Low-energy Cutoff Research Articles

Er3+:NaYb2F7 imbedded fluorotellurite transparent glass ceramic for enhanced upconversion luminescence and related thermometric behavior

Fluorotellurite glass ceramics (GCs) are promising photonic materials owing to their unique characteristic of integration of low cut-off phonon energy of fluorides and the high refractive index of tellurite glasses. Here, appropriate heat treatment to obtain the transparent GC from the parent glass (PG) of TeO2–Al2O3–NaF–CaF2-YbF3-ErF3 was established. The XRD, TEM, and spectroscopy techniques were employed to characterize the structure and properties of the as-prepared samples. The single fluoride phase NaYb2F7 crystallized from the PG was confirmed by XRD. TEM images displayed that in the transparent GC the nanocrystals are uniformly distributed in glassy matrix with an average size of about 6 nm. Under the 980 nm NIR excitation, the transparent GC exhibited bright upconversion luminescence in the visible region with intensity enhancement of ~73% comparing with the PG. The upconversion fluorescence kinetics were studied, along with the upconversion mechanism analyzed in details. Furthermore, the dependence of upconverted fluorescence intensity ratio (FIR) of the 2H11/2 → 4I15/2 emission to 4S3/2 → 4I15/2 emission from Er3+ ions on temperature was studied over a temperature range of 323–548 K. The results have shown that the Er3+:NaYb2F7 imbedded transparent fluorotellurite GC can be favorably employed for temperature sensing.

He i 10830 Å Dimming during Solar Flares. I. The Crucial Role of Nonthermal Collisional Ionizations

Abstract While solar flares are predominantly characterized by an intense broadband enhancement to the solar radiative output, certain spectral lines and continua will, in theory, exhibit flare-induced dimmings. Observations of transitions of orthohelium He i λ λ 10830 Å and the He i D3 lines have shown evidence of such dimming, usually followed by enhanced emission. It has been suggested that nonthermal collisional ionization of helium by an electron beam, followed by recombinations to orthohelium, is responsible for overpopulating those levels, leading to stronger absorption. However, it has not been possible observationally to preclude the possibility of overpopulating orthohelium via enhanced photoionization of He i by EUV irradiance from the flaring corona followed by recombinations. Here we present radiation hydrodynamics simulations of nonthermal electron-beam-driven flares where (1) both nonthermal collisional ionization of helium and coronal irradiance are included, and (2) only coronal irradiance is included. A grid of simulations covering a range of total energies deposited by the electron beam and a range of nonthermal electron-beam low-energy cutoff values were simulated. In order to obtain flare-induced dimming of the He i 10830 Å line, it was necessary for nonthermal collisional ionization to be present. The effect was more prominent in flares with larger low-energy cutoff values and longer lived in weaker flares and flares with a more gradual energy deposition timescale. These results demonstrate the usefulness of orthohelium line emission as a diagnostic of flare energy transport.

Thermal-nonthermal energy partition in solar flares derived from X-ray, EUV, and bolometric observations

Context.In solar flares, energy is released impulsively and is partly converted into thermal energy of hot plasmas and kinetic energy of accelerated nonthermal particles. It is crucial to constrain the partition of these two energy components to understand energy release and transport as well as particle acceleration in solar flares. Despite numerous efforts, no consensus on quantifying this energy balance has yet been reached.Aims.We aim to understand the reasons for the contradicting results on energy partition obtained by various recent studies. The overarching question we address is whether there is sufficient energy in nonthermal particles to account for the thermal flare component.Methods.We considered five recent studies that address the thermal-nonthermal energy partition in solar flares. Their results are reviewed, and their methods are compared and discussed in detail.Results.The main uncertainties in deriving the energy partition are identified as (a) the derivation of the differential emission measure distribution and (b) the role of the conductive energy loss for the thermal component, as well as (c) the determination of the low-energy cutoff for the injected electrons. The bolometric radiated energy, as a proxy for the total energy released in the flare, is a useful independent constraint on both thermal and nonthermal energetics. In most of the cases, the derived energetics are consistent with this constraint. There are indications that the thermal-nonthermal energy partition changes with flare strength: in weak flares, there appears to be a deficit of energetic electrons, while the injected nonthermal energy is sufficient to account for the thermal component in strong flares. This behavior is identified as the main cause of the dissimilar results in the studies we considered. The changing partition has two important consequences: (a) an additional direct (i.e. non-beam) heating mechanism has to be present, and (b) considering that the bolometric emission originates mainly from deeper atmospheric layers, conduction or waves are required as additional energy transport mechanisms.

