Temporal and Spatial Scales in Coronal Rain Revealed by UV Imaging and Spectroscopic Observations

The solar corona is known to have average temperatures above a million degrees. However, not all plasmas in the corona have such high temperature: plasma at chromospheric temperatures at coronal heights is commonly observed, particularly above active regions. Coronal rain is one of such cool and dense materials in the corona, usually appearing in chromospheric lines, and subsequently falling along a loop-like path into the chromosphere. Coronal rain was first observed more than 40 years ago (Kawaguchi, 1970; Leroy, 1972). Coronal rain also represents the existence of various dynamic, mass and energy transport processes in coronal loops (Marsch et al., 2008; McIntosh et al., 2012).

Coronal rain is thought to be produced by thermal instability during the catastrophic cooling part of a thermal non-equilibrium (TNE) cycle in which radiative cooling locally overcomes the coronal heating mechanisms as demonstrated in a one-dimensional numerical simulations (Parker, 1953; Müller, Hansteen, and Peter, 2003; Müller, Peter, and Hansteen, 2004; Müller et al., 2005; Xia et al., 2011). The TNE cycle is induced by concentrated heating localized nearer to the chromospheric footpoints than to the loop apex (Antiochos and Klimchuk, 1991). Chromospheric evaporation and density increase in the loop is induced by the heating, which increases radiative losses in the corona and results in a loss of thermal equilibrium and catastrophic cooling for sustained footpoint heating. Recently, Fang, Xia, and Keppens (2013) and Fang et al. (2015) studied the formation and the evolution of the coronal rain using 2.5-dimensional models and showed that multiple clumps in a coronal loop induce siphon flows which cause shear flows and deform the falling clumps themselves.

The cooling sequence of the loops has been also investigated using several overvations by the Transition Region and Coronal Explorer (Schrijver, 2001) and Extreme Ultraviolet Imaging Telescope onboard Solar and Heliospheric Observatory (e.g. de Groof et al. 2005), which detected EUV intensity variations of coronal loops in ARs. Antolin et al. (2015) showed that chromospheric emission follows the observed cooling in the EUV lines, as expected from catastrophic cooling events. EUV intensity pulsation with long-term periods were observed in warm coronal loops (Auchère et al., 2014; Froment et al., 2015, 2017) and shown to match well with TNE cycles. Antolin, Shibata, and Vissers (2010) argued that coronal rain may point to the agent of the heating of coronal loops as well as the spatial distribution of the heating in loops using a combination of Hinode observations and loop modelling of Alfvènic wave heating.

Antolin et al. (2015) coordinated observations with high-resolution and multi-wavelength instruments, and obtained the specific spatial scale of the coronal rains at each temperature. The most frequent scales of width and length detected in 1400 Å slit-jaw images (SJIs) taken by Interface Region Imaging Spectrograph (IRIS: De Pontieu et al. 2014) are $0^{\prime\prime}.88$ and $1^{\prime\prime}.76$, respectively. Antolin, Vissers, and Rouppe van der Voort (2012) and Antolin and Rouppe van der Voort (2012) analyzed off-limb and on-disk $\mathrm{H\alpha}$ observation data obtained with the CRisp Imaging SpectroPolarimeter at the Swedish Solar Telescope and detected cool and dense clump-like structures. They interpreted the clumps as coronal rain based on their spectral and morphological characteristics. In particular they showed that the rain morphology is clumpy and multi-stranded at high resolution, with an average length distribution of 700 km with a long tail towards longer lengths, and an average width distribution of 300 km with a full-width at half maximum (FWHM) of 100 km. At the same time, they also concluded that there exists undetected, even smaller clumps because the current spatial resolution is not enough.

Kleint et al. (2014) reported the first observation tracing coronal rain into an umbra and associated bright dots with IRIS. They interpreted that the coronal rain falls down along loops and collides with the local plasma in the transition region (TR), increasing density and temperature in the TR above a sunspot. In the IRIS spectral lines, rain is observed as bursts of strong Doppler shifts with an average duration of 20s, indicating supersonic downward flows of up to 200 km s^-1just prior to impact, which is faster than the free fall velocity for a plasma initially at rest.

In this article, we estimate the temporal and spatial scales from observational data obtained by IRIS and SDO. The rest of the article proceeds as follows. In Section 2, we introduce the data that we use. In Section 3, we describe the analysis and results. In Section 4, we summarize and discuss the observational results from the view point of scales in the coronal rain.

For this study, we analyze the observational data of active region (AR) NOAA 12042 obtained by IRIS and the Solar Dynamics Observatory (SDO: Pesnell, Thompson, and Chamberlin 2012). IRIS observed AR 12042 with the sit-and-stare mode of IRIS and Hinode Operation Plan (IHOP) 250 from 10:00 to 11:15 UT on 24 April 2014, providing spectral data in three lines (C ii 1336 Å, Si iv 1396 Å, and Mg ii k 2796 Å). The slit width is $0^{\prime\prime}.33$ and the pixel size and slit length are $0^{\prime\prime}.166$ and $119^{\prime\prime}$, respectively. IRIS also produced simultaneous SJIs data in 1400 Å and 2796 Å, whose field of view is about $119^{\prime\prime}\times 119^{\prime\prime}$. The recording cadences of spectral data and SJIs are 5.6 s and 11 s, respectively. The central sunspot in AR 12042 was located at (x, y)=($475^{\prime\prime},359^{\prime\prime}$) at the beginning of the IRIS observation. We used the level 2 data, where dark-current subtraction, flat-field correction, and geometric and wavelength calibration are applied.

