Tech Note 102: The Mark IV "Patch" dataset
Michael Richmond
Jul 21, 2006
Jul 27, 2006
Aug 2, 2006
Aug 19, 2006
Keywords: astrometry photometry calibration
The entire TASS Mark IV dataset contains a large number
of spurious detections, due a number of factors:
cosmic rays, satellites, airplanes, noise peaks,
etc.
In order to produce a reliable subset,
one must apply a set of rules which discard
the mistakes and admit the good measurements.
This Tech Note describes one attempt to create a
reliable subset,
which I call the "patch" method.
A small amount remains to be done before this dataset is ready for
wide distribution
MWR 8/2/2006
Contents:
Breaking the sky into "patches"
The basic idea is to break the entire sky up into
little "patches", choose objects which appear multiple
times in each patch, and run an ensemble solution
on the patch.
Objects which appear in the output of the ensemble
solution become members of the "patch" dataset.
We can perhaps use the ensemble photometry to help
choose further subsets of even more reliable stars.
Why use little patches?
Earlier work
(see
Tech Note 97 )
revealed significant photometric errors
as a function of position in each 4x4-degree Mark IV image.
If a star happened to fall in the upper-right corner
of an image one night, but the lower-left corner
on the next night,
its measured magnitude might vary by as much
as 0.05-0.10 magnitudes.
However, this large-scale error would apply
nearly equally to all stars within a small
portion of an image.
By dividing the sky into regions just 1x1 degree
on a side -- less than one-sixteenth of an entire image --
and looking at the relative measures of
the stars within each region,
I hoped to find and remove some of the
spurious variation.
Let me describe the procedure in more detail.
- I started with the contents of
the Mark IV Engineering Run database
as of April, 2006.
At that time, the database contained
roughly 9 million unique objects,
with an average of roughly 200 measurements
per object.
The number of objects increased during the two
months it took me to transfer the data
to Rochester.
Recall that the Mark IV database, until recently,
required simultaneous V-band and I-band detections
for each object. I believe that single-band
detections are currently being measured and
stored in the database, but they are a small fraction
of the total.
- I defined a patch as a square region of the sky,
one degree on a side. These patches are arranged in
strips of constant Declination. Each patch has two
neighbors in the same Dec strip, sharing 0.25 degrees
of area on the East and West.
The strips above and below also overlap by 0.25 degrees in
Declination. However, there may be an
offset in RA between the patches in one Dec strip
and the patches above it, and this offset may change
gradually along the strip.
Thus, some stars -- those near the center of patch --
will appear in only a single patch.
Stars near the borders will appear in at least two patches,
and those near the corners may appear in up to four patches.
The Dec strips are centered at intervals of 0.75 degrees,
starting at Dec = -5.0 and ending at Dec = +87.7 degrees.
The Mark IV survey covers very little area south of Dec = -5.0,
and the
pipeline software
does not handle astrometry properly
very near the North Celestial Pole.
There are 39,885 patches in my analysis.
- For each patch, I grabbed all the measurements of all objects
falling within the boundaries of the patch.
Objects falling within the regions of overlap
between patches were grabbed multiple times.
I grouped together measurements taken from
a single Mark IV image.
- I subjected the measurements within each patch
to inhomogenous ensemble photometry ,
which is described clearly in
a paper by R. Kent Honeycutt,
CCD ensemble photometry on an inhomogeneous set of exposures
in Publications of the Astronomical Society of the Pacific,
volume 104, page 435 (1992).
You can read more about this procedure in
the ensemble package manual ;
skip to the end of the document for an example
using some real data.
I placed limits on both images and stars:
in order for an image to be included in the ensemble,
it had to have measurements of at least 25 stars,
and at least 10 of those stars would have to match
the template image for the ensemble;
in order for a star to be included in the ensemble,
it had to appear in at least 5 images.
In the great majority of cases, the patch yielded
a good ensemble solution. Below is a histogram
showing the number of stars in the ensemble solution
for each patch.
