The Slowly Varying Corona. II. The Components of F_10.7 and Their Use in EUV Proxies

Extreme ultraviolet (EUV, 10–121.6 nm) light emitted by the solar atmosphere is absorbed in the terrestrial thermosphere by photoionization, which leads to the creation of the ionosphere as well as the heating of and increased density in the thermosphere (Tobiska 1996). Increased incident EUV during periods of increased solar activity can cause communication problems (due to changing radio propagation in the ionosphere, Dandekar 1985; Klobuchar 1985; McNamara 1985) and disrupt satellite operations by increasing satellite surface charging (due to increased ionospheric density, Garret 1985) and drag (due to increased thermospheric density, De Lafontaine & Garg 1982). In addition, the ionosphere forms the boundary layer of the entire terrestrial magnetosphere system that can cause other dynamic terrestrial effects under the influence of space weather events (Schunk et al. 2004). Therefore, regular monitoring of solar EUV emission is of great interest. However, because they are absorbed in the atmosphere, these wavelengths are not observable from the ground, and regular monitoring must be performed by proxy for periods without satellite measurements.

One EUV activity proxy utilized by the solar and terrestrial community is the F_10.7 index, the 10.7 cm (2.8 GHz) solar microwave spectral flux density. Originally observed by Covington (1947), F_10.7 correlates well with solar EUV over month (Chen et al. 2012), year (Balan et al. 1993; Lean et al. 2011; Girazian & Withers 2015; Huang et al. 2016), and solar cycle timescales (Covington 1969; Tobiska 1991; Bouwer 1992; Chen et al. 2011). F_10.7 has been a particularly popular observational input to models of the terrestrial upper atmosphere (Bhatnagar & Mitra 1966; Jacchia 1971; Hedin et al. 1977; Ridley et al. 2006; Bowman et al. 2008; Bilitza et al. 2014) due to its long history and consistent quality (Tapping 2013) and remains extensively utilized today even when direct EUV observations are available (Tobiska et al. 2008; Bilitza et al. 2017). However, due to observed short-term activity-dependent deviations in F_10.7 that are not reflected in EUV observations, the microwave observation is typically time-averaged before being used as a model input (e.g., Hinteregger 1981). One common method is to construct a new smoothed time series

$$\begin{eqnarray}&&{F}_{\mathrm{ave}}=\left({F}_{10.7}+{F}_{81}\right)/2\end{eqnarray} \tag{ 1 }$$

where F₈₁ is the 81 day centered running average of F_10.7 (Richards et al. 1994).

One reason for the discrepancy between EUV and F_10.7 is that while solar EUV emission is generated by collisionally excited atomic emission (with most lines originating in the optically thin corona), there are three distinct emission sources from the non-flaring Sun observed at 10.7 cm: optically thick (i.e., blackbody) bremsstrahlung emission from the chromosphere (Tapping 1987), optically thin bremsstrahlung emission from the transition region and corona (Landi & Chiuderi Drago 2003), and optically thick gyroresonance emission from the corona in the cores of active regions (White & Kundu 1997). While the chromospheric contribution is thought to be well understood as relating to the solar minimum F_10.7 level, resolving the relative significance of the bremsstrahlung and gyroresonance components has remained elusive. The lack of resolution is due to conflicting results, with studies relying on imaging analyses typically concluding that bremsstrahlung is the dominant coronal component (Felli et al. 1981; Tapping & DeTracey 1990; Tapping et al. 2003; Schonfeld et al. 2015), while studies utilizing time series analysis conclude that gyroresonance is the dominant mechanism (Schmahl & Kundu 1995, 1998; Dudok de Wit et al. 2014). Due to the physical processes responsible for the emission, only the bremsstrahlung component of F_10.7 is related to the EUV emission and directly relevant as an EUV proxy.

Modern solar EUV observations allow the decomposition of F_10.7 into its components based on the physics of the bremsstrahlung and gyroresonance emission mechanisms. Coronal EUV and microwave bremsstrahlung emission are related to the differential emission measure (DEM; Craig & Brown 1976), the plasma density squared integrated over the volume of the optically thin emitting medium as a function of temperature. By determining the DEM using EUV observations, it is possible to calculate the optically thin coronal bremsstrahlung component of F_10.7 and, with well-constrained assumptions about the chromospheric contribution, predict the gyroresonance component.

