Retrieval of interior structure of asteroids with the low-frequency telescope DART
image: Fig. 1. The Daocheng Solar Radio Telescope.
Credit: Space: Science & Technology
In a research article recently published in Space: Science & Technology, researchers from Chinese Academy of Sciences investigated the distribution of scattered waves and signal power alterations resulting from electromagnetic scattering on asteroids within the DART’s frequency range and proposed an electromagnetic scattering model of asteroids, which positioned DART as a promising asset in advancing our understanding of asteroid interiors and offered valuable insights for scientific inquiry and hazard mitigation strategies.
First, an asteroid model is formulated. Given the prevalent elongated shapes of asteroids, an ellipsoid with a dimensional ratio of 2:1:1 is opted as the representative shape for asteroids. The surface layer thickness is estimated by the celestial collisions. The number of impact objects N is expressed through their diameters Dn as N = ∫6D/2 kDn−4 dDn, where D is the long axis of the target asteroid. The diameter R of the impact crater formed on the target asteroid through dimensional analysis is R = KD(ν2p/Y)u/2. The sputter volume V which is the volume of the material expelled from the asteroid’s surface after an impact event is V = C(2π/3)R3(Z−2)/(Z+1). The estimation of surface thickness H follows H = (ΣNi=1 Vi)/S, where S represents the surface area of the target asteroid and Vi is the sputtering volume produced by the ith impact object. The inner layer thickness is calculated based on the maximum size and surface thickness of the target asteroid: Hinner = D – H. The asteroid interior permittivity ϵ and loss tangent tanδ of are derived from the density, titanium iron content, and surface temperature. The loss tangent tanδ is tanδ(p,F) = 100.038F+0.312p–3.26 where density p = p0 + kpln(z+1) is fitted from the lunar soil sample and z is the surface depth. A modified permittivity fitting is ϵ(p,T) = (1.85±0.02)p + (8±1)×10–4T where the surface temperature is T = [k0D–ξ/(6.72×10–8)]2/3. Above completes the asteroid model.
Then, an electromagnetic scattering model of an asteroid is constructed to determine the electromagnetic propagation law. When the VHF/UHF wave meets asteroids, some energy scatters on the surface and a portion penetrates the interior, reducing power in reflection and refraction. Assuming a homogeneous distribution of the asteroid layer, Fig. 2 illustrates the incident scenario on a 3D surface. The blue lines in Fig. 2 represent the tangent plane at the incident point. The red line represents the surface normal at the incident point, where denoted by (nx,ny,nz). It is obtained by taking the gradient of the surface equation. The yellow dashed lines represent the plane of incidence, labeled as plane E. The reflection and transmission, adhering to Snell’s law, propagate along surface E and traverse the incident point. The unit direction vectors for the reflection and the transmission are (bx,by,bz) and (cx,cy,cz), respectively. The ratios of reflection power and transmission power to the incident wave power at the division interface are Pr, Pt, Pi, respectively, evolving reflection coefficients Γν,Γp and the transmission coefficients Tν,Tp of transverse electric (TE) wave and transverse magnetic (TM) wave components. The reflection coefficients Γν,Γp and transmission coefficients Tν,Tp, along with the change in the propagation of electromagnetic waves, are determined by the incidence angle θi and the permittivity ϵ1,ϵ2 on both sides of the interface. When the electromagnetic wave transitions from a medium with a small permittivity to one with a large permittivity, there is a complete transmission angle θB. When electromagnetic wave incident from a large permittivity to a small one, an all-reflection angle θallr exists. As an electromagnetic wave permeates a medium, a fraction of its energy transforms into thermal energy, resulting in energy loss. The extent of energy decay depends on the dielectric properties and the propagation distance within the medium. Considering the propagation direction and attenuation, the power expressions for the reflection and transmission across an interface are:
Pr = (bx,by,bz) ∙ (wνΓν2 + wpΓp2)/(wν + wp) ∙ Pi e–2α1h1
Pt = (cx,cy,cz) ∙ (wνTν2 + wpTp2)(ϵ2 cosθt)1/2/(wν + wp)/(ϵ1 cosθi)1/2 ∙ Pi e–2α2h2
Finally, simulation and discussion are carried out. A thorough study is conducted by varying rotation angles. Fig. 3 illustrates different rotation angles β which are the counterclockwise angle between the major axis of the asteroid and Z axis. The asteroid model contains 2 simplifications: a uniform ellipsoid structure that is not stratified and a double-layer ellipsoid structure. Fig. 4 shows the scattered waves with different numbers come from different interfaces inside the asteroid. Simulation results are concluded as follows. (1) According to Fig. 5 and Fig. 6 the polarization of direct reflection and internal reflected waves is valuable in deducing the asteroid’s surface and inner contour. Discrepancies between inner layer reflected and transmitted waves at different frequencies are associated with the asteroid’s medium loss coefficient, determined by internal medium information. Variations in signals at different frequencies can be utilized to extract information about the asteroid’s internal structure and medium. (2) During signal integration time, the polarization and attenuation of received signal waves exhibit periodicity corresponding to the asteroid’s rotation period. Consequently, signal waves over one rotation period encapsulate information about the entire structure and medium of the asteroid. (3) Despite analytical indications that scattering signals received during one rotation period of a wideband transmitted signal can be used to infer the overall internal structure and medium information of the asteroid, actual received signals are ordered by reception time. This makes it challenging to distinguish signals from each determined rotation angle. Additionally, the asteroid’s distance from Earth is much greater than its size; it can be regarded as a point object. Received scattered waves are superimposed in the azimuth angle, further complicating the inversion of the asteroid’s internal structure and medium information. However, DART can alleviate these problems. In terms of signal reception, empowered DART with the transmission is capable of emitting signals with megawatt-level and satellites or space probes to receive scattered signals, thereby significantly reducing the attenuation of the scattered signal due to long propagation distance, resulting in an enhancement in the received signal. In terms of asteroid internal information acquisition, the scattering differences at different frequencies and the changes in polarization ratio in scattered waves provide a more comprehensive understanding of the asteroid’s internal structure. Simultaneously, DART has a broad bandwidth and polarization ability.