Icarus 215 (2011) 584–595

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Icarus

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An igneous origin for Rima Hyginus and Hyginus crater on the Moon

Lionel Wilson a,b,⇑, B. Ray Hawke b, Thomas A. Giguere b,c, Elspeth R. Petrycki a

a Lancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UKb HIGP, University of Hawai’i, Honolulu, HI 96822, USAc Intergraph Corp., P.O. Box 75330, Kapolei, HI 96707, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 February 2011Revised 8 June 2011Accepted 5 July 2011Available online 4 August 2011

Keywords:Moon, SurfaceVolcanismMoon, InteriorGeological processes

0019-1035/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.icarus.2011.07.003

⇑ Corresponding author. Address: Lancaster EnvUniversity, Lancaster LA1 4YQ, UK.

E-mail address: l.wilson@lancaster.ac.uk (L. Wilson

We propose a detailed model for the formation of the lunar crater Hyginus, the associated Hyginus rille, aseries of collapse pits along the rille, and what we identify as a blanket of pyroclasts surrounding the cra-ter. We show that the geometry of the rille graben is consistent with its initiation by the intrusion of adike that did not breach the surface, and that Hyginus crater may be a caldera formed by surface subsi-dence into a partly evacuated sill that grew from the upper part of the dike. Dike propagation necessarilyentails the formation of a gas-filled cavity in the upper tip of the dike, underlain by a layer of magmaticfoam. Eruption through the graben boundary faults of a mixture of free gas from the dike tip and vesicu-lating and fragmenting magmatic foam from the sill provided enough released gas to explain the extentof the pyroclastic deposit. Subsidence of the crust in various places along the graben into the depressur-ized dike tip gas cavity led to the formation of the collapse pits. The model is strongly supported by theclose agreements between, first, the total volume of the pits measured from images and the volume of thedike tip gas cavity predicted by theoretical calculations and, second, the estimated volume of the pyro-clastic deposit and the calculated magmatic liquid content of the sill.

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1. Introduction

The Rima Hyginus region (Fig. 1a) occupies a broad structuraltrough concentric to the Imbrium basin, which has played animportant role in controlling the geology of the area. Hyginus cra-ter (9 km in diameter) is located south of Mare Vaporum at thejuncture of the two branches of the Hyginus linear rille. The crateris characterized by the absence of a raised rim and numerous dom-ical hills on the crater floor and is surrounded by a flat, smooth,low-albedo unit of controversial origin. Early workers (e.g.,Wilhelms, 1968) mapped the dark material as mare basalt. Pike(1976) concluded that the low-albedo unit was probably basaltlava flows or possibly pyroclastic debris. McCord et al. (1972),Schultz (1976), and Hawke and Coombs (1987) presented a varietyof evidence for a pyroclastic origin. More recently, Carter et al.(2009) used S-band (12.6-cm wavelength) radar images to investi-gate the dark deposit around Hyginus crater. They determined thatthe low-albedo unit has a lower-backscatter cross section thanwould be expected for mare basalts of similar estimated titaniumcontent. Combined with very low circular polarization ratio values,this is very strong evidence that this area is covered in fine-grainedpyroclastic mantling material.

ll rights reserved.

ironment Centre, Lancaster

).

For many linear rilles on the Moon, their locations relative to im-pact basins and their orientation geometries strongly suggest thatthey are graben produced solely by large-scale tectonic stresses(Golombek, 1979; Solomon and Head, 1980). However, the presenceof subtle volcanic features associated with various lunar linear rilles(Schultz, 1976; Head, 1976; Mason et al., 1976; Lucchitta andWatkins, 1978) is evidence that at least some of them are grabenwhose formation is linked to the shallow intrusion of dikes (Headand Wilson, 1993; Petrycki and Wilson, 1999a, 1999b). There hasbeen much discussion of the factors that control whether dikes orig-inating at various depths in the lunar mantle will reach the surfaceand, when they do not, at what depths they will form dike-like orsill-like intrusions (Head, 1976; Head and Wilson, 1991, 1992,1993; Wichman and Schultz, 1995, 1996; Wieczorek et al., 2001,2006). However, the presence of the mare lavas is incontrovertibleevidence that some dikes do reach the surface. Where dikes only ap-proach the surface, there is still an element of tectonic control, inthat the stress state of the lithosphere determines the near-surfaceorientations of dikes propagating from deep within the interior, butthe presence of volcanic features associated with a linear rille cer-tainly requires at least one dike as a magma pathway. Furthermore,the stresses associated with the pressure distribution driving mag-ma upward to emplace a shallow dike intrusion have the potentialto cause the relationships between the width and depth of theresulting rille, if one forms, to be different from those associatedwith graben of purely tectonic origin (Petrycki et al., 2004).

Notation

SymbolD depth to top of dike, 830 (m)Db depth to base of foam layer, 8800 (m)E horizontal surface extension across graben (m)F fraction of bubbles crossing convection cell boundary

layerG width of graben (m)I integral in Eq. (6)K additional kinetic energy per unit mass added above

vent (m2)Mg total gas mass per unit dike width and length along

strike (kg m�2)Ml total liquid mass per unit dike width and length along

strike (kg m�2)Mti initial dike tip cavity gas mass per unit area (kg m�2)Mtf final dike tip cavity gas mass per unit area (kg m�2)N number of convective cycles required to collapse foamP gas pressure (Pa)Pb pressure at base of foam layer, 4 � 107 (Pa)Pf final (negligible) gas pressure after expansion into vac-

uum (Pa)Pg gas pressure in dike tip after foam relaxation (Pa)Pi pressure in gas in propagating dike tip cavity (Pa)Px pressure at any distance x above base of foam layer (Pa)Q universal gas constant, 8314 (J kmol�1 K�1)R maximum range of pyroclasts, �3 � 104 (m)Rel Reynolds number of laminar flowRet Reynolds number of turbulent flowS depth of subsidence of graben floor, 130 (m)T magma temperature, 1750 (K)Ub rise speed of gas bubble (m s�1)Ucl speed of overturning magma in laminar flow (m s�1)Uct speed of overturning magma in turbulent flow (m s�1)Uf final speed of pyroclasts leaving vent region (m s�1)Ug gas flow speed in permeable foam (m s�1)Uh horizontal speed of convecting magma (m s�1)Um rise speed of magma, 30 (m s�1)Uv gas–pyroclast mixture speed in vent (m s�1)

Us speed of sound in gas–pyroclast mixture (m s�1)W dike width, 240 (m)X distance bubbles rise in time sdrift (m)Y average bubble separation in foam layer (m)Z vertical extent of tip cavity during dike propagation (m)Zf final cavity volume per unit area (m)f dimensionless friction factor, �10�2

g acceleration due to gravity, 1.62 (m s�2)m molecular mass of magmatic gas, 28 (kg kmol�1)n mass fraction of gas released from magmavg partial specific volume of gas in magmatic foam

(m3 kg�1)vl partial specific volume of liquid in magmatic foam

(m3 kg�1)x distance above base of foam layer (m)DZ increase in length of dike tip gas cavity mDq effective magma–host rock density difference, 100

(kg m�3)Dr density difference due to cooling of magma (kg m�3)a coefficient of volume expansion of magma, 3 � 10�5

(K�1)c ratio of specific heats at constant pressure and volumee vesicularity, i.e. gas volume fraction in magmag viscosity of bubble-free magma, 1 (Pa s)gb bulk viscosity of magmatic foam (Pa s)gg CO viscosity, 55 � 10�6 (Pa s)j thermal diffusivity of magma, 10�6 (m2 s�1)qc density of crustal rocks, 2800 (kg m�3)qg density of gas after foam collapse (kg m�3)ql liquid magma density, 3000 (kg m�3)s time scale for heat transfer from dike to host rocks (s)sct time for convective overturn of foam layer (s)sdrift time for bubbles to cross convection cell boundary layer

