Simulation of the MOST time series on Procyon

Hans Kjeldsen and Jørgen Christensen-Dalsgaard

Department of Physics and Astronomy, University of Aarhus, Denmark

The aim of this homepage is to present a number of key issues related to the simulations of time-series data on Procyon. The simulations are related to the published null result on Procyon obtained by the Canadian MOST satellite and published by Matthews et al. in Nature.

The present analysis is based on a software package developed to provide time-series simulations for the Danish MONS/Rømer space mission as well as for the ESA Eddington mission. The software package contains a set of routines that can be used to simulate noise as well as p-mode oscillation signal.

The software can be used to simulate the noise using a number of filtered 1/f (in amplitude) noise sources (e.g. granulation) as well as periodic noise and white noise (from e.g. photon noise) terms. Oscillation p-mode signal is simulated using a set of equations that allows one to create stochastically excited oscillations, specifying mode life-time, mean amplitude and frequency for a large number of individual modes.

The figures below show simulations of Procyon using a sampling of one data point per 100 sec. The first figure shows the time series indicating the p-mode signal (black) and a simulation of granulation at the solar level (red). 

The Fourier amplitude spectrum of 32 days of this series is shown below. p-mode signal is indicated by black, while granulation power is shown in red.

Using the simulation software we calibrate the p-mode amplitude using the published p-mode excess in Martic et al. (2004, Astronomy and Astrophysics, 418, p. 295-303) and we also use the upper limit for the intensity power for granulation in Procyon using the values from Hydrogen Balmerline index oscillations (Kjeldsen et al. 1999, Monthly Notices of the Royal Astronomical Society, 303, p. 579-587). This gives a maximum power for the granulation in Procyon of 2 times solar. We use this as a best estimate for the granulation power in Procyon. The figure below shows the power excess obtained by Martic et al. (2004) using the ELODIE spectrograph. 

Using the velocity power excess measured by Martic et al. (2004), we estimate an amplitude in photometry of 7-8 ppm per mode (Kjeldsen and Bedding, Astronomy and Astrophysics, 293, p. 87-106). The mode lifetime is assumed to be around 1.9 days as inferred from the velocity time-series data.

Based on this we have done a number of simulations using different levels of the granulation power background. Below we show the simulated Procyon amplitude spectrum for 3 different levels of the granulation power (solar level, 2 times solar power and 4 times solar power). We recall that a power level of 2 times solar is in agreement with the measured upper limits from ground-based observations (Kjeldsen et al. 1999).

We then simulate a series that contains the same power as the MOST time series presented by Matthews et al. in Nature (2004). In order to reach a result similar to the MOST time series we need to:

(1) Add a granulation power 25 times as large as the solar value (5 times the solar amplitude), or

(2) Include a significant instrumental noise.

We have also simulated ground-based data sets, e.g. the velocity time series obtained by Martic et al. (2004). Again we use a p-mode amplitude of 1.8 times solar (40 cm/s in velocity and 7-8 ppm in photometry), a damping time of 1.9 days per oscillation mode and a granulation background of 2 times solar (in power). The result of those simulations are shown in the figure below, where data corresponding to a full MOST series is shown in velocity (not photometry as measured by MOST) and compared with the 7 times 8 hour data segments obtained by Martic et al. (2004). We also show one figure including instrumental noise (ELODIE noise).

The last figure shows a power excess that can be directly compared with the power obtained by Martic et al. (2004)

Finally we show a direct comparison between the p-mode and granulation signal in Procyon (for an observation without instrumental noise; black) and a simulation of the MOST time series (grey). It is based on such a simulation that we conclude that MOST has not detected the granulation signal in Procyon, but that non-stellar noise is making a significant noise contribution that does not allow detection of p modes nor granulation power.