Near Earth Asteroid "(436724) 2011 UW158"
Light Curve & Other Optical Observations

B. L. Gary, Hereford Arizona Observatory (G95), Last edited 2015.10.02

This web page describes my optical observations of Near Earth Asteroid (436724) 2011 UW158. It was once identified by NASA as a candidate for a future manned mission. Its appeal for this purpose was based on it having an orbit similar to Earth's, rendering any rendezvous with it as low energy. A close approach in mid-July of 2015 brought it to within 0.0165 a.u., or 6.4 times the distance to the moon (on July 19). Radar observations were scheduled for July 13-26 at JPL's GTS (link) and July 14-17 at Arecibo Observatory (link). The planning for any human mission would require knowledge of the asteroid's rotation period, shape, size, mass and surface properties. Since UW158 moving "alongside" Earth at close range for almost 3 months, it has been available for observation since mid-June, even by amateurs. It remains within reach of amateur observing until early October (link), when V-mag ~ 18.

Whereas this asteroid was initially identified as an interesting target because of its perihelion being close to 1.0 a.u., it is no longer of interest as a possible target for a human mission due to the fast rotation and lack of encounter for another century and it has instead become scientifically interesting because of its fast rotation and large size! In fact, it is only one of three known asteroids that rotate faster than the "spin barrier" for asteroids with diameters greater than ~ 250 meters. Since it cannot therefore be held together by self-gravity, it therefore must have sufficient "tensile strength" to qualify as a "coherent rock." The asteroid's shape is very elongated, with a "maximum to minimum dimension ratio" of at least 3.4 (based on radar) or 6.6 (based on photometry). This asteroid is a rare find, and I think it justifies continued observation (until October, 2015).

Until someone takes on the task of hosting a web site specifically for UW158 observations, those observations will be spread across the internet at unknown web sites. I'm not aware of any central location for submitting UW158 observations, where others can see and compare, so I have created this web page as a temporary place for my observations.

My first observation, on June 17 (possibly the first LC observation of the 2015 apparition), suggested a short rotation period (~ 1/2 hr), and my second observation (Jun 20) confirmed this with a high-quality rotation period of 36.665 minutes. The Jun 17 observation was the first suggestion that this asteroid was special, being a fast rotater while not being small (i.e., spinning faster than the 2.2-hr "spin barrier" for asteroids larger than ~ 250 meters). Subsequent observations have confirmed this, and this is only the 3rd asteroid known to be spinning faster than the 2.2-hr spin barrier (meaning that it's a rock, knocked off of a larger asteroid, and not the usual "rubble pile" that most asteroids smaller than ~ 10 km are thought to be.) Low-resolution optical spectra were obtained on 3 dates, showing that the asteroid has a typical slightly reddish color. The "range of variation" exhibits large changes, starting at from ~0.5 magnitude (Jun 17), reaching a peak of 2.05 magnitude (Aug 04) and decreasing to 0.86 magnitude (Oct 01). The largest range of variation corresponds to a solid angle that varies during rotation with a ratio of 6.6:1, meaning that longest dimension would be 6.6 times the shortest dimension under the simplest of assumptions. One pole (axis of rotation) points to RA/DE coordinates 17:30+10. The phase curve suggests that geometric albedo = 39 ± 9 % and the maximum solid angles seen during a rotation corresponds to a sphere with a diameter = 220 ± 40 meters, which is consistent with a radar size of 160 x 550 meters (rectangular equivalent, broadside view).

A more careful analysis shows that UW158 has a smallest radius that permits "rubble pile" dynamics (i.e., a loose regolith around the asteroid's mid-section), while the longest dimension does not permit "rubble pile" dynamics (i.e., a loose regolith would fly away, leaving bare rock). In other words, UW158 is the only known asteroid that straddles the 250 meter "size barrier" while spinning faster than the 2.2-hour "spin barrier"! This situation creates an interesting opportunity for speculation about surface conditions. Either there is a high albedo regolith around the mid-section, with low albedo bare rock exposed at the ends, or the ends are conical shaped and therefore subject to being in shadow when viewed end-on for most phase angles (permitting almost any regolith distribution and albedo). These speculations are described in a manuscript (link) that has just been submitted to the Minor Planet Bulletin.

All observations are theoretically compatible, and can be understood using the phase curve relationships described by Belskaya and Shevchenko (2000), hereafter referred to as B&S. These relationships, using phase curve slope to predict geometric albedo and the size of the opposition effect (OE), are based on measurements of large asteroids for phase angles within the range 1 to 24 degrees. The B&S analysis employs a phase curve relation proposed by Shevchenko (1996, 1997), hereafter referred to as S97. There is interest in evaluating whether the B&S relationship, involving the S97 phase curve model, is valid for small asteroids (<10 km), and for phase angles greater than 24 degrees; the analysis presented here suggests that UW158 is compatible with the B&S model.

