# Issues in Calibrating SNAP

#### Observing nearby and distant supernovae: the basic idea

We assume
1. all Type Ia supernovae are exactly the same
• identical spectra (at all times)
• identical luminosity (at all times)
2. the instrumental systems are known almost perfectly
• passband shapes are known exactly
• passband throughputs (or Quantum Efficiencies) are not known

We want to compare the apparent brightness nearby and distant SNe; deviations from the inverse square law tell us about the geometry of the universe.

Step 1

Here's how we do it:

• observe a nearby SN in the visual, very probably using a smallish telescope on the ground. The result is
```  I(near) =  (nearby SN spectrum) convolve  (visual passband * QE_near)
```
• observe a distant SN in the near-IR (into which the rest-frame visible has been redshifted), using SNAP in orbit. The result is
```  I(far)  =  (distant SN spectrum) convolve (near-IR passband * QE_far)
```
In the equations above, QE_near is the overall QE of the instrument used to observe nearby SNe, and QE_far is the overall QE of the instrument used to observe distant SNe (i.e. SNAP).

The closer the near-IR passband is to a copy of the visible passband, shifted to the redshift of the distant SN, the better.

Step 2

Next, we make a second round of observations, using the same instruments to look at sources of precisely known spectra. We must know both the shape of each source's spectrum, and the relative brightness of each source.

• observe a bright source in the visual, very probably using a smallish telescope on the ground. The result is
```  I(bright) =  (bright known spectrum) convolve  (visual passband * QE_near)
```
• observe a faint source in the near-IR, using SNAP in orbit. The result is
```  I(faint)  =  (faint known spectrum)  convolve  (near-IR passband * QE_far)
```
In the equations above, QE_near is the overall QE of the instrument used to observe nearby SNe, and QE_far is the overall QE of the instrument used to observe distant SNe (i.e. SNAP).

Step 3

We use observations of the standard source to determine the relative throughput, R, of the two instrumental systems:

```
QE_far          I(faint)
----------  =  ---------------    =  R
QE_near          I(near)
```

Step 4

Now that we know the relative throughput of the two instruments, we can compare the observed quantities fairly:

```   I(far)        (distant SN spectrum) convolve (near-IR passband)
-------   =   ---------------------------------------------------  *  R
I(near)       (nearby SN spectrum)  convolve (visible passband)
```

Compare this ratio to the predictions of various models of the universe.

#### Some pitfalls in the calibration process

There are a number of mistakes which can lead to systematic errors and ruin the experiment. This is a partial list of them.

1. error in shape of instrumental passband
2. error in measurement of SN redshift
3. error in relative scale of faint and bright standard sources
4. error in shape of standard sources' spectra
5. error in shape of nearby SN spectrum
6. error in shape of distant SN spectrum

I will address here the first 4 issues only.

Shape of the instrumental passband

One can measure the spectral response of a filter easily; the response of a detector almost as easily; the response of a telescope with some difficulty; and the response of the Earth's atmosphere with much effort. A telescope on the ground has an effective passband which is the product of all these factors; in space, the response depends on the first three.

Instruments launched into space face a very different environment than that in which they were built. The change in temperature, pressure and humidity can cause the effective passband to change signficantly. The spectral response of the main detector on the Hipparcos satellite, for example, appears to have shifted to the blue by about 30 nanometers. The figure below, from Bessell, PASP, 112, 961 (2000) , shows the design passband (heavy dark line) and an estimate of the final, on-flight passband (narrow line to the left of the original).

If the actual passband doesn't match the assumed passband, how large is the resulting error in the photometry?

The figure above shows the fractional error in photometry (the convolution of a spectrum with a passband) as a function of a shift in the effective passband. I used two different filters:

• "narrow": similar to Bessell V in shape, centered at 16000 Angstroms, width 900 Angstroms
• "wide": similar to redshifted Bessell V in shape, centered at 16000 Angstroms, width 2200 Angstroms
The passbands were simply translated by a fixed amount in wavelength, so that both edges moved in the same direction, by the same amount.

