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Solar Transition-Region Lines Observed by the Interface Region Imaging Spectrograph: Diagnostics for the O IV and Si IV Lines

The formation of the transition-region O IV and Si IV lines observable by the Interface Region Imaging Spectrograph (IRIS) is investigated for both Maxwellian and non-Maxellian conditions characterized by a kappa-distribution exhibiting a high-energy tail. The \ion{Si}{4} lines are formed at lower temperatures than the O IV lines for all kappa. In non-Maxwellian situations with lower kappa, the contribution functions are shifted to lower temperatures. Combined with the slope of the differential emission measure, it is possible for the Si IV lines to be formed at very different regions of solar transition region than the O IV lines; possibly close to solar chromosphere. Such situations might be discernible by IRIS. It is found that photoexcitation can be important for the Si IV lines, but is negligible for the O IV lines. The usefulness of the O IV ratios for density diagnostics independently of kappa is investigated and it is found that the O IV 1404.78A /1399.77A ratio provides a good density diagnostics except for very low T combined with extreme non-Maxwellian situations.


Introduction
The solar transition-region (hereafter, TR), is the plasma with temperatures between chromospheric and coronal ones. While the transition-region emission can originate in closed magnetic loops that do not reach the corona, there are large regions of the strong magnetic field, such as plages, where the field lines can be "open" and reach into the corona.
Such regions will be characterized by strong gradients of temperature and density. Under these conditions, the distribution of electron energies can depart from the Maxwellian one and become non-Maxwellian (e.g., Roussel-Dupre 1980;Shoub 1983;Ljepojevic & MacNiece 1988). Some indications of the presence of non-Maxwellian distributions were found from Si III transition-region spectra (Dufton et al. 1984;Keenan et al. 1989;Pinfield et al. 1999), while other authors (e.g., Doschek 1997) did not find any. Dzifčáková & Kulinová (2011) used the SUMER Si III line intensities reported by Pinfield et al. (1999) and performed diagnostics of temperature and density. It was found that different ratios do not yield consistent results if a Maxwellian distribution is assumed.
Large discrepancies between theory and observations were found for active region spectra.
The authors also performed the diagnostics under the assumption of κ-distributions (e.g., Vasyliunas 1968;Owocki & Scudder 1983;Livadiots & McComas 2009). Then, the consistency in terms of temperature and density was found only if the additional effect of photoexcitation by the photospheric radiation was included. The authors diagnosed κ = 7 for the active region spectra, and κ = 10−11 for the quiet-Sun, meaning that the active region TR is more non-Maxwellian than the quiet-Sun. Furthermore, these diagnostics were also shown to be valid for multithermal plasma characterized by a differential emission measure (DEM).
The Interface Region Imaging Spectrograph (IRIS) is a new, powerful instrument dedicated to the observations of the solar chromosphere and transition region. Its second far-ultraviolet channel (1390-1406Å) contains several lines belonging to Si IV, O IV and S IV (Table 1). We note that while direct diagnostics of the electron distribution function are not expected because of the similarity of the transitions observed and wavelength constraints of the instrument, the non-Maxwellian distributions can still have large effects on the formation of these lines. In this Letter, we investigate the formation of the transition region lines under non-Maxwellian conditions characterized by κ-distributions. We also investigate the effects of photoexcitation on line formation and the possible influence of non-Maxwellian effects on the density diagnostics known for Maxwellian distribution (e.g., Doschek 1984). Finally, we are not concerned in this paper with the formation of lines belonging to low ionization stages, such as O II, C II or others, since these may be heavily influenced by opacity effects in dense plasmas and no longer formed under optically thin or non-Maxwellian conditions. We also note that the response of the IRIS TR lines to non-equilibrium ionization already has been investigated by Doyle et al. (2013) and Olluri et al. (2013).