Parametric Evolution of Power-law Energy Spectra of Flare Accelerated Electrons in the Solar Atmosphere

Abstract It is well known that solar hard X-ray bursts (HXRs) and solar radio bursts (SRBs) from solar flares both are produced directly by fast electron beams (FEBs) traveling through the solar atmosphere. The observed characteristics of HXRs and SRBs sensitively depend on the energy distribution of FEBs, which are believed commonly to have a power-law energy spectrum. When FEBs propagating in the solar atmosphere, however, their energy spectra can considerably vary due to the interaction with the atmospheric plasmas and this may significantly influence the observational characteristics of the producing HXRs and SRBs. In the present paper, based on flare atmospheric models, we investigate the parametric evolution of power-law spectra of FEBs due to their energy losses when propagating along flaring loops. The results show that an initially single power-law spectrum with a lower-energy cutoff can evolve into a more complex double power-law spectrum or a broken power-law spectrum with multi-breaking knees because of the dependence of the energy loss on the initial energies. The possible effects of the energy-spectral evolution of FEBs on observational characteristics of their HXR flares and SRBs are discussed. The present results are helpful to understand the physics of dynamical spectra of HXRs and SRBs from solar flares.

Two Complete Spectral Transitions of Swift J0243.6+6124 Observed by Insight-HXMT

Abstract We performed the broadband (1–100 keV) spectral analysis of the first Galactic Be ultraluminous X-ray pulsar (BeULX) Swift J0243.6+6124 observed by Insight-HXMT during the 2017−2018 outburst. The results show spectral transitions at two typical luminosities, roughly consistently with those reported previously via pure timing analysis. We find that the spectrum evolves and becomes softer and has higher cutoff energies until the luminosity reaches L 1 (∼1.5 × 1038 erg s−1). Afterwards the spectrum becomes harder with lower cutoff energies until the luminosity increases to L 2 (∼4.4 × 1038 erg s−1), around which the second spectral transition occurs. Beyond L 2, the spectrum softens again and has larger cutoff energies. Similar behaviors were observed previously in other high-mass X-ray binary systems (HMXBs), especially for the second transition at higher luminosities, which is believed to have a correlation with the magnetic field of the harbored neutron star. Accordingly, we speculate that Swift J0243.6+6124 owns a neutron star with magnetic field strength >1013 G. The spectral transition at around L 1 of Swift J0243.6+6124 is first observed thoroughly for any HMXB outburst characterized by strong evolution of the thermal component: the temperature of the blackbody drops sharply accompanied by a sudden increase of the blackbody radius. These spectral transitions can in principle be understood in a general scenario of balancing the emission patterns between the pencil and the fan beams at the magnetic pole, for which the extreme brightness of Swift J0243.6+6124 may provide an almost unique lab to probe the details.

Response of SDO/HMI Observables to Heating of the Solar Atmosphere by Precipitating High-energy Electrons

Abstract We perform an analysis of the line-of-sight (LOS) observables of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) for models of the solar atmosphere heated by precipitating high-energy electrons during solar flares. The radiative hydrodynamic (RADYN) flare models are obtained from the F-CHROMA database. The Stokes profiles for the Fe 6173 Å line observed by SDO/HMI are calculated using the radiative transfer code RH1.5D, assuming statistical equilibrium for atomic level populations, and imposing uniform background vertical magnetic fields of various strengths. The SDO/HMI observing sequence and LOS data processing pipeline algorithm are applied to derive the observables (continuum intensity, line depth, Doppler velocity, LOS magnetic field). Our results reveal that the strongest deviations of the observables from the actual spectroscopic line parameters are found for the model with a total energy deposited of E total = 1.0 × 1012 erg cm−2, injected with a power-law spectral index of δ = 3 above a low-energy cutoff of E c = 25 keV. The magnitudes of the velocity and magnetic field deviations depend on the imposed magnetic field, and can reach 0.35 km s−1 for LOS velocities, 90 G for LOS magnetic field, and 3% for continuum enhancement for the 1000 G imposed LOS magnetic field setup. For E total ≥ 3.0 × 1011 erg cm−2 models, the velocity and magnetic field deviations are most strongly correlated with the energy flux carried by ∼50 keV electrons, and the continuum enhancement is correlated with the synthesized ∼55–60 keV hard X-ray photon flux. The relatively low magnitudes of perturbations of the observables and absence of magnetic field sign reversals suggest that the considered RADYN beam heating models augmented with the uniform vertical magnetic field setups cannot explain the strong transient changes found in the SDO/HMI observations.

