Slow magnetoacoustic waves have been first observed in coronal plumes with the EIT/SoHO instrument (Deforest & Gurman, 1998). Later they have also been observed in coronal loops (Berghmans & Clette, 1999) with EIT/SoHO and (De Moortel et al., 2000) TRACE. These types of waves are in the low-beta environment of the corona basically sound waves restricted to propagate parallel to the magnetic field. Slow waves are also seen as standing waves (oscillations) in hot coronal loops in spectral data from SUMER/SoHO (Kliem et al. 2002, Wang et al. 2002), BCS/Yohkoh (Mariska 2005) and EIS/Hinode (Mariska 2008).

Sequence of difference images of TRACE 171Å Observations showing propagating slow magnetoacoustic disturbances

 

Damping of slow magnetoacoustic loop oscillations by shocks

Damping time versus oscillation period of SUMER events studied by Wang et al. (2003). Size of circles relate to oscillation amplitude

 

The above figure shows that there is a tendency for larger amplitude oscillations to have shorter damping times. This is a clear indication that nonlinear effects are influencing the damping rate of the SUMER oscillations. One of the possible nonlinear mechanisms is shock formation and dissipation.
Indeed, Haynes et al. (2008) showed numerically that in the absence of thermal conduction, large amplitude slow mode oscillations still damp rapidly due to shock dissipation.

 

Fully nonlinear MHD simulations of slow mode oscillations in the presence of thermal conduction are performed using the Lare code that show that shock dissipation is an important damping mechanism at large amplitudes. A comparison between the numerical simulations and the SUMER observations shows that, although the shock dissipation model can indeed produce an enhanced damping rate that is function of the oscillation amplitude, the found dependency is not as strong as that for the observations, even after considering observational corrections and the inclusion of enhanced linear dissipation.

Theory of propagating slow magnetoacoustic waves in coronal loops

A theoretical one-dimensional model of propagating slow waves in coronal loops by Nakariakov, Verwichte, Berghmans & Robbrecht (2000) includes the effects of stratification, nonlinearity, viscosity and thermal conduction. Stratification and dissipative processes compete as one increases and the other decreases the wave amplitude. It is expected that the wave amplitude with distance along the loop first increases before decreasing. Nonlinearity steepens the profile of the propagating wave but is found not to play an important role for realistic initial wave amplitudes.

Comparison of EIT and TRACE observations of slow magnetoacoustic waves in coronal loops

The paper Slow magnetoacoustic waves in coronal loops: EIT and TRACE by Robbrecht, Verwichte, Berghmans, Hochedez, Poedts & Nakariakov (2001) analyses simultaneous high-cadence observations of propagating slow waves of the 13th of May 1998, with sequences from EIT 195Å and TRACE 171Å. Propagating disturbances in emission are seen to be propagating up along the loops of a large coronal fan within AR 8218.

The propagating disturbances are identified as slow magnetoacoustic waves because:

• The disturbances are all seen to be propagating upward, none propagate down.
• The (projected) propagating speed is always below the speed of sound.
• The disturbances are quasi-periodic trains.
• Many similarities with the slow wave observations in coronal plumes.

• The amplitude enhancements due to a passing disturbance are typically of the order of 10% and below.
• Typical propagation speeds are 110 km/s for EIT and 95 km/s for TRACE. An acceleration of propagation is detected, in some cases, above the loop footpoint.
• The wave quickly decays over a distance of the order of 50 Mm.
• Along the same path waves are seen simultaneously in the EIT and TRACE bandpass, indicating the presence of sharp temperature gradients in the selected paths: either the loops consist of concentric shells at different temperatures or each observed loop consists of a bundle of very thin loop threads each at a different temperature.
• From the measured projected propagation speed, the angle of the loop with the solar surface is derived. The results from the two bandpassed are self-consistent (again reinforcing the idea that the disturbances are indeed slow waves) as well consistent with measurement of the loop geometry when the active region was on the solar limb.

Comparison between theoretical and observational dissipation profiles of slow magnetoacoustic waves in coronal loops

The previous study demonstrated that the slow waves may be used to infer information about the coronal structure they pass through. The paper Slow magnetoacoustic waves in coronal loops by Verwichte, Nakariakov, Berghmans & Hochedez (2001) took this a step further. The main idea was to confront the theoretical model of Nakariakov et al. (2000), extended with the effect of variable loop cross-section, with observations.

Slow wave amplitude as a function of distance with fitted curve from theoretical model

The comparison between an observed wave amplitude profile with the analytical model gives a first observational estimate of the dissipation processes of parallel thermal conduction and bulk viscosity, and it is shown to be in agreement with the theoretical expectations.