Abstract. We analyse the formation of He I lines in late-type dwarfs by statistical equilibrium (or NLTE radiative

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1 (will be inserted by hand later) Your thesaurus codes are: 08 ( ; ; ; ) ASTRONOMY AND ASTROPHYSICS Helium lines in late-type dwarfs. A. C. Lanzafame? and P. B. Byrne Armagh Observatory, Armagh BT61 9DG, N. Ireland, UK Received xxx; accepted xxx Abstract. We analyse the formation of He I lines in late-type dwarfs by statistical equilibrium (or NLTE radiative transfer) computations. Atmospheric models for dk (Eri) and dme V1005 Ori (=Gl 182) stars are considered. The validity of the weakly non-uniform approximation for dme stars established in Lanzafame (1994a) for the lower transition region of dme stars implies that streaming particles have virtually no role in the formation of the lines. Comparison with observations of the He I (10 830A) and He I (5 876A) lines in the dme star, V1005 Ori, indicate that it is possible to reproduce the observed helium lines with a simple model compatible with other observational constraints. Over-ionisation by coronal EUV radiation is found to play a minor role in the formation of the triplet lines. Key words: Stars: atmospheres { Stars: chromospheres { Stars: late-type { Lines: formation 1. Introduction Susceptibility to over-ionisation by coronal EUV-XUV radiation or streaming particles makes the formation of helium lines a stringent test for our understanding of the physics of the chromosphere and the transition regions of the Sun and late-type stars. In dme stars, coronal temperatures and pressures are much higher than in the Sun, so such eects are expected to work under more extreme conditions. Higher EUV-XUV radiation should produce higher over-ionisation, while higher transition region temperature gradients, if present, should enhance particle streaming. On the other hand higher pressure should reduce the latter. Observations of helium lines in the non-aring atmospheres of red-dwarfs have been very dicult and therefore rare. One of the rst measurements of the He I ( A) line in a dme star, for instance, is that of Byrne & Lanzafame (1994), which is here compared with theoretical results. Therefore, the existence of a \helium problem" for dme stars derives mainly by analogy with the solar case, since in the dme case neither observations nor theory have provided sucient ground for independent discussions. In this paper it will be shown that a \helium problem" for dme stars might not exist at all, in the sense that excitation by local thermal electrons (i.e. with an energy distribution described by the local Maxwellian) can be by far the most important mechanism for excitation of helium lines in dme's. A similar result is found for the dk2 star Eridani, conrming the results of O'Brien & Lambert (1986) The Formation of Helium lines in the Sun The formation of the helium lines in the solar spectrum has been an outstanding astrophysical problem for some years. Transition region models based on UV and EUV resonance lines of metals fail to account for the observed intensities of helium resonance lines in the quiet Sun (Jordan 1975) and this discrepancy has led to a variety of proposals for the formation of the helium spectrum by dierent processes at dierent temperatures. The extremes in excitation mechanism are represented by collisional excitation at high temperature and density (Athay & Johnson 1960) or by a Send oprint requests to: A. C. Lanzafame? Present address: Dept. of Physics and Applied Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, Internet: acl@phys.strath.ac.uk

