Vol 17, No 7 (2017) / Yu

Surface thermophysical properties on the potentially hazardous asteroid (99942) Apophis

Surface thermophysical properties on the potentially hazardous asteroid (99942) Apophis

Yu Liang-Liang1, 2, , Ji Jianghui2, , Ip Wing-Huen1, 3,

Space Science Institute, Macau University of Science and Technology, Taipa, Macau, China
CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China
Institute of Astronomy, National Central University, Zhongli, Taoyuan 32049

† Corresponding author. E-mail: yullmoon@live.com jijh@pmo.ac.cn wingip@astro.ncu.edu.tw


Abstract: Abstract

We investigate the surface thermophysical properties (thermal emissivity, thermal inertia, roughness fraction and geometric albedo) of asteroid (99942) Apophis, using the currently available mid-infrared observations from CanariCam on Gran Telescopio CANARIAS and far-infrared data from PACS on Herschel, based on the Advanced Thermophysical Model. We show that the thermal emissivity of Apophis should be wavelength dependent from 8.70 μm to 160 μm, and the maximum emissivity may appear around 20 μm, similar to that of Vesta. Moreover, we further derive the thermal inertia, roughness fraction, geometric albedo and effective diameter of Apophis within a possible 1 scale of , , and , and 3 scale of , , and . The derived low thermal inertia but high roughness fraction may imply that Apophis could have regolith on its surface, where stronger space weathering but weaker regolith migration has happened in comparison with asteroid Itokawa. Our results show that small-size asteroids could also have fine regolith on the surface, and further infer that Apophis may have been delivered from the Main Belt by the Yarkovsky effect.

Keywords: techniques: thermal infrared;variables: thermal inertia;asteroid: individual: (99942) Apophis



1 Introduction

(99942) Apophis (2004 MN4) is categorized as an Aten-group near-Earth asteroid based on its orbital characteristics. The asteroid was identified as a potentially hazardous object with a significant Earth impact probability of 2% in 2029, based on observations from December 2004 reported by JPL-Sentry and ESA-NEODyS. On 2004 December 27, the Spacewatch survey announced pre-discovery observations (Gilmore et al. 2004 ) that were acquired starting from March 2004, and negated any possibility of impact with Earth in 2029.

Radar observations of Apophis were obtained by the Arecibo observatory in January 2005, August 2005 and May 2006. More recently, Thuillot et al. ( 2015 ) reported new astrometric observations obtained by space-based Gaia-FUN-SSO during Apophis’ latest period of visibility from 2012 December 21 to 2013 February 5, and soon afterwards, Wang et al. ( 2015 ) published precise 298 CCD position data observed by the ground-based 2.4-m telescope administered by Yunnan Observatories from 2013 February 4 to 2013 March 2. These observations significantly reduced Apophis’ orbital uncertainty and led to a more accurate estimation of the distance during the encounter of about 5-6 Earth radii from the geocenter in 2029 (Giorgini et al. 2008 ; Thuillot et al. 2015 ; Wang et al. 2015 ). Although the possibility of an impact in 2029 has been eliminated, other potential impacts may still exist in following decades.

Chesley ( 2006 ) showed that the Yarkovsky effect (Bottke et al. 2006 ) significantly affects post-2029 predictions of Apophis’ orbit evolution and thus should be taken into account for its impact predictions. As is well known, the Yarkovsky effect due to the recoil of reflected and thermally emitted photons is one of the most important non-gravitational effects on asteroids. Utilizing selected best astrometric and radar data covering the interval from 2004 March 15 to 2012 December 29, Farnocchia et al. ( 2013 ) carried out a detailed orbital analysis and quantitatively verified that predictions of Apophis impacting Earth between 2060 and 2105 are sensitive to its physical parameters, including diameter, albedo, rotation period, obliquity, density and thermal inertia, which determine the rate of Yarkovsky drift for Apophis’ semimajor axis. In addition, Vokrouhlický et al. ( 2015 ) provided a more advanced estimation of Apophis’ Yarkovsky effect, and predicted that Apophis’ secular change in the semimajor axis may be . Therefore, accurate thermal properties (thermal inertia, roughness fraction and so on) and shape model are necessary to predict its Earth impact probability in the following decades in consideration of the significance played by the Yarkovsky effect.