The target AR was also covered by the Atmospheric Imaging Assembly (AIA: Lemen et al. 2012) onboard the SDO satellite, which makes synoptic observations in multiple wavelengths in the EUV with a cadence of 12 s. In this study, we mainly used the 171 Å channel images to investigate the morphology and evolution.

sec:discussion In the previous section, we estimated the properties of the on-disk coronal rain moving towards the sunspot umbra. The coronal rain clumps fall with Doppler velocity and plane-of-sky velocity of 85 km s^-1and 25 km s^-1, respectively, which yields an actual velocity of 90 km s^-1, i.e., much faster than the local sound speeds in the TR and the chromosphere since the local sound speed is $10-50$ km s^-1when the temperature is $10^{4}-10^{5}$ K if we use an adiabatic sound speed of $\sqrt{\gamma k_{B}T/m}$ where $\gamma$, $k_{B}$, $T$, and $m$ are the heat capacity ratio, the Boltzmann constant, temperature, and mass of a particle, respectively. As shown in Figures \ireffig:corra and b, there are no significant time-lags between the short-term intensity variations of the three IRIS lines. These results indicate that all the lines are heated up concurrently, most probably due to shock waves induced by the supersonic coronal rain. This local heating interpretation is also consistent with the weaker upflows besides the strong downflows seen in Figure \ireffig:vt_st. These weaker upflows suggest that mild evaporation is produced by the heating by the coronal rain besides the strong downflows seen at the Mg ii k line in Figure \ireffig:vt_stf (Kleint et al., 2014). The coronal rain clumps have a width of 580 km and show rapid intensity fluctuations with a timescale shorter than 1 minute. Hereafter we use typical timescale of the coronal rain of 30 seconds. If we multiply the timescale of 30 sec by the velocity of 90 km s^-1, the typical length of the clumps is estimated to be about $2.7$ Mm. Such widths and lengths are consistent with those observed in the same lines and instrument by Antolin et al. (2015). The temperature should be about $10^{5}$ K equivalent to the formation temperature of the Si iv line.

The clear relationship between the apparent flows falling onto the sunspot umbra and the intensity enhancements of stationary components with strong Doppler shift suggest that the coronal rain induces the local heating events. These heating events are possibly due to the shock made by the supersonic downflows of the coronal rain. The general scenario of the local heating by the coronal rain is the same as in previous reports (Kleint et al., 2014; Reale et al., 2013). However, the location of the shock front, or equivalently the height of the plasma heating, remains unclear. The falling material can penetrate the atmosphere to a dense layer whose gas pressure is equal to the ram pressure of the rain. The ram pressure $P_{ram}=\frac{1}{2}\rho v^{2}$ is estimated about $9.5~{}\mathrm{dyn~{}cm^{-2}}$, where we use observed velocity 90 km s^-1and previously reported average electron density $1.4\times 10^{11}~{}\mathrm{cm^{-3}}$ (Antolin et al., 2015).

When the coronal rain collides with the chromospheric plasma, a part of the kinetic energy of coronal rain is converted into thermal energy, heating chromospheric plasma and the falling coronal rain. We can estimate the amount of the kinetic energy of a clump of the coronal rain $E_{clump}$ to be

where $V_{clump}$ is the volume of a clump, and we approximate its shape by a cylinder with the radius $r$ and the length $l$. In this case, the radius is equivalent to the half of the clump’s width of $580~{}\mathrm{km}$ corresponding to 5 IRIS pixels. We use the electron density $1.4\times 10^{11}~{}\mathrm{cm^{-3}}$. If we apply the observed values, $r=290~{}\mathrm{km}$, $l=2.7~{}\mathrm{Mm}$, and $v=90~{}\mathrm{km\ s^{-1}}$, then we get the kinetic energy of about $6.8\times 10^{24}$ erg. Let us assume the condition that the number density in the chromosphere is $10^{12}~{}\mathrm{cm^{-3}}$ and the volume is $\pi r^{2}H$, where $H=300~{}\mathrm{km}$ is the pressure scale height of the chromosphere. If the temperature increase from $\log T=4$ to $\log T=5$, the required heating energy $nk_{B}\Delta T(\pi r^{2}H)$ is estimated to be about $1\times 10^{24}$ erg. Therefore, by converting a fraction of the kinetic energy, the coronal rain can heat the chromosphere.

The most important question is what produces such small-scale structures. When a coronal rain clump is first produced in the corona, the typical size of the clump may reflect the spatial scales of dynamical processes within the loops. In principle, a condensation will form and accumulate plasma as long as a pressure gradient exists. This pressure gradient is created initially by the loss of pressure from thermal instability. During its precipitation from the corona to the lower layers, the coronal rain clump could be broken into a smaller pieces by the Kelvin-Helmholtz instability (KHI) excited by the velocity shear between the clump and the surrounding stationary atmosphere. However, if the velocity vector of the coronal rain clump is parallel to the magnetic field, the KHI may not grow easily since the magnetic tension is likely to suppress KHI vortices. In 2.5-D MHD simulations by Fang et al. (2015) both very long and short clumps can be formed. Although their simulation does not provide the sufficient resolution to investigate the formation of the KHI, they discuss how the shear flows could lead to the break-up of the clumps, and they suggest a possible influence of the KHI. On the other hand, Martínez-Gómez et al. (2019) performed two-dimentional ideal MHD simulation of coronal rain and concluded that the KHI are not expected to develop in typical coronal rain conditions. They argued that the length of coronal rain may be explained by the timescale of the catastrophic cooling. Future high-resolution and multi-wavelength observations such as Solar-C_EUV High-Throughput Spectroscopic Telescope (EUVST: Shimizu et al. 2019) will reveal the formation mechanism of clumps in coronal rain.