Background-subtracted Solar Activity Maps

TL;DR

The paper introduces Background-subtracted Solar Activity Maps (BaSAMs), a new quantitative visualization tool using SDO data to analyze solar magnetic and UV intensity variations over time and across different solar activity conditions.

Contribution

It presents a novel method for creating BaSAMs to assess and visualize solar activity, enabling better analysis of magnetic and UV intensity variations and their relation to solar features.

Findings

BaSAMs effectively distinguish quiet-Sun magnetic contributions.

Flaring and brightenings are clearly visualized in UV BaSAMs.

Sunspot flux systems are connected to supergranular cells.

Abstract

We introduce the concept of a Background-subtracted Solar Activity Map (BaSAM) as a new quantitative tool to assess and visualize the temporal variation of the photospheric magnetic field and the UV 160 nm intensity. The method utilizes data of the Solar Dynamics Observatory (SDO) and is applicable to both full-disk observations and regions-of-interest. We illustrate and discuss the potential of BaSAM resorting to datasets representing solar minimum and maximum conditions: (1) Contributions of quiet-Sun magnetic fields, i.e. the network and (decaying) plage, to solar activity can be better determined when their variation is measured with respect to the background given by "deep" magnetograms. (2) Flaring and intermittent brightenings are easily appraised in BaSAMs of the UV intensity. (3) Both magnetic-field and intensity variations demonstrated that the flux system of sunspots is well connected to the surrounding supergranular cells. In addition, producing daily full-disk BaSAMs for the entire mission time of SDO provides a unique tool to analyze solar cycle variations, showing how vigorous or frail are the variations of magnetic-field and intensity features.

Tables

Table 1. Table 1. : Linear ( above diagonal ) and rank-order ( below diagonal ) correlation coefficients for the four BaSAMs in Figures  \iref FIG06 ( left ) and \iref FIG07 ( right ), respectively.

	2 h	4 h	8 h	16 h
2 h		0.92	0.80	0.71
4 h	0.92		0.91	0.80
8 h	0.86	0.93		0.91
16 h	0.79	0.86	0.93

Equations

$$⟨|S-⟨S⟩|⟩=\frac{1}{N}\sum _{i=1}^N\left|S(t_i)-⟨S⟩\right|\mathrm{with}⟨S⟩=\frac{1}{N}\sum _{i=1}^{N}S(t_i).\text{ilabel}EQN01$$

$$⟨S{⟩}^M=\frac{1}{M+1}\sum _{j=i-M/2}^{j=i+M/2}S(t_j),\text{ilabel}EQN02$$

Full text

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1 Introduction

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The long-term variation of the solar magnetic field was extensively studied using synoptic maps created from full-disk magnetograms. Gaizauskas et al. (1983) utilized synoptic maps of photospheric magnetic fields using the Kitt Peak National Observatory’s full-disk photospheric magnetograms for the ascending phase of solar cycle 21. In their synoptic maps, they followed the “complexes of activity” (Bumba and Howard, 1965) and noticed that these complexes of activity formed within a month, maintaining themselves by addition of fresh magnetic flux for 3 – 6 solar rotations. de Toma, White, and Harvey (2000) carried out a similar study but for the ascending phase of solar cycle 23. In addition to using magnetic synoptic charts, they used time-series of the 10.7 cm radio flux, sunspot numbers, and the Mg ii chromospheric index for determining the origin of the two activity minima in 1996. The synoptic charts provided the details of the activity belt and activity nests, indicating preferred longitude bands where activity reoccurred. The properties of global magnetic evolution are, for example, needed to constrain flux transport dynamo models.

