We examine the needs for infrared calibration with the new generation of 8-10 metre class telescopes, in particular the 10-m Gran Telescopio Canarias (GTC) which will enter operation in the Roque de los Muchachos Observatory, La Palma, Canary Islands in late 2003. Although our study is focussed towards mid-infrared calibration, it is also applicable to the near infrared. The state of infrared calibration is briefly examined, along with the problems of the currently available lists of calibrators. We demonstrate that the current calibration lists, particularly in the mid-infrared are inadequate for reliable calibration of GTC observations and, by extension, observations with other telescopes of a similar diameter. Apart from a low density of stars on the sky, the majority of calibrators for 10 microns are almost 7 orders of magnitude brighter than the sources to be calibrated; we show why both of these factors may cause severe difficulties with data reduction if not remedied.

The second half of the report deals with the progress that has already been made towards the resolution of the problem of calibration, particularly the studies aimed at obtaining an initial list of normal stars with reliable spectral type and good visible photometry and that have a high density on the sky. We discuss a method for templating highly accurate fluxes from 1-30 microns from the visible colours and spectral type of a star of type AV or KIII that will allow us to predict fluxes with great accuracy with a resolution R~30 000. This resolution is well adapted to proposed GTC infrared instruments.

Our aim is to produce an initial list of approximately 500 standard stars with highly accurate calibration from 1-30 microns for Day 1 of the GTC and extend the list to some 1000 stars within 3 years of this date. Work in progress has produced an initial list of ~7000 candidate stars north of declination -44° . MSX infrared photometry has been found for 881 of the stars included in our all-sky survey, allowing us to extend the spectral coverage significant fraction of these stars into the mid-infrared.
 
 

1 Introduction

1.1 The state of mid-IR calibration stars

Infrared photometric calibration lags many years behind the visible. Although some order has been put into infrared calibration standards in the last few years, their state has traditionally been chaotic. Each observatory tends to use its own calibration star list. Traditionally little thought has been given even to the most elementary process of elimination of unsuitable stars (e.g. variables), or to place standard stars on a standard magnitude scale (usually accepted to be that defined by Vega).

Whereas in the visible there is a set of stars that are generally accepted by most observers and observatories as defining the photometric standard (the Landolt stars, Landolt (1983a, b)), there is no such facility available in the infrared. The Landolt system has some deficiencies, however, these stars are known and understood by all astronomers who take visible photometry. To calibrate a field in the visible one observes a basket of stars over a night's observing, taking care to cover as wide a range of airmass as possible. As the Landolt stars cover a wide range of colours, one can obtain the extinction, photometric zero point, its variation, and colour transformations in a single observation. Discrepant stars can be discarded and an excellent overall result obtained.

In the infrared, there is no such sequence of stars available. During the 1960s, '70s and '80s a number of papers appeared presenting photometry in JHKLM of a large number of stars of widely differing classes (e.g.: Johnson et al., 1966; Engels et al., 1981; Korneef, 1983a, b; Glass, 1985). These papers with their tabulated data were used as photometric calibration lists in many telescopes. However, their deficiencies as calibration star lists were serious:

• Problem: The observations were taken mainly with small telescopes.
• Consequence: The stars are very bright. Typically, K < + 4. Many stars were too bright to be observed even on 2-m class telescopes and are totally unusable for an 8-10-metre class telescope such as the GTC.
• Problem: No attempt was made to select stars, adopting criteria of variability, peculiar or combined spectra, binarity, etc.
• Consequence: Many stars in the published lists are variable or unsuitable as calibration stars for other reasons than simply being too bright for modern detectors.
• Problem: Most of the telescopes used for the observations were in the Southern hemisphere.
• Consequence: The northernmost stars were equatorial, or only slightly north of the equator and a large fraction are invisible from the latitude of the Canary Islands, or only visible at high airmass and very few could ever be observed at low airmass.
• Problem: Errors are large, particularly in the fainter stars, but not explicitly presented.
• Consequence: It is difficult to gauge the reliability of the data for any star.
• Problem: Multiple epoch observations were not made.
• Consequence: It is impossible to reject uncatalogued variables.
• Problem: No attempt is made to link the observations to the zero point defined by Vega (a Northern Hemisphere star unobservable from the Southern Hemisphere locations used for most of the published observations).
• Consequence: It is impossible to know what the zero point is on the standard Vega scale.

