreich and Porco, 1987). This in turn would reduce themasses of the shepherds estimated above, as well as theirmigration rates.In summary, and except if Chariklo’s rings are very young,some deep understanding of the shepherding mechanism,and in particular a better knowledge of the ring local col-lisional dynamics are required to better assess the short timescale problems described above. In that context, de-tections of the putative shepherd satellites would be veryhelpful to understand Chariklo’s ring confinement, but thisremains a very challenging observational task.At this point, it is worth mentioning that resonances mayarise not from satellites, but from the very shape of Chariklo.For instance, a topographic feature of some 5 km in heighton Chariklo’s surface might cause (tesseral-type) resonantperturbations that are comparable in strength to those stem-ming from the putative satellites mentioned above. Thesame is true if the body is elongated in one direction by a fewkilometers, in which case non-axisymmetric perturbationsarise from the bulges associated with the elongation. Assum-ing thet Chariklo’s mass is in the range 0 . − × kg, thecorotation radius – where particles have an orbital periodmatching that of Chariklo ( ∼ m + 1 : m between theparticle mean motion and Chariklo’s orbital period wouldappear. It is instructive to note that the 2/1 outer reso-nance (corresponding to particles with orbital period closeto 14 h) should occur somewhere between 290 and 510 km,bracketing the region where the rings are found. It is tooearly to conclude anything before accurate measurementsof Chariklo’s mass and shape are made, but it is worth re-membering that the ring dynamics might be significantlyinfluenced by resonances with the spin of the central body. The general portrait that emerges from the previous sub-sections is that of a ring system composed of underdenseparticles ( ρ < ∼ . − ), partially composed of water ice,and confined by small shepherd satellites of some kilome-ters in size that contain a mass comparable to that of therings. Moreover, a very small fraction of mass ( ∼ − ) andangular momentum ( ∼ − ), compared to Chariklo, arerequired to explain the observed rings. At present, it remains unclear whether Chariklo’s rings aregeneric and frequent features around small bodies, or are anexceptional system resulting from a fine tuning between var-ious physical properties. Hundreds of Main Belt asteroid oc-cultations have been monitored, but no report of secondaryevents possibly due to rings have been reported so far. Ahandful of occultation events involving TNO’s have beenpublished up to now (Elliot et al., 2010; Sicardy et al., 2011;Ortiz et al., 2012; Braga-Ribas et al., 2013), and again noevidence of ring events have been documented. It should benoted, however, that Chariklo’s rings cause very brief stellardrops (at sub-second level, see Fig. 7.2) that are easily over-looked if integration times and/or noise levels are too large.Also, re-analysis of the best occultation data sets obtainedso far might reveal ring-related features. Moreover, imag-ing such systems is challenging from Earth. For instance,Chariklo’s rings do not span more than 0.04 arcsec aroundthe main body. This makes direct detection very hard, even ings beyond the giant planets on the best instruments available nowadays. So, other ringsystems may still be undiscovered due to the lack of high-quality occultation observations or high resolution imagers. The object (2060) Chiron is the second largest Centaurknown to date, with a diameter of 218 ±
20 km (Fornasieret al., 2013) and perihelion-aphelion distances of 8.4-18.8AU. Two stellar occultations observed in 1993 and 1994 ac-tually revealed secondary events that were interpreted asdue to collimated cometary jets (Elliot et al., 1995; Buset al., 1996). A more recent Chiron occultation in 2011 re-vealed symmetric, narrow and sharp double dips, similar indepth and width to those observed around Chariklo. Theyhave been interpreted as being due to a spherical shell sur-rounding Chiron (Ruprecht et al., 2015) or to a ring systemakin to those of Chariklo.The ring hypothesis is supported by various arguments(Ortiz et al., 2015): (1) the strong similarity between theevent reported by Ruprecht et al. (2015) and the one inFig. 7.2, (2) the fact that the reconstructed ring orientationglobally explains the photometric behavior of Chiron since ∼ Several circumstances can make Chariklo (and possiblyother Centaurs) special to allow it to possess rings: ( i ) its he-liocentric distance, ( ii ) possible transient cometary activity,( iii ) its size, and ( iv ) significant gravitational perturbationsfrom the giant planets.Point ( i ) is discussed by Hedman (2015), who consid-ers that water ice particles may have the adequate physicalproperties to meet the condition given in Eq. 7.3 between 8and 20 AU. More precisely, in that heliocentric range, waterice may reach a typical temperature of 70 K, low enough for the ice to avoid sublimation (which explains why no ringsare seen around Main Belt asteroids), but still high enoughto remain weak and consequently be subjected to tidal dis-ruption in the Roche zone. This would be consistent withthe fact that Chariklo travels between 13 and 19 AU fromthe Sun.Another circumstance linked to heliocentric distance is thelower impact velocities prevailing in Chariklo’s region - typ-ically 1 km s − - compared to relative velocities in the MainBelt, about 5 km s − . This results in much less destructivecollisions that may give rise to a debris disk around the im-pacted body, from which rings form, instead of dispersingmost of the pieces to infinity.Turning to point ( ii ), it appears that some Centaurs havecometary activity. This is documented for Chiron (Meechand Belton, 1989; Luu and Jewitt, 1990) and Echeclus(Rousselot, 2008), a Centaur with perihelion-aphelion dis-tances of 5.8-15.6 AU and diameter of about 65 km (Duffardet al., 2014b). In Echeclus’ case, the cometary-like episodeof March 2006 showed a coma around a source that was sep-arated from Echeclus. This coma may have been caused bya 8-km object moving near the main body, that could be asatellite or a fragment ejected from the surface. This addsone case in the list of Centaurs surrounded by (in this case,transient) material.The escape velocity at the surface of a body of density ρ and radius R is v esc = (cid:114) πGρ R ∼ . R km m s − , (7.13)assuming an icy body ( ρ ∼ − ). This implies a roughvalue of v esc ∼
