Observations of Mini Coronal Dimmings Caused by Small-scale Eruptions in the Quiet Sun

Solar eruptive activities, including flares, eruptive filaments, coronal mass ejections (CMEs), and coronal jets, are widely distributed in energy scales. The observed solar eruptions span a range of at least a factor of 10⁸ in energy (Schrijver et al. 2012). Large, highly energetic "X-class" eruptions can release energy substantially exceeding ∼10³³ erg. With the advent of high-resolution observations, the scaled-down versions of the eruptive activities are getting more attention, e.g., nanoflares (Bahauddin et al. 2021), minifilaments (Wang et al. 2000; Innes et al. 2009, 2010; Sterling et al. 2015; Panesar et al. 2016, 2018; McGlasson et al. 2019), and the newly discovered "campfires" (Berghmans et al. 2021), which are at lower energies probably below the current detection limit. Even-smaller-scale eruptive structures have been speculated to exist (Hermans & Martin 1986; Sterling & Moore 2016). The latest observations of the Parker Solar Probe near the Sun (McComas et al. 2019) indicate that small solar energetic particle (SEP) events, which cannot be captured by 1 au spacecraft but are only observable close to the Sun, may be much more common than previously thought. Where do these small SEP events come from? Is it possible that they are generated by these small-scale solar eruptions?

Jackson & Howard (1993) and Webb & Howard (1994) suggest that the ratio of the annualized CME to solar wind mass flux is no more than 16%, and Lamy et al. (2017) indicate that this ratio is only up to 6%. However, it should be noted that the mass of these counted CMEs is usually in the range of ∼10¹⁴–10¹⁵ g. Then what about small solar eruptions with less mass? Aschwanden et al. (2000) and Schrijver et al. (2012) indicate that the events at the lowest energies of ∼10²⁴ erg can occur millions of times each day. Namely, smaller eruptions generally have a higher frequency of occurrence. How do the small-scale eruptions, with the advantages of large numbers and high occurrence rate, contribute to the mass of the solar wind? Most of our knowledge of the energy–mass relation of eruptions is based on the observations of large-scale eruptions. It remains unclear what the actual relationship is between the mass and energy of small-scale eruptions in the source region.

Coronal dimmings are considered to be an important characteristic of solar eruptions, which can provide mass information of eruptions (Rust & Hildner 1976; Thompson et al. 1998). It is generally accepted that they are caused by plasma evacuation during the eruption of a CME (Harrison & Lyons 2000). On the Sun, the dimming regions correspond to the footprint of the CME (Jin et al. 2022). Upflowing expanding plasma has been observed in the dimming region (Harra & Sterling 2001; Tian et al. 2012). Harrison & Lyons (2000) find that the mass loss in the coronal dimmings is on the same order as the estimated mass of the associated CMEs. Therefore, the mass of small-scale eruptions can also be estimated by their associated coronal dimmings. However, small-scale coronal dimmings have been poorly studied. A small dimming associated with an eruption is not easy to identify since the eruption itself and the associated characteristic structures, such as post-flare arcades, flare ribbons, and coronal waves, are difficult to recognize under the previous observational limits. Therefore, it is difficult to determine whether the observed dimming is related to an eruption or not. In short, we do not know much about how small-scale coronal dimmings are produced, what their characteristics are, and how they are distributed.

In this Letter, we identify the characteristic structures associated with a small-scale eruption with greater certainty, owing to the 17.4 nm EUV High Resolution Imager (HRI_EUV) of the Extreme Ultraviolet Imager (EUI; Rochus et al. 2020) ⁵ on board the Solar Orbiter (Müller et al. 2020). We estimate the evacuated mass and the released energy of the eruption. A survey of mini coronal dimmings from Solar Orbiter observations is also carried out for the first time to investigate the distributions and occurrence frequency. These results provide crucial information for understanding small-scale eruptions and their contributions to SEPs, the solar wind, and space weather.