The figure shows the errors for three different stars: a "hot" star (A0 dwarf), a "cool" star (K0 giant), and a Type Ia supernova near maximum light at z=1.5. Note that

• the errors for stars follow simple, linear trends
• the errors for a Type Ia SN are not so linear
• a cool star is a better match for a Type Ia SN at z=1.5 in this spectral range than a hot star
• the smaller the passband, the more the SN differs from stars

The differences between errors for stars and for the SN is due to the difference in their spectra: the spectrum of a Type Ia SN near maximum light is dominated by strong, wide absorption features. It is unlike the spectrum of any ordinary star.

Error in determination of SN redshift

If one makes an error in measuring the redshift of a distant SN, how large is the resulting error in the photometry?

One can calculate the fractional error in photometry for a supernova which is really at z=1.5, but is thought to be at some other redshift. In the figure above, I show the errors when observing through "wide" filters: versions of the Bessell B and V passbands, redshifted to z=1.5. The Bessell passbands have relatively gradual edges, especially on the red side. In the figure below, I show the errors when observing through passbands with relatively sharp edges: they are based on an interference filter, the SDSS i'. One is "wide" (central wavelength 13500 Angstroms, width 2100 Angstroms), the other "narrow" (central wavelength 13500 Angstroms, width 1200 Angstroms).

Note that an error of about 0.05 in redshift can lead to an error of 1-2 percent in photometry.

Error in relative scale of faint and bright standard sources

We will base the calibration process on a very bright fundamental standard star(s), which we will observe in a special manner (probably from a balloon-borne telescope, against a calibrated reference lamp). The fundamental standard(s) must be around magnitude 5, in order to gather enough photons in both the visible and near-IR to reach our required precision.

The nearby SNe will be roughly mag 12, a factor of about 630 times fainter.

The distant SNe will be roughly mag 25, a factor of about 100,000,000 times fainter.

We must transfer the calibration from the fundamental standard to fainter secondary, tertiary, etc. standards. Errors made at each step multiply together. If the faintest standard requires 4 transfers from the fundamental, and if the ratio of brightness is to be known to an accuracy of 1 percent, then each step must incur an error of no more than 0.25 percent, or roughly 0.0025 magnitudes.

Error in shape of standard sources' spectra

If the standard stars do not have exactly the same spectral shape, then we will calculate incorrectly the relative throughput of the instruments used to observe nearby and distant SNe. In order to prevent this effect from causing a 1 percent systematic error between the near and far measurements, we must know that the spectra of stars differing by 20 magnitudes in brightness are alike to 1 percent across the entire visible and near-IR.

#### A plan for the near future

We have argued elsewhere http://spiff.rit.edu/richmond/snap/primaries.html that the fundamental (and fainter) standard stars should be K giants. They

• are stable in brightness
• provide plenty of photons in the visible and near-IR
• are common all over the sky

Our plan for the next six months is to do groundwork for the northern SNAP field, which we assume to be near the North Ecliptic Pole (NEP).

1. Find an area roughly one degree across near the NEP which is free of any bright stars; call this "SNAP field"
2. Search nearby for K giants of mag 5-6: candidates for fundamental standards
3. Use the WIYN 0.9m telescope in late May, 2002, to take images of the SNAP field through both wide (BVRI) and narrow filters in the visible. These images will serve
• as a first epoch(s) in variability studies
• to select candidates for secondary, tertiary standards
4. Test feasibility of aperture mask(s) on the WIYN 0.9m telescope; mask(s) will allow us to transfer measurements from bright to faint stars with confidence
5. Test shutter on WIYN 0.9m MOSAIC camera
6. Test linearity of WIYN 0.9m MOSAIC camera
7. Use the WIYN 3.5m telescope in June, 2002, to take images of the SNAP field through both wide and narrow filters in the visible. We will use these
• as a second epoch in variability studies
• to select candidates for secondary, tertiary standards
8. Test shutter on WIYN 3.5m mini-MOSAIC camera
9. Test linearity of WIYN 3.5m mini-MOSAIC camera
10. Consult with WIYN engineers on the possibility of a "mask" on the 3.5m telescope

In the more distant future, we must

• acquire spectra of candidates for standards in the field
• acquire near-IR images of the field
• continue to monitor the field in both visible and near-IR for 3-5 years