Seismology Research at NMSU

The Sun and many stars ring like a bell, as they are filled with acoustic waves excited by turbulent convection (see animation on right). These waves can be used to “see” into the solar interior using a technique called helioseismology. A useful analogy is Earth seismology. When an earthquake occurs, acoustic “sound” waves generated at the source travel deep into the Earth's interior and refract back towards the surface, where they are subsequently measured by seismographs. Comparisons of the observed travel times and amplitudes of the waves with theoretical models of the expected values allow geophysicists to infer sub-surface properties.

The situation is very similar in the case of the Sun and stars. Waves are continuously excited and travel throughout the stellar interior, some even all the way to the core. They then are refracted back to the surface where they can be measured using ground- and space-based telescopes. For the Sun, the information in the waves tells us about flows, rotation, sound speed, chemical abundances, asphericity, and magnetic fields along the areas where the waves traveled. Helioseismology has given us fascinating insights about the structure of the Sun. For stars, rotation and structure can be inferred from the frequencies of the waves.

The possible structure of the meridional flows in the Sun's convection zone. Such a configuration is a puzzle for those who try to determine how the Sun generates its magnetic fields.

The most important unsolved problems in solar physics concern the generation and evolution of magnetic fields. The Sun has a dynamo, not well understood, that creates its magnetism. The research objective of this project is to provide tight constraints on interior dynamo models so that a better understanding of the Sun and solar-cycle dynamics becomes possible.

This can be achieved by measuring the large-scale plasma flows throughout the entire solar convection zone with unprecedented accuracy using local helioseismology. The role of rotation and interior flows such as the meridional circulation in driving the solar cycle is unquestioned. Key characteristics of the flows are still largely uncertain, such as their depth dependence, strength, and time variation. Yet, as ingredients to dynamo models of solar magnetic fields, such quantities are critically needed. On the left is a recently obtained insight into what the meridional flows structure may look like, adapted from [1Zhao, Junwei; Bogart, R. S.; Kosovichev, A. G.; Duvall, T. L., Jr.; Hartlep, Thomas (2013): "Detection of Equatorward Meridional Flow and Evidence of Double-cell Meridional Circulation inside the Sun", Astrophysical Journal Letters 774(2):L29. (Link)]. Our research attempts to determine this information.

We focus on stars that pulsate like our Sun in what follows, both for simplicity and because the interpretation of the data is much more advanced than for other types of pulsators. Such solar-like oscillators need not be solar-type, main-sequence stars at all; for example, almost all red giants, such as the bright Aldebaran [2Farr, Will M.; Pope, Benjamin J. S.; Davies, Guy R.; North, Thomas S. H.; White, Timothy R.; Barrett, Jim W.; Miglio, Andrea; Lund, Mikkel N.; Antoci, Victoria; Fredslund Andersen, Mads; Grundahl, Frank; Huber, Daniel (2018): "Aldebaran b\textquoterights Temperate Past Uncovered in Planet Search Data", \apjl 865(2):L20. (Link)], display solar-like oscillations. They are the result of acoustic pressure waves that are excited to small, yet observable amplitudes by near-surface turbulent convection [3Goldreich, P.; Keeley, D. A. (1977): "Solar seismology. II. The stochastic excitation of the solar p-modes by turbulent convection.", \apj 212:243-251. (Link)]. These stars, therefore, must have an outer convection zone, with effective (surface) temperature below about 7000K, corresponding to an upper mass of about 1.5 solar masses on the main sequence and spectral types later than mid-F. For evolved subgiants and giants, G, K, and M stars are most typical (and masses can exceed 1.5 solar masses).

The oscillations are global modes in a star, which distort the stellar surface with a spatial pattern that can usually be described by spherical harmonics, resulting in luminosity and radial-velocity variations. The figure shows 4 examples, where the red and blue denote the (highly exaggerated) distortion of the particular part of the surface, and white are nodes (no distortion). Cancellation effects due to the point-source nature of distant stars only allow for observations of the lowest spherical harmonic degrees (L=0 - 3). In the figure, the top 2 animations are for L=1 and L=3, which would be observable. The other two (L=6 and L=10, would not be). Power spectra of a time series of a solar-like oscillator show a comb-like structure of peaks within a broad acoustic mode envelope that has a maximum amplitude at some temporal frequency. This can range from about 20 μHz (half a day period) for evolved giants to a few thousand μHz (periods of minutes) for dwarfs. The comb pattern has peaks that are evenly spaced in frequency, whereby frequency differences between modes of consecutive radial order n and the same spherical degree L are known as the large frequency spacing.

