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Rotation Periods of Binary Asteroids with Large Separations - Confronting the Escaping Ejecta Binaries Model with Observations

Durda et al. (2004), using numerical models, suggested that binary asteroids with large separation, called Escaping Ejecta Binaries (EEBs), can be created by fragments ejected from a disruptive impact event. It is thought that six binary asteroids recently discovered might be EEBs because of the high separation between their components (~100>a/Rp>~20). However, the rotation periods of four out of the six objects measured by our group and others and presented here show that these suspected EEBs have fast rotation rates of 2.5 to 4 hours. Because of the small size of the components of these binary asteroids, linked with this fast spinning, we conclude that the rotational-fission mechanism, which is a result of the thermal YORP effect, is the most likely formation scenario. Moreover, scaling the YORP effect for these objects shows that its timescale is shorter than the estimated ages of the three relevant Hirayama families hosting these binary asteroids. Therefore, only the largest (D~19 km) suspected asteroid, (317) Roxane, could be, in fact, the only known EEB. In addition, our results confirm the triple nature of (3749) Balam by measuring mutual events on its lightcurve that match the orbital period of a nearby satellite in addition to its distant companion. Measurements of (1509) Esclangona at different apparitions show a unique shape of the lightcurve that might be explained by color variations.


Motivation and Background
As the number of discovered binary asteroids and systems of asteroids increased dramatically in the last decade, different physical mechanisms have been suggested to explain the formation of these objects. The rotational-fission of a smallsized (D<10 km) asteroid into two or more components (Scheeres 2007) is one of the most successful mechanisms to explain the existence of these binaries. Rotationalfission occurs after the asteroid is spun-up by the YORP effect: this is a thermal torque on a rotating irregular body active due to the asymmetric re-emission of sunlight (Rubincam 2000). These two mechanisms were observed: the YORP effect was directly measured on four asteroids (Lowry et al. 2007, Taylor et al. 2007, Kaasalenien et al. 2007, Durech et al. 2008, Durech et al. 2009) and recent photometric observations of asteroid "pairs" have showed that the rotational-fission mechanism can disrupt asteroids due to fast rotations (Pravec et al. 2010). This process takes place because asteroids are weak aggregate bodies with negligible tensile strength bound together only by gravity (Richardson et al. 2002). This structure, often referred to as a "rubble-pile" or as a shattered interior structure, determines a critical rotation period of about 2.2 hours; a faster rotation will cause the asteroid to disrupt. Therefore, primaries of binary asteroids and of asteroid pairs usually rotate fast, on order of 2 to 5 hours (Pravec et al. 2006;Pravec et al. 2010), which is a remnant to the crossing of their "self-disruptive speed limit".
However, not all binary asteroids can be explained as results of the rotationalfission mechanism. The YORP effect is probably not efficient enough to spin-up large-sized asteroids in the scale of D>10 km ) and Trans-Neptunian Objects (TNOs) are too distant from the Sun to develop a significant thermal torque. Since such systems obviously exist and were observed (Descamps et al. 2007, Marchis et al. 2005, Sheppard and Jewitt 2004, other mechanisms for binaries formation are needed. One of these suggested mechanisms is based on collisions between main belt asteroids that result in Escaping Ejecta Binaries (EEBs). This mechanism, first described by Durda et al. 2004 (and based on older ideas by Hartmann 1979 andDurda 1996), acts on two asteroidal fragments ejected during a collision incident which become gravitationally bound together as they drift away from their parentbody. Using numerical models, Durda et al. (2004), showed that such scenarios are physically plausible and the resultant components are stable. In addition, such objects can have large values of physical parameters such as the rotation period of the primary, the size ratio between the components, and the separation between them.
Moreover, the recent (2002 -2009) observational discovery using adaptive optics, of six binary asteroids (Merline et al. 2009) with high component separation (~100 > a/Rp > ~20, while the rest of the binaries have values of about 10 and less), enabled Durda et al. (2010) to show how the physical parameters (see Table I), mainly the size-ratio and the components' separation (in units of the primaries radii) of these binaries, are similar to the numerical results of EEBs (see Fig. 3 at Durda et al. 2010).
While these items support the EEB forming mechanism, they cannot rule out other mechanisms, especially the YORP effect followed by the rotational-fission.
Measuring the rotation periods of these asteroids can constrain the binary forming mechanism, and might indicate weather these six objects are YORP-binaries or Escaping Ejecta binaries, and if such EEBs are actually exist. Therefore, we performed a photometric campaign on these asteroids in order to derive their rotation periods.