In Schonfeld et al. (2017), hereafter Paper I, we used the consistent EUV data set provided by the Multiple Extreme ultraviolet Grating Spectrographs (MEGS-A) in the EUV Variability Experiment (EVE) instrument suite on board the Solar Dynamics Observatory (SDO) to compute a four-year time series of full-disk coronal DEMs. Here, we utilize these DEMs to determine the relative contributions of bremsstrahlung and gyroresonance emission in F_10.7 during the same period and investigate the implications of these contributions on the use of F_10.7 as an EUV proxy. We describe the data and processing used to isolate the relevant time series in Section 2. In Section 3, we describe the procedure used to determine the F_10.7 emission components and compare these to the F_10.7 predictions from photospheric magnetic fields presented in Henney et al. (2012). We discuss the implications of these findings when using F_10.7 as an EUV proxy in Section 4 and conclude with comments on the continued use of F_10.7 in Section 5.

This investigation relies on a combination of ground and spacecraft data, and careful attention is paid to ensure data consistency and temporal alignment. The data cover just over four years (2010 April 30 to 2014 May 26, described in Section 2.3) of the rising phase of solar cycle 24 with a consistent observation time of 2000 UT (described in Section 2.1). The rare data gaps in the series⁵ are filled with a spline interpolation to ensure consistent sampling.

2.1. The F_10.7 Index

2.2. Mg ii Core-to-wing Activity Index

2.3. DEMs Calculated from EVE MEGS-A Spectra

2.4. F_10.7 Inferred from the Photospheric Magnetic Field

Essential to separating the F_10.7 emission components is the (to first order) additive nature of the optically thick chromospheric emission (F_chromo), the optically thin coronal bremsstrahlung (F_brem), and the optically thick coronal gyroresonance (F_gyro):

$$\begin{eqnarray}&&{F}_{10.7}={F}_{\mathrm{chromo}}+{F}_{\mathrm{brem}}+{F}_{\mathrm{gyro}}.\end{eqnarray} \tag{ 2 }$$

The following analysis also relies on the relationship between EUV observations and optically thin coronal microwave bremsstrahlung emission. Their mutual dependence on the coronal DEM and the validated ability to compute the DEM from a set of EUV observations (Guennou et al. 2012a, 2012b; Testa et al. 2012) allow the independent determination of F_brem when a suitable set of EUV observations exists. Then, a simple assumption about either F_chromo or F_gyro allows for a complete decomposition of F_10.7 into its source constituents. The limitations of this methodology are explored in Section 3.3.

3.1. Calculating the Bremsstrahlung Component

The optically thin coronal bremsstrahlung emission (with units erg cm⁻² s⁻¹ Hz⁻¹) is related to the DEM by

$$\begin{eqnarray}\begin{array}{rcl}{f}_{\nu } & = & 9.78\times {10}^{-3}\displaystyle \frac{2{k}_{{\rm{B}}}}{{c}^{2}}\left(1+4\displaystyle \frac{{n}_{\mathrm{He}}}{{n}_{{\rm{H}}}}\right)\\ & & \times \,\iint {T}^{-0.5}\mathrm{DEM}(T)G(T)\ {dT}\ d{\rm{\Omega }}\end{array}\end{eqnarray} \tag{ 3 }$$

where k_B = 1.38 × 10⁻¹⁶ g cm² s⁻² K⁻¹ is Boltzmann's constant, c = 3 × 10¹⁰ cm s⁻¹ is the speed of light, n_He/n_H = 0.085 (Asplund et al. 2009) is the density ratio of helium to hydrogen in the emitting medium, T is the temperature in K, ${\rm{G}}(T)=24.5+\mathrm{ln}\left(T/\nu \right)$ is the Gaunt factor where ν is the frequency in Hz, and dΩ is the solid angle of the source (Dulk 1985). The DEM(T) (with units cm⁻⁵ K⁻¹) is

$$\begin{eqnarray}&&\mathrm{DEM}(T)=\mathop{\int }\limits_{L}\displaystyle \frac{d}{{dT}}\left({n}_{{\rm{e}}}{n}_{{\rm{H}}}\right)d{\rm{l}}\end{eqnarray} \tag{ 4 }$$

where L is the optically thin path length of the emitting medium and n_e and n_H are the electron and hydrogen number densities, respectively (Craig & Brown 1976). In the case of irradiance observations, Equation (3) can be rewritten without the solid angle integral if the DEM is given in the volume integrated form computed in Paper I (cm⁻³ K⁻¹):

$$\begin{eqnarray}&&\mathrm{DEM}(T)=\mathop{\int }\limits_{{\rm{V}}}\displaystyle \frac{d}{{dT}}\left({n}_{{\rm{e}}}{n}_{{\rm{H}}}\right)d{\rm{V}}.\end{eqnarray} \tag{ 5 }$$