In the mid-IR the situation becomes progressively worse. A literature search finds just one published paper that lists standard stars for 10 and 20 micron (Rieke et al., 1985). This paper presents accurate 10 and 20 micron (N & Q bands) photometry for 10 stars, all of which, apart from Vega, are of strongly negative magnitude. Most Northern Hemisphere observatories base their mid infrared standards on the list of stars published by Tokunaga (IRTF Photometry Manual, 1986). Rieke et al. suggest that their accuracy is <5%, although experience with mid-IR systems suggests that this figure may be optimistic.

The distribution of the UKIRT mid-IR standard stars on the sky is shown in Figure 1 (10 micron) and in Figure 2 (20 micron) below. The Tokunaga stars (UKIRT primary standards) are supplemented by some secondary standards gleaned from the NASA catalogue of infrared data. Even at 10 micron there are some regions of the sky as large as 40 degrees in diameter without a single standard star.

At 20 microns the surface density of standards is very low. A second factor is the brightness of the standards. In both the N (10 micron) and Q (20 micron) windows the distribution of available standard stars peaks around magnitude - 2, as shown in Figure 3. There is a small number of "faint" 10 micron standards with magnitudes between +2 and +3 (eight, to cover the whole sky) and a single standard of magnitude +4.

There is an evident need for a more extensive network of standard stars that cover the sky to greater depth.

Of the 10-micron standards, 23 are primary standards with consistent photometry. The remaining 15, including most of the faint standards, have been taken from the NASA Catalogue of infrared data. This source has relatively large errors given that there is no homogenisation of the data in the catalogue and it is included "as is". When only the primary standards (i.e. those with reliable photometry of known source) are included, the sky distribution, particularly of the faint standards, becomes highly unsatisfactory, as seen in Figure 4.

As can be seen from this figure, the very few relatively faint standards that exist are all distributed in a small radius around a ~12 hours. In other words, their sky visibility is highly limited and, during part of the year, no faint standard is observable.
 
 

1.2 Why introduce an all-sky network of calibration stars?

The current network of Northern Hemisphere stars suffers, as we have seen, from a series of serious defects that make it highly unsatisfactory for use in the Gran Telescopio Canarias (GTC).

• Low absolute precision
• No careful selection criteria applied to list
• Low spatial density
• Only extremely bright stars are available

Every time that there has been a major improvement in the performance of infrared instrumentation there has been a major problem with calibration. In most cases the improvements in the calibration has lagged years behind the instrumentation. A good example of this was the introduction of the first near-IR array detectors. When introduced little or no thought had been given to the problem of how to calibrate them in normal astronomical observation. Observatories found that the standard star lists that had been used for some years with photometers were unsuitable for calibration, as the stars in those lists were too bright to be observed with the new, more sensitive, array detectors. It has only been in the mid-1990s, more than 10 years after array detectors first became available in the near-IR, that standard star lists suitable for medium to large telescopes have been published. These lists now include stars as faint as magnitude K=12 - however, they remain totally inadequate for telescopes of 8-10m class that will reach a limiting magnitude around K=25.

Experience from the Carlos Sánchez Telescope has shown that the availability of a good photometric calibration system usually lags years behind the availability of the instrument that requires it. Even in large international telescopes this rule has held almost without exception.
 
 

1.2.2 Absolute accuracy of calibration

Even if we accept that the errors on the best stars in the calibration lists is 5%, this value is still poor compared to other ranges of the electromagnetic spectrum. In fact, 5% is probably optimistic and the true error is 10% or greater. This provides a fundamental limitation to the accuracy of observations. Even if there are no other source of error and in the most favourable observational circumstances, it will never be possible to calibrate 10 and 20-micron data with a better accuracy than this. Evidently, in normal astronomical conditions, with a variable atmosphere and photon statistics included, one would be lucky to obtain a final error better than double this value.