100 m s − for Chariklo or Chiron. Thisis typical of the upper limit for terminal velocities of dustgrains in a cometary coma (Delsemme, 1982; Tenishev et al.,2011). This coincidence raises the interesting possibility thatChariklo’s rings have an endogenous origin. They could beformed of cometary material ejected from the surface withvelocities large enough to prevent an immediate in-fall ontothe surface, as is the case for Triton’s geyser material, butstill small enough to prevent escape to infinity, as is the casefor km-sized comets.In any case, no dust production has been observed so farfor Chariklo (Guilbert et al., 2009), with an upper limitof about 2.5 kg s − for the dust production rate (Fornasieret al., 2014). Similarly, no gas production has been found forthat body, with typical upper limits of 2 × molecules s − of CO ( ∼ kg s − ) and 8 × molecules s − of HCN( ∼
400 kg s − ), see Bockel´ee-Morvan et al. (2001). In thatcontext, deeper searches for dust or gas production mightreveal a low level cometary activity for Chariklo, and thusconstrain ring origin models.Finally, we already noted that Chariklo is moving on anunstable, short life-time (10 Myr) orbit controlled by Uranus(Horner et al., 2004). The encounter distance ∆ disrupt atwhich a ring of semi-major axis a is disrupted is given by theHill sphere radius ∆ disrupt ∼ a (3 M U /M C ) / , where M U isthe Uranus mass. Using M U ∼ kg, M C ∼ kg and a ∼
400 km yields ∆ disrupt ∼ Sicardy & at al. ability to occur (some 10%, see Hyodo et al. 2016) duringChariklo’s migration, and that globally Chariklo’s ring sys-tem can survive more than 90% of its encounters with giantplanets (Araujo et al., 2016). In other words, if Chariklo’srings were already formed while the object was in the TNOregion, they should have safely experienced the migrationepisode.However, encounters with Uranus may have destabilizeda pre-existing, marginally stable Chariklo’s satellite system,causing orbit crossing and then collisions between the satel-lites, resulting in ring formation, a scenario that is still to beinvestigated. Note finally that a mere disruption of Charikloduring a close encounter with Uranus may also be envis-aged. This might result in a debris disk around the body,from which small moons shepherding ring material couldemerge near Chariklo’s Roche limit (Hyodo et al., 2016).
Currently, no rings have been confirmed orbiting naturalsatellites in our solar system, but physical evidence suggeststhat such rings could have been a common occurrence inthe past. In fact, equatorial features occur on two moons ofSaturn, Rhea and Iapetus, and could be remnants of suchrings, as discussed below.
The ridge on Iapetus is a puzzling feature, up to 20 kmtall and about 100 km wide, see Denk et al. (2005a,b) andFig. 7.6. It is challenging to reconcile this with the globalhistory of Iapetus. One approach has modeled it as the out-come of endogenic (tectonic or other) processes, but nonecould satisfy the observational constraint of a single equa-torial high-standing ridge, see Castillo-Rogez et al. (2007)and Robuchon et al. (2010). Alternately, an exogenous ori-gin has been proposed - the remnants of a ring that hasfallen to the surface (Ip 2006; Levison et al. 2011; Dom-bard et al. 2012). Following this latter idea, one can usethe constraining observed features of the Iapetan ridge - itsdimensions, morphology/slopes and some localised cases ofparallel ridges or tracks - and combine them with the dy-namics of the Saturnian system and a ring’s tidal evolutionto estimate the origin and properties that this proposed ringcould have had.Note that the Voyager imaging had not high enough res-olution at equatorial latitudes to detect directly any signifi-cant equatorial topography (Smith et al., 1981, 1982). How-ever, the analysis of the limb data many years later stronglypointed to a massive mountain-like structure with heights upto 20 km (Denk et al., 2000). These were identified in theCassini Regio (the dark leading side) between the longitudesof 180 W and 200 W.The most significant imaging of the equatorial ridge wasdone by the Cassini spacecraft during a flyby on 31 Decem-ber 2004. The dark, leading side, was reported by Porco et al.(2005) to have an equatorial ridge up to 20 km in height,
Figure 7.6
An image of the ridge of Iapetus taken from around62,000 km in September 2007 by the Cassini-Huygens mission(image number N00091828: credit to NASA/JPL-Caltech/SpaceScience Institute). confirming Denk’s finding. Profiles from the Digital TerrainModel (DTM) constructed from Cassini data find a diver-sity in the morphology of the ridge. At times it has a strictlysteep-sided triangular shape (see ridge profiles r1 and r2 inFig. 5 of Giese et al. 2008), while at others a more “flat-top” or trapezoidal shape characterized by lower slopes onthe Northern side estimated to decrease to 15 deg down to8 deg in ridge profile r3 and 4 deg in ridge profile r4. Subse-quent global mapping of the topography (by PMS, publishedin Dombard et al., 2012) shows that the ridge is discontinu-ous with a series of linear ridges and isolated quasi-conicalmassifs along the equatorial trace. The elevation is variablealong the length and appears to be absent in some stretches,though it is essentially global in character.The trailing side DTM was constructed of only two setsof stereo pairs, but reveals that the ridge continues on theback hemisphere, and appears to be centered at 30 deg East(Giese et al., 2008). Given the current observations, withconfirmed existence of the ridge spanning the entire well-observed leading side hemisphere (Porco et al., 2005; Gieseet al., 2008), the leading side limb and also the trailing side(Giese et al., 2008) it is safe to assume that this feature isindeed global.The size and the equatorial location of the ridge made itan enigmatic feature, but the larger context at Iapetus alsoincludes its synchronous spin state, and its non-equilibriumglobal shape. Iapetus is synchronously locked with its orbitalperiod around Saturn of 79 days, and estimates based onsolid-body tides suggest that de-spinning to this state wouldtake >
