Time-dependent responses of the neutral mass density to magnetospheric energy inputs into the cusp region in the thermosphere: A high-resolution two-dimensional local modeling

13 Remarkable enhancements of the thermospheric mass density around the 400-km altitude 14 in the cusp region have been observed by the CHAllenging Minisatellite Payload 15 (CHAMP) satellite. We employed a high-resolution two-dimensional local model to gain 16 insights into the extent to which the neutral- ion drag process controls the mass density’s 17 enhancements under the energy inputs typical of the cusp. We expressed those energy 18 inputs by quasi-static electric fields and electron precipitation. We compared two cases 19 and calculated the thermospheric dynamics with and without neutral-ion drags. We found 20 that in the more realistic case containing the neutral-ion drag, the calculated mass density 21 enhancement was 10% at most, which is dramatically smaller than the observations by 22 the CHAMP satellite (33% on average). The results also showed that the neutral-ion drag 23 process suppresses Joule heating and neutral mass density enhancements, as well as the 24 chemical reaction process. The discrepancy between our modeling result and the satellite 25 observation suggests the existence of additional energy sources, such as Alfvén waves 26 propagating from the magnetosphere, which play an important role in the cusp’s density 27 enhancement.

where , , , , , and are the angular velocity of the Earth's rotation, the 95 neutral mass density, the neutral pressure, the neutral-ion collision frequency, the 96 gravitational acceleration, and the dynamic viscosity, respectively. 97 Considering adiabatic expansion, heat conduction, and external heating, the energy 98 equation of neutrals is given by 99 where , , , , and are the neutral temperature, the specific gas constant, the 101 specific heat capacity at constant volume, the heat conductivity, and the volumetric 7 heating rate, respectively. In the auroral region, the external heat sources are mainly Joule 103 heating and particle heating. The former is given by 104 where is the Pedersen conductivity. The latter will be described in 2.3. 106 where is the source term by ionization, recombination, and other chemical reactions. 112 This term will be described again in 2.3. 113 Assuming time derivative, advection, Coriolis force, and viscosity to be zero, the 114 momentum equation of ions is 115

Electron precipitation 135
To describe the effects of electron precipitation, we employed Fang et al.'s (2010) 136 empirical model, which derives the altitude profile of the total ionization rate due to 137 electron precipitation. We assumed the differential number flux of precipitating electrons 138 ( ) as a kappa distribution as follows: 139 where 0 is the total energy flux, and 0 is the characteristic energy. The peak altitude 141 of the ionization increases for lower characteristic energies. In the cusp region, the 142 electron precipitation is characterized by "soft" (~100 eV) electrons coming almost 143 directly from the magnetosheath. 144 Another effect of electron precipitation s particle heating. Precipitating electrons collide 145 with neutral molecules and transfer energy. Some energy is lost by dissociation and 146 radiation, and the rest eventually heats the molecules. Using the total ionization rate 147 Oyama's (2006) thermospheric neutral model. We set the x-axis, y-axis, and z-axis to be 155 directed eastwardly, northwardly, and upwardly. All physical quantities were assumed to 10 be uniform in the x-direction. The numerical domain ranged from 0 to 700 km in altitude 157 and from −3,000 to 3,000 km in meridional distance. We separate the domain into cells 158 with a vertical size of Δz = 5 km and a horizontal size of Δy = 10 km. The time step Δt 159 was set to be 1 ms. We employed the CIP (Cubic-Interpolated Pseudoparticle) method 160 ions. The precipitating electron flux 0 and the northward electric field were set to 166 be Gaussian functions as follows: 167 where is the scale width and set to be 200 km as a typical meridional width of the cusp. 169 The peak of electron precipitation is located at the center ( = 0 km). The electric field 170 peak was shifted from the center to the south to maximize the meridional gradient of 171 and, thus, the upward field-aligned current at the center. In this study, we set the peak 172 electric field to be 60 mV m ⁄ . Electron precipitation was imposed with total energy 173 flux of 1.6 mW m 2 ⁄ and characteristic energy 0 of 100 eV, which indicates "soft"

Modeling runs 182
We performed three modeling runs to investigate the contributions of neutral-ion drags to 183 the neutral atmosphere. We calculated with neutral-ion drags in Case 1 and without them 184 in Case 2. Specifically, the collisional term of (2) − ( − ) was dropped in Case 2. 185 All the modeling runs lasted 7,200 s (two hours). 186 187

