A. V. Mikhailov
Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Troitsk, Russia
Midlatitude ionospheric E layer has been studied for many years, nevertheless there are still problems with its description. While available empirical NmE models like International Reference Ionosphere (IRI) [Bilitza, 1990] reproduce regular NmE variations with sufficient accuracy, a theoretical approach based on current EUV solar flux models and commonly accepted dissociative recombination rate constants for NO+ and O2+ ions usually underestimates NmE by 30-40% [Buonsanto et al., 1995; Titheridge, 1997]. Because of the square-law loss process this 40% deficit in NmE implies a 100% increase in the ionization rate at the E -layer peak (105-110 km). Some approaches have been proposed to overcome this problem. Ivanov-Kholodny and Nusinov  used low a( NO+) value by Mul and McGowan  along with strong seasonal variations in the [O2] scale height in the 100-110 km height range. Antonova et al.  took into account vibrationally excited NO+ and O2+ ions, and this allowed them to explain NmE and hmE seasonal variations. Titheridge [1996, 1997], using a full allowance for secondary ionization with EUV radiations down to 25 Å and a 33% additional increase in the radiation with l< 150 Å in the Extreme Ultraviolet Model for Aeronomic Calculations (EUVAC) [Richards et al., 1994], could describe the observed NmE values. Although there is large uncertainty in EUV fluxes in this spectrum range, such an increase of the EUV flux in the 50-150 Å range seems unjustified, as is shown below. The fluxes in this spectrum range have already been tripled in the EUVAC model [Richards et al., 1994] compared to the reference spectrum F74113 measured on 23 April 1974 (F10.7=74), and this factor is kept in the model for all levels of solar activity.
Calculated NO+/ O2+ ratio is another problem in the E -region theoretical modeling [Buonsanto et al., 1995; Titheridge, 1997]. Usually, the calculated NO+/ O2+ ratio is less, compared to rocket observations in the E region [Danilov, 1994; Danilov and Semenov, 1978; Danilov and Smirnova, 1995, and references therein]. Buonsanto et al.  and Titheridge , analyzing this problem, suggested that our understanding of the NO+ chemistry may be incomplete.
The aim of the paper is to compare E -region simulations with the Millstone Hill Ne(h) observations given by Buonsanto et al.  and to draw a conclusion on EUV model fluxes and a( NO+) dissociative recombination rate coefficient needed to obtain the observed NmE for different levels of solar activity. A possible way to obtain NO concentrations, providing the observed NO+/O2+ ratio in model International Reference Ionosphere calculations, is proposed as well.
Midlatitude regular ionospheric E layer is known to be controlled by photochemical processes. A two-component model by Nusinov [Bruevich and Nusinov, 1984; Nusinov, 1984, 1992] with further corrections by Nusinov et al.  is used to calculate EUV fluxes in 48 wavelength intervals with 8 l 1050 Å. The intensity of the EUV fluxes in this model depends on slowly varying F bg emission at 10.7 cm wavelength and on radio emission from active areas on the Sun, F10.7 [Nusinov, 1984]. The background F bg emission varies from F bg = 60-65 (in 10-22 W m-2 Hz-1 ) at solar minimum to F bg 120 at solar maximum. The X range ( l< 100 Å) includes 13 wavelength bins. Ionization by a strong Lyman- a line ( l=1216 Å) is taken into account according to the Katjushina et al.  model. Although this emission gives only around 1% of the total ionization rate at the E -layer peak, it becomes important at lower heights. For further discussion, Table 1 gives fluxes according to the Nusinov and EUVAC models in the same wavelength bins as used in the EUVAC model. Solar minimum of 23 April 1974 ( F10.7=74, F bg=67), when the F74113 reference spectrum was measured, and solar maximum conditions with F10.7=200, F bg=100 corresponding to the EUVAC model for P=200 are compared in Table 1. Parameter P = (FA10.7+F10.7)/2 is used as the proxy in the EUVAC model [Richards et al., 1994], FA10.7 being an 81-day average of the daily F10.7 index.
Our usual model calculations (a standard mode) are based on the photoionization and photoabsorption cross sections mostly from Torr et al. . Photoionization cross section for O+(4S), O+(2P), and O+(2D) production were taken according to Richards and Torr , with allowance for the secondary ionization for l< 250 Å according to Ivanov-Kholodny and Nikol'sky . Their approach is based on the experimental fact that each act of ionization by short-wave UV or X-ray emission requires e amount of energy. This e = 32 eV for the emission with l 200 Å. Then the effective ionization cross section is defined as
where E is the energy of the initial photon, and siph is the photoionization cross section, and l is the wavelength in Å. For the sake of comparison, the same calculations were performed with the cross sections given by Fennely and Torr , taking into account secondary ionization for l< 400 Å, as proposed by Titheridge .
