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Annual Review of Astronomy and Astrophysics

Volume 48, 2010

Local Helioseismology: Three-Dimensional Imaging of the Solar Interior

Abstract

The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The Global Oscillation Network Group (GONG) network and the SOHO/MDI (/Michelson Doppler Imager) space instrument provide an exceptional database of spatially resolved observations of solar oscillations, covering more than an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered () near-surface vector flows associated with convection, () 250 m s−1 subsurface horizontal outflows around sunspots, () ∼50 m s−1 extended horizontal flows around active regions (converging near the surface and diverging below), () the effect of the Coriolis force on convective flows and active region flows, () the subsurface signature of the 15 m s−1 poleward meridional flow, () a ±5 m s−1 time-varying depth-dependent component of the meridional circulation around the mean latitude of activity, and () magnetic activity on the farside of the Sun.

Keyword(s): solar convection, solar cycle, solar magnetism, solar oscillations, sunspots
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2010-09-22
2025-06-13
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Local Helioseismology: Three-Dimensional Imaging of the Solar Interior
Annual Review of Astronomy and Astrophysics 48, 289 (2010); https://doi.org/10.1146/annurev-astro-082708-101722
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Supplementary Data

  • Supplemental Video 1. Time-series of SOHO/MDI full-disk Dopplergrams. The temporal cadence is one frame per minute and the average Dopplergram was subtracted from each frame to remove rotation. The random fluctuations are caused by the (mostly radial) solar five-minute oscillations. The slowly-evolving pattern in the background is due to supergranulation horizontal velocities. Courtesy of Stanford University and the SOHO/MDI Consortium. Download movie file (MPG)

    Supplemental Video 2. Model of the propagation of an acoustic wave packet in the solar interior. The background model is an isentropic, plane-parallel, polytrope of index 2.2. The wave packet includes modes p2 to p8 with phase speeds around 65 km s-1. Mode power peaks at frequency 3.1 mHz. The movie shows the energy density of the wave packet at times t = 27, 35, 42, and 54 min. In each frame, the maximum value of the energy density has been scaled to unity. Although the wave packet generally follows the acoustic ray path (black curve), there is a lot of wave energy away from the ray path. This illustrates the importance of finite-wavelength effects in local helioseismology. Adapted from Bogdan (1997). Download movie file (GIF)

    Supplemental Videos 3 through 6 show the propagation of rays through various magnetic field configurations. In all cases, the background atmosphere is Model S with an overlying isothermal layer. See Cally (2007) for details. Courtesy of Paul Cally.

    Supplemental Video 3. Ray theory (B = 0). A 5 mHz wave is launched horizontally at z = -5 Mm (this determines the horizontal wave number kx ). There is no magnetic field. The left panel shows its progress in z-kz space, and the right panel shows the ray path in the vertical x-z plane. The red dots on the ray path are one minute apart in group travel time. The wave skips continuously, with each skip corresponding to one passage around the lobe in the z-kz plane. Download movie file (AVI)

    Supplemental Movie 4. Generalized ray theory (B = 2 kG). At 5 mHz again, but with a uniform vertical 2 kG magnetic field superimposed. The "lobe" in the left frame is now the fast wave, and the outer "wings" are the slow wave. This is in 2D, so the Alfvén wave is decoupled, and is not shown. This time there is an avoided crossing near the Alfvén/acoustic equipartition height (a = c), indicated here with the vertical line. Energy may tunnel between the fast and slow modes at this point (through the "star point" in z-kz parameter space). The fraction of energy in a mode is indicated by the color of the moving point: bright red is 100%, with lower energies indicated by red saturation. The first "splitting" sees some energy transmitted into a slow (i.e., predominantly acoustic) wave above a = c. This initially travels upward but is quickly reflected by the acoustic cutoff frequency of 5.2 mHz. The wave then travels back down through a = c, where it splits again. On the other hand, the first splitting also produced a converted wave, which is fast (i.e., predominantly magnetic). This refracts from the increasing Alfvén speed with height, and also passes through a = c again, splitting one more time. Download movie file (AVI)

    Supplemental Movie 5. Generalized ray theory (B = 2 kG, θ = 30 deg). Same as above though with the magnetic field inclined at 30 deg to the vertical. This time most of the energy transmits to the slow wave (acoustic) since the attack angle between the wave vector and the direction of the magnetic field is small. There is very little conversion to the fast wave. Since the wave frequency now exceeds the reduced acoustic cutoff frequency ( ωc cos θ), the acoustic wave can continue to propagate upward in the atmosphere. Download movie file (AVI)

    Supplemental Video 6. Generalized ray theory (B = 2 kG, θ= –30 deg). Same as previous, though with field inclination of –30 deg. Now the attack angle is large; as a result the incident wave is predominantly converted to the fast wave rather than transmitted. On the other hand, when this fast wave refracts back downward to again meet a = c, it does so at fine attack angle and is largely transmitted as a magnetic (slow) wave. This energy is lost in the interior. Download movie file (AVI)

    Supplemental Video 7. Propagation of a p1 wave packet through a model versus observed sunspot. This movie refers to both Figures 11 and 17. The top panel is a combination of a simulated wave packet (top half) and an observed SOHO/MDI cross-covariance function (bottom half). The simulations show the vertical component of wave velocity. The observed cross-covariance is computed between a line at x = –43.7 Mm and all other spatial points; the individual frames are for time lags from 0 min to 140 min. The red circles indicate the outer edges of the umbra and penumbra, for both the model and the observations. The model sunspot has a surface field strength of 3 kG at sunspot center (Cameron et al. 2010). The bottom panel shows the x-component of the wave velocity weighted by the square root of density. The partial conversion of the incoming p1 modes into downward propagating slow magneto-acoustic waves is evident. Courtesy of Robert Cameron. Download movie file (MPG)

    Supplemental Video 8. Superganulation flows and small magnetic features. Movie of the divergence signal (inward travel times minus outward f-mode travel times) with magnetic field signal overlaid. The magnetic field is displayed as green and red for the two polarities when the magnitude of the field is larger than 15 G. The gray scale is for the divergence signal with white shades for outflow and dark shades for inflow. The time-distance data is averaged over 8.5 hours starting at the time shown on top. The movie shows the time evolution of the supergranulation pattern over 6 days. Notice that the small magnetic features are preferentially located at the boundaries of supergranules. Adapted from Duvall and Gizon (2000). Download movie file (AVI)

    Supplemental Video 9 . Farside imaging of Active Region NOAA 9505 during 15-30 August 2001, showing NOAA 9503 crossing the east limb on 27 August 2001 (See Figure 22b). Credit: MDI Farside Graphics Viewer at http://soi.stanford.edu/data/full_farside/farside.html and the SOHO/MDI Consortium. Download movie file (GIF)

    Supplemental Video 10. Polar perspective of farside imaging. View from the north pole of the full solar northern hemisphere during 15-30 August 2001. Download movie file (GIF)

    Supplemental Video 11. Radiative MHD simulation of a sunspot by Rempel et al. (2009). In black and white: Bolometric intensity. In color: Subsurface magnetic field strength on a vertical cut through the center of the sunspot, values range from 0 G (black) to 8 kG (white). Solar oscillations are naturally excited by turbulent convection (see the power spectrum in Figure 26). Courtesy of Matthias Rempel. Download movie file (MOV)

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