A second factor is that the poorer the knowledge of the absolute calibration and the less self-consistent, the larger the number of flux standards that need to be observed to calibrate a data set. When the absolute calibration is well defined, a good calibration can be obtained on a night of photometric quality, with just 3 or 4 observations of a single star at a wide range of airmasses. Where no good absolute calibration is defined, the same night will require the observation of a basket of a minimum of 15 to 20 stars to obtain minimally reliable data. If such a large number of stars cannot be observed, the data for the night may be completely worthless and valuable telescope time wasted.

When a reliable calibration network is available, the amount of time dedicated to absolute calibration on a single night can be reduced from perhaps 25-30% to <10% and, simultaneously, the accuracy of the data greatly increased. The aim must be to obtain an accuracy of ~1% or better in the standard star lists, similar to the best lists of bright 1-2.5-micron standards.
 
 

1.2.3 Selection criteria

Few standard star lists have applied rigid selection criteria to the stars to be included. Scrutiny of a typical list will find a mixture of "normal" stars, with variables (some of quite large amplitude), binaries, stars of unusual spectra, etc. Rarely are the calibration data acquired at different epochs ever compiled to check stars for photometric stability. When one considers the UKIRT calibration star list one finds a number of stars rejected as possible standards for the Carlos Sánchez Telescope because of their known variability. There are also several more stars that have been rejected later from the Carlos Sánchez Telescope (CST) standard star list (Kidger, 1993), as they were found to be significantly variable at JHK (in one case, with amplitude ~0.2 magnitudes).

Experience has shown that a reliable photometric system can only be obtained when rigid selection criteria are employed to select only stars that are suitable as photometric standards and care is taken to define the zero-point for the system carefully. A study of a sub-set of the Carlos Sánchez Telescope standard star list (Cohen et al., 1999) has revealed that the largest zero point offset in the CST data is 0.001 magnitudes (in J and L').
 
 

1.2.4 Spatial density

Less importance is given to the spatial density of standard stars than is desirable. With the advent of the GTC this factor will become extremely important. In the CST, one of the principal drivers in the design of the standard star list was the time occupied in telescope slews, and the extreme lack of suitable standard stars to the north of the celestial equator. For a telescope with a rather slow slew rate such as the CST, it was found that up to 5 minutes could be lost in pointing alone for each standard star observed. Although the GTC will have a much more rapid slew than the CST, when the optimisation of use of telescope time is a key factor, it is desirable to have a density of standard stars in the sky sufficient to ensure that only rather small telescope slews will be necessary.

Particularly in queue observing mode, when efficient use of telescope time is essential, having a high density network of stars is vital as, in most cases, each observation will demand its own individual calibration.

A second and extremely important factor is the need to match the source and calibration backgrounds due to the fact that for a large part of the mid-IR the sky flux dominates and thus any error in background determination has a disproportionate effect on the accuracy of measurements (see below).
 
 

1.2.5 The brightness of current calibrators

A key factor in mid-IR data reduction and, indeed, any data reduction at all at l > 2.5micron, is the assumption that the sky may be exactly subtracted, even though the sky flux may be many orders of magnitude greater than the source flux. Any slight non-linearity in sky subtraction will have serious consequences for the data, particularly as mid-IR observing depends on the summation of many frames. Unless the sky sums exactly as white noise, each new additional frame will introduce an error into the summation. It is precisely because for much of the mid-IR regime (although not all of it) the sky+star >> star that one must test that the subtraction of sky works exactly on known sources of low flux level.

However, given the current state of photometric calibration, if one simply observed a random standard star with a 10-m class telescope from the existing list of "reliable" flux standards then:

• It would usually saturate.
• If the standard star used to calibrate the data were not close to the target, flexure, sky, sky gradients, etc would all be different. It only requires a different 2nd spatial derivative to seriously degrade the accuracy of the chopping+nodding procedure.
• Ideally one wants to customise a standard to be as close as possible to the target pointing so that the attitude of the cryostat is as similar as possible. If this is not done, the differences in flexure, boresight, chopping character all change substantially on a 10-m class field-of-view.

