Neutral Gas Velocity Research Articles

A comprehensive hydrodynamical study of SB DEM L50: understanding off-centre SNe and soft X-ray luminosity

ABSTRACT The superbubbles (SBs) carved in the interstellar medium by stellar winds and supernovae (SNe) are filled with hot (T > 106 K) gas that produces soft X-ray emission (0.3–2.0 keV). Models that assume a constant density medium and central SNe events fail to reproduce the soft X-ray luminosity that is observed in some SBs. We address this problem by generating models that trace the history of SNe in the SB, and produce off-centre SNe, and account for the missing soft X-ray emission. We test the models against archival, radio, optical, and X-ray observations of the SB DEM L50 located in the Large Magellanic Cloud. The soft X-ray properties of DEM L50, including its high luminosity, make it a perfect candidate to test our models. Furthermore, the multiple wave-band observations of this object will help us assess how well our models can reproduce other SB properties beside its soft X-ray properties. We find that a configuration where DEM L50 forms at the edge of a filament reproduces the observed soft X-ray luminosity, optical morphology, shell velocity, and swept-up mass of neutral gas. This configuration is supported by IR observations of the LMC. In addition, we find that off-centre SNe, which enhance soft X-ray emission, naturally occur for all of the initial ambient conditions we tested in our models. Finally, we show that an off-centre SN can explains the observed soft X-ray luminosity of DEM L50, and that the resulting luminosity is consistent with a plasma in non-equilibrium ionization.

Change of plasma propagation state due to force balance with collision

The main findings of this study are that the plasma propagation state changes with the force equilibrium relationship between the driving force due to the electromagnetic field and neutral gas flow. The plasma propagation transitions from a continuous state to a discontinuous state when plasma emission light intensity changes. The plasma emission light intensity changes suddenly as the applied voltage frequency varies. The frequency at which plasma emission light changes is inversely proportional to the dynamic pressure with the flow velocity of neutral gas. The plasma with strong light emission at high frequency propagates continuously, while that with weak light emission at low frequency propagates discontinuously. Because the plasma current with strong light emission is larger than that with weak light emission, the plasma charge quantity—the amount of plasma generated—increases. Consequently, when the plasma quantity is enough to exist continuously as a group, the plasma group propagates in space with time variations like a stationary wave. However, when the plasma quantity is inadequate to exist continuously, the plasma group propagates through the space discontinuously like a bullet state.

Neutral Gas Properties and Lyα Escape in Extreme Green Pea Galaxies∗

Abstract Mechanisms regulating the escape of Lyα photons and ionizing radiation remain poorly understood. To study these processes, we analyze Very Large Array 21 cm observations of one Green Pea (GP), J160810+352809 (hereafter J1608), and Hubble Space Telescope Cosmic Origins Spectrograph (COS) spectra of 17 GP galaxies at . All are highly ionized: J1608 has the highest [O iii] λ5007/[O ii] λ3727 for star-forming galaxies in Sloan Digital Sky Survey, and the 17 GPs have [O iii]/[O ii] ≥ 6.6. We set an upper limit on J1608's H i mass of , near or below average compared to similar-mass dwarf galaxies. In the COS sample, eight GPs show Lyα absorption components, six of which also have Lyα emission. The H i column densities derived from Lyα absorption are high, cm−2 = 19–21, well above the LyC optically thick limit. Using low-ionization absorption lines, we measure covering fractions ( ) of 0.1–1 and find that strongly anticorrelates with Lyα escape fraction. Low covering fractions may facilitate Lyα and LyC escape through dense neutral regions. GPs with all have low neutral gas velocities, while GPs with lower have a larger range of velocities. Conventional mechanical feedback may help establish low in some cases, whereas other processes may be important for GPs with low velocities. Finally, we compare with proposed indicators of LyC escape. Ionizing photon escape likely depends on a combination of neutral gas geometry and kinematics, complicating the use of emission-line diagnostics for identifying LyC emitters.