The list of chemical reactions used in the model is given in Table 2. Reaction rates were taken from Buonsanto et al. , McEwan and Phillips , Oppenheimer et al. , Torr and Torr , and McFarland et al. .
Neutral composition (O, O2, N2, N) and temperature Tn were used from the MSIS 86 thermospheric model [Hedin, 1987]. Nitric oxide, NO, is very important for E -layer chemistry. It was found by fitting the calculated NO+/ Ne and O2+/Ne ratios in the 100-120 km height range to the ion composition model by Danilov and Smirnova , which is based on rocket measurements. An effective scale height of the [NO] height distribution inferred at 115 km was used to extrapolate the [NO] profile above 120 km.
The Millstone Hill daytime observations for three winter -- days 5 February 1992, 10 November 1988, and 15 January 1985 - as they are given in Buonsanto et al. , were compared with our model calculations. These days represent quiet time E region for solar minimum (15 January 1985, FS=74.7 ), middle (10 November 1988, FS=175.3 ), and high solar activity (5 February 1992, FS=207 ) conditions, FS being a three-month average of F10.7.
Calculations with cross sections by Fennelly and Torr  and Titheridge  (Figure 1, middle panel) give the results that are very close to our standard model calculations (Figure 1, top), although our approach of taking into account the secondary ionization effects according to Ivanov-Kholodny and Nikol'sky  is much simpler than the Titheridge  approach. The 50-100 Å flux increased by four times shifts hmE to higher altitudes as in Figure 1 (top), and the valley is not developed in this case. Contrary, the Ne(h) profile calculated with Te/Tn=2.5 demonstrates a well pronounced valley.
Similar results are obtained for moderate solar activity (Figure 2). Although a factor of 4 for the 50-100 Å flux provides the observed Ne around 110 km, the Ne(h) profile is uplifted as a whole and the valley is not well developed with the Fennelly, Torr, and Titheridge cross sections (Figure 2, middle panel). Calculations with Te/Tn=2.5 look more realistic with both sets of cross sections (Figure 2, top and middle boxes). The [NO+ ] ions dominate over [O2+ ] in the 100-120 km height range in agreement with the Danilov and Smirnova model.
General conclusions concerning the results for solar minimum (Figure 3) are the same as above. The only difference is that a factor of 4 for the 50-100 Å flux is not sufficient to get the observed Ne around 110 km, while a factor of 2.5 for Te/Tn may be too high and should be decreased. Such a decrease of Te/Tn ratio does take place at low solar activity [Duhau and Azpiazu, 1985]. It should be stressed that the Danilov and Smirnova  model does not show any relative ion composition variations around 110 km (cf. Figures 1, 2, and 3, bottom panels) in the course of solar cycle (around 55% for NO+/Ne and 45% for O2+/Ne). This implies corresponding small [NO] variations with solar activity in the E -layer maximum (see below).
There are two ways to overcome the problem with low calculated NmE: either to increase the photoionization rate in the E -layer peak or to reduce the recombination rate of NO +, which is the major ion in the E region.
Let us consider the first possibility. For the classic daytime Chapman E layer, the photoionization rate in its peak may be written as
To increase q max, one may increase I (the ionization flux) or decrease H (the scale height of the ionized atmospheric neutral species). In their earlier monograph Ivanov-Kholodny and Nusinov  proposed considering strong seasonal variations of molecular oxygen scale height in the E region with small winter H(O2 ) values. Along with this they used low a( NO+ ) by Mul and McGowan . This approach allowed them to explain many morphological features of the E layer. Unfortunately low winter H(O2 ) results in lower winter hmE as compared to the summer one. On one hand, this contradicts the incoherent scatter observations made in Kharkov (49.43o N, 36.92oE) and presented in the monograph by Antonova et al. , where winter hmE values are higher than summer ones. On the other hand, according to MSIS 86 thermospheric model [Hedin, 1987], the concentration of the major neutral (O2, N2, O) species is higher in winter at the midlatitude E region, and this should result in higher winter hmE values.
The other possibility is to increase I in (2). The ionization rate should be doubled at the E -layer peak if the Nusinov  EUV model is used (Figures 1, 2, and 3, Te=Tn ). This cannot be done for two UV lines with l=977 Å (CIII) and 1026 Å (Lyman- b ), producing the main ionization in the E region as the present day accuracy of measurements in the UV range of spectrum is high enough [Woods et al., 1998]. On the other hand there is large uncertainty with EUV fluxes for l< 150 Å. Initial fluxes have been tripled for the l = 50-150 Å interval in the EUVAC model [Richards et al., 1994], but an additional increase up to a factor of 4 is required to get the experimental NmE values [Titheridge, 1997]. The same increase of the fluxes with l = 50-100 Å by a factor of 4 is needed for the Nusinov model to obtain the observed NmE (Figures 1, 2, and 3). Such an increase of the soft X-ray radiation changes (in favor of X rays) the proportion between UV and X-ray contributions to the E -layer ionization rate. According to Titheridge , about 66% of the E -region ionization is produced by radiation with l< 150 Å. The X-ray contribution will be even larger if one uses the required factor of 4 for this wavelength interval in the EUVAC model. In case of the Nusinov EUV model, such an increase by a factor of 4 would give a 55% X-ray contribution to the total ionization rate at 110 km. It is possible to show that such an increase of the X ray contribution to the E -layer ionization rate leads to a contradiction with ionospheric observations.
