RADYN simulations of non-thermal and thermal models of Ellerman bombs

Ellerman bombs (EBs) are brightenings in the H$\alpha$ line wings that are believed to be caused by magnetic reconnection in the lower atmosphere. To study the response and evolution of the chromospheric line profiles, we perform radiative hydrodynamic simulations of EBs using both non-thermal and thermal models. Overall, these models can generate line profiles that are similar to observations. However, in non-thermal models we find dimming in the H$\alpha$ line wings and continuum when the heating begins, while for the thermal models dimming occurs only in the H$\alpha$ line core, and with a longer lifetime. This difference in line profiles can be used to determine whether an EB is dominated by non-thermal heating or thermal heating. In our simulations, if a higher heating rate is applied, the H$\alpha$ line will be unrealistically strong, while there are still no clear UV burst signatures.Comment: 20 pages, 9 figures, accepted for publication in Ap

Parallel Mapper

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

The Effects of Spatio-temporal Resolution on Deduced Spicule Properties

Spicules have been observed on the sun for more than a century, typically in chromospheric lines such as H-alpha and Ca II H. Recent work has shown that so-called 'type II' spicules may have a role in providing mass to the corona and the solar wind. In chromospheric filtergrams these spicules are not seen to fall back down, and they are shorter-lived and more dynamic than the spicules that have been classically reported in ground-based observations. Observations of type II spicules with Hinode show fundamentally different properties from what was previously measured. In earlier work we showed that these dynamic type II spicules are the most common type, a view that was not properly identified by early observations.The aim of this work is to investigate the effects of spatio-temporal resolution in the classical spicule measurements. Making use of Hinode data degraded to match the observing conditions of older ground-based studies, we measure the properties of spicules with a semi-automated algorithm. These results are then compared to measurements using the original Hinode data. We find that degrading the data has a significant effect on the measured properties of spicules. Most importantly, the results from the degraded data agree well with older studies (e.g. mean spicule duration more than 5 minutes, and upward apparent velocities of about 25 km/s). These results illustrate how the combination of spicule superposition, low spatial resolution and cadence affect the measured properties of spicules, and that previous measurements can be misleading.Comment: Accepted for publication in ApJ. 5 pages, 3 figures. Movies of figures 1 and 3 available via Data Conservanc

Non-LTE Calculations of the Fe I 6173 {\AA} Line in a Flaring Atmosphere

The Fe I 6173 {\AA} line is widely used in the measurements of vector magnetic fields by instruments including the Helioseismic and Magnetic Imager (HMI). We perform non-local thermodynamic equilibrium calculations of this line based on radiative hydrodynamic simulations in a flaring atmosphere. We employ both a quiet-Sun atmosphere and a penumbral atmosphere as the initial one in our simulations. We find that, in the quiet-Sun atmosphere, the line center is obviously enhanced during an intermediate flare. The enhanced emission is contributed from both radiative backwarming in the photosphere and particle beam heating in the lower chromosphere. A blue asymmetry of the line profile also appears due to an upward mass motion in the lower chromosphere. If we take a penumbral atmosphere as the initial atmosphere, the line has a more significant response to the flare heating, showing a central emission and an obvious asymmetry. The low spectral resolution of HMI would indicate some loss of information but the enhancement and line asymmetry are still kept. By calculating polarized line profiles, we find that the Stokes I and V profiles can be altered as a result of flare heating. Thus the distortion of this line has a crucial influence on the magnetic field measured from this line, and one should be cautious in interpreting the magnetic transients observed frequently in solar flares.Comment: 12 pages, 5 figures, accepted by ApJ

The Formation of IRIS diagnostics. IV. The Mg II triplet lines as a new diagnostic for lower chromospheric heating

A triplet of subordinate lines of Mg II exists in the region around the h&k lines. In solar spectra these lines are seen mostly in absorption, but in some cases can become emission lines. The aim of this work is to study the formation of this triplet, and investigate any diagnostic value they can bring. Using 3D radiative magnetohydrodynamic simulations of quiet Sun and flaring flux emergence, we synthesize spectra and investigate how spectral features respond to the underlying atmosphere. We find that emission in the lines is rare and is typically caused by a steep temperature increase in the lower chromosphere (above 1500 K, with electron densities above 10$^{18}$ m$^{-3}$). In both simulations the lines are sensitive to temperature increases taking place at column masses >= 5e-4 g cm$^{-2}$. Additional information can also be inferred from the peak-to-wing ratio and shape of the line profiles. Using observations from NASA's Interface Region Imaging Spectrograph we find both absorption and emission line profiles with similar shapes to the synthetic spectra, which suggests that these lines represent a useful diagnostic that complements the MgII h&k lines.Comment: 8 pages, 7 figures. Accepted for publication in Ap