Borin, P.

Bruno, M.

Cremonese, G.

Martellato, E.

Marzari, F.

English

Bruno, Marco

Institutional Research Information System University of Turin

The Astrophysical Journal Letters, 749:L40 (4pp), 2012 April 20 doi:10.1088/2041-8205/749/2/L40C© 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.NEW CALIBRATION OF THE MICROMETEOROID FLUX ON EARTHG. Cremonese1, P. Borin1, E. Martellato2, F. Marzari3, and M. Bruno41 Istituto Nazionale di Astrofisica-Astronomical Observatory of Padova, 35122 Padova, Italy2 SRE-SM, European Space Agency-ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands3 Department of Physics, University of Padova, 35131 Padova, Italy4 Department of Mineralogical and Petrological Science, University of Torino, 10125 Torino, ItalyReceived 2011 November 21; accepted 2012 March 16; published 2012 April 2ABSTRACTMass accretion rate on Earth is an important tool to discriminate the extraterrestrial nature of particles or isotopesfound in different environments on the ground. In this context, the knowledge of the micrometeoroid flux arrivingin our atmosphere is a key parameter and it needs to be calibrated. We provide a new calibration of the flux ofsubmillimeter particles impacting the Earth in the mass range from 10−9 to 10−4 g, derived by computing a specificscaling law for impact craters on the Long Duration Exposure Facility (LDEF). We use the hydrocode iSALE tocalculate the outcome of impacts on LDEF, adopting realistic impact velocities for dust particles derived from thenumerical integration of their trajectories assuming either asteroidal or cometary origin. We estimate a particlemass accretion rate of (7.4 ± 1.0) × 106 kg yr−1 if the Main Belt is assumed as the major source of dust, while itreduces to (4.2 ± 0.5) × 106 kg yr−1 if cometary dust dominates. These values agree with the estimates provided byindependent measurements made on ice core and ocean sediments and based on the abundance of some elementsin the samples.Key words: Earth – meteorites, meteors, meteoroids – methods: numerical1. INTRODUCTIONEarth’s meteoritic mass accretion rate plays an important rolein many contexts. Meteoroids entering Earth’s upper atmospheredeposit meteoritic matter there, a process which has importantconsequences for the aeronomy of the upper mesosphere andlower ionosphere. It provides important input on the analysisof the deep-sea sediments and ice core samples in terms ofsome element abundance and it may help to quantify themeteoroid collision hazards for spacecraft. The observationsand measurements of meteoroids in our atmosphere could alsobe important for calibrating the models of the terrestrial planetenvironment (Borin et al. 2010). We determined the mass fluxand size distribution of extraterrestrial micrometeoroids in thesubmillimeter radius size range of 5–250 μm from accuratemeasurements of the dimensions of all the hypervelocity impactcraters collected on the space-facing end of the gravity-gradient-stabilized Long Duration Exposure Facility (LDEF) satellite(Love & Brownlee 1993). According to Flynn (2002), more than80% of all the incoming mass of meteoroids entering Earth’satmosphere is concentrated in the mass range 10−7 to 10−3 g.In our model, we considered a slightly larger range, 10−9 to10−4 g, in order to include possible uncertainty. The first stepfor translating the crater data on LDEF into a flux estimate is tointerpret the crater diameters in terms of projectile size. Love &Brownlee (1993) adopted a semiempirical scaling law derivedfrom laboratory experiments that were performed in a rangeof velocities significantly different with respect to the impactspeeds of impacting meteroids. To improve the analysis of LDEFdata, we did a specific exploration of the relation between craterdiameter and projectile size with the hydrocode iSALE. In thenumerical modeling, the ratio between the depth and diameterof the craters of 0.527, accurately measured on LDEF (Love &Brownlee 1993), has been considered as an important constraintfor the iSALE simulations. The range of impact velocities to beused in the hydrocode simulations has been derived using thedynamical model of dust particle orbital evolution describedin Borin et al. (2009). The orbits of dust particles releasedeither from collisions between Main Belt Asteroids (MBAs)or from cometary activity on Jupiter Family Comets (JFCs) arenumerically integrated, including the gravitational attraction ofall planets and the effects of solar radiation and wind forces. Theimpact velocity on the