ASTEROID "2004 MN4" BRIGHTNESS
REVISION SUGGESTION
Bruce L. Gary
2005.02.05
This web page section shows observations of asteroid "2004 MN4" that
have been calibrated using Tycho stars in the same images used for
observing the asteroid (71 x 47 'arc). All-sky photometry was attempted
on several occasions but the atmospheric extinction was too variable
due to scattering from cirrus clouds. I conclude that this asteroid is
~0.3 magnitude brighter than the ephemeris value of H = 19.3, i.e., I
suggest that H = 19.0. Details are given below.
Figure 1. Plot of V-equivalent magnitudes for asteroid
"20044 MN4" based on Tycho stars in the same image as the asteroid. No
adjustments have been made to achieve a fit to the model curve, which
is based on the analysis of Dr. Raoul Behrend. The period for this plot
is 1.250 days instead of Behrend's 1.2764 days. The green symbol was
made using a V-filter, the others were unfiltered. Changes in apparent
brightness due to changing distance from Earth have been removed in a
way that renders the plot valid for January 16. A known instrumental
sensitivity to star color has been applied to the asteroid using an
assumed B-V = 0.80.
For each observing date several Tycho stars were used to establish
a
calibration for that night's images. All but one observing set were
unfiltered. Instrumental corrections for unfiltered observations have
been established on many nights with this observing system, and the
conversion from star flux to equivalent V-magnitude, called C-mag, has
been found to obey the following relationship:
C-mag = 21.37 - 2.5 * LOG ( Fv / g ) - Kv * m + 0.30
* (B-V-0.64) + 0.04 * m * (B-V-0.64),
where Fv = flux (using a V-filter), g = exposure time [seconds], Kv =
zenith extinction (using a V-filter) [mag/air mass], and m = air mass.
On photometric nights Kv = 0.12 [mag/air mass]. On non-photometric
nights it is higher, and must be established using either Tycho stars
or nearby Landolt stars. For these observations Tycho stars were used
for calibration, and they don't have reliable B-V colors, so I assumed
they were typical in having B-V = 0.64 (the average of all 1259 Landolt
stars). The asteroid is assumed to be redder than typical stars, with
B-V = 0.80 +/-
0.05 (as suggested by Prof. Richard Binzel). One V-filter observation
confirms the
unfiltered results taken a few minutes earlier.
The ephemeris currently uses H = 19.3. The magnitudes in the
above plot were adjusted to be valid for January 16, when the ephemeris
predicts a V-magnitude of 17.53. The asteroid appears to be brighter by
0.33 magnitude, implying that H = 18.97.
The uncertainty on this suggested value for H depends upon the validity
of G. But for now, let us adopt the ephemeris value of G = 0.15. Tthe
main uncertainty would then come from the measurements presented here.
The assumed B-V for the asteroid produces an uncertainty of only 0.004
magnitude (i.e., assuming B-V = 0.80 +/- 0.05). Another source of
uncertainty is the use of Tycho stars with unknown B-V. Since different
Tycho stars were used for each observation night, and since an average
of 3 such stars were averaged, it can be estiamted that the average of
4 observing nights (12 Tycho stars) introduces an uncertainty of ~ 0.03
magnitude for the average magnitude of 17.20 (this is based on an
estiamted RMS on B-V for Tycho stars ~ 0.3 magnitude and a star color
sensitivity of 0.30). This is probably
the principal systematic error source for the observations reported
here. Another source of uncertainty relates to the way I used a model
rotational light curve for fitting the observations. If, for example,
all observations were at the peak brightness part of such a light curve
then it is obvious that the asteroid's average brightness would be
over-estimated. However, in this case most of the measurements were
made during the rising portion of the light curve. I estimate that this
source of uncertainty is ~0.05 magnitude. Finally, stochastic
uncertainty ("noise") is present, but with SNR typically > 50 for
each
data group shown in the above plot this source of uncertainty is
estiamted to be < 0.02 magnitude.
I conclude by suggesting that the value for H be revised from 19.3 to
19.0 +/- 0.10, subject to the assumption that G = 0.15.
__________________ The remainder of this web page was created a
month ago, and was a vehicle for presenting observations by two
observer groups _________________________
ASTEROID "2004 MN4" LIGHT CURVE
Bruce L. Gary and Vishnu V. Reddy
2004.01.15
Introduction
Near Earth Object asteroid "2004 MN4" was discovered last June, was
lost, then was recovered in November. By December 23 the orbit had been
established well enough by NASA's Near Earth Object Program Office at
JPL that the NEO Program Office (Yeomans, Chesly and Choda) posted at
MPML that a near Earth pass in 2029, April 13 had a 1 in 300 chance of
Earth impact. Because of the December 27 re-assessment of a 1 in 37
chance of Earth impact in 2029 an effort was made to refine the orbit
with new astrometry observations. Finally, the Spacewatch telescope at
Kitt Peak found an image of the asteroid (mag 22) taken in March
(before the discovery) showing an asteroid position that was quickly
incorporated into orbit calculations that reduced the probability of
Earth impact to near zero. Nevertheless, the pass in 2029 will occur,
and the asteroid may pass close enough (8 Earth radii) to be visible
with the naked eye.
There has been considerable discussion on the MPML about photometry
shortcomings, and the need for better brightness values in order to
estimate asteroid size. Radar observations are planned, and part of the
planning requires approximate maximum Doppler width from the returned
echo. Therefore, to assist in radar planning it is important to obtain
brightness measurements that are not only accurate but precise enough
to establish a rotation period.
On January 6 Raoul Behrend reported to the MPML that Yassine Damerdji
had obtained observations at Haute-Provence Observatory from which a
rotation light curve was derived. The light curve solution (by Damerdji
et al) calls for a period of 0.6 +/- 0.4 day (14.4 +/- 9.6
hours) and an amplitude of 0.2 mag (half of peak-to-peak variation).