Observations, Reduction, Measurements, Calibration and Analysis
Observations were performed using the two telescopes of the Wise Observatory (code: 097): the 1-m Ritchey-Chrétien telescope; and the 0.46-m Centurion telescope (see Brosch et al. 2008 for a description of the telescope and its performance). The 1-m telescope is equipped with a cryogenically-cooled Princeton Instruments (PI) CCD. At the f/7 focus of the telescope this CCD covers a field of view of 13'x13' with 1340x1300 pixels (0.58'' per pixel, unbinned). Two CCDs were used at the prime focus of the 0.46-m while the research took place: a wide-field SBIG ST-10XME (40.5'x27.3' with 2184x1472 pixels, 1.1'' per pixel, unbinned) used until mid-November 2008; and an SBIG STL-6303E with an even wider field of view (75'x55' with 3072x2048 pixels, 1.47'' per pixel, unbinned) used afterwards. An R filter was used on the 1-m telescope while observations with the 0.46-m telescope were in "white light" with no filters ("Clear").
To achieve a point-like FWHM (at a seeing value of ~2.5 pixels), constrained by the observed angular velocity, exposure times of 60-180s seconds were chosen, all using an auto-guider. The observational circumstances are summarized in Table II, which lists the asteroid's designation, the observation date, the time span of the observation during that night, the number of obtained images, the object's heliocentric distance (r), geocentric distance (∆), phase angle (α), and the Phase Angle Bisector (PAB) ecliptic coordinates (L PAB , B PAB -see Harris et al. (1984) for the definition and ways of calculating these parameters). In addition, the object's mean observed magnitude is presented for nights when the measurements were calibrated with standard stars (see calibration method below).
The images were reduced in a standard way using bias and dark subtraction, and division by a normalized flatfield image. Times were corrected to mid-exposure.
We used the IRAF phot function for the photometric measurements. Apertures with four-pixel radii were chosen to minimize photometric errors. The mean sky value was measured using an annulus of 10 pixels wide and inner radius 10 pixels around the asteroid.
After measuring, the photometric values were calibrated to a differential magnitude level using local comparison stars measured on every image using the same method as the asteroid. Variable stars were removed at a second calibration iteration leaving an average of ~650 local comparison stars per image (~30 with the PI CCD of the 1-m which has a much smaller field of view). The brightness of these stars remained constant to ±0.02 mag. A photometric shift was calculated for each image compared to a good reference image, using the local comparison stars. Some measurements were also calibrated to standard magnitude level by using the Landolt equatorial standards (Landolt 1992).
Astrometric solutions were obtained using PinPoint (www.dc3.com) and the asteroids were identified from the MPC web database. Analysis for the lightcurve period and amplitude was done using the Fourier series analysis (Harris and Lupishko 1989) based on periodic functions with two to ten harmonics. A best match of the observations to the Fourier series was found by least squares and is presented on each lightcurve. In case of (3749) Balam, where all the data was calibrated to standard magnitude, we also found the best fit for the H-G system. All results appear in Table   III. See Polishook and Brosch 2008 (1-m) and Polishook and Brosch 2009 (0.46-m) for a complete description of the reduction, measurements, calibration and analysis.

Analysis of Mutual Events
The presence of a satellite around an asteroid can be derived from an asteroid's lightcurve when a mutual event is observed. This is seen as attenuation in the amount of light reflected from the asteroid during an occultation -when one component blocks the light reflected from the other component, or during an eclipse -when one component casts a shadow over its partner (Pravec et al. 2006). Therefore, any periodicity of the mutual events can be interpreted as the orbital period of the secondary around the primary. For this study two asteroids, (1509) Esclangona and (3749) Balam, were routinely observed to searched for mutual events, but only (3749) Balam presented such phenomena.
Since the light attenuations due to the mutual events are superposed on the lightcurve variability, which is in turn caused by the rotational period of the primary, the rotational periodicity must first be subtracted from the data so that the orbital periodicity can be derived. Therefore, the analysis for (3749) Balam also includes the following procedures: 1. Finding the rotation periodicity, as described above, using data without mutual events.
2. Producing a model with the derived rotational properties.
3. Subtracting the magnitude predicted by the model from all the observed data, including data with mutual events. 4. Searching for the period of the mutual events using Fourier series analysis (Harris and Lupishko 1989), with the same code used to derive the rotation period. Since the mutual events curve is characteristically flat with two attenuations, as many as 20 harmonics were used to describe its model.