By comparing spectral and mineralogical characteristics of likely meteorite analogs from 0.55 to 2.45 μm reflectance spectral measurements of Apophis observed by the NASA IRTF and the Baade Telescope at the Magellan Observatory, Binzel et al. ( 2009 ) found that Apophis appears well classified as an Sq-type and most closely resembles LL ordinary chondrite meteorites, which is rather similar to asteroid Itokawa (Abe et al. 2006 ).

With the photometric observations of Apophis from December 2012 to April 2013, Pravec et al. ( 2014 ) showed Apophis has a non-principle axis rotation, and reconstructed its convex shape model, where the retrograde rotation period is h and the spin axis orientation is ( , ). Pravec et al. ( 2014 ) also derived Apophis’ average absolute visual magnitude to be assuming the slope parameter to be .

Generally, the thermal inertia of an asteroid can be evaluated by fitting infrared (IR) observations with a thermophysical model to reproduce thermal emission curves. Following the shape model of Pravec et al. ( 2014 ), Müller et al. ( 2014 ) utilized the so-called thermophysical model (TPM) to analyze Apophis’ Herschel-far-IR observations, and derived its thermal inertia to be with a best solution of about , mean effective diameter of m, and geometric albedo of . All these properties of Apophis are very similar to those of Itokawa (Müller et al. 2005 ; Fujiwara et al. 2006 ), indicating that Apophis might also have a rubble-pile structure. However, recently Licandro et al. ( 2016 ) derived a relatively lower thermal inertia of with a best solution of and low surface roughness, indicating surface material like that of Eros. Licandro et al. ( 2016 ) used the same TPM as Müller et al. ( 2014 ), but added three new mid-IR data measured by CanariCam on Gran Telescopio CANARIAS. Both the work of Müller et al. ( 2014 ) and Licandro et al. ( 2016 ) assumed constant thermal emissivity to derive surface thermophysical properties, but actually thermal emissivity may be wavelength dependent from mid-IR to far-IR infrared (Mueller & Lagerros 1998 ), which should be taken into account when deriving the surface thermophysical properties.

In the present work, we utilize the independently developed thermophysical simulation codes (Yu et al. 2014 ; Yu & Ji 2015 ) Yu&Ji 2015 based on the framework of the Advanced Thermophysical Model (ATPM) (Rozitis & Green 2011 ) to analyze the mid-IR and far-IR data of Apophis observed by CanariCam and Herschel respectively. We show that if wavelength dependent emissivities are used, better solutions can be obtained, and the derived thermal inertia and effective diameter can be different from the results derived on the basis of constant emissivity (CE). Moreover, we find that the surface of Apophis may be a highly rough surface with low thermal inertia materials. The low thermal inertia of the small-size asteroid Apophis reveals that small-size asteroids may also have regolith on the surface, and further suggests that Apophis may have been delivered from the Main Belt by the Yarkovsky effect.

2 Thermophysical Modeling

2.1 Thermal Infrared Observations

Until now, the available IR measurements of Apophis were far-IR data observed by the Herschel Space Observatory (Müller et al. 2014 ), and three mid-IR data measured by CanariCam on Gran Telescopio CANARIAS (Licandro et al. 2016 ). All data used in this work will be compared with the theoretical flux simulated from the so-called ATPM so as to derive the possible scale of surface thermophysical properties. We tabulate data used in the fitting in Table 1.