10 Gyr (Peale, 1977). Meanwhile, the global shapeof Iapetus suggests it is not in hydrostatic equilibrium, as ithas a shape expected for a body with a 16-h rotation rate(Thomas et al., 2007; Castillo-Rogez et al., 2007; Thomas,2010). Combined, the features of the equatorial ridge andthe spin state and global shape of the entire icy satellitepoint to a complicated history, one in which the ridge couldhave formed from an in-falling ring (Ip, 2006).Two distinct takes on this idea have been explored. Levi-son et al. (2011) propose that Iapetus suffered a violent im-pact, and ejecta formed a large disk of debris that quicklydamped to the equatorial plane straddling the synchronous ings beyond the giant planets limit for a then-faster spinning Iapetus (as the global shapeimplies a faster rotation in its past) – similar to the proto-lunar disk at Earth. A sub-satellite forms from the disk be-yond the Roche limit and the synchronous limit, and itstidal interactions with the remaining debris push the ringto the surface of Iapetus forming the equatorial ridge. Thesub-satellite then tidally evolves away from Iapetus, slowingthe rotation of Iapetus and aiding its de-spinning until it iseventually stripped from the orbit of Iapetus.Dombard et al. (2012) propose a similar scenario, but witha different origin and fate for the formed sub-satellite. Here,a ∼
100 km body impacts Iapetus and is captured into orbit– similar to the Pluto-Charon formation scenario. If the or-bit is retrograde it will tidally evolve inward until reachingthe Roche limit, after which it will be tidally disrupted andeventually rain down to the surface piece by piece buildingthe equatorial ridge.While there are some differences in the models, they bothpropose the existence of a substantial ring orbiting Iape-tus in its past. Fundamentally, both models would requirea ring with a minimum mass equal to that needed to createthe equatorial ridge. Estimates for this mass depend on theassumed shape and size of the ridge before its degradationdue to bombardment over Solar System timescales - it hasbeen estimated between 5 . × and 4 . × kg (Ip,2006; Levison et al., 2011), or a fraction up to a few per-cent of the mass of Iapetus. The Levison et al. (2011) modelwould actually require more mass in the ring initially, as itwould eventually build a sizable sub-satellite leaving behindenough mass in the ring to then fall to the surface and buildthe ridge.Neither model predicts a long lifetime for the ring. Lev-ison et al. (2011) find a spreading timescale of only 100’sof years owing to the strong tidal interaction with the sub-satellite. Meanwhile, the timescale for the survival of a ringis longer in Dombard et al. (2012) as there is no externalinteraction with other orbiting debris - the sub-satellite istidally disrupted and then falls piecewise onto the surface ontidal timescales. This was estimated to be quite rapid com-pared to the 10-100’s Myr tidal timescales of the system,owing to the eventual ring having a very high surface massdensity and therefore rapid viscous evolution. The timing ofthe formation, evolution and demise of the ring is differentin each case as well. The ring in Levison et al. (2011) wouldform and be lost coincident with the large impact and birthof the sub-satellite, with a longer tidal scenario to play outwith the sub-satellite. The Dombard et al. (2012) scenariowould have the ring form well after the impact and tidal evo-lution of the sub-satellite, so at the end of the story. Whilethese may not be testable distinctions for Iapetus with thecurrent dataset, they do provide scenarios that could be dis-tinguished in other parts of our Solar System or external toour Solar System.While these are both compelling models, much of their vi-ability lies in the geophysical evolution of Iapetus, the largeuncertainties in tidal evolution timescales, and even in theimpact physics of ring particles pummeling the surface. Fur-ther advances could be made by better understanding the Figure 7.7
This view shows a Cassini color ratio map(IR3/UV3) of the anti-Saturnian facing hemisphere of Rhea.Such maps reveal discrete spots along the equator 20-50 kmacross that have unusual spectral signatures enhanced in theultraviolet, giving them a “bluish” appearance in Cassini 3-colormosaics. Each spot correlates with local highs in topography.Effective resolution is ∼ stratigraphy on the surface of Iapetus to date the ring andunderstand its relationship to some of the largest impacts. In 2009 a putative ring was reported in orbit around Rhea,after sharp drops in measured electron counts from thefields and particles instruments, symmetric about the moon,were detected by the charged-particle detectors aboardthe Cassini spacecraft (Jones et al., 2008). However, deepsearches in both high-phase and low-phase Cassini ISSnarrow-angle camera images ruled out dust material orbit-ing Rhea as an explanation for those drops (Tiscareno et al.,2010). After this report, independent workers examiningmultispectral ISS mosaics of Rhea discovered “blue pearls”on the surface of that moon (Schenk et al. 2011). Thesefeatures take the form of irregularly shaped surface patches5-50 km wide and 50-150 km apart, visible only as coloranomalies, and only along the equator of Rhea (Fig. 7.7).These patches are brighter in the near-UV and hence havea bluish signature when mapped in UV-green-IR filter com-binations. The key observation at Rhea is that these spotsor “Blue Pearls” form only on the highest local topogra-phy along the equator (Schenk et al., 2011), consistent withinfalling orbiting debris striking the surface in the mannersuggested by Ip (2006) for Iapetus. No constructional moun-tains or ridges are associated with these features, however,as the relief along the equator consists of pre-existing craterrims and ridges. The Schenk et al. (2011) proposal was thatfine material spiraled in toward the surface and disturbedregolith on high topographic ridges. Due to the very low im-pact angles, lower lying topography “downstream” of these Sicardy & at al. impact points would be shielded from impact and thus un-colored.