MHD simulations of inward shocks in Cassiopeia A

Cassiopeia A, the brightest radio supernova remnant (SNR) in the sky, has several unique characteristics in comparison to its peers. Besides its radio brightness and prominent soft-concave radio spectrum, its γ-ray spectrum appears to have a low-energy cutoff near 2 GeV, and it is the only SNR with prominent hard X-ray emission. While the unusual radio properties may be attributed to strong emission from reverse shocks, the hard X-ray emission has been associated with high-speed inward shocks induced by high density gases. Then, the low-energy γ-ray spectral cutoff could be attributed to slow penetration of lower energy particles accelerated near the inward shocks into high-density emission zone. In this paper, we carry out magneto-hydrodynamic (MHD) simulations of shocks in Cassiopeia A and demonstrate that its inward shock structure can indeed be reproduced via shock interactions with clumps of gases with a density of ∼ 20 cm−3.

The Fast Radio Burst Luminosity Function and Death Line in the Low-twist Magnetar Model

Abstract We explore the burst energy distribution of fast radio bursts (FRBs) in the low-twist magnetar model of Wadiasingh & Timokhin (WT19). Motivated by the power-law fluence distributions of FRB 121102, we propose an elementary model for the FRB luminosity function of individual repeaters with an inversion protocol that directly relates the power-law distribution index of magnetar short burst fluences to that for FRBs. The protocol indicates that the FRB energy scales virtually linearly with crust/field dislocation amplitude, if magnetar short bursts prevail in the magnetoelastic regime. Charge starvation in the magnetosphere during bursts (required in WT19) for individual repeaters implies the predicted burst fluence distribution is narrow, ≲3 decades for yielding strains and oscillation frequencies feasible in magnetar crusts. Requiring magnetic confinement and charge starvation, we obtain a death line for FRBs, which segregates magnetars from the normal pulsar population, suggesting only the former will host recurrent FRBs. We convolve the burst energy distribution for individual magnetars to define the distribution of luminosities in evolved magnetar populations. The broken power-law luminosity function’s low-energy character depends on the population model, while the high-energy index traces that of individual repeaters. Independent of the evolved population, the broken power-law isotropic-equivalent energy/luminosity function peaks at ∼1037–1040 erg with a low-energy cutoff at ∼1037 erg. Lastly, we consider the local fluence distribution of FRBs and find that it can constrain the subset of FRB-producing magnetar progenitors. Our model suggests that improvements in sensitivity may reveal a flattening of the global FRB fluence distribution and saturation in FRB rates.

A comparative study of non-thermal parameters of the X-class solar flare plasma obtained from cold and warm thick-target models; error estimation by Monte Carlo simulation method

The electron transport and relaxation in the non-thermal plasma of solar flare are often described by cold thick-target model. Recently introduced warm thick-target model however is also found to be more consistent for describing it and hence provide the accurate estimate of parameters of non-thermal solar flare plasma. In this study, we evaluate the consistency of cold and warm thick-target models by estimating non-thermal parameters viz., low-energy cutoff (${E_{c}/E_{wc}} $), kinetic power of non-thermal electrons (${P _{nth}/P_{wnth}} $) and non-thermal energy (${E_{nth}/E_{wnth}} $), along with standard error (SE) and their linear statistical analysis with respect to flare duration (${t _{f}}$). We further evaluate the accuracy of these parameters using Monte Carlo simulation data in $2 \sigma $ limits. We found that cold thick-target model gives high values of mean and SE of the estimated parameters compare to warm thick-target model those were also found consistent with the Monte Carlo data (in both cases). Here, we also found that the variation of ${E_{c}/E_{wc}} $ and ${P _{nth}/P_{wnth}} $ with respect to ${t_{f}} $ give a negative/positive and positive values of correlation coefficient ($r$) and slope ($b$) respectively which account for upper and lower limits of ${E_{c}/E_{wc}} $ and high and slow rate of thermalization of non-thermal electrons. Our results show that the warm thick-target model is more consistent model compare to cold thick-target model that could also lead a multi-temperature component in the thermalized plasma.

