Next: Other noise sources Up: Photometric precision limits Previous: Photon noise

Example

Assuming an aperture of 80 cm, an solar-type star produces electrons s-1 in the CCD. It follows that the photon noise power is Hz-1 = 0.14 ppmHz-1, which is about equal to the solar continuum noise at 3mHz due to granulation. We assume a solar oscillation spectrum with integrated line intensities of about 2 ppm at a linewidth of Hz. The photon noise amplitude in a frequency bin equal to the linewidth is ppm. It follows that the signal to noise ratio for an individual line in the spectrum is of order 2 ppm/0.4 ppm = 5. For a given star this figure is proportional to the diameter of the telescope, but it is independent of the length T of the observation. For the signal to noise ratio is about 2. This renders detection of individual lines difficult, although a series of lines remains well visible. We conclude that the limiting magnitude for detection of solar-type oscillation spectra is between and 10, depending on the excitation level of the oscillations.

Returning to the example of , we see from (3.2) that the photon-noise-induced photometric precision in an individual measurement of seconds is , which is only 120 ppm for s. From relation (3.3) we find that the photometric precision in one month due to photon noise is 0.2 ppm (0.6 ppm for ). There is no contradiction here; it highlights the well-known fact that the amplitude of a periodic signal in a time series can be determined with much greater precision than that of the individual measurements.



Next: Other noise sources Up: Photometric precision limits Previous: Photon noise