Weak Field Approximation Research Articles

π-π scattering lengths: Electric corrections in the linear sigma model

In the frame of the linear sigma model and working in the weak field approximation, we discuss the role played by an external electric field on the behavior of π-π scattering lengths. For this purpose, we have considered all relevant one-loop diagrams in the s, t, and u channels where we have Schwinger propagators for charged pions. An important novelty of our analysis, compared with previous existing discussions in the literature, is the explicit calculation of box diagrams which were previously not considered in discussions regarding magnetic corrections to π-π scattering lengths. Our analysis shows that electric field corrections have an opposite effect with respect to the previously calculated magnetic corrections.

Deflection of charged signals in a dipole magnetic field in Kerr background

This paper investigates charged particle deflection in a Kerr spacetime background with a dipole magnetic field, focusing on the equatorial plane and employing the weak field approximation. We employ the Jacobi–Randers metric to unify the treatment of the gravitational and electromagnetic effects on charged particles. Furthermore, we utilize the Gauss–Bonnet theorem to calculate the deflection angle through curvature integrals. The difference between the prograde and retrograde deflection angles is linked to the non-reversibility of metrics and geodesics in Finsler geometry, revealing that this difference can be considered a Finslerian effect. We analyze the impact of both gravitomagnetic field and dipole magnetic field on particle motion and deflection using the Jacobi–Randers magnetic field. The model considered in this paper exhibits interesting features in the second-order approximation of (M/b), i.e., the ratio between the spacetime mass and impact parameters. When qμ=2MaE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\mu =2MaE$$\\end{document}, where q,E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q,\\,E$$\\end{document} are the charge and asymptotic energy of the charged particle and μ,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu ,\\,a$$\\end{document} are the dipole magnetic moment and spacetime spin, the Jacobi–Randers metric possesses reversible geodesics, leading to equal prograde and retrograde deflection angles. In this case, the gravitomagnetic field and dipole magnetic field cancel each other out, distinguishing it from scenarios involving only the gravitomagnetic field or the dipole magnetic field. We also explore the magnetic field’s impact on gravitational lensing of charged particles.

Retardation theory of eleven galaxies

Abstract The missing mass problem has been with us since the 1970s, as Newtonian gravity using baryonic mass cannot account for various observations. We investigate the viability of retardation theory, an alternative to the Dark Matter paradigm (DM) which does not seek to modify the General Principal of Relativity but to improve solutions within it by exploring its weak field approximation to solve the said problem in a galactic context. This approach have yielded satisfactory results, with respect to galactic rotation curves, the Tully-Fisher relation and missing mass derived from gravitational lensing. Recently it was able to introduce a necessary correction to the virial theorem explaining mass excess in clusters of galaxies. The current work presents eleven rotation curves calculated using Retardation Theory. The calculated rotation curves are compared with observed rotation curves. Values for the change in mass flux to mass ratio are extracted from the fitting process as a free fitting parameter. Those quantities are interpreted here and in previous works using galactic processes. Retardation Theory was able to successfully reproduce rotation curves and a preliminary correlation with star birthrate index is seen, suggesting a possible link between galactic winds and observed rotation curves. Retardation Theory shows promising results within current observations. More research is needed to elucidate the suggested mechanism and the processes which contribute to it. Galactic mass outflows carried by galactic winds may affect rotation curves.

Magnetic field diagnostics of prominences with the Mg II k line 3D Stokes inversions versus traditional methods

The Mg II k resonance line is commonly used for diagnosing the solar chromosphere. We theoretically investigated its intensity and polarization in solar prominences, taking 3D radiative transfer and Hanle and Zeeman effects into account. We used an optically thick 3D model representative of a solar prominence and applied several inversion methods to the synthetic Stokes profiles, clarifying their pros and cons for inferring prominence magnetic fields. We conclude that the self-consistent 3D inversion with radiative transfer is necessary to determine the magnetic field vector, although its geometry cannot be inferred with full fidelity. We also demonstrate that more traditional methods, such as those based on the weak field approximation or the constant-property slab assumption, can offer useful information under certain conditions.