2 an over-ionisation of helium followed by radiative recombination to populate the excited levels; this mechanism has been championed by Hirayama (1971). The transition A (2 3 S P) is very important in distinguishing between these mechanisms as it is the strongest line between excited levels observable in the quiet disk spectrum. Milkey, Heasley & Beebe (1973), assuming that triplet levels are populated primarily by radiative recombination of ionised helium in the lower temperature regions (T K) and by collisional excitation in the higher temperature regions (T K), concluded that the populations of these levels are sensitive to the over-ionisation produced by excess extreme ultraviolet radiation primarily in the region of lower temperature. They found that the optical depth of this line was equally split between high and low temperature regions. The excited singlet levels are under-populated with respect to their triplet counterparts, and this under-population grows as one moves outward in the model. They interpreted this under-population as being due to the provision, by the resonance lines, of a radiative path for the singlets to decay to the ground state, and the absence of such a path for the decay of the triplets. As the probability of escape for a resonance line photon increases, the relative depopulation of the singlets becomes greater. According to Avrett, Vernazza & Linsky (1976), the He I and He II continua are formed by recombination following photoionisation by coronal lines, and, in the case of He I, by the He II 304 A line. Optical depth unity occurs in the chromosphere near 7; 000 K, but there is sucient contribution to the emission at temperatures up to K to produce a colour temperature near K for He I and K for He II. Milkey et al. (1973) had previously shown that the He I continuum is formed by the photoionisation - recombination (PR) process and that I (504 A) increases and colour temperature decreases with increasing photoionisation rate. Shine, Gerola & Linsky (1975) found that ion diusion eects become increasingly important with steeper temperature gradients and with increasing excitation potential. Diusion can produce signicant changes in the ionisation distribution in transition region models and these changes can in turn aect line intensities. Their numerical calculations for the resonance lines of He I and He II show that diusion can enhance these lines. Most transition region lines will be less aected by diusion than is the case for He I or He II. The helium lines may appear relatively weak in coronal holes due to a weakening of this enhancement mechanism. Recently, Fontenla, Avrett & Loeser (1993) have analysed the solar helium emission including ambipolar diusion for hydrogen and helium diusion in the solution of the statistical equilibrium (or NLTE radiative transfer problem), for one-dimensional, hydrostatic atmospheric models which satisfy the energy balance requirements in the transition region. The eects of the coronal illumination on the transition region and upper chromosphere have also been considered. They found that the temperature structure of the transition region is substantially independent of the coronal illumination, but the electron density in the upper chromosphere and particularly hydrogen and helium ionisation are signicantly aected. Diusion causes the He I ionisation to be slightly greater in the upper chromosphere and substantially lower in the transition region compared with local ionisation calculations which ignore the eects of diusion. This greatly changes the He I resonance line emission, but has a less important eect on the He II lines Helium Lines in Late-type Dwarfs The rst attempt to explain the formation of helium lines in late type stars is probably that of Giampapa et al. (1978). They obtained a deeply exposed red quiescent spectrum of AD Leo showing the He I lines at A and A lines in emission (as well as H and Na I A and A lines), at a resolution of approximately 0.25 A. They measured equivalent widths of A and A for the He I (5 876 A) triplet line and A singlet line, respectively. The corresponding triplet-to-singlet line ux ratio is 3.7, close to the ratio of their statistical weights (3.0). In the non-aring Sun the I(5 876)=I(6 678) intensity ratio is observed to lie between high values, typically 45, seen in quiescent prominences at the limb, and low values 3:3 seen in active prominences (Tandberg-Hanssen 1974). Giampapa et al. (1978) considered three competing mechanisms which populate the 3 3 D and 3 1 D upper states of the A and A lines, namely recombination to excited states of He I and cascade following photoionisation of ground state He I by < 504 A photons, collisional excitation from the He I ground state, and excitation of the singlets only by the resonance line series. They argued that the He I subordinate lines that they observed in AD Leo are not excited by recombination and cascade following photoionisation of neutral helium by < 504 A photons. In fact, assuming that the He I lines are excited solely by photoionisation/recombination process, they derived an unrealistically large X-ray luminosity, varying from 0.04 to 0.14 of the total stellar luminosity (L bol = T 4 eff r2 ). Instead, they suggested that A and A lines are probably excited by collisions from the ground state in the hotter (T > K) regions of the stellar chromosphere. Their approximate calculations suggest a chromospheric column density n e l cm?2 at T = ? K for the He I emitting layers. If n e = 10 10?10 12 cm?3, then this layer is geometrically thin compared to the stellar radius. However, we must notice that the Giampapa et al. (1978)