(s)sf time to transfer all gas out of foam (s)/ diameter of gas bubble (m)/0 initial diameter of gas bubble, 2 � 10�5 (m)

L. Wilson et al. / Icarus 215 (2011) 584–595 585

The recognition of a pyroclastic deposit associated with theHyginus crater strongly suggests that the Rima Hyginus linear gra-ben is the result of a shallow dike intrusion. Furthermore, the pres-ence of two caldera-like depressions near the middle of the rille andof 23 smaller rimless craters within or overlapping the rille (Fig. 1a)also suggests a link to volcanism. Hyginus crater is an example ofone of the rare cases where a shallow magma intrusion of signifi-cant volume formed on the Moon (Head and Wilson, 1991). Thepresence of subtle graben and fracture-like features radial to Hygi-nus crater may be residual evidence of the ground deformationcaused by the sill emplacement. The possibility that at least someof the small craters are of primary or secondary impact origin can-not entirely be ruled out, but their morphologies and close spatialassociations with the rille led Wilhelms (1968) and Pike (1976) toclassify most of them as endogenic collapse craters. We have inter-preted the morphological features of Rima Hyginus, its associatedpyroclastics and the rimless depressions in this volcanic context.We show how the various features can be related to the geometryof the dike intrusion and the properties of the magma.

2. Measurements

Morphological data were obtained from Lunar Orbiter V frames96 M and 97 M and from Lunar Orbiter IV frame 97H1; the area

covered is shown in Fig. 1b, on which the measured features areidentified. Auxiliary data from NSSDC (1971) allowed the variationof the horizontal scale as a function of the local position withineach of these frames to be interpolated from the listed imageside-lengths. The local solar elevation was similarly obtained bylinear interpolation from the values listed for the image corners.In the Orbiter V frames the horizontal scale averaged�200 m mm�1 and the solar elevation was �18�; in the OrbiterIV frame the scale was �640 m mm�1 and the solar elevationwas�19.5�. The long and short axes of the two caldera-like depres-sions near the middle of the rille (numbered 18 and 19 in Fig. 1b)and of 23 smaller craters within or overlapping the rille were mea-sured directly (Table 1(a)) along with the width of the graben at 10locations (Table 1(b)). The shapes of the craters (flat floor or bowlshape) were noted. The corresponding depths of the craters andthe graben were obtained from measured shadow lengths andthe interpolated solar elevation.

Some of the collapse craters were pits confined to the grabenfloor; however, others, specifically those numbered 8, 10, 11, 12,13, 14, 15, 16, 17, 18 and 20 in Fig. 1b, were larger than the widthof the rille. The measured volumes of these craters therefore in-cluded the volume of crust that had subsided during the earliergraben-forming event. Thus to find the collapse volume that eachof these craters represented, the estimated width and depth of

Fig. 1. (a) Region surrounding Rima Hyginus and Hyginus crater. Part of LunarReconnaissance Orbiter wide-angle camera global mosaic. (b) Lunar Orbiter V frame96 M showing locations of collapse craters and locations where rille width anddepth were measured. Image rotated with north to the right for clarity. Inset frompart of Orbiter IV frame 97H1 showing eastern part of rille has top left cornercoincident with bottom left corner of main image.

Table 1Morphological measurements on Rima Hyginus features.

Crater # Long (km) Short (km) Depth (km) Volume (km3)

(a) Collapse craters: long and short axis lengths, depths and volumes of cratersidentified by numbers in Fig. 1(b)

1 1.66 1.44 0.13 0.162 0.89 0.77 0.06 0.023 1.11 1.00 0.13 0.074 1.33 0.77 0.16 0.095 1.88 1.22 0.19 0.236 2.66 2.55 0.29 1.017 2.99 2.66 0.32 1.328 3.54 3.32 0.41 2.559 2.44 2.10 0.35 0.94

10 3.76 3.10 0.45 2.7311 2.55 2.10 0.35 0.9812 3.88 3.54 0.48 3.4413 4.43 2.66 0.51 3.1514 5.31 5.09 0.74 10.4215 3.54 3.54 0.48 3.1616 4.43 3.98 0.58 5.3417 3.76 3.10 0.29 1.7718 10.16 8.79 0.84 58.9219 5.54 4.32 0.52 6.4820 6.64 3.76 0.39 5.0921 1.77 1.22 0.23 0.2622 1.99 1.66 0.29 0.5123 3.10 2.66 0.26 1.1324 1.91 1.59 0.11 0.1825 2.87 0.64 0.34 0.33

Location Width (km) Depth (m)

(b) Rille graben: width and depth of graben at locations identified by letters inFig. 1(b)

A 2.11 67B 2.00 68C 2.33 68D 2.66 34E 2.89 136F 2.44 103G 1.80 68H 9.01 840J 3.22 139K 3.55 315

Notes: Location H gives the depth of crater 18, not the rille depth.

586 L. Wilson et al. / Icarus 215 (2011) 584–595

the graben at the location of each crater was interpolated from thenearest actual graben width and depth measurements and the cor-responding volume was subtracted from the measured cratervolume.

While most of the 23 non-caldera craters closely aligned withthe rille and listed in Table 1 appear rimless in the availableimages, and are plausibly collapse craters directly associated withthe rille, not all are mapped as such by Wilhelms (1968) and Pike(1976). In the cases of craters 1 and 2 this was because the resolu-tion available to these mappers was too poor. There is disagree-ment between these authors in the case of crater 23, and thoughWilhelms (1968) interprets crater 24 as an endogenic feature, weconsider it to be part of a secondary crater cluster. We have there-fore calculated the total volume of the non-caldera craters both byincluding craters 1, 2, 23 and 24 (34.2 km3) and by excluding all

four of these craters (32.7 km3) to give an idea of the uncertaintyinherent in using the morphological data. The depths of the twocaldera-like depressions are 840 m (crater 18) and 520 m (crater19) and their total volume is 62.7 km3. The mean depth of the rilleincreases from East to West from �65 m to �315 m as its width in-creases from �2.2 km to �3.6 km; the average rille depth is there-fore 190 m and the average width is �2900 m.

A number of data products (visible albedo, FeO map, TiO2 map,optical maturity image: Lucey et al., 2000a, 2000b) derived fromClementine UV–VIS images were utilized together with the S-bandradar image presented by Carter et al. (2009) to map the asymmet-ric distribution of pyroclastic material around Hyginus crater(Fig. 2). The maximum range of the pyroclasts is 29.5 km (mea-sured from the center of Hyginus crater) to the ESE and 22.5 kmto the SW, with a typical range of 14–15 km. Hawke and Coombs(1987) suggested that the Hyginus pyroclastic deposit was rela-tively thin. Carter et al. (2009) presented an S-band image showingcircular polarization values for the Hyginus region as their Fig. 11.An analysis of the 12.6-cm backscatter and circular polarization ra-tio (CPR) images provided information concerning thickness varia-tions in the Hyginus pyroclastic unit. The visible boundaries of thelow CPR value regions do not extend to cover all of the low albedoareas mapped as pyroclastics in Fig. 2. This indicates that theHyginus pyroclastic deposit is relatively thin (610 m). Adopting amean radius of 15–20 km and a maximum thickness of 10 m

Fig. 2. (A) Clementine 750 nm image of Hyginus region. Pyroclastic deposit indicated by black line. (B) FeO map derived from Clementine UV–VIS images for Hyginus region.(C) TiO2 map of region shown in (A). (D) Optical maturity parameter image produced for area shown in (A). Brighter tones indicate lower maturity (fresher material).