The motion of twisted particles in a stellar gravitational field

Abstract In this work, we explore the motion of a twisted particle possessing intrinsic orbital angular momentum (OAM) as it traverses a weak stellar gravitational field, which we approximate using a polytropic model. We disregard the spin characteristic of the twisted particle, modeling it as a massless complex twisted scalar wave packet to simplify its interaction with gravitational fields. Building on this simplification, we determine the trajectory of this twisted particle by using the center of its energy density and investigate the gravitational birefringence induced by its OAM. In a weak field approximation, we find the gravitational birefringence-OAM relationship parallels that with spin, as described by the Mathisson-Papapetrou-Dixon equations. This indicates that the gravitational birefringence induced by OAM can potentially exceed that induced by spin by several orders of magnitude, significantly enhancing its detectability. To broaden our analysis, we introduce a nonminimal coupling term, $\lambda R|\phi|^2$, into the Lagrangian, resulting in the modified expression $\mathcal{L}=-\frac{1}{2}\nabla _\rho\phi\nabla^\rho\phi^*-\frac{1}{2}\lambda R|\phi|^2$. This adjustment is necessitated by the quantization of the scalar field in curved spacetime. We then explore the effects of this term on the motion of the twisted particle. Our findings show that the trajectory of the twisted particle under nonminimal coupling ($\lambda\neq 0$) differs from that in the minimal coupling scenario ($\lambda=0$). Specifically, for a positive nonminimal coupling constant $\lambda$, the trajectory of the twisted particle is expected to deviate away from the stellar center, compared to the minimal coupling scenario.

Gravitational radiation in generalized Brans–Dicke theory: compact binary systems

This paper investigates the generation and properties of gravitational radiation within the framework of generalized Brans–Dicke (GBD) theory, with a specific emphasis on its manifestation in compact binary systems. The study begins by examining the weak field equations in GBD theory, laying the foundation for subsequent analyses. Solutions to the linearized field equations for point particles are then presented, providing insights into the behavior of gravitational fields in the context of GBD theory. The equation of motion of point mass is explored, shedding light on the dynamics of compact binary systems within the GBD framework. The primary focus of this study lies in the comprehensive exploration of gravitational radiation generated by compact binaries. The energy momentum tensor and the associated gravitational wave (GW) radiation power in GBD theory are investigated, elucidating the relationship between these fundamental concepts. Furthermore, detailed calculations are provided for the GW radiation power originating from both tensor fields and scalar fields. Based on our calculations, both scalar fields contribute to GW radiation by producing dipole radiation. We also study the period derivative of compact binaries in this theory. By comparing with the observational data of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307, we put bounds on the two parameters of the theory: the Brans–Dicke coupling parameter ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}$$\\end{document} and the mass of geometrical scalar field mf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_f$$\\end{document}, resulting in a lower bound ω0>6.09723×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}>6.09723\ imes 10^6$$\\end{document} for a massless BD scalar field and the geometrical field whose mass is smaller than 10-29GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-29} \ ext { GeV}$$\\end{document}. The obtained bound on ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _0$$\\end{document} is two orders of magnitude stricter than those derived from solar system data. Finally, we find the phase shift that GWs experience in the frequency domain during their propagation. These calculations offer a quantitative understanding of the contributions from different components within the GBD theory, facilitating a deeper comprehension of the overall behavior and characteristics of gravitational radiation.

Magnetic catalysis and diamagnetism from pion fluctuations

In the framework of the Nambu–Jona-Lasinio model beyond mean field approximation, the effects of pion fluctuations on (inverse) magnetic catalysis and magnetic susceptibility are studied. The negative magnetic susceptibility at low temperature is observed when contributions from both neutral and charged pions are taken into account. In the weak field approximation, it is observed that at finite temperature, the magnetic inhibition effect in the chiral limit, resulting from the difference between the transverse and longitudinal velocities of neutral pions, converts to weak magnetic catalysis when considering a nonzero current quark mass. Moreover, the magnetic catalysis is amplified by the charged pions. Therefore, no inverse magnetic catalysis is observed when considering pion fluctuations. Published by the American Physical Society 2024

Simultaneous Spectropolarimetric Observations in the Hα and Ca ii 8662 Å Lines of an Active Region

We present spectropolarimetric observations of an active region recorded simultaneously in the Hα and the Ca ii 8662 Å lines. The sunspot exhibits multiple structures, including a light bridge and a region where the Ca ii 8662 Å line core is in emission. Correspondingly, the Hα line core image displays brightening in the emission region, with the spectral profiles showing elevated line cores. The stratification of the line-of-sight magnetic field is inferred through nonlocal thermodynamic equilibrium multiline inversions of the Ca ii 8662 Å line and the weak field approximation (WFA) over the Hα line. The field strength inferred from the Hα line core is consistently smaller than that inferred from inversions at logτ500 = −4.5. However, the study finds no correlation between the WFA over the core of the Hα line and that inferred from inversions at logτ500 = −4.5. In regions exhibiting emission features, the morphology of the magnetic field at logτ500 = −4.5 resembles that at logτ500 = −1, with slightly higher or comparable field strengths. The magnetic field morphology inferred from the core of the Hα line is also similar to that inferred from the full spectral range of the Hα line in the emission region. The field strength inferred in the light bridge at logτ500 = −1 is smaller than the surrounding umbral regions and comparable at logτ500 = −4.5. Similarly, the field strength inferred in the light bridge from the WFA over the Hα line appears lower compared to the surrounding umbral regions.