There were a very small number of patches which did
not produce good ensemble solutions under these
conditions. 148 patches (0.37 percent of the total)
had fewer than 20 stars in their output.
Most of these were near the galactic pole, where
the stellar density is very low.
The cumulative stellar density near the galactic poles
is roughly 20 per square degree down to photographic
magnitude 12, or 50 per square degree down to
photographic magnitude 13 (from Allen's Astrophysical Quantities,
p. 244, 1973).
For these 148 patches, I reduced the number of stars
per image to be only 20, instead of 25.
After this step, 8 patches still failed to produce a
valid ensemble solution. I modified the limits
by hand for each patch until it produced a valid solution.
In these patches, some stars appear only 3 or 4 times.
- Stars which appeared in the output of the ensemble solutions
became part of the patch dataset
which is the subject of this Tech Note.
I will describe properties of these objects
in the following sections.
Properties of the Patch Dataset
Stars might appear in the output for a single patch,
or they might appear in several patches.
I sifted through the output for all patches,
gathering in a single place the results for
each individual star.
I then applied a series of calculations to
each star:
some using the "raw" measurements from the
Mark IV Engineering Database,
some using the ensemble output values.
The dataset includes
4,359,956 objects,
which I will call "stars" from this point onward
for convenience.
Number of measurements
How many times was each star measured?
The mode is around 10 times,
the median 25, and the mean 37.
The total number of measurements is 162,650,980 --
that's more than eighty percent of
the total number of measurements (about 190 million)
in the
Mark IV Engineering Database
as of July 21, 2006.
For convenience, I created two small random subsets
of the entire patch dataset --
it just took too long to make graphs using over
four million points.
A "small" subset contains 1 out of every 1,000 stars:
it has 4,359 items;
a "large" subset contains 1 out of every 100 stars;
it has 43,599 items.
Internal precision of photometry
What is the internal precision
of magnitude measurements?
By "internal", I mean the scatter
around the mean value within the patch dataset;
I will leave "external" statistics --
comparisons against other photometric catalogs --
for a later section.
I computed this precision in three ways:
- using the standard deviation from the mean magnitude,
computed using values in the Mark IV Engineering Database
(the "raw" values)
- using the standard deviation of ensemble output magnitude
values around the ensemble mean
(the "ensemble" values)
The first method will suffer from the systematic photometric
errors across the wide Mark IV field,
and from isolated outliers
due to cosmic rays, satellites, etc.
The second should get rid of most of the
large-scale systematic errors.
Let's look at the V-band photometry first.
The "raw" scatter is shown in red in the figure below;
the "ensemble" scatter is shown in green,
displaced from the origin for clarity.
Just as expected, the scatter in the ensemble
solutions is smaller than in the raw measurements.
Now the I-band photometry.
Again,
the "raw" scatter is shown in red in the figure below;
the "ensemble" scatter is shown in green,
displaced from the origin for clarity.
Again, the scatter in the ensemble
solutions is smaller than in the raw measurements.
In both cases, note that the noise floor
for the brightest stars shrinks from
about 0.05 magnitudes
to about 0.02 magnitudes.
I believe this indicates that the size of the
large-scale photometric errors across
the Mark IV images was roughly 0.04 mag.
Internal precision of positions
How good are the positions of stars?
Below are graphs showing the standard deviations
from the mean positions, with
red points for Right Ascension and
green points for Declination.
First, as a function of V-band magnitude:
And now as a function of I-band magnitude:
We see that the scatter in each individual measurement
of position rises from less than 0.5 arcsec
at the bright end to about 3.5 arcsec at the
faint end.
Note that the scatter is very slightly larger in
Right Ascension than Declination,
which may be due to slight trailing in RA.
There is additional evidence in
a comparison of Tycho2 and TASS positions
later in this document.
