A Preliminary Calibration Plan

I have performed detailed calculations of a simplified calibration plan. Previously I described the acquisition of primary calibration stars using a balloon-borne spectrometer. I showed how the calibration transferred from the primary NIST lamp to the calibration K0III star. I have now propagated the errors from the primary calibration standard star through two transfer steps. Below I briefly summarize the computations. Within the next week I plan to produce a more detailed description of this work.

This calibration plan propagates the errors from a V = 5 primary to a V = 16 secondary standard and keeps the error budget below 1%. The plan is based upon instruments that we can build and telescopes that I have access to. Beyond the second transfer step requires large telescopes on which Indiana University has no guaranteed time.

I. Primary Calibrations

The primary calibrations are obtained using the balloon-borne spectrometer described at the February calibration meeting. The balloon instrument is a 15 inch RC telescope and two arm (optical, near-IR) spectrometer (R = 150) that switches between (star+sky)/sky and (star+sky)/NIST lamp. The primary calibration star is a V = 5 K0III star that is assumed to be unvarying in time. The comparison NIST lamp has the properties described in the NIST documentation for their standard 1kW commercially available lamp. Although this lamp is not suitable for these purposes, NIST can produce a similarly accurately calibrated lamp that does meet our needs for a price. As I described in February, NIST calibrates the lamp at irradiances some 10-12 orders of magnitude brighter than a 5^th magnitude star. In these calculations I have assumed that the irradiance of the lamp has been reduced by geometry, that is, in a non-wavelength dependent way. Although the systematic errors in reducing the irradiance of the lamp have been included in the computations, these errors should be unimportant if only relative flux calibrations are important. For the star observations, sky background was taken from Leinert et al (Astron.Ap.Supp., 127, 1998). OH emission, zodiacal light and faint star emission was included in the near infrared airglow; O_2, zodiacal light, and faint star emission was included in the diffuse night sky brightness.

The errors in the transfer from the NIST lamp to the calibration K0III star on a balloon experiment are shown in the upper panels of Fig.1 for B and Fig.2 for J. These computations were based on 600 Monte Carlo realizations of the proposed experiment. The statistic chosen as a measure of the errors was (Bmag-Bmag_0), where Bmag_0 is the B magnitude without errors included, and (Jmag-Jmag_0). Systematic and statistical errors have been propagated from the NIST lamp to the calibration star wavelength bin-by-wavelength ,bin and the magnitudes computed using standard wide-band filters. The offset in the mean of the lamp and primary calibration star is due to the error in reducing the lamp irradiance.

II. First Transfer

The first transfer was assumed to take place at the 0.9m WIYN telescope on Kitt Peak using the same low-resolution spectrometer used in the balloon flight experiment. The atmosphere was included in the calculations using data taken from the Gemini website for the Gemini N telescope. In the optical, power law was fit to the atmospheric transmission data. For the near infrared, the transmission data for 1.6mm water vapor, the median value for the Gemini site, was used. The atmospheric transmission used in these computations is shown in Fig.3. In Fig.4, the spectrum of the K0III primary standard without atmospheric extinction and with atmospheric extinction for the two arms of the spectrometer is shown. The broad band filter functions used in these computations, taken from the Kitt Peak website, are superposed.

The following observing plan was assumed for the first transfer: 5 minutes on calibration star, 5 minutes to move telescope, 5 minutes on the transfer star for a total of 4 observations of each star/hour. It was assumed that each observing night was 6 hours long. For each set of optical measurements, a 3% error on the broad band magnitudes was introduced; for each set of near infrared measurements, a 7.5% error on the broad band magnitudes was introduced. The effect of multiple measurements of the magnitudes was included by reducing the above errors by .

In the lower panels of Fig.1 and Fig.2, the measured B and J magnitudes, compared with the magnitudes expected with no errors, are shown for 600 Monte Carlo simulations of the experiment. The first transfer is to a K0III star with V = 12. The primary calibration star is assumed to have a zenith angle of 30^o, and the first transfer star is assumed to have a zenith angle of 31^o. Since a 12^th magnitude star in a 36” telescope gives an enormous number of photons, the errors are dominated by the atmosphere and you are better off making fewer transfers and observing longer. In this calculation, 3 nights of observations were assumed. At the plate scale of the 36”, the effect of the airglow is almost the same to the airglow seen from the balloon (the 15” balloon telescope is F17; the 36” telescope is F7).

III. Second Transfer

The second transfer was assumed to take place at the 3.5m WIYN telescope on Kitt Peak, again using the same spectrometer used on the balloon flight experiment. The atmosphere was included in the same way as described previously and the same observing plan was assumed.

In the upper panels of Fig. 5, the measured B and J magnitudes, compared with the magnitudes expected with no errors, are shown for 600 Monte Carlo simulations of the experiment. In the lower panels, the transfer of (B-V) and (B-J) are shown as a measure of the transfer of the calibration from B to J. The second transfer is to a K0III star with V = 16. This star was placed at a zenith angle of 35^o. In this calculation, 5 nights of observations were assumed.

IV. Summary

In transferring the calibration from the NIST lamp to a V = 16 K0III standard star, the following errors are introduced at each step:

	NIST lamp	Primary K0III balloon	Primary K0III ground	1^st Transfer	2^nd Transfer
B-B₀	0.27%	0.29%	0.44%	0.58%	0.64%
J-J₀	0.24%	0.24%	0.42%	0.62%	0.71%
(B-V)-(B-V)₀					0.87%
(B-J)-(B-J)₀					0.95%

The calculations shown here suggest that 1% relative spectrophotometric accuracy propagated from a NIST can be achieved through V = 16 magnitude stars.