Calibration of SNAP Standard Stars

The goal of SNAP is to measure several properties of the universe to high precision: the energy density to 5%, the mass density to 2%, and the curvature to 6%. It will determine these properties by measuring the peak brightness of Type Ia supernovae over a range of redshifts from z = 0 to z = 1.7. In order detect 1-sigma differences from a fiducial flat universe, SNAP must measure relative brightnesses to better than 1%. The key measurement is comparing supernova magnitudes in nearby galaxies (where restframe B-band runs from roughly 3900 to 4800 Angstroms) to those in distant galaxes at redshift z = 1.7 (where restframe B-band runs from roughly 10,500 to 13,000 Angstroms). In other words, SNAP must be able to compare optical and near-IR measurements in a precise, quantitative manner.


Background and Introduction to Astronomical Calibration

Let us define three different ways that astronomers compare the measured brightness of points sources.
  1. Relative calibration is by far the most common. After using the same instrument to measure the spectral irradiance (called "flux" by astronomers) of two sources, one calculates the magnitude difference m between the sources via
                              [ flux(source A) ]
            m   =   2.5 * log [ -------------  ]
                              [ flux(source B) ]
    This yields the relative brightness of the two sources in the same passband.

  2. Absolute calibration allows one to convert a measured brightness into physical units: watts per square meter per second, for example. It requires With an absolute calibration, one can convert a measured magnitude in some passband to the flux in that passband.

  3. Precise color calibration is less stringent than true absolute calibration. It allows one to use measurements of objects in two (or more) different passbands to calculate the ratio of fluxes in those different passbands -- but not the absolute values of those fluxes. For example, given measurements of a star in the optical V-band and near-infrared J band, one could fit a model blackbody spectrum to the measurements. With precise color calibration, SNAP can compare fairly B-band measurements of nearby supernovae to J-band measurements of distant supernovae.

Astronomers typically use relative calibration, comparing magnitudes of target objects to magnitudes of standard stars in the same passbands. If those standard stars have been calibrated absolutely, one can transfer the absolute flux calibration to the target objects (albeit with some loss of accuracy).

It is very difficult to calibrate any star on an absolute scale. In the classic works of Oke and Schild (1970) and Hayes (1970), a telescope alternately observed a star and a calibrated light source placed several hundred meters away from the telescope, on a neighboring dome or tower. One of the principal sources of uncertainty in these experiments was the earth's atmosphere, which scattered and absorbed light from both the star and light source. Together, the two efforts yielded absolute flux calibration in the optical for only a handful of very bright stars. In the ultraviolet, again only a few stars have been absolutely calibrated (with instruments aboard rockets and satellites). A recent paper by Witteborn et al (1999) provides absolute calibration of one star in the infrared, from 3 to 30 microns, but that falls outside the range of SNAP's detectors.

MWR Is the following paragraph correct?

The crucial difference between absolute calibration and precise color calibration lies in the measurements of the calibrated light source. Absolute calibration requires that one know the exact spectral irradiance of the source; hence the standard method of placing the source a precise (and large) distance away from the telescope and shining its light through a small, precisely measured pinhole. Color calibration can be done more simply: use a short optical fiber to transfer (an unknown amount of) light from the source to the detector, bypassing the telescope entirely. As long as one knows the spectral response of the telescope optics and the short optical fiber, one can compare the brightness of the light source and a star accurately at different wavelengths.

There are many sets of secondary standard stars which provide relative calibration only. In the optical, Landolt (1983, 1992) has established an extensive system of stars between eighth and fourteenth magnitude; in the infrared, Persson et al. (1998 and references therein) provide a network of 65 stars between tenth and twelfth magnitude.

SNAP requires a set of standards which are much fainter than the few absolutely calibrated stars, but which do provide precise color calibration across the optical and near-infrared. No existing measurements meet our needs. Gunn and Oke (1983), for example, transfer the absolute flux calibration of Vega to five fainter stars, around tenth magnitude, but their measurements are insufficiently precise (only good about 2-5 percent), and do not extend into the near-IR.

SNAP Calibration

In order to deliver the required 1% accuracy in measurements of supernova light curves, SNAP will need a set of standard stars which satisfy three requirements:
  1. the color calibration from 4,000 to 17,000 Angstroms must be accurate to 1%
  2. the stars must be faint enough to compare directly against distant supernovae
  3. all stars must have measurements in the 15 passbands of the SNAP instrumental system

The key to the entire SNAP mission is comparing the flux in an optical passband from nearby supernovae to the flux in an infrared passband in distant supernovae. Precise color calibration is sufficient to permit us to determine the crucial cosmological parameters. With absolute calibration, we could make additional cosmological tests and compare our measurements more accurately to those in other passbands.