Fig. 3. Schematic diagram, not to scale, showing geometry of rille graben andsubsurface dike and faults.

L. Wilson et al. / Icarus 215 (2011) 584–595 587

implies a total volume of up to �10 km3. Finally, the absence of al-bedo, spectral, and radar anomalies associated with the chains ofendogenic craters northwest of Hyginus crater indicates that littleor no pyroclastic debris was erupted from these features. A col-lapse model for the origin of these craters is supported.

3. Geometry of proposed dike

Fig. 3 shows the geometry of the graben system and the pro-posed dike just after dike emplacement is complete (not to scale).The total horizontal surface extension is E and the depth of subsi-dence of the graben floor is S. The width of the graben is G and thedepth to the dike top is D. The dike width is W. It is not easy toestablish a relationship between the geometry of a graben andthe geometry of an underlying dike. Mège and Masson (1996) dis-cuss a range of possible relationships determined from the treat-ments given by Pollard et al. (1983), Mastin and Pollard (1988),

Table 2Variation with n, the mass fraction of CO gas produced by smelting, of the pressure, Pi,in the gas cavity at the dike tip; the vertical length of the gas cavity, Z; the masses ofgas, Mg, and liquid magma, Ml, per unit dike width and per unit distance along strike;and the mass of gas in the dike tip cavity, Mti.

n (ppm) Pi (MPa) Z (m) Mg (kg m�2) Ml (kg m�2) Mti (kg m�2)

500 0.14 30 1.22 � 104 2.44 � 107 8.01000 0.28 61 2.31 � 104 2.31 � 107 32.21500 0.41 91 3.30 � 104 2.19 � 107 72.52000 0.55 121 4.21 � 104 2.10 � 107 128.9

588 L. Wilson et al. / Icarus 215 (2011) 584–595

and Rubin and Pollard (1988). Analysis of two dike-induced grabenin Iceland using a model taking account of the inelastic response ofthe crust to the fractures forming the graben walls led Rubin(1992) to propose that the ratio of the graben width to the depthto the dike top was a factor of �4 in one case and 2.9 in the other.Based on this we adopt the value 3.5, and note that this ratio is notexpected to be a function of gravity (Rubin, 1992). The same Icelan-dic examples implied that the ratio of dike width to amount of ver-tical subsidence of the graben floor was 1.0 in one case and 1.5 inthe other. These values are consistent with the idea that the exten-sion represented by the width of the graben is approximately equalto the width of the underlying dike: for graben boundary faultsdipping at �60� the ratio would be [(E/S) = 2 tan 30�=] 1.15. Over-all, we adopt the mean value 1.25 as an average estimate. Usingthese ratios, the implied depth to the top of the dike underlyingthe Hyginus graben is D = 2900/3.5 = �830 m and the width ofthe dike is W = 1.25 � 190 m = �240 m, at the upper end of therange predicted by Wilson and Head (2010). These values mustbe assumed to have errors of at least �20–30% but we use thesenominal values in subsequent calculations.

The total lateral extent of the two branches of the rille is close to100 km, so the underlying dike must extend laterally for at leastthis distance. The vertical extent of the dike is less easy to estimate,but it is reasonable to assume that the magma source is in theupper mantle. A depth of 100 km is adopted, based on the recogni-tion (Shearer et al., 2006) that many erupted lunar lavas areinferred on geochemical grounds to have come from at leastthis depth. The dike magma volume is then (100 km � 100 km �0.24 km=) �2.4 � 1012 m3. Assuming a magma density of�3000 kg m�3, the magma mass is �7.2 � 1015 kg.

4. Gas accumulation at the top of the propagating dike

It is inevitable that there will be a concentration of gas at thepropagating tip of any dike while motion is occurring (Lister andKerr, 1991; Rubin, 1995). This is due to the need to maintain alow pressure at the dike tip to maximize the pressure gradientdriving the dike propagation. In a rising dike, a gas-filled cavity willoverly a zone of magmatic foam (Wilson and Head, 2007). In thecase of dikes on the Moon (Wilson and Head, 2003) the gas willbe predominantly carbon monoxide, produced in a pressure-dependent smelting reaction between native carbon (graphite)and various metal oxides (Housley, 1978; Fogel and Rutherford,1995; Nicholis and Rutherford, 2006). The interface between thepure gas cavity and the foam is taken to be the level at whichthe gas bubble volume content of the foam, e, has reached a criticalvalue, probably �85% (see summary in Jaupart and Vergniolle(1989)), at which the foam is no longer stable; liquid drainsthrough the inter-bubble connections and the foam collapses. Tothe extent that the gas properties can be approximated by the per-fect gas law, the partial specific volumes of gas, vg, and liquid, vl, ina foam are readily shown to be

vg ¼nQTmP

ð1Þ

v l ¼1� nql

ð2Þ

where n is the mass fraction of gas in the gas–liquid mixture, ql isthe liquid magma density, P is the gas pressure, T is the magmatemperature, m is the molecular mass of the gas and Q is the univer-sal gas constant. The interface pressure Pi at which the gas volumefraction, e, is 0.85 is therefore given by

Pi ¼ð1� eÞnQTql

emð1� nÞ ð3Þ

The vertical extent Z of the tip cavity can be found from the pressureby assuming that the gradient of the pressure inside the dike isclose to that in the host rocks so that there is a negligible stressacross the dike walls (Wilson and Head, 1981). In this case, whenthe dike top is near the surface the magma pressure gradient isequal to the gradient of the lithostatic load, i.e.

dP=dz ¼ qcg ð4Þ

where qc is the density of the crust, say 2800 kg m�3, and g is theacceleration due to gravity, 1.62 m s�2. The pressure Pb at the baseof the foam layer is the pressure at which the smelting reaction be-gins, estimated by Nicholis and Rutherford (2006) to be close to40 MPa. Eq. (4) shows that, with the same assumption about thenear-lithostatic pressure gradient, this pressure is reached at adepth, Db, equal to 8.8 km below the dike tip, and so n is zero at thislevel and at all greater depths. Nicholis and Rutherford (2006) alsoshow that the smelting process occurs over a very small pressurerange once the threshold pressure is reached, so we can assume thatall of the magma in which the pressure is less than 40 MPa hascompleted the smelting process. The amount of CO produced canbe estimated from the chemistry of returned samples to be in therange 500–2000 ppm by mass (Nicholis and Rutherford, 2006; Saalet al., 2008; Rutherford and Papale, 2009). With the constants m forCO = 28 kg kmol�1 and Q = 8314 J kmol�1 K�1, and adoptingT = 1750 K and ql = 3000 kg m�3, we find the variations of Pi and Zwith n in the range 500–2000 ppm shown in Table 2. The pressureis expected to be less than 0.6 MPa and the cavity length up to�100 m.

