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Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630\,nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. The results show a significant decrease in the mean magnetic flux density -- related to the open flux observed at the disk center -- with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20\,cm aperture telescope yields a 30\% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle., Comment: To be published in A&A

We study the extent to which Milne-Eddington inversions are able to retrieve and characterize the magnetic landscape of the solar poles from observations by the spectropolarimeter onboard Hinode. In particular, we evaluate whether a variable magnetic filling factor is an adequate modeling technique for retrieving the intrinsic magnetic properties from every pixel in the polar field of view. We first generate synthetic spectra emerging from a numerical simulation of a "plage" region at an inclined line of sight of 65$^{\circ}$, and degrade the data to emulate real observations. Then, we invert the synthetic spectra with two Milne-Eddington inversion codes that feature different treatments of the magnetic filling factor, and relate the retrieved magnetic quantities back to their original values in the simulation cube. We find that while the apparent retrieved magnetic properties map well the spatially-degraded simulation, the intrinsic magnetic quantities bear little relation to the magnetic field at the native resolution of the simulation. We discuss the systematic biases caused by line-of-sight foreshortening, spatial degradation, photon noise and modeling assumptions embedded in the inversion algorithm., Comment: Accepted for publication in ApJ

We study the effects of finite spectral resolution on the magnetic field values retrieved through the weak field approximation (WFA) from the cores of the Mg II h & k lines. The retrieval of the line-of-sight (LOS) component of the magnetic field, $B_{\rm LOS}$, from synthetic spectra generated in a uniformly magnetized FAL-C atmosphere are accurate when restricted to the inner lobes of Stokes V. As we degrade the spectral resolution, partial redistribution (PRD) effects, that more prominently affect the outer lobes of Stokes V, are brought into the line core through spectral smearing, degrading the accuracy of the WFA and resulting in an inference bias, which is more pronounced the poorer the resolution. When applied to a diverse set of spectra emerging from a sunspot simulation, we find a good accuracy in the retrieved $B_{\rm LOS}$ when comparing it to the model value at the height where the optical depth in the line core is unity. The accuracy is preserved up to field strengths of B~1500 G. Limited spectral resolution results in a small bias toward weaker retrieved fields. The WFA for the transverse component of the magnetic field is also evaluated. Reduced spectral resolution degrades the accuracy of the inferences because spectral mixing results in the line effectively probing deeper layers of the atmosphere., Comment: Accepted for publication in ApJ

In this work, we study the information content learned by a convolutional neural network (CNN) when trained to carry out the inverse mapping between a database of synthetic Ca II intensity spectra and the vertical stratification of the temperature of the atmospheres used to generate such spectra. In particular, we evaluate the ability of the neural network to extract information about the sensitivity of the spectral line to temperature as a function of height. By training the CNN on sufficiently narrow wavelength intervals across the Ca II spectral profiles, we find that the error in the temperature prediction shows an inverse relationship to the response function of the spectral line to temperature, this is, different regions of the spectrum yield a better temperature prediction at their expected regions of formation. This work shows that the function that the CNN learns during the training process contains a physically-meaningful mapping between wavelength and atmospheric height., Comment: Accepted for publication in ApJ

We take a broad look at the problem of identifying the magnetic solar causes of space weather. With the lackluster performance of extrapolations based upon magnetic field measurements in the photosphere, we identify a region in the near UV part of the spectrum as optimal for studying the development of magnetic free energy over active regions. Using data from SORCE, Hubble Space Telescope, and SKYLAB, along with 1D computations of the near-UV (NUV) spectrum and numerical experiments based on the MURaM radiation-MHD and HanleRT radiative transfer codes, we address multiple challenges. These challenges are best met through a combination of near UV lines of bright \ion{Mg}{2}, and lines of \ion{Fe}{2} and \ion{Fe}{1} (mostly within the $4s-4p$ transition array) which form in the chromosphere up to $2\times10^4$ K. Both Hanle and Zeeman effects can in principle be used to derive vector magnetic fields. However, for any given spectral line the $\tau=1$ surfaces are generally geometrically corrugated owing to fine structure such as fibrils and spicules. By using multiple spectral lines spanning different optical depths, magnetic fields across nearly-horizontal surfaces can be inferred in regions of low plasma $\beta$, from which free energies, magnetic topology and other quantities can be derived. Based upon the recently-reported successful suborbital space measurements of magnetic fields with the CLASP2 instrument, we argue that a modest space-borne telescope will be able to make significant advances in the attempts to predict solar eruptions. Difficulties associated with blended lines are shown to be minor in an Appendix., Comment: Accepted in ApJ, V2 fixed author spelling error