3 all the competitive mechanisms are included Models for the upper chromosphere and lower transition region of dme stars Lanzafame (1994a) (hereafter Paper I) introduced models for the upper chromosphere and the lower transition region of dm0e-dm2e stars. The modelling procedure was based on a modication of the semi-empirical approach useful for evaluating the eects of prescribed transport processes to the energy balance. The statistical equilibrium equations included terms due to hydrogen ambipolar diusion in order to investigate its importance in the ionisation and energy balance. Several spectroscopic diagnostics have been used such as the hydrogen H and Ly lines, Si II resonance multiplets near A and A and the Mg II h & k lines. Lanzafame's analysis of the H prole in the dm1e star V1005 Ori indicates that the temperature gradient in the lower transition region is smaller than solar. Since the gas pressure is higher than solar, these conditions imply the validity of a weakly non-uniform approximation (e. g., the Spitzer-Harm relation for the thermal conductivity is valid in this case). Ambipolar diusion is found ineective for the ionisation balance and therefore for the energy transport in the lower transition region of dme stars. This implies that, unlike the solar case, a signicant local dissipation of mechanical heating must be present to sustain the observed radiative emission from the lower transition region Plan of the paper In Section 2, we discuss the atomic parameters used in the models. The formation of helium lines in Eridani and V1005 Ori is discussed in Sections 3 and 4 respectively. In Section 5 the eects of coronal EUV radiation is analysed. The conclusions are drawn in Section Atomic Parameters for He I Statistical equilibrium computations were carried out for an atomic model for helium which includes 29 LS states up to the principal quantum number n = 5 plus the ground state of He II. The inclusion of He II excited states and He II { He III continua will be discussed in a subsequent paper. Accurate collision cross-sections are available for energy levels up to n = 4. The inclusion of the n = 5 levels, although using only approximate atomic parameters, provides a better description for transitions involving the n = 4 levels as well as for the recombination cascade. Eective collision strengths were extrapolated to the entire range of temperatures involved in the formation of helium lines in late-type dwarfs (see Lanzafame 1993 and 1994b). Such extrapolation has been necessary since current models for the atmospheres of solar-type stars predict electron temperatures for the region of formation of He I lines between approximately and K (Lanzafame 1992 and 1993) while accurate collision strenghts are available only below K. Among the advantages of using the extrapolation method introduced in Lanzafame et al. (1993) and Lanzafame (1994b) is that it ensures that eective collision strengths for exchange transitions (singlet-triplet) decrease rapidly for increasing electron temperature (/ T?1 ), while they increase logarithmically for optically allowed transitions and tend to a constant value in the case of optically forbidden transitions. The atomic model used, together with the Carlsson (1986) code for the solution of the statistical equilibrium problem, provides a much more accurate modelling for the formation of helium lines than in previous works. The energy levels have been taken from Bashkin & Stoner (1975). These are listed in Table 1 together with the statistical weight. Oscillator strengths for He I are taken from Fernley, Taylor & Seaton (1987) and Tully (1992) (Table 2). Tully (1992) calculated oscillator strengths for the transitions 1s3d 1 D-1s4f 1 F, 1s3d 3 D-1s4f 3 F, 1s4d 1 D-1s4f 1 F, and 1s4d 3 D- 1s4f 3 F, which are not included in Fernley et al. (1987). Theoretical photoionisation cross-sections are from Fernley et al. (1987). These calculation shows very interesting atomic resonances. Only a smoothed shape has been considered herein. Eective collision strengths for excitation by electron impact are taken from Lanzafame at al. (1993) for optically allowed transitions, while for other transitions, the values of Sawey et al. (1990) have been extrapolated according to the Burgess & Tully (1992) rules, as discussed in Lanzafame (1994b). Collision coecients for ionisation by electron impact are taken from Janev et al. (1987) for transitions involving the 5 levels up to and including n = 2.