Figure 1. Location of UW158 in the "spin frequency/diameter" diagram. The left end of the red rectangle corresponds to UW158's smallest diameter of an ellipsoidal shape (160 meters), while the right end corresponds to the largest diameter of UW158's ellipsoidal shape (550 meters). The vertical line at 250 meters is a size barrier for fast spinning asteroids: larger ones can only exist if they're a rock, smaller ones can exist even when they are mere rubble piles. (Chart is from IAU Minor Planet Center Asteroid Light Curve Database web site, link below, modified by the author to show the 250 meter barrier and UW158's location). 

Links Within This Web Page 
    Draft article  
    Latest LC & phase-folded LC 
    ASCII data file download links
    Radar truth
    Phase curve
    Location in "Spin Rate vs Diameter" diagram  
    Range of variation vs. date & pole orientation  
    Cucumber models  
    Albedo spectrum in visible 
    Observations by date 
    Moon phase curve 

Draft Article

Another version of this article link 

Latest Phase-Folded Rotation Light Curve 

Rotation LC, showing Aug 04 and last two observing dates. Model fit is for Oct 01.

Latest Light Curve 

Unfiltered LC for 6.2 rotations on 2015 Oct 01.  

ASCII Data Files  

The following links are for text files (ASCII format) of my UW158 observations. All data files have been submitted to the IAU MPC archive (and exist there with ALCDEF format).

For the data files linked below, the 1st column of data is JD for mid-exposure minus 2450000 (not corrected for light time). The 2nd column is magnitude calibrated using APASS r' magnitudes (typically 20 reference stars). All image sets have star-subtraction so there should be a minimal level of artifacts produced by background stars. The 3rd column is estimated SE that is a gross over-estimate. These SE uncertainties assume that real variations are slow compared with image spacing (because they are calculated from neighbor differences). The actual SE values are probably 1/4th of those given.  

Jun 17    First photometric LC (showing that P is very short, ~ 1/2 hr, and RoV ~ 0.5 mag))
Jun 20    Second photometric LC (3.1 rotations, establishing P = 36.66 min & RoV = 0.52 mag)
Jun 24    Four filter LCs (g'r'i'z'), aborted early due to clouds
Jul 02    Four filter LCs (g'r'i'z'), showing a slightly blue SED & suggesting presence of weak Band I feature
Jul 08    Unfiltered LC, 2.6 rotations, showing shape change: RoV increase to 0.70 mag. SA-100 spectrum.
Jul 09    SA-100 spectrum. Slightly red SED. LC data possible but would require additional analysis
Jul 11    SA-100 spectrum. Slightly red SED. LC data possible but would require additional analysis
Jul 12    Unfiltered LC, showing essentially the same rotation LC as on Jul 08; RoV ~ 0.70 mag
Jul 20    Unfiltered LC, showing big change in rotation LC shape since Jul 12; RoV = 0.92 mag
Aug 03    Unfiltered LC, 1.77-hr observation, showing RoV = 1.95 mag and fading of secondary maximum
Aug 04    Unfiltered LC, 1.62-hr observation, showing slight change in rotation LC; RoV = 2.05 mag
Aug 13    Unfiltered LC, 3.27-hr observation, showing slight change in rotation LC; RoV = 1.84 mag
Aug 29    Unfiltered LC, 1.91-hr
observation, showing slight change in rotation LC; RoV = 1.46 ma
Sep 06    Unfiltered LC, 2.45-hr observation, showing slight change in rotation LC; RoV = 1.25 mag
Sep 15    Unfiltered LC, 3.21-hr observation, showing slight change in rotation LC; RoV = 1.07 mag
Sep 16    Unfiltered LC, 3.52-hr observation, showing slight change in rotation LC; RoV = 1.08 mag
Sep 24    Unfiltered LC, 3.62-hr observation, showing slight change in rotation LC; RoV = 0.94 mag  
Sep 25    Unfiltered LC, 3.76-hr observation, showing slight change in rotation LC; RoV = 0.89 mag
Sep 26    U
nfiltered LC, 3.22-hr observation, showing slight change in rotation LC; RoV = 0.85 mag  
Oct 01    Unfiltered LC, 3.21-hr observation, showing essentially no change in rotation LC; RoV = 0.86 mag.

Radar Truth

JPL & Arecibo radar observations have shown that the effective diameter is larger than anyone predicted. The JPL dimensions are >150 x >320 m while Arecibo measures 300x600 m. Since Arecibo SNR is greater it sees "more" of the asteroid, so this size is preferred.

Left: Arecibo Observatory radar image (average of frames 36-39, rotated & aligned). Right: Arecibo Observatory animation.