Variability: the "varmult" and "wsphot" indices
The ensemble solution provides a measure of the scatter
of each star around the mean;
it creates rough averages of this quantity
as a function of magnitude,
and then computes for each star
(scatter for this star - avg scatter)
varmult = -------------------------------------
avg scatter
A well-measured variable star should have values of this
varmult quantity which are
significantly above 1.0.
Now, since this quantity is computed using only
the stars in a single ensemble (a few tens to a few hundreds
of stars), it can be noisy:
the characterization of the typical scatter as a function
of magnitude can be poor, due to the small number
of stars which may fall into a bin.
Still, this statistic may prove useful for identifying
candidates for variable -- or constant -- stars.
Below are histograms of the varmult
values for each passband.
In each passband,
we see that the histogram is roughly centered on zero --
good --
but has asymmetric wings:
there are an excess of stars with large positive values.
Good!
The large values might be due to real variability,
or due to a few bad measurements.
We don't know yet....
If a star really does vary significantly,
it will probably do so in both passbands.
We would then expect the varmult values
to be large and positive in both passbands.
Let's compare them, star-by-star, and see:
Yes, there is a correlation between the
amount of scatter in the two passbands.
Some types of contamination -- an airplane
flying through the field in one image --
could affect measurements in both passbands
in a similar way, so we must still be cautious.
Another indicator of variability is the
Welch-Stetson variability index ,
or "wsphot" for short.
This was defined in the paper
Here's the relevant excerpt from their paper.
The variability index will be close to zero for stars with
random variations which are independent in each passband,
or stars which vary by less than the uncertainty of
each measurement.
It will be a large (greater than 2 or 3) positive value
for stars which really do change significantly in brightness.
I looked at the big random subset of all stars to determine
rough values for the uncertainty in a single magnitude
measurement as a function of magnitude in each passband --
we need that to compute the wsphot statistic.
I then computed the WS variability index for every star.
Here is the distribution of its values:
The great majority of stars have values
close to zero, suggesting that they are constant
to within our ability to measure.
But there is a tail of values in the positive direction,
as we would expect for variable sources.
We have two statistics which ought
to tell us something about the variability of a star.
If both are meaningful, then they ought to
agree with each: a truly constant source
should have a small value in both methods,
a truly variable source ought to have
a large positive value in both methods.
Let's plot the varmult index against the
Welch-Stetson index on a star-by-star basis:
The great majority of stars lie close to the origin
in both measures --- good.
Note that most of the points far from the origin
lie in the first quadrant of the graph:
they have large positive values for both methods.
Again, good.
Not all the stars which lie in the first quadrant
must be real variables -- there are objects which
have one or two very bad measurements --
but we can hope that a good fraction
of them may truly vary.
They will be good candidates for further followup.
Likewise, stars which lie near the origin of this
graph are almost certainly constant in light.
Variability in position: the "wsastro" index
The Welch-Stetson technique relies on having two
independent measurements of a star;
if they both change in a systematic manner with time,
then that change is probably not due to random
measurement errors.
One can apply the idea to measurements of position
as well as magnitude.
I defined a quantity based on the difference between
each recorded position of a star and its average position:
(this RA) - (avg RA)
delta_RA = --------------------------------------------------
typical scatter in RA for star of this brightness
(this Dec) - (avg Dec)
delta_Dec = --------------------------------------------------
typical scatter in Dec for star of this brightness
[ 1 ]
wsastro = sqrt [ ------- ] * Sum ( delta_RA * delta_Dec )
[ n(n-1) ]
If a star is not moving, then the value
of this wsastro statistic should be
close to zero.
If a star does happen to move in a significant
and systematic manner (very unlikely, as this
would require a proper motion on the order of
arcseconds per year),
the statistic will under some circumstances
be a large value --
either positive or negative, depending on the direction
of its motion.
Unfortunately, if a star happens to move nearly
in a East-West or North-South direction,
this statistic will yield a value near zero
(since one of the two factors in each product
will move randomly around zero, with both
positive and negative signs in roughly equal numbers).
Thus, this method cannot yield any
"complete" sample of proper motions.
