ASTRONOMY

G. M. NIKOLSKY

RESONANCE LINES 304 Å HeII AND 584 Å HeI ON THE SUN

(Presented by Academician V. G. Fesenkov, July 4, 1962)

Beginning in 1958, when the 304 Å HeII and 584 Å HeI lines were photographically recorded by Violet and Rense (^1) with the aid of a spectrograph carried on a rocket, observations of λ304 Å and λ584 Å have been carried out repeatedly (^2–^6). The lines λ304 Å and λ584 Å possess a number of special features: they belong to an element of high cosmic abundance, and their excitation potential is close to the ionization potential.

At present, in accordance with experiment, it is accepted that the radiation flux from the entire Sun near the Earth is equal to: for λ304 Å, \(\sim 0.3\) erg/cm\(^2\)·sec; for λ584 Å, \(\sim 0.03\) erg/cm\(^2\)·sec. A prediction of the intensities of solar emission lines in \(\lambda = 19\)–2800 Å (^7) made it possible to identify most of the observed lines in the spectral region \(\lambda \leqslant 1100\) Å (^8). The principal result of the latter work is the conclusion that the observed line intensities in \(\lambda = 200\)–500 Å are underestimated by approximately one order of magnitude. According to (^8), \(F_{304}/F_{584} \simeq 20\)–30, and not 10, as follows from observations. In this connection, a determination of the intensity of solar radiation in λ304 Å and λ584 Å is highly desirable. On the other hand, the question of the formation of helium lines in the solar atmosphere is of independent interest. At present nothing is known about the distribution of λ304 Å and λ584 Å radiation over the disk of the Sun, or about the heights of formation of these lines in the solar atmosphere.

In works (^9,^10), on the basis of a study of rocket data on solar radiation in the far ultraviolet, of materials obtained during solar eclipses, and also of data on the thermal radio emission of the Sun in the range 1–30 cm, a model was constructed of the active and undisturbed regions of the solar atmosphere. This model includes the distribution with height \(h\) of the electron temperature \(T_e\) and concentration \(n_e\), the concentration of neutral and ionized helium \(n_{\mathrm{He\,I}}, n_{\mathrm{He\,II}}, n_{\mathrm{He\,III}}\). We shall use the data of (^9,^10) in what follows.

1. The He II line \(1s^2S — 2p^2P^0\) 303.8 Å. Excitation of the initial level \(2^2P^0\) is due to: 1) electron impacts acting on the ground level, and 2) photorecombinations. The principal processes by which atoms leave the \(2^2P^0\) level are spontaneous transitions.

It is not difficult to show that, under the conditions of the solar atmosphere, only these processes are significant and practically all helium atoms are in the ground state. Then the number of λ304 Å quanta formed in 1 cm\(^3\) in 1 sec is

\[ n'_{\mathrm{He\,II}} A_{21} = n_{\mathrm{He\,II}} n_e W_{12} + n_{\mathrm{He\,III}} n_e \sum R . \tag{1} \]

The coefficient of excitation by electron impact, according to (^11), is

\[ W_{12} = \frac{10f}{T_e^{3/2}} \left[ \frac{e^{-x}}{x} - \operatorname{Ei}(x) \right], \tag{2} \]

where, for HeII \(\lambda 304\ \text{Å}\), \(f=0.42\) is the oscillator strength, and \(x=4.74\cdot 10^5/T_e\); \(\operatorname{Ei}(x)\) is the exponential-integral function.

The recombination excitation of \(\lambda 304\ \text{Å}\) will occur through photorecombinations to all levels with principal quantum number \(m\geqslant 2\), except for the \(mp\) terms, since the latter combine with the ground level \(1^2S\), bypassing the state \(2^2P^0\). Taking into account the statistical weight of the various terms, for the recombination coefficient in (1) one obtains the estimate

\[ \sum R \approx \left[\frac{2}{3}\sum_{m=2} R_m+\frac{1}{3}R_2\right], \tag{3} \]

where \(R_m\) is the Menzel recombination coefficient for a hydrogen-like ion \({}^{12}\)

\[ R_m=3.2\cdot 10^{-6}m^{-3}Z^4T_e^{-3/2}e^x\operatorname{Ei}(x). \tag{4} \]

The sum of recombinations, according to \({}^{11}\),

\[ \sum_{m=2} R_m= \frac{1.6\cdot 10^{-6}Z^4}{xT_e^{3/2}} \left[e^{x_1}\operatorname{Ei}(x_1)+\ln(1.8x_1)\right], \quad x_1= \left(\frac{m_1}{m_1+1/2}\right)^2 x=\frac{4}{9}x . \tag{5} \]

Fig. 1. HeII, \(\lambda 304\ \text{Å}\). 1—active regions, 2—quiet regions; \(a\)—recombinations, \(b\)—electron impacts

For HeII, \(Z=2,\ x=6.3\cdot 10^5/T_e\).

Using the data \({}^{9,10}\) and expressions (1)—(5), we calculated the distribution of the volume emission of the solar atmosphere in \(\lambda 304\ \text{Å}\). The results are presented in Fig. 1. The areas under the curves in Fig. 1 give the radiation of an elementary column of the solar atmosphere (quanta/cm\(^2\cdot\)sec.) in all directions.

Thus, active regions on the Sun in the \(\lambda 304\ \text{Å}\) line turn out to be 6 times brighter than quiet regions. If the area of helium flocculi is taken as \(S=0.3\) (active Sun), then the radiation flux in \(\lambda 304\ \text{Å}\) from the whole Sun is \(0.9\ \text{erg}/\text{cm}^2\cdot\text{sec.}\)* In this case, 0.7 of all the \(\lambda 304\ \text{Å}\) radiation comes from active regions. It follows from this that, with the solar-activity cycle, \(\lambda 304\ \text{Å}\) should vary by a factor of 2–3.

