3.1 The Sample

This observation program was designed in the framework of the commitments acquired by INAOE when requesting its inclusion in the IAWN, an international asteroid warning network under the auspices of the United Nations (UN) and the leadership of the NASA’s Planetary Defense Coordination Office (PDCO). IAWN was established in 2014 as a result of recommendations made by the UN General Assembly in 2013 to create an international network of organizations involved in detecting, tracking, and characterizing NEOs, as an international response to a potential NEO impact threat. At the time of writing of this article, IAWN had a membership of 40 observatories. The IAWN is tasked with developing a strategy using well-defined communication plans and protocols to assist governments in the analysis of asteroid impact consequences and in the planning of mitigation responses.

The observed asteroids presented here were selected using the Ephemeris Generator of the Collaborative Asteroid Light Curve Link¹. From the list of observable asteroids from the CST location, we selected those whose periods are known as they are necessary for shape determination. In addition, we wanted to verify the accuracy of periods as observed by the CST. We chose asteroids with rotational periods between two and three hours that can be covered at least twice per night. Nevertheless, we made some exceptions. We also observed objects with periods that could not be observed completely in one night to see if we could construct the phase plot light curve by observing the object during 2-3 nights. Other selection criteria were the possibility of covering a phase angle variation greater than 20 degrees during the observed opposition and that the orbital velocities should be less than 4.45 arcsec/min in order to keep the asteroid in the same field throughout the night, avoiding the need to change the reference stars used to construct the light curve.

On the other hand, in order to apply the light curve inversion method to determine the asteroid shape, it is necessary that the selected asteroids have publicly available light curves on the Asteroid Light curve Photometry Database (ALCDEF). According to the minor planet Light curve Database (LCDB) file description ^{Warner et al.(2009)}, the U code provides an assessment of the quality of the period solution, not necessarily of the data per se. The rating goes from 3, for a completely unambiguous light curve, in terms of the calculated period, to 0 for a result that later was proven to be incorrect. It is therefore desirable that the parameter defining the LCDB Status has values U=3 or 3-, which means that the quality of the light curves is optimal.

The observed set of objects consisted of 14 asteroids: nine main-belt asteroids (MBAs), four Near-Earth Asteroids (NEAs), and one Mars-crossing asteroid (MCAs), as listed in Table 1.

3.2 Observations and Data Reduction

Photometric observations were carried out with the 77.4 cm Tonantzintla Schmidt Camera of INAOE between October and December 2015 and between March and May 2018. The telescope’s current optical system has a field-flattening lens that provides a focal distance of 2135.2 mm and an image scale of 96.6 arcsec mm^-1. During the 2015 observing runs we used a 1530 × 1020 pixel (9.0 × 9.0 μm²) SBIG ST-8 CCD camera, that produced an image scale of 0.86 arcsec pix^-1, and a field-of-view (FOV) of 22.2×14.8 arcmin.

At the beginning of 2018 we upgraded the image acquisition system with the installation of a SBIG STF-8300 color CCD Camera, equipped with a 3326 × 2540 pixel (5.4×5.4μm²) high resolution Kodak KAF-8300C full frame sensor with microlens technology and antiblooming for improved quantum efficiency. This new system provides an image scale of 0.52 arcsec pix^-1, and a FOV of 28.8 × 22.0 arcmin.

Selected physical parameters of the observed asteroids, such as semi-major axis (a), eccentricity (e), taxonomic class, absolute magnitude (H), diameter, and albedo, are listed in Table 1, while their observational circumstances, including geocentric (r) and heliocentric (Δ) distances, and phase angle (α), are shown in Table 2. Where there were different albedo values reported for the same asteroid, we gave preference to the Wide-field Infrared Survey Explorer WISE measurements ^{Mainzer et al.(2011)}.

When the absolute magnitude and the albedo of observed asteroids were known, their diameters were calculated using equation (1), where pν is the reported albedo. Otherwise, when there were no reports on the asteroid albedos, we used equation (2), assuming that the average albedo of asteroids is 14 % and that an asteroid whose absolute magnitude is 17.75, corresponds to an asteroid of 1 km in size.

Depending on the brightness of the observed objects and weather conditions, the integration times varied between 30 and 120 s. For each observing run, master bias, dark and flat-field images were produced. Scientific images were corrected for bias, dark and flat-field effects using Image Reduction and Analysis Facility (IRAF) packages.