A histogram of the values of this statistic is shown below.
The great majority of values are close to zero,
as expected.
There are a small number of outliers
which are candidates for further attention.
I checked out the stars yielding
a few of the largest positive values in this subset:
in each case, the star was relatively
close -- within 80 arcseconds --
to a brighter neighbor.
I suspect that what is happening
is that in just a few of the images,
the brighter star's light contaminated the
fainter star's position,
causing its position to lie far from the average position
(but still close enough to be assigned to this
faint star in the database).
We can check that idea,
that outliers in the wsastro index may
be due to confused companion stars.
If the light of a companion influences
the measurement of position, it might
also influence the measurement of magnitude.
Let's see if there is a correlation between
outlying values in the
Welch-Stetson photometric index wsphot
and astrometric index wsastro.
Below is a graph showing all values:
Three of the four largest outliers in photometric index
are also far from zero in the astrometric index.
If we zoom in, we see that this is true of
some less prominent outliers as well.
However, there are also groups of stars
which have large values in one index, but not the other.
Samples from the "patch" dataset
The information available for each star consists of
22 elements.
I have created simple ASCII text files with this information,
one line per star.
The columns in each line are:
- ID number inside the Mark IV Engineering Database (integer)
- number of measurements (integer)
- mean of all measured Right Ascension values, in
decimal degrees and equinox J2000.0
(floating point)
- standard deviation from the mean RA value,
decimal degrees
(floating point)
- mean of all measured Declination values, in
decimal degrees and equinox J2000.0
(floating point)
- standard deviation from the mean Dec value,
decimal degrees
(floating point)
- number of valid magnitude values used
in the V-band photometric ensemble
(integer)
- mean of all measured V-band magnitude values
(floating point)
- interquartile mean
( see note on iqm below )
of V-band magnitude values
(floating point)
- average of output mean V-band ensemble values
in all patches in which this star appeared
( see note on ensemble mean below )
(floating point)
- standard deviation from the mean V-band magnitude value
(floating point)
- average of output stdev V-band ensemble values
in all patches in which this star appeared
( see note on ensemble stdev below )
(floating point)
- number of valid magnitude values used
in the I-band photometric ensemble
(integer)
- mean of all measured I-band magnitude values
(floating point)
- interquartile mean
( see note on iqm below )
of I-band magnitude values
(floating point)
- average of output mean I-band ensemble values
in all patches in which this star appeared
( see note on ensemble mean below )
(floating point)
- standard deviation from the mean I-band magnitude value
(floating point)
- average of output stdev I-band ensemble values
in all patches in which this star appeared
( see note on ensemble stdev below )
(floating point)
- average of output varmult V-band ensemble values
in all patches in which this star appeared
( see note on varmult below )
(floating point)
- average of output varmult I-band ensemble values
in all patches in which this star appeared
( see note on varmult below )
(floating point)
- Welch-Stetson photometric variability index
(floating point)
- Welch-Stetson astrometric variability index
(floating point)
Notes:
-
iqm = interquartile mean:
-
All values are sorted numerically.
The top quartile (25 percent) and bottom quartile (25 percent)
are discarded, leaving only the half of the measurements
closest to the middle.
The mean of these remaining "interquartile" values is computed.
- average ensemble mean:
-
I don't think this will turn out to be a useful magnitude
for ordinary users;
I include it largely for diagnostic purposes.
The ensemble photometric solution for each patch
produces a list of output differential magnitudes for the
stars. The relative values are accurate,
but there is an arbitrary zeropoint.
To reset the magnitudes,
I computed the difference
between the input (standard) magnitude of each star
and its output
(differential) magnitude,
for all stars in the range
7.5 < V < 12.0 or 8.0 < I < 12.0 .
I then added the average of all these differences
to the output magnitudes.
In other words, I used all the bright (but not saturated)
stars within each ensemble to set the magnitude zeropoint.
