Aberystwyth University The way forward for coronal heating Moortel, Ineke De; Browning, Philippa; Bradshaw, Stephen J.; Pintér, Balázs; Kontar, Eduard P. Published in: Astronomy & Geophysics DOI: 10.1111/j.1468-4004.2008.49321.x Publication date: 2008 Citation for published version (APA): Moortel, I. D., Browning, P., Bradshaw, S. J., Pintér, B., & Kontar, E. P. (2008). The way forward for coronal heating. Astronomy & Geophysics, 49(3), 21-26. https://doi.org/10.1111/j.1468-4004.2008.49321.x General rights Copyright and moral rights for the publications made accessible in the Aberystwyth Research Portal (the Institutional Repository) are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the Aberystwyth Research Portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the Aberystwyth Research Portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. tel: +44 1970 62 2400 email: [email protected] Download date: 28. Sep. 2021 DE MOORTEL ET AL.: MEETING REPORT The way forward for coronal heating Ineke De Moortel, Philippa K Browning, Stephen J Bradshaw, Balázs Pintér and Eduard P Kontar consider approaches to the longstanding and enigmatic problem of coronal heating, as presented at the RAS discussion meeting on 11 January 2008. Downloaded from n the 1940s it was demonstrated that the ABSTRT AC for dissipating the wave energy with adequate temperature of the plasma in the Sun’s outer efficiency. Fast waves are totally reflected before atmosphere (the solar corona) is over a mil- The coronal heating problem is one reaching the corona, and the energy flux in I of the major outstanding challenges lion degrees Kelvin (Edlén 1942). This is rather acoustic waves is too low, so attention mainly surprising, given that the Sun’s surface tem- in astrophysics and, while there has focuses on Alfvén waves. It has been suggested http://astrogeo.oxfordjournals.org/ perature is only about 6000 K. Although this been considerable progress in both (Hollweg 1984) that in long loops (>10 000 km), discovery removed the difficulty of an otherwise theory and observations, it remains a enough energy for coronal heating can be trans- unknown element (“coronium”), it presented a subject of controversy. There have been mitted by loop resonances. Efficient dissipation new puzzle, explaining how the coronal plasma exciting developments recently on the requires the generation of small length scales, is heated to such high temperatures. The coronal observational front, with new results with favoured mechanisms, both relying on the heating problem requires us to find a mechanism from, in particular, Ramaty High Energy inhomogeneity of the corona, being phase mix- (or mechanisms) to supply the energy losses of Solar Spectroscopic Imager (RHESSI) ing and resonant absorption. Spatial gradients the hot coronal plasma. These energy losses are (Lin et al. 2002) and Hinode (Kosugi et of Alfvén speed lead to phase mixing of shear due to conduction and radiation – estimated to al. 2007). But there is something of a Alfvén waves (Heyvaerts and Priest 1983). In a be up to 104 W m–2 in active regions. The key to gulf between theory and observations. closed field configuration, with the wavelength at University of Wales Aberystwyth on October 13, 2014 this problem is accepted to be the strong coronal The idea of forward modelling has fixed by the fieldline length, each fieldline oscil- magnetic field, which plays a crucial role in the arisen as a means of bridging this gulf lates with a different frequency; thus, neighbour- and enabling theories to be confronted solar corona (the plasma β – the ratio of thermal ing fieldlines become increasingly out of phase energy density to magnetic energy density – is with observations. The RAS discussion and strong spatial gradients build up, leading to around 10–4). meeting held in January this year focused enhanced dissipation. The damping time scales There is a very strong correlation between on new developments in coronal heating with the cube root of the Lundquist number. the brightness of coronal emission and the and the role of forward modelling. The theory has been extended to account for strength of the magnetic field. Indeed, active effects such as the generation of Kelvin–Helm- regions, which are bright in X-ray and EUV holtz instability due to the velocity shear images and hence hotter, have a much greater corona; in the opposite case, we have AC (Browning and Priest 1984), nonlinearities and heating requirement than the quiet Sun, and heating, with coronal magnetohydrodynamic mode coupling (e.g. Nakariakov et al. 1997), also have the strongest magnetic field. There is (MHD) waves. gravitational stratification (De Moortel et al. now a substantial body