Differential photometry and period analysis were done using the MPO Canopus analysis tool ^Warner(2014). In each case, we used four solar analogs non-variable comparison stars, in the same FOV, to generate light curves. Comparison stars were selected near the path covered by the asteroids during the night.

5.1 (711) Marmulla

(711) Marmulla (1911 LN, 1927 AB) is an Inner Main-Belt asteroid, that belongs to the Flora family (a = 2.2369 AU., i = 6.0991°). It was discovered on March 1, 1911 by J. Palisa at Vienna. (711) Marmulla has albedo values that correspond to a S-class asteroid; pV=0.22±0.09 ^{Nugent et al.(2016)}, and pV=0.224±0.030 ^{Usui et al.(2011)}.

We observed this asteroid at four different values of phase angle, α = 7.68°, 9.52° (grouped in a single light curve), 12.95°, and 22.11°. We obtained 37 images on March 12, 2018, 187 images on March 16, 2018, 109 images on March 24, and 88 images on April 9, 2018; exposure times ranged from 50 to 90 s.

The best values for the periods obtained from the Fourier analysis of our three light curves (2.804 ± 0.001 h, 2.876±0.074 h, and 2.627 ± 0.041 h) are very similar to the values on the LCDB database reported by different authors.

5.2 (1036) Ganymed

Asteroid (1036) Ganymed is the largest NEA that we observed. It belongs to the Amor group, and is classified as S type with an albedo of 0.218 ± 0.048 ^{Mainzer et al.(2011)} and a corresponding diameter of 40.76 km. It was discovered by W. Baade at the Bergedorf Observatory in Hamburg on 23 October, 1924.

We observed this asteroid at three different values of phase angle, α = 6.18°, 6.26° and 6.35°. Observations are grouped in a single light curve. We obtained 382 images on March 19, 2018, with an exposure time of 40 seconds, and 653 images on March 20, 2018, and 276 images on March 21, 2018, with exposure times of 30 s.

From the Fourier analysis of the light curve we show here, we obtained a value of the period equal to 10.318 ± 0.013 h, very similar to the 35 values compiled on LCDB.

5.3 (1117) Reginita

(1117) Reginita (1927 KA) is an Inner Main-Belt asteroid. It was discovered on May 24, 1927 by J. Comas Solú at the Fabra Observatory in Barcelona ^{Schmadel(2012)}. (1117) Reginita has a very high albedo among the taxonomic class ^{S. Pravec et al.(2012)} reported a value of pV=0.3516 from WISE thermal observations while ^{Nugent et al.(2016)}) obtained an albedo of 0.36±0.13, and a diameter D=9.82±2.35 km from NEOWISE Reactivation Mission observations. ^{Mainzer et al.(2011)} derived pV=0.3585±0.0785, and D =10.193±0.250 km applying thermal models to the NEOWISE data at 3.4, 4.6, 12, and 22 μm.

On October 4, 2015, at a phase angle of 16.73°, we obtained 221 images with a 30 s exposure time. Fourier analysis of the light curve produced the best fit at 2.942±0.012 h, similar to the values reported by ^{Wisniewski, Michalowski Harris(1995)}, ^{Kryszczyńska et al.(2012)}, ^{Chang et al.(2015)}, ^{Waszczak et al.(2015)}, and another seven authors included on LCDB. The obtained peak-to-peak amplitude, 0.16 magnitude, is in the range of values reported by the previously mentioned authors for this asteroid. We observed again Reginita in 2018, obtaining almost the same result 2.945±0.002 h, by using 81 images of 60 s exposure time at a phase angle of 22.70°, obtained on April 8, and 74 images of 90 s exposure time, at a phase angle of 22.43°, obtained on April 9.

5.4 (1318) Nerina

(1318) Nerina is an inner Main-Belt asteroid, belonging to the Phocaea family. It was discovered on March 24, 1934 by C. Jackson at Johannesburg ^{Schmadel(2012)}. ^{Mainzer et al.(2011)} derived a value of pV=0.1721±0.208 that is in correspondence with an M-type asteroid.

We observed (1318) Nerina at two values of phase angle, α = 6.52°, and 12.27°. We obtained 377 images with 30 s exposure time on March 17, 2018, and 84 images on March 27, 2018, with a 60 s exposure time.

The Fourier analysis of the two light curve data we obtained gave us the period values 2.586 ± 0.013 h and 2.463±0.033 h, both with a difference of less than one percent with respect to the 11 values found on the LCDB database.