However, as we have seen, the majority of available calibrators have a magnitude ~- 2 at 10-microns. In contrast, the GTC+CanariCam (the GTC's planned mid-IR camera-spectrograph) will be aiming to reach a magnitude limit N~ 15. Hence the available calibrators are typically 17 magnitudes brighter than the sources to be observed (close to 7 orders of magnitude). To ensure an accurate calibration it is important to observe standard stars that are of similar magnitude to the sources to be calibrated, thus ensuring that the sky subtraction algorithms work in nearly similar circumstances for source and calibrator. It may be argued that, as the sky dominates the source in most cases, the difference between "faint source" and "bright calibrator" is considerably less than 7 orders of magnitude. However, with such a large difference between source brightness and calibrator brightness it only requires a minimal non-linearity in the detector to make the sky subtraction unreliable (in addition to the effects detailed above).

However, it's not always true that the sky is enormously brighter than every target. Figure 5 shows the atmospheric transmission at Mauna Kea for a 1.2-mm water vapour column (we expect conditions at least this good on ³ 10% of the nights on the GTC). Note how a significant part of the 10-micron window (shown on an expanded scale in Figure 6) has close to 100% transmission. Even the 20-micron window has regions suitable for low background narrow-band photometry and spectroscopy with a transmission ~97%.

As we can see in Figures 5 & 6, a significant fraction of the operational wavelength range of the GTC+CanariCam will have low atmospheric background. The ultimate limit in these ranges is always the 270-290K black body sky emission, combined with the GTC's own emissivity.

We thus have to deal with two main regimes. One, principally from 10-12.5 microns, but also to a lesser degree at 8-9 microns and close to 18 microns, is a low sky emissivity regime where the (low) telescope and optics emissivity dominate the sky background and thus the source is relatively bright compared to the sky. The second regime is the high emissivity one, for example at 7.7 microns in the water edge, or 2.6-2.8 micron water edge, or at 9.6 microns in the ozone line, etc.

Figure 6: As Figure 5 showing the 10-micron window at Mauna Kea with an exploded scale.

A third important factor in the case of the GTC is the pixel size on CanariCam. With small pixels and diffraction-limited seeing, the solid angle of sky+telecope is minimised per pixel, thus minimising the effects of the background on a faint target star.
 
 

2 Building up a suitable all-sky calibration network

2.1 The issues

There are several independent requirements that we have defined above.

• One needs a network of calibration stars across the entire sky visible from the Canaries.
• To support both spectroscopy and imaging, calibrators must be provided for the entire usable wavelength range of the MIR spectrographs/imagers, roughly from 3 to 30 microns.
• Calibrators must be created far in advance of our knowledge of the actual optical response curves of the combination of CanariCam's detector + optics + filter + atmosphere.
• These calibrators must be rigorously constrained so that, for both imaging and spectroscopy, usage of the brighter members of the network will yield the same output voltages for input physical irradiance values as the faintest stars, after correction for detector non-linearities on the basis of Laboratory characterisations.
• It must be possible to trace the lineage of any calibrator and to relate it to other ground-based and spaceborne calibration systems.
• To set this in context, CanariCam will require MIR calibrators that are at brightest between 1000 and 10000 times fainter than the reference stars currently available. Ideally, we require calibrators to close to the limiting magnitude of the telescope.
• Further, CanariCam's calibrators must span a dynamic range appropriate to all the instrument's imaging and spectroscopic modes, and with relevant spectral resolutions.

One of our team (M. Cohen) has spent much of the past 9 years working specifically on the creation of absolute stellar calibrators. Another, (M. Kidger) spent more than 5 years working on the definition of the standard star system for the Carlos Sánchez Telescope (still in use and unmodified since then).

The products generated by Cohen and his colleagues have appeared in the literature as a series of ten papers and are widely available. In Paper X (Cohen et al., 1999) the photometry of the CST standard stars was combined with observations at other telescopes and previous work to provide an all-sky network of radiometric stars with very accurately defined photometry over the range from 1-20 microns (the J to Q photometric bands). This paper thus effectively produces a unification of all significant published near and mid-infrared calibration systems

These calibrators are confined to the range K0-M0IIIs, for which the combination of observed airborne and spaceborne spectra have made complete 1.2-35micron spectral coverage a possibility for at least one bright archetype of each spectral type. These have already supported the needs of OSCIR on the Keck, where a calibrator was required below 6 Jy at 10 microns in a particular region of the sky, in OSCIR's specific bands.

