MAIN-BELT ASTEROIDS IN THE K2 ENGINEERING FIELD OF VIEW

The Kepler spacecraft retained much of its operational characteristics (Borucki et al. 2010) in the K2 Mission, except its pointing (and consequently photometric) accuracy and the way its pointing is maintained (Howell et al. 2014). The space telescope observed a star field in Pisces (center coordinates: $\alpha =359{}^\circ$, δ = −2°) in 2014 February. The primary goal of the K2 Two-Wheel Concept Engineering Test (hereafter K2-E2) was to test the performance of the telescope in fine guidance mode. The observed 2079 long-cadence (30 minute sampling), and 17 short-cadence (1 minute) targets were made available to the scientific community. In the K2 Mission, 50 × 50 pixel sub-frames containing the targets are stored,  which is much larger than the usual optimal mask applied in the nominal mission to avoid any flux loss due to the drift of the telescope. These will be optimized as the characteristics of the pointing accuracy and necessary corrections are worked out later during the Mission. An approximately 1 pixel variation in the position of the stars is clearly seen during the 8.9 day K2-E2 data. In addition, the boresight was shifted by multiple pixels at BJD = 56695.36, i.e., 2.3 days after the start of the run.

During the first inspection of the public data, we noticed that a large number of asteroids cross the 50 × 50 pixel masks, which is obviously due to the selection of the fields close to the Ecliptic plane. Based on the brightness of these objects, the overwhelming majority should be main-belt asteroids. Most of the objects are seen in 6–8 consecutive long-cadence frames as elongated stripes, many of them approaching the main photometric target. A large fraction of them actually cross the PSF of the stars. Since Kepler has a large pixel size (395/pixel) to gather as many photons as possible, the target stars have increasingly higher chances to be occasionally blended with asteroids than traditional ground-based telescope-detector systems (typically 0.1–05/pixel for minor planet astrometry observations). This problem will be relevant in future space photometric missions with a scope and design similar to Kepler, such as TESS (Ricker et al. 2014) and PLATO (Rauer et al. 2014). In this paper we use the term encounter when an asteroid enters a user-defined pixel mask of the K2 target, since the probability of an occultation (when the asteroid passes in front of the stellar disk as seen from Kepler) is extremely low.

This work is devoted to investigating the following questions.

• 1.  
  How many asteroid crossings are seen in the original K2-E2 data?
• 2.  
  What is the photometric effect that these crossings might cause and how should they be taken into account when high-precision photometry is derived?
• 3.  
  What photometric methods are best suited to derive accurate photometry of these solar system objects?
• 4.  
  Can we identify these main-belt minor planets taking into account Kepler's position in the solar system? Are there any new ones among them?

The structure of the paper is as follows. In Section 2 we discuss the selection of our sample and the number of asteroid encounters. Then in Section 3 the photometric effects of main-belt asteroids on K2-E2 light curves are investigated. In Section 4 we introduce our methods that led to the identification of these minor bodies (the details of the method will be published in a subsequent paper). In Section 5 we demonstrate the possibilities of accurate photometry of moving targets (i.e., main-belt asteroids) in the K2 Mission. Finally, we close the paper by summarizing our results in Section 6.

In order to create a statistically meaningful sample, we selected the first 300 LC targets of the available 2079 long-cadence targets. We created short animations from the FITS frames and these "movies" were scrutinized for asteroid contamination. Each movie was inspected visually by two persons independently. Using visual inspection we counted those encounter events where the asteroid "crossed" or "touched" a pixel that belonged to the target star. Later, a posteriori, we established that before and after the encounter event these pixels had at least a flux value of $3\;\sigma$ above the background level.

The minor bodies were identified using the method outlined in Section 4. That method enabled us to check those asteroids that we missed in the visual inspection. We found that we recovered all the encounter events that belonged to asteroids brighter than 21 magnitudes. Only a few, fainter asteroids were missed in the 21–21.5 magnitude range.

During the 9 days of engineering observations, we found that 147 stars suffered encounter(s) out of our sample of 300, which amounts to 49%, although the number of stars suffering significant effects is much smaller. However, the total number of asteroid encounter events is much larger in our subsample of 300 stars, namely 232. Thus, multiple encounters were frequent during the 9 day observational period, as shown in a histogram in the left panel of Figure 1. As we show with the first red bar, about half of the stars were not approached by visible minor planets during the observations, 94 stars had one asteroid, 38 targets had two, and multiple approaches also occurred: two stars had as many as seven asteroid fly-bys.

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The magnitude distribution of all the K2-E2 long-cadence targets is shown in the right panel of Figure 1, again in the form of a histogram (red columns). Smaller blue bars denote the subsample that was scrutinized for asteroid encounters. Both the total sample and our subsample cover the whole apparent brightness range (in Kp, the Kepler magnitude system) of 9–20, with a strong increase between Kp 14–15 in the original sample, which reflects a priori target selection criteria instead of the underlying magnitude distribution of the population of stars in the K2-E2 field. There were only a few relatively bright asteroids in the selected pixel masks, and we counted 15 in the 15.5–18.5 magnitude range. All the others are fainter, with a clear peak apparent around 20–21 (V) magnitudes. The magnitude distribution of the asteroids is shown in the right panel of Figure 1 by the black columns.

