Replaced all Vesta albedo
plots on the Vesta summary page with ones based on G = 0.28 (I
won't place them on this page). Finished processing Apr 14 Ceres
data & re-processed Mar 20 & 23 Ceres data for use of G =
0.12. The albedo spectrum based on Apr 14 data (longest observing
session) is shown below
Decided to adopt the phase effect given by the
HG equations and G values shown on the plot below.
More bands for Vesta albedo vs rotation phase. A
better presentation of all Vesta data, summarized, can be found at
the Vesta Summary web page (linked above). All Vesta geometric
albedos in the graphs below will be adjusted downward by ~ 2%
after I implement a revised phase effect model (using G = 0.28).
[Note: the plots for this date have been superseded by ones
located in the Vesta summary web page.]
Summary of Vesta albedo vs wavelength for 5 rotation phases.
Summary of Vesta albedo vs. rotation phase for 8 bands.
Vesta albedo at 966 nm for 5 observing sessions.
Vesta albedo at 915 nm for 5 observing sessions.
Vesta albedo at 828 nm for 5 observing sessions.
Here's a Vesta albedo vs. rotation phase for the
548, 649 & 748 nm bands. They are less noisy than the 429 nm
band data due to lower atmospheric extinction and lower levels of
systematic errors due to extinction trend corrections.
Albedo at 548 nm for 5 observing sessions.
Albedo at 649 nm for 5 observing sessions.
Albedo at 748 nm for 5 observing sessions.
Obs'd Vesta all night last night (1.3
rotations), & have processed Ch2. A significant temporal trend
in extinction required that I incorporate a trend term in the
spreadsheet analysis. In order to obtain shape information for a
plot of albedo vs. phase I created a graph that employs arbitrary
offsets (averaging 0.1 ± 0.9 %) that are applied to each observing
Albedo at 429 nm for 5 observing sessions.
Added Ceres albedo result for Mar 23 image set.
I don't know if the differences are real until we get more data on
phase-folded light curve. The 748 nm "dip" feature is not present
in the Mar 23 data, so I suspect the dip is not real (I
double-checked analysis for it & couldn't find an error).
Geometric albedo spectrum for one phase (Mar 20 & 23), made
at different dates & phases.
I've begun processing Ceres data
(available for Mar 20, 23 & 25). I've adopted a G value of
0.09 (which ~ doubles flux for phase of 12 deg). This G value is
uncertain, ranging from 0.05 to 0.12 in the literature, so I chose
an average value.
Geometric albedo spectrum for one phase (Mar 20).
Changed adopted Vesta radius to 260 km (from 265
km) & replotted geometric albedos.
All geometric albedo measurements for 3 bands and smoothed
version (median running filter).
Obs'd last night, 5 hrs; first session
emphasizing asteroids (vs. calibrating secondary stars). Processed
S2 and Vesta image sets. Data are generally compatible with
previous (sparse) data. Amplitude of variation with rotation is ~
Phase-folded rotation light curve for 3 of the 8 bands
available from 4 observing sessions.
Geometric albedo for Ch 5 & 7 (748 & 915 nm)
vs. phase for 4 observing sessions.
Data is binned by rotation phase and averaged, then plotted
All Vesta albedo data has been smoothed and plotted vs
rotation phase and wavelength.
Here are another two ways to plot Vesta
albedo vs wavelength & rotation.
Data is binned by rotation phase and averaged, then plotted vs.
All Vesta albedo data has been smoothed and plotted vs rotation
phase and wavelength.
Determined rotation period to be 5.3408 ±
0.0010 hours, based on Jan 28 and Mar 20,23,25 comparison
(corrected for STO change). Below is a plot of Vesta magnitude vs.
rotation phase for a sampling of bands.
Revised phase-folded rotation light curve for 3 of the 8 bands
available from 3 observing sessions.
The next plot shows albedo vs. rotation phase for two bands (the
first 5 data, from Mar 20, Ch 5, at rotation phase ~0.95, are
noisy due to high airmass scintillation).
Geometric albedo for Ch 5 & 7 (748 & 915 nm) vs.
Added Mar 23 Vesta data to phase-fold rotation
Phase-folded rotation light curve for 3 of the 8 bands
available, for all 3 observing sessions available to date.
Processed Vesta obsn's for a 2nd date;
created phase-folded rotation LC showing magnitude for 3 bands.