Earth of the particles is computed for bothsources, giving two significantly different average values. Forasteroidal dust particles, we obtain an impact speed of about18.6 km s−1 while it rises to 29.0 km s−1 for JFCs. Both thesevalues differ from those adopted by Love & Brownlee (1993)and by those adopted in the derivation of the experimentalscaling law adopted by Love & Brownlee (1993). This fullyjustifies a re-analysis of the LDEF data with a more reliablescaling law based on a better impact velocity estimate andon hydrocode simulations that also account for the differentporosity and composition of the dust grains depending on theirorigin (asteroidal or cometary).2. iSALE MODELINGTo simulate the impact process, we used iSALE shock physicscode, which represents an extension and an improvement ofthe SALE hydrocode developed by Amsden et al. (1980),and includes an elasto-plastic constitutive model, fragmentationmodels, various equations of state (EoSs), the implementationof multiple materials, and a novel porosity compaction model,the ε −α-model (Melosh et al. 1992; Ivanov et al. 1997;Collins et al. 2004; Wu¨nnemann et al. 2006). The code iswell tested against laboratory experiments at low and highstrain rates (Wu¨nnemann et al. 2006) and other hydrocodes(Pierazzo et al. 2008). We assumed the projectile radius rangeto be from 5 to 250 μm, with a step of 20 μm. Under theassumption that the average flight angle of the LDEF facilitywas 45◦ with respect to the local zenith, following Love &Brownlee (1993), we adopt vertical impact components of 13.2and 20.5 km s−1, respectively. The measured craters from whichthe meteoroids flux was derived have been collected in a 5.66 m21The Astrophysical Journal Letters, 749:L40 (4pp), 2012 April 20 Cremonese et al.0 50 100 150 200 250 300 350 400 450 500050010001500200025003000Projectile Diameter (µ m)Crater Diameter (µ m)  Asteroids iSALEComets iSALEFigure 1. Scaling law obtained from iSALE simulations.thermal control panel surface exposed to space for 5.77 yearsat altitudes ranging from 480 to 331 km (Love & Brownlee1993). To model the impact events, we considered an Eulerianmesh large enough that the target could be considered “infinite”with respect to the final expected crater, and a gravity field of8.6963 m s−2. The target was made up by a sheet of aluminum6061-T6 alloy, which is described by the Tillotson Equationof State (see Table AII.3 in Melosh 1989) to account for bulkdeformations and the Johnson-Cook model (see Table 4 in Rule1997) to account for deviatoric deformations. All the projectileshave been assumed basalt spheres at 50 cells per projectileradius of resolution, having a density of 2.86 g cm−3. Thebasalt is chosen to be representative of a general brittle rockbehavior. The thermodynamic state of basalt is described bythe ANEOS-based tabular material EoSs. The strength modelimplemented in iSALE is described in Collins et al. (2004),who used the Lundborg (1968) approximation to account forthe effect of pressure on yield strength for intact rock, and aCoulomb dry-friction law in the case of totally fragmented rockmaterial. The constitutive parameters adopted are the following:Y0 (cohesion for intact material) = 10 MPa, μi (coefficientof internal friction) = 0.8, YM (von Mises plastic limit) =1 GPa, Yd (cohesion for damaged material) = 0.01 MPa, μd(coefficient of friction) = 0.6. We have run the simulations eventaking into account a much lower cohesion value of 10 kPa(Trigo-Rodriguez & Llorca 2006), but the results are notsignificantly affected. To differentiate the two types of testparticles, we set a different porosity: 25% for asteroidal dust,giving a density of 2.14 g cm−3, and 70% for cometary dustyielding a density of 0.86 g cm−3. These values are consistentwith recent literature on the expected density and porosityof meteoroids (Greenberg & Aigen 1999; Greenberg 2000;Rietmeijer & Nuth 2000; Sykes et al. 2004). As a further test, wealso assumed a higher porosity for the cometary dust particlesof 90% yielding a density of 0.286 g cm−3. This is an extremevalue for the density according to Blum et al. (2006). In oursimulations, the formation time of the crater ranges from afraction of μs to few μs. The resulting average ratio betweendepth and diameter is 0.582 for asteroids and 0.529 for comets.Both these values are in very good agreement with the averageratio measured on LDEF of 0.527 (Love & Brownlee 1993).We must also acknowledge that these ratios depend on theprecision of the hydrocode simulations