Method
The κ-distributions are defined as a two-parametric distribution with parameters T and κ (e.g., Owocki & Scudder 1983;Livadiots & McComas 2009) where k B = 1.38 ×10 −16 ergs cm −1 is the Boltzmann constant and A κ = Γ(κ + 1)/ Γ(κ − 0.5)(κ − 1.5) 3/2 is the normalization constant. We note that κ ∈ (3/2, +∞) and T is defined in terms of mean energy E as T = 2 E /3k B . Maxwellian distribution is recovered for κ → +∞. For finite κ, the distribution has increased number of both low-energy and high-energy electrons compared to Maxwellian distribution and exhibits a high-energy power-law tail and a near-Maxwellian core with temperature T core = T (κ−3/2)/κ (Oka et al. 2013). The differences with respect to Maxwellian increase with decreasing κ (see, e.g., Fig.   1 in . The intensity I ji of an optically thin emission line with a wavelength λ ji can be written as (c.f., Phillips et al. 2008) where n e is the electron density, A X is the relative abundance, DEM(T ) is the differential emission measure along the line of sight l, defined as DEM(T ) = n 2 e dl/dT . The G ji (T, n e , κ) is the line contribution function, which can be expressed as where hc/λ ji is the photon energy, A ji is the Einstein coefficient for spontaneous emission, n H is the hydrogen density, n +k X /n X is the relative abundance of the ion +k, and n +k X,i /n +k X is the fraction of the ion +k with the electron in the excited upper level i. The We calculated the distribution-averaged collision strengths Υ ji (T, κ) by integration of the collision strengths Ω ji (non-dimensionalised excitation/de-excitation cross-sections) over the distribution function (Seaton 1953) The Ω ji used here were calculated within the APAP network 1 by Liang et al. (2009) and Liang et al. (2012) for Si IV and O IV, respectively. These represent the state-of-art atomic data and will be implemented in the upcoming CHIANTI v8. The numerical integration of the collision strengths for these ions was performed using a method similar to Bryans (2006).
We compared the Υ ji (T, κ) obtained, shown in Fig. 1 bottom, with the ones calculated by the approximative method of Dzifčáková & Mason (2008). Excellent agreement within a few per cent was found. For comparison, previous atomic data calculations of Sampson et al. (1990), Martin et al. (1995), and Aggarwal et al. (2008), available within CHIANTI v7.1 (Dere et al. 1997;Landi et al. 2013), are also plotted in Fig. 1 Our G ji (T, n e , κ) for O IV and Si IV using Υ ji (T, κ) from the original collision strengths are subsequently calculated using our own modification of the CHIANTI v7.1 software. For S IV, we utilize the atomic data of Kelleher et al. (1999), Tayal (2000), and Hibbert (2002) available within CHIANTI v7.1 and the method of Dzifčáková & Mason (2008), since no collision strength data are available. The abundances are taken from Asplund et al. (2009), i.e., are assumed to be photospheric. We also assume a contribution from photoexcitation by a Sun-like black-body, characterized by T eff = 6000 K and R/R ⊙ = 1.

Contribution functions for κ-distributions
The G ji (T, n e , κ) of the O IV 1401.16Å and Si IV 1402.77Å are shown in Fig. 2, top. We chose these two lines since they are close in wavelength and belong to the strongest TR lines observed by IRIS. The contribution functions are calculated either under the assumption of constant pressure P e = 3×10 15 Kcm −3 , or constant density of log(n e /cm −3 ) = 10. The first assumption is appropriate for a locally "open" magnetic structure, such as a TR portion of a coronal loop footpoint, while the second one is neccessary for investigating the density sensitivity (Sect. 3.3). Note that the same value of P e was used to derive the DEM files within CHIANTI (Dere et al. 1997).
With decreasing κ, i.e., increasing departure from the Maxwellian distribution, the contribution functions for both lines becomes broader in temperature and their maxima move towards lower T . This is caused chiefly by the changes in the relative ion abundances ( Fig. 1, top). However, temperatures corresponding to the G(T, n e , κ) peak are not as low as the temperatures at which the O IV and Si IV ions have maximum abundance. This is caused by the level population, which increases with T in the temperature interval where the ion is formed. For log(n e /cm −3 ) = 10, the O IV 1401.16Å line has peak formation temperature at log(T /K) ≈ 5.15 for the Maxwellian distribution, and at ≈ 4.8 for κ = 2.
For Si IV, these values are ≈ 4.9 and 4.3, respectively. We note that the peak formation temperature for the Maxwellian distribution is significantly higher than the one given by Doyle et al. (2013, Fig. 1 therein). The peak temperatures obtained here for both the Si IV and O IV are largely independent of n e . However, the contribution function does change with n e (Sect. 3.3). For this reason, the peak temperatures are located at slightly higher T if constant pressure is assumed (Fig. 2, top).
We investigated the O IV line ratios for possible diagnostics of κ. Since the lines are formed from similar energy levels (