We assumed the solar atmosphere to be transparent for \(\lambda 304\ \text{Å}\). In work \({}^{11}\) it was shown that, despite a considerable optical thickness \(\tau\) in resonance lines caused by scattering, the radiation may be regarded as “optically thin” as long as true absorption of quanta is not substantial. The condition for the absence of the latter \({}^{11}\) is

\[ \tau<\tau_0=(A_{21}/n_eB_{21})^{1/2}, \tag{6} \]

where \(B_{21}\) is the coefficient for quenching of the excited state by electron impact. In our case condition (6) is satisfied (\(10^2<10^4\)). In the lower layers of the solar atmosphere the \(\lambda 304\ \text{Å}\) radiation will be “optically thick”; however, as calculations show, because of the low temperature \(T_e\) this radiation is negligibly small.

In the region of formation of \(\lambda 304\ \text{Å}\), \(T_e\sim 10^5{}^\circ\), and therefore the line width, determined by the Doppler effect, is \(0.04\ \text{Å}\).

* This value agrees well with that obtained by us earlier \({}^{11}\) by reducing the results of \({}^{1}\) for atmospheric absorption (\(1.2\ \text{erg}/\text{cm}^2\cdot\text{sec.}\)).

Recently, on 7 March 1962, the OSO (“Orbiting Solar Observatory”) satellite was launched in the USA with a spectrophotometer continuously recording the solar spectrum at $\lambda 10$–$400$ Å. A preliminary report$^{(13)}$ at the Third COSPAR Symposium contains the results of measurements of three lines during a chromospheric flare on 13 March 1962, 15h U.T., of class $1+—2+$. According to$^{(13)}$, with the appearance of the flare the flux from the whole Sun at $\lambda 304$ Å increased by 10% and remained so, at least, throughout its entire duration ($\sim 2\cdot 10^3$ sec). The area of the flare was $\sim 2\cdot 10^{-3}\odot$, and the flux emitted by it at $\lambda 304$ Å is equal to $0.9\cdot 10\% \simeq 0.1$ erg/cm$^2\cdot$sec; therefore the surface brightness of the flare is approximately 10 times greater than the brightness of the active region where flares usually occur. The enhancement of $\lambda 304$ Å may be associated with an increase in the density of matter in the flare region by a factor of 3–4, or with a rise in temperature. A sudden increase in density seems unlikely to us. Since the probability of excitation by electron impact depends exponentially on $T_e$ with an exponent $\sim 5 \div 6$, an increase of $T_e$ by a factor of 1.5–2 in the flare region is sufficient for the intensity of $\lambda 304$ Å to increase by one order of magnitude.

Fig. 2. He I, $\lambda 584$ Å. The designations are the same as in Fig. 1.

The estimate of the time required to establish the elevated $T_e$ gives a small value ($\sim 10$–100 sec). Since the flare flux at $\lambda 304$ Å is $\simeq 0.1$ erg/cm$^2\cdot$sec, the total energy emitted by the flare during its lifetime is $\sim 10^{29}$ erg. The total energy of the flare in all short-wavelength lines ($\lambda \leqslant 1000$ Å) is apparently one order of magnitude higher ($10^{30}$ erg). As a result of radiation, the gas in the flare will cool very rapidly; calculations show that its energy will be exhausted in 1 sec. It follows from this that a continuous influx of energy with a power of $\sim 0.1$–$0.01$ erg/cm$^3\cdot$sec is necessary in the flare region. Strictly speaking, this value is a lower limit to the real value. It seems to us that these facts limit the possibility of treating a chromospheric flare as an explosion and are an argument in favor of representing the flare as a region of prolonged energy release.

2. The He I line $1s^2\,{}^1S — 2p^1\,{}^1P^0$ 584.3 Å. As in the case of $\lambda 304$ Å, the “optically thick” radiation of He I is negligibly small, since it comes from regions with $T_e \simeq 6300^\circ$. This result was obtained by us from condition (6) and the model of the solar atmosphere$^{(9,10)}$. Consequently, $\lambda 584$ Å will arise in an optically thin layer, and the flux of quanta will be determined by equation (1). For calculating $W$ one may use expression (2) with $f = 0.36$ and $x = 2.37\cdot 10^5/T_e$. The recombination coefficient can also be calculated from formula (3); however, a factor $1/4$ should be introduced, accounting for the statistical weight of the system of singlet and triplet levels. In this case $x = 2.9\cdot 10^5/T_e$.

Figure 2 shows the distribution of the volume emission of $\lambda 584$ Å obtained by us for active and undisturbed regions of the solar atmosphere.

The glow in $\lambda 584$ Å occurs mainly (80%) due to recombination excitation. The contrast between active and undisturbed regions of the Sun is 3.5. The flux at $\lambda 584$ Å from the whole Sun near the Earth is $\sim 0.03$ erg/cm$^2\cdot$sec. About $1/2$ of all the radiation deter-

is determined by active regions; therefore the variations of $\lambda 584\ \mathring{\mathrm{A}}$ with the solar-activity cycle should not exceed a factor of 2.

The emission of $\lambda 584\ \mathring{\mathrm{A}}$ in a flare, if it is associated with an increase in $T_e$, should increase only slightly, since recombination depends only weakly on $T_e$. If the fraction of the $\lambda 584\ \mathring{\mathrm{A}}$ emission due to electron impacts increases by one order of magnitude, then the flux from the entire Sun in $\lambda 584\ \mathring{\mathrm{A}}$ will increase by 2–3% during a flare of average power.

Institute of Terrestrial Magnetism, the Ionosphere,
and Radio-Wave Propagation,
Academy of Sciences of the USSR

Received
28 VI 1962

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