This is just the beginning of phase-fold analysis because
observing emphasis until now has been for transferring calibration
from Vega to the secondary standards with lower priority for Vesta
and Ceres observations. From now on the observations will
emphasize Vesta and Ceres, using S2 as a calibration star.
Phase-folded rotation light curve for 3 of the 8 bands
Adjusted Vesta geometric albedo for phase effect, using phase
slope of 0.02654 and opposition effect of 0.35 magnitude.
Vesta geometric albedo before & after correcting for
phase (using phase slope = +0.02654 magnitude/degree and
opposition effect of 0.35 magnitude).
Below is a Vesta "light curve" for Mar 25.
Vesta light curve for Mar 25, for 8 bands.
I've finished processing all S1 & S2
image sets (2 & 3 dates). The RMS scatter of 1.9 & 2.6%
implies a SE of 1.3% & 1.8% on the averages. Star A2 has a
scatter of 1.0%, implying a SE of 0.7% for the average of 3
spectra. Each star can serve as a calibration standard for Vesta
and Ceres observations. This concludes my transfer of calibration
from Vega to 3 stars near the Vesta/Ceres part of the sky. Any one
of these 3 secondary standard stars can be used to achieve
acceptable calibration for an observing session of Vesta/Ceres.
Magnitudes of secondary standard stars A2, S1 and S2 (near
Vesta & Ceres), based on Vega being zero magnitude for 3
Processed Mar 25 obsns of Vega & A2
(109 Vir), and was pleased to learn that A2 fluxes for the 3
obseravation dates (Mar 20, 23 & 25) exhibit an RMS scatter of
Magnitudes of secondary calibration star A2 (109 Vir) based on
transfer from Vega as a zero magnitude primary standard.
Because of the magnitude agreement on 3 dates for star A2 it can
serve as a standard for its part of the sky (near Vesta and
Ceres). It will therefore no longer be necessary to observe Vega
(much later in the morning sky) to provide calibration of Vesta
and Ceres observations. Stars S1 and S2 calibrations have not been
completed so I don't know if they can also be used for providing
calibrations in the Vesta/Ceres part of the sky. They're next on
my processing agenda.
Obs'd all last night: S1, S2, A2, Vega,
Ceres, Vesta. Processed rest of Mar 23 data (Vesta & Ceres).
defined = zero) for 3
secondary calibration stars (Mar
20 & 23) and Vesta and Ceres (Mar23).
Comparing the Vesta and Ceres fluxes (from their
magnitudes) enables calculation of albedo. Since I'm
not prepared to apply a phase effect adjustment these
really aren't "geometric" albedo, but they would be if
phase were zero. Since the Vesta and Ceres phases
and 11 degrees, we can expect my albedos to be less than the
"Albedo" for Vesta and Ceres, defined as measured flux divided
by Lambertian flux from flat disk (with diameters of Vesta and
Ceres) and facing the sun. In other words, I've ignored
changes in brightness with phase angle. The geometric
albedo will therefore be slightly greater.
2014.03.24. Temporary hold on processing Mar
20 Ceres & Vesta data in order to process Mar 23 cal
star data (Vega, A2 & S2). Below is a plot of
the Mar 20 & 23 magnitudes for all secondary standard
stars. The A2 overlap is good, whereas the S2 overlap is
Secondary Calibration star magnitudes (Vega
defined = zero) for both Mar 20 & 23.
Table of FC Secondary Calibration
star magnitudes for Mar 23. The equation for
converting magnitude to flux is given.
Comparisons of Mar 20 and 23 mag's are given in
the bottom section.
Caption correction: Flux [watts/m2/um] = Cmf * 1e-8
* 2.5119 ^ (-mag).
The differences between the Mar 20 & 23 magnitudes for
A2 average 0.005 magnitude, with a RMS per filter band of
0.035 magnitude. This is satisfactory.
The differences between the Mar 20 & 23
magnitudes for S2 average 0.032 magnitude, with a RMS per
filter band of 0.043 magnitude. This is not satisfactory.
A third observing session is needed, and it will emphasize
removal of temporal extinction trends (by observing Vega
and S2 when both are high in the sky and can be observed
close together in time).