One of the ways to estimate the X-ray contribution to the E -layer total ionization rate is to analyze NmE variations during solar flares [Ivanov-Kholodny et al., 1976, 1977]. According to rocket and satellite observations, a strong increase of the X-ray emission takes place in 1-8, 8-20, and 44-60-Å spectrum intervals during solar flares while only small changes of the UV radiation were observed [Chubb et al., 1957]. Therefore, we may suppose for our estimates that the UV ionization rate does not change during solar flares. The Ix flux in the 8-165 Å spectrum range, which ionizes the E region, is related to the 8-20 Å flux as Ix (I8-20)0.5 [Ivanov-Kholodny et al., 1976]. Regular observations of X-ray emission in the ionization chambers on board satellites are available and published in Solar Geophysical Data. For strong flares analyzed by Ivanov-Kholodny et al. , the I8-20 emission measured on board the SOLRAD 9 and 10 satellites increased by five to 25 times. Therefore, for our estimates we may take an average factor of 3.6 for the Ix increase during the flare events considered. Then the proposed increase by a factor of 4 of the X-ray emission with a 55-66% (mean 60%) X-ray contribution to the total E -layer ionization rate results in
where q0 and qf are the total E -layer ionization rate for quiet and flare conditions, respectively, and FacIx = 3.6 is an average X-ray emission increase. Therefore, we get qf = 2.56q0. On the other hand, the observed NmE variations for the flares considered [Ivanov-Kholodny et al., 1977] give, on the average, qf= (1.44- 1.60)q0 with a lower value for winter and a larger one for summer periods. This is much less than a factor of 2.56 obtained for the fourfold increase in X-ray emission required to get the observed NmE in model calculations. Thus this proposal should be ruled out. The observed qf = (1.44 - 1.60)q0 implies only a 17-23% X-ray contribution to the total E -region ionization rate. X-ray relative contribution of 18% was obtained by Ivanov-Kholodny and Nusinov  for moderate solar activity. The EUV model by Nusinov provides the required X-ray relative contribution while the EUVAC model strongly overestimates it (see Table 1 for the 50-100 Å bin) not to mention an additional increase of the flux in this wavelength bin proposed by Titheridge . Therefore, there is no way to solve the problem of low calculated NmE by a photoionization rate increase. It should be mentioned that according to recent soft X-ray measurements (20-100 Å) on board the Student Nitric Oxide Explorer (SNOE) satellite [Bailey et al., 1999], the extrapolation of the measured irradiance to the solar minimum gives much lower values than the EUVAC predictions.
Let us consider the other possibility -- a decrease of a( NO+). The NmE observations can be well reproduced in our calculations if Te > Tn is accepted in the daytime E region in agreement with the probe measurements [Duhau and Azpiazu, 1985]. A moderate Te/Tn=2.5 ratio is required at the E -layer peak (around 110 km) with a conventional a( NO+)=4.5 10-7 (300/Te)0.83 to obtain the observed NmE (Figures 1, 2, and 3). The required Te/Tn ratio may be even 1.5 if a small a( NO+) = 2.3 10-7 (300/Te)0.5 rate coefficient given by Mul and McGowan  is used (Figure 4). Unlike Duhau and Azpiazu , who found strong dependence of Te/Tn ratio on solar activity, practically an unchanged Te/Tn is required in our calculations at all levels of solar activity. Physical mechanism of such Te heating at middle latitudes is not clear yet [Duhau and Azpiazu, 1985]. It should be mentioned that no difference between Te and Ti (which coincides with Tn in the midlatitude E region) is observed by the incoherent scatter method at middle latitudes. Such Te enhancement over Ti due to the relative electron-ion drift takes place in the auroral zone, according to the EISCAT observations [Igarashi and Schlegel, 1987]. Nevertheless, a possibility of Te being higher Tn seems very promising in solving the problem of low calculated q/a eff for the daytime E layer.