2.1. High-resolution Observations by Solar Orbiter

2.2. Temperature and Mass in the Mini Dimming Region

We use a differential emission measure (DEM) analysis to examine the temperature and density properties of the coronal dimming. In this work, we adopt the "simple_reg_dem.pro" routine (Plowman & Caspi 2020) in SolarSoftWare (SSW) packages to compute the DEM with the AIA EUV images at six passbands (94, 131, 171, 193, 211, and 335 Å) in the temperature range of 5.5 ≤ ${\mathrm{log}}_{10}(T)$ ≤ 7.5. This algorithm is fast and relatively free from idiosyncrasies, which is suitable for long time series analysis of the DEM of numerous pixels.

Figure 2 shows the evolution of emission measure (EM) for 0.7 MK plasma. We select a heart-shaped area (contoured in red), which almost contains all the dimming areas during the eruption and meanwhile excludes the bright plasma (i.e., the core region of the eruption under the post-eruption arcades within the black contours). The cool-color region within the heart-shaped area (lower density) gradually expanded (Figures 2(a)–(c)). At 21:07 UT, the beginning of the eruption, there are some preexisting dim locations in the corona (within the heart-shaped area) that are not associated with the eruption. At 21:40 UT, we can observe a small dimming area appearing near the core region. Then, the dimming area rapidly expanded around 22:00 UT and filled the whole heart-shaped area by 22:26 UT.

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Figure 2(e) shows that the changes of the normalized intensities of the flare region exhibit a trend of increase before 21:00 UT. Figure 2(f) shows a significant decrease in the intensity curve of the heart-shaped area after 21:40 UT, which is attributed to the occurrence of coronal dimming in that area. Prior to the flares associated with the dimming, the flare region exhibited continuous EUV brightenings, which may have been caused by magnetic reconnection resulting from the motion of the photospheric magnetic field.

Figure 2(g) shows the averaged EM within the dimming region as a function of time, which is calculated using

$$\begin{eqnarray}&&\mathrm{EM}=\int \mathrm{DEM}(T){dT}.\end{eqnarray} \tag{ 1 }$$

The EM has an obvious decrease after 21:40 UT and almost keeps constant after 22:00 UT, which indicates that coronal plasma probably escaped from the dimming region during the eruption. The EM-weighted median temperature (red curve) in Figure 2(e) is defined as

$$\begin{eqnarray}&&\overline{T}=\displaystyle \frac{\int \mathrm{DEM}(T)\times {TdT}}{\int \mathrm{DEM}(T){dT}}.\end{eqnarray} \tag{ 2 }$$

It almost keeps constant below 10^6.5 K, which is a typical temperature in a dimming region (Cheng et al. 2012). This implies that the EUV dimming mainly resulted from plasma depletion during the eruption. By the DEM analysis, the mass loss within the heart-shaped area is estimated to be (1.65 ± 0.54) × 10¹³ g (see Appendix). This mass is 1 to 2 orders lower than the normal CME mass of ∼10¹⁴–10¹⁵ g (Vourlidas et al. 2010).

2.3. Minifilament Eruption and the Associated Magnetic Fields

Our results indicate that the small-scale coronal dimming results from an eruption of a minifilament, which is likely to have similar eruption features (e.g., post-eruption arcades and flare ribbons), trigger mechanisms (associated with magnetic cancellation), and magnetic topology (e.g., flux-rope structures and magnetic dips) to large eruptions. We compare the mass and energy loss with previous statistics on the power-law relationship between the flare X-ray fluence and CME mass (Drake et al. 2013). Our results fit the energy–mass relation, i.e., an eruption of ΔE_free ∼ 10²⁷ erg carries the mass in the order of ∼10¹³ g.