Effect of magnetic field directionality on discharging characteristics of Hall effect thruster with azimuthal diversion rail

The structure of an azimuthal diversion rail causes the neutral gas in the Hall effect thruster to possess a certain circumferential velocity. Two different directions of the magnetic field can be formed in the discharge channel, where the direction of the magnetic field depends on the direction of the excitation current. The aim of this work is to study the effect of magnetic field directionality on the discharging characteristics of a Hall effect thruster with an azimuthal diversion rail. The experimental results demonstrate that a change in the magnetic field direction corresponds to a change in the electronic Hall drift direction. When the electronic Hall drift direction is opposite to the circumferential velocity of the neutral gas, its thrust, specific impulse, and efficiency are higher than the case in which the electronic Hall drift direction is in the same direction as that of the circumferential velocity of neutral gas. The increase in performances is due to the increase in the propellant utilization. The reasons for the increase in the propellant utilization are explained. The experimental result provides a guide for the selection of the direction of excitation current of the Hall effect thruster with an azimuthal diversion rail.

Effect of azimuthal diversion rail location on the performance of Hall thrusters

It is commonly accepted that high neutral density or low bulk axial velocity will efficiently enhance ionization. At present, all the operation of neutral gas flow inside the Hall thruster is an attempt to reduce axial velocity of neutral gas and extend residence time. Based on the idea, we proposed the azimuthal diversion rail (ADR) Hall thruster for the first time in preliminary work, and provided a kind of brand new method to reduce axial velocity of neutral gas. Compared to other modes, such kind of mode features simple structure, light weight and significant effect, in which axial movement is transformed to circumferential movement through elastic collision, thus the residence time and neutral density in the channel can be increased, ionization degree and discharge performance are improved accordingly. However, we found in the ADR research process made at later stage, the location of ADR in the discharge channel exerts significant impact on discharge. Therefore, this paper studies the effect of the ADR location on the discharge performance of Hall thrusters. The location of the ADR can affect the distribution of the propellant density in the channel of the Hall thruster, thereby affecting the propellant utilization and performance. The thrust, specific impulse, efficiency and propellant utilization of the ADR are measured in three different locations in the channel, respectively. The propellant density in the ionization zone is higher when the ADR is flush with the anode top surface. Furthermore, the propellant utilization can be increased by 12% and 9% compared with that at the bottom and the middle of the anode, respectively, resulting in the thrust being increased by up to 3.2 mN (10%) and 2 mN (8.5%) and the anode efficiency being increased by up to 9% and 6%. The location of the ADR has a significant effect on the performance of the thruster. The sensible placement of the rail can effectively increase the propellant density in the ionization zone to improve the performance. The results of the study can be used to guide the design of Hall thrusters with ADR.

Scaling Relations of Starburst-driven Galactic Winds

Abstract Using synthetic absorption lines generated from 3D hydrodynamical simulations, we explore how the velocity of a starburst-driven galactic wind correlates with the star formation rate (SFR) and SFR density. We find strong correlations for neutral and low ionized gas, but no correlation for highly ionized gas. The correlations for neutral and low ionized gas only hold for SFRs below a critical limit set by the mass loading of the starburst, above which point the scaling relations flatten abruptly. Below this point the scaling relations depend on the temperature regime being probed by the absorption line, not on the mass loading. The exact scaling relation depends on whether the maximum or mean velocity of the absorption line is used. We find that the outflow velocity of neutral gas can be up to five times lower than the average velocity of ionized gas, with the velocity difference increasing for higher ionization states. Furthermore, the velocity difference depends on both the SFR and mass loading of the starburst. Thus, absorption lines of neutral or low ionized gas cannot easily be used as a proxy for the outflow velocity of the hot gas.