Scattering polarization tends to dominate the linear polarization signals of the Ca II 8542 A line in weakly magnetized areas ($B \lesssim 100$ G), especially when the observing geometry is close to the limb. In this paper we evaluate the degree of applicability of existing non-LTE spectral line inversion codes (which assume that the spectral line polarization is due to the Zeeman effect only) at inferring the magnetic field vector and, particularly, its transverse component. To this end, we use the inversion code STiC to extract the strength and orientation of the magnetic field from synthetic spectropolarimetric data generated with the Hanle-RT code. The latter accounts for the generation of polarization through scattering processes as well as the joint actions of the Hanle and the Zeeman effects. We find that, when the transverse component of the field is stronger than $\sim$80 G, the inversion code is able to retrieve accurate estimates of the transverse field strength as well as its azimuth in the plane of the sky. Below this threshold, the scattering polarization signatures become the major contributors to the linear polarization signals and often mislead the inversion code into severely over- or under-estimating the field strength. Since the line-of-sight component of the field is derived from the circular polarization signal, which is not affected by atomic alignment, the corresponding inferences are always good., Comment: Accepted for publication in ApJ

One important feature of sunspots is the presence of light bridges. These structures are elongated and bright (as compared to the umbra) features that seem to be related to the formation and evolution of sunspots. In this work, we studied the long-term evolution and the stratification of different atmospheric parameters of three light bridges formed in the same host sunspot by different mechanisms. To accomplish this, we used data taken with the GREGOR Infrared Spectrograph installed at the GREGOR telescope. These data were inverted to infer the physical parameters of the atmosphere where the observed spectral profiles were formed of the three light bridges. We find that, in general, the behaviour of the three light bridges is typical of this kind of structure with the magnetic field strength, inclination, and temperature values between the values at the umbra and the penumbra. We also find that they are of a significantly non-magnetic character (particularly at the axis of the light bridges) as it is deduced from the filling factor. In addition, within the common behaviour of the physical properties of light bridges, we observe that each one exhibits a particular behaviour. Another interesting result is that the light bridge cools down, the magnetic field decreases, and the magnetic field lines get more inclined higher in the atmosphere. Finally, we studied the magnetic and non-magnetic line-of-sight velocities of the light bridges. The former shows that the magnetic component is at rest and, interestingly, its variation with optical depth shows a bi-modal behaviour. For the line-of-sight velocity of the non-magnetic component, we see that the core of the light bridge is at rest or with shallow upflows and clear downflows sinking through the edges.

The Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities which will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the Daniel K. Inouye Solar Telescope hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members, who generously shared their experiences, plans, knowledge and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute.

The weak field approximation (WFA) is a conceptually simple and computationally light method for inferring the magnetic field strength and its orientation in the Sun's atmosphere. In this work we study the validity and limitations of this tool when applied to full Stokes Ca II 8542 A profiles to extract information about the chromospheric magnetic field. We find that the range of validity of the WFA depends, amongst other things, on the component of the magnetic field that one is trying to infer. The retrieval of line-of-sight component of the chromospheric magnetic field from the core of the spectral line is reliable for field strengths up to ~1200 G, even when moderate velocity gradients are present. The horizontal component, on the other hand, is suitably derived using the wing-core boundary of the spectral line, but typically yields systematic errors of >10%. The effects of scattering polarization further compound the problem by rendering the transverse field inference problematic in quiet Sun areas, and for observing geometries within 30 degrees of the limb. Magneto-optical effects disproportionately challenge the determination of the magnetic field azimuth in the transverse plane, leading to errors of ~10 degrees. Typical noise levels of 10d-3 relative to the continuum intensity preclude the accurate retrieval of the transverse field strength and its azimuth below a threshold of a few hundred gauss. Striving for a noise level of 10d-4 significantly improves the diagnostic capability of the WFA with this spectral line, at which point the magnetic field inference becomes limited by systematic errors., Comment: Published in ApJ

In this work we seek evidence for global torsional oscillations in alpha sunspots. We have used long time series of continuum intensity and magnetic field vector maps from the Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) spacecraft. The time series analysed here span the total disk passage of 25 isolated sunspots. We found no evidence of global long-term periodic oscillations in the azimuthal angle of the sunspot magnetic field within $\sim$ 1 degree. This study could help us to understand the sunspot dynamics and its internal structure.