Our calculations (Figures 1, 2, and 3, top panels) reproduce a reasonable depth of the E-F1 valley. According to the IRI 90 model [Bilitza, 1990], the valley depth ( N val/NmE ) is 10-12% for the conditions in question. The valley depth of 13-15% is given by the empirical models [Chasovitin et al., 1983; Fatkullin et al., 1981]. Kharkov incoherent scatter observations [Tkachev, 1981] give the depth of the noon valley as 12-18%. The calculated Ne(h) profiles (Figures 1, 2, and 3, top panels, Te=2.5Tn ) have the valley depth of 10-15%. The profiles calculated with FacX=4 for the 50-100 Å wavelength interval show an undeveloped valley. Normal valley with a depth of 10-13% is provided by the Mul and McGowan [1979, (Figure 4)] calculations with Te=1.5Tn, FacX=1 , and a( NO+). Close results are obtained with the Fennelly and Torr  and Titheridge  cross sections (Figures 1, 2, and 3, middle panels). Therefore, a proper EUV spectrum is more important for development of a normal valley than different sets of cross sections used in calculations.
Problems with calculated NO+/ O2+ ratio [Buonsanto et al., 1995; Titheridge, 1997], which contradicts rocket measurements in the E region, mostly is related with a correct specification of the [NO] distribution. In our approach we make a self-consistent [NO] fitting to get NO+/Ne and O2+/Ne ratios as in the Danilov and Smirnova  model, which is based on rocket observations. The calculated [NO] profiles (Figure 5) demonstrate small variations with solar activity, the [NO] peak density at 107 km being larger only by 40% at high solar activity. This is much less than solar cycle variations (4-5 times for winter) used by Titheridge  in his analysis. The other difference is in the NO peak density which is lower in his model by 10-2.5 times when we pass from low to high solar activity. On the other hand, a theoretical model by Gerard et al.  gives the NO peak values, which are much closer to our results. Close NO values were observed by SNOE satellite at geomagnetic latitudes of Millstone Hill for a quiet ( Ap=12 ) day following a period of moderate disturbance with Ap=28 [Solomon et al., 1999]. However, it should be stressed that the obtained [NO] solar cycle variation is an estimate based on the model [Danilov and Smirnova, 1995] ion composition, which demonstrates very small solar activity variation in the E region.
The effective scale height inferred at 115 km from the calculated [NO] distribution is about 8-12 km, depending on the calculation mode. This is close to H( NO)=8- 9 km used by Titheridge [1997, and references therein], but unlike his dependence on solar activity there is a tendency for H( NO ) to be less at solar maximum (Figure 5, top and middle panels). Similar dependence of H (NO) at 120 km on solar activity may be found in Gerard et al. .
The main results of our analysis are the following:
1. The observed at Millstone Hill daytime NmE may be reproduced in model calculations provided that the 50-100 Å flux is increased by a factor of 4 in the Nusinov  EUV model. The same increase is required in case of the EUVAC model as was proposed by Titheridge . But such an increase distorts the proportion between UV and X-ray contributions in favor of X ray (around 60%) to the total photoionization rate in the E region. This leads to a contradiction with NmE observations during solar flares. As was shown by Ivanov-Kholodny and Nusinov , the X-ray contribution to the E -layer total ionization rate for quiet conditions is around 20%, depending on solar activity; our analysis gives a similar estimate. The EUV model by Nusinov  provides this contribution while the EUVAC model (where the 50-150 Å flux was tripled) does not. Therefore, a proposal to obtain the observed NmE values in model calculations through an X-ray emission increase should be ruled out.
2. The other way to obtain the observed NmE is to reduce a( NO+ ). One of the ways to do this is to take into account Te >Tn in the E region as it follows from the probe measurements [Duhau and Azpiazu, 1985]. A moderate Te/Tn=2.5 ratio at the E -layer peak (around 110 km) along with a conventional a( NO+) and the Nusinov EUV model is required to get the observed daytime NmE values at different levels of solar activity. The same results may be obtained with even lower Te/Tn=1.5 ratio and a( NO+ ) by Mul and McGowan . Both calculations reproduce a reasonable depth of the E-F1 valley with N val/NmE = 10-15% close to the empirical ionospheric models. But the reality of Te > Tn in the midlatitude daytime E region is questionable because the probe results are not confirmed by incoherent scatter observations.
3. The E -layer ion composition with [NO +] > [ O2+ ] corresponding to the rocket observations can be reproduced in model calculations using an appropriate [NO] height distribution. These [NO] profiles may be obtained by fitting the calculated ion composition in the 100-120 km height range to the model based on rocket measurements. The calculated [NO] is a Chapman type layer with a peak around 107 km and a scale height of 8-12 km inferred at 115 km. The [NO] peak density varies with solar activity being larger by 40% at F10.7=207 compared to solar minimum ( F10.7=75) conditions. The obtained [NO] solar cycle variation should be considered as an estimate based on model [Danilov and Smirnova, 1995] ion composition variations; the latter show no solar activity variation at the E -layer maximum around 110 km.
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