Mass accumulation of Earth from interplanetary dust, meteoroids, asteroids and comets

Transcription

1 220 Proceeding of the IMC, Mitelbach, 2015 Ma accumulation of Earth from interplanetary dut, meteoroid, ateroid and comet Sandra Drolhagen 1, Jana Kretchmer 1, Detlef Kochny 2,3, Gerhard Drolhagen 2, Björn Poppe 1 1 Univeritätternwarte Oldenburg, Carl von Oietzky Univerity of Oldenburg, Ammerländer Heertr , D Oldenburg, Germany andra.drolhagen@uni-oldenburg.de 2 European Space Agency, ESA/ESTEC, Keplerlaan 1, NL AZ Noordwijk, The Netherland 3 Chair of Atronautic, TU Munich, Boltzmanntr. 17, D Garching, Germany The goal of thi paper i to determine the ma that reache the Earth a interplanetary material. For the large object the flux model by Brown et al. (2002) wa ued which i valid for bodie greater than 1 m and i baed on enor data of fireball that entered the Earth atmophere. For the mall ize the flux model by Grün et al. (1985) wa ued, which decribe the ma flux at 1 AU for meteoroid in the ma range g to about 100 g. The Grün flux wa converted to 100 km height by taking the Earth attraction into account and all unit were adjuted to compare the model with the one by Brown. In a econd tep both model were combined by an interpolation, which lead to a flux model that cover 37 order of magnitude in ma. Uing recent meaurement and alternative flux model the uncertaintie of the obtained model wa etimated. Recent meaurement include in-itu impact data on retrieved pace hardware and optical meteor data. Alternative flux model are e.g. a NASA model for large ize that i an extrapolation of known Near-Earth Object (NEO) and a model by Halliday et al. (1996) which i baed on optical meaurement of fireball. Up to a diameter of 1 km the total calculated ma influx i 54 ton per day. 1 Introduction Every day, dut, meteoroid and ometime larger object from pace hit the Earth. Size of thee object range from a mall a 1 nm to meter or larger. The correponding total ma range exceed 30 order of magnitude. Quantitative information on the flux of the object come from variou ource. Information on the mallet object i mainly obtained from the analyi of impact crater (e.g. on lunar ample), or on atellite hardware retrieved from pace. From thee in-itu meaurement the ma range kg up to 10 3 kg can be covered. Optical and radar meteor provide information in the ma range kg to a few kilogram. Bright fireball extend the ma range up to ize of m ( kg). Even larger object called ateroid impact Earth in interval of everal hundred, thouand or more year. Their impact rate can be etimated from the crater record on Earth and from imulation of the near-earth ateroid population. The preent paper tudie the ma influx on Earth for the complete ize range and addree ource of information and uncertaintie. 2 Baic model Grün Model The model by Grün et al. (1985) cover the ize range of the mallet object ( kg) and i baed on pacecraft meaurement, lunar micro crater tudie and zodiacal light photometry. The model i given in Formula (1) which decribe the flux per m 2 and econd to one ide of a randomly tumbling plate in dependence of the ma m in gram. F (m) = ( m ) (-4.38) (-9) (m m m 4 ) (-0.36) (1) (m m 2 ) (-0.85) Since Grün doe not make a clear tatement about the concrete ize range in which the model i valid, the mentioned range wa choen for firt calculation. Moreover, the model decribe the meteoroid flux at 1 AU, the ditance between Earth and Sun in our olar ytem. Therefore it doe not conider the Factor G, which decribe the effect of gravitation of the Earth which attract the meteoroid and therefore increae the number of impacting object on the Earth. To calculate thi gravitational enhancement factor G a contant velocity v of 20 km i aumed for impacting meteoroid. Then, Formula (2) (ECSS, 2008) i ued to calculate the ecape velocity v ec which decribe the velocity needed to ecape from the Earth gravitational attraction for a given altitude. v ec = 2 μ r+h It depend on the ditance between the altitude of the meteoroid and Earth center r+h, in which r decribe the mean Earth radiu that i equal to 6371 km and H i the altitude above Earth urface. In thi cae H i choen to be 100 km, ince thi i the altitude in which meteoroid tart to become viible meteor. Furthermore it depend on the contant μ = km 3 2, which i the product of the Earth ma and the gravitation contant. Uing the given value v ec i calculated to be (2)

