The stars were chosen as potential infrared standards, so they are predictable (i.e. non-variable and single) and are well measured at other wavelengths. Hence the results presented here provide a good test on the validity of using models to extrapolate mid infrared magnitudes from near infrared data.
Figure 5: The difference between the predicted and measured N magnitude
Figure 6: The difference between the predicted and
measured 8.7
m magnitude
Figure 7: The difference between the predicted and measured
9.8m magnitude
Figure 8: The difference between the predicted and
measured 12.5m magnitude
Figure 9: The difference between the predicted and measured Q
magnitude
In Figs. 5 (click here)-9 (click here) are presented the difference between the magnitudes
predicted using the model SEDs and the measured magnitude. The main calibrators
are marked as a solid square (HR 1457) and a solid triangle (HR 5340).
The error bars include the errors from the measurement and the predicted
magnitude. The latter comes primarily from the error in the near IR
magnitudes used to normalise the model SED, typically this is of
order 1% but a few of the stars are less well measured and for these
the error could reach 2 to 3%.
The SiO bands are not included in the model grid used, so in order to allow
for this a
low order polynomial fit has been put through the difference for the N, 8.7
and 9.8 m filters.
The SiO is not significant in the 12.5 m and Q filters so the
line was drawn through zero difference.
It can be seen in Figs. 5 (click here)-9 (click here) that the fitted line goes through the majority of the error bars. The fitted line was subtracted from the data points and the standard deviation of the difference calculated (Table 7 (click here)). In calculating the standard deviation the three points with the largest errors in the predicted magnitudes were ignored because the error comes from the near IR magnitude used to normalise the SED. It is intended to improve the near IR measurements of these stars, but this has not yet been possible.
| Filter | sd | comment |
| N | 0.014 | |
|
8.7 m | 0.013 | |
|
9.8 m | 0.014 | |
|
12.5 m | 0.023 | (0.017 if worst 2 points are deleted) |
| Q | 0.035 |
The size of the standard deviation of the difference between the measured
magnitude and the predicted magnitude indicates that the errors in the
measurements presented
in Table 2 (click here) are reasonable and that the random errors in the SEDs are of
the order quoted. The previous discussion on the zero points indicates
that there is a possible error in the zero points of about 0.015 mags
although this is at the same level as the errors used to compare
with other zero points so it is difficult to assign a significance to it.
We therefore conclude that the method of determining the zero points for
the IRTF 10 and 20m filters presented here is valid within the
quoted errors. Further, the method should be valid for any filter within
the wavelength range covered here, although if measurements are to be taken
in the SiO bands then stars hotter than 4500 K should be used.
The target accuracy
at 10m for the ISO calibration programme was 5%. This data set shows that the difference between
the measured and predicted flux densities, including the error in the
zero point,
is about 2% over the wavelength range covered here. In fact, at Q the
predicted magnitudes are in general more accurate than the measured ones.
Although the SiO bands at 8 to 10m are not included in the
stellar models, the data presented here clearly show that the SiO
does have a significant effect for stars cooler than 4500 K. For the coolest
stars in this sample the error between the measured and predicted magnitudes
is as high as 0.11 magnitudes in the 
m filter.
Figures 5 (click here)-7 (click here) indicate that for stars with effective temperatures
between 3850 K and 4500 K the effect of the SiO can be approximated to a linear regression in the N, 8.7 and 9.8 m filters. The difference between
the measured and predicted magnitudes are:
With the advent of infrared observatories such as ISO and the availability
of powerful mid IR instrumentation on the latest generation
of 8 and 10 m class telescopes, the mid IR will gain
in importance. If stellar models are to accurately represent the flux density
between 8 and 10 m for stars cooler than 4500 K it is imperative
that the SiO bands be included.
m filters
As can be seen from Tables 2 (click here) and 6, the errors in the 8.7, 9.8 and
12.5 m filters are comparable to those in the full N filter and
so in terms of accuracy there is nothing lost by using the narrow bands.
In fact, as the narrow band filters use a smaller portion of the
atmospheric window, they are much less susceptible to changes in atmospheric condition than the broad band N. This should be particularly true for the
8.7m filter which appears to be relatively clean (see Fig. 1 (click here)).
As the N filter covers from 8.2 to 13.5 m, about half of the wavelength
range is affected by the SiO. Therefore, the magnitudes have to be
corrected for studies which require a continuum flux, e.g. the IRFM. Clearly
these studies would be better using the 12.5m filter, at least
for the cool stars, as it is almost purely continuum. However, when the
object of the observations is to measure SiO then the effect
on the 8.7m filter magnitude is about twice that on the N magnitude
(see above). Further, the difference in magnitude between the 8.7 and
12.5m filters would directly give the amount of SiO in the star.
There are significant advantages in interpretation of the narrow
band data. The N filter has a very low spectral resolution and so the
changes significantly with spectral type; the
for a K5III is about 1% longer than an A0V. However, for the
narrow band filters the change in is at most 0.2%
between A0 and K5.
The effective wavelength is an approximation to (see Golay 1974) but often the effective wavelength is quoted in preference as
it has a simpler definition. For the narrow band filters the effective
wavelength is within 0.2% of the and hence does provide a
good approximation. However, for the broad band N the difference is
about 3%. As the flux changes as 
, a 3% change in wavelength
is equivalent to a 12% change in flux. Hence, if the N isophotal flux
were given at the N effective wavelength there would be, in effect, an error
of 12% in the flux.