The visibility of low‐frequency solar acoustic modes

Abstract

We make predictions of the detectability of low-frequency p modes. Estimates of the powers and damping times of these low-frequency modes are found by extrapolating the observed powers and widths of higher-frequency modes with large observed signal-to-noise ratios. The extrapolations predict that the low-frequency modes will have small signal-to-noise ratios and narrow widths in a frequency-power spectrum. Monte Carlo simulations were then performed where timeseries containing mode signals and normally distributed Gaussian noise were produced. The mode signals were simulated to have the powers and damping times predicted by the extrapolations. Various statistical tests were then performed on the frequency-amplitude spectra formed from these timeseries to investigate the fraction of spectra in which the modes could be detected. The results of these simulations were then compared to the number of p-modes candidates observed in real Sun-as-a-star data at low frequencies. The fraction of simulated spectra in which modes were detected decreases rapidly as the frequency of modes decreases and so the fraction of simulations in which the low-frequency modes were detected was very small. However, increasing the signal-to-noise (S/N) ratio of the low-frequency modes by a factor of 2 above the extrapolated values led to significantly more detections. Therefore efforts should continue to further improve the quality of solar data that is currently available.Comment: 9 pages, 6 figures, accepted for publication in Astronomische Nachrichte

A comparison of frequentist and Bayesian inference: searching for low-frequency p modes and g modes in Sun-as-a-star data

“…Even so, it is possible that this method under‐estimates the power of the signal from a mode. For example, Broomhall et al (2008) found that the l = 0, n = 6 mode at ∼ 972 μ Hz is excited to a larger power than is expected from the extrapolations. In fact, the simulations performed by Broomhall et al indicated that if the actual power was equal to the value given by the extrapolation, the probability that the l = 0, n = 6 mode would be excited to the observed power is approximately 0.01.…”

“…The observed width of a mode is dependent on the mode's lifetime and the length of the respective data set. Although the lifetimes of low‐frequency p modes are uncertain, evidence from higher frequency p modes implies that in a time series of a length of 8.5 yr, which is the length of the data series analysed here, even very low‐frequency p modes could have resolved widths (Broomhall et al 2008). The lifetimes of g modes are less predictable and so it is uncertain whether or not the width of g modes will be resolved.…”

“…For p modes the value of H was estimated in two different ways, each of which will now be described. Broomhall et al (2008) extrapolated to low frequencies the total mode powers, V 2 , and widths, Δ, of well‐defined, higher frequency modes, whose profiles in a frequency–power spectrum can be fitted accurately. The total power, V 2 , was extrapolated in preference to H as it is not dependent on Δ. Broomhall et al did this in two different ways and here we have used the method that produced the largest H values.…”

“…More realistic probabilities may be obtained if we overestimate the range of heights over which the integration in equation ( 4) is made. Therefore, we have also performed a search where the maximum power spectral density per unit bin, H, was assumed to be constant at all frequencies and to have the height predicted by Broomhall et al (2008) for a mode with a frequency of 1500 µHz. A larger value of H should allow signals to be detected more easily as when H tends to 0, p(x|H1) tends to p(x|H0) and so it is very difficult to determine which hypothesis is most likely to be correct (see Fig.…”

Detecting individual gravity modes in the Sun: Chimera or reality?

“…There is a general consensus that the observational limit for low-degree, low-order p modes is around 1 mHz (Bertello et al 2000, Broomhall et al 2008, Salabert et al 2009). This is due to the raising convective background (e.g.…”