Keep in mind that since the asteroid does not have a rectangular shape, but is not rounded in all cross-sections, the equivalent size for the radar cross-section is ~ 500 x 170 m. Also, keep in mind that the radar y-axis is depth (distance from observer), which is not the same as the dimension in the sky plane that is orthogonal to the rotation axis. In other words, it would not be correct to state that the "solid angle" in the sky can be calculated from the two dimensions of the radar cross-section. Nevertheless, the radar cross-section dimensions would be a good first-guess for estimating the "solid angle" in the sky plane (which is needed for converting photometry to equivalent size). Thus, a good first-guess estimate for solid angle is a sphere with diameter ~ 300 meters.

The following graph will be useful in estimating geometric albedo, Ag, for an assumed H, provided we know diameter.

If we adopt a diameter of 300 meters, for example (red trace), and if we further assume H = 19.5, then geometric albedo = 0.30 (30%).

Phase Curve

The discovery V-mags were fitted by the HG model with H = 19.5 and G = 0.15, which means that the rotation-averaged V-mag must have been ~ 20.65 (averaged over a 10-day hypothetical observing window, during which phase angle ranged from 21.6 to 14.3 deg). Since all my observations are calibrated using stars with APASS r'-mags, I have adjusted the 2011 mag's by -0.23 to arrive at their r' values (this is based on UW158's color, as measured on 3 occasions and described below). The following phase curve shows these rotation-averaged r'-mags with a thick, light blue trace. The green box above it is a suggested region for the maximum brightness during rotation. We don't know the orientation yet so this box is a conservative estimate. My r'-mag measurements for maximum brightness with rotation (rotation phase 0.5) are shown for phase angles > 17 deg. 

Reduced r'-mags vs. solar phase angle, corresponding to maximum rotation brightness, for my observing sessions, fitted using a model first proposed by Shevchenko (1996, 1997) and elaborated by Belskaya & Shevchenko (2000). The 2011 discovery V-mag (rotation-average) is shown as a light blue line at phase angles 14 to 22 deg (2011 Oct 25 to Nov 3), where V-mag is converted to r'-mag by subtracting 0.23 mag (corresponding to UW158's color). The green box above the rotation-averaged 2011 r'-mags is my suggestion for maximum brightness during rotation (a rotation LC was not produced in 2011 so I've had to estimate how much brighter the green box could have been). The model fit is compatible with all of the 2015 measurements (except for the one with PA = 109 deg) and it is also compatible with the range of brightness estimated for 2011.

In this phase curve the July 20 observation at PA = 109 deg is fainter than the straight-line fit, and is not used for constraining the model since shadowing may have been severe. All of my photometry LC observations can be fitted by the B&S model, except for the large phase angle one (Jul 20) just mentioned.

If UW158 obeys the Belskaya & Shevchenko (2000) relationship between phase effect slope and geometric albedo, as well as the opposition effect delta-mag vs albedo, and if these relationships apply to large phase angles for UW158, then UW158 has a geometric albedo = 39 ± 10 % and diameter = 220 ± 50 meters. This diameter is compatible with the radar observation.

Spin Rate vs. Diameter Diagram 

UW158 is unusual in the sense that it's an outlier in the "rotation frequency/diameter" diagram, as we can now be confident that it is located above the 2.2-hour rotation period "barrier" for asteroids larger than ~ 250 meters (next figure). Because it rotates so fast we can speculate about regolith thickness at the ends. We may also speculate about the possibility of large OE. An IRTF spectrum can help in understanding a high albedo, if that's the case. Regardless of my outrageous speculations I think it's sufficiently prudent to claim that UW158 is an interesting asteroid.

Figure 1 (repeat). Plot of asteroid rotation frequency vs. size (as compiled and displayed at the IAU Minor Planet Center Asteroid Light Curve Database web site, link below). The left end of the red rectangle corresponds to UW158's smallest radius of an ellipsoidal shape (160 meters), while the right end corresponds to the largest radius of UW158's ellipsoidal shape (550 meters). The vertical line at 250 meters is a size barrier for fast spinning asteroids: larger ones can only exist if they're a rock, smaller ones can exist even when they are mere rubble piles. (Chart is from IAU Minor Planet Center, modified by the author to show the 250 meter barrier and UW158's location). The red rectangle shows where UW158 would lie if it has a diameter of 320 meters.

Range of Variation vs. Date and Spin Axis Orientation 

Range of variation vs. JD - 2450000, with smoothed fit (11th-order), plus location along a 180-deg long arc on the celestial sphere that the asteroid traversed during the 90 days of observations (dashed trace). [I'm using the term "inclination" in the way it is used by the exoplanet community.]

The first observation of this 2015 apparition had the smallest range of variation, so this is when we must have been viewing it closest to pole-on. The range of variation changed fast after closest approach, when the asteroid's motion brought it into an equatorial view on about Aug 05. The Earth's sub-latitude changed more slowly after then because the asteroid moved more slowly along it's celestial sphere arc.