5.
Folding the data with the orbital period of the secondary. Such a lightcurve should present two mutual events (Pravec et al. 2006), usually a total event, when the attenuation reaches a plateau before increasing back to the average brightness, and a partial event, recognizable by its V-shape.
The properties of the mutual events curve can provide many insights about the characteristics of the asteroid system. A total eclipse/occultation seen in the lightcurve takes place when the light from the secondary is completely blocked by the primary or when the secondary is in front the primary blocking a fixed fraction of its surface. The depth of the total eclipse (A mut ) is a function of the two components' size ratio (Rs/Rp): When Rs is the radius of the secondary and Rp is the radius of the primary Brosch 2008, Descamps et al. 2008).

Results
We observed five out of the six objects suspected as EEBs: (1509) Esclangona, (3749) Balam, (4674) Pauling, (17246) 2000 GL 74 and (22899) 1999 TO 14 . The sixth, (317) Roxane, whose binary nature was discovered only recently (Merline et al. 2009) was previously observed photometrically by Harris et al. (1992) who found a rotation period of 8.1691±0.0003 hours for the asteroid's primary with an amplitude of 0.606±0.003 mag. The results for the other objects are described below and summarized in Table III.
[put Table III (Fig. 1). We could not find any mutual events during all these nights, therefore, if (1509) Esclangona has a second close satellite, in addition to its already known and distant satellite, its orbital plane was not in the line of sight from Earth at the time of our observations. Future observations could derive the spin axis orientation of (1509) Esclangona, and might be able to completely reject the existence of a close binary.
In addition, the 2009 observations do present the unique features on the lightcurve seen on the 2008 apparition. These consist of (i) two peaks (phase 0 to 0.4) with varying amplitudes from 0.09 to nearly zero magnitude; (ii) followed by a wide minimum (phase 0.4 to 0.7) with small-scaled changing features; (iii) and a large amplitude peak (phase 0.7 to 1) of about 0.13 to 0.16 mag. While Warner et al. (2010) managed to remove some of these features by analyzing the lightcurve as two superposed periods (the rotation periods of the primary and the secondary), our data, taken on a wider range of observing nights, do not present any second periodicity (including their published periodicity of 6.6423±0.0003 hours), while the unique features on the lightcurve remain. We suggest that at least part of the unique shape of the lightcurve might be due to the color variations measured by . More observations at different apparitions and aspects could reveal the true shape of (1509) Esclangona and to determine the complete nature of its unique lightcurve.

(3749) Balam
Located in the main belt (a=2.237 AU) and part of the Flora family, this asteroid is actually a complex system that presents different types of asteroidal Here we report independent photometric measurements of (3749) Balam taken from July to December 2007. We derived a rotation period of 2.80490±0.00008 hours and an amplitude of 0.14±0.04 mag (Fig. 2), in agreement with the values published by Marchis et al. (2008a) of 2.80483±0.00002 hours and 0.13 mag respectively. We also present the phase curve of (3749) Balam from 7 to 27 degrees (Fig. 3)

(4674) Pauling
This Hungaria-group asteroid was found to be a binary by Merline et al. 2004 using AO at ESO's 8-m VLT. They estimated the satellite size as 2.5 km, assuming a primary with a diameter of 8 km, and a projected separation of about 250 km (a/Rp = 63).