In June 2013, the two scientific instruments onboard the second Sunrise mission witnessed, in detail, a small-scale magnetic flux emergence event as part of the birth of an active region. The Imaging Magnetograph Experiment (IMaX) recorded two small (~5 arcsec) emerging flux patches in the polarized filtergrams of a photospheric Fe I spectral line. Meanwhile, the Sunrise Filter Imager (SuFI) captured the highly dynamic chromospheric response to the magnetic fields pushing their way through the lower solar atmosphere. The serendipitous capture of this event offers a closer look at the inner workings of active region emergence sites. In particular, it reveals in meticulous detail how the rising magnetic fields interact with the granulation as they push through the Sun's surface, dragging photospheric plasma in their upward travel. The plasma that is burdening the rising field slides along the field lines, creating fast downflowing channels at the footpoints. The weight of this material anchors this field to the surface at semi-regular spatial intervals, shaping it in an undulatory fashion. Finally, magnetic reconnection enables the field to release itself from its photospheric anchors, allowing it to continue its voyage up to higher layers. This process releases energy that lights up the arch-filament systems and heats the surrounding chromosphere., Comment: Accepted for publication in the Sunrise II Special Issue in the Astrophysical Journal Supplement Series

The Sun is replete with magnetic fields, with sunspots, pores and plage regions being their most prominent representatives on the solar surface. But even far away from these active regions, magnetic fields are ubiquitous. To a large extent, their importance for the thermodynamics in the solar photosphere is determined by the total magnetic flux. Whereas in low-flux quiet Sun regions, magnetic structures are shuffled around by the motion of granules, the high-flux areas like sunspots or pores effectively suppress convection, leading to a temperature decrease of up to 3000 K. The importance of magnetic fields to the conditions in higher atmospheric layers, the chromosphere and corona, is indisputable. Magnetic fields in both active and quiet regions are the main coupling agent between the outer layers of the solar atmosphere, and are therefore not only involved in the structuring of these layers, but also for the transport of energy from the solar surface through the corona to the interplanetary space. Consequently, inference of magnetic fields in the photosphere, and especially in the chromosphere, is crucial to deepen our understanding not only for solar phenomena such as chromospheric and coronal heating, flares or coronal mass ejections, but also for fundamental physical topics like dynamo theory or atomic physics. In this review, we present an overview of significant advances during the last decades in measurement techniques, analysis methods, and the availability of observatories, together with some selected results. We discuss the problems of determining magnetic fields at smallest spatial scales, connected with increasing demands on polarimetric sensitivity and temporal resolution, and highlight some promising future developments for their solution., Comment: Accepted for publication in "Space Science Reviews"; 42 pages, 16 figures

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The primary 720s observables were released in mid 2010, including Stokes polarization parameters measured at six wavelengths as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180 degree azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne-Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report., Comment: 42 pages, 19 figures, accepted to Solar Physics

We take advantage of the HMI/SDO instrument to study the naked emergence of active regions from the first imprints of the magnetic field on the solar surface. To this end, we followed the first 24 hours in the life of two rather isolated ARs that appeared on the surface when they were about to cross the central meridian. We analyze the correlations between Doppler velocities and the orientation of the vector magnetic field finding, consistently, that the horizontal fields connecting the main polarities are dragged to the surface by relatively-strong upflows and are associated to elongated granulation that is, on average, brighter than its surroundings. The main magnetic footpoints, on the other hand, are dominated by vertical fields and downflowing plasma. The appearance of moving dipolar features, MDFs, (of opposite polarity to that of the AR) in between the main footpoints, is a rather common occurrence once the AR reaches a certain size. The buoyancy of the fields is insufficient to lift up the magnetic arcade as a whole. Instead, weighted by the plasma that it carries, the field is pinned down to the photosphere at several places in between the main footpoints, giving life to the MDFs and enabling channels of downflowing plasma. MDF poles tend to drift towards each other, merge and disappear. This is likely to be the signature of a reconnection process in the dipped field lines, which relieves some of the weight allowing the magnetic arcade to finally rise beyond the detection layer of the HMI spectral line., Comment: Accepted for publication in ApJ

The Helioseismic and Magnetic Imager (HMI) has just started producing data that will help determine what the sources and mechanisms of variability in the Sun's interior are. The instrument measures the Doppler shift and the polarization of the Fe I 6173 A line, on the entire solar disk at a relatively-high cadence, in order to study the oscillations and the evolution of the full vector magnetic field of the solar Photosphere. After the data are properly calibrated, they are given to a Milne-Eddington inversion code (VFISV, Borrero et al. 2010) whose purpose is to infer certain aspects of the physical conditions in the Sun's Photosphere, such as the full 3-D topology of the magnetic field and the line-of-sight velocity at the solar surface. We will briefly describe the characteristics of the inversion code, its advantages and limitations --both in the context of the model atmosphere and the actual nature of the data--, and other aspects of its performance on such a remarkable data load. Also, a cross-comparison with near-simultaneous maps from the Spectro-Polarimeter (SP) onboard Hinode will be made., Comment: Proceedings of the Solar Polarization Workshop 6 held in Maui (May 31- June 4)