We calculate the daily optically thin bremsstrahlung emission (F_brem) for F_10.7 (at 2.8 GHz) along with the assumed 15% error from the DEMs calculated with MEGS-A spectral lines in Paper I.

F_brem plus a constant chromospheric offset (F_chromo, calculated in Section 3.2) is plotted in red in Figure 1 and compared with the F_10.7 in black. While the bremsstrahlung component accounts for much of the F_10.7 variability during the solar minimum period identified in Paper I before 2011 February, there is much more variability during solar maximum that cannot be attributed to bremsstrahlung emission. In other words, the F_10.7 series varies significantly more than the EUV during solar maximum as has previously been noted (by e.g., Anderson 1964). This has been the primary motivation for using F_ave instead of F_10.7 (Jacchia 1964).

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F_brem is plotted as the red points and blue crosses versus F_10.7 in Figure 2. It is immediately obvious that this relationship is well constrained and linear at low activity levels but becomes more variable and nonlinear at high activity levels. We fit this bremsstrahlung distribution with a continuously differentiable piecewise function that is linear at low activity and a power function at high activity such that

$$\begin{eqnarray}{F}_{\mathrm{fit}}=\left\{\begin{array}{ll}a+{{bF}}_{10.7}, & \mathrm{for}\ {F}_{10.7}\lt c\\ d{\left({F}_{10.7}-e\right)}^{f}, & \mathrm{for}\ {F}_{10.7}\geqslant c\end{array}\right.\end{eqnarray} \tag{ 6 }$$

is the best-fit bremsstrahlung component of F_10.7. The best least-squares solution has a = −25.1 ± 1.1, b = 0.592 ± 0.013, c ≈ 96, d = 13.9 ± 1.2, e ≈ 80, and f = 0.298 ± 0.019 and is found using the IDL MPFIT package of Markwardt (2009). Requiring continuity and smoothness (continuous first derivative) in this functional form provides two constraints to the fit and the function has been arranged so that c and e are uniquely determined by the other best-fit parameters and do not have derived errors. In Figure 2, the red points are fit by the linear component, the blue Xs are fit by the power component, and the solid black line indicates the best-fit function with 1σ errors. F_brem is very different from both F_ave (indicated by the gray crosses that show 5 sfu binned averages with 1σ standard deviations) and the canonically assumed linear EUV–F_10.7 relationship (dotted gray line).

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3.1.1. Bremsstrahlung and Photospheric Magnetic Fields

The procedure of Henney et al. (2012) involved parameterizing F_10.7 using observations of the photospheric magnetic field magnitude. This was done using two components, a "plage" component with fields between 25 and 150 G, and an "active region" component with fields greater than 150 G. The moderate magnetic field strength of the "plage" magnetic fields is associated with increased coronal plasma density (e.g., Kelch & Linsky 1978) and it is therefore natural to expect correlation with F_brem. This relationship is plotted in Figure 3 and shows a generally linear correlation with a Pearson coefficient of 0.92 and a slope near one, but with significantly more F_brem than F_10.7 plage-field component. This is due to the assumption in Henney et al. (2012) that attributed all solar minimum F_10.7 to a constant (presumably chromspheric) component whereas we find a solar minimum coronal bremsstrahlung contribution (details in Section 3.2). Correcting for this difference in the solar minimum level yields much better agreement, indicated by the solid black line (compared to the dotted line without this correction) that represents equality between F_brem and the F_10.7 plage-field component.

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This agreement suggests that the method of Henney et al. (2012) naturally identifies F_brem based on the observed photospheric magnetic field strength. This is particularly valuable because of the demonstrated ability to evolve ADAPT photospheric magnetic field maps to predict F_10.7 (Henney et al. 2012) and EUV irradiance (Henney et al. 2015). The correlation in Figure 3 indicates it is possible to approximate F_brem from photospheric magnetic field measurements even when EUV observations are not available.