Energetic Particle Signatures Above Saturn's Aurorae

AbstractNear the end of its mission, NASA's Cassini spacecraft performed several low‐altitude passes across Saturn's auroral region. We present ultraviolet auroral imagery and various coincident particle and field measurements of two such passes, providing important information about the structure and dynamics of Saturn's auroral acceleration region. In upward field‐aligned current regions, upward proton beams are observed to reach energies of several tens of keV; the associated precipitating electron populations are found to have mean energies of about 10 keV. With no significant wave activity being apparent, these findings indicate strong parallel potentials responsible for auroral acceleration, about 100 times stronger than at Earth. This is further supported by observations of proton conics in downward field‐aligned current regions above the acceleration region, which feature a lower energy cutoff above 50 keV—indicating energetic proton populations trapped by strong parallel potentials while being transversely energized until they can overcome the trapping potential, likely through wave‐particle interactions. A spacecraft pass through a downward current region at an altitude near the acceleration region reveals plasma wave features, which may be driving the transverse proton acceleration generating the conics. Overall, the signatures observed resemble those related to the terrestrial and Jovian aurorae, the particle energies and potentials at Saturn appearing to be significantly higher than at Earth and comparable to those at Jupiter.

A Remarkably Narrow RHESSI X-Ray Flare on 2011 September 25

Abstract The unusually narrow X-ray source imaged with the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during an impulsive spike lasting for ∼10 s during the Geostationary Operational Environmental Satellite C7.9 flare on 2011 September 25 (SOL2011-09-25T03:32) was only ∼2″ wide and ∼10″ long. Comparison with Helioseismsic and Magnetic Imager magnetograms and Atmospheric Imaging Assembly images at 1700 Å shows that the X-ray emission was primarily from a long ribbon in the region of positive polarity with little if any emission from the negative polarity ribbon. However, a thermal plasma source density of ∼1012 cm−3 estimated from the RHESSI-derived emission measure and source area showed that this could best be interpreted as a coronal hard X-ray source in which the accelerated electrons with energies less than ∼50 keV were stopped by Coulomb collisions in the corona, thus explaining the lack of the more usual bright X-ray footpoints. Analysis of RHESSI spectra shows greater consistency with a multi-temperature distribution and a low-energy cutoff to the accelerated electron spectrum of 22 keV compared to 12 keV if a single-temperature distribution is assumed. This leads to a change in the lower limit on the total energy in electrons by an order of magnitude, given the steepness of the best-fit electron spectrum with a power-law index of ∼6.

Evolution of an electron beam pulse influenced by coulomb collision effects in the solar corona

Electrons accelerated in the corona during solar activity give rise to radio emission events that can be observed over a wide range of frequencies. Among different finer-scale structures in the dynamic spectra observed in the radio range, fast transients with extents of some milliseconds known as solar radio spikes are observed accompaning the background continuum emission. Fundamental to the generation of radio spikes is a propagating electron beam and following its evolution allows us to understand the physical processes occurring in the solar corona. With the use of a numerical Fokker–Planck code we follow a previous numerical study to simulate the propagation of an electron beam pulse injected in a small region at the top of a magnetic field and outwards the solar corona under typical flare conditions. It was found that in large ambient densities of 1010 cm−3 at the injection point, Coulomb collision effects have an important effect on the propagation of the electrons, causing that the injected electrons thermalize faster in a time of 0.1 and 0.4 s for an electron distribution with a low-energy cut off of 16 and 7 keV respectively and a spectral index of 3. For a tenous ambient medium of density 109 cm−3 thermalization occurs only for an electron distribution with smaller low-energy cut off (7 keV) with a duration of ≈1.5 s, while for a larger low-energy cut off (16 keV) the loss of accelerated electrons is very slow, regardles of the spectral index (3,7). The electron loss time by Coulomb collisions, which depends on the low boundary ambient density, might be an important parameter that influences the generation of radio spikes due to the formation of instabilities in the corona.