This procedure can cause small errors in the
in the output magnitude for all stars in a patch,
especially if the number of stars in the patch is small.
If a star appears in several patches, there will probably
be small differences in its output magnitude for each
patch.
The number in this column is the simple average
of output ensemble magnitudes from all patches containing
the star.
- average ensemble standard deviation:
-
The ensemble photometric solution for each patch
produces both a magnitude for each star,
and the standard deviation of the measurements from that
magnitude (after adjustments have been made to each image).
This indicates the scatter of the measurements for this star
in the ensemble solution.
I averaged these standard deviation numbers for
all the patches containing a star.
- average ensemble varmult:
-
Based on the
ensemble photometric solution for each patch,
we can estimate the typical scatter in magnitude measurements
as a function of magnitude:
it will be small for bright stars and large for faint ones.
The varmult statistic is the ratio of the scatter
for a particular star to the scatter for other stars
of similar brightness.
If a star appears in several patches, the value in the
table is the average of varmult in each patch.
You may grab samples of data in this format.
The entire dataset is so large --
about 776 MBytes --
that I have not yet figured out a way to
distribute it properly.
It is also possible that
I might add or remove some quantities
from the dataset before making
it "official."
Photometric calibration
The pipeline which reduces Mark IV images performs a preliminary
photometric calibration for each night's data as a group.
It compares the measured instrumental magnitudes to
values generated for a subset of the Tycho-2 catalog,
using transformations
V' = Vt + 0.008 - 0.0988*(Bt - Vt)
I' = Vt - 0.039 - 0.9376*(Bt - Vt)
where Bt and Vt are the Tycho-2 magnitudes,
and V' and I' are the preliminary standard
magnitudes.
Each night's photometry is placed into the database.
As described in the sections above,
I computed the interquartile-mean (IQM) for V-band
and I-band magnitudes of each star in the database;
I'll refer to these as "original" magnitudes.
Let us now compare these original magnitudes
to the standard Johnson-Cousins magnitudes
for stars described by Landolt
in a pair of papers.
I pruned the Landolt stars in several ways.
First, because the Mark IV images have a very large pixel size,
about 7.5 arcseconds, the aperture used to measure starlight
is very large: a circle 4 pixels (= 30 arcseconds) in radius.
This is larger than most of the apertures Landolt used
to measure the stars: his diaphragms ranged from 14 down to 5
arcseconds in radius.
Therefore,
I used the Vizier service to cross-match the list of
Landolt standards against the USNO B1.0 catalog,
and searched for neighboring stars which might be bright
enough to influence the measurement within the
large TASS aperture.
I discarded Landolt stars which had neighbors
within 60 arcseconds which were less than
2 magnitudes fainter than the target.
Stars which survived this first step
I call the cleaner subset.
Second, I tried to remove stars which might vary
in brightness with time.
I used Vizier to search for items in the
Combined General Catalogue of Variable Stars
(Samus N.N., Durlevich O.V., et al., 2004)
which were within 60 arcseconds of each Landolt star,
and discarded any stars with matches.
I also examined the TASS measurements themselves,
and removed
stars with internal scatter far above the typical level
for their magnitude.
Stars which survived this second pruning
I call the isolated2 subset.
I compared the surviving list of Landolt standards
against items in the
TASS patch dataset.
Using a matching radius of 10 arcseconds,
I found 153 matches,
of which 99 fell within
the range of most reliable TASS photometry:
8.0 < V' < 12.5
7.5 < I' < 12.5
Below are graphs showing the difference between the
Landolt and "original" TASS magnitudes for these
stars, in the sense Δ = (Landolt - TASS).
Please focus on the large red dots in the graphs below,
which should be the most reliable.
The V-band differences appear to have a relatively wide
spread. The brightest stars show negative values
of (Landolt - TASS), due to saturation in the Mark IV images.
Although the scatter is very large for the faintest stars,
there appears to be a systematic shift in the opposite
direction: the TASS measurements are brighter,
on the average, than the Landolt values.
