FUSE

Exposure Time Calculator Instructions

A Guide to Using the FUSE Exposure Time Calculator

Version 2.0

2000 October 2

Edward Murphy (Update by William Blair)

1.0 Introduction

The ETC has been specifically designed for calculations involving point source continuum objects which comprise the vast majority of FUSE targets. Section 3.0 below discusses some strategies needed to use the ETC for emission line objects.

1.1 Wavelength
Enter the wavelength at which the exposure time or signal-to-noise ratio is to be calculated. FUSE covers the 905.0 Å to 1187.7 Å part of the far-UV spectrum. The ETC performs checks on the given wavelength to ensure that it is in the FUSE bandpass, and will alert the user if the wavelength falls in or near one of the detector segment edges or gaps. See the FUSE Observer's Guide Section 2.4.1 for more details.

1.2 Source Flux
The given flux should correspond to the flux of the source at the wavelength given above. The user can input an observed (or attenuated flux, already including extinction), in which case they should use E(B-V)=0.0. Otherwise the user can input an unattenuated (or assumed intrinsic) flux and then enter an appropriate E(B-V). The ETC will attenuate the flux using the reddening models of Cardelli, Clayton, & Mathis, 1989, ApJ, 345, 245 (CCM). NOTE: When using IUE or HST fluxes, it is insufficient to assume that that the reddening at the shorter wavelengths is similar to the reddening above 1200 Å. For example, with an E(B-V)=0.1, the attenuation at 950 Å is twice that at 1200 Å. Table 1 contains a listing of the flux attenuation as a function of wavelength for the CCM model. The CCM extinction relations were extrapolated to cover wavelengths below 1000 Å.

1.3 E(B-V)
If the given flux has been attenuated then use E(B-V)=0.0 which introduces no additional reddening. If the given flux is unreddened, enter the E(B-V) and the ETC will calculate the attenuation based on the reddening models of Cardelli, Clayton, & Mathis, 1989, ApJ, 345, 245. See the section above on Source Flux for more details.

1.4 Aperture
FUSE has four spectrograph apertures. See the FUSE Observer's Guide Section 2.3 for more details.

Notes: The aperture throughputs are computed assuming nominal PSF (90% encircled energy in 1.3 arcsec diameter), pointing jitter of <0.5 arcsec (1 sigma), and pointing accuracy of <0.2 arcsec, all of which have been achieved on orbit. However, maintaining channel alignments for MDRS and HIRS on orbital timescales is difficult at best, and is worst for the SiC (short wavelength) channels. Hence, a throughput averaged over a typical observation with MDRS or HIRS is much lower than this Table indicates.

1.5 Science Requirements
The Exposure Time Calculator can either calculate the exposure time necessary to reach a given signal-to-noise ratio or can calculate the signal-to-noise ratio given an exposure time. Starting in cycle 2, we have added the capability to specify the S/N assuming either a particular channel (which assumes the effective area for just the specified channel), or assuming TOTAL (which uses the total effective area from any and all channels that contribute at the specified wavelength). Note that if a single channel is specified, the ETC also reports the "total" value that will be achieved (if different from the single channel value). If "total" is selected, the ETC will also report the S/N expected in the individual channels. Be careful to list self-consistent information in your target/observation listings!

1.6 Effective Area
The ETC uses the most recent, measured on-orbit effective areas. The effective area was expected to decrease by about 10% per year or more, but to date (Oct. 2000) has decreased by less than 5%. You may want to note the ETC version number of your calculations in case changes are made in the future.

1.7 Spectral Bin Size
The spectral bin size is the wavelength bin over which the calculations should be performed, in Angstroms. For full resolution, the actual spectral resolution varies with wavelength and detector segment (see FUSE Observer's Guide Section 2.4.3). However, if you do not need full resolution, you can enter a larger bin size (e.g. 0.1 Å, 0.5 Å, etc.).

1.8 Dark Count
The dark count is the intrinsic detector background in counts cm^-2 s^-1. The FUSE project believes that the dark count will be less than 1 count cm^-2 s^-1. For very faint objects, the uncertainty in our ability to measure the background will limit the available signal-to-noise ratio. See the FUSE Observer's Guide Section 2.5.1 for more details. The ETC defaults to the current measured dark count rate, although the user can override this value.

1.9 Airglow
The ETC has the ability to account for scattered Lyman-alpha airglow at the wavelength of interest. The daytime Ly-alpha airglow is typically 20 kR while the nighttime airglow is around 3 kR. Since most long integrations will have at least part of the observation in orbital day, we have used 10 kR as the default value. For faint sources, users can experiment with higher or lower values to determine the sensitivity of their observations to this faint background. Note that the ETC only accounts for scattered Ly-alpha. It does not include individual airglow lines. Example FUSE airglow spectra are available HERE.

2.0 The Output

Additional parameters are given in table format. In addition to repeating the input parameters, the output list includes many important derived parameters such as the effective area at the wavelength of interest, the reddened source flux, aperture throughput, and the fraction of astigmatic spectrum which can be recovered. It also includes the number of SiC and LiF channels in use at the reference wavelength, the astigmatic height(s) of the spectra, and the source, dark and airglow counts in a spectral bin at the wavelength of interest. The ETC attempts to estimate the total count rate and total number of counts assuming a flat spectrum over the 900 Å to 1200 Å band. For a more accurate treatment, follow the link at the top of the page to the Count Rate Tool. The total count rates are included for determining the observing mode (time-tag or histogram) and data rate and memory usage onboard the satellite. They are not used in determining the exposure time nor in calculating expected the S/N ratio. The total count assumes that the full area of the detectors is being read out. This means that the total dark includes contributions from the whole detector and that the total airglow includes airglow emission from all the apetures.

3.0 Using the ETC for Emission Line Objects

3.1 Unresolved Emission Lines
Unresolved emission lines will typically have a FWHM < 15 km/s. They can be treated with the ETC after converting the total line flux (in ergs cm^-2 s^-1) to a flux density (ergs cm^-2 s^-1 Å^-1). Divide the integrated line flux by the width of a resolution element (typically 0.032 Å) at the wavelength of the line and enter this width in the spectral bin size box. After that, the treatment is the same as for a continuum source.

3.2 Resolved Emission Lines
Resolved emission lines are treated in much the same way as unresolved lines in that the integrated line flux is converted to a flux density. In the case of resolved lines, divide the integrated flux by the FWHM of the line (provided that the FWHM is greater than a resolution element). Use a spectral bin size appropriate to your science requirements as long as it is less than or equal to the FWHM of the line.

4.0 Using the ETC for Spatially Extended Objects

Observations of spatially extended objects in the MDRS (4") and LWRS (30") apertures will reduce the spectral resolution. If the source completely fills the MDRS (4") or LWRS (30") aperture, the maximum resolution is 0.054 Å or 0.33 Å, respectively.

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