Modeling of lightcurves of binary asteroids

We present a numerical method for inverting long-period components of lightcurves of asynchronous binary asteroids. Data of five near-Earth binary asteroids, (175706) 1996 FG₃, (65803) Didymos, (66391) 1999 KW₄, (185851) 2000 DP₁₀₇ and (66063) 1998 RO₁, for two of them from more than one apparition, were inverted. Their mutual orbits' poles and Keplerian elements, size ratios, and ellipsoidal shape axial ratios were estimated via this inversion. The pole solutions and size ratios for 1999 KW₄ and 2000 DP₁₀₇ are in a good agreement with independent estimates from radar measurements. We show that uncertainties of estimates of bulk densities of binary systems can be large, especially when observed on short arcs.     

Angular momentum of binary asteroids: Implications for their possible origin

We describe in this work a thorough study of the physical and orbital characteristics of extensively observed main-belt and trojan binaries, mainly taken from the LAOSA (Large Adaptive Optics Survey of Asteroids [Marchis, F., Baek, M., Berthier, J., Descamps, P., Hestroffer, D., Kaasalainen, M., Vachier, F., 2006c. In: Workshop on Spacecraft Reconnaissance of Asteroid and Comet Interiors. Abstract #3042]) database, along with a selection of bifurcated objects. Dimensionless quantities, such as the specific angular momentum and the scaled primary spin rate, are computed and discussed for each system. They suggest that these asteroidal systems might be the outcome of rotational fission or mass shedding of a parent body presumably subjected to an external torque. One of the most striking features of separated binaries composed of a large primary (Rp>100 km) with a much smaller secondary (Rs<20 km) is that they all have total angular momentum of ∼0.27. This value is quite close to the Maclaurin-Jacobi bifurcation (0.308) of a spinning fluid body. Alternatively, contact binaries and tidally locked double asteroids, made of components of similar size, have an angular momentum larger than 0.48. They compare successfully with the fission equilibrium sequence of a rotating fluid mass. In conclusion, we find that total angular momentum is a useful proxy to assess the internal structure of such systems.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Keck observations of near-Earth asteroids in the thermal infrared

We present the results of thermal-infrared observations of 20 near-Earth asteroids (NEAs) obtained in the period March 2000-February 2002 with the 10-m Keck-I telescope on Mauna Kea, Hawaii. The measured fluxes have been fitted with thermal-model emission continua to determine sizes and albedos. This work increases the number of NEAs having measured albedos by 35%. The spread of albedos derived is very large (p_v=0.02−0.55); the mean value is 0.25, which is much higher than that of observed main-belt asteroids. In most cases the albedos are in the ranges expected for the spectral types, although some exceptions are evident. Our results are consistent with a trend of increasing albedo with decreasing size for S-type asteroids with diameters below 20 km. A number of objects are found to have unexpectedly low apparent color temperatures, which may reflect unusual thermal properties. However, the results from our limited sample suggest that high thermal-inertia, regolith-free objects may be uncommon, even amongst NEAs with diameters of less than 1 km. We discuss the significance of our results in the light of information on these NEAs taken from the literature and the uncertainties inherent in applying thermal models to near-Earth asteroids.     

Equilibrium figures of inhomogeneous synchronous binary asteroids

The present paper deals with the application of the classical theory of equilibrium figures of two rotating liquid masses to the case where bodies exhibit a radially stratified internal density distribution so that they can be considered as inhomogeneous bodies. The derived ellipsoidal shape solutions are applied to five real systems of equal-sized synchronous asteroids. Furthermore, internal inhomogeneity puts strong constraints on the surface grain density. A satisfactory model fit is achieved with internal densities of asteroids steadily increasing outwards. In particular, from such an approach we derived grain densities of the considered systems in agreement with their mineralogical composition inferred from reflectance spectroscopy. According to this new approach, 4492 Debussy, presently of unknown spectral type, is predicted to appear as a C-type object with a grain density on the order of 2 g/cm³.     

Constraining near-Earth object albedos using near-infrared spectroscopy

Low-albedo near-Earth objects (NEOs) are warm enough to emit detectable thermal flux at 2.5 μm when near perihelion. Thermal radiation can account for 33% or more of the total flux for an object with an albedo ?0.04 at 1.0 AU. This is measurable using near-infrared spectroscopic instruments enabling albedos to be constrained for a larger sample of NEOs.     