In the I-band, we again see the effect of saturation
for the brightest sources.
Most of the stars fall within a band which is narrower than
that of the V-band differences.
At the faint end, there is no obvious systematic bias,
though one might guess at a shift towards negative
values -- TASS measurements might be fainter
than the Landolt ones.
Are there systematic differences due to the color of the
stars?
We can plot the differences against the (V-I) color
of the stars to check.
In the diagrams below,
I use small black crosses to show the residuals
for all stars,
and large blue circles to indicate
the stars within the range of best TASS photometry
(excluding the saturated bright end and noisy faint end):
8.0 < V' < 12.5
7.5 < I' < 12.5
There does appear to be a systematic effect in the V-band
residuals: red stars are seen as brighter than blue stars.
The reddest star, at (V-I) = 2.3, is G163-51, a dwarf of
spectral class M6. The lines drawn on the diagram show
linear fits to residual as a function of color: the red line
includes G163-51, while the cyan line excludes it.
I prefer to exclude this star, since it's very difficult
to compare measurements of extremely red stars through
different instruments.
An unweighted linear least-squares fit to the data
within the good magnitude range yields
(Landolt V - TASS V') = -0.03534 + 0.09362*(TASS V' - TASS I')
where the uncertainty in the slope is +/- 0.0288; thus, the slope
is non-zero at significance of roughly 3.2-sigma.
The scatter from the line is about 0.052 magnitudes.
Now, let's examine the I-band residuals as a function
of stellar color.
There is no trend with color in this case;
formally speaking,
a linear fit to the residuals yields a slope
of 0.0067 +/- 0.0274, consistent with zero.
Again, we see a constant offset of about 0.05 magnitudes
between Landolt and TASS.
After performing a single round of 2-sigma
clipping of the residuals,
I derive a mean offset of
(Landolt I - TASS I') = -0.0503
So, I propose to correct the "original" TASS magnitudes
stored in the Mark IV Engineering Database by the following
procedure:
corrected TASS V = V' - 0.0353 + 0.09362*(V' - I')
corrected TASS I = I' - 0.0503
After making these corrections, the differences between the
Landolt and TASS measurements are
unclipped V mean -0.0151 stdev 0.0356 N = 97
clipped V mean -0.0115 stdev 0.0284 N = 91
unclipped I mean -0.0097 stdev 0.0351 N = 97
clipped I mean -0.0052 stdev 0.0239 N = 90
where clipped refers to a single iteration
of removing items more than 2 standard deviations from the mean.
Checking the photometric calibration against Henden sequences
To check the calibration of the Mark IV photometry,
I used a large set of sequences of stars
near interesting targets,
measured by Arne Henden.
I began by choosing stars which
- were measured by Henden at least 3 times and
- had mean V-band magnitudes brighter than 15.0 and
- had standard deviations from the mean of
less than 0.1 mag in V, (V-R) and (R-I), and
- had standard deviation in I,
estimated as the sums of uncertainties
in V, (V-R) and (R-I) added in quadrature,
of less than 0.15 mag
There were 6986 stars which satisfied
these criteria.
Next, I removed stars which
might be variable,
by cross-matching against the GCVS with a radius of 30 arcseconds.
Finally, I made a loose check for
crowding by looking within the remaining
6265 stars
for objects which appeared within 30 arcseconds,
or 60 arcseconds, of another object.
There were
4228 stars within the first (iso30) subset,
and 1948 stars within the more stringently isolated (iso60) subset.
I then matched items in these subsets of Henden's
sequences against stars in the TASS patch dataset.
Shown below are the differences in photometry,
in the sense Δ = (Henden - TASS) .
The small red dots show residuals from the
"original" TASS measurements,
while the large black dots indicate
residuals from the corrected TASS magnitudes.
First, the V-band:
There are a number of outliers in the positive direction
(TASS values brighter than Henden)
even among bright stars;
I inspected these outliers and found that most are caused
by neighbors which fall within the large TASS aperture.