Using spectropolarimetric data of an Active Region (AR) filament we have carried out inversions in order to infer vector magnetic fields in the photosphere (Si I line) and in the chromosphere (He I line). Our filament lies above the polarity inversion line (PIL) situated close to disk center and presents strong Zeeman-like signatures in both photospheric and chromospheric lines. Pore-like formations with both polarities are identified in the continuum under the PIL. The azimuth ambiguity is solved at both heights using the AZAM code. A comparison between the photospheric and chromospheric vector magnetic fields revealed that they are well aligned in some areas of the filament. However, especially at chromospheric heights, the magnetic field is mostly aligned with the dark threads of the filament. Velocity signatures indicating upflows of field lines are found at both heights. The combination of all these findings strongly suggests an emerging flux rope scenario., Comment: 4 pages, to appear in the ASP Conference Proceedings of the "Solar Polarization Workshop 6"

Velocity oscillations "measured" simultaneously at the photosphere and the chromosphere -from time series of spectropolarimetric data in the 10830 A region- of different solar magnetic features allow us to study the properties of wave propagation as a function of the magnetic flux of the structure (i.e. two different-sized sunspots, a tiny pore and a facular region). While photospheric oscillations have similar characteristics everywhere, oscillations measured at chromospheric heights show different amplitudes, frequencies and stages of shock development depending on the observed magnetic feature. The analysis of the power and the phase spectra, together with simple theoretical modeling, lead to a series of results concerning wave propagation within the range of heights of this study. We find that, while the atmospheric cut-off frequency and the propagation properties of the different oscillating modes depend on the magnetic feature, in all the cases the power that reaches the high chromosphere above the atmospheric cut-off comes directly from the photosphere by means of linear vertical wave propagation rather than from non-linear interaction of modes., Comment: Accepted for publication in The Astrophysical Journal. 29 pages, 9 figures, 12pt, preprint

We examine the hypothesis that ``cool loops'' dominate emission from solar transition region plasma below temperatures of $2\times10^5$K. We compare published VAULT images of H L$\alpha$, a lower transition region line, with near-contemporaneous magnetograms from Kitt Peak, obtained during the second flight (VAULT-2) on 14 June 2002. The measured surface fields and potential extrapolations suggest that there are too few short loops, and that L$\alpha$ emission is associated with the base regions of longer, coronal loops. VAULT-2 data of network boundaries have an asymmetry on scales larger than supergranules, also indicating an association with long loops. We complement the Kitt Peak data with very sensitive vector polarimetric data from the Spectro-Polarimeter on board Hinode, to determine the influence of very small magnetic concentrations on our analysis. From these data two classes of behavior are found: within the cores of strong magnetic flux concentrations ($> 5\times10^{18}$ Mx) associated with active network and plage, small-scale mixed fields are absent and any short loops can connect just the peripheries of the flux to cell interiors. Core fields return to the surface via longer, most likely coronal, loops. In weaker concentrations, short loops can connect between concentrations and produce mixed fields within network boundaries as suggested by Dowdy and colleagues. The VAULT-2 data which we examined are associated with strong concentrations. We conclude that the cool loop model applies only to a small fraction of the VAULT-2 emission, but we cannot discount a significant role for cool loops in quieter regions. We suggest a physical picture for how network L$\alpha$ emission may occur through the cross-field diffusion of neutral atoms from chromospheric into coronal plasma., Comment: Accepted by ApJ, 9 May 2008

Velocity oscillations in sunspot umbrae have been measured simultaneously in two spectral lines: the photospheric Silicon I 10827 A line and the chromospheric Helium I 10830 A multiplet. From the full Stokes inversion of temporal series of spectropolarimetric observations we retrieved, among other parameters, the line of sight velocity temporal variations at photospheric and chromospheric heights. Chromospheric velocity oscillations show a three minute period with a clear sawtooth shape typical of propagating shock wave fronts. Photospheric velocity oscillations have basically a five minute period, although the power spectrum also shows a secondary peak in the three minute band which has proven to be predecessor for its chromospheric counterpart. The derived phase spectra yield a value of the atmospheric cut-off frequency around 4 mHz and give evidence for the upward propagation of higher frequency oscillation modes. The phase spectrum has been reproduced with a simple model of linear vertical propagation of slow magneto-acoustic waves in a stratified magnetized atmosphere that accounts for radiative losses through Newton's cooling law. The model explains the main features in the phase spectrum, and allows us to compute the theoretical time delay between the photospheric and chromospheric signals, which happens to have a strong dependence on frequency. We find a very good agreement between this and the time delay obtained directly from the cross-correlation of photospheric and chromospheric velocity maps filtered around the 6 mHz band. This allows us to infer that the 3-minute power observed at chromospheric heights comes directly from the photosphere by means of linear wave propagation, rather than from non-linear interaction of 5-minute (and/or higher frequency) modes., Comment: aastex preprint, 32 pages, 12 figures