3.2. Utilizing the Low-activity Linearity

There is significant value in examining in detail the linear component of the bremsstrahlung–F_10.7 relationship plotted again as red points in Figure 4. First, by extrapolating this linear trend back to the 66.3 ± 1.2 sfu F_10.7 solar minimum level, we find that 14.2 ± 2.1 sfu of it is due to coronal bremsstrahlung emission, implying 52.1 ± 2.4 sfu is a constant chromospheric component. This is important because time series analyses typically consider only the rotationally variable component of F_10.7 (Schmahl & Kundu 1995, 1998; Dudok de Wit et al. 2014), but this necessarily excludes the solar minimum bremsstrahlung component that indicates significant coronal EUV emission, even at solar minimum. In addition, the slope of the relationship of this linear regime is informative for the nature of F_10.7 emission during the solar minimum period. If bremsstrahlung emission accounted for all of the variation in F_10.7 observed during this period, the slope of this relationship would be unity. The fact that it is less than one has three potential explanations: gyroresonance emission contributed a significant fraction of F_10.7 even during the low-activity period, the iron abundance used to calculate the DEMs in Paper I was too large, or the contribution from the chromosphere is also activity dependent. Each of these explanations are explored in the following subsections.

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3.2.1. Magnetic Field Dependence of Gyroresonance Emission

Due to the nature of the gyroresonance mechanism, coronal observations at a fixed frequency only detect gyroresonance emission from discrete, narrow layers in the atmosphere. In particular, emission is only observed at harmonics of the gyrofrequency (in MHz) given by:

$$\begin{eqnarray}&&{\nu }_{B}=2.80B\end{eqnarray} \tag{ 7 }$$

where B is the total magnetic field strength in G (White & Kundu 1997). The fundamental emission at a gyrofrequency of 2.8 GHz (F_10.7) is produced in magnetic fields of 1000 G that only exist at altitudes below the optically thick floor. Consequently, emission is typically observed from the second, third and fourth harmonics which, for 2.8 GHz observations, originate in magnetic field layers with B = 500, 333, and 250 G, respectively (White 2005). In addition, due to the decrease of the coronal magnetic field with altitude (Kuridze et al. 2019), it is reasonable to expect photospheric magnetic fields of at least 500 G in order to yield appreciable coronal gyroresonance emission at 2.8 GHz.

Figure 5 shows the area weighted sum of photospheric magnetic fields greater than 500 G, which we interpret as the total magnetic field capable of producing gyroresonance emission, plotted against F_10.7. The black crosses indicate the average over 5 sfu bins with the vertical error bars representing the 1σ standard deviation in the measured values. From this we can see a significant increase in the 500 G magnetic field sum during the power-fit period and that the average during the linear-fit regime is within a standard deviation of zero. This suggests that while isolated low activity days may have gyroresonance emission, the majority of the linear-fit period should have essentially no gyroresonance emission component in F_10.7. This is consistent with an intuitive understanding that during solar minimum there are relatively few active regions with intense magnetic fields, and long periods with no visible active regions at all.

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3.2.2. The Effect of Coronal Iron Abundance

Another possible explanation for the non-unity slope in Figure 4 is a true iron abundance significantly different from N_Fe/N_H = 1.26 × 10⁻⁴ used in Paper I, an enhancement by about a factor of four above photospheric values (Feldman 1992). This is a commonly used value for the "coronal" iron abundance (e.g., Kashyap & Drake 1998; White 1999; Landi & Chiuderi Drago 2003, 2008; Warren et al. 2012; Schonfeld et al. 2015), but other work has suggested the coronal enhancement may be less, as low as a factor of two (e.g., Zhang et al. 2001; Warren & Brooks 2009; Del Zanna 2013; Guennou et al. 2013) or even no enhancement in coronal holes (Chiuderi Drago et al. 1999). The DEMs in Paper I were calculated using only iron emission lines and are thus inversely related to the coronal iron abundance (see Paper I Section 3.3 for more details). This means the calculated bremsstrahlung emission which is related to the total plasma density (primarily hydrogen) also scales inversely with the iron abundance. It is therefore possible to "recalculate" the bremsstrahlung prediction with different coronal iron abundances by applying a simple multiplicative scaling.

