Online multi-parameter phase-curve fitting and application to a large corpus of asteroid photometric data

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Abstract

We apply the new H,G12 and H,G1,G2 phase functions to a large corpus of asteroid photometric data. We make use of low-precision (generally rounded to 0.1 mag) and low-accuracy (rms magnitude uncertainties of ±0.2–0.3 mag) data obtained from the Minor Planet Center and modified at Lowell Observatory. We find (1) a correlation between G1,G2 values derived for asteroid families and albedos; (2) G12 homogeneity in families. In addition, we make available an online Java applet (titled Asteroid Phase Function Analyzer). The applet may be used to compute asteroid absolute magnitudes and slope parameters using three different phase functions: the H,G, H,G1,G2, and H,G12. The tool also includes non-Gaussian error analysis using Monte Carlo methods. The applet is available at http://asteroid.astro.helsinki.fi/astphase/.

Highlights

► We present online, open-source, multi-parameter phase-curve fitting Java applet. ► We apply the tool to a large number of data, in particular we focus on results for asteroid families and taxonomic groups. ► We discuss plans for adoption by the astronomical community of the H,G12 and H,G1,G2 photometric systems and our tabulation of asteroid photometric parameters.

Introduction

We apply the new H,G12 and H,G1,G2 phase functions [1] to photometric data of about half a million asteroids. We present an online Java applet for computing asteroid absolute magnitudes and slope parameters using three different phase functions: H,G, H,G1,G2, and H,G12. The absolute magnitude H of an asteroid is defined as the apparent V-band magnitude that the object would have if it were one astronomical unit from both the Sun and the observer and at zero solar phase angle (angle between incident and reflected light).

Absolute magnitudes and slope parameters are correlated with a number of other parameters, such as asteroid diameter, geometric albedo, and the physical properties of the surface. The correlations can be used for a number of different studies; for example, deriving the size-frequency distributions or albedo distributions of various asteroid populations. Given an asteroid's absolute magnitude, slope parameter(s), and observing geometry (and ignoring lightcurve variation) the apparent reduced magnitude can be calculated. Computing the absolute magnitude of an asteroid from its photometric observations at different phase angles requires fitting a phase curve. The phase function describes the relationship between the reduced magnitude (apparent V-band magnitude at 1 AU distance from the Sun and the observer) and phase angle. This relationship is mostly linear, except at small phase angles (where the so-called opposition effect occurs) and phase angles larger than 80°. Coherent backscattering by wavelength-scale particles, pores, and pits in the regolith causes nonlinear brightening towards small phase angles. Further brightening can result from mutual shadowing due to regolith particles large compared to the wavelength. For further information about the opposition phenomena, the reader is referred to a recent review by [2].

In what follows, we will briefly review the phase functions, numerical methods and software used (Section 2); describe photometric calibration used (Section 3); give examples of what can be accomplished using the Asteroid Phase Function Analyzer (Section 4); and point to future avenues of study (Section 5).

Section snippets

Overview of phase functions

Absolute-magnitude computation relies on magnitude phase-curve fitting. A number of different mathematical formulations for magnitude phase functions have been developed. Here we make use of the H,G, the H,G1,G2, and the H,G12 phase function. The H,G phase function, developed to predict the magnitude of an asteroid as a function of solar phase angle [3], was adopted by the International Astronomical Union in 1985. The H,G phase function is not valid for phase angles greater than 120. The H,G1,G

Photometric data and data calibration

We make use of the Lowell Observatory orbital data file maintained by EB and LHW. As of December 2010 it contained data for about 536,000 asteroids [10]. The orbital data are used in combination with photometric data from the Minor Planet Center (MPC). Most of the photometric data are of low-precision (generally rounded to 0.1 mag) and low-accuracy (rms magnitude uncertainties of ±0.2 to 0.3 mag are typical). The MPC data comprise photometric observations from many sources (each having different

Results and discussion

First, we apply the online tool to create fits to the Lowell observatory data set. Table 2 summarizes fits to the data of the first ten numbered asteroids. Fits using different phase functions resulted in the same rms values for an object. The last columns in Table 2 contain H and G values derived by other authors, based on different data sets. Figs. 4(a)–(c) show typical fits to a photometric data set lacking observations at small phase angles, and Figs. 5(a)–(c) show typical fits to data sets

Conclusions and future work

We have developed an online open-source applet application for analyzing asteroid phase curves. The tool is available at : http://asteroid.astro.helsinki.fi/astphase/ and comes with documentation, such as a user manual and Javadoc. We have indicated uses of the so-called Asteroid Phase Curve Analyzer tool.

At the time of writing, we have almost completed MC computations for the complete photometric data set, which contains more than 500,000 asteroids. Although there are caveats regarding our

Acknowledgments

Research has been supported by the Magnus Ehrnrooth Foundation, Academy of Finland (project Nr. 127461), Lowell Observatory, and the Spitzer Science Center. We would like to thank Michael Thomas Flanagan for developing and maintaining the Java Scientific Library, which we have used in the Asteroid Phase Function Analyzer. DO thanks Berry Holl for help with Java plotters and Saeid Zoonemat Kermani for valuable advice on Java applets. We thank the Department of Physics of Northern Arizona

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