Evaluating the volume of gas in the foam layer is not trivial, be-cause the density of the gas is a function of the pressure. The mag-matic liquid density is assumed constant at ql and the gas densityis assumed to be given by the perfect gas law as [(mP)/(QT)]. Thegas volume fraction is [vg/(vg + vl)] and the liquid volume fractionis [vl/(vg + vl)]. The total masses of gas and liquid per unit dikewidth and per unit dike length along strike, Mg and Ml, are thenthe integrals of the corresponding products of the volume fractionand density over the depth range corresponding to the pressurerange Pi–Pb. Substituting Eqs. (1) and (2) for vg and vl and integrat-ing, we find

Mg ¼nmql

gqc

� �I ð5aÞ

and

Ml ¼ð1� nÞmql

gqc

� �I ð5bÞ

where

I ¼Z Pb

Pi

PdPnQTql þ ð1� nÞmP

¼ Pb � Pi

ð1� nÞm�nQTql

ð1� nÞ2m2ln

nQTql þ ð1� nÞmPb

nQTql þ ð1� nÞmPi

$ %ð6Þ

Table 2 shows how Mg and Ml vary with n. Also given is the corre-sponding value of Mti, the very much smaller mass of gas per unit

L. Wilson et al. / Icarus 215 (2011) 584–595 589

dike width and per unit dike length along strike initially residing inthe dike tip cavity. This is found by multiplying the density of thegas, [(mPi)/(QT)], by the cavity extent Z.

5. Processes after dike propagation ceases

Immediately after the cessation of magma movement, gas bub-bles within the foam layer will be rising through the magmatic li-quid under buoyancy. Bubble migration in the upper part of thedike will have been occurring throughout dike propagation, but itis easy to show that the time scale of dike emplacement will havebeen short enough that negligible concentration of bubbles wouldhave occurred. The rise speed Um of mafic magma in a W = 240 mwide dike will be turbulent and is given by

Um ¼WgDq

fql

� �1=2

ð7Þ

where f is a dimensionless friction factor of order 10�2 (Wilson andHead, 1981) and Dq is the effective density difference between themagma and its host rocks, determined by the net contributionsfrom the positive buoyancy of the magma in its mantle source re-gion and its probably negative buoyancy in the crust. Consider-ations of likely density values (Wilson and Head, 2010) show thatDq will be of order 100 kg m�3 and so Um will be �36 m s�1. Thusthe time required for the dike emplacement event from a 100 kmsource depth is �2800 s, i.e. less than 1 h. The rise of gas bubblesof diameter / in magma of viscosity g will involve laminar motionrelative to the host liquid at a speed Ub given by

Ub ¼/2qlg18g

ð8Þ

where neglect of the density of the gas relative to the much greaterdensity of the magma introduces at most �2% error. The CO gasbubbles are likely to nucleate with diameters of �20 lm (Sparks,1978; Larsen and Gardner, 2004; Yamada et al., 2005; Bai et al.,2008), giving them initial rise speeds in a lunar magma with viscos-ity �1 Pa s (Spera, 1992) of Ub = �0.1 lm s�1; thus during the�2800 s taken to emplace the dike, bubbles of this size will have ri-sen at most �280 lm. However, bubbles will grow after nucleationby decompression. In terrestrial magmas it is also likely that bub-bles will grow by absorbing gas molecules diffusing through themagmatic liquid, but in the lunar case this will probably be of minorimportance. This is because the smelting reaction will be completeeverywhere within the foam, and the only potential for adding gasto bubbles is if significant amounts of other species such as sulphuror chlorine are present. However, the vapour pressures of these vol-atiles in lunar magmas are expected to be much less than 0.1 MPa(Sato, 1979). Thus decompression will dominate, and the bubblesat the top of the foam layer will have expanded from their initialdiameters, �20 lm, due to the pressure decrease from Pb = 40 MPato Pi = �0.1 to �0.6 MPa. This implies a volume change by a factor ofbetween 400 and 70 and hence a diameter change by the cube rootof this factor, in the range �7 to �4, giving the bubbles diameters inthe range �140–80 lm. The corresponding bubble rise speeds are�5.3–1.7 lm s�1, and the rise distances during dike emplacementare �15–5 mm. These bubble rise speeds and travel distances all as-sume that the magma liquid viscosity is 1 Pa s. In the lower part ofthe foam layer this will be appropriate but, toward the top of thefoam layer, close packing of bubbles will lead to interactions caus-ing the effective viscosity of the liquid to increase. The bulk viscos-ities, gb, of foams are proportional to the host liquid viscosity, g, butare complex functions of the bubble volume fraction, e, and the bub-ble size distribution (Kraynik, 1988). A simple function proposed byJaupart and Vergniolle (1989) for mafic magmas is

gb ¼ gð1� eÞ�5=2 ð9Þ

which, with e as large as 0.85, would imply that gb was as much as100 times larger than g, i.e. �100 Pa s. This would reduce the risespeeds of largest bubbles to �0.05 lm s�1, and reduce the distancesthat they could rise in 2800 s to �140 lm. Thus bubble migrationduring dike emplacement can be neglected.

After dike propagation ceases, bubble rise will continue and gaswill be added to the dike tip cavity, raising the gas pressure there. Ifthe magma in the dike were stagnant, bubbles in the foam layerwould rise until either all of them accumulated into the gas pocketat the top of the dike or cooling of the magma inward from the dikewalls increased its viscosity to the point where bubble motion wasnegligible, eventually ceasing completely as solidification began.The time scale s for the penetration of a thermal wave from theedge to the middle of a dike of width W by conduction alone is gi-ven (Carslaw and Jaeger, 1947) by

s ¼ ðW=2Þ2

2:3jð10Þ

where j is the thermal diffusivity of magma, �10�6 m2 s�1. Thuswith W = 240 m, s is �6.3 � 109 s, i.e. �200 years. Note that thetimescale for complete freezing of the dike is about 30% longer thanthis (see Turcotte and Schubert, 2002, Sections 4–19). If bubble risethrough the central, so far uncooled, part of the stagnant foam layercontinued for all of the �200 year cooling time, 20 lm diameterbubbles rising at 0.1 lm s�1 would travel �615 m, and �140 lmdiameter bubbles rising at 0.05 lm s�1 in the viscous upper partof the foam would rise�300 m. The vertical extent of the foam layeris �8.8 km, and so only a small fraction of the gas in the foam wouldmigrate into the gas cavity at the top of the dike as a result of simpleupward drifting of bubbles in stagnant magma.

However, other processes aid gas migration. Magmatic foamsare at least partially permeable (Burton et al., 2007). Percolationtheory suggests that permeability may become large at vesiculari-ties greater than �30% in all magmas (Sahimi, 1994; Blower, 2001;Takeuchi et al., 2005), and there is evidence that the threshold maybe as low�10% in basaltic liquids (Saar and Manga, 1999). The flowspeed of gas through a foam is influenced by the typical pathwaydiameter, here in the same range as the bubble diameters /, andthe tortuosity of the foam network. For CO at magmatic tempera-tures the viscosity gg will be �55 � 10�6 Pa s (Kaye and Laby,1995) and the (laminar) gas flow speed Ug will be given by

Ug ¼gql/

2

32ggð11Þ

where the gas density can be neglected relative to the magmatic li-quid density. For / in the range 20 to �100 lm, Ug is in the range 1–30 mm s�1. The corresponding Reynolds number for the gas motionis in the range 2 to �300, confirming the laminar flow. Even at thesmaller speed, and allowing a factor of, say, �3 for the tortuosity ofthe network, CO gas could percolate the �8.7 km extent of the foamlayer in a little less than 1 year. We consider this to be a likely upperlimit for the time needed for gas concentration at the top of thedike.

