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Ion-neutral coupling in the high-latitude F region Evaluation of ion heating terms from Dynamics Explorer 2

Ion and neutral motions in the high latitude F layer were studied simultaneously during six passes of the Dynamics Explorer 2 spacecraft. The passes were made over the south polar cap in October 1981. An ion energy balance equation was defined to express the exchange of energy between the F layer and other atmospheric constituents. A momentum equation expressed the momentum exchange between the species. An approximate form of the energy balance equation was also formulated. The time constant for ion-neutral collisional momentum transfer significantly affected Joule heating in the F layer. Regions of large velocity disparities and ion temperature enhancements were detected as hot spots. The results indicate that a feedback mechanism may arise in terms of neutral compositional changes and enhanced ionospheric recombination. The approximate equation furnished values for ion heating rates which matched the data.

Killeen, T. L.↗

Understanding the Long-Term Spectral Variability of Cygnus X-1 with Burst and Transient Source Experiment and All-Sky Monitor Observations

We present a comprehensive analysis of all observations of Cyg X-1 by the Compton Gamma Ray Observatory Burst and Transient Source Experiment (BATSE; 20-300 keV) and by the Rossi X-Ray Timing Explorer all-sky monitor (ASM; 1.5-12 keV) until 2002 June, including approximately 1200 days of simultaneous data. We find a number of correlations between fluxes and hardnesses in different energy bands. In the hard (low) spectral state, there is a negative correlation between the ASM 1.5-12 keV flux and the hardness at any energy. In the soft (high) spectral state, the ASM flux is positively correlated with the ASM hardness but uncorrelated with the BATSE hardness. In both spectral states, the BATSE hardness correlates with the flux above 100 keV, while it shows no correlation with the 20-100 keV flux. At the same time, there is clear correlation between the BATSE fluxes below and above 100 keV. In the hard state, most of the variability can be explained by softening the overall spectrum with a pivot at approximately 50 keV. There is also another, independent variability pattern of lower amplitude where the spectral shape does not change when the luminosity changes. In the soft state, the variability is mostly caused by a variable hard (Comptonized) spectral component of a constant shape superposed on a constant soft blackbody component. These variability patterns are in agreement with the dependencies of the rms variability on the photon energy in the two states. We also study in detail recent soft states from late 2000 until 2002. The last of them has lasted thus far for more than 200 days. Their spectra are generally harder in the 1.5-5 keV band and similar or softer in the 3-12 keV band than the spectra of the 1996 soft state, whereas the rms variability is stronger in all the ASM bands. On the other hand, the 1994 soft state transition observed by BATSE appears very similar to the 1996 one. We interpret the variability patterns in terms of theoretical Comptonization models. In the hard state, the variability appears to be driven mostly by changing flux in seed photons Comptonized in a hot thermal plasma cloud with an approximately constant power supply. In the soft state, the variability is consistent with flares of hybrid, thermal/nonthermal, plasma with variable power above a stable cold disk. The spectral and timing differences between the 1996 and 2000-2002 soft states are explained by a decrease of the color disk temperature. Also, on the basis of broadband pointed observations simultaneous with those of the ASM and BATSE, we find the intrinsic bolometric luminosity increases by a factor of approximately 3-4 from the hard state to the soft one, which supports models of the state transition based on a change of the accretion rate.

Zdziarski, Andrzej A.↗

Preliminary design of composite wing-box structures for global damage tolerance

A procedure is presented that incorporates the influence of potential global damage conditions into the design process for minimum-mass wing-box structures. The procedure is based on mathematical-programming optimization techniques. Material-strength, minimum-gage, and panel-buckling constraints are introduced by penalty functions, and Newton's method with approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. A potential global damage condition is represented by a structural model with the damaged components removed. Example minimum-mass designs are obtained that simultaneously satisfy the constraints of the damaged and undamaged configurations of both graphite-epoxy and aluminum wing-box structural models. These examples are designed with and without the influence of potential damage conditions, and results indicate that for equal mass cases the residual strength of a damaged structure is higher when the influence of potential damage is properly included in the design from the outset. Results of these examples also identify the minimum structural mass increase required to increase residual strength levels.