of evidence from other In both cases, the main challenge is to explain 1999) and a diverging field geometry (Ruder- stars that X-ray coronae are associated with how energy is dissipated in the solar corona: man et al. 1998, De Moortel et al. 2000). More magnetic fields. Indeed, there is a good correla- because the conductivity is extremely high, the recently, phase mixing in collisionless plasmas tion of X-ray luminosity with magnetic flux over ratio of the ohmic dissipation time to the Alfvén was modelled by Tsiklauri et al. (2005). many orders of magnitude, ranging from solar time (the Lundquist number) is very large, quiet regions through active regions, to dwarf around 1013. Thus, in order to explain coronal Resonant absorption and T Tauri stars (Pevtsov et al. 2003). heating, the energy dissipation must take place Resonant absorption (Ionson 1978) considers on scales smaller than typical MHD scales, resonances of incoming waves where the wave Energy transfer where kinetic effects are likely to be significant. frequency matches the local Alfvén frequency, The basic paradigm of coronal heating is that Moreover, the theories must include the cou- creating narrow layers where the wave ampli- there is an energy transfer from kinetic energy pling between global scales, i.e. on which the tude builds up and energy is dissipated. Interest- of flows below the solar surface into free mag- photospheric driving occurs, and local scales, ingly, resonant absorption may lead to sporadic netic energy in the corona, through motion of where the dissipation must take place. Further heating, more akin to the nanoflare scenario the footpoints of the coronal magnetic fields. difficulties for theory are presented by the cou- described below; since the localized heating at Existing theories can be classified according to pling between the dense interior and tenuous the resonant layer will create a rise in density the ratio of the timescale of this photospheric outer atmosphere, as well as the complex geom- due to chromospheric evaporation, altering the driving and the Alfvén wave transit time along etry and topology of coronal magnetic fields, Alfvén speed profile and creating new resonant a coronal field line. When the driving is slow and the dynamic nature of the corona. layers (Ofman et al. 1998). compared to the Alfvén travel time, we have Theories of wave heating have to account both At the RAS meeting, T Van Doorsselaere DC heating, with quasi-static currents in the for transmission of waves into the corona and (University of Warwick) compared resistive and A&G • June 2008 • Vol. 49 3.21 DE MOORTEL ET AL.: MEETING REPORT DE MOORTEL ET AL.: MEETING REPORT 1: Comparison between SXT/ Yohkoh (top row) and EIT/SOHO (bottom row) observations and synthesized emission for different values of the parameters α and β. (Taken from Warren and Winebarger 2006) Downloaded from viscous dissipative effects on footpoint heating Nakariakov and Verwichte 2005). which are significant at small length scales. For by waves. According to analytical and numeri- Consider now the alternative scenario, DC example, the Hall effect, which allows separa- http://astrogeo.oxfordjournals.org/ cal results, ohmic heating has to dominate any heating: the Poynting flux of energy into the tion of electron and ion fluids, can significantly wave heating mechanisms in order to accom- corona can be expressed as: affect the reconnection rate (Vekstein and Bian modate the constraint of footpoint heating (Van 2006). Magnetic reconnection during collision- F = __1 ​ B B v Doorsselaere et al. 2007). µ v h ph less X-point collapse is also an efficient source Both ground- and space-based observa- where Bv and Bh are the vertical and horizon- of heat, according to the computational simula- tions have recently found evidence that waves tal magnetic field components, respectively, tions by D Tsiklauri (Salford), presented at the are omnipresent in the solar atmosphere. For and vph is the photospheric footpoint velocity. meeting. example, Tomczyk et al. (2007) report observa- Taking typical coronal values, Bv = 0.01 T and Parker (1988) proposed that the corona is –1 tions of upwardly propagating coronal waves vph =m 1 k s , gives a Poynting flux of about heated by the combined effect of many small from intensity, line-of-sight velocity and linear 104 W m–2: sufficient for active region heating, as (and currently unobservable) nanoflares – tiny at University of Wales Aberystwyth on October 13, 2014 polarization measurements obtained with the long as the horizontal field component is around heating events with the same energy release Coronal Multi-Channel Polarimeter (CoMP) 10% or more of the vertical field in magnitude.