Shadows, rings and optical appearance of a magnetically charged regular black hole illuminated by various accretion disks

Abstract The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers of Messier 87 galaxy (M87) and the Milky Way galaxy (Sgr A) marks a significant step in observing the photon rings and central brightness depression that define the optical appearance of black holes with an accretion disk scenario. Inspired by this, we take into account a static and spherically symmetric magnetically charged regular black hole (MCRBH) metric characterized by its mass and an additional parameter q, which arises from the coupling of Einstein gravity and nonlinear electrodynamics (NLED) in the weak field approximation. This parameterized model offers a robust foundation for testing the coupling of Einstein gravity and NLED in the weak-field approximation, using the EHT observational results. In this study, we investigate the geodesic motion of particles around the solution, followed by a discussion of its fundamental geometrical characteristics such as scalar invariants. Using null geodesics, we examine how the model parameter influences the behavior of the photon sphere radius and the associated shadow silhouette. We seek constraints on q by applying the EHT results for supermassive black holes M87* and Sgr A*. Furthermore, it is observed that the geodesics of time-like particles are susceptible to variations in q, which can have an impact on the traits of the innermost stable circular orbit and the marginally bounded orbit. Our primary objective is to probe how the free parameter q affects various aspects of the accretion disk surrounding the MCRBH using the thin-disk approximation. Next, we discuss the physical characteristics of the thin accretion disk as well as the observed shadows and rings of the MCRBH, along with its luminosity, across various accretion models. Ultimately, variations in accretion models and the parameter q yield distinct shadow images and optical appearances of the MCRBH.

Enhanced Approaches to Gravitational Lensing: A Regular Charged Black Hole in Weak Field Limit

Gravitational lensing, an integral aspect of general relativity, profoundly impacts our understanding of black holes (BH’s). The presence of a centered singularity resulting from gravitational collapse is a fundamental characteristic of a BH Nonetheless, the exploitation of non-linear electrodynamics (NLED) divulges the emphatic concept of non-singularity. Our analysis primarily focuses on calculating the deflection angle in the weak field approximation, deliberately excluding the original spacetime configuration. The photon’s effective geometry is typically linked to NLED. Instead, a photon traverses an effective null geodesic that aligns with the geometry of a regular metric. The findings reveal an additional term in the deflection angle compared to the Reissner-Nordström (RN) metric, evidenced by a shifted positional displacement of the tertiary image associated with a regular BH This study succinctly encapsulates these findings, positioning them within the extensive terminology ambient to BH’s singularity and GL, thus edifying the scientific memoir with precise astrophysical insights.

Evolution of light deflection and shadow from a gauge-potential-like AdS black hole under the influence of a non-magnetic plasma medium

We investigate the light deflection in the weak field approximation from the accelerating charged AdS black hole. For this purpose, we apply the Gauss–Bonnet theorem to calculate the light deflection in the weak field area and use the Gibbons–Werner approach to analyze the optical geometry of the accelerating charged AdS black hole in the non-magnetic plasma absence/presence of a non-magnetic medium. We also represent the graphical behavior of the light deflection angle w.r.t. the impact parameter. We also compute the light deflection angle using Keeton and Petters approximations under the impact of accelerating charged AdS black hole geometry. Furthermore, by using the ray-tracing approach, we determine the shadow in the non-magnetic plasma presence and also demonstrate that graphical shadow has an impact on the gauge potential, non-magnetic plasma frequencies and charge.

Aharonov-Bohm effect in Generalized Electrodynamics

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.