Paper X presents a set of 422 calibrated stellar spectra forming an all-sky network fainter than the primary (Sirius), or secondary standards (e.g. a Tau), but entirely consistent with them. The calibration framework of these stars already supports DIRBE, IRTS, MSX, and ISO. Self-consistency has already been tested by spaceborne observations from the IRTS, ISO, and MSX.

Building on this secure foundation we can address issues 1, 2, 3, 4, and 5: the fainter elements of the network defined in Paper X provide the bright portion of the new network with all-sky coverage. The creation of complete absolute spectra readily provides calibrators for ANY well-characterised passband lying entirely in the range 1.2 to 35m m; the constraints that already govern these calibrators have yielded traceability and self-consistency, tested from space primarily via the rigorous programme of absolute calibration on MSX. In this fashion, CanariCam's measurements will share a common heritage with these space-based archives, facilitating transparent intercomparisons of spectra and photometry from a variety of diverse instruments.
 
 

2.3 Extending the network for GTC calibrators

We now address issue 6. This is not a trivial requirement. Its achievement will necessitate highly specialised methods to provide complete wavelength flexibility, independent of the eventual choice of any specific imaging passband or grating. The faintest current calibrators still have an IRAS 12micron flux density of 5 Jy and about 1.5 Jy at 25 microns. CanariCam needs the network to be extended down by a factor of ~4000 at N, or 1000 at Q. To permit near-IR calibration on the GTC, which is a logical extension of this work, the network must be extended even further at 1-5 microns.

The method proposed is a modular approach, by which we plan to develop and test such a network in readiness for CanariCam's first light, which is planned for 2003.
 
 

2.3.1 The "Landolt" stars

As the initial approach to the extension of calibrators (by a factor of about 100--1000 in brightness) there is a potential to use "supertemplates" (i.e. intrinsic spectral shapes for each K0-M0III spectral subclass covering the range 0.11-35micron), applied to the set of Landolt stars in the celestial equator. For these several thousand objects, Landolt has furnished exquisitely well-measured UBVRI data.

For these stars, the steps are:

• To use the optical colours to determine the reddening, predict the NIR (JHK) and MIR (IRAS/MSX) brightness and test these predictions against observations.
• To make NIR measurements (with the CST, as its passbands have already been accurately characterised and calibrated in Paper X) to test the method by comparing measured fluxes with template predictions.
• If we can predict JHK to within a few hundredths of a magnitude then we can pursue this approach for K0-M0III stars with V~ 9-15, K~ 5-11. This will create an adequate number of K0-M0III calibrators in the northern sky, this time using all available optical, NIR and MIR photometric data.

We will also investigate the option to use Hipparcos/Tycho optical photometry (Hp, Bt, Vt bands) to assess reddening and provide optical normalisation of the templates. Beyond this, we will use fainter stars and their NIR photometry, drawn from DENIS and 2MASS, if cross-identifications provide reliable spectral types.
 
 

2.3.1.3 Hipparcos/Tycho stars

Recently, an alternative and highly attractive option has become available. As part of the calibration effort for the WIRE satellite, investigation of the Hipparcos database allowed stars of any given spectral type to be separated for magnitudes as faint as V=12. The Hipparcos database includes complete and detailed information on every star, including a spectral classification. The database also provides complete information that allows the acceptability of a star for calibration to be determined based on criteria for spectral class, variability, binarity, and colour.

This avoids many of the complications of the alternative Landolt programme. Stars may be easily separated by spectral class, searching for the types of interest. Those stars with unusual spectra may be rejected. Known and Hipparcos-observed variables are flagged in the archive and may be easily rejected. A further benefit is that the luminosity class of a star may be checked by using the Hipparcos parallax, combined with the observed magnitude. This allows possibly mis-classified stars to be reliably identified.

After selection of the stars to be studied further, the process proceeds in an identical fashion to that for the Landolt stars described above.