Sterling et al. (2015) and Sterling & Moore (2016) indicate that solar coronal jets probably result from eruptions of small-scale filaments. Panesar et al. (2016, 2018) suggest that the continuous cancellation can destabilize minifilaments and result in eruptions, where internal magnetic reconnection occurs. The minifilament as shown here has similar size and takes comparable energy of ∼10²⁷ erg with the small filaments for driving jets. Moreover, the EUI/HRI_EUV observations present jet-like structures at the beginning of the eruption and post-flare arcades (see animation of Figure 1). Therefore, this eruption is likely to have similar formation and trigger mechanisms as coronal jets. McComas et al. (2019) indicate that small, longitudinally distributed SEP events are associated with jet-like coronal emissions, some of which are not observed at 1 au but only detected close to the Sun. Thus, the mini eruptions as shown here become the potential candidates for these small SEP events. There have been quite a few reports of small-scale eruptions with coronal dimming (e.g., Innes et al. 2009, 2010; Yang et al. 2012; Innes & Teriaca 2013; Zhang & Ji 2014; Sterling et al. 2022), but due to limitations in observation conditions, it is difficult to discern the intricate features of the eruption sources associated with these events, such as the post-flare arcades or the temperature and density of the corona. These difficulties result in challenges in determining, for instance, whether the coronal dimming is a long-lasting effect caused by mass evacuation or just a wave-like dimming and whether they are associated with the aforementioned on-disk jets. The combined observations of Solar Orbiter and SDO in this work have helped to address some of these challenges.

The small-scale eruptions are omnipresent features in the quiet Sun, estimated with as many as 1400 events per day over the whole Sun (Innes et al. 2009; Madjarska et al. 2022). Meanwhile, the total number of mini dimmings (associated with eruption or not) for a full disk in a day (e.g., Alipour et al. 2012) is much more than twice that of Innes et al. (2009). We make a survey of mini coronal dimmings from EUI/HRI_EUV high-resolution observations as shown in Table 1, which gives the approximate time and location of the dimmings. These dimmings are all associated with small-scale eruptions. Although the valid EUI/HRI_EUV observations are only available on certain days in certain months, we still identify at least one dimming event from the valid 1 or 2 hr observation periods for a day. We only select the relatively obvious events in the field of view (FOV) of a local area. There should be more events on a global scale.

On the other hand, we check the torus instability of the flux rope in the lower coronal (below ∼70 Mm) by the decay index $n=-\partial {ln}\parallel {{\boldsymbol{B}}}_{p}\parallel /\partial {lnR}$ (Kliem & Török 2006), where ∥ B _p ∥ is an external poroidal field and R is the height of the flux-rope axis's apex above the photosphere, which shows a low critical height ∼8 Mm above the PIL. This height is favorable for the escape of a CME from its source region. Understandably, weaker quiet-Sun magnetic fluxes result in weaker constraining force above the flux rope. However, it does not mean that CMEs can successfully escape into interplanetary space. Figures 4(c) and (d) show that the minifilament propagated slowly along a radial direction in the lower corona with an average speed only ∼5.4 km s⁻¹. In fact, the slow speed is not unexpected, which is also attributed to the weaker quiet-Sun magnetic fluxes. Namely, they generate a non-strong toroidal current inside the flux rope, which results in a relatively weak upward hoop force. On the other hand, quiet-Sun eruptions in the current solar cycle are mainly under streamer belts where closed background fields are generally dominated (see Figure 4(c)). Nonetheless, it remains challenging to determine whether quiet-Sun eruptions are confined or eruptive. In our case, we find many narrow blobs moving outwards in the STEREO-A/COR2 view. However, due to the lack of usable COR1 data, we cannot determine the exact origin of these blobs. Regardless, quiet-Sun eruptions are more likely to get into torus-unstable regions due to the relatively weak quiet-Sun magnetic fluxes. The mass and magnetic free energy can be transferred from the lower corona to the middle or higher corona, which could become a possible source of the solar wind. Chitta et al. (2023) gave a direct observational evidence for a coronal separatrix web driving highly structured slow solar wind through complex middle-coronal dynamic processes. Perhaps the minifilament eruption we observed could transport mass and energy to the middle or higher corona, which then becomes the solar wind through the mechanism proposed by their research.