Comparing the contributions of various ionospheric processes 189
We define fractional density change as , where is the initial neutral mass 190 density, and is the difference of neutral mass density from . Therefore, 191 indicates the relative enhancement of mass density. For instance, = 0.1 means a 192 10% increase from the initial condition. Figure 1 shows the resulting north−south profiles 193 around the center at t = 7,200 s. The right side (positive values) of the horizontal axis is 194 the north. The contour maps in Figure 1a show the fractional density change, and vectors 195 show the neutral flow velocity. Figures 1b and 1c show the neutral temperature change 196 and specific heating rate, respectively. In altitudes of 200 to 400 km, the specific heating 197 rate is maximized, and then neutral air heats, which causes neutral upwelling and mass 198 density enhancements. Figure 1 shows that mass density enhancement, upward neutral 199 velocity, and the specific heating rate of Case 1 are all smaller than those in Case 2. The 200 peak values of mass density changes, neutral temperature changes, and vertical neutral 201 velocity are summarized in Table 1. The peak of mass density is located north from the 202 center in Case 1. When neutral-ion drags are present, the neutral air is pulled into the 203 direction of the E × B drift (westward). After that, the Coriolis force pulls the neutrals 204 northward, causing the large mass density in the northern region. The differences in peak 205 locations between the electric field and electron precipitation also cause weak 206 asymmetry. 207 Figure 2 shows the neutral atmosphere profiles at the 400-km altitude. Figures 2a, 2b, 2c,  208 and 2d show the mass density enhancements, temperature changes, northward velocity, 209 and upward velocity. Similar to Figure 1, the three neutral parameters in Case 1 are all 210 13 smaller than those in Case 2. The mass density in the north in Case 1 is larger than that in 211 the south. Figure 2c shows that the Coriolis force suppresses the southward flow in the 212 south region in Case 1. The peak values of the mass density changes at the 400-km 213 altitude are 9.5% in Case 1 and 12.1% in Case 2. Considering that CHAMP's mean mass 214 density enhancements are 33% (Kervalishvili and Lühr 2013), as mentioned above, the 215 peak values in our results are smaller than the observations. This will be discussed in 216 At present, we make a simple estimation of Alfvénic power to reproduce the observations. 283 Oscillating electric fields, on average, result in no horizontal ion motion. Thus, we can 284 estimate the average horizontal ion velocity ⊥ ′ as follows: 285 We used ⊥ ′ to calculate (2) and (5), but original ⊥ was used in (10). Additionally, 287 the electric field peak was placed simply at the center rather than (13) in-depth discussion, it is essential to precisely calculate the height profile of Alfvénic 295 heating, which will be explored in our future works. 296 297

Summary 298
We used a high-resolution numerical model to investigate the neutral mass density's 299 time-dependent responses to magnetospheric energy inputs into the cusp region. 300 Contributions of neutral-ion drags were compared using two cases with and without 301 neutral-ion drags. Neutral-ion drag forces decrease velocity differences between neutrals 302 and ions. Chemical reactions reduce ions at F layer altitudes in response to neutral 303 upwelling. Both two processes suppress the Joule heating rate and mass density 304 enhancements. The mass density enhancement in the calculation containing the 305 neutral-ion drag process is 10% at most, which is remarkably smaller than the 306 observations by the CHAMP satellite (33% on average). This non-negligible discrepancy 307 indicates additional energy sources such as Alfvén waves propagating from the 308 magnetosphere, which play an important role in the cusp's density enhancement. Preparing tables 473 Table 1 The resulting mass density enhancements, neutral temperature change, and 474 vertical neutral velocity 475 Figure 1 The resulting north−south pro les of the fractional density change and neutral velocity (top), neutral temperature change (middle), and speci c heating rate (bottom) in each case. In the top, the contour maps show the fractional density change, and vectors show the neutral ow velocity. The right side (positive values) of the horizontal axis is the north. The peak of electron precipitation is located at the horizontal center.

Figure 2
The resulting pro les of the fractional density change (top), neutral temperature change (middle top), northward neutral velocity (middle bottom), and vertical neutral velocity (bottom) at the 400-km altitude in each case. Positive distance is directed to the northward. The peak of electron precipitation is located at the center.

Figure 3
The time evolution of the fractional density change (top) and volumetric heating rate (bottom) at the 400km altitude in each case.

Figure 4
The resulting pro les of the ion density (left), speci c heating rate (middle left), ion temperature (middle right), and vertical ion velocity (right) at 40 min (top) and 120 min (bottom) intervals in each case.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. table1.xls