By itself, the equatorial ridge on Iapetus remained enig-matic, though all efforts to identify a tectonic mechanismfailed. The discovery of a second non-tectonic equatorialfeature on Rhea strengthens the case for ring deposition.The major difference at Rhea (compared to Iapetus) is thatthere is no significant accumulation of a topographic depositat Rhea, suggesting that the mass of the ring system therewas also much less than at Iapetus.This said, two major features link the Rhean Blue Pearlsand the Iapetus ridge. The first is the narrow equatorialgreat circle pattern of both. The second is the discontinuousnature of both. The Blue Pearls are widely separated andoccur only on high-standing topography. The Iapetus ridgeis also discontinuous and forms widely separated sub-ridgesand promontories along the equator (Fig. 7.6s). In the caseof a low-mass ring system, only the tops of high-standingfeatures crossing the equator would be disturbed by infallingdebris (as at Rhea). In the case of a massive ring system,material would accrete “backwards” along the equator athigh standing blocking ridges, forming a partial ridge. Withenough mass, a more continuous ridge is built up.The two moon putative ring deposits appear to be of dif-ferent ages. The Rhea color anomaly is a surficial effect andeasily erased. The inference is that it is not ancient as bluecolor signatures fade over time and are not visible in oldereroded craters. The small-scale complexity of these spotsalso points to a relatively young age as small scale featuresalways tend to be ground up into the regolith of airless plan-etary bodies within a billion years or so, depending on lo-cation. The Iapetus ridge is much more massive and noteasily destroyed or eroded. Landslides have affected its pro-file (Singer et al., 2013) and it is heavily cratered. Some largecraters cut into it. It is inferred that it is very ancient, butalso it does not appear to be primordial as its profile wouldbe much more dissected than it appears. We infer that itformed sometime within the first 1-2 Gyr of formation butthat tighter constraints on age are lacking.Finally, no equatorial features (ridge, color anomaly, orotherwise) have been observed on other icy moons of Sat-urn, while mapping on the Uranian satellites is limited bypoor coverage of the equatorial regions. Color and topo-graphic mapping are at least as good on the other Saturniansatellites as they are on Rhea and Iapetus, and if such ringdeposits ever formed they have either been erased by subse-quent bombardment or E-ring deposition (e.g., Schenk et al.,2011) or never formed. The surficial Rhean Blue Pearls areeasily erased over time, and are therefore geologically recent,but the apparent great age of the Iapetus ridge is such thatlarge massive ring deposits of this kind would have beenpreserved through much of Saturn System history. The lackof prominent ridges on other Saturnian satellites is thus realand indicates that if any formed at those bodies, they formedvery early and were erased in the accretional storm of pro-jectile bombardment.
Finally, the case for rings or ridges associated with the Ura-nian moons is not clear, namely because Voyager lackedthe color filters that Cassini observed the Rhea ring depositwith, but also because the 1986 Uranus encounter providedour only mapping to date. Like Voyager at Saturn, thesemaps are incomplete, and provided imaging on the outerUranian satellites Titania and Oberon (where rings are likelyto be more stable) at no better than 2 to 5 km/pixel, respec-tively, and only of the southern hemispheres. Thus it is likelythat both Blue Pearls and an equatorial ridge on one or moreof these moons were missed by Voyager, if they exist. A re-turn to the Uranian system will be required to determine ifmoon-rings ever formed there.
Studies of the giant planets have revealed a distinct connec-tion between small moons and dusty rings (see Chapter 13).The concept is simple—meteoroids impact the surface of amoon and raise a cloud of dust. That dust escapes fromthe moon’s weak gravity but remains in orbit around thecentral planet. For example, Jupiter’s gossamer rings areassociated with Amalthea and Thebe (Burns et al., 1999).Similar rings emerge from several small satellites of Saturn(e.g., Pan, Anthe, Aegaeon and Phoebe), Uranus (Mab) andNeptune (Galatea). In an analogous way, we would expectimpacts into Phobos and Deimos to populate faint Martiandust rings. Soter (1971) was the first to predict the existenceof rings of Mars, using a similar argument. Since then, thehypothetical Martian rings have been the topic of over thirtytheoretical publications; see Krivov and Hamilton (1997) fora historical summary.Dynamical simulations by Krivov and Hamilton (1997),building upon previous work (Juhasz and Horanyi, 1995;Krivov and Titov, 1995; Ishimoto, 1996), indicate that theMartian rings will have some peculiar properties. Because ofthe strong influence of solar radiation pressure, both ringsare offset from the center of the planet, with the Phobos ringdisplaced toward the Sun by ∼ one Martian radius, whereasthe Deimos ring should be displaced away from the Sun byseveral radii. This peculiar result follows from the dynamicsof individual dust grains. Briefly, Mars’ oblateness causes el-liptical orbits of Phobos’ ring particles to precess faster thanMars’ mean motion around the Sun, whereas for Deimos,this precession is slower than Mars’ mean motion. Solar ra-diation pressure, which drives orbital eccentricities, is verysensitive to the difference between the two motions; the re-sults are rings offset in opposite directions. The Phobos ringshould be equatorial and ∼
400 km thick. The Deimos ring ispredicted to be much thicker, 10,000–15,000 km, and tiltedout of the equatorial plane toward the ecliptic by ∼ ◦ .The larger thickness and tilt are both due to solar radiationpressure, which is a more effective perturbation for this moredistant ring. Similar solar perturbations are responsible forthe warps in Saturn’s E ring, and for the tilt and thickness ings beyond the giant planets of the Phoebe ring (see Chapter 13). Also, the strong so-lar radiation pressure quickly drives micron-sized grains outof orbit, by inducing eccentricities large enough that theystrike the planet; this leaves behind a ring that should becomposed primarily of particles tens of microns or larger(Hamilton, 1996; Krivov and Hamilton, 1997).So far, attempts to observe rings around Mars have beenunsuccessful. Duxbury and Ocampo (1988) used Viking im-ages to put an upper limit on the ring’s normal optical depth τ < × − . In situ observations by Mars-orbiting space-craft of anomalies in the solar wind magnetic field were in-terpreted in the 1980s as being due to Martian rings, butmore extensive measurements by the magnetometer aboard