5.5 (1346) Gotha

(1346) Gotha is a Main-Belt asteroid that belongs to the Eunomia family. It was discovered in 1929, on February 5, by K. Reinmuth at Heidelberg ^{Schmadel(2012)}. ^{Mainzer et al.(2011)} derived a value of pV=0.2794±0.0411, in agreement with a S-type taxonomic classification established by ^Tholen(1984).

From the light curve generated with 62 images of 120 s exposure time obtained on March 29, 2018, at a phase angle α equal to 23.88°, the best fit value obtained for the period, from the Fourier analysis, is 2.563±0.057 h, consistent with five out the six values reported on the LCDB database.

5.6 (1363) Herberta

(1363) Herberta (1935 RA) is an Outer Main-Belt asteroid, belonging to the Konoris family (2.83<a<2.91, i<3.5). It was discovered on August 30, 1935 by E. Delporte at the Royal Belgium Observatory in Uccle ^{Schmadel(2012)}. Based on MOVIS NIR colors, ^{Popescu et al.(2018)} proposed a S-type taxonomic classification. The value of albedo pV=0.337±0.157, determined by ^{Masiero et al.(2012)}, is close to the upper limit for S-complex asteroids.

A total of 427 images of Herberta were taken over three nights, from December 15 to 17, 2015 with 60 s of exposure time. The phase angle values for the observation nights were 6.18°, 6.56° and 6.94°, respectively. All the observations were grouped in a single light curve.

The best value we obtained for the period, from the Fourier analysis, is equal to 3.018±0.002 h; meanwhile, the only value reported on LCDB is equal to 3.015±0.005 h.

5.7 (1492) Oppolzer

(1492) Oppolzer was discovered in 1938 by Y. Väisälä ^{Schmadel(2012)}. (1492) Oppolzer is a S-type ^{Vereet al.(2015)} Inner Main-Belt asteroid. The taxonomy for this asteroid was determined from photometry obtained at the Pan-STARRS PS1 telescope; however, the albedo (pV=0.089±0.026) reported by ^{Tedesco et al.(2004)}, using the observations of the IRAS mission, is very low and corresponds more closely to a C-class asteroid.

We observed this asteroid at two values of phase angle, α = 5.85° and α = 10.27°. We obtained 375 images of 40 s exposure time on March 18, 2018, and 129 images on March 26, 2018, of 60 s exposure time. One of the values we obtained for the period, 3.77±0.02 h, is in complete agreement with the seven values on LCDB, with a difference of less than 0.1 percent. For the second value, 3.566±0.076 h, the difference is larger.

5.8 (1627) Ivar

(1627) Ivar was discovered on September 25, 1929 by E. Hertzsprung at Johannesburg ^{Schmadel(2012)}.

We obtained 600 images of 30 s exposure time for this asteroid on March 17, 2018, at phase angle α=26.71∘, and 68 images of 60 s exposure time on March 27, 2018, at phase angle, 24.33°. As the phase angles have very similar values, we grouped the observations in a single light curve.

The value we obtained for the period, 4.795±0.001 h is exactly the same as the best value reported on LCDB. This asteroid has been well observed; there are 16 values reported on this database.

5.9 (1831) Nicholson

(1831) Nicholson was discovered on April 17, 1968, by P. Wild at Zimmerwald, Switzerland ^{Schmadel(2012)}. It is an S-type asteroid ^{Bus Binzel(2002)} from the inner region of the Main-Belt. ^{Masiero et al.(2012)} has estimated an albedo value of pV=0.296±0.053 which is in good agreement with the values for S-complex asteroids.

We observed this asteroid in 2018. We grouped the March 10, 11 and 14 observations in a single light curve, the March 25 observations in another, and in a third light curve we grouped observations carried out on April 14, 20 and 21. We obtained 756 images with exposure times ranging from 30 s to 120 s. The phase angles covered were α = 10.40° to 24.98°.

The best period values obtained from the Fourier analysis for our three light curves, 3.216 ± 0.001 h, 3.220±0.022 h, and 3.217±0.001 h, are completely consistent with the four values on LCDB.

5.10 (1847) Stobbe

(1847) Stobbe was discovered on 1916 February 1, by H. Thiele at Bergedorf, Germany ^{Schmadel(2012)}. This is a middle Main-Belt asteroid that was originally classified as a Xc asteroid by ^{Bus Binzel(2002)} during the Phase II of the Small Main-Belt Asteroid Spectroscopic Survey. More recently, ^{Mainzer et al.(2011)}, using NEOWISE photometry, suggested an M-type taxonomy for this asteroid. P-type, M-type and E-type asteroids are included in the larger X-type group and are differentiated by optical albedo values ^{Tholen Barucci(1989)}.