Starnes, J. H., Jr.↗

The Kepler Data Processing Handbook: A Field Guide to Prospecting for Habitable Worlds

The Kepler telescope hurtled into orbit in March 2009, initiating NASA's first mission to discover Earth-size planets orbiting Sun-like stars. Kepler simultaneously collected data for approximately 165,000 target stars at a time over its four-year mission, identifying over 4700 planet candidates, over 2300 confirmed or validated planets, and over 2100 eclipsing binaries. While Kepler was designed to discover exoplanets, the long-term, ultrahigh photometric precision measurements it achieved made it a premier observational facility for stellar astrophysics, especially in the field of asteroseismology, and for variable stars, such as RR Lyrae. The Kepler Science Operations Center (SOC) was developed at NASA Ames Research Center to process the data acquired by Kepler from pixel-level calibrations all the way to identifying transiting planet signatures and subjecting them to a suite of diagnostic tests to establish or break confidence in their planetary nature. Detecting small, rocky planets transiting Sun-like stars presents a variety of daunting challenges, including achieving an unprecedented photometric precision of ~20 ppm on 6.5-hour timescales, and supporting the science operations, management, processing, and repeated reprocessing of the accumulating data stream. A newly revised and expanded version of the Kepler Data Processing Handbook (KDPH) has been released to support the legacy archival products. The KDPH details the theory, design and performance of the algorithms supporting each data processing step. This paper presents an overview of the KDPH and features illustrations of several key algorithms in the Kepler Science Data Processing Pipeline. Kepler was selected as the 10th mission of the Discovery Program. Funding for this mission is provided by NASA, Science Mission Directorate.

high performance computing↗

Final STS-35 Columbia descent BET products and results for LaRC OEX investigations

Final STS-35 'Columbia' descent Best Estimate Trajectory (BET) products have been developed for Langley Research Center (LaRC) Orbiter Experiments (OEX) investigations. Included are the reconstructed inertial trajectory profile; the Extended BET, which combines the inertial data and, in this instance, the National Weather Service atmospheric information obtained via Johnson Space Center; and the Aerodynamic BET. The inertial BET utilized Inertial Measurement Unit 1 (IMU1) dynamic measurements for deterministic propagation during the ENTREE estimation process. The final estimate was based on the considerable ground based C-band tracking coverage available as well as Tracking Data and Relay Satellite System (TDRSS) Doppler data, a unique use of the latter for endo-atmospheric flight determinations. The actual estimate required simultaneous solutions for the spacecraft position and velocity, spacecraft attitude, and six IMU parameters - three gyro biases and three accelerometer scale factor correction terms. The anchor epoch for this analysis was 19,200 Greenwich Mean Time (GMT) seconds which corresponds to an initial Shuttle altitude of approximately 513 kft. The atmospheric data incorporated were evaluated based on Shuttle derived considerations as well as comparisons with other models. The AEROBET was developed based on the Extended BET, the measured spacecraft configuration information, final mass properties, and the final Orbiter preoperation databook. The latter was updated based on aerodynamic consensus incrementals derived by the latest published FAD. The rectified predictions were compared versus the flight computed values and the resultant differences were correlated versus ensemble results for twenty-two previous STS entry flights.

Oakes, Kevin F.↗

Transient nucleate pool boiling in microgravity: Some initial results

Variable gravity provides an opportunity to test the understanding of phenomena which are considered to depend on buoyancy, such as nucleate pool boiling. The active fundamental research in nucleate boiling has sought to determine the mechanisms or physical processes responsible for its high effectiveness, manifested by the high heat flux levels possible with relatively low temperature differences. Earlier research on nucleate pool boiling at high gravity levels under steady conditions demonstrated quantitatively that the heat transfer is degraded as the buoyancy normal to the heater surfaced increases. Correspondingly, it was later shown, qualitatively for short periods of time only, that nucleate boiling heat transfer is enhanced as the buoyancy normal to the heater surface is reduced. It can be deduced that nucleate pool boiling can be sustained as a quasi-steady process provided that some means is available to remove the vapor generated from the immediate vicinity of the heater surface. One of the objectives of the research, the initial results of which are presented here, is to quantify the heat transfer associated with boiling in microgravity. Some quantitative results of nucleate pool boiling in high quality microgravity (a/g approximately 10(exp -5)) of 5s duration, obtained in an evacuated drop tower, are presented here. These experiments were conducted as precursors of longer term space experiments. A transient heating technique is used, in which the heater surface is a transparent gold film sputtered on a qua rtz substrate, simultaneously providing the mean surface temperature from resistance thermometry and viewing of the boiling process both from beneath and across the surface. The measurement of the transient mean heater surface temperature permits the computation, by numerical means, of the transient mean heat transfer coefficient. The preliminary data obtained demonstrates that a quasi-steady boiling process can occur in microgravity if the bulk liquid subcooling is sufficiently high and if the imposed heat flux is sufficiently low. This is attributed to suface tension effects at the liquid-vapor-solid junction causing rewetting to take place, sustaining the nucleate boiling. Otherwise, dryout at the heater surface will occur, as observed.