Mars Global Surveyor showed that observable fluctuationsare likely due to well-known solar wind or bowshock phe-nomena (Øieroset et al., 2010).Earth-based, telescopic detection of rings around Mars ismore difficult than for analogous rings of the gas giants, be-cause of the former’s lack of atmospheric methane. Methanehas very strong absorption bands at, e.g., 2.2 µ m, so thethe brightness of the giant planets drops substantially at se-lected wavelengths, facilitating the detection of faint rings.Mars has no analogous absorption bands. Nevertheless, theHubble Space Telescope (HST) has been used four timesto search for Martian rings. Two early attempts (HST pro-grams GO-5493 and GTO-7176) used inappropriate view-ing geometries and did not succeed; these results are un-published. On May 28, 2001, Mars’ hypothetical ring planeappeared edge-on to Earth within weeks of its opposition,providing the best Earth-based opportunity to detect theserings for several decades. Using the Wide Field/PlanetaryCamera 2 (WFPC2), Showalter et al. (2006) obtained upperlimits of τ < × − for the Phobos ring and τ < − forthe Deimos ring. This limit was sufficient to rule out rings atthe upper end of the dust density predictions by Krivov andHamilton (1997). A final attempt with HST, by the sameteam, employed a slightly inferior viewing opportunity inDecember 2007. Using the finer sensitivity of the AdvancedCamera for Surveys (ACS), the observing plan had the po-tential to detect rings 30–100 times fainter than the previouslimit. However, due to the failure of the ACS prior to theobservations, the system was again imaged using WFPC2and the ring detection threshold could not be improved.Despite the lack of detections, the dynamics of dust in theMartian environment is well understood, and there remainslittle doubt that dust rings, at some very low level, must bepresent. The most plausible remaining method for detectingthem would entail placing a sensitive dust detector into orbitaround Mars. Japan’s Nozomi spacecraft did carry such aninstrument, but it failed to enter orbit around Mars in 1999as planned. Perhaps some future Mars mission will finallyreveal these long-sought rings. The discoveries of Pluto’s small moons Nix and Hydra in2005 (Weaver et al., 2006) raised the possibility that it, like Mars, could harbor a tenuous ring system. Charon is lesslikely to be a major source of dusty rings because its gravita-tional field will more efficiently retain any dust ejected fromits surface. Using the discovery images from HST, Steffl andStern (2007) searched for rings in the orbits of the two smallmoons. They obtained upper limits of a few × − in reflec-tivity which, depending on the rings’ albedos, correspondsto τ (cid:46) − . This is comparable to the conservatively esti-mated τ < − suggested by Stern et al. (2006).The limiting factor in the search by Steffl and Stern (2007)was the extensive glare from Pluto and Charon. Showalteret al. (2011) used an alternative technique with HST to con-trol for and subtract the glare pattern, making a more sen-sitive ring search possible. That program did not detect anyrings, setting a new upper limit of τ < a few × − . How-ever, it did reveal a fourth moon, Kerberos. The followingyear, a more extensive HST observing program revealed afifth moon, Styx (Showalter et al., 2012).With New Horizons en route to its July 2015 flyby ofPluto, the revelation of such an extensive satellite sys-tem raised concerns about a possible dust hazard to thespacecraft. However, dynamical studies in advance of theflyby tended to minimize that risk. Showalter and Hamilton(2015) showed that the satellite system is on the edge ofchaos, which reduces the likelihood of a stable ring system.Porter and Stern (2015) showed that relatively few stableorbits exist between the four small outer moons, and thosethat do exist require a nonzero inclination. Furthermore, ithad been noted that, somewhat counterintuitively, solar ra-diation pressure is an important consideration in the Plutosystem because, although the Sun is very far away, Pluto’sgravity is also quite weak.Showalter and Hamilton (2010) showed that micron-size grains are quickly driven into orbits that collide withCharon, leaving behind particles primarily larger than ∼ µ m. More detailed models showed that Nix and Hydrashould be the main dust provider for broad and tenuousrings through micrometeoroid impacts. Combined effects ofradiation pressure, collisions of the ejecta with the largerbodies Pluto and Charon and escape, however, seriouslylimit the optical depth of such rings. Poppe and Hor´anyi(2011) estimated optical depths on the order of 10 − forgrains between 0.1 and 100 µ m in size. On the other hand,Pires dos Santos et al. (2013) showed that radiation pres-sure remove very rapidly (on year-scales) particles with sizesaround 1 µ m, leaving rings with normal optical depth on theorder of 10 − .An extensive survey of the Pluto system was conductedthroughout the New Horizons mission approach phase. Nonew moons and no rings were detected, and the spacecraftpassed through the system safely. The final upper limit onthe dust optical depth was 10 − (Spencer et al., 2015). Afterthe flyby, the spacecraft conducted an outbound search forfaint rings at high phase angles. However, the analysis ofthat data set is still underway and no results have beenreported.Stellar occultations also provide an opportunity to searchfor rings. Optically thin rings would be generally unde-tectable by this method, but rings that are narrow and/or Sicardy & at al. dark could potentially show up in occultations before theyare imaged directly. Historically, this is how the rings ofUranus and the arcs of Neptune were discovered. Boisselet al. (2014) conducted one such search, setting an upperlimit of 30–100 m for the equivalent depth of a narrowring (see Chapter 4 for the formal definition of “equivalentdepth,” a form of radially-integrated optical depth). Simi-larly, Throop et al. (2015) set a limit of ∼
170 m assuminga nominal ring of width 2.4 km.