The ecliptic latitude of the stars spanned β = −8.6°– +5.5°, which is representative of the K2-E2 and future K2 targets. Figure 2 shows the uniform distribution of our subsample in the K2-E2 field.

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In Figure 3 we show the light curve of the encounter of the relatively bright asteroid 732 (Tjilaki) with the star EPIC 60017873, which is a bright target (Kp = 9.8). Images of this event are presented in Figure 4. We choose to follow a typical aperture photometric procedure for the K2 field observations. We applied a 14 × 14 pixel mask for simple aperture photometry. The local background was removed. We also removed 64 outlier points from the short-cadence time series, which corresponds to less than 0.5% of the total number of exposure points (13,088). These points are egregiously bright outliers, standing out by more than $10\;\sigma$ from the light curves. These anomalies most probably correspond to the pointing adjustments performed every 6 hr, based on their timing and their common appearance in all the light curves we investigated. We did not apply any decorrelation with external parameters, nor trend filtering, and thus our figures show the original "raw" K2 light curves, except for a few outliers that were removed. We chose this star because it was observed in short-cadence mode as well (red points). The additional flux from the asteroid is clearly seen. We note that the long-cadence data points also show the flux excess, and the duration of the event makes it possible to differentiate between cosmic ray or other short timescale instrumental events and asteroid encounters. We did not remove all the LC points that contain a removed SC photometric data point in order to prevent the removal of too many LC data. This led to a slight discrepancy between the LC and the SC light curve, which can be seen in Figure 3, but has no consequences for the results that follow.

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In Figure 5 we show three examples with targets of different brightnesses (Kp = 9.8, 14.0, and 19.4 from left to right), all showing one or more asteroid encounters. It is easy to see that very faint asteroids can cause outlying photometric points when our target is faint.

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In order to efficiently identify the apparent "flow" of minor planets in the fields, we computed their standard J2000 heliocentric ecliptic celestial positions based on the orbital data provided directly by MPC.⁵ As Kepler has a heliocentric, Earth-trailing orbit, we need to compute the directions as seen from the spacecraft. The actual coordinates of the Kepler spacecraft have been retrieved from Horizons.⁶ The retrieval has been performed on a fine sampling (1 day step size) while intermediate coordinates have been computed using cubic spline interpolation. Then we used the Kepler coordinates as the origin for the computations.

The heliocentric positions of the minor bodies have been computed using numerical integration based on the initial conditions provided by the MPC database. The integration scheme is based on the Lie-series (Pál & Süli 2007), which provides both a fast method and an easy way of precise interpolation between subsequent steps, i.e., lacking complex series of operations. During integration, restricted N-body dynamics have been considered.

Apparent positions are then computed, including the light-time effect and proper handling of TT–TAI–UTC differences. Compared with outputs of the Horizons service, the aforementioned procedure yields the same series of coordinates within 03 (i.e., 00001). Hence, safe cross-identification of known moving objects is quite effective and reliable down to within an arcsecond. This accuracy does not practically yield any ambiguity, even at low ecliptic latitudes where the apparent density of such objects is the largest. Even if we neglect mutual perturbations in the computations, the uncertainty is still 2–3 pixels in the Kepler field of view, ensuring unambiguous identification. In addition, the procedure does not require flooding external services, which is a prominent issue when one has to handle several hundreds of disjointed microfields in the same run.

Among the 232 asteroids that we found, all of them were known and numbered objects except one, 2013 OE, a Near-Earth Object. 2013 OE was identified only on two frames due to its high velocity. Based on this result and our previous experiences in finding asteroids in this magnitude range, we conclude that only a few new main-belt asteroid discoveries are expected during the K2 Mission; the majority of the observable asteroids will be already known objects.

Here we demonstrate that the K2 Mission is capable of measuring the light curves of asteroids in microfields above 50–100 pixel diameters, and of course in observations of larger swaths of pixels, possibly leading to several thousand asteroid light curves in the entire mission. To date, rotation periods of >10,000 asteroids are known (Szabó & Kiss 2008), but very few asteroids are found below the limiting magnitude of 17–18, and only 170 of them have reliable spin axis determinations (Asteroid Photometry Catalog⁷ ; La Spina et al. 2004; Kryszczyńska 2013). Thus, rotation periods for asteroids fainter than H ≈ 13–14 mag are mostly known for a spatially (and rotationally; La Spina et al. 2004) selected sample of NEOs. For a significant number of asteroids, however, where photometric data have low coverage, ground-based observations do not provide a unique period, but a set of alias periods instead.