Date Wavelength Flux α Observation
(UT) (μm) (mJy) (AU) (AU) (○) instrument
2013–01–06 00:10 70.0 36.3 ± 1.1 1.03593 0.096247 +60.44 Herschel/PACS
2013–01–06 00:10 160.0 8.7 ± 3.3 1.03593 0.096247 +60.44 Herschel/PACS
2013–01–06 00:44 100.0 22.8 ± 1.7 1.03599 0.096234 +60.40 Herschel/PACS
2013–01–06 00:44 160.0 7.4 ± 3.8 1.03599 0.096234 +60.40 Herschel/PACS
2013–01–06 01:15 70.0 37.5 ± 1.3 1.03604 0.096221 +60.36 Herschel/PACS
2013–01–06 01:15 160.0 9.8 ± 2.5 1.03604 0.096221 +60.36 Herschel/PACS
2013–01–06 01:47 100.0 25.0 ± 1.5 1.03609 0.096208 +60.32 Herschel/PACS
2013–01–06 01:47 160.0 8.2 ± 2.2 1.03609 0.096208 +60.32 Herschel/PACS
2013–03–14 06:40 70.0 12.6 ± 2.7 1.093010 0.232276 –61.38 Herschel/PACS
2013–03–14 06:54 70.0 11.4 ± 2.7 1.093003 0.232307 –61.38 Herschel/PACS
2013–03–14 07:07 70.0 10.4 ± 2.7 1.092996 0.232338 –61.39 Herschel/PACS
2013–03–14 07:21 70.0 12.5 ± 2.6 1.092989 0.232368 –61.39 Herschel/PACS
2013–03–14 07:35 70.0 13.3 ± 2.7 1.092983 0.232397 –61.40 Herschel/PACS
2013–03–14 07:49 70.0 12.4 ± 2.6 1.092976 0.232427 –61.40 Herschel/PACS
2013–01–29 22:04 12.5 240.0 ± 20 1.079706 0.113407 –31.73 CanariCam/GTC
2013–01–29 23:09 17.65 310.0 ± 70 1.079761 0.113478 –31.74 CanariCam/GTC
2013–01–29 23:52 8.70 140.0 ± 10 1.079816 0.113549 –31.75 CanariCam/GTC

Table 1Observational Data used in This Work (Müller et al. 2014 ; Licandro et al. 2016 ).

2.2 Advanced Thermophysical Model

In the ATPM (Rozitis & Green 2011 ; Yu et al. 2014 ; Yu & Ji 2015 ), we treat an asteroid as a polyhedron composed of N triangular facets. For each facet, the roughness is modeled by a fractional coverage of hemispherical micro-craters, denoted by ( ), whereas the remaining fraction, , represents a smooth flat surface. For such a rough surface facet, conservation of energy leads to an instant heat balance between sunlight, thermal emission, heat conduction, multiply-scattered sunlight and thermally-radiated fluxes from other facets. If each facet is small enough and far larger than the spatial scale of roughness, heat conduction in that region can be approximatively described as one-dimensional heat conduction. Meanwhile, the temperature of each facet varies with time as the asteroid rotates. In this process, can be significantly affected by shading, multiply-scattered sunlight and thermally-radiated fluxes from other facets, which explains the so-called thermal IR beaming effect well. When the entire asteroid comes into the final state of thermal equilibrium, will change periodically following the rotation of the asteroid. Therefore, we can build numerical codes to simulate at any rotation phase for the asteroid. For a given observation epoch, ATPM can reproduce a theoretical profile for each observed flux as

where ε(λ) is the monochromatic emissivity at wavelength λ, S(i) is the area of facet i, f(i) is a factor related to the view of facet i with respect to the telescope defined by
such that indicates facet i is visible (otherwise ), and is the Planck function

Thus the calculated can be compared with the thermal IR fluxes summarized in Table 1 derived from the fitting process.

2.3 Fitting Procedure

In order to derive the thermophysical properties of Apophis via the ATPM procedure, several physical parameters are needed, including the three-dimensional (3D) shape model, effective diameter and the so-called thermal parameter

where ω is rotation frequency, Γ is thermal inertia, is averaged thermal emissivity over the entire emission spectrum and
In addition, geometric albedo is related to the effective Bond albedo by
where is the phase integral that can be approximated by (Bowell et al. 1989 )
in which G is the slope parameter in the H, G magnitude system of Bowell et al.( 1989 ). We use , G = 0.24 ± 0.11 and the results of Pravec et al. ( 2014 ) in the fitting procedure.

