Observing Convectively Excited Gravity Modes in Main Sequence Stars


This paper will primarily focus on a study by (Shiode 2013) on how gravity modes could be excited by convection in massive main sequence stars. The first portion of this paper will explain the more commonly understood method of how gravity modes are driven by adiabatic expansion at the core and why gravity modes produced this way are so difficult to observe. The second part of this paper will briefly go over the methods for detecting gravity modes and the observational challenges faced. The third portion will look at models (Shiode 2013) constructed using the MESA stellar evolution code that were used to estimate mode frequencies, excitation amplitudes and where in the stellar interior of various sized main sequence stars, gravity modes would propagate. The final portion of this paper will look at future advancements in detecting gravity modes and promising observations taken from the Kepler space satellite.


The detection of gravity modes (g-modes) is crucial for the understanding of the solar interior. Although some teams over the past couple decades have claimed to have detected g-modes, to date there has been no concrete evidence of g-modes being detected in main sequence stars. Future concrete g-mode discoveries would provide researchers with a powerful tool for obtaining more detailed data on the stellar interior. P-modes do not provide enough quality information about the deep interior of stars because P-modes are typically excited by outer convective regions and typically do not penetrate deep depths in the star. Old style adiabatic expansion driven g-modes are excited by operations near the core, but are often too dampened to for modern instruments to make meaningful observations. Gravity modes from other stellar types such as white dwarfs have been observed. (Shiode 2013) showed that g-modes, which produce variations in magnitude, could potentially be detected for main sequence stars with \(M>5M⊙\) and may even be detectable in the 2-3 solar mass range (Shiode 2013). These modeled g-modes are excited in the outer convective region of the stellar interior which is different from the g-modes previously sought after that are excited near the core driven by adiabatic expansion. G-modes propagating in the outer regions could make their instrumental detection more likely. These g-modes may penetrate deep into the star and be able to provide large amounts of information about the interior of stars that p-modes have not been successful at. Gravity modes are difficult to detect in smaller main sequence stars (MS) around ~\(1{M}_{⊙}\) due to smaller MS stars tending to have smaller convective regions and larger radiative sections in the core.

Old School G-Modes

Conditions for Gravity Mode Oscillations

Unlike the more easily detectable p-modes that use pressure as the restoring force, g-modes are waves of dense material that use gravity as its restoring force. The power these g-mode waves require to oscillate comes from adiabatic expansion in the stellar interior. A star that could produce a gravity mode would have a core with a very poor temperature gradient. When a hot gas packet begins to move upwards away from the hot center it starts to cool and when a gas cools it becomes denser. This cooling gas becomes dense enough that the buoyant force that caused it to rise is now too small to overcome the gravitational force of the stellar core and the gas begins falling back towards the denser center. This makes gravity the restoring force that restores the density wave back to its starting place. These oscillations happen deep in the stellar interior and are extremely difficult to detect. This initial adiabatic expansion and the restoring gravitational pull from the core result in this oscillating movement of large amounts of gas in the interior, and this is what drives g-modes. Because this process happens deep in the stars interior, the oscillations weaken dramatically as they pass through the outer convective region which acts as a dampening cushion in a similar way to how grabbing a tunning fork quickly dampens out the fork’s vibrating oscillations. Unlike p-modes, which often have much larger amplitudes at much higher frequencies making them more easily detectable, these types of g-modes will only produce small amplitudes given they are strong enough to reach the surface.

Observational Challenges for Detecting G-Modes

One of the big challenges faced with detecting g-modes is lowering the upper limit for g-mode amplitudes. The upper limit defines the current possible range of a potential g-mode amplitude for a given a mode frequency. The current predicted theoretical amplitude for a low order high frequency solar g-mode is estimated to be \(~{}{10}^{-2}\)cm/s and \(~{}{10}^{-3}\)cm/s for moderate to high order modes (Kumar 1996). Current upper limits for g-mode amplitude are under 10 mm/s and vary based on the instrument and length of the time series. The GOLF instrument on board the SOHO spacecraft is roughly 6.5 mm/s because its data set was taken over six years. BiSON has calculated an even lower upper limit of 3.5 mm/s from a ground based instrument using a nine year time series. The upper limit comes from a probability limit calculated in (Appourchaux 2000). The upper limit is important because instrumental observations return large amounts of noise and to hastily lower the the probability limit and thus the upper limit would mean accepting more peak values that could just be solar noise and potentially missing real g-mode peaks (Appourchaux 2003). Lowering the upper limit is extremely advantageous to helping find an actual g-mode as long as it is done carefully. A lower upper limit means a smaller range of data that must be processed and a higher likelihood of finding a g-mode. However, lowering the upper limit has been a very slow process. Alternatives to drastically lowering the upper limit will be discussed in the Future Observational Prospects section.

G-Mode Detection Techniques

There are a number of methods for detecting g-modes from instrument data. Spectrum estimators are a common technique with the Fourier spectrum being one of the most widely used estimators (Appourchaux 2003). The Fourier transform applied to large oscillation redshift data can identify potential g-modes. Mode masking is another technique used for detecting g-modes. Masking is often used to detect modes produced by the sun. Masking helps boost the signal-to-noise ratio and assist in masking other mode peaks that would otherwise interfere with potential g-modes (Wachter 2003). Patterns is also a technique used on low frequency stars that takes advantage of the asymptotic predictable behavior of low frequency stars. However low frequency g-modes have a very poor signal-to-noise ratio that makes this method difficult. One other promising method for mode detection is the use of multiple instruments (Appourchaux 2003). This would help clean up the signal and make and modes more prominent and make noise less of an obstacle.