Merte, Herman, Jr.↗

Clouds in ECMWF's 30 KM Resolution Global Atmospheric Forecast Model (TL639)

Global models of the general circulation of the atmosphere resolve a wide range of length scales, and in particular cloud structures extend from planetary scales to the smallest scales resolvable, now down to 30 km in state-of-the-art models. Even the highest resolution models do not resolve small-scale cloud phenomena seen, for example, in Landsat and other high-resolution satellite images of clouds. Unresolved small-scale disturbances often grow into larger ones through non-linear processes that transfer energy upscale. Understanding upscale cascades is of crucial importance in predicting current weather, and in parameterizing cloud-radiative processes that control long term climate. Several movie animations provide examples of the temporal and spatial variation of cloud fields produced in 4-day runs of the forecast model at the European Centre for Medium-Range Weather Forecasts (ECMWF) in Reading, England, at particular times and locations of simultaneous measurement field campaigns. model resolution is approximately 30 km horizontally (triangular truncation TL639) with 31 vertical levels from surface to stratosphere. Timestep of the model is about 10 minutes, but animation frames are 3 hours apart, at timesteps when the radiation is computed. The animations were prepared from an archive of several 4-day runs at the highest available model resolution, and archived at ECMWF. Cloud, wind and temperature fields in an approximately 1000 km X 1000 km box were retrieved from the archive, then approximately 60 Mb Vis5d files were prepared with the help of Graeme Kelly of ECMWF, and were compressed into MPEG files each less than 3 Mb. We discuss the interaction of clouds and radiation in the model, and compare the variability of cloud liquid as a function of scale to that seen in cloud observations made in intensive field campaigns. Comparison of high-resolution global runs to cloud-resolving models, and to lower resolution climate models is leading to better understanding of the upscale cascade and suggesting new cloud-radiation parameterizations for climate models.

Cahalan, R. F.↗

Radiation Transport of Heliospheric Lyman-alpha from Combined Cassini and Voyager Data Sets

Heliospheric neutral hydrogen scatters solar Lyman-alpha radiation from the Sun with '27-day' intensity modulations observed near Earth due to the Sun's rotation combined with Earth's orbital motion. These modulations are increasingly damped in amplitude at larger distances from the Sun due to multiple scattering in the heliosphere, providing a diagnostic of the interplanetary neutral hydrogen density independent of instrument calibration. This paper presents Cassini data from 2003-2004 obtained downwind near Saturn at approximately 10 AU that at times show undamped '27-day' waves in good agreement with the single-scattering models of Pryor et al., 1992. Simultaneous Voyager 1 data from 2003- 2004 obtained upwind at a distance of 88.8-92.6 AU from the Sun show waves damped by a factor of -0.21. The observed degree of damping is interpreted in terms of Monte Carlo multiple-scattering calculations (e.g., Keller et al., 1981) applied to two heliospheric hydrogen two-shock density distributions (discussed in Gangopadhyay et al., 2006) calculated in the frame of the Baranov-Malama model of the solar wind interaction with the two-component (neutral hydrogen and plasma) interstellar wind (Baranov and Malama 1993, Izmodenov et al., 2001, Baranov and Izmodenov, 2006). We conclude that multiple scattering is definitely occurring in the outer heliosphere. Both models compare favorably to the data, using heliospheric neutral H densities at the termination shock of 0.085 cm(exp -3) and 0.095 cm(exp -3). This work generally agrees with earlier discussions of Voyager data in Quemerais et al., 1996 showing the importance of multiple scattering but is based on Voyager data obtained at larger distances from the Sun (with larger damping) simultaneously with Cassini data obtained closer to the Sun.