Global Energetics of Solar Flares and Coronal Mass Ejections

We investigate the global energetics and energy closure of various physical processes that are energetically important in solar flares and coronal mass ejections (CMEs), which includes: magnetic energies, thermal energies, nonthermal energies (particle acceleration), direct and indirect plasma heating processes, kinetic CME energies, gravitational CME energies, aerodynamic drag of CMEs, solar energetic particle events, EUV and soft X-ray radiation, white-light, and bolometric energies. Statistics on these forms of energies is obtained from 400 GOES M- and X-class events during the first 3.5 years of the Solar Dynamics Observatory (SDO) mission. A primary test addressed in this study is the closure of the various energies, such as the equivalence of the dissipated magnetic energies and the primary dissipated are energies (accelerated particles, direct heating, CME acceleration), which faciliate the energy of secondary processes (plasma heating, shock acceleration) and interactions with the solar wind (aerodynamic drag). Our study demonstrates energy closure in the statistical average, while individual events may have considerable uncertainties, requiring improved nonlinear force-free field models, and particle acceleration models with observationally constrained low-energy cutoffs.

Hydrogen Emission in Type II White-light Solar Flares

Abstract Type II white-light flares (WLFs) have weak Balmer line emission and no Balmer jump. We carried out a set of radiative hydrodynamic simulations to understand how the hydrogen radiative losses vary with the electron-beam parameters and more specifically with the low-energy cutoff. Our results have revealed that for low-energy beams, the excess flare Lyman emission diminishes with increasing low-energy cutoff as the energy deposited into the top chromosphere is low compared to the energy deposited into the deeper layers. Some Balmer excess emission is always present and is driven primarily by direct heating from the beam with a minor contribution from Lyman continuum backwarming. The absence of Lyman excess emission in electron-beam driven models with high low-energy cutoff is a prominent spectral signature of type II WLFs.

The Multi-instrument (EVE-RHESSI) DEM for Solar Flares, and Implications for Nonthermal Emission

Abstract Solar flare X-ray spectra are typically dominated by thermal bremsstrahlung emission in the soft X-ray (≲10 keV) energy range; for hard X-ray energies (≳30 keV), emission is typically nonthermal from beams of electrons. The low-energy extent of nonthermal emission has only been loosely quantified. It has been difficult to obtain a lower limit for a possible nonthermal cutoff energy due to the significantly dominant thermal emission. Here we use solar flare data from the extreme ultraviolet Variability Experiment on board the Solar Dynamics Observatory and X-ray data from the Reuven Ramaty High Energy Spectroscopic Imager to calculate the Differential Emission Measure (DEM). This improvement over the isothermal approximation and any single-instrument DEM helps to resolve ambiguities in the range where thermal and nonthermal emission overlap, and to provide constraints on the low-energy cutoff. In the model, thermal emission is from a DEM that is parameterized as multiple Gaussians in Log(T). Nonthermal emission results from a photon spectrum obtained using a thick-target emission model. Spectra for both instruments are fit simultaneously in a self-consistent manner. Our results have been obtained using a sample of 52 large (Geostationary Operational Environmental Satellite X- and M-class) solar flares observed between 2011 and 2013. It turns out that it is often possible to determine low-energy cutoffs early (in the first two minutes) during large flares. Cutoff energies at these times are typically low, less than 10 keV, when assuming coronal abundances. With photospheric abundances, cutoff energies are typically ∼10 keV higher, in the ∼17–25 keV range.

Global Energetics of Solar Flares. VIII. The Low-energy Cutoff

Abstract One of the key problems in solar flare physics is the determination of the low-energy cut-off: the value that determines the energy of nonthermal electrons and hence flare energetics. We discuss different approaches to determine the low-energy cut-off in the spectrum of accelerated electrons: (i) the total electron number model, (ii) the time-of-flight model (based on the equivalence of the time-of-flight and the collisional deflection time), (iii) the warm target model of Kontar et al., and (iv) the model of the spectral cross-over between thermal and nonthermal components. We find that the first three models are consistent with a low-energy cutoff with a mean value of ≈10 keV, while the cross-over model provides an upper limit for the low-energy cutoff with a mean value of ≈21 keV. Combining the first three models we find that the ratio of the nonthermal energy to the dissipated magnetic energy in solar flares has a mean value of q E = 0.57 ± 0.08, which is consistent with an earlier study based on the simplified approximation of the warm target model alone (q E = 0.51 ± 0.17). This study corroborates the self-consistency between three different low-energy cutoff models in the calculation of nonthermal flare energies.