4 Table 1. Energy levels included in the atomic models for He I level State energy (cm?1 ) stat. weight 1 1s 2 1 S s2s 3 S s2s 1 S s2p 3 P o s2p 1 P o s3s 3 S s3s 1 S s3p 3 P o s3d 3 D s3d 1 D s3p 1 P o s4s 3 S s4s 1 S s4p 3 P o s4d 3 D s4d 1 D s4f 3 F o s4f 1 F o s4p 1 P o s5s 3 S s5s 1 S s5p 3 P o s5d 3 D s5d 1 D s5f 1 F o s5f 3 F o s5g 1 G s5g 3 G s5p 1 P o Helium lines in Eridani Several observations of He I ( A) in Eridani are available in literature. Notably, O'Brien & Lambert (1986) reported an EW ( A)=49060 ma from a single observation while Zirin (1982) reported an EW ( A)=200 ma from several observations spanning 13 years. High-resolution, low-noise spectra of He I (5 876 A) by Lambert & O'Brien (1983) indicate an EW between 16 and 19 ma over a period of about two weeks. A statistical equilibrium analysis of the He I ( A) and He I (5 876 A) lines in Eridani was discussed by O'Brien & Lambert (1986). The atmospheric models adopted were those of Kelch (1978) and Simon, Kelch & Linsky (1980) (hereafter SKL). Both He I lines were predicted satisfactorily by the SKL model while the Kelch model predicted both lines to be much weaker than observed. Their calculations did not include the photoionisation induced by the corona leading to the suggestion that coronal radiation need not be invoked in the formation of helium lines in this star. The calculations presented here make use of more extended and accurate atomic data for helium than in O'Brien & Lambert (1986). The photospheric and lower chromospheric structure adopted (temperature vs. column mass) is taken from Thatcher, Robinson & Rees (1991), while the upper chromosphere and lower transition region structure is obtained combining the emission measure analysis of Jordan et al. (1987) with the assumption of hydrostatic equilibrium and an estimate of the electron density at a given temperature from electron density diagnostics. Jordan et al. (1987) suggested < N e < at T K, their density diagnostics deriving mainly from the intesystem line Si III (1892 A). The electron density upper limit in this range is consistent with the lower chromospheric structure of Thatcher et al. (1991). Here, in order to take into account the uncertainties in the electron density, two models for Eridani have been considered with dierent structures for the upper chromosphere and lower transition region, namely, N e = cm?3 in model e1 and N e = cm?3 at T K in model e2 (Fig. 1).

5 Table 2. Absorption oscillator strenghts (length form) for He I upper lev. lower lev. f l E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-01 Table 3. Absorption oscillator strenghts (length form) for He I for transitions involving n = 5 levels upper lev. lower lev. f l E E E E E E E E E E E E E-02

6 Fig. 1. Upper chromosphere - lower transition region temperature structures for Eridani obtained from Jordan et al. (1987) models (see text). Fig. 2. He I ( A ) line source function (solid line) compared with the Planck function (dashed line) Formation of He I (10830 A) The theoretical equivalent widths predicted from the Eridani models e1 and e2 with no EUV back-radiation are shown in Table 4. The triplet at A derives from the transitions 2 3 S P 2;1;0 corresponding to the wavelengths , and A respectively. Initially, statistical equilibrium calculations have been performed for the triplet with no ne-structure splitting. Subsequently, the resulting populations have been distributed among the ne-splitting levels proportionally to their statistical weights and the formal solution iterated to obtain the scattering contribution to the source functions consistent with the radiation eld. The same procedure has obviously been applied to other triplet transitions (e.g. the line at A), but attention here will be focused on the He I ( A) triplet only. Although a more rened treatment taking into account the line-overlapping would be required, the ne-structure calculations are expected to give more realistic results than those considering the triplet as a whole. Above T e K, the 2 3 S state is suciently populated to produce optically thin absorption of the photospheric continuum at 10830A (Figs 2 and 3). When no EUV back-radiation is included, the 2 3 S state is populated mainly by de-excitations of the 2 3 P state (Fig. 4). Below T e K, the 2 3 S state is populated also by direct recombination from the continuum. Above such temperature, ionisation depopulates the 2 3 S state. The 2 3 S state is depopulated by collisional excitation to the 2 1 S and 2 1 P states end de-excitation to the 1 1 S state. The line contribution function to the emerging radiation, as dened by Achmad, de Jager & Nieuwenhuijzen (1991), shows that the region of formation of He I ( A) embraces