Neutral gas outflows in nearby [U]LIRGs via optical NaD feature

We studied the properties of the neutral gas in a sample of 38 local [U]LIRGs, which mainly covers the less explored LIRG luminosity range. This study is based on the analysis of the spatially integrated and spatially resolved spectra of the NaD feature obtained with the VIMOS/VLT-IFS. Analyzing spatially integrated spectra, we find that the contribution of stars to the observed NaD-EWs is generally small (<35%), and therefore this feature is dominated by ISM absorption. After subtracting the stellar contribution, we find that the pure-ISM integrated spectra generally show blueshifted NaD profiles, indicating neutral gas outflow velocities V in the range 65-260 km/s. Excluding galaxies with AGNs, V shows a dependency with the SFR of the type V \propto SFR^0.15 (in rather good agreement with previous results). The spatially resolved analysis was performed for 40 galaxies, 22 of which have neutral gas velocity fields dominated by noncircular motions with signatures of cone-like winds. However, a modest number of targets (11/40) show disk rotation. We found that the wind masses are in the range (0.4-7.5)x10^8 Msun, reaching up to 3% of the dynamical mass of the host. The mass rates are typically only 0.2-0.4 times the SFR indicating that, the mass loss is too small to slow down the SF significantly. In the majority of cases, the velocity of the outflowing gas is not sufficient to escape the host potential well and, therefore, most of the gas rains back into the disk. On average V/v(esc) is higher in less massive galaxies, confirming that the galaxy mass has a primary role in shaping the recycling of gas and metals. The comparison between the wind power and kinetic power of the starburst associated with SNe indicates that the starburst could drive the outflows in nearly all the [U]LIRGs galaxies, as the wind power is generally lower than 20% of the kinetic power supplied by the starburst.

The low-mass end of the neutral gas mass and velocity width functions of galaxies in ΛCDM

We use the high-resolution Aquarius cosmological dark matter simulations coupled to the semi-analytic model by Starkenburg et al. (2013) to study the HI content and velocity width properties of field galaxies at the low mass end in the context of $\Lambda$CDM. We compare our predictions to the observed ALFALFA survey HI mass and velocity width functions, and find very good agreement without fine-tuning, when considering central galaxies. Furthermore, the properties of the dark matter halos hosting galaxies, characterised by their peak velocity and circular velocity at 2 radial disk scalelengths overlap perfectly with the inferred values from observations. This suggests that our galaxies are placed in the right dark matter halos, and consequently at face value, we do not find any discrepancy with the predictions from the $\Lambda$CDM model. Our analysis indicates that previous tensions, apparent when using abundance matching models, arise because this technique cannot be straightforwardly applied for objects with masses $M_{vir} < 10^{10} M_{\odot}$.

Magnetic field generation in Galactic molecular clouds

We investigate the magnetic field which is generated by turbulent motions of a weakly ionized gas. Galactic molecular clouds give us an example of such a medium. As in the Kazantsev-Kraichnan model we assume a medium to be homogeneous and a neutral gas velocity field to be isotropic and delta-correlated in time. We take into consideration the presence of a mean magnetic field, which defines a preferred direction in space and eliminates isotropy of magnetic field correlators. Evolution equations for the anisotropic correlation function are derived. Isotropic cases with zero mean magnetic field as well as with small mean magnetic field are investigated. It is shown that stationary bounded solutions exist only in the presence of the mean magnetic field for the Kolmogorov neutral gas turbulence. The dependence of the magnetic field fluctuations amplitude on the mean field is calculated. The stationary anisotropic solution for the magnetic turbulence is also obtained for large values of the mean magnetic field.

General Analytical Solution for the Dispersion Equation of an Ionized Gas in a Constant Background Magnetic Field

Understanding how radio waves propagate in the Earth's upper atmosphere requires a model for the conductivity of an ionized gas. A basic linear model requires the solution of three simultaneous vector equations for v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> , and v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , respectively the ion, electron, and neutral gas velocities. Of these, v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> alone determine the current density. When a uniform background magnetic field is present, some of the coefficients in the equation are cross products, rather than just simple scalars. This article demonstrates that in contrast to the more obvious route of finding an approximate solution or one computed via 9×9 matrices, an algebraic approach leads to a systematic analytical solution of this reasonably complex problem. For example, the dispersion equations for plane electromagnetic waves may be found exactly, and using the effective resistivity requires less effort than the conductivity. In addition, an interesting method of finding v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> /v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> develops out of an equation of the form av <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> + bΩ × v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> = a'v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> + bΩ × v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> .