The light curve can be found at http://obswww.unige.ch/~behrend/page5cou.html#04m04n.
January 8 and 9 Light Curve Observations
On UT dates January 8, 9 and 11 Vishnu V. Reddy (University of
North Dakota
graduate student) and Ken Archer (Ironwood Observatory, Hawaii) used
the 10-inch Takahashi Baker-RC f/5 telesope and SBIG ST8 CCD of the
Ironwood Observatory, Hawaii (F60) to observe 2004 MN4.
These observations were conducted remotely from North Dakota by VVR
using the Share My Sky program. On January 8, 9 and 11 Bruce
Gary
observed "MN4" using the Hereford Arizona Observatory (G95) Celestron
14-inch SCT and SBIG ST-8XE CCD. The January 9 and 11 observations were
made through cirrus clouds with
extinction variations of 0.6 magnitude. Our data have been combined and
are shown in the following figure.
Figure 1. Equivalent V-magnitudes (from unfiltered
observations) during a 4-day observing interval. The magnitude scale is
set by a January 11 image (by BLG) with several Tycho stars in the same
FOV as the
asteroid. All other data sets were zero-shifted to agree with the
BLG Jan 11 data. The BLG observations (at Hereford Arizona Observatory,
G95) were
made by Bruce L. Gary with a 14-inch Celestron and SBIG ST-8XE
CCD, and were processed by median combining sets of three 60-second
exposures using the asteroid for alignment. The VVR
observations (at Ironwood Observatory, Hawaii, F60) are 5-point
averages of
60-second exposures.
Figure 2. Same as previous figure except showing only
the Jan 8 and 9 observations.
Figure 3. Same as first figure except showing only the
Jan 11 observations.
The fitted sinusoidal model solution has two periods per rotation
period. The rotation period from this data (alone) is estimated to be
~24.6 hours. The amplitude (half of peak-to-peak) is 0.42 magnitude. I
hesitate to give SE uncertainties since I've been wrong about this
several times in the past week.
Note that using a sinusoid is just a first approximation for fitting an
asteroid rotation light curve. Shape matters, and all real asteroid
shapes produce light curve shapes that depart from sinusoidal.
Analysis Procedure Used by BLG
The procedure used by BLG for reducing images to asteroid magnitudes
involves two analysis phases. The first phase transfers magnitudes from
Tycho stars in the FOV to secondary stars near the asteroid's path. The
second phase uses these secondary calibration stars to determine the
magnitude of the asteroid in sets of 3 median combined images.
The first phase consists of the following: calibrate raw images (dark
and flat), median combine neighbor sets of 3 images using stars for
alignment (MCs images), median combine the same 3 images using the
asteroid for alignment (MCa images), read intensity of MCs Tycho stars
for several images, determine extinction and zero-shift parameter in a
spreadsheet, use these extinction and zero-shift values to determine
magnitude of stars near the asteroid's path, adopt the average
magnitude for these secondary calibration stars for use as reference
stars.
The second phase consists of the following: perofrm two
median combines for each set of 3 images, one aligned using the
asteroid and the other aligned using the stars. Intensity readings are
made of the (three) secondary reference stars on the MCs images, and
intensity readings are made of the asteroid on the MCa iamges (placing
the photometry pattern so as to minimize the influence of background
level biases). These intensity readings are entered in a spreadsheet
that has been prepared for this specific analysis procedure. A block of
cells for each image is used to establish an extinction for that image
in a way that produces reference star magnitudes that agree (on
average) with those adopted in the first phase of analysis (taking into
account the image's air mass). The zero-shift and extinction values
allow for a conversion of the asteroid's intensity to be converted to a
magnitude.
This analysis procedure may be unique in the way it allows for asteroid
motion between images. Notice that all intensity readings are done with
images that have cosmic ray defects removed and SNR enhanced by median
combining. Also note that the median combining is performed separately
for images intended for reference star intensity readigns and asteroid
intensity readings. This median combining using the asteroid for
alignment requires that the asteroid can be seen in each image, which
places a practical limit on how faint the asteroid can be for using the
procedure. For an asteroid moving at the rate of 2004 MN4 when these
observations were made (~3.8 "arc/minute) the longest exposure time for
avoiding oval asteroid source functions was 60 seconds for my image
scale of 2.8 "arc/pixel. For a 14-inch aperture telscope and 50-second
exposures the faintest asteroid for which this method can work is about
V-mag = 18. For a larger telescope, such as 32-inch aperture, the
limiting asteroid magnitude ~ 20 (unless sophisticated techniques are
used to anticipate the asteroid's pixel location.)
Raoul Behrend's Analysis
Raoul Behrend has combined this data with measurements by Yassine
Damerdji and the early data by VVR and BLG to produce a new period of
22.97 +/- 0.14 hours. The amplitude
for the solution of the data in the previous figure (0.27 +/- 0.10
magnitude) is compatible with the 0.3 +/- ~0.05 magnitude amplitude
given
by Behrend using the combined data. The combined data calculated by
Raoul Behrend can be found at Raoul Behrend's
rotation light curves . The light curve solution at this site is
likely to change as new observations are added to the analysis.
Here's my version of Raoul Behrend's rotational light curve period of
1.2733 +/- 0.0026 days, fitted to the data available to me (VVR and
BLG).
Figure 4. Adopting Raoul Behrend'srotation period solution
of 1.2733 days (30.6 hours) and allowing for zero-offset adjustemtns,
it is possible to achieve an acceptable fit to the VVR and BLG
observations.
___________________________________________________________
This site opened: January 9,
2005. Last Update: February
5,
2005