Distant SNe will peak at about V = 25 mag, but we must monitor their light curves until they fade to about V = 28 mag. In order to avoid non-linear response in our detectors, we must compare the SNe to stars which are at most 5 or 6 magnitudes brighter. Therefore, the local standards in the SNAP fields must be no brighter than V = 22 mag, about 10 magnitudes fainter than most current standards. If we start by calibrating (nearly) absolutely a set of bright stars around V = 10, we must transfer this calibration twice to a series of intermediate stars, and finally to the faint stars in the SNAP fields.

The 15 SNAP passbands will not (all) correspond closely to any existing passbands; in addition, they will cover both optical and near-IR wavelength ranges, which have traditionally been calibrated independently. The simple number of passbands makes the job of transferring measurements from a bright set of standards to a fainter set an ardous task.

We are currently exploring balloon-based and ground-based calibration programs.

Ground Based Program

There are several issues to consider when establishing a ground-based calibration system:

  1. Atmospheric absorption: the earth's atmosphere is largely transparent across the optical, and in several windows in the near-IR (see Figures 1 and 2).
  2. Sky brightness: the night sky emits radiation at all wavelengths, especially in the near infrared, due to OH and water in the earth's atmosphere (see Figures 3 and 4). The background in the B and V bands is 2-3 times lower in space than from the ground; in the J band, about 100 times lower in space.
  3. Stability: the water content and other properties of the air above an observatory can change on timescales of an hour or less. Observers on the ground must devise strategies to remove variations in the sky brightness and opacity from their data.

MWR insert Figure 1: ICARUS Spectral Channels in the UV to NIR

MWR insert Figure 2: Near IR Atmospheric Absorption

MWR insert Figure 3: Zenith Sky Brightness

MWR insert Figure 4: Atmospheric Emission in the Near Infrared

Plan of Action

  1. Perform precise color calibration in the optical and near-IR using a calibrated source on a small number (6 or so) of primary standards around tenth magnitude. Reduce systematic errors by using

  2. Observe both sides of the terrestrial water absorption band between 0.9 and 1.0 microns with the same detector, which should lead to lower systematic uncertainties in the calibration. New HgCdTe devices now under development for NGST will work at wavelengths as short as 0.6 microns, overlapping significantly with CCDs in the optical.

  3. Extend calibration to intermediate secondary standards with accurate spectrophotometry as needed. A 10% error in the equivalent width (EW) of a spectral line with true EW = 4 Angstrom, in a 40-Angstrom-wide bandpass, leads to an uncertainty of only 1% in the calculated flux. MWR thinks Figure showing AAO and CIT color transformation isn't relevant here.

  4. Measure very accurately the spectral responses of the SNAP filters, detectors, and optics; combine to form overall passbands for all the SNAP filters.

  5. Extend the ground-based SNAP system from ground-based measurements of intermediate standards to space-based measurements of faint standards. We could use existing space telescopes for this step:

Models and Observations of Standard Stars

We will choose for our standards stars with smoothly varying continua: metal poor F subdwarfs with -3 < [Fe/H] < -2, and hot white dwarfs with weak H lines and little or no He or metals (see Figure 6 below). We would use use models of stellar spectra as an aid for interpolating over terrestrial atmospheric bands.

MWR: wait a minute -- this implies that we plan to do absolute calibration of our standards. I thought that the plan was to do color calibration (aka absolute relative calibration) only, not absolute. What's the truth here?

MWR insert Figure 6, Transmission and Model g191b2b

Figure 6 shows the transmission of the earth's atmosphere (upper curve), the actual spectral energy distribution of a hot white dwarf (solid line), simulated observations of the white dwarf through the clear windows of the earth's atmosphere (crosses), and the best fit SED using these simulated observations (dashed line). For a star with smooth energy distribution, the errors due to interpolating across highly absorbing regions of the earth's atrmosphere are small.

Below, we show the effect of doubling the IR Extinction (Figure 7) and tripling the water content (Figure 8). In both cases, the effect is confined to the absorption bands and negligible in the "clear" windows.

MWR insert Figure 7, Doubling of IR extinction

MWR insert Figure 8, Tripling of water content

Balloon-Based Program

Ground-based observations in the near-IR suffer from time-variable transparency and sky brightness. We can avoid some of these problems by moving the detector above most of the earth's atmosphere. In this section, we concentrate on the benefits one can gain by placing the calibration system aboard a high-altitude (45 km) balloon.