With the advent of digital imaging, time-series analysis became an important tool to obtain information about the variation, dynamics, and evolution of solar features. For example, extracting the intensity along a spatial slice at a given time from a time-sequence yields so-called space-time or time-slice diagrams. They are commonly used, e.g. to infer information about exploding granules (Title et al., 1986), to detect oscillatory motions of bright points in continuum images (Wang et al., 1995), to compare magnetic flux measurements derived from near-infrared and visible spectropolarimetric observations (Lin and Rimmele, 1999), and to determine the divergence of the horizontal velocity field (Shine, Simon, and Hurlburt, 2000). More recently, Verma et al. (2016) followed the complete evolution of an active region using space-time diagrams based on synoptic line-of-sight (LOS) magnetograms. Various other time-series analysis methods are widely used and implemented fostering a better understanding the physical processes on the solar surface, e.g. difference maps (see Aschwanden et al., 1999, for solar active region loops), sliding averages (see Rouppe van der Voort et al., 2003, for umbral flashes and running penumbral waves), time-lag maps (see Viall and Klimchuk, 2012, for coronal loops), decorrelation times for lifetimes of flows and of active region magnetic structures (Welsch et al., 2012; Verma and Denker, 2012), and spatial correlation analysis (see Verma and Denker, 2011, for an adaptation of Local Correlation Tracking (LCT)). Although many of these methods are versatile, not all of them are suitable for determining the global or large-scale evolution of solar intensity and magnetic field.

To visualize variations of the magnetic field in and around a decaying sunspot, Verma et al. (2012) presented a map of temporal variations in the magnetic flux above and below the local background, i.e. the long-term average of the magnetic field. Analyzing a 12-hour time-series of LOS magnetograms revealed regions of enhanced activity. A spoke-like structure was discovered in the background-subtracted variation map, which indicated moving magnetic features (MMFs) emanating from the photometric sunspot border, traveling along preferential paths, and reaching all the way to the surrounding supergranular boundary. Kummerow (2015) and Verma, Kummerow, and Denker (2018) extended this work by computing a large sample of these background-subtracted variation maps for various sunspots complemented by time-series of UV images. While these studies were focused on a specific region-of-interest (ROI) covering individual sunspots, we will carry our initial work forward and propose in this study efficient tools to infer properties of the global magnetic field and the solar activity in general.

In Beauregard, Verma, and Denker (2012), we extended our implementation of LCT (Verma and Denker, 2011), originally developed by November and Simon (1988), to full-disk continuum images, and we used the Differential Affine Velocity Estimator (DAVE, Schuck, 2005, 2006) to derive flux transport velocities from full-disk magnetograms. Large volumes of data are involved in computing horizontal flow fields. Having these three-dimensional data cubes in hand (two spatial and the time coordinate) motivated us to explore the temporal variation of magnetic and UV activity for each pixel in the field-of-view (FOV), complementing optical flow techniques. All methods mentioned above deal with images and magnetograms one way or the other. The purpose is to extract as much information as possible regarding solar activity and evolution of solar features from these kinds of datasets. In the present study, we extend our previous work related to the variation of magnetic fields and UV intensity (e.g. Verma et al., 2012; Verma, Kummerow, and Denker, 2018) and formally introduce the method as Background-subtracted Solar Activity Map (BaSAM).

In the following, we describe typical datasets (Section \irefSEC2), present briefly the straightforward, though computationally extensive, implementation of our method (Section \irefSEC3), show results for full-disk and ROI data (Section \irefSEC4), and discuss some of the common applications (Section \irefSEC5).

2 Observations

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One day during solar maximum (2014 April 17) and another day during the declining phase (2018 February 19) of solar cycle 24 were selected for case studies to illustrate the potential of BaSAM (see Figures \irefFIG01 and \irefFIG02). In addition, a two-hour time window was selected for each day of the Solar Dynamics Observatory (SDO, Pesnell, Thompson, and Chamberlin, 2012) mission so far (2010 May 1 – 2018 July 31), which resulted in a long-duration dataset containing about 3000 observing days. This long-duration dataset is the basis for the derivation of BaSAM indices tracing solar activity.