Neutral gas in Lyman-alpha emitting galaxies Haro 11 and ESO 338-IG04 measured through sodium absorption

Context. The Lyman alpha emission line of galaxies is an important tool for finding galaxies at high redshift, and thus probe the structure of the early universe. However, the resonance nature of the line and its sensitivity to dust and neutral gas is still not fully understood. Aims. We present measurements of the velocity, covering fraction and optical depth of neutral gas in front of two well known local blue compact galaxies that show Lyman alpha in emission: ESO 338-IG 04 and Haro 11. We thus test observationally the hypothesis that Lyman alpha can escape through neutral gas by being Doppler shifted out of resonance. Methods. We present integral field spectroscopy from the GIRAFFE/Argus spectrograph at VLT/FLAMES in Paranal, Chile. The excellent wavelength resolution allows us to accurately measure the velocity of the ionized and neutral gas through the H-alpha emission and Na D absorption, which traces the ionized medium and cold interstellar gas, respectively. We also present independent measurements with the VLT/X-shooter spectrograph which confirm our results. Results. For ESO 338-IG04, we measure no significant shift of neutral gas. The best fit velocity is -15 (16) km/s. For Haro 11, we see an outflow from knot B at 44 (13) km/s and infalling gas towards knot C with 32 (12) km/s. Based on the relative strength of the Na D absorption lines, we estimate low covering fractions of neutral gas (down to 10%) in all three cases. Conclusions. The Na D absorption likely occurs in dense clumps with higher column densities than where the bulk of the Ly-alpha scattering takes place. Still, we find no strong correlation between outflowing neutral gas and a high Lyman alpha escape fraction. The Lyman alpha photons from these two galaxies are therefore likely escaping due to a low column density and/or covering fraction.

Measurement of the plasma and neutral gas flow velocities in a low-pressure hollow-cathode plasma jet sputtering system

We present results from two mutually independent measurements of plasma and neutral gas flow velocities in a plasma jet deposition system. Operation of a hollow-cathode discharge within the plasma jet nozzle in the pulse regime enables the simple use of a classical Langmuir probe for the plasma flow velocity measurement. In this method, we assume that the plasma is generated solely inside the nozzle during the power impulse and we measure the time of flight of the ions along a known distance between the nozzle end and the probe. The plasma velocity at the plasma jet axis is then determined by differentiation of the dependence of the distance covered by ions on time. As the second method the well-known Pitot tube is used for measurement of the neutral gas velocity. By comparison of both methods we have experimentally proved that the neutral gas flow velocity is almost unaffected by the presence of the plasma, i.e. it does not substantially depend on whether the discharge is switched on or off. The results of both methods correspond well; detected differences are qualitatively explained. It is documented that the plasma jet can be operated both in a subsonic and in a supersonic regime. We present the dependences of the plasma and neutral gas flow velocity on the distance from the cathode, on the pressure in the reactor chamber, and on the flow rate of the working gas.

Global modeling of hot O distribution in the upper thermosphere

The existence of hot oxygen (hot O, Oh) in the upper thermosphere is mainly confirmed by optical observations of high-altitude airglow. In the experiments described here, a peak of Oh population was found at an altitude of approximately 550 km with a temperature of about 4000 K. Although it was shown that Oh concentration could reach a value of 1–2% with respect to ambient (cold) O, a realistic global distribution of Oh concentration and temperature has not been established. The presence of non-thermal atoms in the thermosphere leads to variations in the thermo-dynamical regime in the upper atmosphere. The major chemical processes involved in Oh production were taken into account in the time-dependent, Global Self-consistent Model of Thermosphere, Ionosphere and Protonosphere (GSM TIP) of the Earth in order to simulate global distribution of Oh concentration and temperature (Th). Calculations were carried out in the geomagnetic coordinate system for moderate solar, quiet geomagnetic conditions, and winter season. It was shown that the maximum Oh is located at −60° latitude, 300° longitude, and 24 UT. The Th maximum is about 2050 K. This temperature and Oh concentration cause an increase in neutral gas temperature at high thermosphere by ∼100 K during daytime and by ∼70 K during nighttime. Variations in the neutral gas velocity circulation were calculated. The maximum increase in neutral velocity was about 36 m/s, corresponding to Φ = 50°, Λ = 180° in the northern and Φ = −50°, Λ = 270° in the southern hemisphere.

