Many
amateur astrometrists use the USNO A2.0 or its compressed version, USNO
SA2.0 for calibrating their measures of comets, asteroids and even supernovae. One
reason
for this is the convenience given that the USNO catalogue is widely available,
has a high astrometric precision, covers the entire sky and reaches a limiting
magnitude
(>20)
that is fainter than the limiting magnitude of most amateur observers.
Although
it is preferable to obtain direct photometric calibration in the system
defined by each observers telescope and instrument, through standard astronomical
filters, this
is
beyond the means of most amateur astronomers. A major problem is that photometric
calibration using standard stars can only be carried out in completely
photometric
conditions
and has a very large overhead in times of observing time (typically 1 hour
should be spent calibrating for every 3 hours of total time spent observing).
However, a
CCD
field of view will typically contain tens or even hundreds of stars that
have magnitudes in the USNO A2.0 catalogue. These stars can be used to
calibrate observations
even
in poor conditions with cloud or bad seeing. Having many stars in the field
of view allows "bad" star measures to be eliminated.
A
new version of the USNO catalogue, the USNO B1.0 has just been made available
and adds additional facilities such as proper motion, 5-colour photometry,
and
identification
of extended sources. The new USNO B1.0 averages 3.6 observations each of
more than a thousand million sources. This catalogue is not yet widely
used
though
and it will be some time before most standard astrometry packages are converted
to use it. Its large size (80Gbt) is also an inconvenience to amateur users,
but the
addition
of proper motion is a great improvement given that many nearby stars have
proper motions large enough for their apparent position to have moved considerably
since
the 1950s (a star with a proper motion of 0.1 arcsecs per year will have
moved 5 arcseconds in the 50 years since the original plates used in USNO
A2.0 were taken,
thus
leading to a huge astrometric error).
The
USNO A2.0 and its successors make no claim to be photometric catalogues,
although their photometry is of a good enough level to be valuable if one
understands its
limitations.
The
standard visible magnitude scale is that defined by Arno Landolt in a seminal
series of papers published in the Astronomical Journal in 1982 and 1992.
Landolt
measured
some 750 stars with an accuracy in the milli-magnitude range. Landolt's
stars are mostly in the celestial equator and have a rather bright limiting
magnitude: the
median
magnitude of Landolt's stars is V=13. For the study presented here the
catalogue of stars calibrated on the Landolt system by the IAC has been
used
(González-Pérez,
Kidger & Martín-Luis: 2001, Astronomical Journal, 122, 2055-2098). This
catalogue reaches a limiting magnitude close to V=20, 3 magnitudes fainter
than
the faintest stars calibrated by Landolt.
The
following plot shows the comparison of the widely used USNO A2.0 photometry
with the scale defined by Landolt's standards.
Blue
symbols are USNO A2.0 "B" photometry.
Green
represents the standard approximation to "V" from USNO A2.0 (0.125*(5*R+3*B)).
Red
symbols are the comparison of USNO "R" with Landolt "R".
For
each colour the least squares fit is shown. Click on the plot for the highest
resolution version.
The
plot shows the agreement for stars in four fields from González-Pérez,
Kidger & Martín-Luis (2001, Astronomical Journal, 122,2055-2098):
3C66a; PKS0528+13;
PKS1510-08;
and 3C345. A total of 83 stars are included in B, 87 in V and 89 in R.
This study is provisional and will be expanded to include many more fields
and stars in
the
near future.
We
see that the USNO "R" photometry agrees closely with the Landolt R magnitudes
to R=18. In contrast, the USNO "B" magnitude is significantly brighter
than the
standard
Landolt B magnitude; at magnitude 19 the USNO "B" magnitude is approximately
0.6 magnitudes brighter than the Landolt magnitude (i.e. a magnitude of
B=19.0
in
USNO is equivalent to a true magnitude of B=19.6. We also see though that
at the bright end of the magnitude scale, all three bands are in good agreement
with the
standard
Landolt scale. This result is expected due to the way that the USNO magnitudes
were calibrated (see below).
Results
Transformations
The
photometric transformations that are calculated for the three colours (B,
pseudo-V, and R) to convert USNO photometry to the standard Landolt scale
are:
B:
Landolt = 1.097*USNO - 1.216
V:
Landolt = 1.064*USNO - 0.822
R:
Landolt = 1.031*USNO - 0.417
Unless
specifically instructed to apply the corrections reported here, observers
should report the photometry as measured from USNO A2.0 given that there
is no method of
reporting
whether or not magnitudes are on the USNO scale or transformed to the Landolt
magnitudes. This transformation should normally be carried out by the person
who
receives and analyses your data.
Photometric
accuracy
Here
we treat only the R magnitudes as these are the most widely used and most
amateur CCDs approximate to the R band. We can define two measures of photometric
accuracy:
The
median error in the USNO magnitude is 0.15 magnitudes. In other words,
50% of USNO R magnitudes agree to within 0.15 magnitudes with the Landolt
magnitude.
The
rms error in the USNO magnitude is 0.26 magnitudes. In other words, the
one sigma error in a single USNO magnitude is 0.26 magnitudes and thus
67% of USNO
magnitudes
will be accurate to this level or better.
Note
that both these values include the built-in error that comes from the transformation
of the USNO magnitude to the Landolt magnitude scale. The internal consistency
of
the
USNO R photometry is actually significantly better than these errors.
We
can get an idea of the expectation of the accuracy of a given star by looking
at the following table:
38%
of USNO stars in this study have an R magnitude accurate to <0.1 mags.
62%
of USNO stars in this study have an R magnitude accurate to <0.2 mags.
78%
of USNO stars in this study have an R magnitude accurate to <0.3 mags.