2 Proceeding of the IMC, Mitelbach, km for H = 100 km. Thi reult i now ued to calculate the G-Factor uing Formula (3) (ECSS, 2008). G = v 2 v 2 v ec 2 (3) Thi calculation yield a factor of by which the formula given by Grün ha to be multiplied. Since the function of Grün decribe the flux per m 2 and econd while we need for further calculation the flux per year and Earth urface, the Grün model i caled. It hould be mentioned, that in the preent tudy, the Earth urface i aumed to be at 100 km height, ince the meteor tart to evaporate at thi height and do not reach the Earth urface a a meteor. the total ize range it i extended toward larger event up to a ize of 20 km diameter. The flux i given in Equation (6). F B (E) = 3.7 E -0.9 (6) Converting kinetic energy to ma one obtain: F B (m)=3.7 ( mv )-0.9 (7) Uing thi formula the flux according to Brown wa plotted in function of ma and diameter a hown in Figure 2. The time caling of the Grün model i done by multiplying F(m) with a factor of , which i the number of econd, that equate to one year. Afterward the Earth urface S in 100 km height i calculated uing Formula (4), where r i again the mean Earth radiu and H the altitude of 100 km. S=4 π (r+h) 2 (4) The Earth urface in 100 km height reult in m 2. Thi factor i now multiplied to F(m), to get the flux per year and Earth urface. Equation (5) how the modified formula by Grün. F (m) = ( ) (( m ) (-4.38) (-9) (5) (m m m 4 ) (-0.36) (m m 2 ) (-0.85) ) Figure 2 Flux by Brown in function of ma and diameter. The next tep wa to plot the function of Grün and Brown together in one plot and to extrapolate both to ee whether they meet in a reaonable way, or if they have to be interpolated. Thi i hown in Figure 3. Thi expreion give the predicted Grün model flux per year to the complete Earth at 100 km altitude. Uing thi formula the flux according to Grün wa plotted in function of ma and diameter a hown in Figure 1. Figure 3 The flux by Grün and Brown, extrapolated, a a function of ma and diameter. It can be een, that their extenion already eem to meet in a pretty acceptable way, ince there are no big deviation between both lope. Anyway an interpolation i made, in order not to overtretch the validity of the original flux model. Figure 1 Flux by Grün in function of ma and diameter. Brown model The next tep wa to plot the function F B (E) by Brown et al. (2002), which decribe the cumulative number of meteoroid impacting the Earth per year in dependence of their energy E, given in kiloton. Thi formula i derived from atellite enor data of fireball that entered the Earth atmophere and i baed on object with diameter between 1 and 9 m o only in thi ize range it i trictly valid. Neverthele, for a firt approach of the flux over Interpolation The interpolation i done uing a power law, which will create a traight line in the double logarithmic plot, which i uppoed to connect both lope pretty well. Fitting a power law of the form F int =a m b to the tartand end value of the model from Grün and Brown, the following expreion for the interpolated flux i obtained: F int (m)= m (-0.993) (8)

3 222 Proceeding of the IMC, Mitelbach, 2015 A a lat tep F int i ued to replace the extenion of Grün and Brown a hown in Figure 4. Figure 4 Interpolation uing a power law between Grün and Brown in function of ma and diameter. Ma calculation To derive the total ma according to the flux model hown in Figure 4, it i neceary to know how many particle there are in each ma interval. For thi, the cumulative plot i changed into a differential plot. Thi i done by ubtracting the cumulative flux of the next higher ma, from the flux of the ma that i conidered. Afterward, the derived flux i aigned to the mean ma value of that interval. Thee tep are repeated for all mae. Next, the total ma in each bin i calculated. Therefore the flux i multiplied by it aigned ma. By thi the total ma impacting Earth per year for each ma bin i derived, a hown in Figure 5 for two ma interval per ma decade. Solar Array were analyzed (UnipaceKent, 2002). The olar array were hit by mall meteoroid in pace (in 600 km altitude), which created mall crater. Thee crater gave information about the exiting flux in thi height. The ize range of triking meteoroid wa between and 0.6 micrometer. The ued data were taken from Table 1 of Appendix 1 of UnipaceKent (2002). In thi table an impact velocity of 21.4 km and a denity of 2.5 g 3 for the meteoroid were aumed. cm The flux ha to be adjuted, o that the ame aumption are made a for the flux by Grün. Therefore everal effect have to be conidered a the G-Factor, the Earth hielding factor (the olar array could not be hit from all around) and the fact that the Hubble Space Telecope i moving in pace. Thee effect lead to a total correction factor of 1.44 by which the flux ha to be multiplied. The in-itu impact data from the HST olar array agree quite well with the model from Grün. The fluxe are lightly above the model prediction but till within the model uncertainty. CILBO meteor data Next the model by Grün i compared to the flux model derived uing the CILBO double tation camera. A precie decription, how thi flux wa derived i given in thee proceeding by Kretchmer et al. (2015). The comparion can be een in Figure 6. Figure 6 The flux derived by the CILBO data compared to the Grün model. Figure 5 The ma impacting Earth per year for each ma bin. The lat tep i to add all calculated impacting mae together. By thi a total impacting ma of t per year and 60 t per day i derived. The upper ma limit conidered here i kg, correponding to a diameter of 20 km for a material denity of 2.5 g cm 3. In the following the accuracy of the variou model i tudied by comparion with available data. 3 Aement of model Comparion of Grün model with obervation Hubble Solar Array impact data The firt model to be tudied i the one by Grün et al.. The data from the retrieved Hubble Space Telecope The lope of the flux according to the meteor data of the CILBO double tation agree pretty well with the lope of the flux by Grün. However, it alo lie lightly above the Grün flux. Therefore, the flux by Grün might underetimate the flux in thi ize range but overall it eem to be a well validated model and will be ued for the further ma calculation. Check of the interpolation Halliday fireball data Next the interpolation i checked. The extrapolation of Grün and Brown, a well a the interpolation, eem to connect the end of Grün and Brown in a uitable way. Therefore, a third model (from Halliday et al., 1996) i plotted in the ame plot, to ee with which connection it agree bet. Thi model i baed on fireball obervation.