DAMPED LYα ABSORBER KINEMATICS AND OUTFLOWS FROM STARBURST GALAXIES

We present results from a numerical study of the multiphase interstellar medium in sub-Lyman-break galaxy protogalactic clumps. Such clumps are abundant at z=3 and are thought to be a major contributor to damped Ly-alpha absorption. We model the formation of winds from these clumps and show that during star formation episodes they feature outflows with neutral gas velocity widths up to several hundred km/s. Such outflows are consistent with the observed high-velocity dispersion in DLAs. In our models thermal energy feedback from winds and supernovae results in efficient outflows only when cold (~ 300 K), dense (> 100 msun/pc^3) clouds are resolved at grid resolution of 12 pc. At lower 24 pc resolution the first signs of the multiphase medium are spotted; however, at this low resolution thermal injection of feedback energy cannot yet create hot expanding bubbles around star-forming regions -- instead feedback tends to erase high-density peaks and suppress star formation. At 12 pc resolution feedback compresses cold clouds, often without disrupting the ongoing star formation; at the same time a larger fraction of feedback energy is channeled into low-density bubbles and winds. These winds often entrain compact neutral clumps which produce multi-component metal absorption lines.

A new satellite-borne neutral wind instrument for thermospheric diagnostics

The bulk motion of the neutral gas at altitudes between about 200 and 600 km is an important factor in predicting the onset of plasma instabilities that are known to distort and/or disrupt high frequency radio communications. These neutral winds have historically been quite difficult to measure, especially from a moving spacecraft. A new space science instrument called the ram wind sensor has been developed to measure the component of the neutral gas velocity that lies along the orbit track of a satellite in low Earth orbit. Laboratory tests of an engineering model of the instrument have been carried out using a supersonic neutral argon beam, in order to validate the measurement concept. The results show that the technique is viable for measurements of neutral flow velocities in future satellite missions.

Numerical simulation of the global distributions of the horizontal and vertical wind in the middle atmosphere using a given neutral gas temperature field

The mathematical model of the global neutral wind system in the Earth's middle atmosphere is described. The model produces three-dimensional global distributions of the zonal, meridional, and vertical components of the neutral gas velocity and density in the middle atmosphere. The characteristic feature of the model is that the all three components of the neutral gas velocity are obtained by means of a numerical solution of the appropriate momentum equations for a viscous gas. The hydrostatic equation, usually utilized in the global circulation models, is not used in the new model. Another characteristic feature of the model is that the model does not include the internal energy equation for the neutral gas. Instead, the global temperature field is assumed to be a given distribution, i.e. the input parameter of the model, and obtained from one of the existing empirical models. The model is applied in order to investigate the formation of the middle atmosphere circulation, in particular, the large-scale circumpolar vortices.

Integral Field Spectroscopy of the Luminous Infrared Galaxy Arp 299 (IC 694 + NGC 3690)

The luminous infrared galaxy Arp 299 (IC 694 + NGC 3690) is studied using optical integral field spectroscopy obtained with the INTEGRAL system, together with archival Hubble Space Telescope WFPC2 and NICMOS images. The stellar and ionized gas morphology shows λ-dependent variations due to the combined effects of the dust internal extinction and the nature and spatial distribution of the different ionizing sources. The two-dimensional ionization maps have revealed an off-nuclear conical structure of about 4 kpc in length, characterized by high-excitation conditions and a radial gradient in the gas electron density. The apex of this structure coincides with B 1 region of NGC 3690, which in turn presents Seyfert-like ionization, high extinction, and a high velocity dispersion. These results strongly support the hypothesis that B1 is the true nucleus of NGC 3690, where an AGN is located. In the circumnuclear regions H II-like ionization dominates, while LINER-like ionization is found elsewhere. The Hα-emitting sources with ages from 3.3 to 7.2 × 106 yr, have masses of between 6 and 680 × 106 M⊙; and contribute about 45% to the bolometric luminosity (extinction corrected). The ionized (Hα) and neutral (Na D) gas velocity fields show similar structure on scales of several hundred to about 1 kpc, indicating that these gas components are kinematically coupled. The kinematic structure is complex and on scales of about 0.2 kpc does not appear to be dominated by the presence of ordered, rotational motions. The large velocity dispersion measured in NGC 3690 indicates that this galaxy is the most massive of the system. The low velocity amplitude and dispersion of the interface suggest that the ionized gas is slowly rotating or in a close to quiescent phase. © 2006. The American Astronomical Society. All rights reserved.

