3 Spectral analysis of UV line emission

 

 

Table 1: Dates of the observations, emission lines, their wavelengths and formation temperatures, $T_{\rm f}$. Also listed are the types of regions in the fields of view the difference in ground and excited state energies, $\chi$, and a factor, $\alpha$, which is the ratio of the fractional change in brightness to the corresponding change in electron temperature. The $\alpha$ values for the optically thick Lyman lines were not computed and are not listed in the table.

Date	Line	Wavelength/Å	$T_{\rm f}$/K	Area	$\chi$/eV	$\alpha$
10/19a	N II	1084.5	27000	CH + QS	11.4	4.5
''	He II	1085.5	47000	''	52.2	12.4
''	S III	1077.1	63000	''	12.9	1.9
''	S IV	1072.9	138000	''	11.7	0.5
10/19b	H I Ly$\beta$	1025.7	10000	CH	12.1	-
''	C II	1036.3	23000	''	12.0	5.5
''	O VI	1031.9	288000	''	12.0	-0.02
10/22	H I Ly$\beta$	1025.7	10000	CH	12.1	-
''	C II	1036.3	23000	''	12.0	5.5
''	O VI	1031.9	288000	''	12.0	-0.02
10/24	H I Ly 4	949.7	10000	CH + QS	13.1	-
''	O I	948.7	10000	''	13.1	14.0
''	He II	958.6	47000	''	53.7	12.8
10/29	Si II	1533.4	14000	CH + QS	8.1	6.2
''	N IV	765.1	140000	''	16.2	0.84
''	O V	760.4	230000	''	26.5	0.84
''	Ne VIII	770.4	630000	''	16.1	-0.2

From Table 1, it is evident that the SUMER ECH observations cover most of the electron temperature range from the upper chromosphere through the transition region with minimal gaps. If the ECH radio enhancements are due to a difference in the electron temperature height profile in the 10000 K to 630000 K range between the QS and portions of the ECH we would expect to see enhancements in some of the UV lines measured. In fact, there are no corresponding differences in UV line intensity in any of the ECH radio enhancement sub-regions observed from October 19-28, 1999 beyond the normal network UV brightening (Wilhelm et al. 2001), however, as mentioned above relative maxima were observed. Increases in line width were measured in all of the chromospheric and transition region lines observed in the ECH network, consistent with previous observations (Lemaire et al. 1999). These increases are probably due to line-of-sight spicular motions and not directly related to the electron temperature, which determines radio brightness. Outflow velocities of 5 to 10 km s^-1were detected for lines formed above 100000 K. The investigation demonstrated that ECHs were very similar to PCHs in all measurable aspects.

We may estimate the effect of temperature increases on the UV spectral lines observed with SUMER. The computation depends upon the line optical depth. For lines from optically thin regions, the brightness B is computed by integrating the local emissivity E along the line of sight:

$$B = \int E {\rm d}l$$ (1)

where the integral is performed over the path L, which spans the radiating plasma. The local emissivity is given by:

$$E = n_{\rm s} n_{\rm e} Q$$ (2)

where $n_{\rm e}$ is the electron density, $n_{\rm s}$ is the species density and Q is the excitation coefficient, computed by integrating the electron collisional excitation cross-section over the Maxwellian electron energy distribution, and therefore a function of electron temperature. The species density is given by: $n_{\rm s} = A_{\rm E} f_{\rm ion} n_{\rm e}$, where $A_{\rm E}$ is the elemental abundance fraction and $f_{\rm ion}$ is the ionization state fraction, also a function of electron temperature.

If $n_{\rm e}$, Q, $f_{\rm ion}$ are taken to be the mean quantities along the effective path length rather than local quantities, the brightness is given by:

$$B = A_{\rm E} \hspace{.05 in} n_{\rm e}^{2} \hspace{.05 in} f_{\rm ion}(T) \hspace{.05 in} Q(T) \hspace{.05 in} L$$ (3)

where the temperature dependence of $f_{\rm ion}$ and Q is explicitly noted.

The ionization fraction may be calculated by simultaneously solving a set of rate equations for the population of each ionization state. These calculations are involved and detailed results are not readily available. However, for the purpose of this study, we assume that all ions are at temperatures which are near the peak of their abundance versus temperature curves, and therefore the ionization fractions are not sensitive to the small temperature changes being considered here. While this might not hold for all the lines observed, this assumption allows an upper limit to be determined for any possible temperature increase. In the fixed abundance case, the temperature dependence of the line brightness is determined only by the excitation coefficient, Q.

The temperature dependence of Q determines the ratio between the fractional changes in line brightness and electron temperature under the assumption of all other quantities remaining constant. This factor, denoted by $\alpha$, satisfies the relation:

$$\frac{{\rm d}B}{B} = \alpha \hspace{.05 in} \frac{{\rm d}T}{T}\cdot$$ (4)

From Eqs. (3) and (4),

$$\alpha = \frac{T}{Q} \hspace{.05 in} \frac{{\rm d}Q}{{\rm d}T}\cdot$$ (5)

For a Maxwellian electron energy distribution and allowed dipole transitions, Q is given by (McWhirter 1965):

$$Q = C \hspace{.05 in} T^{-1/2} \exp(-\chi /kT)$$ (6)

where C is a constant dependent on atomic physics, k is Boltzmann's constant and $\chi$ is the difference between upper state and lower state energies in the collisional excitation. The ratio of the fractional change in brightness to the fractional change in electron temperature is given by:

$$\alpha = \frac{\chi}{kT} - \frac{1}{2}\cdot$$ (7)

All of the lines observed except for the hydrogen Lyman lines are assumed to be from optically thin regions. The ratios, $\alpha$, for these lines were computed and are listed in Table 1.

The range of $\alpha$ is from -0.02 to 14.0, with the lowest values of -0.02 and -0.2 for lines formed at the highest temperatures, 288000 K and 630000 K. For lines formed at temperatures between 10000 K and 230000 K, we find $0.5 < \alpha < 14.0$, and therefore those lines are sensitive to changes in temperature. If the radio enhancement was caused by an increase in electron temperature of at least 15 to 20% at the formation height of the lines measured, there would be corresponding increase of at least 7.5% in line brightness for the least sensitive line and a factor of 14 increase in brightness for the most sensitive line. Since any increase in line brightness with respect to quiet sun levels is less than 2%, the evidence is not strong for the optically thin case of higher electron temperatures in ECH radio enhanced regions. It is possible that the assumptions of constancy in $n_{\rm e}$, L, etc. are invalid, but it is highly unlikely that these other factors would change in such a way as to keep all of the line brightness constant under a significant temperature change. For the nearly optically thick case, such as SUMER lines H I Ly$\beta$ and Ly 4, the brightness B is approximated by the Planck distribution:

$$B = C \hspace{.05 in} \frac{\nu^{3}}{{\rm e}^{h\nu /kT} - 1}$$ (8)

where C is a constant, $\nu$ is the photon frequency and h is Planck's constant. When the photon energy, $h\nu$, is large compared with the thermal energy, kT, the brightness is very sensitive to temperature changes. In the case of the Ly$\beta$ and Ly 4 lines, $h\nu \approx 5~kT$, and a 1.5% change in temperature would cause a 15% change in brightness. These are rough estimates, since the conditions in question are not completely optically thick. Since no brightness increase was measured in the enhancement region, there is no evidence for an increased temperature at the Ly$\beta$ and Ly 4 formation height, where the temperature is 20000 K.