Correcting the slope in Figure 4 to unity by scaling F_brem corresponds to a coronal iron abundance of N_Fe/N_H = 7.45 × 10⁻⁵, a factor of 2.3 enhancement above the photosphere. In addition to modifying the slope of the bremsstrahlung-F_10.7 relationship, this also changes the expected solar minimum bremsstrahlung contribution to 24.0 ± 3.6 sfu, suggesting only 42.3 ± 3.8 sfu of chromospheric emission. Considering Equation (2), we use F_10.7 and the known bremsstrahlung and chromosphere components to calculate the expected gyroresonance emission. F_10.7 and its three components are plotted in Figure 6 for the standard coronal abundance (left panel) and the modified coronal abundance (right panel). These figures demonstrate that not only does decreasing the iron abundance lead to significantly more bremsstrahlung emission as expected, it also suggests significantly more gyroresonance emission due to reduced chromospheric emission.

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This greater-than-10-sfu minimum gyroresonance contribution is inconsistent with our earlier analysis on a number of levels. First, it is at odds with the physical nature of gyroresonance emission, which is concentrated in active regions (Schonfeld et al. 2015) that are not consistently present on the visible solar disk during solar minimum. It is also in conflict with the suggestion from Figure 5 that there are insufficient strong magnetic fields to produce significant gyroresonance emission during the low-activity period. Finally, the assumption behind forcing the linear-fit component of the bremsstrahlung series into agreement with F_10.7 was that there should be no gyroresonance emission during this period, which is wholly opposite to the effect created by this correction. The conflict of this significant redistribution of the emission components with these other observable characteristics suggests that decreasing the coronal iron abundance to force a unity bremsstrahlung-F_10.7 relationship during solar minimum is inappropriate.

3.2.3. The Implications of Chromospheric Variability

The final explanation of the less than unity slope in Figure 4 is the variability of the chromosphere. In all previous analyses, we have assumed that the chromosphere is constant, but this is obviously suspect since the chromosphere is observed to be highly dynamic (Hall 2008, and references therein) and the source of the Mg ii 280 nm doublet that is itself used as a solar activity proxy (Heath & Schlesinger 1986). We can use the linear regime of Figure 4 assuming only contributions from the chromosphere and coronal bremsstrahlung to construct an estimated variable chromosphere by finding the best-fit linear correlation between F_chromo = F_10.7–F_brem and the Mg ii index. This is shown in Figure 7, which reveals a roughly linear relationship with Pearson correlation coefficient r = 0.55 in the linear bremsstrahlung regime. Because this is a small correction relative to the bremsstrahlung variability, this relatively low correlation should be sufficiently accurate given the 15% errors inherited from the DEM calculation. Using the observed Mg ii during these four years, this correlation allows us to estimate the contribution from a variable chromosphere even during solar maximum when F_gyro is significant.

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The F_10.7 time series with components determined using this best-fit variable chromosphere is shown in Figure 8. Including this variable chromosphere increases its contribution compared to the assumed constant chromosphere, leading to a decrease in the calculated gyroresonance component. During solar maximum, this accentuates the effect of individual solar rotations, with these series suggesting that many solar rotations have no gyroresonance during their local minima. This variable chromosphere also reduces the gyroresonance contribution during the solar minimum period (as identified in Paper I before 2011 February 8 when solar activity abruptly turns on) to a level that is consistent with no gyroresonance within the uncertainties. This is by construction, since we assumed no gyroresonance in the linear regime when calculating the variable chromosphere.

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This variable chromospheric correction also brings the calculated gyroresonance component into better agreement with a Very Large Array (VLA) full-disk image at 2.782 GHz from 2011 December 9 (Schonfeld et al. 2015). That analysis found 6.2 ± 0.3 sfu of gyroresonance emission and is delineated as the maroon cross in Figure 8. When using a variable chromosphere, this disk-integrated time series analysis suggests 16.2 ± 9.9 sfu of gyroresonance, compared to 34.9 ± 8.3 sfu with a constant chromosphere. The reduced gyroresonance calculated with the variable chromosphere is consistent (given the uncertainties) with the previous imaging analysis.