First simulation results of Titan's atmosphere dynamics with a global 3-D non-hydrostatic circulation model

Abstract. We present the first results of a 3-D General Circulation Model of Titan's atmosphere which differs from traditional models in that the hydrostatic equation is not used and all three components of the neutral gas velocity are obtained from the numerical solution of the Navier-Stokes equation. The current version of our GCM is, however, a simplified version, as it uses a predescribed temperature field in the model region thereby avoiding the complex simulation of radiative transfer based on the energy equation. We present the first simulation results and compare them to the results of existing GCMs and direct wind observations. The wind speeds obtained from our GCM correspond well with data obtained during the Huygens probe descent through Titan's atmosphere. We interpret the most unexpected feature of these data which consist of the presence of a non-monotonicity of the altitude profile of the zonal wind speed between 60 and 75 km.

A high-resolution radio study of neutral gas in the starburst galaxy NGC 520

We present subarcsec angular resolution observations of the neutral gas in the nearby starburst galaxy NGC 520. The central kpc region of NGC 520 contains an area of significantly enhanced star formation. The radio continuum structure of this region resolves into ∼10 continuum components. By comparing the flux densities of the brightest of these components at 1.4 GHz with published 15-GHz data we infer that these components detected at 1.4 and 1.6 GHz are related to the starburst and are most likely to be collections of several supernova remnants within the beam. None of these components is consistent with emission from an active galactic nuclei. Both neutral hydrogen (HI) and hydroxyl (OH) absorption lines are observed against the continuum emission, along with a weak OH maser feature probably related to the star formation activity in this galaxy. Strong H i absorption (N H ∼ 10 2 2 atoms cm - 2 ) traces a velocity gradient of 0.5 km s - 1 pc - 1 across the central kpc of NGC 520. The HI absorption velocity structure is consistent with the velocity gradients observed in both the OH absorption and in CO emission observations. The neutral gas velocity structure observed within the central kpc of NGC 520 is attributed to a kpc-scale ring or disc. It is also noted that the velocity gradients observed for these neutral gas components appear to differ with the velocity gradients observed from optical ionized emission lines. This apparent disagreement is discussed and attributed to the extinction of the optical emission from the actual centre of this source hence implying that optical ionized emission lines are only detected from regions with significantly different radii to those sampled by the observations presented here.

High‐latitude ground‐based observations of the thermospheric ion‐drag time constant

From previous studies, it has been conclusively demonstrated that F‐region thermospheric winds follow, but generally lag behind, the ion drift pattern of magnetospheric convection. Analysis of the ion‐neutral momentum exchange equation shows that ion‐drag and thermal pressure are the major contributors to neutral momentum forcing at F‐region heights with relatively minor effects from coriolis, advection and viscous forces. An ion‐neutral coupling time constant (e‐folding time) has been defined which describes the time taken for the neutral gas velocity to approach the ion velocity after a step change in convection. In this study, F‐region ion drift and neutral winds have been observed by the EISCAT tristatic incoherent scatter facility and a ground‐based Fabry‐Perot interferometer, respectively, from northern Scandinavia. The e‐folding time varies in the range 0.5–6.5 hours, with an average of 1.8 and 3.3 hours for a geomagnetically active and quiet period, respectively, which compares well with previous satellite measurements of 0.5–3.5 hours.