Pryor, W.↗

Mitral inertance in humans: critical factor in Doppler estimation of transvalvular pressure gradients

The pressure-velocity relationship across the normal mitral valve is approximated by the Bernoulli equation DeltaP = 1/2 rhoDeltav(2) + M. dv/dt, where DeltaP is the atrioventricular pressure difference, rho is blood density, v is transmitral flow velocity, and M is mitral inertance. Although M is indispensable in assessing transvalvular pressure differences from transmitral flow, this term is poorly understood. We measured intraoperative high-fidelity left atrial and ventricular pressures and simultaneous transmitral flow velocities by using transesophageal echocardiography in 100 beats (8 patients). We computed mean mitral inertance (M) by M = integral((DeltaP)-(1/2 x rho v(2))dt/integral(dv/dt)dt and we assessed the effect of the inertial term on the transmitral pressure-flow relation. ranged from 1.03 to 5.96 g/cm(2) (mean = 3.82 +/- 1.22 g/cm(2)). DeltaP calculated from the simplified Bernoulli equation (DeltaP = 1/2. rhov(2)) lagged behind (44 +/- 11 ms) and underestimated the actual peak pressures (2.3 +/- 1.1 mmHg). correlated with left ventricular systolic pressure (r = -0.68, P < 0.0001) and transmitral pressure gradients (r = 0.65, P < 0.0001). Because mitral inertance causes the velocity to lag significantly behind the actual pressure gradient, it needs to be considered when assessing diastolic filling and the pressure difference across normal mitral valves.

NASA Discipline Cardiopulmonary↗

Monitoring the Black Hole Binary GRS 1758-258 with INTEGRAL and RXTE

The microquasar GRS 1758-258 is one of only three persistent black hole binaries that spend most of their time in the hard spectral state, the other two being Cyg X-l and 1E 1741.7-2942. It therefore provides the rare opportunity for an extensive long term study of this important black hole state which is associated with strong variability and radio jet emission. INTEGRAL has been monitoring the source since the first Galactic Center Deep Exposure season in spring 2003 during two 2-3 months long Galactic Center viewing epochs each year, amounting to 11 epochs including spring of 2008. With the exception of the last epoch quasi-simultaneous RXTE monitoring observations are available as well. Here we present an analysis of the epoch averaged broad band spectra which display considerable long term variability, most notably the occurrence of two soft/off states, extreme examples for the hysteretic behavior of black hole binaries. The hard source spectrum and long exposures allow us to extend the analysis for several epochs to approximately 800 keV using PICsIT data and address the question of the presence of a non-thermal Comptonization component.

Pottschmidt, Katja↗

The X-ray emission of 3C 273 observed with ASCA

We report preliminary results of an Advanced Satellite for Cosmology and Astrophysics (ASCA) observation of 3C 273. There is no spectral variability within the ASCA observation, in contrast to the longer term behavior found with European X-ray Observatory Satellite (EXOSAT) and Ginga which established significant changes in the spectral index of the power-law continuum on timescales of a week or more, uncorrelated with luminosity. Comparison of the ASCA data with a simultaneous Roentgen Satellite (ROSAT) Ginga observation in 1990 December shows that while the shape of the spectrum above approximately 1 keV is essentially the same, the flux in the soft component, below approximately 1 keV, considerably weaker relative to the hard component in the ASCA observation. The 2-10 keV luminosity is at least a factor of approximately 1.5 greater in the ASCA observation than in the ROSAT/Ginga observation while the ratio of 2-10 keV luminosity to 0.4-1.0 keV luminosity increases by a factor of approximately 1.2. Thus the spectral shape of the hard component appears to be independent of the relative magnitude of the soft component and is an important constraint on emission and reprocessing models. We find no significant Fe K line-emission in this observation. The data also highlight very well some of the outstanding problems in the instrumental responses.