In order to determine the spin axis orientation we must consider the fact that UW158 resembles an ellipsoid that is much longer than it is wide. The 2.05 mag range of variation on Aug 05 means that the solid angles varied during rotation with a maximum to minimum ratio = 6.6 (assuming uniform albedo across the surface). An ellipsoid is defined by 3 radii, a, b and c, as illustrated by the following figure.

Ellipsoid with radii a, b and c, viewed from an inclination of ~ 45 deg (assuming that the rotational axis is parallel to "a").

A pole-on view will project the maximum solid angle for all rotation phases, given by π × b × c / d, where d = distance from Earth. An equatorial view will project a solid angle that ranges from π × a × b / d to π × a × c / d. If we could assume that a = b then we could convert rotation brightness ratio to inclination. The actual equation is quite complicated, but an approximation for the ratio of brightness (maximum / minimum) as a function of inclination, i, is:

    R(i) = x / (sin i + x (cos i))

    where x = c/b = c/a (i.e., a = b).

For UW158 we know that i = 90 deg on Aug 05, when R(i) = 6.6. The first observation (Jun 17), with R = 1.54 (delta-mag = 0.47), must be at i = 59 deg. When each observation is converted to an i value in this way it is possible to draw arcs on the celestial sphere, and where they intersect is one of the rotational axis pole positions (we don’t yet know whether rotation is prograde or retrograde, so there will be two RA/DE pole locations). One pole position is RA/DE = 17:30/+10.

Cucumber Mmodel #1

Note the extreme range of variation when JD-2450000 = 7238 (Aug 04). This must be an equatorial view (sub-Earth latitude of zero, inclination = 90 deg). The range of variation is 2.05 +/- 0.10 mag, which corresponds to a brightness ratio of 6.6 +/- 0.6. If we were dealing with an ellipsoid with uniform albedo across the surface, and if PA were zero, the 6.6 ratio would correspond to the solid angle ratio, and this would mean that a x b / c^2 = 6.6. This elongation resembles a cigar. But the radar dimensions call for a more modest ratio of 3.44 +/- 0.15 (550 / 160). This elongation resembles a cucumber. What model can produce a much larger range of variation for a cucumber shape?

Consider that fact that in Fig. 1 the longer dimension exceeds the 250-meter barrier for fast rotaters, and the smaller dimension is smaller than the 250-meter barrier. This means that loose regolith will fly off the ends of the asteroid, but will be stable around the mid-section. In other words, there might be a belt of regolith around the mid-section. Imagine a cucumber with a cloth wrap around the middle, as depicted here.

Cucumber wrapped in cloth, resembling a cucumber-shaped asteroid with regolith covering the mid-section (Cucumber Model #1).

If the bare rock has a lower albedo than regolith material, then an end-view will be fainter than the solid angle argument would predict. This is my Cucumber Model #1.

There's one potential problem with this model. Regolith is usually darker than the rock that it's made from, not brighter. Throughout the solar system regolith darkens with time. I'm not completely abandoning this model, but it does lead to my Cucumber Model #2.

Cucumber Model #2

Consider a cucumber viewed edge-on but illuminated by the sun at some phase angle, such as 45 deg. If we model the end of the cucumber as a cone, then it will be apparent that ~ 1/2 of the cone will be in shadow. Thus, the brightness of an end-on view will be ~ 1/2 of what the solid angle argument would predict. The broadside view would be less affected by shadowing. This, in turn, would cause the ratio of brightnesses  during a rotation (as viewed from the equatorial plane) to approximately double. This is almost exactly what was observed.

Albedo Spectrum in the Visible Region

Transmission grating observations on two dates (July 9 & 11) yield identical results for albedo spectral shape. I have chosen to present them in the form of "geometric albedo" instead of "relative reflectivity."

Albedo spectrum for two observing sessions, showing agreement of overall value and shape (red slope). The overall albedo is highly uncertain due to inherent shortcomings in attempting to interpret the phase curve. Because of this uncertainty the albedo scale is subject to an unknown multiplier; the albedo structure is unaffected by this uncertainty. Due to low SNR at short and long wavelengths only data between 420 and 820 nm are shown.

On these dates (and for the rotation phases sampled) UW158 was slightly red. There is no information about the presence of a 1 micron absorption feature due to the low SNR beyond ~ 820 nm.

Observing Session Data

2015.10.01 Observation

This observing session was made using C filter that included 5.2 rotations, showing slightly smaller "range of variation" as the day before, 0.86 mag.

2015.09.26 Observation

This observing session was made using C filter that included 5.3 rotations, showing slightly smaller "range of variation" as the day before, 0.85 mag.

2015.09.25 Observation

This observing session was made using C filter that included 6.2 rotations, showing slightly smaller "range of variation" as the day before, 0.89 mag.

2015.09.24 Observation

This observing session was made using C filter that included 5.9 rotations, showing slightly smaller "range of variation" as the day before, 0.94 mag.

2015.09.16 Observation

This observing session was made using C filter that included 5.7 rotations, showing same "range of variation"  as the day before, 1.07 mag.

