Investigation of Asteroid Phase Curves Extracted from the ATLAS Survey
Authors: Robinson James , Fitzsimmons Alan , Young David , Denneau Larry , Smith Ken , Bannister Michele , Heinze Aren , Tonry John 
Published: September 2022

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&lt;p&gt;&lt;strong&gt;Introduction&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The Asteroid Terrestrial Last-impact Alert System (ATLAS; Tonry et al., 2018) is a network of robotic telescopes which scan the sky searching for transient phenomena from potentially hazardous Near Earth Objects to distant supernovae. The units at Haleakala and Mauna Loa have been operating since 2015 and 2017 respectively and together they can scan the visible night sky every two nights down to a limiting magnitude of ~19.5 mag in wideband orange and cyan filters. We have matched the ephemerides of ~445,000 asteroids to ATLAS pointings from these two units up to January 2022, providing us with a photometric database of 9.6&amp;#215;10&lt;sup&gt;7&lt;/sup&gt; detections.&lt;/p&gt;
&lt;p&gt;We can investigate the surface scattering properties of asteroids by observing the change in brightness as a function of the observer-asteroid-Sun phase angle. A well determined phase curve is required to obtain an accurate absolute magnitude for an asteroid, and hence its size if albedo is known. The form of the phase curve depends on the scattering properties of the surface, primarily its composition and roughness, and is described by one or more slope parameters. These slope parameters can be used as a proxy for taxonomic information when more detailed measurements such as spectra are unavailable (e.g. Mahlke et al., 2021).&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Methods&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We have analysed the phase curves of all asteroids in our dataset of selected ATLAS photometry, considering &lt;em&gt;o&lt;/em&gt; and &lt;em&gt;c&lt;/em&gt; filter data separately. We fit a variety of phase curve models to the data using Levenberg-Marquadt least squares fitting but we focused on the results for the &lt;em&gt;HG&lt;/em&gt; (Bowell et al., 1989) and &lt;em&gt;HG&lt;/em&gt;&lt;sub&gt;12&lt;/sub&gt;&lt;sup&gt;*&lt;/sup&gt; (Penttil&amp;#228; et al., 2016) phase curve models specifically. We found that outlying photometric detections were present in the dataset due to brightness contamination from nearby stars/galaxies or incorrect matching of ephemerides. Such data points were dealt with by initial cuts and an iterative sigma clip during fitting.&lt;/p&gt;
&lt;p&gt;For simplicity we did not account for rotational brightness variation in the phase curve model as for most asteroids this is not accurately constrained. Rotation effects manifest as an additional variation in brightness which leads to greater uncertainty in determining phase curve parameters. However, we show in our results that the fitted phase curve parameters of an ensemble of objects with sufficient phase angle coverage are still useful for science on a population statistics level. Furthermore, we automatically identify asteroids in the dataset that show a significant apparition effect. The phase curves of these objects display shifts in absolute brightness between different apparitions, caused by changes in the asteroid aspect angle as viewed from Earth.&lt;/p&gt;
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&lt;p&gt;The resulting phase curve parameters were then filtered down to a subset of nearly 100,000 objects with high quality phase curves suitable for comparing the surface properties of different asteroid populations. Objects were selected that have sufficient phase angle coverage, high number of observations, low formal uncertainties from the fitting process, and no strong apparition effects.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Results&lt;/strong&gt;&lt;/p&gt;
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&lt;p&gt;We have derived phase curve parameters for a large number of asteroids obtained in a consistent manner from a single survey over a long baseline and we find this dataset to be useful for a range of science cases. We shall present results comparing the distribution of phase parameters and surface colours measured in the ATLAS &lt;em&gt;c&lt;/em&gt; -&amp;#160;&lt;em&gt;o&lt;/em&gt; filters of different asteroid populations. Considering the Jupiter Trojans, we can compare the properties of the leading and trailing dynamical groups and also assess trends in the &amp;#8220;Red&amp;#8221; and &amp;#8220;Less-Red&amp;#8221; compositional classes (Wong &amp; Brown, 2016).&lt;/p&gt;
&lt;p&gt;Alongside this phase curve database we have generated a list of ~5000 Main Belt and Jupiter Trojan asteroids that exhibit strong apparition effects. Such objects must have high spin axis obliquity and would make interesting targets for studies of asteroid spin axis evolution and shape modelling via lightcurve inversion. Only 25% of the objects in our list are currently present in the Asteroid Lightcurve Database (LCDB; Warner et al., 2021).&lt;/p&gt;
&lt;p&gt;In general our work highlights the possibilities and potential limitations of sparsely sampled photometric surveys for investigating the properties of large numbers of asteroids. The upcoming Legacy Survey of Space and Time (LSST) will discover a huge number of new asteroids, however, characterisation of these objects will depend on survey design choices such as cadence and filter selection as well as follow up campaigns from other surveys/observers.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
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&lt;p&gt;Figure 1: ATLAS photometry for 766 Moguntia, an asteroid that shows clear apparition effects. Left: Phase curves for each apparition, fixing &lt;em&gt;G&lt;/em&gt; = 0.15 and fitting only for &lt;em&gt;H&lt;/em&gt;. Observations are colour-coded by apparition. Right: Absolute magnitude of Moguntia over time, where each observation has been corrected for distance and phase effects. Error bars indicate the fitted &lt;em&gt;H&lt;/em&gt; and standard deviation of the residuals for each apparition, highlighting the shifts in brightness between apparitions and rotational brightness variations.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Acknowledgements&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;This work has made use of data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project. ATLAS is primarily funded to search for near earth asteroids through NASA grants NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images and catalogs from the survey area. The ATLAS science products have been made possible through the contributions of the University of Hawaii Institute for Astronomy, the Queen&amp;#8217;s University Belfast, the Space Telescope Science Institute, the South African Astronomical Observatory (SAAO), and the Millennium Institute of Astrophysics (MAS), Chile.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Bowell, E., Hapke, B., Domingue, D., et al. 1989, Application of Photometric Models to Asteroids., 524&amp;#8211;556&lt;/p&gt;
&lt;p&gt;Mahlke, M., Carry, B., &amp; Denneau, L. 2021, Icarus, 354, 114094&lt;/p&gt;
&lt;p&gt;Penttil&amp;#228;, A., Shevchenko, V., Wilkman, O., &amp; Muinonen, K. 2016, Planetary and Space Science, 123, 117&lt;/p&gt;
&lt;p&gt;Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, Publications of the Astronomical Society of the Pacific, 130, 064505&lt;/p&gt;
&lt;p&gt;Warner, B. D., Harris, A. W., &amp; Pravec, P. 2021, Asteroid Lightcurve Database (LCDB) Bundle V4.0 Wong, I. &amp; Brown, M. E. 2016, The Astronomical Journal, 152, 90&lt;/p&gt;
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