Studies of transient photometric changes have predomi-nantly focused on objects that brighten, such as novae orgravitationally micro-lensed objects. The exceptions to thisrule are the recent searches for exoplanet transits that findperiodic but shallow and short dimming events. Thousandsof exoplanets have been discovered using transit searches,however, with one exception, J1407 (Kenworthy and Ma-majek, 2015), these have not been interpreted in terms ofexoplanetary ring systems. Detection algorithms that relyon periodicity, fitting a known transit shape to the dim-ming event or that ignore deep events from eclipsing binarieswould likely discard an eclipse from a circumsecondary andcircumplanetary disk (Mamajek et al., 2012; Meng et al.,2014; Zuluaga et al., 2015). Such eclipses could be rare orhave long periods and if periodicity is required for a searchthey would not be found (Quillen et al., 2014; Petrov et al.,2015). They could have an unusual light curve transit shape,and so would not be well fit by a planet transit or eclipsingbinary light curve model (Meng et al., 2014; Dong et al.,2014; Rattenbury et al., 2015). The transits could be deeperthan expected for a planet transit and so would be classi-fied as a possible eclipsing binary and so ignored in planettransit searches.During an occultation (Fig. 7.8), structure in an occult-ing disk can be measured on the scale of a stellar radius or ∼ d object in orbit with semi-major axis a covers a band of area 2 πda during one revo-lution, i.e. a solid angle of 2 πd/a as seen from the star.An observer viewing the star with line of sight intersect-ing this band would see an eclipse of the star. The to-dal solid angle covered by a sphere being 4 π , the ratio p = (2 πd/a ) / (4 π ) = d/ (2 a ) gives the probability that aneclipse is seen from a distribution of systems during a sur-vey that goes on long enough to include the period of the star%J1407%planet’s%mo2on%around%the%star%to%observer% planet% Figure 7.8
Sketch illustrating the modeling of possible ringsaround J1407b, the putative companion of J1407 (see text).During its motion around the star, an exoplanet surrounded byrings may cause the dimming of the star as seen by an observer(here far away on the lower left side of the figure). The sizes ofthe planet and its ring system are not on scale, they have beenenlarged for better viewing. orbit, taking into account all possible orientations and as-suming a uniform distribution of orientations. If disks fill alarge fraction of a secondary’s Hill radius, then the probabil-ity that a sample of young stars star exhibits eclipses couldreach as high as 10 − (see equation 14 of Mamajek et al.2012).With the discovery of the J1407 dimming event, it wasargued from the number above that the probability of find-ing a dimming event by an eclipse of a circumsecondary orexoplanetary ring system in a large photometric survey isnot small (Mamajek et al., 2012). A large uncertainty af-fecting the detection probability for eclipsing disks is thelifetime of circumplanetary and circumsecondary disks, withyounger stars being most likely to host extended and densecircumplanetary or circumsecondary disks, and suggestingthat young stellar populations would be most likely to ex-hibit disk or ring system eclipses.The low fraction of field eclipsing binaries that exhibit disklike features suggests that the size and optical depth of ringsystems and circumbinary disks decreases with age (Menget al., 2014). A survey of 40,000 stars in the 2MASS calibra-tion database that searched for dimming events and did notrestrict the search to periodic light curves, primarily foundnew eclipsing binaries but also found dimming events fromvariable young stars (Quillen et al., 2014). The KELT pho-tometric survey recently discovered long and deep dimmingevents from young stars. The 2014 dimming of RW Auri-gae A was greater than 2 magnitudes and lasted 6 months(Petrov et al., 2015). The star RW Aur also exhibited a6 month long 2 mag dip in 2010 (Rodriguez et al., 2013),while DM Ori exhibited, twice, dips of 1.5 mag lasting 6months (Rodriguez et al., 2016). These types of events aresometimes called “dippers”. Even though the Kepler missiondiscovered thousands of short period planets in transit, noneso far exhibit ring systems – perhaps short period planetscannot support extended ring systems (Hedman, 2015). Be-cause they did not restrict their search to periodic systemsor light curves that brighten, the citizen scientists in thePlanet Hunters consortium recently discovered an F star,KIC 8462852, exhibiting irregularly shaped, aperiodic dips ings beyond the giant planets Table 7.3.
Eclipsing Circumsecondary Disks
Object Eclipse length Period Depth a Primary Disk Temp.EE Cep b c d e
15 days 468 days 1.5 B9 6000KOGLE-BLG 182.1.162852 f
100 days 3.5 years 1–2 n.a. 300 KJ1407 g
60 days > a Measured in magnitude drop. b Ga(cid:32)lan et al. (2012). c Chadima et al. (2011). d Meng et al. (2014). e Dong et al. (2014). f Rattenbury et al. (2015). g Kenworthy et al. (2015).in flux down to below the 20% level (Boyajian et al., 2016).Surprisingly this star does not exhibit the behavior of ayoung star. The dips in the light curve might be explainedwith a dust cloud created by a destructive impact betweentwo large planetesimals or families of evaporating comets(Bodman and Quillen, 2016). Another star, the white dwarfWD1145+017 exhibits 3-12 minute deep (0.5 mag) transitevents (or dips) that could be due to disintegrating comets(G¨ansicke et al., 2016). Recently more than twenty young( ∼
10 Myr old) late-K and M dwarf stars were observed inthe Kepler Mission K2 Campaign Field 2 that host proto-planetary disks and exhibit quasi-periodic or aperiodic dip-pers (Ansdell et al., 2016). Magnetospheric truncation andaccretion models can explain why dusty material is lifted outof the midplane to obscure the star causing the light curvedips and why so many young low mass stars are dippers(Bodman et al., 2016).