A second issue is that the dike magma is unlikely to remainstagnant. Cooling through the dike walls will increase the densityof the magma at the margins relative to magma in the central partof the dike. In all of the dike below the foam layer, the resultingnegative buoyancy will promote convection, with magma initiallydescending at the walls and rising in the middle of the dike, thoughthe pattern may subsequently be more complex (Stevenson andBlake, 1998). Within the foam layer, the presence of the gas bub-bles reduces the density relative to that of deeper magma, but itis still the case that foam near the dike wall is denser than foamin the middle of the dike. An estimate of the likely density

590 L. Wilson et al. / Icarus 215 (2011) 584–595

difference, Dr, driving convection can be obtained by assumingthat magma in the core of the dike is at the liquidus temperatureand magma near the wall is at a temperature close to the solidus.The difference between these two temperatures for lunar basaltsmay range from �100 to 300 K (see Table 1 in Williams et al.(2000)). The coefficient of thermal expansion of mafic magmas isa = �3 � 10�5 K�1 (Turcotte and Schubert, 2002), and so the 100–300 K of cooling of a bubble-free magma of density 3000 kg m�3

would induce a density increase of�10–30 kg m�3. In an 80% foam,with bulk density �600 kg m�3, Dr would be �2–6 kg m�3. Theconvection speed will also be controlled by the magma viscosity.The speed is inversely proportional to the viscosity in laminar flowbut only very weakly dependant on viscosity if turbulent flow pre-vails. Initially the more viscous, upper part of the foam layer at thetop of the dike will resist taking part in the convection that rapidlydevelops beneath it. However, some of the lower part of the foamnear the wall may get swept into the convective flow, and hot, bub-ble-free magma will then rise into the central part of the base ofthe foam layer. This fresh magma will pass through the 40 MPapressure level which defines the onset of smelting and as a conse-quence will start to produce new bubbles of CO (though converselysome of the CO in bubbles in the descending flow near the dikewalls may react with metal in the magma in the reverse of thesmelting reaction that produced it).

More importantly for the present calculation, it will be the vis-cosity of the most viscous part of the foam that is included in theconvection cell that will determine whether convection is laminaror turbulent and, in the former case, will control the speed of theconvecting magma. To establish which convection mode is relevantwe calculate the flow speed using formulae for both laminar andturbulent flow and examine the implied Reynolds number in eachcase: self-consistency requires that turbulent flow must imply aReynolds number greater than �2000 whereas fully laminar flowmust imply a Reynolds number less than�100. Stevenson and Blake(1998) show that convection cells in dikes are slightly asymmetric,but using the approximation, adequate for the present purpose, thatequal volumes of magma take part in the ascending and descendingparts of the convection cell, the average magma flow speed in thelaminar regime, Ucl, in magma of bulk viscosity gb is given by

Ucl ¼gDrW2

48gbð12aÞ

In the turbulent regime, the average magma flow speed, Uct, is givenby the analog of Eq. (7) as

Uct ¼gDrW

2fql

� �1=2

ð12bÞ

Table 3Variation with bulk viscosity of magma, gb, and density difference driving motion,Dr, of the magma speed in a convection cell in a dike. Ucl is the magma speed if themotion is laminar and Uct is the speed if the motion is turbulent. Rel and Ret are thecorresponding Reynolds numbers. Dr = 4 kg m�3 refers to the foam layer andDr = 30 kg m�3 to the underlying bubble-free magma.

gb (Pa s) Dr (kg m�3) Ucl (m s�1) Uct (m s�1) Rel Ret

1 4 7776 2.9 1.1 � 1010 4.2 � 106

1 30 58,320 8.0 8.4 � 1010 1.2 � 107

10 4 778 2.9 1.1 � 108 4.2 � 105

10 30 5832 8.0 8.4 � 108 1.2 � 106

100 4 78 2.9 1.1 � 106 4.2 � 104

100 30 583 8.0 8.4 � 106 1.2 � 105

103 4 7.8 2.9 1.1 � 104 4.2 � 103

103 30 58.3 8.0 8.4 � 104 1.2 � 104

104 4 0.8 2.9 110 420104 30 5.8 8.0 840 1200105 4 0.08 2.9 1.1 42105 30 0.58 8.0 8.4 116

For each of a series of magma viscosities, Table 3 gives values of Ucl

and Uct, together with the corresponding Reynolds numbers Rel andRet, for Dr = 4 kg m�3, appropriate for foam, and for Dr =30 kg m�3, appropriate for bubble-free magma. It is clear that forall bulk viscosities less than 10,000 Pa s the laminar solution pre-dicts extremely large speeds and Reynolds numbers correspondingto turbulence, and is therefore not appropriate. The turbulent solu-tion, however, does lead to self-consistent solutions in these cases,and the motion is fully turbulent, with magma flow speeds of�3 m s�1 for the foam and �8 m s�1 for the bubble-free magma.Only if the magma viscosity exceeds 104 Pa s will the convectionbe laminar. This is, of course, irrelevant for the bubble-free magmaat depth in the dike, but is relevant for the foam. Eq. (9) implies thatwith a magma viscosity of g = �1 Pa s the bulk foam viscosity gb

will be �100 Pa s. Table 3 therefore shows that the foam shouldconvect in a turbulent manner at a speed Uct just less than�3 m s�1. One convective overturn of the �8.7 km deep foam layerwould require a time, sct, of �100 min.

Assuming convective overturn does occur, bubbles in the top-most part of the foam will burst into the free gas cavity in thetip of the dike. We assume that the interface between free gasand foam is fixed relative to the dike walls, in which case the frac-tion of the available bubbles that bursts depends on the bubble risespeed Ub, the bubble spacing, Y, and the time, sdrift, available for thebubbles to drift upward while being transferred horizontally acrossthe top of the convection cell at a speed Uh similar to the convec-tion speed, Uct, found above. sdrift is equal to the �120 m half-width of the dike divided by Uh. The fraction of the bubbles thatcan cross the boundary can be estimated by noting that thebubbles in a boundary layer at a depth where the pressure is P rep-resent a volume fraction, found by combining Eqs. (1) and (2),equal to {(nQTql)/[nQTql + (1 � n)mP]}. However, it is also the casethat if the bubbles are imagined arranged in a cubical array with aseparation Y, the volume fraction that they occupy is equal to thebubble volume (p/3/6), divided by Y3. Equating the two expres-sions for the volume fraction gives

Y ¼ /ðp=6Þ1=3 nQTqþ ð1� nÞmPnQTql

� �1=3

ð13Þ

The bubble rise speed Ub is given by Eq. (8) with the appropriatebulk magma viscosity gb substituted for g. Both Ub and Y requireknowledge of the bubble size / and hence of the pressure P at thetop of the foam layer, both of which vary with the magma CO con-tent, n. Table 2 gives the relevant values of P as a function of n; thebubble diameter / is given by

/ ¼ /0Pb

P

� �1=3

ð14Þ

where /0 is the 20 lm bubble nucleation size and Pb is the pressureat the base of the foam, 40 MPa. The distance a bubble at the top ofthe foam layer rises in time sdrift is X = (Ubsdrift). The fraction, F, ofthe bubbles that cross the boundary layer in one convective cycleis thus (X/Y) and the number of convective cycles required to trans-fer all the bubbles is N = 1/F = Y/X. With a convective overturn time

Table 4Variation with magma CO content, n, of conditions at the top of the foam layer:bubble diameter, /; bubble spacing, Y; bubble rise speed, Ub; bubble rise distance, X;number of convective cycles to transfer all bubbles, N; and total time to completebubble transfer, sf.

n (ppm) / (lm) Y (lm) Ub (nm s�1) X (lm) N sf (days)

500 132 112 47 1.94 58 4.01000 105 89 30 1.22 73 5.11500 92 78 23 0.95 83 5.72000 84 71 19 0.78 91 6.3

Table 5Variation with magma CO content, n, of the initial value, Z, the increment due to foamcollapse, DZ, and the final value, Zf, of the vertical extent of the gas-filled cavity in thedike tip, the final mass of gas per unit horizontal area of the cavity, Mtf, the resultingfinal density of the gas, qg, and the final gas pressure, Pg.

n (ppm) Z (m) DZ (m) Zf (m) Mtf (kg m�2) qg (kg m�3) Pg (MPa)

500 30 652 682 1.22 � 104 17.9 9.31000 61 1073 1134 2.31 � 104 20.4 10.61500 91 1411 1502 3.31 � 104 22.0 11.42000 121 1696 1817 4.22 � 104 23.2 12.1

L. Wilson et al. / Icarus 215 (2011) 584–595 591

of sct, the total time to transfer all of the gas from the foam to thedike tip cavity is sf = (Nsct). Table 4 gives the values of /, Y, Ub, X,N and sf for the range of magma CO contents, n. The gas transfertime, sf, is seen to be somewhat less than 1 week. We consider thisto be a likely lower limit for the time needed for gas concentrationat the top of the dike.