4 Proceeding of the IMC, Mitelbach, The formula for the flux by Halliday i given in Equation (9.1) and (9.2), where the flux i per year and 10 6 km 2 and the ma ha to be paed in gram to the function. For mae between 0.1 and 2.4 kg: N(m) = m (9.1) For mae between 2.4 and 12 kg: N(m) = m (9.2) After multiplying the flux by a factor of to get it per Earth urface, it i plotted in the ame plot, a the other two extrapolation, a hown in Figure 7. For mae larger than approximately 30 g the curve fit perfectly the lope of the extended flux model by Grün. For maller particle it appear that not all meteor were detected, ince there i a decreae in the flux. Moreover, there i only a mall amount of data point for large meteor, which lead to random error. To get ignificant reult a minimal number of 10 event hould be contained per ma bin, thi i the cae for 140 g meteoroid. Therefore, a new plot i created, in which only particle in the ma range of g are plotted, ince thee are the mot reliable data point. Moreover, the error of the calculated mae are conidered. Thee are due to uncertaintie of the luminou efficiency, which value lie omewhere between and Therefore the correponding mae repreent the upper and lower error etimation. A mean luminou efficiency a value of e 9.32 v 2 wa choen. Thi i hown in Figure 9. Figure 7 The three poible interpolation between Grün and Brown. It can be een, that for large mae the flux by Halliday agree very well with the interpolation, but for maller mae the flux i everely lower and therefore deviate from the interpolation. However, at the lower end of it domain it interect preciely the extended flux from Grün. Since the integrated time-area product i le than one full day of global coverage the Halliday reult have coniderable uncertaintie. Thi i why a econd model for thi ma range i conidered to check the accuracy of the interpolation. Sugg lunar impact flahe The model i available a ingle data point contained in the paper of Sugg et al. (2014) and i baed on the obervation of lunar impact flahe. A cumulative plot of their data compared to the previou model can be een in Figure 8. Figure 9 The mot reliable data point of Sugg, including the error, compared to the previou model. Thi plot point toward two finding. The firt i, a already mentioned, that the interpolation between the model by Grün and Brown eem to be an upper limit for the flux, ince all compared model lie below the predicted flux. The econd i that the Grün model eem to be valid for even larger particle than aumed o far. Halliday doe connect perfectly with the extrapolation of the flux by Grün and alo Sugg doe fit thi curve very well. Therefore, the Grün model i now aumed to be valid for particle up to at leat 100 g, a alo tated in the ECCS. The next tep i to calculate a new interpolation between the fluxe by Grün and Brown, becaue none of the compared model i precie enough to be aumed to be completely correct and therefore an alternative connection between Brown and Grün hould be found. The new interpolation i connected to the flux by Grün at 100 g and give: F int100 (m) = m (10) In Figure 10 all model and connection between Grün and Brown can be een. Figure 8 Data of Sugg compared to the previou model.

