{"id":997,"date":"2023-06-08T19:17:48","date_gmt":"2023-06-08T19:17:48","guid":{"rendered":"https:\/\/library.iiap.res.in\/collaborate\/?p=997"},"modified":"2025-06-20T06:57:49","modified_gmt":"2025-06-20T06:57:49","slug":"chromospheric-heating-by-acoustic-shock-waves","status":"publish","type":"post","link":"https:\/\/library.iiap.res.in\/collaborate\/?p=997","title":{"rendered":"Chromospheric heating by acoustic shock waves"},"content":{"rendered":"\n

Harsh Mathur<\/mark><\/strong><\/p>\n\n\n\n

The chromosphere is the most dynamic layer of the solar atmosphere, located between the bright solar surface and the million-degree hot corona. It is the region above the photosphere where the plasma is not in radiative equilibrium, and hydrogen is predominantly neutral, resulting in the characteristic H\u03b1 spectral line. The non-thermal energy that heats the solar corona and drives the solar wind propagates through the chromosphere into the outer layers of the solar atmosphere. Most of that energy is converted to heat and radiation, with only a small portion remaining to power the hot corona and solar wind. Thus, sustaining the chromosphere requires almost two orders of magnitude more energy than the corona and heliosphere combined [1, 2].<\/p>\n\n\n\n

Many questions remain about the physical mechanism of chromospheric heating and how energy is supplied to the outer layers of the solar atmosphere. Magnetic reconnection and wave heating are widely accepted candidates for explaining chromospheric and coronal heating. Magnetic reconnection is a physical process in which the topology of the magnetic field lines is rearranged from a higher potential to a lower potential. The difference is converted to kinetic and thermal energy and particle acceleration. The other proposed mechanism is through waves; observations and theoretical modeling have suggested three types: acoustic waves, magneto-acoustic waves, and Alfv\u00e9n waves. Acoustic waves are mechanical waves that propagate upwards in solar plasma through compression and rarefaction. Magneto-acoustic waves are acoustic waves that are altered by the presence of the magnetic field. Alfv\u00e9n waves are transverse waves that propagate in the magnetic field direction, with magnetic tension acting as a restoring force. Although it is well established that waves can transport energy from the lower to the upper atmosphere, how they dissipate energy remains debated.<\/p>\n\n\n\n

In this article, we will focus on the region of the Sun with little to negligible magnetic activity,  called the internetwork region. Due to the absence of magnetic activity, acoustic waves remain the likely candidate to heat the chromosphere. Earlier theoretical works have shown that acoustic waves propagate upwards from the lower to the upper atmosphere; when they reach the chromosphere, they turn into shocks due to a steep decrease in density. Shocks dissipate their energy into the medium by compressing the local plasma, increasing pressure, density, and thus temperature. These acoustic shock waves in the chromosphere appear as small-scale brightenings in the narrowband images of the blue wing, also called the K2V<\/sub> position, of the Ca II H & K lines, and are called grains.<\/p>\n\n\n\n

Earlier observational studies of grains to quantify temperature enhancements and line-of-sight (LOS) velocities had limitations like limited spatial resolution and less optimal assumptions like local thermodynamic equilibrium (LTE). In our recently accepted article for publication, we used high spatial and spectral resolution spectropolarimetric observations of the grains (quasi-) simultaneously recorded in the Ca II K 3933 \u00c5, Ca II 8542 \u00c5, and Fe I 6173 \u00c5 lines to infer the evolution of stratified atmospheric properties such as temperature and line-of-sight (LOS) velocity during acoustic shock events in non-LTE using STockholm inversion Code (STiC).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Fig. 1: Evolution of a grain: (a) The time evolution of the continuum at 4000 \u00c5, LOS magnetic field (B<\/em>LOS<\/sub>), and images at wavelength offsets of \u2212108.2 m\u00c5, +22.6 m\u00c5, and +153.3 m\u00c5 from the core of the Ca II K line are shown column-wise. Panels (b) and (c) display \u03bb\u2013t <\/em>diagrams for the pixel marked with a \u201c+\u201d in panel (a) in the Ca II K and Ca II 8542 \u00c5 lines, respectively. A few selected profiles marked in panels (b) and (c) are shown in panels (d) and (e). The outer contour (cyan), the middle contour (azure blue), and the inner contour (navy blue) in panel (a) show the region of grain in the order of increasing enhancement in intensity. The dashed vertical lines in panel (d) show the position of the narrowband images in panel (a). Reference [3].<\/p>\n\n\n\n