2015.09.15 Observation

This observing session was made using C filter that included 5.2 rotations, showing slightly smaller "range of variation" = 1.07 mag.

Model fit is for 2015 Sep 15 data.

2015.09.06 Observation

An observation was made using C filter that included 4.0 rotations, showing slightly smaller "range of variation" = 1.25 mag.

Rotation LC with model fit to Sep 06 data.

2015.08.29 Observation

An observation was made using C filter that included 3.1 rotations, showing slightly smaller "range of variation" = 1.46 mag.

Rotation LC with model fit to Aug 29 data.

2015.08.13 Observation

An observation was made using C filter that included 5.4 rotations, showing slightly smaller "range of variation" = 1.84 mag. 2.0 hrs of g'r'i' observations were also made (reduction in progress).

Using the above model fit the g', r' & i' mag's can be forced to agree, and the required offsets can then be used to determine a 3-band relative reflectivity spectrum.

The black symbols are high SNR unfiltered observations (calibrated to r' band). After the unfiltered observing are g'r'i' mag's with offset adjustments that force them to agree with an extrapolation of the unfiltered data model.

This relative reflectivity spectrum corresponds to a reddish color.

2015.08.04 Observation

An observation was made using C filter that included 2.7 rotations, confirms yesterday's large amplitude variation. The "range of variation" is now 2.05-mag. The solid angle ratio during a rotation is 6.6:1.

2015.08.03 Observation

This observing session was made using C filter during conditions of continuous thin cirrus (this is the middle of the Arizona monsoon). The next LC, showing 2.9 rotations, reveals that the amplitude of variation has increased dramatically to ~2-mag's. In addition, the second maximum is almost 1 mag fainter than the primary maximum.

This phase-folded rotation LC shows the dramatic change in "range of variation" as well as shape during the past 2 weeks (since Jul 20). The "range of variation" of 1.95 mag implies a solid angle variation of 6.0:1. The primary maximum, at phase 0.5, appears to be "well-behaved," which means that this is a broadside view that should be used for establishing a phase curve. It is obvious that "rotation-average magnitude" should NOT be used for a phase curve analysis.

2015.07.20 Observations

After heavy rain just before sunset a clearing occurred, so I observed unfiltered to establish rotation LC and observed with the SA-100 transmission grating to determine relative reflectivity. The rotation LC underwent a change, increasing "range of variation" from 0.7 mag to 0.9 mag, and with increased asymmetry. The C-band observations (1.2 hrs) are shown as two FOV LCs, below.

Rotation LCs for July 8 & 12 (very similar, with model fit) and July 20 (different). The Jul 12 RoV = 0.92 mag.

The SA-100 transmission grating response function is defined as "counts per second per pixel" versus wavelength. It is affected by CCD QE, telescope optical transmission, focal reducer transmission, etc, so it goes to zero at short and long wavelengths. However, since it will be the same for any star or asteroid it is possible to compare ratios of response functions. When a calibration star is a "solar analog" then it can serve as a stand-in for the sun. The next figure shows the response functions for one solar analog star and UW158.

Response functions for a solar analog star and UW158.

Below is a graph of UW158 albedo vs. wavelength (with a couple assumptions).

Geoemtric albedo assuming H = 19.5 and diameter = 450 m, for 4 SA1-00 image groups. The thick gray trace is the average.

Since UW158's rotation causes brightness to vary by ~ 0.9 mag the SA-100 image groups vary in their "response function," leading to an apparent variation in albedo when the average diameter is adopted. Data shortward of 410 nm, and longward of ~ 850 nm lack sufficient SNR to be useful. The subtle fade beyond 800 nm probably isn't real.

2015.07.12 Observation

A 1-hour observation was made using a C filter, calibrated using APASS r'-mags, for assessing whether the phase-folded (rotation) LC has changed since solar phase angle has increased to its largest value so far, 96 deg. There has been no change in either shape or amplitude of variation.

Phase-fold of July 8 & 12 data, showing essentially no change in shape or amplitude between these two dates (PA = 89 & 96 deg).

The rotation average r'-mag is 14.99, which allows a new data point to be added to the phase curve (1st figure on this web page). A revised diameter solution is 256 ± 35/29 meters is determined, with the caveat that this may be totally meaningless since it is based on a phase curve restricted to a PA range of 60 to 96 degrees (vs. the 0 to 25 deg range from which the B&S 2000 relationships were determined).

2015.07.11 Observation

A 2-hour observation was made using a SA-100 transmission grating. One solar-analog star was observed at the same approximate air mass as UW158. The next figure is the geometric albedo spectrum derived from these observations (subject to the caveats described below).

Geometric albedo spectrum based on 3 groupings of UW158 images and a consensus of the solar-analog star spectrum. Due to SNR data are valid only within the 400 nm to 820 nm region.