Radar and optical observations and physical modeling of triple near-Earth Asteroid (136617) 1994 CC

We report radar, photometric, and spectroscopic observations of near-Earth Asteroid (136617) 1994 CC. The radar measurements were obtained at Goldstone (8560 MHz, 3.5 cm) and Arecibo (2380 MHz, 12.6 cm) on 9 days following the asteroid’s approach within 0.0168 AU on June 10, 2009. 1994 CC was also observed with the Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes (PROMPT) on May 21 and June 1-3. Visible-wavelength spectroscopy was obtained with the 5-m Hale telescope at Palomar on August 25. Delay-Doppler radar images reveal that 1994 CC is a triple system; along with (153591) 2001 SN263, this is only the second confirmed triple in the near-Earth population. Photometry obtained with PROMPT yields a rotation period for the primary P = 2.38860 ± 0.00009 h and a lightcurve amplitude of ∼0.1 mag suggesting a shape with low elongation. Hale telescope spectroscopy indicates that 1994 CC is an Sq-class object. Delay-Doppler radar images and shape modeling reveal that the primary has an effective diameter of 0.62 ± 0.06 km, low pole-on elongation, few obvious surface features, and a prominent equatorial ridge and sloped hemispheres that closely resemble those seen on the primary of binary near-Earth Asteroid (66391) 1999 KW4. Detailed orbit fitting reported separately by Fang et al. (Fang, J., Margot, J.-L., Brozovic, M., Nolan, M.C., Benner, L.A.M., Taylor, P.A. [2011]. Astron. J. 141, 154-168) gives a mass of the primary of 2.6 × 10¹¹ kg that, coupled with the effective diameter, yields a bulk density of 2.1 ± 0.6 g cm⁻³. The images constrain the diameters of the inner and outer satellites to be 113 ± 30 m and 80 ± 30 m, respectively. The inner satellite has a semimajor axis of ∼1.7 km (∼5.5 primary radii), an orbital period of ∼30 h, and its Doppler dispersion suggests relatively slow rotation, 26 ± 12 h, consistent with spin-orbit lock. The outer satellite has an orbital period of ∼9 days and a rotation period of 14 ± 7 h, establishing that the rotation is not spin-orbit locked. Among all binary and triple systems observed by radar, at least 25% (7/28) have a satellite that rotates more rapidly than its orbital period. This suggests that asynchronous configurations with P_rotation < P_orbital are relatively common among multiple systems in the near-Earth population. 1994 CC’s outer satellite has an observed maximum separation from the primary of ∼5.7 km (∼18.4 primary radii) that is the largest separation relative to primary radius seen to date among all 36 known binary and triple NEA systems. 1994 CC, (153591) 2001 SN263, and 1998 ST27 are the only triple and binary systems known with satellite separations >10 primary radii, suggesting either a detection bias, or that such widely-separated satellites are relatively uncommon in NEA multiple systems.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.     

Optical and thermal infrared observations of six near-Earth asteroids in 2002

We present thermal infrared photometry and spectrophotometry of six Near-Earth Asteroids (NEAs) using the 3.8 m United Kingdom Infrared Telescope (UKIRT) together with quasi-simultaneous optical observations of five NEAs taken at the 1.0 m Jacobus Kapteyn Telescope (JKT). For Asteroid (6455) 1992 HE we derive a rotational period P=2.736±0.002 h, and an absolute visual magnitude H=14.32±0.24. For Asteroid 2002 HK₁₂ we derive . The Standard Thermal Model (STM), the Fast Rotating Model (FRM) and the Near-Earth Asteroid Thermal Model (NEATM) have been fitted to the measured fluxes to derive albedos and effective diameters. The derived geometric albedos and effective diameters are (6455) 1992 HE: pv=0.26±0.08, Deff=3.55±0.5 km; 1999 HF₁: pv=0.18±0.07, ; 2000 ED₁₀₄: pv=0.18±0.05, Deff=1.21±0.2 km; 2002 HK₁₂: , Deff=0.62±0.2 km; 2002 NX₁₈: pv=0.031±0.009, Deff=2.24±0.3 km; 2002 QE₁₅: , Deff=1.94±0.4 km. The limitations of using the NEATM to observe NEAs at high phase angles are discussed.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