2014.03.23. Almost done
processing Mar 20 data. Obs'd last night (Vega, A2, S2, Ceres,
Vesta); will take 3 or 4 days to process. I determined a more
accurate magnitude conversions for the two aperture mask holes
(1.0-inch hole = 4.985 ± 0.014 magnitude, 2.5-inch hole
= 3.062 ± 0.013 magnitude); notice that
the accuracy for these conversions is ~ 1.4%. These new
conversion values were used to revise the Mar 20
observations. My hope for the Mar 23
observations is that I'll get the same results for FC
Secondary Calibration star magnitudes as obtained from Mar 20
data. Here's a plot of the revised Mar 20 magnitudes.
FC Secondary Calibration star magnitudes (Vega
defined = zero).
As expected, star A2 is a flat line because it's the same
spectral type as Vega. Also as expected, stars S1 and S2 have
the same spectral "shape" as the sun because they're close to
the same spectral type as the sun. Here's a table of FC
Secondary Calibration star magnitudes.
Table of FC Secondary Calibration star magnitudes. The
equation for converting magnitude to flux is given.
Flux [watts/m2/um] = Cmf * 1e-8 * 2.5119 ^
2014.03.22. I'm still processing the Mar 20 image
sets. All secondary stars that were observed on this date have
been processed and provisional fluxes (& magnitudes) have
been assigned to them. Below is a plot of their fluxes (on a
of secondary standard stars A2 (109 Vir), S1 (beta CrB),
S2 (59 Vir), compared with the re-scaled versions of Vega
and solar spectra.
As expected, the A2 secondary star has a spectrum similar to Vega
(since both have a spectral type of A0V). Als as expected, the two
solar-like stars have a spectral shape similar to the sun's,
although the shortest wavelength band doesn't have the same "drop"
as the sun's spectrum (maybe related to lower metallicity).
An abundance of
extinction slopes continue to support the earlier
determination (this also supports the filter assignments to
The only data from this observing date remaining to be
processed are those for Vesta and Ceres.
2014.03.22. I'm still
processing the Mar 20 image sets. The secondary standard star
S2 has been calibrated.
spectrum of secondary standard stars S1 (beta CrB) &
S2 (59 Vir), compared with the sun's spectrum
Next up: calibration of secondary standard A2 (109 Vir).
Then it will be Vesta and Ceres. When that's done the
analysis for Mar 20 data will be complete.
2014.03.21. I'm still processing
the Mar 20 image sets. The secondary standard star extinction
curves look pretty good.
Extinction plot for secondary standard star S1
(beta Corona Borealis). Dot symbols represent data that exceed
a chi-square acceptance threshold. The dotted traces are
subjective stimates of a SE range.
The Vega extinction curves are noisier, due to 1) using 1-inch
aperture, 2) short exposure times (0.3 to 10sec), and 3)
observing at low elevations (13 - 30 deg). Some cirrus clouds
were noted in my observing log for Vega observations, and they
indeed are present at low level in the extinction plots. A
method for identifying and disregarding the cirrus affected data
has been developed, as the following two plots show.
Vega extinction plot showing unaccepted data with small black
dot symbols (caused by thin cirrus).
Departures from above extinction plot show when thin cirrus
Extinction spectra for S1 and Vega have been obtained, and they
agree, as the following graph shows.
Extinction spectrum for Mar 20 data using stars Vega and S1.
The model fit has 4 free parameters (Rayleigh scattering,
stratospheric ozone, aerosol sccattering and water vapor
burden), all of which have a priori uncertainties for
the chi-square fitting.
The atmospheric extinction model is a strong guide in selecting
an adopted set of extinction values for re-processing all data.
For example, since star S1 provided better quality extinction
estimates than Vega the final Vega fluxes are based on mostly S1
Secondary star S1 (beta Corona Borealis) has been calibrated to
high accuracy from the Mar 20 data. It's spectrum resembles an
"earlier" spectral type than I expected (based on B-V), as the
Flux spectrum of secondary standard S1 (beta CrB), compared
with the sun's spectrum (re-scaled).
Error propagation is now included in the analysis.
Much analysis remains for the Mar 20 data set. Secondary
standards S2 and A2, as well as Vesta and Ceres image sets, are
ready for analysis using procedures developed for Vega and S1.
The latest spreadsheet section for converting measured source
counts (DN), apertures and exposure times to fluxes is shown
Example of spreadsheet section that converts measured source
counts for a standard star (such as Vega) and a target star (such
as S1) to fluxes at each FC band. Aqua colored cells are for
user input (from another spreadsheet page) and the
yellow cells are the "answer" (flux spectrum).