On the other hand, the asteroid’s effective Bond albedo is the averaged result of both albedos of the smooth and rough surfaces, which can be expressed by the following relationship

where is the Bond albedo of a smooth Lambertian surface, which should be related to the composition of surface materials. Thus an input roughness fraction and geometric albedo can lead to a unique Bond albedo and effective diameter to be used to fit the observations.

Then we have three free parameters — thermal inertia, roughness fraction and geometric albedo (or effective diameter) that can be extensively investigated in the fitting process. Other parameters are listed in Table 2.

Property Value Reference
Number of vertices 1014 Pravec et al. ( 2014 )
Number of facets 2024 Pravec et al. ( 2014 )
Shape (a:b:c) 1.1135:1.0534:1 Pravec et al. ( 2014 )
Angular momentum vector ( , ) Pravec et al. ( 2014 )
Spin period 30.56 h Pravec et al. ( 2014 )
Absolute magnitude 19.09 ± 0.19 Pravec et al. ( 2014 )
Slope parameter 0.24 ± 0.11 Pravec et al. ( 2014 )
Thermal emissivity 0.9 assumption

Table 2 Assumed Physical Parameters used in ATPM

It should also be noticed here that the utilized observational data are observed at various wavelengths from mid-IR to far-IR, thus it may no longer be suitable to assume an average CE for all wavelengths when calculating flux by Equation (1), because the spectral emissivity may differ with wavelength from mid-IR to far-IR (Mueller & Lagerros 1998 ). Therefore, the spectral emissivity remains a free parameter as well.

For the input free parameters, we use an initial geometric albedo , but scan thermal inertia Γ in the range , and roughness fraction in the range . For the spectral emissivity , we firstly assume it to have CE of 0.9, then vary it to see if we can get better solutions. For each pair of (Γ, ), we could find a new (or ) that gives a minimum reduced defined as

which is used to assess the fitting degree of our model with respect to observations. Herein, the predicted model flux is a rotationally averaged profile assuming rotation is along the angular momentum vector, for the rotation phases of Apophis at the time of observation are uncertain due to its non-principal axis rotation. Through the rotationally averaged procedure, the influence arising from the tumbling rotation would somewhat decrease, but the thermal properties can be revealed well from the effect of seasons, because we have observations at different epochs.

3 Analysis and Results

As mentioned above, we firstly assume the spectral emissivity to be constant 0.9 for each observed wavelength, and obtain the reduced for each input Γ and (shown in Table 3).