Discussion and Conclusions
We presented here photometric observations and rotation periods for four of the six binary asteroids with relatively large (~100 > a/Rp > ~20) separations between their components, suspected to be EEBs by Durda et al. (2010)  has an unknown rotation period). Such spins match the theory of rotational-fission of a small-sized (D<10 km) asteroid: after the asteroid rotation rate increased due to the thermal YORP effect, the centrifugal force overcomes the weak gravity between the components of the rubble pile structure and the object disintegrate into two or more components (Scheeres 2007). All five asteroids have small diameters of 4.5 to 8.2 km; such bodies can be spun-up efficiently by the YORP effect and cross the rotation barrier for a rubble pile.
To estimate the timescale of the YORP effect on these asteroids, we scaled from timescales of asteroids demonstrated to have been spun-up by YORP. The rotation periods and spin acceleration rates of the following asteroids: (1620) Geographos (Durech et al. 2008), (1862) Apollo (Kaasalenien et al. 2007), (3103) Eger, (Durech et al. 2009) and (54509) YORP (Lowry et al. 2007 andTaylor et al. 2007) were taken from the relevant papers, while their diameters were taken from the asteroid LCDB (Warner et al. 2009a). Better estimation of 54509 YORP's diameter of 114 m appears in Lowry et al. (2007), based on radar observations. The YORP spin acceleration rates (dω/dt) were scaled by the semi-major axis (a) and the diameter (D) of each object (Table I) following the theory that dω/dt from YORP decreases with increasing a 2 ·D 2 . We derived a range of timescales, from ~115 to ~175 Myr, for the asteroids discussed here to double their spin rate. This excludes the sixth suspected EEB, (317) Roxane, that is too big to be affected by YORP. Such timescales are significantly shorter than the estimated ages of the three involved families: Flora -0.5 to 1 Gyr (Nesvorný et al. 2002), Hungaria -~0.5 Gyr (Warner et al. 2009b) and Koronis -2 to 3 Gyr (Vokrouhlický et al. 2003). Moreover, the timescales calculated here represent the time needed to double the spin rate of an asteroid, meaning they might have been disrupted a long time before, considering their current fast rotations.
The fact that the YORP effect has been measured to align the spin axes of other objects from the Koronis family (Slivan 2002), adds strength to the idea that the YORP effect had enough time to efficiently spin-up the rotation periods of (17246) 2000 GL 74 and (22899) 1999 TO 14 that could cause their fission. In addition, if these binaries were created when their family parent-body was destroyed by a collision, the binary YORP (BYORP) mechanism (Ćuk and Burns 2005) that destabilizes and dissolves binaries by radiation effects would by now have destroyed those binaries.
Even though the BYORP mechanism was not measured yet, different models suggest that its timescale is about 10 5 years (Ćuk andBurns 2005, McMahon and, which is very short compared to the ages of these collisional families.
Therefore, the original collisions that created these families were probably not the mechanisms that created the studied binaries.
The only asteroid from the suspected EEBs list that was probably not created by the YORP effect and the rotational-fission mechanism is (317) Roxane: it is too big (D=18.7 km) to be spun-up efficiently by the YORP effect and it rotates too slowly (8.1691±0.0003 hours; Harris et al. 1992) for any type of rotational fission to have taken place. Therefore, this might be the only real EEB among the studied list of asteroids.
The Escaping Ejecta Binaries formation model may still be the trigger for the creation of the studied binaries in the case of more recent collisions. However, such energetic collisions should have resulted in a Hirayama family of their own, and currently, such are unknown for these objects. Moreover, the fast rotation periods of the measured binaries pose another difficulty for the EEB model. An ejected rock with a fast rotation should originate from a collision with a relatively fast impact velocity. However, high velocity impacts will results in less EEBs since few components will have the same trajectory and drifting velocity that might result in gravitationally bound objects. This is best shown in Fig. 6 of Durda et al. 2004, where the number of EEBs decreases for high-energy impacts. To conclude, orbital, physical and rotational properties of five out of the six suspected EEBs support the idea that these asteroids were probably spun-up by the YORP effect and then torn apart by the rotational fission mechanism to become binary asteroids.
Tables: Table I: Physical parameters of the six binaries with high separation (Durda et al. 2010): semi major axis (a), primary radius (Rp), ratio between the secondary and the primary radii (Rs/Rp), projected separation between the components in km (a s ) and in units of the primary radius (a/Rp).  (Tedesco et al. 2004).
* (3749) Balam parameters were presented by Marchis et al. 2008b that measured a semi major axis for the distanced satellite of 289 km, and a primary radius of 3.3 km. However, this radius value is actually the effective radius of the primary in addition to the near satellite of (3749) Balam. Therefore the real radius of the primary is smaller, and the Rs/Rp and a/Rp values should be modified accordingly.  Orbital frequency of (3749) Balam's secondary