The typical optical albedo for M-type asteroids is between 0.1 and 0.3, so the albedo of pV=0.2315±0.0162 reported by ^{Mainzer et al.(2011)} corresponds to this type.

We observed this asteroid on April 18, 2018. We obtained 52 images with 60 s exposure time at a phase angle α = 9.77°. The period we obtained from the light curve Fourier analysis is equal to 5.621±0.012 h, very similar to three out of the four values on LCDB. The largest difference with our result corresponds to the value 6.37±0.02 ^{Malcolm(2002)}, that is also the least recent value obtained.

5.11 (1866) Sisyphus

(1866) Sisyphus was discovered on December 5, 1972 by P. Wild at Zimmerwald, Switzerland ^{Schmadel(2012)}. It is a NEA that belongs to the Apollo group. ^{Mainzer et al.(2011)} reported a value of pV=0.255±0.049, which is in correspondence with the taxonomic classifications S-type and Sw-type provided by ^{Bus Binzel(2002)} and ^{Binzel et al.(2019)}, respectively, both observing this asteroid as part of optical spectroscopic surveys.

This asteroid was observed on March 25, 2018. We obtained 48 images with a 210 s exposure time at a phase angle α = 16.74°. Even though the amplitude of this light curve is of a similar order as the photometric uncertainties on the individual points, the best fit we obtained for the period, 2.391±0.028 h, is in agreement with the thirteen values reported on LCDB, most of them around 2.4 h.

5.12 (3800) Karayusuf

(3800) Karayusuf is an S-type ^{Bus Binzel(2002)}, ^{Binzel et al.(2019)} Mars-crosser (MC) asteroid discovered on January 4, 1984, by E. F. Helin at Palomar in California, USA ^{Schmadel(2012)}. A very high value of its albedo, pV=0.66±0.12, not corresponding to an S-type asteroid, was reported by ^{Nugent et al.(2015)}. With an absolute magnitude H = 15.09, this albedo value gives a size of 1.59 km, one of the smallest asteroids in our sample. However, ^{Alí-Lagoa & Delbo' (2017)}, using the NEA thermal model to provide diameters and albedos of MCs with available WISE/NEOWISE data, proposed an albedo pV=0.281±0.056 for this asteroid. With this correction, the size of (3800) Karayusuf can increase to 2.43 km.

With an exposure time of 120 s, we obtained 60 images of this asteroid on March 28, 2018. Its phase angle on that night was 34.23° and the derived period was 2.270±0.084 hours. There are 11 values reported on LCDB, all of them quite similar to the one derived from our data.

5.13 (5692) Shirao

(5692) Shirao was discovered on March 23, 1992 by K. Endate and K. Watanabe at Kitami ^{Schmadel(2012)}. It is an S-type ^{Vere et al.(2015)} middle Main-Belt asteroid. ^{Mainzer et al.(2011)} reported a typical S-type albedo pV=0.2218±0.0290.

We observed this asteroid in 2018, on March 18 and 26, and April 7. A total of 235 images were obtained. Exposure time for March 18 images was 30 s and 60 s for the other two nights. The phase angle for March 18 was 6.22°, for March 26 was 2.21° and 4.86° for April 7, so we decided to construct three different light curves. The corresponding periods derived from Fourier analysis are 2.957±0.032 h, 2.900±0.055 h, and 2.866±0.085 h, very similar to the best value reported on the LCDB summary table (2.8878 h).

5.14 (25916) 2001 CP44

(25916) 2001 CP44 is the only Amor-type NEA in our sample. It has a diameter of 5.7 km and was discovered by LINEAR at Socorro, New Mexico. This is clearly an S-complex asteroid, classified as an Sq-type ^{Thomas et al.(2014)}, ^{Popescu et al.(2019)}, S-type ^{Lin et al.(2018)}, and Sw-type ^{Binzel et al.(2019)}. ^{Mainzer et al.(2011)} reported a typical S-type albedo pV=0.262±0.047.

We obtained a total of 250 images of this asteroid in 2018. On April 14 (53 images, exposure time 120 s, phase angle 27.17°) and April 16 (197 images, exposure time 60 s, and phase angle 26.86°).

From our light curve we derived a period equal to 4.2020±0.0024 h, while, on LCDB there are two clear sets of values, one around 4.2 h, reported during 2012-2014, and another around 4.6 h, reported during 2018. The difference can be due to observations being made during different apparitions.