A great advantage of the Hipparcos programme is the fact that it also allows main sequence class A stars (AV) to be separated easily too. These stars have the major advantage over KIIIs that their colours are virtually zero. Whereas a moderately KIII star of magnitude V=10 will have N~6 (too bright for our photometric needs), an AV of V=10 will have N=10. Thus, to obtain some faint standards adapted to the mid-IR calibration needs of the GTC we only need to extend the calibration down to AV stars of V~12, although to reach a fainter limit would be more desirable. This is a significant disadvantage of this sample over the Landolt stars as the latter reach a magnitude limit of V=17, even fainter than our requirement.
 
 

2.3.3 Broadening the types of star templated

2.3.3.1 A-type stars

K/M-giant templates are not the only intrinsic spectral shapes that can be employed though they are the only ones with a solid, continuous-in-wavelength, empirical foundation. One can rely also on hot and solar-type stars if one is willing to adopt purely model atmospheres to generate their emergent spectra (as was also used for some calibrators on ISO). Model spectra are used identically to the fully-observed K/M-giant template spectra in that one normalises them by observed NIR and MIR photometry. The chief advantage of A-dwarfs is that one does not require visually such faint stars as for cool giants in order to attain faint MIR magnitudes.
 
 

• Progress to date

 

 
 
 

After careful consideration of the issues it was decided that the best approach to use initially in this study would be to take advantage of the stars selected for the WIRE mission but which, with the loss of the mission, would otherwise not be used. The initial selection process was simple. The Hipparcos catalogue was searched for the strings: "AV" and "KIII" and all stars selected that fell in the range from A0V to A5V and from K0III to M0III were saved to an individual file for each spectral division (i.e. A0V, A1V, K0III, K0.5III, etc.). For AV stars no further criterion was used, for KIII stars, two further criteria were applied. Stars selected for spectral type were rejected if their parallax was found to have been measured to better than 10 sigma (suggesting that they could be mis-classified nearby dwarfs) or their (B-V) colour index was larger than +1.5.

These files formed the basis of the initial lists. For the AV stars the initial distribution over the sky was as seen in Figure 7. Note that there is a sharp cut-off in the sky distribution at Dec.=-12°. This is seen in the distribution of all types of stars within the Hipparcos catalogue. The cut-off corresponds to the declination limit of the southern objective prism spectral surveys. As the declination limit of the GTC straddles this more heavily observed band of the sky it is inevitable that, with the strong southern bias in the stars selected, many of the stars will only be observable at high airmass from the GTC. 

Figure 7: The distribution on the sky of type AV stars after the initial selection from the Hipparcos catalogue. The solid horizontal line marks the horizon limit for the GTC.







Note too that, somewhat unexpectedly, the Milky Way is barely seen in the distribution. This is due to the fact that most of the type AV stars in the Hipparcos catalogue are comparatively local and thus show an all-sky distribution.



Figure 8: The distribution on the sky of type KIII stars after the initial selection from the Hipparcos catalogue. The solid horizontal line marks the horizon limit for the GTC.







For the type KIII stars (Figure 8) the effect is even more pronounced. More than 80% of all the stars are concentrated below the Dec.-12° cut-off point. A second strong concentration is seen in the North Galactic Pole, close to R.A.=12 hrs, Dec.=+40°.

Despite the large number of stars in the sample, the strongly non-homogeneous distribution means that some areas of the sky are heavily over-sampled, while others already begin to show significant gaps in coverage.
 
 

• First steps in the selection of stars

We start with:

The first step was to reject all stars flagged as variables by Hipparcos. This includes all variables known previously to the Hipparcos mission and all the stars for which Hipparcos detected a scatter in the data larger than can be accounted for by the errors. This step removes only a small number of rather strongly variable stars and can be seen as an initial coarse filter.

The following step is to examine more closely the spectral classification of the remaining stars. As Hipparcos gives a complete spectral designation this can be checked for a number of undesirable characteristics, for example, binarity, peculiar spectrum, uncertain or incomplete spectral classification, etc. For example, a star with a spectral type shown as A1V+O7I would be rejected, as would a designation of A3p, or K2II/III. The remaining stars are later checked in the SIMBAD database, where ambiguous or contradictory classifications are revealed (e.g.: a conflict between SIMBAD and Hipparcos spectral data for a star).