Forward modeling of the Mg I 12.32 μm line from a 3D magnetohydrodynamic model of an enhanced network

Context. The Mg I 12 μm lines, 12.22 and 12.32 μm, represent a pair of emission lines, and their line cores originate around the temperature minimum region. These lines exhibit the highest ratio of Zeeman to Doppler broadening in the infrared solar spectrum, making them crucial for accurately investigating the solar magnetic field. Aims. We synthesized the Mg I 12.32 μm Stokes profiles from a 3D magnetohydrodynamic (MHD) model and studied the validity of different methods for extracting the magnetic field. The observational profiles at different spatial resolution were simulated, which are helpful for the design of future solar telescopes with large apertures. Methods. We used a 3D MHD simulation model for an enhanced network computed using the Bifrost code. We performed nonlocal thermal equilibrium calculations for Stokes profiles of the Mg I 12.32 μm line using the Rybicki–Hummer code. Results. From the simulation we determined the average formation height of the Mg I 12.32 μm line to be around 450 km. The various solar features have different formation heights, and the variance of formation height in magnetic concentration regions is about 160 km. The wavelength-integrated method is proven effective in calibrating the integrated Stokes profiles to obtain the longitudinal (Bl) and horizontal (BH) field components for weak magnetic fields; the Bl is below 300 G. Furthermore, the weak field approximation was found to be valid only for estimating magnetic fields with Bl below 150 G. The Stokes I profiles clearly show Zeeman triple splitting around the magnetic flux concentration with a grid resolution of 48 km. We determined that a resolution of 0.97″, equivalent to the diffraction limit of a telescope with a diameter of 3.2 m, was necessary to detect the Zeeman splitting for the simulated snapshot. Our results from this 3D MHD model are valuable for interpreting data from the Accurate Infrared Magnetic Field Measurements of the Sun (AIMS) telescope and designing future solar infrared telescopes.

Impact of an external magnetic field on vortex-like magnetic structures in perforated films

The paper examines the effect of an external magnetic field on inhomogeneous magnetic structures formed in the region of a pair of closely spaced holes in a ferromagnetic film with strong easy-plane anisotropy. It is shown that the impact of a field normal to the film plane can lead either to the destruction of a vortex-like structure when the field strength exceeds a certain critical value, or to transformation of the magnetic structure without changing its topology. Such a transformation is associated with the deviation of the magnetization vector from the film plane, and the greatest deviation is observed in the gap between the perforations near their boundaries. The features of magnetization distributions formed under the influence of an external field have been studied both by analytical methods within the framework of approximate models (weak field approximation, single antidot model, “pretzel” model) and by numerical simulation.

Energy-momentum tensor of the dilute (3+1)D glasma

We present a succinct formulation of the energy-momentum tensor of the glasma characterizing the initial color fields in relativistic heavy-ion collisions in the color glass condensate effective theory. We derive concise expressions for the (3+1)D dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with nontrivial longitudinal correlations. Utilizing Monte Carlo integration, we calculate in unprecedented detail non-trivial rapidity profiles of early time observables at RHIC and LHC energies, including transverse energy densities and eccentricities. For our setup with broken boost invariance, we carefully discuss the placement of the origin of the Milne frame and interpret the components of the energy-momentum tensor. We find longitudinal flow that deviates from standard Bjorken flow in the (3+1)D case and provide a geometric interpretation of this effect. Furthermore, we observe a universal shape in the flanks of the rapidity profiles regardless of collision energy and predict that limiting fragmentation should also hold at LHC energies. Published by the American Physical Society 2024

Improved reconstruction of solar magnetic fields from imaging spectropolarimetry through spatio-temporal regularisation

Context. Determination of solar magnetic fields with a spatial resolution set by the diffraction limit of a telescope is difficult because the time required to measure the Stokes vector with sufficient signal-to-noise ratio is long compared to the solar evolution timescale. This difficulty becomes greater with increasing telescope size as the photon flux per diffraction-limited resolution element remains constant but the evolution timescale decreases linearly with the diffraction-limited resolution. Aims. We aim to improve magnetic field reconstruction at the diffraction limit without averaging the observations in time or space, and without applying noise filtering. Methods. The magnetic field vector tends to evolve more slowly than the temperature, velocity, or microturbulence. We exploit this by adding temporal regularisation terms for the magnetic field to the linear least-squares fitting used in the weak-field approximation, as well as to the Levenberg-Marquardt algorithm used in inversions. The other model parameters are allowed to change in time without constraints. We infer the chromospheric magnetic field from Ca II 854.2 nm observations using the weak field approximation and the photospheric magnetic field from Fe I 617.3 nm observations, both with and without temporal regularisation. Results. Temporal regularisation reduces the noise in the reconstructed maps of the magnetic field and provides a better coherency in time in both the weak-field approximation and Milne-Eddington inversions. Conclusions. Temporal regularisation markedly improves magnetic field determination from spatially and temporally resolved observations.