The transfer of gas from the foam into the dike tip gas cavitywill cause an increase in the gas cavity pressure. To evaluate thiswe need to find the original and final values of the mass of gas inthe cavity and the cavity volume, all expressed per unit width ofthe dike and per unit length along strike, for each of our range ofmagma CO contents. We already have the original gas massesper unit horizontal area: Mg and Mti in Table 2, so the final valueMtf is equal to (Mti + Mg). The initial volume per unit horizontalarea of the dike tip cavity is simply Z, also in Table 2. The increasein the volume per unit horizontal area of the gas cavity, DZ, will beequal to the total volume occupied by the bubbles in the foam intheir initial positions divided by the width and horizontal lengthof the cavity. This can be found by integrating the volume of thebubbles in an analogous way to the evaluation of the gas mass inEqs. (5a) and (6), giving

DZ ¼ nQTql

gqcð1� nÞm lnnQTql þ ð1� nÞmPb

nQTql þ ð1� nÞmPið15Þ

and so the final cavity volume per unit area is Zf = (Z + DZ). DividingMtf by Zf gives the new gas density, qg, and the perfect gas law thenrequires that the new pressure in the gas is Pg = [(qgQT)/m]. Table 5summarizes the relevant values as a function of the magma COcontent, n. Final gas pressures are in the range 9–12 MPa. Fig. 4

Fig. 4. Configuration of CO gas, magmatic foam and bubble-free magma in dikeimmediately on emplacement (left), and after complete segregation of the gasoriginally in the foam (right) assuming an eruption does not begin before completesegregation. Horizontal scale exaggerated by a factor of 2 for clarity.

compares the configurations of magma and gas in the dike: beforegas segregation on the left, and after complete segregation of theoriginal foam gas on the right, assuming that the eruption doesnot begin before this occurs. Note that transfer of the gas in the ori-ginal foam layer inevitably allows convection of fresh magma intothe zone where the pressure is less than 40 MPa, potentially provid-ing additional CO to the growing gas cavity.

6. Consequences of pressure rise: pyroclastic volcanism

The at least �10 MPa pressure just calculated applies to thewhole of the dike tip gas cavity, the top of which is at a depth of�830 m. The lithostatic pressure at this depth, from Eq. (4), willbe �3.8 MPa. The resulting �6 MPa stress increase is comparableto or greater than the typical tensile strengths of common rocks(Schultz, 1995) and it occurs in a region that has recently under-gone faulting associated with the graben formation process. Weconsider it very likely, therefore, that at some stage before thecomplete transfer of gas from the foam to the cavity has takenplace, either the existing graben boundary fractures were pushedopen or new fractures propagated to the surface, allowing the on-set of the escape of the accumulated gas. This initial escape of puregas into the lunar vacuum will have had little effect other than,perhaps, to cause elutriation and dispersal of the finest grains inthe regolith. The most likely location for the onset of these pro-cesses was at or near the center of the top of the dike; dikes inplanetary crusts will tend toward ‘‘penny’’ shapes in three-dimen-sions, such that the upper edge of the dike is convex upward andtherefore nearest the surface at its center, which, in the case ofthe Hyginus system, is now occupied by Hyginus crater. The shapeof the inferred pyroclastic deposit clearly indicates a source (or asmall number of sources) in this vicinity (see Fig. 2).

If, as we have assumed, the sill was injected from the shallowestpart of the dike, the graben boundary fractures will have inter-sected the sill, and release of gas pressure will have caused anexpansion wave to propagate downward into the magmatic foamin the sill, expanding gas bubbles, fragmenting the foam, and initi-ating the pyroclastic eruption. The speed of sound in the foam wasrestricted to �100 m/s because of the presence of the gas bubbles(Kieffer, 1977), and the expansion wave traveled at about 60% ofthis speed. Thus the expansion wave will not have traveled far lat-erally into the dike magma while it was excavating the sill magma.

The absolute maximum dispersal of the pyroclastic materialproduced by the eruption of the foam can be found by assumingthat magma at any given distance x above the base of the foamlayer expands from its initial pressure Px to the zero pressure ofthe lunar surface vacuum. The expansion will occur in two stages.In the subsurface, the expansion of the gas component of the mag-matic foam will be close to isothermal, buffered by intimate con-tact with the much larger mass of magmatic liquid. The volumefraction of gas in the foam will increase until it reaches the criticalvalue, 0.85, at which the foam disrupts into free gas and entrainedmagmatic liquid droplets. The gas will continue to expand as it car-ries the entrained magma droplets to the level of the vent. The gaspressure at the vent will be determined by the fact that the flow ofthe mixture of gas and droplets will almost certainly be choked, i.e.limited to be equal to the local speed of sound in the mixture. Thiscondition occurs in eruptions on bodies with no, or minimal, atmo-sphere because the speed of sound in any gas-particle mixture isrelatively low (Kieffer, 1989), and an extremely strongly out-ward-flared vent shape is needed to allow the mixture to passthrough the sub-sonic to super-sonic speed transition (Wilsonand Head, 1981). Such a shape is not likely to exist early in an erup-tion; it may evolve during a long-lived eruption due to a combina-tion of conduit wall erosion and pyroclast deposition on the surface

Table 6Variation of the initial pressure, Px, the pressure in the vent, Pv, the eruption speed atthe vent, Uv, the final eruption speed, Uf, and the maximum range, R, for dropletsderived from magma starting its ascent from various depths below the surface, z, inthe magmatic foam at the top of the dike when the magma CO content is 1500 ppm.

z (m) Px (MPa) Pv (MPa) Uv (m s�1) Uf (m s�1) R (km)

921 5.7 1.46 46.5 99.8 6.151000 6.0 1.49 46.9 100.1 6.182000 10.4 1.73 50.0 102.4 6.473000 14.7 1.86 51.7 103.7 6.644000 19.1 1.96 52.9 104.6 6.765000 23.4 2.02 53.7 105.3 6.846000 27.8 2.06 54.3 105.7 6.897000 32.1 2.09 54.6 106.0 6.938000 36.5 2.11 54.9 106.2 6.968818 40.0 2.12 55.0 106.3 6.97

592 L. Wilson et al. / Icarus 215 (2011) 584–595

surrounding the vent, but in a transient eruption of the kind in-ferred here this is not likely to happen. The pressure in the vent,Pv, can be found by equating the local gas–pyroclast mixture speed,Uv, to the sound speed, Us. Uv is found by equating the work doneby gas expansion to the sum of the potential and kinetic energygains of the mixture (Wilson, 1980):

12

U2v ¼

nQTm

lnPx

Pvþ 1� n

qlðPx � PvÞ � gðDb � xÞ ð16Þ

where Db is the depth to the base of the foam layer, x is the distanceabove that base, and Px is the localpressure. This treatment neglectsfriction between the rising magmatic materials and the dike walls,but this is a small contribution to the energy loss in a dike as wideas the one modeled here. Us is given with sufficient accuracy for vol-canic systems (Wilson and Head, 1981) by

U2s ¼

nQTm

1þ ð1� nÞmPv

nQTql

� �2

ð17Þ

Equating the two speeds yields

1þ ð1� nÞmPv

nQTql

� �2

¼ 2 lnPx

Pvþ 2mð1� nÞðPx � PvÞ

nQTql

� 2mgðDb � xÞnQT

ð18Þ

This equation must be solved recursively: an initial estimate of thevalue of Pv (one-quarter of Px is suitable) is inserted into the right-hand side and the equation is solved to obtain an improved esti-mate of Pv from the left-hand side. After an adequate level of con-vergence has been obtained, either of Eqs. (16) or (17) can beused to obtain the eruption speed through the vent, Uv.