These first two steps remove most seriously unacceptable stars (spectral binaries, variables, and unusual spectral and possibly wrongly classified stars). However, this relies on the Hipparcos criterion and on available data in the Hipparcos database. The following steps make a finer sifting of the stars to remove remaining variables of lower amplitude and possible undetected close binaries.

To detect variables we study the error associated with the Hipparcos magnitude H_p). We expect variables to reveal themselves by deviating strongly from the trend defined. We also expect the error to increase as a function of the observed magnitude, with fainter stars having poorer photometry. The plot obtained is shown in Figure 9.

The results in Figure 9 make it obvious that there are a significant number of unflagged variables in the data set. When we centre on stars with smaller errors, expanding the scale until the maximum error is 5%, we see the expected strong trend of error against magnitude (Figure 10). Even in this range we see that there are a significant number of obvious low-amplitude variables undetected within the data set.

A least squares fit is made to the distribution and a least squares fit calculated. We then eliminate any star whose error deviates more than 4 sigma as being a probable variable. This figure is chosen to avoid giving a large number of false detections of variability. If we were to accept, for example, a 2 sigma criterion, we would expect to wrongly eliminate almost 1000 non-variable stars, given that 1 in 18 stars would be expected to give this deviation or greater just by Poisson statistics.

A similar criterion is used to eliminate possible unresolved binaries. We find that some stars have an unexpectedly large error in their parallax determination. One possible cause of this is that the star is an unresolved, or barely resolved binary. A similar plot to Figure 10 shows that a significant number of stars are possible astrometric binaries. One again we see, as expected, that the error in the parallax depends on the magnitude of the star. However, in this case the relation is somewhat different. We find that there is a constant error on the parallax measurement down to magnitude 6 (Figure 11), and then an exponential increase at fainter magnitudes (Figure 12).

We use the same criterion as previously that any star deviating by more than 4 sigma is assumed to be a possible astrometric binary and rejected.

All possible variable and close binary stars have, at this stage, been rejected.

With the remaining stars a close scrutiny is made of the spectral classification using the information found in the SIMBAD database. Where information is contradictory, doubtful, or incomplete, the star is assumed to be unsuitable for our purposes and rejected. This process required a careful star by star search of the SIMBAD database.

The following step is to search for visual doubles or wider binary systems that might potentially cause difficulties during observations. In many cases the existence of a companion will not affect the star's suitability as a calibrator. However, as the diffraction limit for the telescope is 0.2 arcseconds and some closer systems will have a separation not very much larger than this value, contamination by a companion star may be a problem in a number of cases. There is also the danger that a bright companion could saturate data.

These doubles and binaries are thus separated, but not eliminated, as they can still be of use to fill in significant gaps in sky coverage. A separate set of files is prepared with suitable stars that are listed as double in the ADS catalogue of visual doubles.

The final stage is to separate too the stars that are normal and fulfil all the selection criteria, but are observed to have strong CN lines in their spectrum. These stars are of uncertain value to us until the impact of this spectral characteristic can be evaluated. Similarly, stars that are normal but whose spectral classification falls between two types are also separated (e.g. K3III/K3.5III).

We thus now have three large groups:

The first of these groups is our prime sample, the second and third groups may be used if gaps appear in sky coverage to fill inconvenient holes.

Finally, we separate the stars southwards of declination -44° . These are valid stars for calibration and for testing of the models (e.g. against satellite observations), but of no interest as standard stars for the GTC.
 
 

3.2 The current state of the data set

After the different phases of elimination detailed above the state of the database is:

These represent the set of stars that may potentially be used to calibrate infrared data on the GTC. The distribution of these stars on the sky is seen in Figure 13 for type AV (above) and KIII (below).

Note that some areas of the sky show significant gaps in coverage, particularly of the type AV stars. Some regions as large as 30° across are found to lack type AV stars, although the sky coverage of type KIII is more complete. In some regions of the sky it is evident that both the type KIII stars and the type AV are heavily over-sampled and that only a small fraction of the stars need be used finally.