However,
there is a significant fraction of stars with much larger errors:
22%
of USNO stars in this study have an error R in magnitude >0.3 mags.
12%
of USNO stars in this study have an error in R magnitude >0.4 mags.
6%
of USNO stars in this study have an error in R magnitude >0.5 mags.
It
is thus very important to use a reduction routine that uses all the stars
in the field to take photometry and that can eliminate those stars that
are for whatever reason, highly
discrepant.
It is very bad practice and extremely dangerous to use single USNO stars
for photometry.
The
reason for using all stars is two-fold apart from the one given above.
Firstly, by using many stars we are taking advantage of all the information
in our CCD frame -
effectively
we are increasing the signal to noise of the stars that we use for photometry.
The second reason is that the uncertaintly in the magnitude that we calculate
reduces
with
the square root of the number of stars that we measure. Effectively we
are measuring the average calibration of the stars in the CCD's field of
view. The more stars
that
we use to calculate this average, the better and more exactly we define
the average. With just 1 star in each field, our rms error (for many measures
of different fields)
will
be 0.26 magnitudes. If we measure 100 stars in each field though we reduce
this uncertainty to 0.26/root(100)=0.026 magnitudes. Of course, at a certain
level, other
uncertainties
in our photometry will take over and we will thus only reduce the uncertainty
in the photometry that we take assymptotically to a certain limit that
is defined by
our
instrumentation and reduction.
--------------------------------------------------------------------------------
How
was USNO A2.0 prepared and calibrated?
Many
people who use the USNO catalogue habitually are unaware of how it was
prepared and its limitations. Here some brief details are given.
The
USNO catalogue is based largely on the famous Palomar Observatory Sky Survey
(POSS) plates made in the early 1950s with the 1.2-m Oschin Schmidt at
Palomar
Observatory
and, in the southern hemisphere the SERC southern sky survey made with
the UK Schmidt, the 1.2-m Schmidt at the Anglo-Australian Observatoy at
Siding
Spring
that is, to a large degree the twin of the Oschin Schmidt.
The
POSS plates were taken using two different photographic emulsions: the
"O" plates, sensitive to the blue; and the "E" plates, using a red-sensitive
emulsion. No attempt
was
made to use standard filters. In fact, the modern UBVRI magnitude system
was only defined in the 1950s in a series of papers that were published
first defining the
basis
of the modern UBV system and, later, the red extension to R and I. The
former was published with the POSS collection already well advanced and
the latter after it
was
essentially complete. In other words, although we assume that the Palomar
blue plates give magnitudes in the Johnson B system and the red plates
give Kron-Cousins R
magnitudes,
there is no good reason to assume that this is so.
The
POSS and SERC plates were scanned to digitise them. Scanning is a process
that is known to cause occasional errors in digitisation however carefully
it is done, largely
due
to the limitations of the original plates themselves.
Photometric
calibration of the POSS plates has been a problem that has occupied astronomers
ever since the POSS survey became available in the 1950s. The reason is
that
the
original plates were taken under a wide range of conditions of sky transparency
and seeing and the plates themselves have small sensitivity variations
from batch to batch
(for
a detailed discussion of the problems with matching survey plates, see
Chapters 9 and 13 of "Out of the Darkness" by Clyde Tombaugh and Patrick
Moore, Stackpole
Books
(Harrisburg, Pennsylvania)). This makes a standard global calibration impossible,
except at the most basic level.
However,
in the late 1990s a radically new possibility of calibration has been opened.
The Hipparcos satellite was launched to measure very accurate, positions,
proper
motions
and paralaxes of millions of brighter stars. A by-product of the Hipparcos
observations was extremely accurate photometry of millions of stars. Although
the main
instrument
of Hipparcos was limited to magnitude 10 approximately, stars too bright
to be measured accurately on the POSS plates because they are too heavily
saturated,
Hipparcos
also carried a scanning instrument called Tycho that measured fainter stars
as it scanned across the sky. The faintest Tycho stars are approximately
magnitude 12
and
their photometric precision is typically better than 0.001 magnitudes.
Each
POSS plate, which is some 5x5 degrees in size, contains typically some
tens of stars measured by Tycho. This allows the bright end of the USNO
photometry to be
defined
with some accuracy. As we can see, the USNO and Landolt magnitude scales
coincide very exactly at magnitude 12, at the magnitude limit of the Tycho
stars. The
USNO
A2.0 photometry should be good to about 0.15 magnitudes where it is fixed
by the Tycho photometry, but the errors will increase steadily to fainter
magnitudes. The
USNO
B1.0 catalogue claims 0.3 magnitude accuracy in its photometry, consistent
with the errors found in USNO A2.0.
One
important problem is that as USNO A2.0 is essentially a single-epoch catalogue,
there is no way that stars can be flagged for variability. Of course, within
the USNO
catalogue
a substantial fraction of stars will be significantly variable. Even in
the USNO B1.0 catalogue, which is multi-epoch, it would be difficult or
impossible to make a
reliable
indication of variablity given the differences between the characteristics
of different surveys. Thus discrepant stars in the catalogue may be due
to plate flaws, plate
sensitivity
variations, or intrinic variability of the stars themselves.
--------------------------------------------------------------------------------
This
version: 16/03/2003
Prepared
by: M.R.Kidger
E-mail:
mrk@ll.iac.es
--------------------------------------------------------------------------------
This
text and the enclosed graphic(s) are prepared for the benefit of amateur
or professional astronomers who use the USNO A2.0 catalogue. The author
has no relation
with
the USNO team and this work is not endorsed by the USNO team in any way,
although it is based in part on correspondance with the USNO team and on
the
information
publically available on the USNO web site.
------------------------------
This
text and its associated graphic(s) may be freely distributed and reproduced
provided that its source is clearly stated.