7 Fig. 3. Helium population densities, model e1 for Eridani. The thicker lines indicate the 1 1 S state (solid line) and the He II ground state (dashed line). Thinner lines are used for the populations of other states. The dotted line indicates the 2 3 S state, dashed the 2 1 S, dot-dashed the 2 3 P, triple-dot-dashed the 2 1 P. The other solid lines indicate the population densities for higher levels. Table 4. Helium lines equivalent widths for Eri models. The y sign indicates the results obtained without splitting the triplet in its ne structure levels. EW (ma) model y e e a considerable part of the lower transition region, with most of the emerging ux (line contribution function C l > 0:1 of its maximum) originating approximately from K to K (Fig 4). In order to test the eects of over-ionisation by EUV radiation, the upper boundary conditions in the models have been modied to include an arbitrary ux with a at spectrum at wavelengths below 504 A. Since most of the radiation at these wavelengths would be produced by the He II continuum and the He II (304 A) line, a at spectrum is not realistic. However, this approach can be used to understand the eects of over-ionisation by EUV radiation followed by recombination on the formation of the lines. In Figs. 4 and 5, ICX is a parameter which indicates the specic intensity of an EUV back-radiation having a at spectrum. It is important to stress that this parameter cannot reasonably be compared with, say, the specic intensity at a given wavelength on the Sun. Furthermore, because of the large interstellar absorption, very little information on the amount of radiation near the 504 A threshold which illuminates the atmosphere and produces He I over-ionisation can be obtained from EUVE observations. As ICX increases, the importance of the recombination process to the 2 3 S obviously increases, but this takes place mainly in the lower temperature part of the region of formation of the He I _ (10830 A) line. This result is consisten with Milkey et al. (1973) computations in the solar case. The increase in EUV back-radiation causes also the formation of the line to take place at progressively lower temperatures, and the contribution of the wings of the line to the emergent radiation tends to increase. However, that collisional excitation by electron impact should be by far the dominant mechanism in the formation of He I and 5876 A can be seen by comparing the theoretical ratio F (5876)=F (10830) with observations. In Fig. 5 the equivalent width of the two lines is shown as a function of parameter ICX. The calculations show that when EUV back-radiation starts to play an important role in the formation of He I (10830 A) line (through over-ionisation followed by recombination), the He I (5876 A) line absorption increases well above the observed value. The closer agreement of the theoretical F (5876)=F (10830) ratio with the observations without including a substantial EUV back-radiation in the models indicates that over-ionisation followed by recombination is to be considered of secondary importance in populating the 2 3 S state and therefore in the formation of He I ( A) in Eridani.

8 Fig. 4. Principal net rates involving the 2 3 S state (left pannels) and He I ( A ) line contribution function normalised to the maximum (right pannels) at increasing EUV back-radiation (parameter ICX), e1 atmospheric model for Eridani. On the left pannels, positive values indicate a net rate out of the state. The net rates are to the 1 1 S (solid line), 2 1 S (dotted), 2 3 P (dashed), 2 1 P (dot-dashed) and to the He II ground state (triple-dot-dashed).