Overall, there appears to be a small bias towards
negative values, by a few hundredths of a magnitude.
There is also evidence for a growing trend in the negative
direction for the faintest stars.
Now, the I-band:
This graph is very similar to the V-band graph.
We see again very large positive outliers due to
crowding.
The significance of a systematic trend to negative residuals
for faint stars is stronger in I-band
than in V-band.
Comparing TASS astrometry to Tycho-2 and Henden
The TASS Mark IV pipeline uses a subset of the Tycho-2 catalog
to determine the position of objects in each image.
How good are the positions?
Let's find out.
There are three factors to keep in mind:
- the pixel size of the Mark IV is about 7.5 arcseconds,
which means that neighboring stars may appear
as a single blob in crowded regions
- the large pixel size also causes best sub-pixel centering
of an isolated star to have a relatively large
uncertainty (compared to typical optical images
with pixel scales of less than 1 arcsecond per pixel)
- the very wide field of Mark IV images -- over 4 degrees
on a side -- means that there are significant distortions
across each image.
The standard pipeline processing uses a cubic
model for the relationship between (row, col)
and (RA, Dec),
as described in
the documentation for "match"
For all these reasons, we can expect positions computed by
the Mark IV pipeline to be significantly less precise
than those quoted in "typical" astronomical references.
The
Minor Planet Center,
for example,
requires observers to measure the positions of asteroids
with precisions of (significantly) better than 1 arcsecond.
First, let's compare the TASS "patch" dataset mean positions
to the positions from the
Tycho-2 catalog.
For convenience, I picked a subset of all Tycho-2 stars,
those with particularly good photometry;
you can find the details and the entire subset at
http://spiff.rit.edu/tass/tycho/tyc2_photom.dat .
The entire subset contained about 360,000 stars,
but half of those were in the southern celestial hemisphere
not observed by TASS.
Using a matching radius of 10 arcseconds, I found
a total of 178,608 stars in common between the
"patch" dataset and this subset of Tycho-2.
The differences between the Tycho-2 and mean TASS positions,
in the sense (Tycho2 - TASS), are
differences in arcseconds
(Tycho2 - TASS) mean stdev median
------------------------------------------------------------------
delta (Right Ascension) -0.005 1.000
delta (Declination) +0.011 0.661
delta (total) +0.574 1.051 0.290
------------------------------------------------------------------
No systematic differences, and a typical difference
of less than one arcsecond. Note that the Right Ascension
measurements have a larger scatter than the Declination
measurements,
which suggests further
(as in the
"Internal precision of positions"
section)
that the Mark IV PSF was slightly
trailed in the East-West direction;
this is no surprise given the simple nature of the
Mark IV mount and RA drive.
Below are histograms showing the differences (Tycho2 - TASS)
graphically.
We can also compare the TASS positions to those
in Henden's sequences.
Since the Henden data goes much fainter than the
Tycho-2 data, we can look for any dependence on magnitude.
The "isolated 60" subset of Henden's data includes
stars which should be relatively free of nearby neighbors.
I broke this group of 486 stars into two groups:
- "bright and isolated" V < 12.5, 181 stars
- "faint and isolated" V ≥ 12.5, 305 stars
A plot of the vector differences between Henden's positions
and the mean TASS positions, in the sense (Henden - TASS),
is shown below:
The bright stars appear to have slightly more accurate
positions.
The statistics bear this out:
total differences in position (arcsec)
subset N mean stdev median
----------------------------------------------------------------
bright and isolated 181 1.02 1.20 0.70
faint and isolated 305 2.19 1.77 1.75
----------------------------------------------------------------
It appears that bright stars are measured more accurately by
TASS than faint stars.
This is likely due due to
a combination of simple shot noise in the images
of faint stars -- they have too few photons to determine
a sub-pixel centroid accurately --
and to the increasing asymmetry in the images of
stars near the edges of the field with faintness.