These results reconcile the apparent contradiction between previous analyses that disagreed about the relative contribution of bremsstrahlung and gyroresonance emission in F_10.7. It suggests that those studies that attribute the majority of coronal F_10.7 to bremsstrahlung (Felli et al. 1981; Tapping & DeTracey 1990; Tapping et al. 2003) may be correct during all but the most active periods. Furthermore, the studies that suggest gyroresonance dominates the F_10.7 variability (Schmahl & Kundu 1995, 1998; Dudok de Wit et al. 201-) may also be correct, particularly during active periods when the variation over a single rotation due to gyroresonance emission can be greater than the total bremsstrahlung. The cause of these previous disagreements is the low-level background coronal bremsstrahlung, which persists throughout the solar cycle. This contribution is apparent in images but was subtracted during previous time series analyses of F_10.7 variability.

3.3. Complicating Details of Optical Depth

Numerous studies (e.g., Tapping 1987; Tobiska 1991; Balan et al. 1993; Tobiska 2001; Chen et al. 2012; Bruevich et al. 2014; Huang et al. 2016) have previously identified the imperfect relationship between EUV and F_10.7, and corrective strategies (such as the utilization of F_ave) have been developed to adapt F_10.7 for use as an input to ionospheric and thermospheric models. The most direct implementations correlate F_10.7 with observable atmospheric parameters, such as thermospheric temperature (Jacchia 1970) and density (Bowman et al. 2008), without directly considering details associated with atmospheric absorption. Models interested in capturing the atmospheric response to solar spectral variability instead parameterize EUV emissions and then simulate the energy deposition into the atmosphere based on its absorption profile and physical state.

One such example is the EUV flux model for aeronomic calculations, EUVAC (Richards et al. 1994). The EUVAC model creates a coarse spectrum covering 5–105 nm in 37 partially overlapping spectral bands (Solomon & Qian 2005) based on F_ave observations by linearly interpolating between two spectra observed on days with significantly different activity levels. In this way, models like EUVAC use a single frequency F_10.7 measurement to parameterize the entire EUV spectrum.

The EUVAC model assumes that the observed variability in F_10.7 reflects variability in coronal EUV emission. The decomposition of F_10.7 into its various components allows us to test that assumption. Using F_brem and F_gyro from Figure 8, we can examine the fraction of coronal F_10.7 (F_brem+F_gyro) that is attributable to F_brem as plotted in Figure 9. This illustrates the fact that in the linear-fit regime, the bremsstrahlung emission accounts for nearly all of the coronal F_10.7. For the power fit, this fraction decreases approximately linearly with increasing activity, dropping below half at the maximum activity observed in this study. The decreasing fraction is due to the highly variable contribution from gyroresonance emission, which necessitates the use of F_ave in model applications. However, the deviation in the bremsstrahlung fraction at a given activity level is typically ±7%, significantly more constrained than the overall variability due to gyroresonance. This suggests the potential for significant improvements when using F_fit in place of F_ave.

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The correlation of the MEGS-A spectra with multiple EUV proxies is plotted as a function of wavelength in Figure 10. Across nearly the entire MEGS-A spectral range, F_ave has the worst correlation with the EUV observations compared with the other proxies examined in this paper. However, in an absolute sense F_ave is still an effective proxy with a Pearson linear correlation coefficient typically greater than 0.85. All of the other tested proxies, F_fit, the Mg ii index, and the plage component of the photospheric magnetic field proxy from Henney et al. (2012), have correlations greater than 0.9 in most spectral bins. Interestingly, the two bins with the worst correlations with F_ave (centered at 175 and 305 Å) are also the bins containing the strongest emission lines, a complex of coronal iron lines and He ii 304 Å, respectively. These two bins have the smallest relative variation (between minimum and maximum) in the EVE MEGS-A spectra which may be responsible for their slightly reduced linear correlations. The other proxies improve on F_ave significantly in the He ii 304 Å bin, the single brightest band in this spectral range containing ≈15%–30% of the irradiance observed by MEGS-A, depending on the activity level.

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Figure 10 demonstrates that F_fit generally correlates with the observed EUV better than F_ave and as well as Mg ii and the Henney et al. (2012) index while requiring only a single F_10.7 measurement. This means it should be possible to improve current atmospheric models and EUV spectral parameterizations simply by using the best-fit bremsstrahlung component of F_10.7 instead of F_ave. F_fit has the improved correlation of Mg ii while maintaining the long observational history of F_10.7 and without the risk associated with needing to observe from space. It has the further benefit that it does not require foreknowledge of the future 40 days of F_10.7, which is required to compute F_ave, making it potentially even more effective in an operational application. Though the fit was performed using a broad range of solar conditions near minimum to solar maximum, one drawback of F_fit is that it is generated with data from a single partial (and fairly weak, Komitov & Kaftan 2013; Huang et al. 2016) solar cycle and the exact fit parameters may change slightly between solar cycles. However, the efficacy of this fit can be evaluated using current models, and it was performed using a broad range of solar conditions from near minimum to solar maximum.