9 Fig. 5. He I (10 830A) and He I (5 876A) equivalent width vs. ICX parameter (see text) for Eridani model e1. As for the more active dme stars (see Paper I and below), Eridani models e1 and e2 predict l(r ln T ) < 1 10?3 in the lower transition region, where l is the particle mean free path. This implies the validity of weakly non-uniform approximations and that collisional excitation rates are expected not to be aected by streaming particles or, in other words, by strong non-maxwellian electron energy distributions (see, e. g., Shoub 1983 and Ciaravella, Peres & Serio 1993). 4. New Results for Helium Lines in dme Star V1005 Ori In Paper I it has been shown that the analysis of the H emission prole implies that in dme atmospheres the plasma in the lower transition region is weakly non-uniform, so that free-streaming particles eects (see, e. g., Shoub 1983; Ciaravella, Peres & Serio 1993) should have virtually no role in the formation of helium lines in dme stars with a lower transition region similar to V1005 Ori. One of the consequences of the presence of an electron free streaming component - or, in other words, of a non-maxwellian electron energy distribution function - would be a modication of the functional form of the collisional rates versus temperature. Paper I has also shown that hydrogen ambipolar diusion is ineective in altering the ionisation balance and atmospheric structure of such stars. Therefore, collisions with thermal electrons are expected to be the main excitation and ionisation mechanism for He I. In this case, a purely thermal model atmosphere could reproduce the observed helium lines within the uncertainties in both the observations and the modelling, as introduced, for instance, by ignoring inhomogeneities, velocity elds and time variations. The models derived in Paper I and used here for the analysis of the formation of helium lines are shown in Fig. 6. Table 5. Helium lines equivalent widths for the dme models. Emission lines are indicated with a minus sign. The y sign indicates the results obtained without splitting the triplet in its ne structure levels. EW (ma) model y w w w w In Table 5 the resulting equivalent widths for He I ( A) and He I (5 876 A) for the models introduced in Paper I are shown. As in the Eridani case, statistical equilibrium calculations have been initially performed for the triplet with no ne-structure splitting. Subsequently, the resulting populations have been distributed among the ne-splitting levels proportionally to their statistical weights and the formal solution iterated to obtain the scattering contribution to the source functions consistent with the radiation eld. As stressed before, a more rened treatment taking into

10 Fig. 6. Grid w of upper chromosphere - lower transition region models for dme stars (V1005 Ori, AU Mic) from Paper I. The solid line represents model w1, the dotted line model w2 and, at increasing column mass, w3 and w4 (dashed lines). account the line-overlapping would be required. However, the ne-structure calculations are expected to give more realistic results than those considering the triplet as a whole. Fig. 7. Spectrum of V1005 Ori around A made using the CGS4 spectrograph at UKIRT on 9 November 1992 at spectral resolution = (histogram). The nearby lines are those of Si I on the shorter wavelengths side and of Na I on the longer wavelengths side. The theoretical prole is obtained from model w1 by summing the residuals of the ne-splitting components. The dashed line represents the spectrum convolved with a gaussian with a corresponding to the resolution of the instrument. Observations of He I ( A) in V1005 Ori have been obtained using the CGS4 spectrograph at UKIRT on 9 November 1992 at spectral resolution = Byrne & Lanzafame (1994). Comparison with a similar spectrum of the bright A0V star BS3314 showed that the spectrum was virtually uncontaminated by terrestrial H 2 O lines. The theoretical prole shown in Fig 7 has been obtained from model w1 by summing the residuals of the ne-splitting components of the triplet. The helium line overlaps with the Si I line at shorter wavelengths and is obviously blended with an unknown line at longer wavelengths. The agreement in the line-core is excellent.