which, according to codevalidation against laboratory experiments (10), is 3%–4% inradius and 12% in depth. The results of the iSALE simulationsprovide a new scaling law (Figure 1) that is significantly differentfrom that used by Love & Brownlee (1993), suggesting that theysystematically overestimated the projectile size for any givencrater diameter.3. RESULTSFrom the new scaling laws specific for asteroidal or cometarydust grains, we have re-analyzed the LDEF data and computedupdated values of the dust flux. In Figures 2 and 3, we show thecumulative and differential flux of dust particles on the Earth as afunction of the grain mass. By comparing our curves with that ofLove & Brownlee (1993) a noticeable difference stands out. Theflux estimated with the scaling law adopted in Love & Brownlee(1993) has a peak value that is more than three times higher thanthe one we obtained for either asteroidal or cometary dust. It hasto be noted that the estimated flux for dust coming from JFCs islower than the asteroidal counterpart, since cometary dust has ahigher impact velocity and this leads to smaller projectiles forthe same impact energy. This is confirmed in Figures 2 and 3,where the mass range for cometary and asteroidal dust particlesis different with the asteroidal mass range shifted toward largervalues.From the curves of Figure 3 we have re-calculated the integralof the mass flux, and we obtain a value for the total massaccreted by the Earth of (4.2 ± 0.5) × 106 kg yr−1 for cometsand of (7.4 ± 1.0) × 106 kg yr−1 for asteroids, where the sigmahave been derived from the 4% uncertainty of the hydrocodein the diameter determination and the consequent variationof the curves. In the extreme case where a porosity of 90%is assumed for the cometary dust, we obtain a total mass of14.3 × 106 kg yr−1. All these values of total mass accretedare significantly lower than that estimated by Love & Brownlee2The Astrophysical Journal Letters, 749:L40 (4pp), 2012 April 20 Cremonese et al.10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−310−1210−1110−1010−910−810−710−610−5Mass (g)Cumulative Flux (N/m2  s)  Love and BrownleeAsteroids iSALEComets iSALEFigure 2. Cumulative flux of dust grains derived interpreting the LDEF data with the iSALE scaling laws and adopting the impact speeds derived by our dynamicalmodel. The flux is expressed as the number of particles N per m−2 s−1. The curves derived with the iSALE scaling laws are compared to the original flux computedby Love & Brownlee (1993).−10 −9 −8 −7 −6 −5 −4 −3051015x 106log m (g)Flux (kg/year dlogm)  Love and BrownleeAsteroidsCometsFigure 3. Mass accretion rate of micrometeoroids on Earth according to our model and to Love & Brownlee (1993).(1993) ((40 ± 20)×106 kg yr−1) even after the revision proposedby Mathews et al. (2001) is applied ((25±12.5)×106 kg yr−1).An error can be evaluated for our estimates taking into accountthat there is a 4% uncertainty in the diameter determination fromthe hydrocode simulations.Our values for the mass accretion rate are in agreementwith estimates obtained with different methods (see Table 1 ofKarner et al. 2003). In particular, Mathews et al. (2001), on thebasis of radar observations of micrometeors, derived a value of(1.6–2.3) × 106 kg yr−1, and in order to reconcile their findingswith the mass accretion rate computed by Love & Brownlee(1993), they revised the Love & Brownlee (1993) calculationsassuming a much higher impact speed for the dust particlesusing the value 50 km s−1. In this way, they derive a value of1.8 × 106 kg yr−1 from the data analyzed by Love & Brownlee(1993). However, according to our dynamical model, an impactspeed of 50 km s−1 is by far too high, almost a factor of two largerthan the value expected for cometary dust (29.0 km s−1), andcannot be adopted. Gru¨n et al. (1985) provided another estimate,based on impact craters and meteoroid flux, of 14.6×106 kg yr−1that is not far from our estimate considering the uncertainties.However, it is worth noticing that previous works based on the3The Astrophysical Journal Letters, 749:L40 (4pp), 2012 April 20 Cremonese et al.analysis of impact craters and meteoroid dynamics did not takeinto account asteroids or comets as different sources of dustrelease.4. CONCLUSIONSThe data recoiled by LDEF on the flux of dust particles onthe Earth have been re-evaluated adopting a better estimate ofthe grain impact velocity and more reliable scaling laws. In thisLetter, we consider both dust coming from the MBA and fromJFCs, which are the most