We have some experience in this field. Since 1987, the Indiana High Energy Astrophysics Group has collaborated in the construction of 3 balloon experiments (PBAR, SMILI, HEAT), and participated in 7 successful campaigns. A fourth HEAT flight is planned for fall, 2001. These flights have all been devoted to cosmic ray studies. The experimental packages have all contained a superconducting magnet with its associated cryogenics, and various combinations of time-of-flight detectors, hodoscopes, Cerenkov detectors, and dE/dx detectors. These packages are at the 6,000 lb weight limit.

There are three issues that must be considered in defining the primary calibration program in the near-IR:

Signal Strength of the Standard Stars

The SNAP mission plans to measure supernovae in the wavelength range 0.4 - 1.7 microns. We consider below the requirements for standard stars, concentrating on the worst case: at the longest wavelength, 1.7 microns, where the background sky is brightest. The flux of a zeroth magnitude star in H band is
                                  -10       -1   -2  -1
           F(lambda)  =  1.17 x 10     erg s   cm   A

A telescope of diameter D (cm) observing a star of H-band magnitude m through a passband of width w (Angstroms) with overall quantum efficiency e will collect

                              2        -0.4*m             -1
            S(star)   =  80  D  w e  10         photons  s

OH Airglow

The OH airglow originates approximately 90-125 miles above the earth's surface, far above the altitude of any balloon. The SOFIA website states that the background sky brightness per square arcsecond at 1.7 microns due to OH airglow is of order
                                  4          -1  -2       -1              -1
                N     =    3  x 10   photon s   m   micron    (sq. arcsec)
A telescope of diameter D (cm) observing through a passband of width w (Angstroms) with overall quantum efficiency e will collect over an aperture of A square arcseconds
                                   2                   -1  
            S(sky)    =  0.0003   D  w e A   photons  s    

Atmospheric Absorption

The atmospheric absorption in the near infrared is mainly due to water vapor. The absorption is variable and heavily dependent on the altitude of the observations. The primary reason for making observations at high altitude is to reduce the effect of atmospheric absorption.

MWR shouldn't we say something quantitative about absorbtion in the paragraph above?

We can estimate the signal-to-noise ratio for spectrophotometric measurements of standard stars from a balloon, assuming that the instrument is above all of the absorbing water vapor, but below all the glowing OH. As long as the sky background light is stronger than the light from the star,

             signal            D               -0.4*m       
            -------  =  2600  --- sqrt(wet)  10        
             noise             r               

MWR please check my calculations


We are considering a program of overnight flights based in Palestine, TX. These flights would be able to acquire both the NGP and SGP during the required summer launch. These missions are the cheapest and safest flights carried out by NBSF, and they do not fly over water.

Gondola Model

Several attitude control systems currently being deployed define state of the art:

These missions claim a pointing precision 15-20 arcsec RMS and 5 arcsec pointing stability. Since the star tracker data used to reconstruct the photon arrival direction is updated every 2 seconds, there is no reason in principle that 5 (arc sec) pointing precision cannot be achieved.

MWR I'm not sure I understand the previous sentence and claim. Could a balloon expert clarify it, please?

Magnitude Limit Achievable by Balloon

Given the current limits on pointing stability, it seems necessary to use a relatively large aperture to collect light from a candidate standard star: the aperture radius cannot be much smaller than r = 10 arcsec. The weight limit of a typical balloon flight, about 6,000 points, constrains the telescope to be roughly D = 100 cm in diameter at most. For a reasonable overall system (telescope plus spectrograph plus detector) efficiency of e = 0.02, and resolution of R = 425 (wavelength bins w = 40 Angstroms wide), we find that a tenth magnitude star requires about half an hour of exposure time to reach a signal-to-noise ratio of 100. See the signal-to-noise equation above to evaluate other possibilites.

Choosing even slightly fainter stars leads to much longer exposure times; for example, replacing the m = 10 star by an m = 12 star increases the exposure time to twenty hours (!) in order to reach the same S/N ratio. In order to calibrate a set of ten stars during the course of a two-day balloon flight, we must place a limit of roughly m = 10 in H-band.

MWR I believe these calculations agree roughly with independent estimates based on Gemini exposure time calculators; Jay Frogel claimed for a 1-m telescope, R = 1200, a star with mag m = 12 in H-band would require about 6 hours exposure time to reach S/N = 100. That scales down to t = 45 minutes for m = 10. When I used the Gemini calculator, I found roughly the same result. As always, please check the calculations.

One might wonder if SOFIA might provide a better platform than a balloon. The primary advantages of SOFIA over balloons are, first, its 3 arcsec pointing accuracy, which allows for a considerable reduction in the fiber size (and thus sky background); second, its 2.5-m telescope, much larger than any which can be carried on a balloon. Its primary disadvantage is the lower transmission (only 90% in J band) due to its lower altitude. In a half-hour exposure, the same spectrograph used in the examples above (with a smaller fiber aperture, r = 5 arcsec) could reach S/N = 100 for a star of about m = 12 in H-band; in other words, SOFIA could extend the limit for standard stars about two magnitudes fainter. Note that none of the first-generation instruments being built for SOFIA will provide sufficient spectral resolution in the near-IR for our purposes.