Above the surface the gas-droplet mixture accelerates through aseries of shocks and expansion waves (Kieffer, 1982) to establish aradial gas flow regime. Increased droplet separation reduces thethermal contact with the gas and most of the gas expansion andconsequent droplet acceleration take place under adiabatic condi-tions above the vent. The droplets cool to become solid pyroclasts,and eventually these decouple from the gas flow as the system en-ters the Knusden regime, where the mean free path of the gas mol-ecules becomes much greater than the droplet sizes and thenormal gas laws no longer apply. Before the Knudsen regime isreached, large droplets lag behind the vertical component of thegas speed by an amount equal to their terminal velocity in thegas. The terminal velocity is a function of the droplet size and den-sity, and of the gas properties – its viscosity if the gas flow aroundthe droplets is laminar and its density if the flow is turbulent. Asthe Knudsen regime is approached, droplets decouple from thegas flow as a function of their size. The combined effect of thesetwo processes is that only the smallest droplets acquire a verylarge fraction of the gas speed. Also, the fact that the larger dropletsdo not acquire as much kinetic energy per unit mass as the smallerdroplets means that effectively the gas mass fraction acceleratingthe smaller droplets is larger than the actual gas mass fraction inthe foam. However, this issue was addressed for volcanic eruptionsinto a vacuum on asteroids by Wilson and Keil (1997) who showedthat for a droplet size distribution similar to that seen in the Apollolunar pyroclast samples, with maximum diameters of order 1 mm,the gas would be effectively enriched by only a few percent.

To a sufficient approximation for the present purpose, therefore,we assume that the pyroclastic droplets all acquire the same speedas the gas, which we assume expands above the vent isentropicallyto some extremely low (essentially zero) final pressure Pf, so thatthe additional kinetic energy per unit mass, K, transferred to thedroplets is

K ¼ nQTcc� 1

� �1� Pf

Pv

� � c�1cð Þ

!þ ð1� nÞ

qlðPv � PfÞ ð19Þ

where c is the ratio of the specific heats at constant pressure andvolume for CO. The final velocity of the droplets, Uf, is then given by

Uf ¼ ðU2v þ 2KÞ1=2 ð20Þ

and the maximum range, R, to which they can travel, assuming themost favorable ejection angle of 45�, is

R ¼ U2f

gð21Þ

Values of the relevant parameters are given in Table 6 as a functionof the depth below the surface, z, from which a given part of thefoam begins its ascent. The table relates to a magma CO contentof 1500 ppm, near the upper end of the expected range, and as-sumes that the eruption occurs when the gas pressure in the diketip cavity has reached one-half of the final value given in Table 5,i.e. 5.7 MPa.

Table 6 shows that the maximum range achievable when themagma CO content is 2000 ppm, at the top of the likely range, is�9 km. This is less than the typical (�15 km) or maximum(�30 km) observed radius of the inferred pyroclastic deposit. Toexplain this apparent discrepancy we return to the issue of thethree-dimensional shape of the dike, specifically the fact that theupper tip of the dike is likely to be closer to the surface at the dikecenter, near the current location of Hyginus crater, than elsewhere.Thus as soon as magma discharge to the surface begins, there willbe a tendency for the free gas in the dike tip cavity to migrate side-ways toward the eruption site to be incorporated into the eruptinggas–pyroclast mixture. A sufficiently great enrichment of the gascontent of the disrupted foam in this way would potentially pro-vide a great enough eruption speed to explain the observed pyro-clast ranges. To quantify this we repeated the calculationsunderlying Table 6 but with greater CO contents than initially as-sumed. Table 7 shows the values corresponding to magma leavingthe deepest part of the dike and the implied ranges are showngraphically in Fig. 5. This figure shows that to project pyroclasticdroplets to the average range requires a 1.5-fold CO enrichmentand to reach the maximum observed range requires enrichmentby a factor of about 3. These ratios are plausible: the surface areaof the sill underlying Hyginus crater is �60 km2 and the surfacearea of the �100 km long, 240 m wide dike is �25 km2. If �50%foam drainage had taken place at the onset of the eruption, a rea-sonable amount to explain the pressure increase needed to triggerthe activity, the dike tip cavity would have provided nearly a dou-bling of the effective gas content of the erupting material.

Table 7Variation of the pressure in the vent, Pv, the eruption speed at the vent, Uv, the finaleruption speed, Uf, and the maximum range, R, for droplets derived from magmastarting its ascent from the deepest part of the foam layer when the CO content, n, iseffectively enriched by gas converging on the eruption site from the more distantparts of the dike.

n (ppm) Pv (MPa) Uv (m s�1) Uf (m s�1) R (km)

1500 2.12 55.0 106.3 6.972000 2.62 61.2 120.9 9.023000 3.49 71.0 145.0 12.985000 4.91 85.2 182.4 20.547000 6.07 96.0 212.2 27.80

10,000 7.49 108.8 249.3 38.37

Fig. 5. Variation of maximum pyroclastic droplet range as a function of total CO gascontent of erupted mixture of gas and droplets.

Fig. 6. Sequence of events during formation of Hyginus crater and rille. Parts (a),(b), (g) and (h) show both side- and end-elevations, parts (c)–(f) show end-elevationonly. Not to uniform scale. (a) Dike grows upward from mantle with gas cavity andfoam layer both increasing in vertical extent; (b) dike top stalls near surface; (c)lateral sill is injected from near center of top of dike; (d) stresses around dike topinitiate graben formation; (e) pressure increase in gas cavity forces grabenboundary faults open to allow start of explosive eruption; (f) eruption formspyroclast layer on surface; (g) evacuation of sill causes caldera subsidence nearcenter of graben; (h) collapse of surface rocks into evacuated gas cavity along dikeforms collapse craters.

L. Wilson et al. / Icarus 215 (2011) 584–595 593

7. Consequences of the pyroclastic volcanism: collapse cratersand calderas

In Section 2 we measured the total volume of the collapse cra-ters, other than Hyginus crater itself, to be �33–34 km3 and de-scribed the stratigraphic evidence for these collapse cratershaving formed after the formation of the graben. In Table 5 wegave the variation with magma CO content of the values of Zf,the maximum vertical extents of the gas cavities that might haveaccumulated before an eruption began. Multiplying the values ofZf by the 240 m dike width and the assumed 100 km dike lengthalong strike gives total volumes in the range 16–44 km3. The sim-ilarity of these volumes to the total collapse crater volume is takenas an indication that our inferences in Section 6 about gas migra-tion from the top of the distal parts of the dike to enhance thegas content of the explosive activity are correct, and that it was thisrapid gas removal that lead to the formation of the collapse craters.

