View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Helsingin yliopiston digitaalinen arkisto The Astrophysical Journal Letters, 822:L21 (5pp), 2016 May 10 doi:10.3847/2041-8205/822/2/L21 © 2016. The American Astronomical Society. All rights reserved. ASTEROID SIZING BY RADIOGALAXY OCCULTATION AT 5 GHZ K. Lehtinen1,U.Bach2, K. Muinonen1,3, M. Poutanen1, and L. Petrov4 1 Finnish Geospatial Research Institute FGI, Geodeetinrinne 2, FI-02430 Masala, Finland; kimmo.lehtinen@nls.fi 2 Max-Planck-Institut für Radioastronomie, Radioobservatorium Effelsberg, Max-Planck-Str. 28, D-53902 Bad Münstereifel-Effelsberg, Germany 3 Department of Physics, P.O. Box 64, University of Helsinki, FI-00014 Helsinki, Finland 4 Astrogeo Center, Falls Church, VA 22043, USA Received 2016 February 15; revised 2016 April 15; accepted 2016 April 17; published 2016 May 2 ABSTRACT Stellar occultations by asteroids observed at visual wavelengths have been an important tool for studying the size and shape of asteroids and for revising the orbital parameters of asteroids. At radio frequencies, a shadow of an asteroid on the Earth is dominated by diffraction effects. Here, we show, for the first time, that a single observation of an occultation of a compact radio source at a frequency of 5 GHz can be used to derive the effective size of the occulting object and to derive the distance between the observer and the center of the occultation path on the Earth. The derived diameter of the occulting object, asteroid (115) Thyra, is 75 ± 6 km. The observed occultation profile shows features that cannot be explained by diffraction of a single asteroid. Key words: minor planets, asteroids: individual (Thyra) – occultations 1. INTRODUCTION diffraction pattern on the Earth, not the physical size of the occulter. In this case, the distance between the first interference Occultation is a phenomenon where a distant object, usually fringe maxima of the diffraction pattern (the size of the Airy a star, is hidden by the Moon, a planet, or its ring or a small ring) is 2 3 in Fresnel scale units. In practice, this enables one body in our solar system. At visual wavelengths, a shadow of a to get the distance of the occulter if the size of the shadow on main-belt asteroid on the Earth during an occultation closely the Earth is known. The size of the occulter mainly affects the resembles its true silhouette on the plane of the sky. Thus, the amplitude of the interference fringes of the diffraction pattern. shape and size of an asteroid can be deduced if there are several In principle, if the diffraction effects are significant, one can simultaneous observations of an occultation made at different derive both the size of the occulter and its distance without an distances from the center of an occultation path. A single independent measurement of the size (that is, the velocity) of observation of an occultation at visual wavelengths gives only the shadow (Cooray 2003). In practice, this requires that both a lower limit for the size of an asteroid. In this Letter, we the projected size of the occulted object on the sky and the show that it is possible to deduce the effective size of an occultation light curve are known with a better than ∼5% asteroid from a single observation of an occultation at radio accuracy. wavelengths by modeling the occultation with Fresnel– Kirchhoff diffraction. During an occultation, the limb of an asteroid works as a 2. OCCULTATION PREDICTIONS sharp edge for the plane wave coming from the occulted object, The occultation predictions were made with the LinOccult5 producing diffraction that is mathematically expressed by the program, a free program made by A. Plekhanov. The use of Fresnel–Kirchhoff diffraction formula for monochromatic LinOccult requires three auxiliary data sets. First, for the radiation. The visibility of diffraction fringes on the shadow positions of the background objects, we use the latest Radio of the occulter is governed by the value of the Fresnel number Fundamental Catalog, available at http://astrogeo.org/rfc,here- F = r2/(Dλ), where r is the radius of the occulter, D is the after Astrogeo (L. Petrov & Y. Y. Kovalev 2016, in preparation; distance between the occulter and the observer, and λ is the Petrov et al. 2008 and references therein). Second, we obtain the wavelength of radiation. The case F 1 corresponds to the asteroid orbital elements from the latest astorb.dat6 file.Third,we regime of Fresnel diffraction, where the shadow of the occulter use the JPL ephemerides7 forthemajorplanets. on the Earth closely resembles its silhouette because on a Thyra was predicted to