The calibration instrument must be able to measure stars from 0.45-1.7 microns with a relative spectrophotometric accuracy of one percent. That is, we require that the ratio R of the flux of the star relative to its flux at a standard wavelength when compared with the flux of the light source relative its flux at a standard wavelength,
         flux of star at lambda / flux of star at lambda_0
   R  =  -------------------------------------------------
         flux of lamp at lambda / flux of lamp at lambda_0
be measured to a precision of one percent. The light source, in turn, must be calibrated relative to a blackbody to a higher precision.

Light source

Discussions with several engineers, including engineers at NIST, find no showstoppers in building a long-lived (> 30 hours) stable, lightweight light source accurately calibrated relative to a blackbody.

NIST calibrated blackbody sources available from many commercial vendors. The published accuracy of such sources is

Because blackbody sources are hot, heavy, power hogs, and loaded with plumbing, they are not portable. We can not include one in a balloon-borne instrument package, and must instead use one to calibrate our light source before flight.

Optical-grade light sources are commercially available. They are relatively long lived and light weight. The stability of a lamp is limited only by the stability of its power supply, and there are commercial power supplies that are stable to < 0.3%.

We are currently exploring the possibility of having NIST calibrate our light source so that we can take advantage of their experience.


The preliminary spectrograph design is a fiber-fed, 3 arm spectrophotometer which alternates between chopping star/lamp and star/sky (for OH air glow emission). We will use relatively Large fibers (radius r approximately 10 arcsec) to minimize balloon pointing requirements minimize near/far field effects. The three-arm design has two cameras for the optical bandpass and a third camera for the near infrared. The optical measurements will be made with CCDs and the near infrared measurements will be made with an HgCdTe detector. The spectrograph design is compact and light enough for flight.

The spectrograph is optimized for features important for the task: little scattered light, proper resolution, beam switching, etc. The spectrophotometric measurements require multiplexed detectors and the plan is to use SNAP flight detectors. The spectrograph can serve as a test bed for prototype for SNAP flight detectors. The same spectrograph can be used both on the ground and on a balloon.

Optical fibers will scramble the signal to minimize near field/far field effects. The thruput of low-OH quartz fibers is good from .45-1.7 microns, with no strong spectral features. We do not expect any differential fiber transmission variations due to misalignment, flexure, polishing, or centering. We can use relatively large fibers to minimize effects of atmospheric refraction, pointing and centering.

We will use beam-switching fibers to measure simultaneously star and sky, which allows correction for variable OH airglow in the near infrared. Since the flat-field cancels exactly, we can measure the ratio of starlight to lamplight directly. The wavelength dependence of fiber thruput cancels. In addition, the spectograph design allows us to measure the wavelength dependence of our optical train.

MWR The second and third sentences of the above paragraph confuse me. Can someone clarify?

Primary Spectrophotometric Standard Stars

The selection of the primary spectrophotometric standard stars is an early priority of this program. At the present time our initial searches have concentrated on high gravity stars with only a few strongly pressure-broadened lines. The best candidates so far are therefore hot white dwarfs and sd0 stars. Other selection criteria include proximity to the North Galactic Pole or the South Galactic Pole, near the SNAP fields, which minimizes the airmass differences between the primary and secondary standards.

Our searches for primary spectrophotometric standards have so far concentrated on stars mentioned in papers by Oke and Gunn (1983), Finley et al. (1997), the Hamuy et al. (1992, 1994). The most promising sources so far are

RA, Dec
Gal. long, lat
HZ 44 13:23:35.3 +36:08:00
87 +79
Feige 66 12:37:23.5 +25:04:00
245 +86
EG 21 03:10:29.0 -68:35:54
286 -44

Although these sources are too faint for balloon measurements, they do demonstrate that candidate primary calibration sources can be found without confusing sources within a radius of 15 arc sec. Since these sources are essentially black bodies, (V - H) is approximately zero.

MWR insert image of Feige 66 here

Broadband Calibrations

Filter sensitivity function can be obtained by inserting filters into spectrograph beam, using the lamp as a source.

Establish grad of standard stars of varying colors whose measurement defines the SNAP broadband system.

Use of transformation coefficients circumvents the need to reproduce the ground-based (or balloon-based) passbands precisely with flight hardware. Changes in during mission can also be corrected.

MWR I am not convinced that the statements in the previous paragraph are correct. I would argue that we ought to do all we can to make the flight hardware match our calibration hardware.