Photometric survey of binary near-Earth asteroids

Photometric data on 17 binary near-Earth asteroids (15 of them are certain detections, two are probables) were analysed and characteristic properties of the near-Earth asteroid (NEA) binary population were inferred. We have found that binary systems with a secondary-to-primary mean diameter ratio Ds/Dp?0.18 concentrate among NEAs smaller than 2 km in diameter; the abundance of such binaries decreases significantly among larger NEAs. Secondaries show an upper size limit of Ds=0.5-1 km. Systems with Ds/Dp?0.5 are abundant but larger satellites are significantly less common. Primaries have spheroidal shapes and they rotate rapidly, with periods concentrating between 2.2 to 2.8 h and with a tail of the distribution up to ∼4 h. The fast rotators are close to the critical spin for rubble piles with bulk densities about 2 g/cm³. Orbital periods show an apparent cut-off at Porb∼11 h; closer systems with shorter orbital periods have not been discovered, which is consistent with the Roche limit for strengthless bodies. Secondaries are more elongated on average than primaries. Most, but not all, of their rotations appear to be synchronized with the orbital motion; nonsynchronous secondary rotations may occur especially among wider systems with Porb>20 h. The specific total angular momentum of most of the binary systems is similar to within ±20% and close to the angular momentum of a sphere with the same total mass and density, rotating at the disruption limit; this suggests that the binaries were created by mechanism(s) related to rotation near the critical limit and that they neither gained nor lost significant amounts of angular momentum during or since formation. A comparison with six small asynchronous binaries detected in the main belt of asteroids suggests that the population extends beyond the region of terrestrial planets, but with characteristics shifted to larger sizes and longer periods. The estimated mean proportion of binaries with Ds/Dp?0.18 among NEAs larger than 0.3 km is 15±4%. Among fastest rotating NEAs larger than 0.3 km with periods between 2.2 and 2.8 h, the mean proportion of such binaries is (66⁺¹⁰₋₁₂)%.     

Simulation and analysis of the dynamics of binary near-Earth Asteroid (66391) 1999 KW4

Near-Earth Asteroid (66391) 1999 KW4 was the subject of the recently published first extensive radar imaging, shape and mutual orbit modeling, and physical and dynamical characterization of a binary asteroid. In this paper we present in detail our numerical simulation of KW4 behind that work. Our propagations of the system with some variation in estimated parameters cover the set of KW4's possible current dynamical states consistent with the body models and other information obtained directly from the observations. We also apply our implementation of this simulation capability to address some of the dynamical mechanisms by which KW4 may be moved into the more energetically excited of those possible current states, particularly solar gravity interaction. Through comparison of the results with certain features of the observation data, we conclude that the actual KW4 system is not in the most energetically relaxed configuration but must be moderately excited. The system occupies a generalized Cassini state 2 which is different from that considered in most previously published treatments of Cassini states in that it involves co-precession of the primary's spin frame and the mutual orbit rather than co-precession of a satellite's spin frame and that satellite's orbit about the primary. We present a simple analytical theory describing the system's dynamics, which should be applicable to any other binary systems, of which KW4 is representative, in which a massive, roughly oblate primary is spinning rapidly relative to the rate of its mutual orbit with an on-average synchronous, elongated secondary. We examine separately both the effect of the larger binary component's oblateness, and the effect of the smaller component's roughly triaxial ellipsoid shape. The simple analytical formulae obtained agree with full-detail numerical simulation results, and can be used for remote estimation of binary mass properties from observed system motion.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.     

Photometry and models of eight near-Earth asteroids

We present new observations and models of the shapes and rotational states of the eight near-Earth Asteroids (1580) Betulia, (1627) Ivar, (1980) Tezcatlipoca, (2100) Ra-Shalom, (3199) Nefertiti, (3908) Nyx, (4957) Brucemurray, and (5587) 1990 SB. We also outline some of their solar phase curves, corrected to common reference geometry with the models. Some of the targets may feature sizable global nonconvexities, but the observable solar phase angles were not sufficiently high for confirming these. None is likely to have a very densely cratered surface. We discuss the role of the intermediate topographic scale range in photometry, and surmise that this scale range is less important than large or small scale lengths.     

New V-type asteroids in near-Earth space

We present new visible and near-infrared spectroscopic observations of 4 small, previously unclassified, near-Earth objects (NEOs). They appear to have basaltic surfaces, and hence they can be classified as V-types. Their visible spectra exhibit a closer spectral match with the Main-Belt (MB) Asteroid (4) Vesta than the other, presently known, V-type NEOs and MB asteroids. The near-infrared spectrum of Asteroid 2003 FT3 shows—for the first time among NEOs—a peculiar shape of the 1 μm band, maybe suggesting an overabundance of olivine compared to the other V-types and to (4) Vesta. The presence of V-type objects among NEOs may be a consequence of the delivery processes connecting the inner MB to the near-Earth region. On the basis of the orbital parameters of the NEOs presented here, both the resonances (3:1 and ν₆), usually considered as the most relevant gateways for the production of near-Earth asteroids, should have been active to transfer the bodies from the MB region.     

