Creation and operation of the MSSP

Creation of an Ideal Spectrum

To produce simulated spectral observations, the MSSP requires the user first to synthesise ideal normalised spectra of various stellar types. We have used the University of California at Los Angeles SYNthesis code (UCLASYN) (Dworetsky & Jacobs 1985; Etzel 1982) for this purpose; line lists and oscillator strengths were taken from Thévenin (1989, 1990). The synthesised spectra were then modified by the MSSP for the observational variables listed below, to produce an ideal noise-free spectrum. The method used by the MSSP is outlined below.

Rotational Broadening:

This is simulated in the MSSP by convolving the spectrum being studied with a rotational broadening curve based on the star's projected rotational velocity . Other broadening effects are assumed to be minimal, especially as most of the stars in the Monash observing program are rapid rotators.

Blackbody Curve:

The spectra produced by UCLASYN have a normalised continuum level. To have the spectrum more representative of an actual stellar spectrum, the MSSP puts the spectrum into a blackbody form based on the effective temperature of the star.

Doppler Shift:

The spectrum is Doppler shifted in wavelength by the MSSP for the chosen line-of-sight radial velocity.

Atmospheric Scattering:

The effect of Rayleigh scattering in the atmosphere is simulated by reducing the spectrum's flux using the equation

where

is the spectrum's flux at the top of the Earth's atmosphere, is the spectrum's flux at the bottom of the Earth's atmosphere, is the wavelength in microns, and z is the star's zenith angle. The factor of assumes that the Earth's atmosphere is flat and is reasonably valid for zenith angles less than about 60 (Hardie 1962).

Mirror Reflectivity:

The reflectivity of each of the four mirrors in the telescope and spectrograph was taken to be 73% at all visible wavelengths studied. This assumes a basic reflectivity of 80% reduced over a year by unavoidable deterioration. See Walker (1984) for data on dust build-up on mirrors at the South African Astronomical Observatory.

Slit-width:

The throughput of the Monash spectrograph's entrance slit was calculated using data from the Royal Greenwich Observatory (RGO) spectrograph of the Anglo-Australian Observatory (Robinson 1985). These data give the percentage slit throughput for a given slit-width for four Full-Width at Half-Maximum (FWHM) seeing disks (0.5, 1.0, 2.0, and 5.0 arcseconds). To convert this to the Monash spectrograph slit-width, the plate scales of the two spectrographs were used. As the data are given for only these four FWHM values and given that a seeing of 0.5 arcseconds is very unlikely at our observatory, the MSSP simulates only the latter three values of seeing.

Instrumental Profile:

This is simulated by convolving the spectrum being studied with a gaussian based on the spectrograph's coma, spherical aberration, linear reciprocal dispersion, and on the chosen slit-width.

Grating Sensitivity:

For this simulation the MSSP uses data from the manufacturer and assumes that the incident light is polarised equally parallel and perpendicular to the grating's grooves.

Detector Sensitivity:

The sensitivity of the CCD detector used in the Monash spectrograph was supplied by the CCD's manufacturer and is given as the Quantum Detection Efficiency (Q) of the CCD. Q is based upon the detector's Signal-to-Noise Ratio (SNR).

However, the actual efficiency required for the MSSP is the probability that any given photon will be detected by the CCD as a function of wavelength. This is called the Quantum Efficiency (Q) of the detector:

If we assume that the CCD detector is ideal, then

This has been assumed to be the case in the MSSP, which is a reasonable approximation. However, Q is usually less than Q.

Rebinning:

Once all the previously mentioned effects have been simulated, the MSSP rebins the spectrum into the pixel size of the CCD. The relative flux at each pixel is calculated to produce a normalised noise-free spectrum.

Creation of a simulated spectrum

To convert the normalised noise-free spectrum into one likely to be observed with the Monash spectrograph, the MSSP must calculate the number of photons detected by the CCD and the amount of noise during each exposure.

To calculate the number of photons detected by the CCD, the average flux arriving at the top of the Earth's atmosphere (Allen 1973) is used. This is converted to the flux detected by the CCD by the processes outlined in Section 2.1, and thus into the average number of photons detected by the CCD from a star of given visual magnitude.

Because the actual number of photons arriving in any given time is random, the average number of photons calculated above is put through a Poissonian distribution before each exposure. This gives the actual number of photons detected by the CCD during each exposure. Then, using the noise-free spectrum obtained after rebinning as a probability template, the photons are randomly `fired', using a uniform distribution to determine the pixel number at the CCD. The chance of being detected by the CCD is based upon the intensity of the noise-free spectrum at the corresponding pixel. This is continued until all the photons have been detected by the CCD.

This creates a photon spectrum containing only photon noise, to which must still be added the non-statistical noise. The two types of non-statistical noise simulated by the MSSP are background light and the electrical noise produced by the CCD and its associated electronics.

In order to simulate the background noise in the spectrum, the MSSP uses data based upon photometric data taken at the site, as there are no other data available. Thus the background light is only an estimate and contains no information on additional spectral lines or the dependence of the intensity of the background light upon wavelength. The background light added to the spectrum by the MSSP can have one of three levels: dark sky (new moon), average sky (quarter moon), and bright sky (full moon).

The second source of non-statistical noise in the spectrum, from the CCD and its associate electronics, was calculated from data on the electronic noise of the CCD (Coutures & Boucharlat 1987) and an estimate of the off-chip noise of the electronics.

Once the amount of non-statistical noise is calculated, from both the background light and the CCD noise, both are converted to electron numbers and are each randomised by a Poissonian distribution before each exposure, similar to that done to the photon numbers, to represent the random nature of the noise. The electrons are then distributed randomly through the photon spectrum by using a uniform distribution. This then produces a simulation of a spectrum similar to that produced by the Monash spectrograph.

This simulated spectrum can then be cross-correlated with a spectrum from a comparison star to give a simulated radial velocity measurement.

© Copyright Astronomical Society of Australia 1997