As the figure states, I have assumed that the phase curve (as of Jul 08) can be interpreted using the B&S 2000 relationship. This is a dubious assumption for 2 reasons: 1) B&S 2000 is based on large asteroids (and it is not known if small ones exhibit the same relationships), and 2) B&S 2000 is based on phase curves for phase angles < 25 degrees, and the present UW158 observations are at much larger phase angles (60 to 90 deg). Nevertheless, the "shape" of this albedo spectrum should be valid, so the conclusion that UW158 has a red albedo slope (is slightly redder than the sun) is valid. The possible presence of a 1 micron absorption feature should also be unaffected by the B&S 2000 assumption, though this feature is very uncertain due to SNR limitations (there was too much water vapor in the atmosphere, producing large extinction at 820 nm & beyond 900 nm). The albedo spectrum for this date is essentially compatible with the one obtained from Jul 09 observations.

The albedo spectrum (above) was derived from a set of ~ 60 30-second images that had star effects subtracted (i.e., median of star-aligned images was subtracted from all individual star-aligned images, and these were then asteroid-aligned for subsequent averaging). The resulting asteroid spectrum is essentially devoid of interfering effects of background stars. Here's an example of a "clean" image of UW158 with its zero- and first-order spectrum.

Average of "star-subtracted" spectra of UW158. The asteroid's zero-order image is on the left, and the first-order spectrum is to the right (brightest portion corresponds to ~ 600 nm, and wavelength to pixel conversion is proportional to distance from zero-order image location).

Readings of ADU counts vs location from the zero-order image are entered into a spreadsheet and converted to response functions, illustrated in the next figure.

Three image groups produced these "response functions" (ADU counts per second per pixel vs wavelength).

The average response functions for UW158 and a solar-analog star (at 12:44:17-00:27:33) are compared in the next figure.

A re-scaled version of the solar-analog star's response function is compared with the UW158 response function, showing that UW158 is redder than the solar analog star.

2015.07.09 Observation

A 2-hour observation was made using a SA-100 transmission grating. Five solar-analog stars were observed at the same approximate air masses as UW158. The ratio of responses can be used to determine the shape of the reflectivity spectrum.

Response vs. wavelength of UW158 for 9 images (40-sec exposures) median combined in 3 groups (tgt 1,2,3) and averaged (tgt4).

Atmospheric extinction features in the above spectral response at 763 nm (oxygen), 820 nm (water vapor) and 920 - 1000 nm (water vapor).  

Response of 3 solar-analog stars (rescaled to be same) & average UW158 response.

From this plot it is apparent that 1) all 3 solar-analog stars have the same spectral response shape, and 2) UW158 is redder than solar-analog stars.

Geometric albedo spectrum of UW158 for groups of 7 images (air mass ~ 1.9, V-mag ~ 15.7). The phase curve as of Jul 08 was used to estimate brightness at zero phase, which in turn led to a diameter of 290 meters, both of which are adopted for calculating albedo. Due to the uncertainty of interpreting the phase curve this way the albedo spectrum is subject to an unknown multiplier; i.e., the slope is valid but no necessarily the overall value.

I conclude that UW158 has an albedo slope that makes it slightly redder than the sun. I believe this result more than the g'r'i'z' albedo spectrum (July 02), and will investigate the discrepancy.

2015.07.08 Observation

A 2-hour observation was made using C filter & SA-100 transmission grating with exposure times of 50 seconds.

LC for July 8, lasting 2.6 rotations.

Phase-fold of July 8 data, using a period based on data for all observing sessions.

The "range of variation" is increasing with solar phase angle.

2015.07.02 Observation

A 2-hour observation was made using g'r'i'z' filters in alternation with exposure times of 60 & 100 seconds.

Average g'r'i'z' magnitudes were used to produce the following SED.

This was used to produce a relative reflectivity plot.

Ratio of asteroid flux to solar flux averaged over the respective g'r'i'z' bands, normalized so that albedo ~ 30% at V-band (as derived using the phase slope and B&S 2000 relationships for albedo & OE, described above).

There is a risk in attempting to determine albedo spectrum from observations of a large amplitude, fast-rotating asteroid when filters are used in alternating groups. As the next graph illustrates, one filter group may occur preferentially at the peak of the variation (e.g., green symbols, for g'-band), while another filter group may occur preferentially near the minimum (e.g., purple symbols, z'-band). If average magnitude is then used to create a spectrum these biases will distort the spectral shape. I think this is what happened for these observations. A better procedure is to keep track of offsets required to fit a model variation, etc. I plan on doing this.

By adjusting mag's for each band for minimum chi-square agreement with r'-mag's reveals a LC shape similar to the high SNR LC shape from unfiltered observations on  previous date (Jun 20).

The r' images had sufficient SNR for adding to the unfiltered rotation LC solution. An improved rotation period was obtained. So far the G=0.15 phase curve model is OK.

Rotation (phase-folded) LC combining early unfiltered observations with r' observations on Jul 02. 