In this task, the main power of the K2 Mission is the continuous observation of main-belt asteroids in the fields, leading to ∼40 hr of continuous coverage for full frames. The limiting magnitude in K2 asteroid photometry is ∼2 mag below the current databases of asteroid light curves, which is sufficient for reliable period determination.⁸

In this exercise we used short-cadence data. In Figure 6 we present the light curve of asteroid (120934) 1998 SE149 that exhibited a brightness of 20.4 magnitudes at 2.917 AU heliocentric radius and at 3.222 AU distance from the observer, i.e., the Kepler spacecraft. The object passed through the 50 × 50 pixel area on 3/4 February, between 22.55 and 02.99 UT. To increase the signal-to-noise ratio (S/N), five consecutive images were co-added. Since the asteroid trailed over the time of five exposures, photometry was performed in a 3 × 3 aperture, centered on the brightest pixel of the asteroid image.

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The most sensitive task is the subtraction of the background, especially for an object near the faint limit. The difficulty is that the pointing of the Kepler spacecraft varies a little, therefore the image position of stars varies in the sub-pixel range. This is enough to disable the construction of a global template image of the background that can simply be subtracted from the observed images. Instead, we determined the similarity between the processed image and all other images with a cross-correlation, masking out the brightest (most saturated) star and the asteroid itself. Then we selected the most similar 30% of images and calculated their median. This way, the stars could have been satisfactorily removed whenever there were enough similarly pointed observations in the data set.

The asteroid crossed the image of star 60017839 (Kp = 13.9). The light curve shows two humps (probably when the asteroid is seen from the sides) and a fainter state in between. There is no clear periodicity, while the general trend in the light curve suggests that the rotation period exceeds the 4.5 hr of observation. The scatter of the light curve was estimated in the shallow local minima (between the 23rd and 40th stacked image). After removing the linear trend, the standard deviation of the photometric points is 0.12 mag during 5 minutes of observation.

This observation therefore demonstrates that acceptable quality photometry can be performed in K2 images down to around 20.5 magnitudes. Since we expect 2 days of observability of main-belt asteroids in K2 full frames, and the same time range for slowly moving trans-Neptunian objects in a few-hundred-pixel sized apertures, the $a/b$ shape asphericity can be fitted with an accuracy better than 0.5% and the period can be securely detected if the brightness variation of the asteroid exceeds about 0.01 mag, down to a 20.5 limiting magnitude. The estimate was based on a >2 day observation at the 0.12 mag scatter level, accounting for 96 photometric points. Assuming white noise, the expected value of the noise will be 0.01, and therefore a 0.01 mag amplitude variation will emerge as an S/N = 1 peak. When we can expect 5 days of observability of main-belt asteroids, their rotation periods can be detected at an S/N > 2 level down to 20.0 limiting magnitude if the brightness variation of the asteroid exceeds about 0.01 magnitude.

This work demonstrates for the first time that apparently close encounters of main-belt asteroids with photometric targets will be very common in the Ecliptic K2 Mission. We examined 300 of the 2079 publicly available light curves and found that in around half of them the effect of asteroids causes an increase in brightness. The typical length of this event (when brightening occurs due to the large aperture that is usually applied to extract photometry) is less than 3 hr. The typical brightness of the asteroids we found are 18–21.5 (the faintest is 21.7) magnitudes. We successfully identified all of our solar system bodies because this engineering field was pointed around 70° elongation, where the asteroids are 1.6–3.4 mag (in the r = 3.5–1.9 AU heliocentric distance range) fainter than the opposition magnitude, and our asteroid sample is complete down to an opposition magnitude of about 20. In principal it would be possible to discover new asteroids with the K2 Mission because the observations are typically taken starting from an elongation of 135°, where the main-belt asteroids are fainter than their opposition brightness by only 0.8–1.3 magnitudes. However, as the measurements are taken on the evening sky (as seen from Earth), after the opposition point, and as the 1.5–1.8 m telescopes of the ongoing large asteroid searching surveys like the Mt. Lemmon and the Pan-STARRS surveys search the vicinity of the opposition point down to 21.5 magnitudes, we do not expect a significant number of new main-belt asteroid discoveries from K2. We plan to publish the details of our identification process in a forthcoming paper. Finally, we demonstrated that accurate photometry of asteroids is possible. This process will be particularly relevant in large contingent fields of the K2 ecliptic fields, where thousands of main-belt asteroids are expected, and in future space photometric missions, such as TESS (Ricker et al. 2014) and PLATO (Rauer et al. 2014), where ecliptic fields will be also targeted.

This project has been supported by the "Lendület-2009 and LP 2012-31 Young Researchers" Program of the Hungarian Academy of Sciences; the Hungarian OTKA grants K-83790, K-109276, and K-104607; and by the city of Szombathely under agreement No. S-11-1027. The research leading to these results received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreements No. 269194 (IRSES/ASK), No. 312844 (SPACEINN), and the ESA PECS Contract No. 4000110889/14/NL/NDe. Gy.M.Sz. was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. We thank L. Molnár for fruitful conversations on K2 photometry and the referee for insightful comments that improved the quality of the paper.