5 224 Proceeding of the IMC, Mitelbach, 2015 Figure 10 All conidered connection between Grün and Brown. In Figure 10 it can be een, that only the data by Sugg (for object larger than 100 g) eem to lie lightly below the new interpolation. Thi might be due to the fact, that Sugg aume a meteoroid velocity of 24 km in free pace. Therefore the calculated mae are maller than the one calculated in all other model auming a velocity of 20 km. By adjuting thi dicrepancy one would expect that the data point by Sugg would hift toward larger mae and therefore lie in the area between both interpolation. The new interpolation eem to be a lower limit for the flux in thi ma range. However, the extrapolation by Brown eem to be a pretty good alternative to connect with Grün, ince it lie central between both interpolation and alo croe the flux by Halliday quite centric. Therefore thi extrapolation i ued to calculate the total ma. Flux model for larger object Brown tated in a recent paper (Brown et al., 2015) that hi flux etimation from 2002 might underetimate the number of impactor larger 10 m. Other model for larger ize include thoe from Silber et al. (2009) and NASA (2003). Thoe model were aeed a well and conidered for the total ma etimation. 4 Ma calculation The total ma accumulation of Earth depend on the maximum ize of infalling object conidered. For a meaningful ma etimation an upper ize limit ha to be introduced. In thi work that limit ha been et at a diameter of 1 km. Object of thi ize or larger are expected to impact Earth only about every year. Mot of uch object that come cloer to Earth than 45 million km (near-earth object) are already known and an impact can be excluded. According to thee model, the total ma coming down per day in the ma range of kg i 53.9 ton. 5 Concluion and future work We tudied the ma influx on Earth per day for the ma range kg. In-itu impact data, meteor data, lunar impact flahe and ateroid flux model were conidered. Up to a diameter of 1 km the calculated ma influx i 54 ton per day. The maximum ma influx come from ize around and from the larget ize. The ma influx in the ize range covered by meteor and fireball ha till coniderable uncertaintie and there are indication for a reduced ma influx in thi ize range. It i unclear whether there i a phyical reaon for thi apparent minimum in the ma influx. Further analyi of ongoing meteor and fireball data for Earth and the Moon hould provide more inight. Reference Brown P., Bolough M., Harri A. (2015). Updated Population and Rik Aement for Airburt from Near-Earth Object (NEO). IEEE Aeropace Conference, Big Sky, Montana. Brown P., Spalding R. E., ReVelle D. O., Tagliaferri E., Worden S. P. (2002). The flux of mall near- Earth object colliding with the Earth. Nature, 420, ECSS (2008). European Cooperation for Space Standardization, Space Engineering, Space Environment, ECSS-E-ST-10-04C. Noordwijk, Netherland: ESA Requirement and Standard Diviion. Grün E., Zook H. A., Fechting H., Giee R. H. (1985). Colliional Balance of the Meteoritic Complex. Icaru, 62, Halliday I., Griffin A. A., Blackwell A. T. (1996). Detailed data for 259 fireball from the Canadian camera network and inference concerning the influx of large meteoroid. Meteoritic & Planetary Science, 31, Kretchmer J., Drolhagen S., Kochny D., Drolhagen G., Poppe B. (2015). De-biaing CILBO meteor obervational data to ma fluxe. In Rault J.-L. and Roggeman P., editor, Proceeding of the International Meteor Conference, Mitelbach, Autria, Augut IMO, page McDonnell J. A. M., UniSpaceKent ONERA, National Hitory Mueum (2005). Pot-Flight Impact Analyi of HST Solar Array-2002 Retrieval. Final Report of ESA contr /NL/LvH. Silber E. A., ReVelle D. O., Brown P. G., Edward W. N. (2009). An etimate of the terretrial influx of large meteoroid from infraonic meaurement. Journal of geophyical reearch, 114, Iue E8, 1 8. Stoke G. H., Yeoman D. K., Bottke Jr. W. F., Jewitt D., Cheley S. R., Kelo T., Evan J. B., McMillan R. S., Gold R. E., Spahr T. B., Harri A. W., Worden S. P. (2003). Study to determine the feaibility of extending the earch for near-earth

6 Proceeding of the IMC, Mitelbach, object to maller limiting diameter. Report of the Near-Earth Object Science Definition Team, 154 pp., Solar Syt. Explor. Div., Off. Of Space Sci., NASA, Wahington, D.C.. Sugg R. M., Moer D. E., Cooke W. J., Sugg R. J. (2014). The flux of kilogram-ized meteoroid from lunar impact monitoring. Icaru, 238, The author, Sandra Drolhagen, during her lecture (Photo by Axel Haa).