# Step-by-Step procedure for transferring SNAP calibration

#### Assumptions

We assume that
1. the SNAP field is the North Ecliptic Pole (we ignore the southern SNAP field for now)
2. the SNAP field is one square degree
3. the primary standard(s) have been chosen
4. the primary standard(s) are within 10 degrees of the SNAP field
5. the primary standards have been measured with an accurate spectrometer

#### Pick field(s)

The actual SNAP field should not have bright stars in it; they will contaminate measurements of the faint, V=25 SNe. We assume that no stars brighter than V=11 fall within the SNAP field itself. We expect to find roughly 10 K giants with V<15 in the SNAP field.

#### Step 1: Transferring Primary (outside SNAP field) to Secondary (outside)

• Comparing stars of approx V=6 to stars of approx V=10
• Stars should all be K giants
• Must worry a lot about extinction, since the stars are likely to be 5-15 degrees apart
• requires all-sky photometry
• must observe stars at different airmasses interspersed with SNAP standards
• requires absolutely clear skies
• skies may be bright, since there will be plenty of photons
• should repeat measurements on at least 2 different nights within a few weeks; 3 nights would be better
• if can repeat N times, will beat down some significant random errors in extinction
• can be done easily on 1-m class telescope with aperture mask
• can be done with difficulty on 4-m class telescope, because aperture mask would be massive
• necessary to use aperture masks (one big, one small) to double-check shutter effects

#### Step 2: Transferring Secondary (outside SNAP field) to Tertiary (inside)

• Comparing stars of approx V=10 to stars of approx V=15
• Stars should all be K giants
• Stars will be within 2 or 3 degrees of each other, so corrections for extinction are less critical
• number of auxiliary observations of stars at different airmasses may be smaller
• possibly could carry out observations though thin clouds
• must pay attention to scattered light, since will be looking at bright stars close to (but outside) the field of view
• can be done easily with 1-m class telescope, without aperture mask
• may possibly be done on WIYN 3.5-m telescope, even without aperture mask (depends on shutter accuracy)
• aperture mask(s) may not be necessary (on 1-m telescope)

#### Step 3: Transferring Tertiary (inside SNAP field) to Quaternary (inside)

• Comparing stars of approx V=15 to stars of approx V=20
• Stars should all be K giants
• Stars are in the same field, so extinction corrections are easy
• Should concentrate on stars of the same color and spectral class as primary standards
• is necessary to use telescope larger than 1-m class, in order to get adequate signal-to-noise
• exposure times on 3.5-m are more than 100 seconds, so shutter probably accurate enough; no need for aperture mask except as sanity check

#### Step 4: Transferring Quaternary (inside SNAP field) to Final (inside)

• Comparing stars of approx V=20 to stars of approx V=25
• Stars are in the same field, so extinction corrections are easy
• will have to choose stars of a range of colors, since SNe will have different colors as they age
• is necessary to use telescope larger of 8-m class in order to get adequate signal-to-noise

#### Internal checks

We can very easily build two aperture masks for the WIYN 0.9-m telescope: one with a diameter about 0.9 meters, one with a diameter about 0.2 meters. These will allow us to check the shutter motion and the linearity of the CCD. They will also permit us to take images of stars as bright as V = 6 with 10 second exposures. If necessary, the smaller mask could be made 0.15 or 0.10 meters in diameter to accomodate the primary standards.

Building an aperture mask for the WIYN 3.5-m telescope is not so easy, because the darn structure is too large, and sits far above the ground. It might be relatively easy to place a mask of some sort into the light beam at the Nasmythe focus. However, the beam has converged a lot by that point, and a simple circular hole will not dim all stars in the field by the same amount. I have been thinking about various kinds of obstructions (wire mesh screens, plates with many holes drilled into them), and haven't found one that will meet our needs yet. It is possible that we might use a neutral density filter at this point to perform certain internal checks, even if we don't use it in calibration observations. The narrower our filters, the better the neutral density filter will work for us.

In any case, we should do at least the following tasks to verify our ground-based calibration.

1. measure the shutter motion of the all cameras we use (MOSAIC on 0.9-m, miniMosaic on 3.5-m)
2. measure the CCD linearity of all the cameras we use
3. compare relative magnitudes derived from WIYN 0.9-m to relative magnitudes derived from WIYN 3.5-m, for at least the Secondary-Tertiary step
4. place limits on the variability of all secondary, etc. standard stars
• requires observations for at least 2 years
• 0.9-m okay except maybe for quaternaries and finals
5. acquire spectra of all secondary, etc. standard stars
• requires moderate telescope + spectrograph

#### Passbands

Which passbands should we choose when comparing one set of stars to another? The choices are:
• wide: approx 1000 Angstroms (Johnson-Cousins BVRI, JHK). Advantages:
1. requires less exposure time, smaller telescope for faint stars
2. less sensitive to narrow spectral features
3. same filters used by astronomers in many disciplines
• narrow: approx 70 Angstroms Advantages:
1. requires more exposure time or a larger telescope, can help when looking at very bright stars
2. less sensitive to color-dependent atmospheric extinction
3. less sensitive to color differences between stars

I believe we should use a set of narrow-band filters for the first transfer of primary-to-secondary at least. The narrow filters will allow us to use large telescopes and reasonable exposure times to look at stars as bright as V = 10.

Some of the filters which are available for the WIYN telescopes and appear to suit our needs are shown below.

```                           WIYN_Imager_Filter_List
wiyn # cwl fwhm  %T maxsize         name   comments       date_measured age
16 6618   72     874x4   UWisc                        1-97          1997
17 6725   70     874x4   UWisc                        1-97          1997

19 4063   56     634x4   comet set 2 C3               3-97          1997
20 4448   62     744x4   comet set 2 Blue Cont        3-97          1997

25 7026  190     874x4   comet set 2 H2O+             3-97          1997
26 7121   60     874x4   comet set 2 Red Cont         3-97          1997

```

I have checked to make sure that the filters above do not fall across any strong spectral features in K giants. The filter number 15 is close to H-alpha, but may be okay.

#### The result

After all the photometric observations and reductions, we end up with the following information:

```primary standards:       know relative intensity as a function of wavelength
from visible to near-IR, due to balloon-borne
spectrograph

all other standards:     know the flux integrated over several passbands
relative to the flux of the primaries,
integrated over the same passbands
know the flux of each star, integrated over several
passbands, relative to the flux of itself,
integrated over other passbands

```

In other words, for the secondary standards, we do NOT know the ratio (for example)

```              flux at 5000 Angstroms
----------------------
flux at 14000 Angstroms
```
Instead, we know only these ratios (where V and J are examples of the several passbands we may choose to use for calibration):
```          flux of self integrated over V band
-----------------------------------
flux of self integrated over J band
and

flux of self integrated over V band
----------------------------------
flux of primary integrated over V band
```

The narrower the passbands we use for calibration, the smaller the uncertainty in these ratios (I claim).

In other words, if we pick a set of narrow-band filters and observe all standards through them, we will end up with known ratios of flux at a number of wavelengths. We can then calibrate an observed spectrum by forcing it to pass through these points.

In order to perform cosmological tests of nearby SNe versus distant SNe, one must know

1. the shape of the spectra of SNe
2. the shape of the passbands used to calibrate the SNAP standards
3. the shape of the passbands used to observe the nearby SNe
4. the shape of the passbands used to observe the distant SNe

Note that the passbands in items 2 and 4 above WILL NOT BE IDENTICAL, because the instruments on board the SNAP spacecraft will not be the same ones used to calibrate the standard stars.