The activity maps are based on full-disk datasets of two SDO instruments, i.e. the Helioseismic and Magnetic Imager (HMI, Scherrer et al., 2012; Schou et al., 2012) and the Atmospheric Imaging Assembly (AIA, Lemen et al., 2012). Time-series of line-of-sight (LOS) magnetograms and UV $\lambda 160$ nm images serve as input for the case studies, which cover a period of $\pm 8$ hours around 12:00 UT. The cadence of HMI and AIA data are $\Delta t=45$ s and 24 s, respectively. Thus, 1280 magnetograms and 2400 UV images are potentially available during the time period of $\Delta T=16$ h. However, on 2018 February 19, only 1157 magnetograms were retrieved, i.e. no magnetic field data were available for the time period from 06:42 to 08:08 UT. In the UV time-series only about 10 images are missing, which is negligible. All magnetograms and UV images in the time-series are compensated for differential rotation using 12:00 UT as time reference. The long-duration dataset comprises only magnetograms, which cover a period of $\pm 1$ hour around 12:00 UT. However, eclipse seasons of SDO, when the view towards the Sun is obstructed, cause gaps in the time-series. These gaps were filled with two-hour times-series of magnetograms that are as close in time to 12:00 UT as possible. While the bulk processing of the daily magnetogram data can be automated, some manual interaction was needed to fill the gaps caused by the eclipse seasons.

The differential rotation is corrected using the standard mapping routines of the SolarSoftWare library (SSW, Freeland and Handy, 1998), which implements by default the differential rotation rate of small magnetic features (Howard, Harvey, and Forgach, 1990). Compared to other differential rotation laws, for example for different solar features or derived with other methods, the largest error is expected at the central meridian, where projection effects are minimal. For a rough error estimate, the default differential rotation rate was compared to that given by Snodgrass and Ulrich (1990), which is based on photospheric Doppler velocity features. In the temporal sampling window of one hour, the error is less than one third of a pixel, which is negligible. Even for the longest sampling window of eight hours, the error is only about 2.5 pixels. Hence, these mismatch errors may lead to some diffusion of the magnetic flux or intensity, which however can be safely neglected.

Co-adding all magnetograms subsequent to differential-rotation correction yields the deep magnetogram in Figure \irefFIG01, where the magnetic field strength $B$ was corrected for the cosine of the heliocentric angle $\mu=\cos\theta$. This first-order correction ensures that magnetic fields near the limb and disk center are equally well represented. However, in difference images, this straightforward correction may lead to complications because small differences will be strongly enhanced in proximity to the solar limb. The deep full-disk magnetogram is a composite of the Sun’s quiet northern hemisphere on 2018 February 1 and the very active southern hemisphere on 2014 April 17. The northern hemisphere on 2014 April 17 is also very active, i.e. it contains a large number of active regions, which are however not as prominent as those in the southern hemisphere. This type of composite display allows us to directly compare activity levels at solar minimum and maximum. The selected threshold of $\pm$50 G for the deep magnetogram enhances both the network magnetic fields and the active plage regions. The superposed Stonyhurst grid represents solar longitude and latitude in $10^{\circ}$ increments for both observing days at 12:00 UT. The solid horizontal line does not mark the solar equator, it just separates the northern and southern hemispheres. All full-disk data in the following sections adhere to the same display style.

A long-integration UV intensity composite map was created using a similar procedure. However, we first determined the center-to-limb variation (CLV) on 2018 February 19 by fitting a 4th-order polynomial in $\mu$ (see Denker et al., 1999, for a description of the procedure), when the solar activity was very low, and divided the UV intensity map by a two-dimensional representation of the CLV. The same CLV correction was applied to the UV intensity map on 2014 April 17 after appropriate scaling, taking into account variations of the disk-center intensity. Thus, the composite of two full-disk images shown in Figure \irefFIG02 displays the UV intensity normalized with respect to the local quiet-Sun intensity. The imprint of the supergranulation, i.e. the bright network (“orange peel pattern”) is much more pronounced in this normalized UV image as compared to the deep magnetograms. In any case, even though some structural contents is lost when taking the long-duration averages, some solar features will be enhanced so that this type of image processing has merits of its own. Apart from that further processing of time-series data comprised of magnetograms and UV images reveals additional information (see Section \irefSEC4).