Effect of DEM on line formation
The shifts of the peak temperatures of the contribution function with κ is potentially important, given the slope of the DEM at TR temperatures. To illustrate the effect of DEM on the contribution function, we chose the "Active region" (AR) and "Quiet Sun" (QS) DEMs available within CHIANTI v7.1, based on the data of Vernazza & Reeves (1978).
The AR DEM has a much steeper transition region than the QS DEM. We note that the spectra used to produce these DEMs are averages over many exposures and thus represent average physical conditions in the solar atmosphere over a selected type of structure on the solar surface; e.g., a quiet-Sun or an active region. This means that such DEMs may not be representative of any particular, sub-arcsecond feature observed by IRIS. Moreover, the DEMs were derived under the assumption of a Maxwellian distribution, so that using them in conjunction with finite κ is not self-consistent. Nevertheless, we use these DEMs to illustrate the general effect of the DEM slope on the formation of the IRIS TR lines. We note that the true DEMs for κ-distributions may differ mainly for very low temperatures due to the behaviour of G(T, n e , κ) with κ described in Sect. 3.1. However, evaluating the DEMs for κ-distributions is beyond the scope of this paper.
The results are shown in Fig. 2 middle and bottom. In this figure, the contribution functions are also multiplied by the dT = T d(logT )/log(e) factor, so that the intervals of log(T /K) which contribute most to the total intensity can be immediately discerned. It is seen that for κ = 2-7 and the QS DEM, the Si IV 1402.77Å line is dominantly formed in regions with very low temperature: log(T /K) → 4. The situation is even more pronounced for the AR DEM, where the line is formed at such low temperature even for κ = 10. The situation is different for the O IV 1401.16Å line, which is formed at very low T only for κ 3 for QS DEM and κ 5 for AR DEM. For higher κ, the contribution function is slightly shifted to lower T and has a pronounced low-temperature wing.
The synthetic spectra arising in regions characterized by such DEMs are shown in Fig.   3. These spectra have been scaled by the IRIS effective area and the FWHM of IRIS lines have been artificially increased so that the line intensities for different κ are better visible.
We note here that the Si IV 1393.76Å /1402.77Å ratio is approximately constant and equal to 2 independently of κ or any other assumptions. This is in agreement with the SUMER results presented by Doschek & Mariska (2001). As shown in Fig. 3, the O IV lines are strongly sensitive to κ. For the AR DEM, they are very weak except for κ = 10. For the QS DEM, they are weaker compared to Maxwellian distribution, but still observable even for κ = 5.
We note that given the possible values of κ, which are ≈ 7 for the active region and ≈ 9-12 for quiet-Sun (Dzifčáková & Kulinová 2011), the Si IV and O IV lines may be formed under very different conditions, i.e., in different structures. These differences might be resolvable by IRIS. The effect of finite κ would be to move the Si IV emission into the low TR closer to the chromosphere, i.e., into lower-lying, more dense structures that are possibly more narrow due to constriction by the expanding magnetic flux-tubes. In this scenario, the O IV emission would lie higher up, in the region where log(T /K) ≈ 5. We finally note that the relative intensities might be modified by abundance effects, especially for Si IV, which is a low-FIP element.

Electron density diagnostics
It is known that the intercombination multiplet of O IV can be used for diagnostics of n e (e.g., Vernazza & Mason 1978;Feldman 1981;Nussbaumer & Storey 1982;Doschek 1984;Hayes & Shine 1987;Dwivedi & Gupta 1992;Keenan et al. 2009). Here, we investigate the effect of κ on the density diagnostics. To do that, we plot the n e −dependence of a chosen ratio of O IV lines observable by IRIS (Table 1) for the peak formation temperature and temperatures corresponding to the 1% of the contribution function peak. This gives the indication of the sensitivity of the given ratio to T (Fig. 4, top).
If the Maxwellian distribution is assumed, the O IV line ratios yield a good density diagnostics in the log(n e /cm −3 ) = 9−11 range (black lines in Fig. 4, top), with lines at different T producing variations of about ±0.2 in log(n e /cm −3 ). At even higher densities, the ratios reach a plateau and are unusable for log(n e /cm −3 ) > 11.5.
In principle, the density diagnostics can depend on κ, but the exact manner can be different for each ratio. The 1401.16Å /1404.78Å ratio is not recommended for density diagnostics, since it changes with κ (Fig. 4, top left). On the other hand, the 1404.78Å /1399.77Å ratio is only weakly dependent on κ for κ 5, yielding slightly lower n e . For the extreme non-Maxwellian situation, i.e., κ = 2, the ratio is useful only for temperatures close to or higher the peak formation temperature. For very low log(T /K) → 4, the density dependence is lost (Fig. 4, top right).
We note that the O IV 1404.78Å line is blended with the S IV 1404.81Å transition.
This blend can become important at higher densities, since the intensity of the O IV 1404.78Å line decreases with n e . The contribution of this blend can in principle be estimated using the neighboring S IV 1406.02Å line, since the ratio of these two S IV lines is insensitive to n e except for very high densities of log(n e /cm −3 ) 12 (Doschek 1984, Fig. for the Maxwellian distribution and 4.6 for κ = 2.

Photoexcitation
To quantify the effect of photoexcitation, we recalculated the contribution functions without it. It is found that the O IV lines are unaffected by photoexcitation, which contributes less than 0.1% to the O IV 1401.16Å line (Fig. 4, bottom).
The situation is different for the Si IV 1402.77Å line. Here, the effect of photoexcitation is dependent on the conditions under which the line is formed. For constant P e = 3 ×10 15 K cm −3 , photoexcitation contributes 2-7%. For constant density, the relative contribution depends on T , n e , and κ. In general, the relative contribution increases with decreasing T , κ, or n e (Fig. 4). It can be larger than 10% for log(n e /cm −3 ) = 10, and much larger still for even lower n e . We conclude that the effect of photoexcitation cannot be neglected for the Si IV lines, and suggest that a real radiation field should be used instead of a black-body spectrum as done here.