One of the most important sources of information about asteroid physical parameters is photometry - typical kilometer-sized asteroids (up to diameters of ~1000 km, corresponds to Ceres) are rather non-spherical and rotate around their axis with periods of several hours, thus their apparent brightness (reflected light from the Sun) as observed from the Earth is changing in time. We measure a lightcurve. The photometry can be divided into disk-integrated, where we measure the total brightness of the object, and disk-resolved, where we have the information of the brightness across the asteroid surface. The latter case is currently achievable only with 8-10m class telescopes equipped with adaptive optics systems (such as Keck, VLT, and Gemini telescopes) or from space by the Hubble Space Telescope (HST). Actual 2D projection of the real asteroid shape can be extracted from the disk-resolved image.

Disk-integrated photometry

Two different types of disk-integrated photometry are used: (i) dense-in-time, which typically consists of tens to a few hundreds of individual data points observed during one revolution (typically several hours), and (ii) sparse-in-time, where the typical separation of individual measurements is large compared to the rotation period. For sparse data, we usually have a few measurements per night in a particular sequence (e.g., for data from the Catalina Sky Survey project, where there are typically four individual observations separated by ∼20 minutes). By sparse-in-time data, we usually mean photometry produced by large astrometric sky surveys. There is no proper boundary between dense and sparse data, because one can create an observational strategy that is in some aspects similar to both dense and sparse data. Based on the type of the photometry, we use the terms “dense lightcurves” and “sparse lightcurves”.

Dense data well define the rotational period. These lightcurves are typically observed by many “backyard“ observers, but also by professionals, who, for example, dedicate their observational campaigns to particular asteroid groups.

The information about the absolute calibration of the dense lightcurves is usually missing or not reliable, and thus we use this photometry as relative only. Lightcurves from one apparition (i.e., one observational season, typically ∼3-4 months) can be processed by the Fourier analysis to find the synodic rotational period.

Figure. ​Dense-in-time disk-integrated photometry of asteroid (51) Nemausa observed by Marek Wolf and Josef Hanus at Ondrejov observatory.

Sparse photometric measurements are produced by many astrometric surveys, but mostly as a by-product. In most cases, asteroid magnitudes are given to only one decimal place, i.e., the accuracy is 0.1 mag at best. Such photometry is useful only for asteroids with higher lightcurve amplitudes (>0.1 mag). Contrary to dense data, sparse data usually cover a long time interval, typically over several apparitions, and carry information about brightness variations for different geometries, which constrains the pole orientation. While the dense data are available for several thousands of asteroids, sparse photometry is available for almost all of them.

Figure. ​Sparse-in-time disk-integrated photometry of asteroid (121) Hermione from USNO- Flagstaff station (IAU code 689).

Disk-resolved data

Disk-resolved images give us momentary two-dimensional shape projections of the asteroids. Disk-resolved images of asteroid (4) Vesta observed by the Hubble Space Telescope (see below) reveal the non-spherical nature of this large (D = 525 km) body. Such observations can also expose non-convexities and thus constrain the size. Asteroids can be resolved only by a few ground based 8-10m class telescopes equipped with adaptive optics (AO) systems (VLT, Keck, Gemini) or by the Hubble Space Telescope.

The great advantage of the AO images is that the pixel scale on the image is known (from the asteroid distance to the observer). Thus, by combining resolved direct images of asteroids with their shape models (simple ellipsoidal models or those derived by the lightcurve inversion method), we can infer the sizes of these asteroids. Moreover, if a realistic shape model is used, we can derive a volume-equivalent diameter (thus volume) or remove the ambiguity between two ambiguous pole solutions (typical outcome from the shape modeling). Thanks to the adopted mass values, it is also possible to compute average (bulk) densities of several asteroids.

Figure. Four adaptive optics images of asteroid (45) Eugenia, contours were computed by the AIDA deconvolution algorithm (Marchis et al. 2006; Hom et al. 2007).


Hom, E. F. Y., Marchis, F., Lee, T. K., et al. (2007). AIDA: An adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 24(6), p 1580-1600.

Marchis, F., Kaasalainen, M., Hom, E. F. Y., et al. (2006). Shape, size and multiplicity of main-belt asteroids. I. Keck Adaptive Optics survey. Icarus, 185, p 39-63.

-- JosefHanus - 27 Aug 2015
Topic revision: r2 - 27 Aug 2015, JosefHanus
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