Two bright stars, EE-Cep and Epsilon Aurigae, have longbeen known to exhibit deep eclipses. These are both long pe-riod systems hosting circumsecondary eclipsing disks withearly type primary stars. Both disks have radial struc-ture such as a central clearing and in EE-Cep this causesasymmetry in the light curve (e.g., Ga(cid:32)lan et al. 2012). Re-examination of eclipsing binary light curves in archival datahave revealed three more eclipsing disk systems, OGLE-LMC-ECL-11893 with a 468 day period (Dong et al., 2014)and OGLE-BLG 182.1.162852, a bulge object with a 3.5year period (Rattenbury et al., 2015) and OGLE-LMC-ECL-17782, exhibiting 2 day eclipses in a 13 day period; this likelyhost a transient B-star blow-out disk (Meng et al., 2014).Each eclipse of OGLE-LMC-ECL-11893 is remarkably sim-ilar and multi-color photometry shows that dust in the diskcauses reddening (Dong et al., 2014). The eclipse shape canbe fit with either a thin dusty disk or a thick gas and dustdisk (Scott et al., 2014). Existing multicolor photometricobservations could in the future be used to study the dustproperties. These known eclipsing disk systems are listed inTable 7.3. Disk temperatures are estimated from the orbitalperiod and the luminosity of the primary and span a widerange suggesting that these systems may in future provideinteresting settings to study disk composition through spec-troscopy. An interesting case is J1407 (1SWASP J140747.93-394542.6), a 16 million year old, pre-main sequence K5-typestar of some 0.9 solar mass in the Sco-Cen OB association. Itexhibited a complex 54 day deep eclipse in April 2007, witha maximum depth greater than 3 magnitudes (Mamajeket al., 2012; van Werkhoven et al., 2014). The long eclipsewas discovered in a Super Wide Angle Search for Planets(SuperWASP) light curve but a few data points from theAll Sky Automated Survey (ASAS) confirmed that the stardropped in brightness in 2007. Continued monitoring andhigh contrast imaging rule out a bright or stellar secondaryobject (Kenworthy et al., 2015). An optically thick ringpassing in front of the star, causes a change in slope (fluxvariation per unit time) dependent on the angular rotationrate of the ring (also see limits on radius of occulting objectsin the KIC 8462852 system by Boyajian et al. 2016).More detailed modelings of the slopes have been con-ducted by Kenworthy and Mamajek (2015) and Kenworthyet al. (2015), see Fig. 7.8. Using slope changes in the lightcurve, each corresponding to a ring edge, the J1407 eclipsingsystem has been modeled as a complex set of more that 35thin rings lying in a oblique plane. The large slopes at someepochs suggest that the secondary object hosting the ringsystem orbits at no more than a few AU from the primarystar on an eccentric orbit, with a period estimated from afew to some 30 years. The ringed object would be a giantplanet of some 15-25 Jovian masses, while the ring systemwould contain about one Earth mass and span a diameter ofabout 180 millions km (1.2 AU). This can be compared toSaturn’s rings, which contain about 10 − Earth mass andis more than 600 times smaller than the system consideredhere.The complex substructure suggests that the ring systemis very thin and hosts moons that maintain sharp edges atLindblad resonances, or open gaps in the disk. Crude esti-mations based on the width of one of these gaps suggest thatit could stem from a Mars-size or small-Earth type object(Kenworthy and Mamajek, 2015). As more constraints ofthe disk thickness and planet mass are gathered, Eqs. 7.10and 7.11 may be used to better assess the masses of thoseputative moons.As a word of caution, we note that continued photometricmonitoring of J1407 (Erin Scott, private communication)has not revealed new eclipse episodes, as is expected if theringed planet has an orbital period of a few years. If ongoing Sicardy & at al. monitoring fails to find new eclipses over the next decades,then it may become impossible to account for the eclipsewith an extended ring system orbiting a secondary object.This said, an intringuing issue is the fact that the J1407putative ring system would extend much beyond the planetRoche limit (usually some 2-3 planetary radii). These ringswould then represent transient features en route towards anaccretion process that will form a retinue of moons aroundthe planet. Scaling from models of the proto-Jovian nebula,Mamajek et al. (2012) estimate that the lifetime of a circum-Jovian disk could be as long as several millions years, thuscomparable to the age of J1407. However, this challengesthe mainstream idea that rings exist only inside the Rochelimit of their central planets, as accretion should proceedvery rapidly (over a few orbital revolutions) to form moons.To prevent such outcome, Toomre’s parameter Q should bemaintained just above unity. In that context, Eq. 7.4 can bere-written (Sicardy, 2006): ha ∼ M r M p , (7.14)assuming a uniform ring of radius a , mass M r and thickness h surrounding a planet of mass M p . For M r comparable toEarth’s mass, M p of some 20 Jovian masses and a a littlebit above 1 AU (see above), this implies h ∼ ,
000 km. Atthis point, the mechanism causing the stirring of the diskand maintaining this thickness remains to be explained.