That is, in regions where the PSF is asymmetric,
faint stars will lose their extended wings,
causing the algorithm in the Mark IV pipeline
to find a centroid offset with respect to the
asymmetric images of bright stars.
The Mark IV pipeline measures stellar positions in the following
way: it initially finds the peak pixel belonging to an object,
then focuses on pixels within a square box centered on this peak.
After subtracting a sky value from these pixels, the routine
computes marginal sums in each direction, along rows and along columns.
The program then fits a 1-D gaussian to the marginal sums to
find the centroid in each direction.
The Mark IV "patch" dataset is certainly not
a good astrometric catalog.
However, it does provide positions accurate enough
to match TASS objects against
entries in other optical or infrared catalogs,
outside of crowded fields.
Systematic differences between Mark IV units?
There are three Mark IV units, each of which contains a
V-band telescope and camera, and an I-band telescope and camera.
The units scan different regions of the sky:
- TOM1 has images centered on strips with -04 < Dec < +16
- TOM2 has images centered on strips with +20 < Dec < +48
- TOM3 has images centered on strips with +52 < Dec < +88
There are regions of overlap in which some stars are
measured by two cameras.
I looked for differences in the magnitudes of stars
in these overlap regions.
The data I chose came from two sets of patches:
- where TOM1 and TOM2 overlap, patches centered on Dec = +18.2
- where TOM2 and TOM3 overlap, patches centered on Dec = +50.2
I chose only patches in the range 250 < RA < 360,
where the stellar density was highest.
Each set of patches covers a long, thin strip of the sky,
one degree wide in Dec and about 100 degrees long in RA.
I started with stars which had at least 5 measurements
from each unit.
I isolated the measurements from each unit and
computed the mean and standard deviation;
then I calculated the difference between the mean
magnitudes, in the sense
delta_mag = (TOM2 - TOM1) for the strip around Dec = +18.2
delta_mag = (TOM2 - TOM3) for the strip around Dec = +50.2
Let's look at some graphs of the differences, plotted
against various quantities.
I'll summarize the results afterwards.
First, the (TOM2 - TOM1) unit differences, around Dec = +18.2.
Now, the (TOM2 - TOM3) unit differences, around Dec = +50.2.
A brief summary of the results is that
- there are systematic differences between units
- the differences are roughly equal to or smaller than
the standard deviation from the mean for
an individual unit
- the differences do depend on magnitude and Dec
- the differences do not depend on color or RA
I can explain these results.
Recall that the field of view of each Mark IV image is about 4.2 degrees.
There are systematic changes in the PSF across this wide
field, which are largest at the edges and corners.
The stars in these overlap samples will appear near the
top edge of images from one unit,
and the bottom edge of images from the other unit.
The calibration pipeline
for all units considers all the stars in one image at a time:
it uses a set of Tycho-2 stars in the image -- which will
be scattered all over the image --
to set the zeropoint in each passband.
If the PSF near the top of an image differs from the PSF near
the center of the image,
then the measured instrumental aperture magnitudes
for stars at the top will be, say, smaller than those
near the center.
The calibration procedure will average over all stars,
adding the same constant shift to all instrumental magnitudes.
Thus, if stars the near top have instrumental magnitudes
which are (for example) fainter by 0.03 mag than stars near
the center,
then the calibrated magnitudes of these stars near the top
will likewise be 0.03 mag fainter than stars near the center.
In short, we expect to see systematic errors in photometry
as a function of position in the field.
Survey operations led to images which always have very nearly
the same Dec position, but vary in RA from night to night.
That means that position-dependent errors will be averaged
out in RA, but remain in Dec.
And that is what we see.
These systematic errors will be proportionally larger for faint
stars than bright stars, because the centroid of
faint stars will be affected more strongly by changes
in the PSF than the centroid of bright stars --
because the changing wings of the faint stars will
be influenced by background noise more than the stronger
wings of bright stars.
Thus, errors which depend both on magnitude and on position
within a frame.
Last modified 08/02/2006 by MWR.