We thank Xudong Sun for providing suggestions on HMI data processing and D. Berghmans for valuable suggestions on EUI data. The research was supported by National Key R&D Program of China No. 2021YFA0718600 and No. 2022YFF0503800, NSFC under grants 12073032, 42274201, 42004145 and 42150105, the Specialized Research Fund for State Key Laboratories of China. We acknowledge the use of data from Solar Orbiter and SDO. Solar Orbiter is a space mission of international collaboration between ESA and NASA, operated by ESA. The EUI instrument was built by CSL, IAS, MPS, MSSL/UCL, PMOD/WRC, ROB, LCF/IO with funding from the Belgian Federal Science Policy Office (BELSPO/PRODEX PEA 4000134088); the Centre National d'Etudes Spatiales (CNES); the UK Space Agency (UKSA); the Bundesministerium für Wirtschaft und Energie (BMWi) through the Deutsches Zentrum für Luft- und Raumfahrt (DLR); and the Swiss Space Office (SSO).

We use the DEM techniques to determine the CME masses from coronal dimmings. Considering the limitations posed by the signal-to-noise ratio of the AIA passbands, we only utilize the passbands centered at 171, 193, and 211 Å, which are sufficient to encompass the temperature range of the quiet Sun within the heart-shaped area.

To determine the total evacuated mass M of the eruption, we use

$$\begin{eqnarray}\begin{array}{rcl}M & = & \displaystyle \sum _{i=0}^{n}\mu {m}_{p}{A}_{s}{\displaystyle \int }_{0}^{L}N(z){dz}\\ & = & \displaystyle \sum _{i=0}^{n}\mu {m}_{p}{A}_{s}{\lambda }_{p}{N}_{0}I\left(\displaystyle \frac{{\lambda }_{p}}{{R}_{\odot }}\right),\end{array}\end{eqnarray} \tag{ A1 }$$

where n is the total number of the pixels within the heart-shaped area, μ the mean molecular weight of the hydrogen ion (μ = 1.27), m_p the proton mass, A_s the area of each pixel, ${\int }_{0}^{L}N(z){dz}$ the total number of coronal plasma at each pixel in the dimming region along the LOS, and λ_p the pressure scale height defined as

$$\begin{eqnarray}&&{\lambda }_{p}=\displaystyle \frac{2{k}_{{\rm{B}}}{T}_{e}}{\mu {m}_{p}{g}_{\odot }},\end{eqnarray} \tag{ A2 }$$

where k_B is the Boltzmann constant, T_e the electron temperature at each pixel calculated from the DEM analysis by Equation (2), and g_⊙ the gravitational acceleration at the solar surface.

We obtain the value of the basal electron density N₀ with the help of the EM measurement (for a detailed derivation, please refer to the previous implementation about CME mass determination of López et al. 2017), i.e.,

$$\begin{eqnarray}&&{N}_{0}=\sqrt{\displaystyle \frac{\mathrm{EM}}{\tfrac{{\lambda }_{p}}{2}I\left(\tfrac{{\lambda }_{p}}{2{R}_{\odot }}\right)}},\end{eqnarray} \tag{ A3 }$$

where R_⊙ is the solar radius, and I the integral quantity defined as

$$\begin{eqnarray}&&I(\alpha )={\int }_{0}^{2L/{\lambda }_{p}}\exp \left(-\displaystyle \frac{x}{\alpha x+1}\right){dx}.\end{eqnarray} \tag{ A4 }$$

We have set L = 5λ_p in order to include as much mass as possible along the LOS.

The total evacuated mass ΔM is determined by the difference between the mass M_before before the eruption and the mass M_after after the eruption, i.e.,

$$\begin{eqnarray}&&{\rm{\Delta }}M={M}_{\mathrm{before}}-{M}_{\mathrm{after}}.\end{eqnarray} \tag{ A5 }$$