As shown in this chapter, rings beyond the giant planets ap-pear to be more common features than previously thought.This has important implications at different levels.First, this raises the question of whether rings share somebasic, universal physics, or, on the contrary, if they followa wide variety of disconnected behaviors depending on thecontext. For instance, Chariklo’s rings and the material sur-rounding J1407b exhibit sharp edges or gaps, that are alsoencountered in Saturn’s and Uranus’ rings. Are those fea-tures all caused by shepherding nearby bodies (satellites orplanets), or do they stem from other, yet to be describedphysical processes? In fact, none of the “moonlets” that arethought be responsible for the narrow rings or gaps in theSaturnian C ring and Cassini Division have been discoveredso far (Colwell et al., 2009). As high resolution imaging issteadily improving thanks to larger telescopes, adaptive op-tics or space instruments, it is now of paramount importanceto discover (or rule out) the presence of confining bodies as-sociated with sharp edges and gaps in the newly discoveredrings.At another level, rings can tell us a lot about the bodythey encircle. With the advent of the European SpaceAgency GAIA mission, star catalogs with absolute accuracyof a fraction of milliarcsec will be released soon. In thatcontext, stellar occultations by Chariklo’s rings will be rou-tinely observed by many teams. Those campaigns will thenprovide accuracies of better than one kilometer on the rings’ orbital elements. This might lead to the discovery of ringproper modes, as observed in Uranus’ rings (see the Chap-ter 4 by Nicholson et al. ) and then provide the ring par-ticles’ mean motion, a direct way to determine Chariklo’smass, and thus its density through its dimensions. In thesame vein, the rings’ precession rates could yield Chariklo’sdynamical oblateness J , an important parameter to under-stand its internal structure. In short, rings may be preciousprobes of the gravity field of their host body.Those programs are not restricted to Chariklo, but alsoaimed at searching for material around other Centaurs,TNOs and asteroids. This may lead to the discovery of newring systems, or rule them out with a safe margin. It willthen be possible to address on firmer ground the questionof whether “small body” rings exist only around Centaurs,and why it is so, or if on the contrary, they are also presentaround very remote TNOs or even nearby asteroids. If exclu-sive to Centaurs, rings could be the witnesses of the troubledhistory of those objects (e.g. stemming from close encounterswith giant planets), or a mere endogenous product associ-ated with cometary activities of those bodies, or the outcomeof a fine tuning of icy composition, size and temperatureconditions, or the result of some other unkown processes.As discussed in this chapter, rings might also have existedaround the Saturnian satellite Iapetus and Rhea. However,those rings should have been quite different from each other,with a massive (relative to the satellite) disk that fell alongIapetus’ equator early in the history of the Solar System,and a relatively recent low-mass ring that sprinkled Rhea’sequator. In any case, they would be remnants of interestingprocesses, and would tell us how a collisional disk or an ob-ject can be driven toward a body through tidal interactionsand fall onto its equator. In that vein, it is important tocheck – using well-sampled stellar occultations – if a ridgeexists along Chariklo’s equator (or around other Centaurs).This would be a nice confirmation that rings may indeedexplain Iapetus’ equatorial feature.Turning to exoplanetary rings, we note that in 2012 tran-sient events were considered uninteresting and completelyignored. The discovery of new eclipsing circumsecondarydisks (Dong et al., 2014; Rattenbury et al., 2015), a candi-date exoplanetary ring system (Mamajek et al., 2012; Ken-worthy and Mamajek, 2015) and deep transient dimmingevents in both young and old stars from Kepler Mission data(Boyajian et al., 2016; Ansdell et al., 2016) imply that photo-metric observations can uncover new eclipsing disk systems.Up to now all eclipsing and transient dimming events havebeen found in archival data, making it difficult to follow upnon-periodic or long period eclipsing systems. In two cases,the same dimming events were found in more than one pho-tometric archive, giving confirmation (J1407, Mamajek et al.2012 and the dimming of V409 Tau, Rodriguez et al. 2013).Some of the dimming events seen in KIC 8462852 could havebeen detected from the ground. This system is now beingmonitored for new dimming events which may allow a mul-ticolor photometric study. It is possible to mount a transientdetection program that triggers on dimming events allowingmulticolor or high cadence observations (and possibly spec- ings beyond the giant planets troscopic observations) of rare, and long period, dimmingevents.Future and more accurate photometric studies of largerpopulations of stars could detect dimmings caused by anexoplanetary ring system as rich and old as Saturn’s as wellas counterparts at earlier epochs.In that context, an interesting issue is the location ofthose rings relative to the exoplanet’s Roche limit. WhileChariklo’s rings seem to lie a little bit outside of, but stillnear Chariklo’s Roche limit, the putative exoplanetary ringsassociated with J1407b are well outside that range. Thisundermines the paradigm of rings as collisional disks resid-ing inside the Roche limit of the central body in order toprevent rapid accretion into individual objects. So, we areeither very lucky to observe today the J1407b ring systembefore it coalesces into satellites, or our understanding ofaccretion time scales needs revisions. In any case, an esti-mation of the probability to detect by mere chance a ringsystem among all the transit events now observed is verymuch wanted. This might put constraints on the efficiencyof confining mechanisms and on accretion time scales, thusallowing us to better understand the various steps that ledto the formation of planets and satellites, including in ourown Solar System.B.S. acknowledges funding from the French grant “BeyondNeptune II” (ANR-11-IS56-0002) and from the EuropeanResearch Council under the European Community’s H2020(2014-2020/ ERC Grant Agreement no. 669416 “LUCKYSTAR”). K.J.W. acknowledges funding from the NASA Ori-gins program, and NASA SSERVI program (Institute ofthe Science of Exploration Targets) through institute grantnumber NNA14AB03A. E F E R E N C E S
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