Roughness fraction Thermal inertia Γ ( )
0 50 100 150 200 250 300
0.00 0.316 4.64 0.342 5.49 0.346 5.94 0.347 6.33 0.347 6.70 0.347 7.08 0.347 7.42
0.05 0.313 4.46 0.335 5.28 0.338 5.73 0.339 6.12 0.339 6.49 0.339 6.88 0.339 7.23
0.10 0.312 4.29 0.335 5.08 0.337 5.53 0.338 5.92 0.338 6.29 0.338 6.68 0.338 7.04
0.15 0.312 4.12 0.334 4.89 0.337 5.33 0.337 5.72 0.337 6.10 0.337 6.49 0.337 6.86
0.20 0.311 3.97 0.333 4.70 0.336 5.13 0.336 5.52 0.336 5.90 0.336 6.31 0.336 6.67
0.25 0.310 3.84 0.333 4.53 0.335 4.95 0.336 5.34 0.335 5.72 0.335 6.12 0.335 6.49
0.30 0.310 3.71 0.332 4.36 0.334 4.77 0.335 5.15 0.334 5.53 0.334 5.94 0.334 6.32
0.35 0.309 3.60 0.331 4.20 0.333 4.59 0.334 4.98 0.333 5.36 0.333 5.77 0.333 6.15
0.40 0.308 3.49 0.330 4.04 0.332 4.43 0.333 4.80 0.332 5.18 0.332 5.60 0.332 5.98
0.45 0.307 3.40 0.330 3.89 0.331 4.27 0.332 4.64 0.331 5.01 0.331 5.43 0.331 5.82
0.50 0.306 3.32 0.329 3.75 0.330 4.11 0.330 4.48 0.330 4.85 0.330 5.27 0.329 5.65
0.55 0.305 3.25 0.328 3.62 0.329 3.96 0.329 4.32 0.329 4.69 0.328 5.11 0.328 5.50
0.60 0.304 3.19 0.326 3.49 0.328 3.82 0.328 4.17 0.327 4.54 0.327 4.95 0.326 5.34
0.65 0.303 3.14 0.325 3.37 0.327 3.68 0.326 4.02 0.326 4.39 0.326 4.80 0.325 5.19
0.70 0.302 3.10 0.324 3.26 0.325 3.55 0.325 3.88 0.324 4.24 0.324 4.65 0.323 5.04
0.75 0.300 3.07 0.323 3.15 0.324 3.43 0.323 3.75 0.323 4.10 0.322 4.51 0.322 4.90
0.80 0.299 3.05 0.321 3.05 0.322 3.31 0.322 3.61 0.321 3.96 0.321 4.37 0.320 4.76
0.85 0.297 3.05 0.319 2.96 0.320 3.19 0.320 3.49 0.319 3.83 0.319 4.23 0.318 4.62
0.90 0.296 3.05 0.318 2.87 0.319 3.08 0.318 3.37 0.317 3.70 0.317 4.10 0.316 4.48
0.95 0.294 3.06 0.316 2.79 0.317 2.98 0.316 3.25 0.315 3.57 0.315 3.97 0.314 4.35
1.00 0.290 3.08 0.318 2.71 0.319 2.88 0.318 3.14 0.317 3.45 0.316 3.84 0.315 4.22

Table 3 ATPM Fitting Results to Observations with Constant Spectral Emissivity = 0.9 for Each Wavelength

From Table 3, we can see that low thermal inertia and high roughness fraction tend to fit the observations better; the best-fit solution, corresponding to the lowest reduced , appears at about , and . With this result, we plot the ratio of ‘observation/model’ to examine how these theoretical model results match the observations at various wavelengths (Fig. 2).

Fig. 2 The observation/model ratios as a function of wavelength for , , and when using . The ratios with their errors at each wavelength are all error-weighted average results. The red fitting curve is obtained from a 4th degree polynomial fitting for , .

In Figure 2, we can see that the ratios at each wavelength are not randomly distributed around 1.0, but reveal a wavelength dependent feature like the red fitting curve, where the maximum ratio may appear around 20 μm. This feature implies that the spectral emissivity used in Equation (1) should not be a constant , but should be wavelength dependent, where the maximum emissivity may occur around 20 μm. Thus we should introduce a wavelength dependent spectral emissivity to do the fitting process again.

Mueller & Lagerros ( 1998 ) reported the wavelength dependent spectral emissivity of asteroids Ceres and Vesta. As the spectral feature of Vesta may be much closer to Apophis than Ceres, we imagine that Apophis’ emissivity changes with wavelength in a similar way to that of asteroid Vesta (Mueller & Lagerros 1998 ) as shown in Table 4. With this wavelength dependent emissivity, we derive better solutions.

Wavelength (μm) Emissivity
8.7, 12.5 0.90
17.65 0.96
70, 100 0.80
160 0.75

Table 4 Assumed Emissivity for Different Wavelength

Table 5 summarizes the reduced obtained from each input pair of thermal inertia and roughness fraction when using the emissivity given in Table 4. We can see that, in this case, the high roughness fraction tends to fit better as well. But the best-fit thermal inertia and geometric albedo shift to and respectively. We compare the reduced obtained from the two cases of CE and wavelength dependent emissivity (WDE) in Figure 3, where the black curves represent the reduced obtained from CE input while the red curves stand for WDE. We can see that the obtained minimum reduced can be significantly lower when the WDE is used to fit observations, indicating that the spectral emissivity of Apophis should be wavelength dependent.