plausible candidates for refilling withdust the Earth environment (Dermott et al. 2002; Nesvorny et al.2010). In the two cases, the scaling law giving the projectile sizefrom the crater diameter will differ because the grains have adifferent porosity and structure. In addition, for the same impactenergy, the collision velocities are different due to the differentdynamical source. The scaling laws we find for asteroids andcomets significantly depart from that used by Love & Brownlee(1993), leading to significantly different curves describing theflux as a function of the dust grain mass and a different total massaccretion rate. Our values are approximately 10 times lower andare in better agreement with other independent estimates basedon different methodologies.The dust concentrates extracted from Greenland Ice SheetProject 2 ice core samples by Karner et al. (2003) allowed usto estimate the rate of extraterrestrial accretion for particlesin the size range 0.45–20 μm of (0.22 ± 0.11) × 106 kg yr−1,one order of magnitude lower than that estimated by Love &Brownlee (1993) in the same range (5 × 106 kg yr−1). Theyextrapolated their results to larger particles, up to 4 cm, by usingboth1. the particle distribution of Gru¨n et al. (1985) with MonteCarlo simulations, in order to determine an upper limit of6.25 × 106 kg yr−1, and2. the Love & Brownlee (1993) particle distribution, 12.5 ×106 kg yr−1.Karner et al. (2003) emphasized that the results of Love &Brownlee (1993) would imply that they were missing 96% of theextraterrestrial material because of undersampling, suggestingthat the Love & Brownlee (1993) distribution function mayrepresent a systematic overestimate of particle masses as aconsequence of the underestimation of impact velocity. Asimilar problem was also pointed out by Taylor et al. (1998)in their collection of cosmic spherules at the South Pole. In theircase, to comply with the Love & Brownlee (1993) flux theyassumed that 96% of the mass would have been ablated duringatmospheric entry. Assuming that the size range consideredby Karner et al. (2003) could account for less than 10% ofthe incoming mass of meteoroids entering Earth’s atmosphere(Flynn 2002), our particle distribution in that size range yields<0.42 × 106 kg yr−1 and <0.74 × 106 kg yr−1 for cometsand asteroids, respectively. Our mass accretion rate would thenagree with even the Taylor results of (1.6 ± 0.3) × 106 kg yr−1,within the uncertainties, without assuming a large percentage ofmeteoroids ablated.Analysis of ocean sediment samples has been used to estimatethe mass accretion rate on Earth, but the values determined havelarge uncertainties or have been revised in following works.Indeed, the value yielded by the IR measurements of Kyte& Wasson (1996) has been revised downward by Peucker-Ehrenbrink (1996) to (30 ± 15) × 106 kg yr−1, which is highercompared to our results but still significantly lower than thevalue given by Love & Brownlee (1993). It can be consideredin agreement with our values if the large uncertainty in theirestimate is taken into account. We found a better agreementwith the excess 3He in ocean sediments. The studies of Farley& Patterson (1995) and Marcantonio et al. (1999) yieldedmeasurements of 3He very consistent with Karner et al. (2003),and assuming that the He is correlated with Interplanetary DustParticle surface area the estimated mass flux of extraterrestrialmaterial to the deep ocean is 7.5 × 106 kg yr−1, which is verysimilar to our value obtained for asteroids.We gratefully acknowledge the developers of iSale, includingKai Wunnemann, Gareth Collins, Boris Ivanov, Jay Melosh, andDirk Elbesbausen (see www.iSALE-code.de).REFERENCESAmsden, A. A., Ruppel, H. M., & Hirt, C. W. 1980, Sale: A Simplified ALEComputer Program for Fluid Flows at All Speeds, Los Alamos NationalLaboratories, Report LA-8095Blum, J., Schrapler, R., Davidson, B. J. R., & Trigo-Rodriguez, J. M. 2006, ApJ,652, 1768Borin, P., Bruno, M., Cremonese, G., & Marzari, F. 2010, A&A, 517, A89Borin, P., Cremonese, G., Marzari, F., Bruno, M., & Marchi, S. 2009, A&A,503, 259Collins, G. S., Melosh, H. J., & Ivanov, B. A. 2004, Meteorit. Planet. Sci., 39,217Dermott, S. F., Durda, D. D., Grogan, K., & Kehoe, T. J. J. 2002, Asteroids III(Tucson, AZ: Univ. 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New calibration of the micrometeoroid flux on Earth

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New calibration of the micrometeoroid flux on Earth

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