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).
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.
Prepared by: M.R.Kidger
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.