11 Pierce solar telescope at KPNO on 2nd October 1993 at U.T. 12:02 (Byrne et al., in preparation). He I (5 876 A) was observed to be weakly in emission (EW 30 ma). The observed spectrum is shown in Fig 8. Fig. 8. Spectrum of V1005 Ori around the Na doublet obtained at KPNO using the stellar spectrograph on the McMath-Pierce solar telescope on 2nd October 1993 at spectral resolution = He I (5 876 A) (D3) appears in weak emission, with an equivalent width 30 ma. The results for the grid of models w are in good agreement with the Byrne & Lanzafame (1994) measurement of He I ( A) in V1005 Ori while the theoretical strength for He I (5 876 A) (EW 10 ma for models w) is comparable with the observations, expecially in view of the non-simultaneity and diculty in setting local continuum accurately Analysis of Line Formation in V1005 Ori The physics of the formation of He I (10 830) in a dme star like V1005 Ori is similar to the Eridani case in the sense that above a certain temperature, approximately K in V1005 Ori, the 2 3 S state is suciently populated to produce optically thin absorption of the photospheric continuum at A. Numerical experiments show that in dm0e-dm2e stars with a H equivalent width larger than about 1 A (or during are) the He I ( A) line will gradually go from absorption into emission. V1005 Ori is on a critical regime, were variations in the transition region pressure could cause an increase in the H equivalent width above this limit and the He I ( A) could be driven in emission. 5. Eects of EUV radiation A correlation is detected between the X-ray luminosity, L X, and the luminosities of chromospheric and transition region lines for are stars. The correlation is well represented by the relation L X = 10 L line where the value of lies between 1 and 2 for dierent lines (Agrawal, Rao & Sreekantan 1986). The physical signicance of this is not clear. Given the paucity of observational data, no study on the correlation between He I ( A) lines and coronal radiation in M dwarfs exists in literature. The investigation by Zarro & Zirin (1986) does not include stars with spectral type later than K5. However, it seems reasonable that the mechanism of formation of He I ( A) in Eridani and in V1005 Ori could be common at least among late-type dwarfs characterised by a gas pressure in the lower transition region greater than approximately 1 dyne cm?2. Obviously this statement needs to be conrmed by extensive observational and theoretical investigations. In such a scenario the existence of a correlation would reect the fact that a higher dissipation rate of mechanical energy in the transition region and corona implies a higher pressure in the lower transition region. In this case, the existence of such correlation would not be a proof that coronal EUV radiation constitutes an important source of excitation for He I as has been suggested elsewere. As for the Eridani models, the upper boundary conditions in the models have been modied to include an arbitrary ux with a at spectrum at wavelengths below 504 A. We stress that, since most of the radiation at these wavelengths would be produced by the He II continuum and the He II (304 A) line, a at spectrum is not realistic. However, here we are interested in establishing the regime in which EUV over-ionisation would dominate the formation of the triplet

12 Fig. 9. He I ( A ) line source function (solid line) compared with the Planck function (dashed line), model w1. Fig. 10. Population densities for helium in V1005 Ori, w1 model. The thicker lines indicate the 1 1 S state (solid line) and the He II ground state (dashed line). The dotted line indicates the 2 3 S state, the dashed the 2 1 S, dot-dashed the 2 3 P, the triple-dot-dashed the 2 1 P. The other solid lines indicate the population densities for higher levels. lines in the dense dme atmosphere. A more accurate modelling is planned in a future work using EUVE He II (304 A) observations. In Fig. 12 the response of He I (10 830A) and He (5 876A) equivalent widths to EUV radiation is shown for model w1 of Paper I. As before, ICX is a parameter which indicates the specic intensity of a at EUV back-radiation which cannot reasonably be compared with the specic intensity at a given wavelength. Below ICX 1 10?10 (Fig. 12) the lines are more sensitive to a variation in the electron density than in EUV radiation. Because of the larger electron density, the formation of the He I triplet lines in dme stars is dominated by photoionisation followed by recombination at EUV ux considerably larger than in dk stars. The dependence of the He I ( A) equivalent width on ICX does not present, in the dme case, any maximum in absorption before going into emission (see Fig. 5). Comparison of Fig. 12 with observed EW (Table 5) indicates that the formation of He I triplet lines is dominated by excitation by electron impact, with photoionisation followed by recombination likely to play only a secondary role. 6. Conclusions We have described new model atmospheric calculations for the formation of He I lines in the active late-type dwarfs, Eridani and V1005 Ori (=Gl 182). We have demonstrated that collisional excitation can be the dominant mechanism for the formation of He I ( A) and He (5 876 A) in the non-aring atmospheres. Other mechanisms which may play an important role in the solar atmosphere, like EUV over-ionisation and streaming particles, have a negligible eect in late-type stars with a transition region pressure greater that approximately 1 dyne cm?2.

13 Fig. 11. Principal net rates involving the 2 3 S state (left pannels) and He I ( A ) line contribution function normalised to the maximum (right pannels) at increasing EUV back-radiation (parameter ICX), w1 atmospheric model for V 1005 Ori. On the left pannels, positive values indicate a net rate out of the state. The net rates are to the 1 1 S (solid line), 2 1 S (dotted), 2 3 P (dashed), 2 1 P (dot-dashed) and to the He II ground state (triple-dot-dashed).

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