CFW#1 is a r'-band filter. The fluxes at r'-band will be used as
a "sanity check" later because the literature has coefficients
for converting r'-mag to flux. So far the r' fluxes agree with
the flux spectrum based on FC filters, which is another sanity
2014.03.18. Refined non-parfocality focus offsets,
and exposure times for A0V & solar type stars (to assure
capability of sharp imaging when needed). Obs'd S1 (beta CrB),
A2 (109 Vir) and S2 (59 Vir) for practice (there were cirrus
clouds) in converting flux from an A-type star (the A stars in
my list) to solar-type star (the S stars in my list). The image
below is a screen capture of a spreadsheet showing how the A0V
star "A2" (109 Virginis) was used to determine magnitudes for
the sun-like star "S1" (beta Corona Borealis) at two bands. The
star A2 was assumed to be exactly 3.730 magnitudes fainter than
Vega in all bands (good assumption given that A2 has B-V ~
zero), and this permitted approximately correct assignment of
the A2 star's flux for all bands. The zenith extrapolated
magnitudes for A2 and S1 were entered into the spreadsheet and
the fluxes for S1 were calculated (bottom row). Provision is
made for entering which mask hole was used for each star (it was
the 2.5" hole for both stars in this case). More than two
bands weren't processed because this data is unsuitable for such
an analysis due to the presence of cirrus clouds; this is just a
demonstration of how magnitude systems can be created and used
to convert to fluxes.
Demonstration of determining a solar-like star's spectrum by
comparing its magnitude with an A-type star's
magnitude for various filters. CFW# is "color filter wheel #."
"WL Vega" is the Vega flux weighted wavelength for a
band. "WL sun" is the solar spectrum weighted wavelength for a
band. Flux values are in units [watts/m2/micron].
A Spectral Energy Distribution (SED) can be constructed from
the data in the above spreadsheet. The SED version below is for
Fλ [watts/m2/micron], and the sun's Fλ spectrum has been
re-scaled for overlap to show shape similarity. A SED using λFλ using a log-log scale
(commonly used) could also be easily created.
Example of spectrum of target star compared with the sun's
2014.03.17. Obs'd sun-like star "59 Vir" (V=5.3)
for 5 hours with all filters in order to establish a better
quality extinction plot. There are two reasons for doing this:
1) to provide support to my proper identification of which
filters are in the 10-position filter wheel locations (I was
told they went from shortest WL to longest; only 3 had WL labels
and at least they agreed with what I was told), and 2) to
improve atmospheric extinction model for future use (I may need
2nd-order corrections for extinction when I'm transferring
magnitudes from a secondary standard to a target, and if air
mass values aren't exactly the same I'll need to perform small
extinction corrections). The result is given below. This
extinction plot is much better behaved than my first attempt,
made the night before with a much more limited air mass range.
extinction vs. effective wavelength for FC filters for
2014.03.17. Model is a 40 nm wide smoothed version of a high
resolution spectrum incorporating 1.3 x typical aerosol
burden and 5 cm of precipitable water vapor (higher than
expected for this season at my site).
Finalized list of A-type and solar-type stars for
use as secondary standards.
Calibration stars for this task. Vega is the primary
standard (all mag's = zero), while the others are secondary
2014.03.16. Obs'd 3 A-type stars and 3
G-type stars using all FC filters. Determined extinction for all
bands (graph below), and they are compatible with a model
atmosphere. The model includes 6 cm precipitable water vapor
(higher than I think is likely) and 3 times greater than typical
aerosol burden (quite possible given that the previous day was
hazy due to wind-blown dust). Determined magnitude differences
observing through an aperture mask with 1.0- and 2.5-inch holes
that can be flipped open or closed for accommodating very bright
stars (such as Vega): 11-inch to 2.5-inch produces 3.076 ± 0.010
magnitude difference, 11-inch to 1.0-inch produces 5.040 ± 0.010 magnitude difference. A
star with same B-V as Vega was included among the A-type stars
observed; it has B and V magnitudes of ~3.732, so by adjusting
its flux by the factor 2.512-3.732 = 0.0321 it should
be possible to obtain an approximate calibration of the 3
sun-like stars (magnitudes on a scale with Vega as zero for all
bands), which would then allow any magnitudes based on these
sun-like stars to be converted to flux [watts/m2/micron].