USNO photometry
1.0 The USNO A2.0 photometric scale compared to the standard Landolt BVR
magnitudes
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).
2.0 Results
2.1 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.
2.2 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.
3.0 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.
4.0 Acknowledgements
This version:
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.