2015.06.24 Observations

I observed UW158 for an hour on this date, using g'r'i'z' filters in alternation, using 60-second exposures. The goal was to obtain a Spectral Energy Distribution (SED), from which an albedo spectrum can be derived. A specific goal was to see if a Band I absorption feature at 920 nm was present; its presence would indicate a surface with olivine and pyroxene. Intermittent mid-level clouds were present, but during a 15 minute clearing useable observations for all filter bands were obtained. Only 3 or 4 images were available for each filter band, so the results are noisy. APASS magnitudes of background stars were used to calibrate each image. The next figure is my SED for these data.

Spectral Energy Distribution (SED) for UW158 on Jun 24.

A SED that has the same shape as the sun indicates a uniform albedo versus wavelength. The above SED is too noisy to say much about the albedo spectrum, except that the data are compatible with a flat albedo spectrum within the 0.4 to 0.8 nm region. It's unfortunate that the z' data, centered at ~ 0.92 nm, was too noisy for use. Future observations should be better.

2015.06.20 Observations

A 1.9-hour observation was made on Jun 20. It revealed a definitive rotation light curve for UW158: P = 36.6 minutes, range of variation = 0.52 mag.

Light curve (LC) during a 1.9-hour observing session, revealing a sinusoidal variation with period 0.3 hrs.

The next figure is a phase-folded LC using the same data (above) with a model solution based on chi-square minimization.

Phase-folded "rotation LC" using a solved-for rotation period of 36.665 minutes (solution includes some data for Jun 17).

The following is a power spectrum of the Fig. 1 LC data.

Power spectrum (actually square-root of power) showing one main peak at 3.26 cycles/hour (18.4 minutes).

The above power spectrum has one distinct peak corresponding to half the rotation period. Power exists at ~ 1/2 of the main frequency, signifying the presence of slight differences in neighboring peaks (all odd numbered cycles are the same, as are all even numbered ones, but odd and even cycles are slightly different from each other). The power at ~ 5 cycles/hour merely shows that the variations are not purely sinusoidal. All of these properties can be discerned by inspection of the first figure for this observing session.

It's rare for asteroids as large as UW158 to rotate this fast, as the next figure shows.

Plot of asteroid rotation frequency vs. size (as compiled and displayed at the IAU Minor Planet Center Asteroid Light Curve Database web site, link below). The cross-hairs show where UW158 would lie if it had a typical albedo (geometric albedo = 12%, H = 19.5, G = 0.15).

In the above plot only two other asteroids lie well above the "spin barrier" for large asteroids (rotation period = 2.2 hours). Such asteroids can't be unconsolidated "rubble piles" because such asteroids would simply fly apart! Only rocks ("monoliths") can spin this fast (for this size range). If UW158 has an albedo > 30% then its size would be withing the "permitted" region for high spin rate. This might constitute a case for believing that UW158 has a high albedo and is ~ 250 meters in diameter.

2015.06.17 Observation

A brief (1/2-hour) exploratory observation was made with a 14" telescope on Jun 17. It quickly revealed that UW158 rotates fast (P ~ 1/2 hr), and exhibiting a large amplitude (~ 0.5 mag).

Future Prospects

UW158 will brighten until ~ Jul 21, according to an assumption of an HG phase effect model with G = 0.15. It is currently ~ 2 magnitudes fainter, but it is moving slower, which permits 2 to 3 minute exposure times for amateur telescopes with ~ 3.2 "arc atmospheric seeing. At the present time UW158 is observable for only 3 hours, starting at twilight. For northern hemisphere observers UW158's increasing declination will permit longer observing times. Fully one month of observations are feasible for amateur observers. 

Figure 6. JPL Horizons ephemeris for daily intervals, at 04 UT (and EL at my Southern Arizona observing latitude), showing that UW158 is observable by amateurs for more than a month.

When UW158 is close to its brightest I plan on observing it with a SA-100 transmission grating. This should produce a spectrum from ~ 450 to 950 nm with ~ 1% spectral resolution. Previous observations with this hardware has clearly shown the Band I absorption feature at 920 nm. The exact wavelength of this absorption is affected by the relative abundances of olivine and pyroxene.

The phase angle (S-T-O, sun-target-observer) varies from 66 deg (Jun 20) to 109 deg at closest approach. This may be adequate for measuring the phase effect slope [mag/deg]. Knowledge of phase slope can then be used to infer albedo, as described by Belskaya I. N. & Shevchenko V.G. (2000, Icarus 147, 94 ). And with albedo it is possible to determine diameter. Of course, radar observations should provide a better diameter, without the B&B assumption of phase slope to albedo correlation, so when the radar diameter is available we can state whether or not the B&B correlation holds up for an asteroid this small - which is also a useful check.

Feasibility Track 

Last year I developed a useful way for an observer to learn if it is feasible to observe a NEA for producing a LC based on the NEA's rate of motion and brightness. The following graph is for my hardware (Meade 14", f/5, SBIG ST-10XME, KAF3200E, 80% QE max).