occult the radio source J0014+0854 typical observation, the diffraction effects are negligible on 2015 March 23 at 09:43:32 UT. The distance of the compared to the noise of an observation. At visual wave- Effelsberg radio telescope from the center of the occultation lengths, occultations by main-belt asteroids are in the region of path was predicted to be 70 ± 90 km. The velocity of the − Fresnel diffraction. The case F1 corresponds to the regime shadow of Thyra on the Earth was 52.5 km s 1 during the of Fraunhofer diffraction, where the diffraction pattern of an occultation. occultation is larger than the physical size of the occulter and dominated by interference fringes. This condition is fulfilled 3. OBSERVATIONS when observing an occultation at radio wavelengths. In the case ( ) ≈ The receiver used for the observations at the Effelsberg radio of our observation of the asteroid 115 Thyra, F 0.06. The “ ” characteristic scale of a diffraction pattern is given by the telescope was chosen to be the S60mm Double Beam Fresnel scale FD= l 2 . Also, other definitions for F have s s 5 http://andyplekhanov.narod.ru/occult/occult.htm been used, such as ()()lpD 2 and lD . In the Fraunhofer 6 ftp://ftp.lowell.edu/pub/elgb region, if the diameter of the occulter is less than about the 7 The file lnxp1600p2200.405 is available at ftp://ssd.jpl.nasa.gov/pub/ Fresnel scale, the Fresnel scale determines the size of a eph/planets/Linux/de405. 1 The Astrophysical Journal Letters, 822:L21 (5pp), 2016 May 10 Lehtinen et al. receiver: first, the frequencies at 20 GHz are less affected by variable atmospheric emission and absorption than at higher frequencies; second, it has the lowest noise of the receivers in the 20 GHz frequency range, having rms noise of about 1.4 mJy in 1 s of integration time and with 500 MHz bandwidth. The frequency range of the receiver is ∼4.6–5.1 GHz. We use the measured bandpass of the receiver to derive an effective frequency of 4.79 GHz. A signal from a noise diode calibrator, with a noise temperature of 1.8 K, is periodically inserted into the measured signal, giving the relation between temperature and instrumental units. The antenna temperatures were converted to Jansky units using an observation of the flux density calibrator 3C48. The derived sensitivity of 1.56 K Jy−1 is in good agreement with the theoretical estimate of 1.55 K Jy−1. The flux density was corrected for atmospheric absorption using an estimated opacity of 0.018 at 4.79 GHz, which is a typical value at Effelsberg. The original data were averaged over two samples to give a time resolution of about 0.03 s. The standard deviation of the occultation profile is ≈8 mK, corresponding to ≈5 mJy. 4. ASTEROID (115) THYRA Figure 1. A 3D model of Thyra as seen by an observer on the Earth at the time of the occultation. The model, obtained from the DAMIT database (http:// Thyra is a main-belt asteroid, categorized as a stony S-type astro.troja.mff.cuni.cz/projects/damit), is based on light curve inversion. The ( ) contours show the structure of J0014+0854 as based on C-band (4.3 GHz) asteroid DeMeo et al. 2009 . The effective diameter of Thyra ( ) ± ( ) VLBI observations on 2015 October Astrogeo , with contour levels of 0.3, 1, is estimated to be 79.8 1.4 km Tedesco et al. 2004 , derived 5, and 20 mJy/beam. The relative positions and orientations of J0014+0854 by modeling IRAS infrared data with a refined Standard and Thyra do not follow their actual values at the time of the occultation. The Thermal Model (STM; Lebofsky et al. 1986). Based on FWHM size of the circular Gaussian restoring beam of the VLBI observations thermophysical modeling (Delbò et al. 2015 and references is shown in the lower left corner. Both the physical and angular scales are valid for Thyra, while for J0014+0854 and the beam only the angular scale is valid. therein) of IRAS data using shape and spin vector solution of Thyra from light curve inversion (Michalowski et al. 2004), the equivalent diameter of Thyra is estimated to be 92 ± 2km core has FWHM axes of 0.7 × 0.8 mas and peak flux density of (Delbò & Tanga 2009). The AKARI mid-IR asteroid survey 35 mJy/beam. The smallest baseline length of the VLBA gives a mean diameter of 80.7 ± 0.9 km for Thyra (Usui et al. experiments was 2.4 Mλ. Therefore, the C-band image 2011), based on STM. The geocentric distance and angular size accounts for all emission that comes from regions with (assuming a diameter of 80 km) of Thyra were ∼2.97 au and characteristic sizes less than 80 mas. The integral flux density 0 037 during the occultation. at 7.6 GHz was 37 mJy in 2014 an 33 mJy in 2015.