Fig. 3 curves for both the CE and WDE cases considering .
Roughness fraction Thermal inertia Γ ( )
fraction 0 50 100 150 200 250 300 350 400 450 500
0.00 0.283 3.64 0.305 4.18 0.308 4.55 0.309 4.89 0.309 5.22 0.309 5.57 0.308 5.89 0.308 6.21 0.307 6.52 0.306 6.80 0.306 7.09
0.05 0.284 3.52 0.304 4.01 0.306 4.37 0.307 4.70 0.307 5.03 0.307 5.38 0.306 5.70 0.306 6.03 0.306 6.34 0.305 6.63 0.305 6.93
0.10 0.284 3.40 0.304 3.84 0.306 4.19 0.307 4.52 0.306 4.84 0.306 5.20 0.306 5.52 0.305 5.85 0.305 6.17 0.304 6.46 0.304 6.76
0.15 0.284 3.31 0.304 3.68 0.306 4.02 0.306 4.34 0.306 4.66 0.306 5.02 0.305 5.35 0.305 5.68 0.304 6.00 0.304 6.30 0.303 6.60
0.20 0.283 3.22 0.303 3.53 0.305 3.85 0.305 4.17 0.305 4.49 0.305 4.84 0.305 5.18 0.304 5.51 0.304 5.84 0.303 6.14 0.303 6.45
0.25 0.283 3.15 0.303 3.40 0.305 3.70 0.305 4.00 0.305 4.32 0.304 4.68 0.304 5.01 0.303 5.35 0.303 5.68 0.302 5.98 0.302 6.30
0.30 0.282 3.10 0.302 3.27 0.304 3.55 0.304 3.84 0.304 4.16 0.304 4.51 0.303 4.85 0.303 5.19 0.302 5.52 0.301 5.82 0.301 6.14
0.35 0.282 3.06 0.302 3.14 0.303 3.41 0.304 3.69 0.303 4.00 0.303 4.35 0.302 4.69 0.302 5.03 0.301 5.37 0.301 5.67 0.300 6.00
0.40 0.281 3.03 0.301 3.03 0.303 3.27 0.303 3.55 0.302 3.85 0.302 4.20 0.301 4.54 0.301 4.88 0.300 5.22 0.300 5.52 0.299 5.85
0.45 0.281 3.01 0.301 2.93 0.302 3.15 0.302 3.41 0.301 3.71 0.301 4.05 0.300 4.39 0.300 4.73 0.299 5.07 0.299 5.38 0.298 5.71
0.50 0.280 3.01 0.300 2.83 0.301 3.03 0.301 3.28 0.300 3.57 0.300 3.91 0.299 4.24 0.299 4.58 0.298 4.92 0.298 5.23 0.297 5.57
0.55 0.279 3.02 0.299 2.74 0.300 2.92 0.300 3.15 0.299 3.43 0.299 3.77 0.298 4.10 0.298 4.44 0.297 4.78 0.296 5.09 0.296 5.43
0.60 0.279 3.04 0.298 2.66 0.299 2.81 0.299 3.03 0.298 3.30 0.298 3.63 0.297 3.96 0.297 4.30 0.296 4.64 0.295 4.95 0.295 5.29
0.65 0.278 3.07 0.298 2.59 0.298 2.71 0.298 2.92 0.297 3.18 0.297 3.50 0.296 3.82 0.295 4.16 0.295 4.51 0.294 4.82 0.294 5.16
0.70 0.277 3.12 0.297 2.53 0.297 2.62 0.297 2.81 0.296 3.06 0.296 3.38 0.295 3.69 0.294 4.03 0.294 4.37 0.293 4.69 0.292 5.03
0.75 0.276 3.17 0.296 2.47 0.296 2.54 0.296 2.71 0.295 2.94 0.294 3.25 0.293 3.57 0.293 3.90 0.292 4.24 0.291 4.56 0.291 4.90
0.80 0.275 3.24 0.294 2.42 0.295 2.46 0.294 2.61 0.293 2.83 0.293 3.14 0.292 3.44 0.291 3.78 0.291 4.12 0.290 4.43 0.290 4.78
0.85 0.274 3.32 0.293 2.38 0.294 2.38 0.293 2.52 0.292 2.73 0.291 3.02 0.290 3.33 0.290 3.65 0.289 3.99 0.288 4.31 0.288 4.65
0.90 0.273 3.42 0.292 2.34 0.292 2.32 0.291 2.43 0.290 2.63 0.290 2.91 0.289 3.21 0.288 3.53 0.288 3.87 0.287 4.18 0.286 4.53
0.95 0.272 3.52 0.291 2.32 0.291 2.26 0.290 2.35 0.289 2.53 0.288 2.81 0.287 3.10 0.286 3.42 0.286 3.76 0.285 4.07 0.285 4.41
1.00 0.263 3.63 0.286 2.30 0.286 2.21 0.285 2.28 0.284 2.44 0.283 2.71 0.282 2.99 0.281 3.31 0.280 3.64 0.279 3.95 0.278 4.30