Results from EDGES High-Band. III. New Constraints on Parameters of the Early Universe

Abstract We present new constraints on parameters of cosmic dawn and the epoch of reionization derived from the EDGES High-Band spectrum (90–190 MHz). The parameters are probed by evaluating global 21 cm signals generated with the recently developed Global21cm tool. This tool uses neural networks trained and tested on ∼30,000 spectra produced with semi-numerical simulations that assume the standard thermal evolution of the cosmic microwave background and the intergalactic medium. From our analysis, we constrain at 68% (1) the minimum virial circular velocity of star-forming halos to V c < 19.3 km s−1, (2) the X-ray heating efficiency of early sources to f X > 0.0042, and (3) the low-energy cutoff of the X-ray spectral energy distribution to ν min < 2.3 keV. We also constrain the star formation efficiency (f *), the electron scattering optical depth (τ e), and the mean-free path of ionizing photons (R mfp). We recompute the constraints after incorporating into the analysis four estimates for the neutral hydrogen fraction from high-z quasars and galaxies, and a prior on τ e from Planck 2018. The largest impact of the external observations is on the parameters that most directly characterize reionization. Specifically, we derive the combined 68% constraints τ e < 0.063 and R mfp > 27.5 Mpc. The external observations also have a significant effect on V c due to its degeneracy with τ e, while the constraints on f *, f X, and ν min, remain primarily determined by EDGES.

The role of an invariant IR cutoff in late time cosmological dynamics

We study the role of an invariant infra-red cutoff in the late time cosmological dynamics. This low energy cutoff originates from the existence of a minimal measurable uncertainty as a result of the curvature of background manifold, and can be encoded in an extended uncertainty relation. Inspired by black hole entropy-area relation, we extend the analysis to the thermodynamics of apparent horizon of the universe. By treating both the Newtonian and general relativistic cosmologies, we show that the contribution of infra-red cutoff in the equations of dynamics can be interpreted as an effective fluid which is capable of explaining late time cosmic speed up and even transition to a phantom phase of expansion. We use the latest observational data from PLANCK2018 to constrain the parameter of an extended uncertainty relation.

Circular Polarization in Compact Radio Sources: Constraints on Particle Acceleration and Electron–Positron Pairs

Abstract It is shown that the frequency distribution of the degree of circular polarization for a homogeneous source is sensitive to the properties of the synchrotron emitting plasma. Most of the circular polarization comes from the region around the turnover frequency, where the synchrotron radiation becomes optically thick. However, nearly circular characteristic waves result in circular polarization dominated by frequencies above the turnover frequency, while in the case of nearly linear characteristic waves, it is dominated by frequencies below. Observations argue in favor of nearly circular characteristic waves. This implies a low-energy cutoff in the electron distribution that is substantially below that corresponding to the turnover frequency and simultaneously provides an upper limit to the fraction of electron–positron pairs.

Mixed-Valent Ruthenocene-Vinylruthenium Conjugates: Valence Delocalization Despite Chemically Different Redox Sites.

Ruthenocene-vinylruthenium conjugates Rc/Rc*-CH═CH-Ru(CO)(L)(P iPr3)2 (Rc = (η5-C5H5)Ru(η5-C5H4); Rc* = (η5-C5Me5)Ru(η5-C5H4); L = Cl or κ O, O' -acetylacetonato) have been prepared and investigated in their neutral, mono-, and dioxidized states by cyclic voltammetry, IR and UV/vis/NIR spectroelectrochemistry, and EPR spectroscopy. Their corresponding radical cations are (almost) completely delocalized mixed-valent systems as indicated by the low half-widths, the absence of solvatochromism, and the low-energy cutoff of their IVCT bands in the near-infrared (NIR) and their IR and EPR spectroscopic signatures. The degree of electronic coupling even exceeds that of their ferrocene analogs despite comparable differences between the intrinsic half-wave potentials of the vinylruthenium and the metallocenyl entities and substantially smaller half-wave potential splittings, Δ E1/2, in the ruthenocene congeners. All experimental results are backed by quantum chemical calculations.