The inversion codes infer the stratification of the atmospheric properties, that is, variation with depth, from the observed spectral profiles. For each spectral profile, starting with an initial guess atmosphere, the inversions perturb the atmosphere at predefined specific depth locations called nodes, then interpolate to the full depth grid. Providing an initial guess atmospheric model close to the solution helps reduce the time it takes for inversion codes to converge. We grouped the spectral profiles into 100 clusters using the k<\/em>-means clustering algorithm to derive the initial guess atmospheres for inversions for all spectral profiles. The mean profile of each of the groups was inverted to derive the stratification of atmospheric parameters. Then the stratification was used as the initial guess atmosphere to invert the actual spectra. The approach described above significantly reduced computation time. The inversions and the k<\/em>-means algorithm were run on the Indian Institute of Astrophysics\u2019s NOVA supercomputer cluster.<\/p>\n\n\n\n

We found that the lifetimes of presented grains range between 25 and 67 s. The Ca II K profiles of grains show emission at the nominal K2V<\/sub> position of the spectral line. We found an average enhancement in temperature at the lower chromosphere of 1.1 kK (kilo-Kelvin) and a maximum enhancement of up to 4.5 kK. These enhancements were co-located with upflows in the direction of the LOS. The average strength of these upflows is about \u20132.5 km s-1<\/sup> and can be as large as \u20136 kms-1<\/sup>. At the higher chromosphere, we found strong downflows greater than +8 kms-1<\/sup>. Our value of temperature enhancement is three times higher than the estimate provided by earlier studies.<\/p>\n\n\n\n

These results can be explained as follows. The upflows in the lower chromosphere shift the opacity at which atoms emit and absorb to the blue wing (nominal K2V<\/sub> position) of the Ca II K line. These upward propagating acoustic shock waves enhance the gas density in the lower chromosphere, which couples the Ca II populations to local atmospheric conditions. The local temperature enhancements at the lower chromosphere enhance the source function at the nominal K2V<\/sub> position. Since the upper chromosphere is downflowing, the opacity to which atoms emit and absorb is red-shifted; that is, there is little opacity to absorb the blue-shifted emission from the lower chromosphere, resulting in an enhanced emission at the K2V<\/sub> wavelength position.<\/p>\n\n\n\n

The study supports the interpretations from earlier simulations that the grains are manifestations of upward propagating acoustic shocks against a background of downflowing atmospheres.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Fig. 2: \u200bMaps showing the time evolution of temperature, velocity, and microturbulence (row-wise) in the lower chromosphere. The contours indicate the location of the grains (acoustic shocks). At the location of acoustic shocks at t = 49.6, 57.8, and 66.1 s, there is an enhancement in temperature of about 2000 K and upflows of about \u20133 km s-1<\/sup>. Reference [3].<\/p>\n\n\n\n

References:<\/strong><\/p>\n\n\n\n

[1] https:\/\/www.annualreviews.org\/doi\/10.1146\/annurev-astro-081817-052044<\/a> (Review paper on chromosphere)<\/p>\n\n\n\n

[2] https:\/\/link.springer.com\/article\/10.1007\/s41116-020-0024-x#Sec17<\/a><\/p>\n\n\n\n

[3] https:\/\/ui.adsabs.harvard.edu\/abs\/2022arXiv221001045M\/abstract<\/a> (our work accepted to be published in A&A)<\/p>\n\n\n\n

\n

About the author<\/strong><\/p>\n\n\n\n

Harsh Mathur is a senior research fellow working with Dr. K. Nagaraju on interpretations of spectropolarimetric observations of the solar chromosphere through forward modeling and inversions using non-local thermodynamic equilibrium (non-LTE) radiative transfer. His thesis project is about inferring the chromospheric magnetic field using simultaneous multi-line spectropolarimetric observations.<\/strong><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"

Harsh Mathur The chromosphere is the most dynamic layer of the solar atmosphere, located between the bright solar surface and the million-degree hot corona. It is the region above the photosphere where the plasma is not in radiative equilibrium, and hydrogen is predominantly neutral, resulting in the characteristic H\u03b1 spectral line. The non-thermal energy that…<\/p>\n","protected":false},"author":5,"featured_media":1003,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false},"categories":[17],"tags":[29,28],"_links":{"self":[{"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/posts\/997"}],"collection":[{"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=997"}],"version-history":[{"count":12,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/posts\/997\/revisions"}],"predecessor-version":[{"id":3278,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/posts\/997\/revisions\/3278"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=\/wp\/v2\/media\/1003"}],"wp:attachment":[{"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/library.iiap.res.in\/collaborate\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}