Table 5 ATPM Fitting Results to Observations with WDE

Since we cannot obtain the best solutions by assuming CE, we have no reason to fit the observations with ATPM by using CE. Therefore, we adopt the WDE similar to that of asteroid Vesta to further derive the surface thermal inertia, roughness fraction and geometric albedo here.

Figure 4 shows the contours of , Γ) according to Table 5, where the color variation from blue to red means increase of the reduced . The deep blue curve labeled by 1 corresponds to from the minimum , constraining the scale of the free parameters with probability of about , whereas the blue curve labeled by 3 refers to , giving the scale of free parameters with probability of about (Press 2007).

Figure 5 shows the obtained in consideration of the above derived Γ and as well as the absolute visual magnitude , where 1 and 3 limits are the same as above. The scale of absolute visual magnitude does not affect the distribution of reduced derived from each pair of thermal inertia and roughness fraction, but has significant influence on the corresponding geometric albedo and effective diameter. Thus we do not treat as a free parameter, but consider its influence by only using the upper limit, mid-value and lower limit of ; each was adopted to be a constant in the fitting process. The final results of geometric albedo and effective diameter are constrained by considering three cases of together, leading to the 1 and 3 scales being non-Gaussian.

Fig. 4 , Γ) contours according to Table 5. The color (from blue to red) means increase of the profile for . 1 corresponds to while 3 corresponds to (Press 2007).
Fig. 5 profiles fit to the observations in consideration of the derived 1 and 3 range for and Γ and the absolute visual magnitude .

Using the assumed WDE in Table 4, we can derive thermal inertia Γ, roughness fraction , geometric albedo and effective diameter , where they are considered to be free parameters in the fitting procedure, on the likely 1 and 3 scales. We summarize the relevant results in Table 6.

Properties 1σ scale 3σ scale
Thermal inertia Γ( )
Roughness fraction 0.78 ∼ 1.0 0.2 ∼ 1.0
Geometric albedo
Effective diameter (m)

Table 6 The Derived Parameters for Apophis

4 Discussion and Conclusions

In this work, the mid-IR and far-IR data of Apophis observed by CanariCam on Gran Telescopio CANARIAS and PACS on Herschel are analyzed by the ATPM, where four parameters, including thermal emissivity, thermal inertia, roughness fraction and geometric albedo, are investigated. We found that the thermal emissivity of Apophis should be wavelength dependent, and using a similar emissivity like that of Vesta could obtain a better fitting. As a result, we derive the thermal inertia, roughness fraction, geometric albedo and effective diameter of Apophis in a possible 1 scale of , , and , and 3σ scale of , , and . The derived thermal inertia supports the result of Licandro et al. ( 2016 ) despite being a little lower. The best fit high roughness is different from the result of Licandro et al. ( 2016 ), but is inconsistent with the work of Müller et al. ( 2014 ) where the best fit solution also supports a high roughness.