Using four years of DEM results from Paper I, we investigated the physical emission components of the solar F_10.7 index. This analysis assumed F_10.7 is a combination of three independent emission components: optically thick bremsstrahlung from the chromosphere, optically thin bremsstrahlung from the corona, and optically thick gyroresonance from the corona. From the DEMs computed in Paper I, we directly calculated the coronal bremsstrahlung emission and found that it accounts for 14.2 ± 2.1 sfu (∼20%) of the solar minimum F_10.7 and more than 40% of the total during more active periods.

We also fit this relationship with a continuously differentiable piecewise function that is linear at low activity levels and a power function at high activity levels. The variable chromosphere was determined by correlating the Mg ii activity proxy with the non-bremsstrahlung F_10.7 during the linear, low-activity component of the fit. The remaining F_10.7 is attributed to gyroresonance emission which accounts for almost none of the coronal F_10.7 in the linear-fit regime and up to more than half during the most active periods of the power-fit regime. This analysis explains the historic disagreement in the literature about the relative contribution of bremsstrahlung and gyroresonance emission in F_10.7. While bremsstrahlung emission typically contributes the majority of the coronal emission, gyroresonance tends to dominate the rotational modulation due to the discrete nature of active regions.

The piecewise fit to the bremsstrahlung emission as a function of F_10.7 can be used to define a new activity proxy. We find that this achieves a correlation with observed EUV that is significantly better than F_ave and is comparable with using Mg ii or a photospheric magnetic field index. In addition to its improved correlation, this fit proxy has two distinct advantages over the traditional F_10.7 averaging used to characterize solar EUV variability. First, using the bremsstrahlung trend requires only a single daily F_10.7 observation. This is preferable if F_10.7 is used in an operational setting where EUV is monitored daily and in real time because it does not require 40 day foreknowledge like the averaging method. Second, the best-fit trend line provides an uncertainty in the bremsstrahlung prediction. This can be translated into a characteristic range of possible EUV irradiance which allows for the uncertainty in the solar input to be properly accounted for in models.

It is possible that the exact parameterization of the bremsstrahlung component identified here is not the true relationship since it encompasses only the rising phase of a single solar cycle. We might expect a slightly different relationship during the decline of a solar cycle or even minor changes in this relationship between cycles. In addition, the analysis presented does not contain the contributions of a true solar minimum, which would greatly help anchor the linear regime and the calculation of the chromospheric contribution. S. M. White et al. (2019, in preparation) will analyze data from a single EVE sounding rocket calibration flight during solar minimum, which provides an additional constraint on the true solar minimum characteristics of this emission.

There has been considerable concern in recent years that F_10.7 is insufficient for modern applications (Chen et al. 2011) and should be replaced by other EUV proxies (Tobiska et al. 2008; Maruyama 2010, 2011; Dudok De Wit & Bruinsma 2011), potentially including microwave observations at 30 cm (1 GHz, Dudok de Wit et al. 2014). Our analysis suggests there is still significant value in using F_10.7 when the physical characteristics of its emission components are considered and the bremsstrahlung component is isolated. This is particularly true in light of its long legacy and familiarity within the community. Even so, this F_fit parameterization needs to be tested against observed ionosphere/thermosphere variability to determine if it provides a similar improvement as suggested by its correlation with EUV. In addition, there are situations (e.g., higher cadence input or specific spectral bands that are better modeled with another proxy) that could motivate moving away from F_10.7 even when it remains effective in its current usage.

Data supplied courtesy of the SDO/EVE consortium. SDO is the first mission to be launched for NASA's Living With a Star (LWS) Program. The F_10.7 data are provided by the National Research Council of Canada, with the participation of Natural Resources Canada, and support from the Canadian Space Agency. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA), and the University of Cambridge (UK). This research has been made possible with funding from AFOSR LRIR 14RV14COR and 17RVCOR416, FA9550-15-1-0014, NSF Career Award #1255024, PAARE NSF:0849986. S.J.S.'s research was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Universities Space Research Association under contract with NASA.