It remains to consider the origin of the Hyginus crater and thenearby similarly flat-floored depression (numbered 18 and 19 inFig. 1b). These represent a total missing volume of �63 km3. How-ever, our estimate of the volume of the pyroclastic deposit in Sec-tion 2 was only �7 km3. The discrepancy can be reconciled byrealizing that the sill, the evacuation of which produced the calde-ras, contained magmatic foam, not bubble-free magma. The verti-cal extent of the subsidence to form the main caldera, crater 18, is�840 m. If �100 m of this represents the gas pocket at the top ofthe sill, the remaining �740 m represents a foam layer with a

gas volume fraction of �85%. Thus �15% of �740 m will be thedense rock equivalent vertical extent (we neglect the slightly dif-fering densities of liquid and solid basalt), �110 m. Multiplied bythe �64 km2 area of crater 18 this corresponds to a volume of�7 km3. The equivalent calculation for the smaller depression, cra-ter 19, yields �1.2 km3. The total dense rock equivalent volume forthe two craters, �8 km3, is so similar to the �10 km3 volume ofpyroclasts estimated in Section 2 that again we infer that our mod-el adequately explains the observations.

8. Summary

We now summarize the inferred sequence of events involved inthe formation of the Hyginus crater and rille (Fig. 6).

(1) A vertically propagating �240 m wide dike approached thesurface from the mantle (Fig. 6a). As it neared the surface,ongoing gas segregation into the low-pressure region inthe dike tip had formed a gas cavity �100 m deep beneathwhich was a foam layer �8 km deep. The central section ofthe top of the dike stalled at a depth of �800 m below thesurface (Fig. 6b) and the dike continued to propagate later-ally, inducing a stress field that caused graben formationover a horizontal extent of �100 km.

594 L. Wilson et al. / Icarus 215 (2011) 584–595

(2) A sill or laccolith began to be intruded laterally from somepoint near the top of the dike (Fig. 6c). The sill may haveextended laterally from the upper part of the feeder dikefor more than the �5 km radius of the main Hyginus crater.If the caldera of crater 19 formed in the same way, the sillmay have extended for �10 km on this side of the dike.The dike was still propagating sideways away from its centerat this time. The two main arms of the graben were formingradially away from the middle of the dike as the top of thesideways-spreading upper edge of the dike applied stressesto the crust (Fig. 6d). Lateral sill intrusion stopped at somestage that could have been before or after the dike stoppedspreading laterally.

(3) After the dike top stopped rising vertically, gas migratedupward from the foam below the gas cavity, enlarging thevertical extent of the cavity and raising the gas pressure.Eventually the combination of dike stress and gas pressureforced the graben faults open, initiating an eruption(Fig. 6e). The eruption first released essentially pure CO gasbut soon ejected a mixture of pyroclasts and gas as anexpansion wave propagated downward and laterally,decompressing and fragmenting the foam in the sill andnearby dike.

(4) The resulting eruptive activity projected pyroclastic dropletsto distances of up to �30 km to produce the observed low-albedo, enhanced iron and titanium deposit (Fig. 6f). Thedroplet eruption speed was enhanced above that corre-sponding to the locally-produced CO by the lateral migrationof free gas from the more distal parts of the dike tip cavitythat were not erupting to the surface.

(5) Relaxation of the gas pressure in the dike tip cavity, coupledwith surface subsidence around the eruption site to produceHyginus crater and the secondary caldera of crater 19, termi-nated the explosive activity (Fig. 6g). The volumes of the cal-dera depressions are consistent with the estimated pyroclastvolumes when due allowance is made for the gas volumefraction in the sill magma that provided most of the eruptedpyroclasts.

(6) After the upper and lateral dike tips ceased to propagate, andthe dike geometry had stabilized, the pressure decrease inthe now largely evacuated gas cavity at the top of the dikeallowed completion of the subsidence events along the rillethat produced the �23 collapse craters (Fig. 6h). The totalmeasured volume of these craters closely matches the theo-retically predicted gas volume.

9. Implications for other lunar rilles and pyroclastic deposits

We have described how shallow intrusions, in this case a com-bination of a dike and a sill, can cause fracturing of the lunar sur-face leading to an explosive eruption producing a pyroclasticdeposit but no lava eruption. An important element of this scenariowas the eruption of a mixture of a magmatic foam from one part ofthe system (the sill in this case) and free gas from another part ofthe system (here the dike tip cavity some distance from the sill),causing greater eruption speeds and pyroclast ranges than wouldbe predicted on the basis of the smelting reaction widely inferredto have provided the commonest lunar volatile, CO. The conceptof gas accumulation at the top of a shallow dike after its emplace-ment was introduced by Head et al. (2002) to explain an inferredpyroclastic deposit in Mare Orientale. Wilson and Head (2003) ex-tended the idea by pointing out that the well-understood dynamicsof dike propagation, which cause a low pressure to be present inthe tip of any propagating dike (Rubin, 1995), are particularlyimportant for the Moon. This is because the unusually greatdepths, relative to Earth, from which lunar dikes propagate imply

that all such dikes approaching the lunar surface are expected tohave a very significant concentration of gas at their upper tips.Here we have combined and extended these ideas, showing thatsignificant gas enrichment can occur in explosive eruptions fromshallow intrusions on the Moon.

Shallow dike intrusions may be common on the Moon. Using amodel of giant (i.e. crust-traversing) dike emplacement developedfor Mars by Wilson and Head (2002, 2009), Scott and Wilson(2001) showed that many combination of magma density, crustaldensity and stress state on the Moon cause dikes to fail to erupt,instead stalling with their tops at depths of �1 km. Such dikesshould commonly have widths of �100 m and produce crustalstresses leading to surface graben formation. The implied geome-tries of such graben are consistent with the morphologies of theclass of lunar linear rilles that have associated minor volcanic con-structs (Petrycki et al., 2004).

We therefore suggest that the mechanisms described in this pa-per may have been more common on the Moon than previouslysupposed. Gaddis et al. (2003) cataloged the diameters of pyroclas-tic deposits on the Moon and found that the maximum radii of 76such deposits were �55 km with a median of �15 km. The medianand smaller-sized deposits can be explained by pyroclastic erup-tions from dikes underlying graben with no need to invoke any-thing other than minor gas concentration by lateral flow throughthe cavity at the top of the dike. However, the largest deposits re-quire more significant gas enrichment. Extrapolation of the data inTable 7 (which shows that deposit range is very nearly linearly pro-portional to n) implies that a deposit radius of 55 km requires amagma CO content of �14,000 ppm, a �7-fold enhancement overthe likely magmatic maximum of 2000 ppm. Linear rilles withassociated volcanic features on the Moon have lengths up to�150 km and their depths imply common dike widths of �100 m(Petrycki et al., 2004). Thus associated sill-like intrusions wouldonly need to have horizontal surface areas of �2 km2 (equivalentcircular radii of 800 m) to permit gas enhancements by a factorof 7 in scenarios similar to that analyzed here. The median widthof lunar linear rilles associated with minor volcanic features is�1200 m (Petrycki et al., 2004), and so an 800 m extension of a lo-cal sill-like intrusion from the dike underlying such a rille mightnot be immediately obvious against the background of inherentfluctuations in rille width along strike. Of course, such a smallintrusion would not provide a large volume of pyroclastic material,but clearly a systematic search for topographic features implyingsill intrusions associated with lunar linear rilles, especially thosenear the centers of large pyroclastic deposits, should be a targetof future work.

Acknowledgments

We thank Jennifer Petrycki for discussions about the morpho-logical measurements. Reviews by an anonymous reviewer andespecially by Laszlo Kesthelyi greatly improved the first versionof this paper. This work was supported by NASA research grants.This is Hawai’i Institute of Geophysics and Planetology PublicationNo. 1901 and School of Ocean and Earth Science and TechnologyPublication No. 8383.

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