Thermal infrared and optical observations of four near-Earth asteroids

We present thermal infrared photometry and spectrophotometry of four near-Earth asteroids (NEAs), namely (433) Eros, (66063) 1998 RO₁, (137032) 1998 UO₁, and (138258) 2000 GD₂, using the United Kingdom Infrared Telescope (UKIRT) in 2002. For two objects, i.e. (433) Eros and (137032) 1998 UO₁, quasi-simultaneous optical observations were also obtained, using the Jacobus Kapteyn Telescope (JKT). For (127032) 1998 UO₁, we obtain a rotation period P=3.0±0.1 h and an absolute visual magnitude HV=16.7±0.4. The Standard Thermal Model (STM), Fast Rotating Model (FRM) and near-Earth asteroid Thermal Model (NEATM) have been fitted to the IR fluxes to determine effective diameters Deff, geometric albedos pv, and beaming parameters η. The derived values are (433) Eros: Deff=23.3±3.5 km (at lightcurve maximum), pv=0.24±0.07, η=0.95±0.19; (66063) 1998 RO₁: , ; (137032) 1998 UO₁: Deff<1.13 km, pv>0.29; (138258) 2000 GD₂: Deff=0.27±0.04 km, , η=0.74±0.15. (66063) 1998 RO₁ is a binary asteroid from lightcurve characteristics [Pravec, P., and 56 colleagues, 2006. Icarus 181, 63-93] and we estimate the effective diameter of the primary (Dp) and secondary (Ds) components: and . The diameter and albedo of (138258) 2000 GD₂ are consistent with the trend of decreasing diameter for S- and Q-type asteroids found by Delbó et al. [Delbó, M., Harris, A.W., Binzel, R.P., Pravec, P., Davies, J.K., 2003. Icarus 166, 116-130]. A possible trend of increasing beaming parameter with diameter for small (less than about 3 km) S- and Q-type asteroids is found.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.     

Detailed prediction for the BYORP effect on binary near-Earth Asteroid (66391) 1999 KW4 and implications for the binary population

A previous theory by the authors for detailed modeling of the binary YORP effect is reviewed and expanded to accommodate doubly-synchronous binary systems, as well as a method for non-dimensionalizing the coefficients for application to binary systems where a shape model to compute its own coefficients is not available. The theory is also expanded to account for the effects of primary J₂ and the Sun’s 3rd body perturbation on the secular orbit evolution. The newly expanded theory is applied to the binary near-Earth Asteroid 1999 KW4, for which a detailed shape model is available. The result of simulation of the secular evolutionary equations shows that the KW4 orbit will be double in size in approximately 22,000 years, and will reach the Hill radius in approximately 54,000 years. The simulation also shows that the eccentricity will alternate growing and shrinking in magnitude, depending on the location of the solar node in the body-fixed frame. Therefore the eccentricity is not fixed to evolve in the opposite sign as the semi-major axis unless the circulation of the node (with a period of 500 years) is averaged out as well. The current orbit expansion rate for KW4 of 7 cm per year is shown to be detectable with observations of the mean anomaly which grows quadratically in time with an expanding orbit. Finally, the KW4 results are scaled for application to a number of other binary systems for which detailed shape models are not available. This application shows that the orbits considered can expand to their Hill radius in the range of 10⁴-10⁶ years. This implies rapid formation of binary systems is necessary to support the large percentage of binaries observed in the NEA population.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

The Yarkovsky-driven origin of near-Earth asteroids

We investigate the relevance of the Yarkovsky effect for the origin of kilometer and multikilometer near-Earth asteroids (NEAs). The Yarkovsky effect causes a slow migration in semimajor axis of main belt asteroids, some of which are therefore captured into powerful resonances and transported to the NEA space. With an innovative simulation scheme, we determine that in the current steady-state situation 100-160 bodies with H < 18 (roughly larger than 1 km) enter the 3/1 resonance per million years and 40-60 enter the ν₆ resonance. The ranges are due to uncertainties on relevant simulation parameters such as the time scales for collisional disruption and reorientation, their size dependence, and the strength of the Yarkovsky and YORP effects. These flux rates to the resonances are consistent with those independently derived by Bottke et al. (2002, Icarus 156, 399-433) with considerations based only on the NEA orbital distribution and dynamical lifetime. Our results have been obtained assuming that the main belt contains 1,300,000 asteroids with H < 18 and linearly scale with this number. Assuming that the cumulative magnitude distribution of main belt asteroids is N(< H) ∝ 10^γ′H with γ′ = 0.25 in the 15.5 < H < 18 range (consistent with the results of the SDSS survey), we obtain that the bodies captured into the resonances should have a similar magnitude distribution, but with exponent coefficient γ = 0.33-0.40. The lowest value is obtained taking into account the YORP effect, while higher values correspond to a weakened YORP or to YORP-less cases. These values of γ are all compatible with the debiased magnitude distributions of the NEAs according to Rabinowitz et al. (2000, Nature 403, 165-166), Bottke et al. (2000b, Science 288, 2190-2194), and Stuart (2001, Science 294, 1691-1693). Hence the Yarkovsky and YORP effects allow us to understand why the magnitude distribution of NEAs is only moderately steeper than that of the main belt population. The steepest main belt distribution that would still be compatible with the NEA distribution has exponent coefficient γ′ ∼ 0.3.