Multipole expansion of the gravitational field in a general class of fourth-order theories of gravity and the application in gyroscopic precession

A viable weak-field and slow-motion approximation method is constructed in F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity, a general class of fourth-order theories of gravity. By applying this method, the metric, presented in the form of the multipole expansion, outside a spatially compact source up to 1/c 3 order is provided, and the closed-form expressions for the source multipole moments are all presented explicitly. The metric consists of the massless tensor part, the massive scalar part, and the massive tensor part, where the former is exactly the metric in General Relativity, and the latter two are the corrections to it. It is shown that the corrections bear the Yukawa-like dependence on the two massive parameters and predict the appearance of six additional sets of source multipole moments, which indicates that up to 1/c 3 order, there exist six degrees of freedom beyond General Relativity within F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity. By means of the metric, for a gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of the Thomas precession, the geodetic precession, and the Lense-Thirring precession are derived, and from them, the corrections to the angular velocities of the three types of precession in General Relativity can be read off. These results indicate that differently from f(R) or f(R,𝒢) gravity, the most salient feature of the general F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity is that it gives the nonvanishing correction to the gyroscopic spin's angular velocity of the Lense-Thirring precession in General Relativity.

Classical and quantum cosmology for two scalar field Brans–Dicke type theory: a Noether symmetry approach

The paper deals with a cosmological model containing two scalar fields which can be considered as an extension of the Brans–Dicke scalar field model. Due to highly coupled non linear field equations, Noether symmetry analysis has been imposed and as a result the Lagrangian as well as the field equations become much simple in form to have the classical solutions. The relevant cosmological parameters are analyzed graphically. Finally, quantum cosmology has been studied by constructing the Wheeler–DeWitt equation and the solution of this second order partial differential equation has been done using this symmetry analysis.

Detectability of Single Spinless Stellar-Mass Black Holes through Gravitational Lensing of Gravitational Waves with Advanced LIGO.

We investigate the detectability of gravitational waves that have been lensed by a spinless stellar-mass black hole, with respect to the advanced LIGO. By solving the full relativistic linear wave equations in the spacetime of a Schwarzschild black hole, we find that the strong gravity can create unique signals in the lensed waveform, particularly during the merger and ring-down stages. The differences in terms of fitting factor between the lensed waveform and best-fitted unlensed general relativity template with spin precession and higher-order multipoles are greater than 5% for the lens black hole mass within 70M_{⊙}<M_{lens}<133.33M_{⊙} under advanced LIGO's sensitivity. This is up to 5 times more detectable than the previous analysis based on the weak field approximation for a point mass and covers most part of the black hole mass gap predicted by stellar evolution theory. Based on Bayesian inference, the lensing feature can be distinguished with a signal-to-noise ratio of 12.5 for M_{lens}=70M_{⊙} and 19.2 for M_{lens}=250M_{⊙}, which is attainable for advanced LIGO.

Magnetic Fields and Plasma Heating in the Sun’s Atmosphere

We use the first publicly available data from the Daniel K. Inouye Solar Telescope to track magnetic connections from the solar photosphere into the corona. We scrutinize relationships between chromospheric magnetism and bright chromospheric, transition region, and coronal plasmas. In 2022 June, the Visible Spectro-Polarimeter (ViSP) instrument targeted unipolar network within a decaying active region. ViSP acquired rastered scans with longitudinal Zeeman sensitivities of 0.25 Mx cm−2 (Fe i, 630.2 nm) and 0.5 Mx cm−2 (Ca ii, 854.2 nm). ViSP was operated in a “low” resolution mode (0.″214 slit width, spectral resolution R≈70,000 ) to produce polarization maps over a common area of 105″ × 50″. Data from the Solar Dynamics Observatory and Interface Region Imaging Spectrograph are combined to ask: Why is only a fraction of emerging flux filled with heated plasma? What is the elemental nature of the plasmas? No correlations were found between heated plasma and the properties of chromospheric magnetic fields derived from the weak field approximation, on scales below supergranules. Processes hidden from our observations control plasma heating. While improved magnetic measurements are needed, these data indicate that “the corona is a self-regulating forced system.” Heating depends on the state of the corona, not simply on boundary conditions. Heating models based upon identifiable bipolar fields, including cool loops, tectonics, and observable magnetic reconnection, are refuted for these regions with unipolar chromospheric magnetic fields.