To verify the reliability of our fitting procedure and derived outcomes, we employ the ratio of ‘observation/model’ (Müller et al. 2005 , 2011 , 2012 ) to examine how these theoretical model results match the observations at various wavelengths (see Fig. 6).

Fig. 6 The observation/model ratios as a function of wavelength for , , and in consideration of WDE. The ratios with their errors at each wavelength are all error-weighted average results.

In Figure 6, the observation/model ratios are shown at each observational wavelength for , , and . The ratios are distributed more nearly around 1.0 compared to Figure 2, despite the ratios at 17.65μm becoming larger than unity which again support the idea that Apophis’ spectral emissivity should be wavelength dependent. However, we cannot know exactly how the spectral emissivity varies with wavelength at present, for the available spectral data are not enough. If, in the future, more spectral data observed from mid-IR to far-IR are obtained, we may find out how the emissivity of Apophis depends on wavelength.

Given the low gravitational acceleration on the surface of asteroids, it was generally thought that regolith formation would not be possible, especially on small-size asteroids. The statistical results of thermal inertia versus the size of asteroids in the work of Delbo’ et al. ( 2007 ) suggest that small-size asteroids should have high thermal inertia, indicating a rocky surface, also supporting the above idea. However, regolith on the small-size asteroid Itokawa was detected by the Hayabusa spacecraft (Saito et al., 2006 ), which suggests that regolith formation on asteroids, even small-size asteroids, is also possible. The low thermal inertia result of Apophis in this work somewhat adds support to the idea that regolith formation may not be dominated by the size of an asteroid. If a small asteroid has experienced a sufficiently long process of space weathering, the presence of regolith should be also reasonable. On the other hand, the size of Apophis is similar to that of asteroid Itokawa, indicative of a similar dynamical lifetime in principle. But the derived thermal inertia of Apophis is much lower than the observed thermal inertia of Itokawa (Müller et al. 2005 ), indicating Apophis may actually either have existed for a longer lifetime or experience stronger space weathering but weak reoligth migration on its surface, causing more dust to be produced and retained. We notice that Apophis has much slower rotation, h, than Itokawa ( h), which may account for Apophis’ lower thermal inertia, for the produced dust should more easily accumulate on a slowly-rotating asteroid.

Generally, a rough surface would generate stronger Yarkovsky orbit drift than a smooth surface (Rozitis & Green 2012 ). Thus the Yarkovsky effect that induced a decreasing rate of Apophis’ semimajor axis should be even larger than the predicted value of Vokrouhlický et al. ( 2015 ), because our results show Apophis tends to have a rough surface, which should be taken into account to predict its orbit movement. In addition, it is possible that Apophis may be one of Vesta’s fragments delivered from the Main Belt by the Yarkovsky effect, in consideration of its long existence time suggested by low thermal inertia, and similar surface properties to Vesta implied by albedo and thermal emissivity.

In conclusion, when we attempt to investigate surface thermophysical properties of a target asteroid by utilizing the thermal IR radiometric method to fit observed data from mid-IR to far-IR, CE may not always be the best choice. For asteroid Apophis, the combined data of mid-IR from CanariCam and far-IR from Herschel reveal possible wavelength dependent thermal emissivity from 8.70 μm to 160 μm, where the maximum emissivity may appear around 20 μm like that of Vesta, because this kind of emissivity can achieve a better degree of fitting through the use of ATPM. Moreover, the derived results of low thermal inertia and high roughness fraction indicate that Apophis may have experienced a long process of space weathering, but less regolith migration, enabling the produced dust to stay on its surface. These new deductions would be important for predicting Apophis’ orbital movement and potential Earth impact probability by so as to establish an artificial mechanism to avoid the probable impact.


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Cite this article: Yu Liang-Liang, Ji Jianghui, Ip Wing-Huen. Surface thermophysical properties on the potentially hazardous asteroid (99942) Apophis. Res. Astron. Astrophys. 2017; 7:070.

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