These observed modal properties are often interpreted in terms of the asymptotic theory of stellar oscillations [4Tassoul, M. (1980): "Asymptotic approximations for stellar nonradial pulsations.", \apjs 43:469-490. (Link)]. In this case, the large frequency spacing is related to the sound crossing time of an acoustic wave across the star, and therefore scales with the mean density. An empirically-motivated relationship connects the frequenc of maximum power with the surface gravity and effective temperature [5Brown, Timothy M.; Gilliland, Ronald L.; Noyes, Robert W.; Ramsey, Lawrence W. (1991): "Detection of Possible p-Mode Oscillations on Procyon", \apj 368:599. (Link)]. When these two relations are combined, scaling relations for a star's mass and radius can be derived [6Kjeldsen, H.; Bedding, T. R. (1995): "Amplitudes of stellar oscillations: the implications for asteroseismology.", åp 293:87-106.]

Other types of modes provide even more powerful diagnostics of interior conditions. In subsurface convectively-stable regions of stars, such as the cores of red giants, low-frequency gravity modes are excited. While they are not visible at the surface, they can interact and `mix' with acoustic modes and impart new information in the power spectrum. New frequency spacings appear, which can be used as diganostics of the core region, capable of providing the evolutionary state or inferring the core rotation rate.

All of the above may be considered as a broad application of asteroseismic analysis of global observables. Some high-precision observations, such as those from SONG, will go much further than applying the scaling relations. They can provide very precise individual mode frequencies for more modes than space photometry can, including mixed modes, L=3 modes, and modes split into multiplets by internal rotation. In fact, the relative amplitudes of the frequency multiplets can be used to measure the inclination of the stellar rotation axis [7Gizon, L.; Solanki, S. K. (2003): "Determining the Inclination of the Rotation Axis of a Sun-like Star", \apj 589(2):1009-1019. (Link)]. In any case, the measured frequencies can then be confronted with the frequencies predicted from sophisticated numerical models. The result is a deeper understanding of all of the interior stellar properties and evolutionary state of stars.

A detailed discussion about this topic can be found on the JIVE page.

[1]

Zhao, Junwei; Bogart, R. S.; Kosovichev, A. G.; Duvall, T. L., Jr.; Hartlep, Thomas (2013): "Detection of Equatorward Meridional Flow and Evidence of Double-cell Meridional Circulation inside the Sun", Astrophysical Journal Letters 774(2):L29. (Link)

[2]

Farr, Will M.; Pope, Benjamin J. S.; Davies, Guy R.; North, Thomas S. H.; White, Timothy R.; Barrett, Jim W.; Miglio, Andrea; Lund, Mikkel N.; Antoci, Victoria; Fredslund Andersen, Mads; Grundahl, Frank; Huber, Daniel (2018): "Aldebaran b\textquoterights Temperate Past Uncovered in Planet Search Data", \apjl 865(2):L20. (Link)

[3]

Goldreich, P.; Keeley, D. A. (1977): "Solar seismology. II. The stochastic excitation of the solar p-modes by turbulent convection.", \apj 212:243-251. (Link)

[4]

Tassoul, M. (1980): "Asymptotic approximations for stellar nonradial pulsations.", \apjs 43:469-490. (Link)

[5]

Brown, Timothy M.; Gilliland, Ronald L.; Noyes, Robert W.; Ramsey, Lawrence W. (1991): "Detection of Possible p-Mode Oscillations on Procyon", \apj 368:599. (Link)

[6]

Kjeldsen, H.; Bedding, T. R. (1995): "Amplitudes of stellar oscillations: the implications for asteroseismology.", åp 293:87-106.

[7]

Gizon, L.; Solanki, S. K. (2003): "Determining the Inclination of the Rotation Axis of a Sun-like Star", \apj 589(2):1009-1019. (Link)