3 Background-subtracted Solar Activity Maps

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The availability of high-cadence synoptic full-disk data with a moderate spatial resolution of about one second of arc is the prerequisite for our method to assess variations in magnetic field and UV/EUV imaging data. Instead of exploring the rms-contrast of two-dimensional surface data, we explore the temporal variation for each pixel on the solar disk. Thus, we implemented BaSAM as the mean absolute deviation of a time-series calculated for each pixel on the solar disk. In principle, the method can also be based on rms-measurements. However, stronger variations will receive a higher weight in this case, which is undesirable when computing activity indices. In general, the background-subtracted variation of a quantity $S$ with time, for example that of the magnetic field strength $B$ or the UV intensity $I$, is computed according to

[TABLE]

The individual images in a time-series are given by $S(t_{i})$. The notation on the left-hand side of the equations is just shorthand for the mathematical formalism on the right-hand side. The expression $\langle\,|\,B-\langle B\rangle\,|\,\rangle_{\mathrm{2h}}$, for example, refers to a BaSAM based on a time-series with a duration of $\Delta T=2$ h containing typically $N=160$ magnetograms (Figure \irefFIG03), whereas $\langle B\,\rangle_{\mathrm{16h}}$ is an abbreviation for a sixteen-hour deep magnetogram (Figure \irefFIG01). Since the cadence of the UV images is about two times higher, the UV BaSAM $\langle\,|\,I-\langle I\rangle\,|\,\rangle_{\mathrm{2h}}$ is based on $N=300$ images (Figure \irefFIG04).

In Equation \irefEQN01, the local background $\langle S\rangle$, which was computed just once, across the entire time-series, may be replaced by a simple sliding average

[TABLE]

which has to be updated for each time step $t_{i}$ in order to compute the absolute difference $\left|\,S(t_{i})-\langle S\rangle\,\right|$ in Equation \irefEQN01. Thus, $\langle\,|\,I-\langle I\rangle\,|\,\rangle_{\mathrm{16\,h}}^{\mathrm{30\,min}}$ refers to a 16-hour BaSAM of the UV intensity that was computed with a 30-minute sliding average. Using sliding averages is advantageous, for example, when studying transient events such as flares. The notation in Equation \irefEQN02 does not address how to compute the sliding averages at the beginning and end of the time-series. We simply opted for computing the sliding average based on images contained within a time-series of given duration, i.e. no images before or after the time-series were included in the average. Thus, the duration of the sliding average is shorter at the beginning and end of the times-series, which is however negligible as long as the duration of the sliding average is much shorter than the duration of the time-series.

Photon noise is the dominant noise term for magnetograms and UV images. Thus, the CLV introduces a systematic increase of the noise from disk center to the limb. Table 1 in Couvidat et al. (2016) lists an uncertainty of 7 G for the 45-second cadence, LOS magnetograms near disk center, which increases by a factor of about 1.7 at the limb. Relevant information on the wavelength dependent solar limb darkening is given by Pierce and Slaughter (1977) for HMI magnetograms and by Pierce, Slaughter, and Weinberger (1977) for AIA UV images, which can be used to compute the noise level as a function of heliocentric angle. In addition, solar differential rotation shifts the spectral line profile across the HMI filter positions, which results in an additional noise component that increases with distance from the central meridian. Since the noise in $\langle S\rangle$ is significantly lower than in $S(t_{i})$, the latter will dominate $\left|\,S(t_{i})-\langle S\rangle\,\right|$, which leads to a basal noise floor in the summation of Equation \irefEQN01. Moreover, magnetic BaSAMs and deep magnetograms are governed by the same photon statistics based on the number of “integrated” single magnetograms. The quiet-Sun magnetograms in Figure \irefFIG05 visualize the noise being present in single and deep magnetograms, respectively. The magnetograms were clipped at different thresholds ensuring that about 10% of the pixels are saturated at the threshold. The single magnetogram only shows the strongest network elements, whereas the 2-hour averaged magnetogram shows both strong network and weak internetwork magnetic fields. The latter can lead to an additional basal component in magnetic BaSAMs based on very deep magnetograms (see Figure \irefFIG05c), where the contributions by weak internetwork fields are washed out over the 16-hour averaging period.