3.3 The extinction correction

An essential part of the technique of templating is the extinction correction, tilting the stars the correct amount to compensate for interstellar extinction. However, interstellar extinction is difficult to apply accurately, even for nearby stars. All stars will be reddened to a certain degree by interstellar matter in the line of sight. The Hipparcos data set allows us to use this effect to make a first order check of the spectral classification.

For type A0V stars we can start from the principle that their (B-V)=0.00, thus any colour different to zero is due to colour excess from extinction, or misclassification.

For an A0V star we assume that:

Given that:

Where A_V is the total line of sight extinction in the visible and E(B-V) the colour excess in (B-V) caused by the extinction.

We assume a plane parallel atmosphere of scale height 0.11kpc, with a mean extinction of 0.7 magnitudes per kiloparsec. Thus a star at high Galactic latitude, at distance "D" from the Sun, is assumed to have a line of sight extinction A_V=0.7mags/kpc up to distance "x" (the limit of the Galactic disk) and A_V=0.7 henceforth (Figure 14).

Note that a star at low Galactic latitude may be wholly within the disk. We can thus use the parallax to calculate the distance of the star and its expected extinction and the observed colour to calculate the observed extinction. This allows us to calculate if a star's observed colour and magnitude are consistent with its distance, or not. In some cases it is probable that stars are mis-classified. Others appear to have very large line of sight extinctions (i.e. are seen behind relatively dense clouds in the Interstellar Medium) and are thus unsuitable for that reason. An example of this effect is shown in Figures 15 & 16.
 
 

When applying this technique, we find that the line of sight extinction to some of the stars in the sample needs to be as great as 14 magnitudes/kpc (20 times the expected value) to explain the observed colours (Figure 17), therefore we reject them as potential calibrators.

To date, we have only investigated the type A0V stars in detail. Some 50 stars are found to have colours that imply either very large line of sight extinction, or misclassification of the spectrum. In a few cases, as can be seen in Figure 15, the colour is even bluer than expected. However, most of these stars are close to the Galactic Plane, suggesting that dense local clouds are responsible for highly reddening the stars (Figure 18). In the case of the KIII stars (Figure 16), we see that a significant fraction of stars have much bluer colours than expected. In many classes the colours are consistent with a type KV rather than a KIII, although it is also possible that some stars are misclassified as GIII, or even GV.

In the case of the KIII stars we have only made an initial approach to the problem. These stars were already selected in such a way that objects with very red colour were excluded. However, there is still a potential confusion with stars of type GIII, or KV, which have similar spectral characteristics and can be mistaken for a KIII in an objective prism search. The number of stars that are seen to have much bluer colours than expected for a type KIII gives support for this. A significant fraction of the sample has (B-V)~+0.8, similar to the expected colour for a type KV star (Figure 16).
 
 

• Work in progress

• Further study of the extinction correction, particularly in relation to the AV stars. Only when these are completed will the work be extended to the type KIIIs.
• Rejection by colour of mis-classified stars.
• Cross-checking of the final list of normal stars (all-sky) against the MSX and IRAS catalogues to search for stars with spaceborne infrared photometry.
• A search for catalogues of faint type AV stars and of faint K giants.
• An observing programme to measure JHK colours for some 200 stars from the selected list (this programme was initiated in 2000).
• Identification of candidate KIII and AV stars from the Landolt lists from their visible colours and in quasar fields from their visible and infrared colours and the observation of their spectra to confirm their spectral type.
• Extension of Landolt's photometry to much fainter stars (V~19-20) in quasar fields and in selected areas observed by Landolt. Information on and results from this programme can be found in González-Pérez et al. (2001) and in Kidger et al. (2001).

The templated fluxes will then be compared with the measured fluxes at the CST to demonstrate the validity of the method.

Further details of work in progress may be found in Martín-Luis et al. (2001, a, b) and in Kidger et al. (2001). A demostration of the validity of the template method with real data for a type KIII star can be found in Cohen (2001).
 
 

3.5 Problems identified

We have identified a number of additional problems that must be treated to produce a complete and adequate product. In some cases these relate to difficulties found in the course of the studies reported here.

• The need for faint AV stars

• The extinction correction

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