Figure 7. UW158's track in a magnitude/motion diagram for 5 day intervals. The region enclosed by the red boundary shows what's feasible for a 14" telescope (with a typical CCD in a Cassegrain configuration). The upper border corresponds to a brightness yielding SNR > 5, which is a minimum criterion for producing a LC. The right border corresponds to the assumption that FOV changes at intervals as short as 45 minutes are acceptable. Exposure times are set to the PSF crossing time; for this telescope I have adopted PSF = 3.2 "arc. FOV is 18x27 'arc, and FOV changes are for 75% track across either FOV dimension.  

The above graph shows that for my telescope UW158 is "observable" during the entire time it is close to Earth. Graphs can be easily produced for other observers with a different telescope and CCD.

Moon Phase Curve

An eclipse of the moon on 2015 Sep 28 offered an opportunity to begin observations of the moon's phase curve that would include small phase angles.

NE quadrant of moon showing 3 maria and 3 highlands used for phase curve measurement.

Phase curve for lunar highlands and maria.

Two notable features of the lunar phase curve are: 1) the slope functions for both maria and highlands are linear out to phase angles of 45 deg, and 2) the high albedo highland slope is shallower than the low albedo maria slope. Both features are compatible with the B&S model, and this provides support to the position that the B&S model can be used for phase angles > 24 deg.


I’m probably familiar with the cultures of more science disciplines than most scientists, based on 55 years of earning a living in them and dealing with the principal scientists within those fields. My first exposure (in the 1950s) was as an undergraduate astronomy student, working my way through college as a part-time employee of a radio astronomer. I felt welcomed by everyone in the Astronomy Department, where I had office space. I was invited to department Christmas parties and other social gatherings. My first experience as a professional radio astronomer entailed studies of Jupiter, the moon and other planets. After a decade I transitioned to boundary layer meteorology, emphasizing remote sensing. Then aviation safety, including remote sensing of CAT (leading to several patents). Then atmospheric science of the stratosphere; I was a PI for all of NASA's airborne ozone hole missions, until retirement. A few years into  retirement I became involved with exoplanet transit observing, including a couple consulting contracts and a how-to book for amateurs. Finally, during the past 1.5 years I observed asteroids for pay, characterizing 27 NEAs within 9 months (for a Tucson astronomer).

Each science discipline has a “culture” which is greatly influenced by the most experienced and most competent practitioners. I would characterize the radio astronomy community (of the 1960s) as welcoming, tolerant and honest. The boundary layer meteorology community was fast-paced and open to new ideas, and since I had new ideas using the latest technology I was welcome. The aviation safety community was the same. The community of atmospheric scientists studying the stratosphere was well-organized and adhered to high standards; I became a welcome fixture for all of NASA's aviation-based ozone hole investigations. The exoplanet community was young and fast-growing, and well-disciplined.
The scientific discipline that is most important to me is sociobiology, but I’ve never had dealings with anyone working in the field – in spite of the fact that I’ve written a book on the subject. Based on my attendance at a few conferences, and reading many articles and books on the subject, I have a sense that within this field is a welcoming of anyone with new ideas, but with a requirement that you’d better be able to back them up. It’s such a controversial field that they are wary of both public criticism and academics with a social agenda (i.e., on matters relating to a culture's social fairness) who want to continue their hijacking of the field that started 130 years ago; I suspect that everyone in sociobiology is prepared for controversy regardless of what they propose.

But it's the asteroid community that still puzzles me. They are somewhat insular, and resentful of newcomers, and are prone to bickering as they seem quick to criticize others (behind their back) as if this will help fend-off competition for funding. Maybe that’s what happens when NASA funding for a discipline has a doubling-time of 1 or 2 years: "we can’t let those idiot newbies get any of our money." (The only time in the past 55 years that someone questioned my integrity was a couple months ago, by a well-known asteroid person whose complaint was totally unfounded, and was done in a way that I was supposed to not know about it). A few established asteroid workers are welcoming, but most seem resentful of newcomers.

Each scientific discipline has a different level of discipline, honesty and welcoming of new people with new ideas. A small cadre of leaders set the tone for anyone wanting to contribute. Each discipline resembles a tribe, with tribal elders who pass on requests for joining. The asteroid tribe has a “No Trespassing” sign out front and a sign on the door that says “Stay Out.”

Got it! Time for another transition (after UW158).

Related Links

    JPL Horizons ephemeris generating web site
    JPL's GTS asteroid radar observing schedule  and Arecibo Observatory observing schedule 
    IAU Minor Planet Center Asteroid Light Curve Database  
    Tips for amateurs observating faint asteroids 
    Master list of my web pages & Resume


This site opened:  2015.06.24.  by Bruce L. Gary (B L G A R Y at u m i c h dot e d u)