In case studies, ROI processing is often more appropriate when focusing on objects such as pores, sunspots, or more complex active regions. However, additional processing steps may be necessary: (1) Proper motions related to active region evolution will be present in time-series. The cross-correlation between single magnetograms and images and their respective long-duration averages identifies these residual drifts, which are subsequently removed. (2) Resampling on a regular grid with an equidistant spacing will be advantageous if the same data are used to determine horizontal proper motions, which ensures that the sampling window to derive velocity vectors covers equal areas. (3) If the ROI is located in proximity to the solar limb, geometric corrections for the magnetic field inclination or photometric corrections for the CLV will be expedient. The data processing steps in these situations essentially follow the procedures elaborated in Verma and Denker (2011) and Beauregard, Verma, and Denker (2012). Thus, the choice of additional processing steps is driven by the specific science case. Only in statistical or comparative studies standardized processing steps are required.

4 Results

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Various parameters affect the appearance of BaSAMs. Thus, they must be carefully chosen according to the science case. In the following, we provide a parameter study, investigating the impact of the duration for which BaSAMs are computed and of the duration of the sliding averages. We selected an ROI in the northern hemisphere (not shown in the composite full-disk BaSAMs in Figures \irefFIG01 – \irefFIG04) of the mature but decaying $\beta\gamma$-region NOAA 12034, which showed minor flare activity in X-rays at the C-class level.

Varying the duration over which the background is computed affects significantly the morphology of the BaSAM (see Figure \irefFIG06). We computed BaSAMs with a duration 2 to 16-hours. The significant morphological changes that are apparent cannot be attributed to sparse temporal sampling. Already for the 2-hour case, about 160 images are used to compute the BaSAM, which is sufficient to assume a Gaussian distribution for the magnetic field variation in each pixel. The longer the duration, the smoother becomes the appearance of deep magnetograms. Quiet-Sun magnetic fields become enhanced but with fuzzy boundaries. As a consequence, most fine structure is visible in BaSAMs for backgrounds with a short duration because the background did not have time to evolve. This allows us to identify areas with pronounced instantaneous magnetic field variations. In contrast, a longer duration for the background leads to larger variations of the magnetic field above a smoother background. Persistent variations stand out more clearly, which is advantageous when investigating magnetic connections within an active region or with its surroundings, e.g. the magnetic network (see Verma et al., 2012).

Using sliding averages for the background places emphasis on instantaneous variations. The duration of the sliding averages impacts the appearance of BaSAMs as shown for the UV intensity variation over a 16-hour period (see Figure \irefFIG07). The duration of the sliding average was doubled in each step from 30 min, over 60 and 120 min, to 240 min. Even though no C-class flares or larger were recorded for active region NOAA 12034 on 2014 April 17, all UV BaSAMs show clearly brightenings between opposite-polarity sunspots at a location with mixed polarities. Interestingly, these brightening are absent around the leading sunspot. The strength of the brightenings increases with the duration of the sliding average for the same reasons mentioned above for the magnetic BaSAMs (Figure \irefFIG06). For the shortest sliding averages the brightenings decompose into point-like features, indicating that small-scale flaring occurs at very localized regions, which are smeared out for longer duration sliding averages.