Yaqoob, Tahir↗

Adapting Waste Processing for Space Applications

It has been estimated that on a 1-year mission, a four-astronaut crew will produce approximately 2,600 kg of waste materials. The current International Space Station practice for waste management is a stow and jettison model in which the trash is simply ejected. The immediate challenge waste poses for long duration space flight is that it represents unproductive mass. Longer term, waste accumulation on planetary surfaces will also pose challenges. A waste management/disposal solution is greatly needed. Simultaneously, significant research and development efforts are being made to enable in-situ resource extraction and recovery for lunar and Mars surface operations. A waste management solution could free up volume, reduce mass and thereby propellant needs, as well as contribute to resource recovery for spacecraft, and eventually, surface operations. The adaptation of many chemical engineering unit operations to the microgravity environment is critical to achieve this goal. An ideal spacecraft waste treatment system would convert waste into useful gases. It should be largely self-sustaining in that it should have the ability to recycle commodities to avoid imposing mass penalties associated with transporting feedstock on the spacecraft at launch. At NASA KSC, a model of what such a system would look like is being developed. In addition, the team has recently completed a suborbital flight campaign with a combustion reactor to demonstrate rudimentary conversion in a microgravity environment and identify challenges for future design. This presentation will discuss what a full waste treatment system could look like, point out challenges relating to various unit operations involved in such a system, and highlight recent progress in space waste management research and development.

Waste Processing↗

X-ray spectrum and variability of the quasar PG 1211+143

We present preliminary results of an ASCA observation of the classic soft-excess quasar PG 1211+143. The overall ASCA spectrum can be characterized by a blackbody with a temperature of approximately 125 eV (quasar frame) and a power law with photon index of approximately 2. Simultaneous ROSAT data are suggestive of further steepening of the spectrum just below the ASCA band. Comparison with previous observations shows that the soft flux in the 0.1-2 keV band varies by at least a factor of approximately 16, scaling roughly as the square of the hard flux in the 2-10 keV band over a timescale of approximately 13.5 yr. We also find evidence of short-term amplitude variability of up to a factor of approximately 2 on a timescale of approximately 2 x 10(exp 4) sec, in both the soft and hard flux so that the soft and hard photons are likely to originate from the same, compact, region. The data rule out variable absorption (cold or ionized) as the origin of the soft excess, favoring an intrinsic emission component. However, we argue against optically thin emission for the 'blue bump' in PG 1211+143. The large amplitude soft X-ray variability may be indicative of variations in the effective temperature, or peak, of the soft component. There is only marginal evidence for Fe K line emission between 6-7 keV in the quasar frame.

Yaqoob, Tahir↗

A High Frequency Model of Cascade Noise

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

Envia, Edmane↗

Cytoskeletal filament assembly and the control of cell spreading and function by extracellular matrix

This study was undertaken to analyze how cell binding to extracellular matrix produces changes in cell shape. We focused on the initial process of cell spreading that follows cell attachment to matrix and, thus, cell 'shape' changes are defined here in terms of alterations in projected cell areas, as determined by computerized image analysis. Cell spreading kinetics and changes in microtubule and actin microfilament mass were simultaneously quantitated in hepatocytes plated on different extracellular matrix substrata. The initial rate of cell spreading was highly dependent on the matrix coating density and decreased from 740 microns 2/h to 50 microns 2/h as the coating density was lowered from 1000 to 1 ng/cm2. At approximately 4 to 6 hours after plating, this initial rapid spreading rate slowed and became independent of the matrix density regardless of whether laminin, fibronectin, type I collagen or type IV collagen was used for cell attachment. Analysis of F-actin mass revealed that cell adhesion to extracellular matrix resulted in a 20-fold increase in polymerized actin within 30 minutes after plating, before any significant change in cell shape was observed. This was followed by a phase of actin microfilament disassembly which correlated with the most rapid phase of cell extension and ended at about 6 hours; F-actin mass remained relatively constant during the slow matrix-independent spreading phase. Microtubule mass increased more slowly in spreading cells, peaking at 4 hours, the time at which the transition between rapid and slow spreading rates was observed. However, inhibition of this early rise in microtubule mass using either nocodazole or cycloheximide did not prevent this transition. Use of cytochalasin D revealed that microfilament integrity was absolutely required for hepatocyte spreading whereas interference with microtubule assembly (using nocodazole or taxol) or protein synthesis (using cycloheximide) only partially suppressed cell extension. In contrast, cell spreading could be completely inhibited by combining suboptimal doses of cytochalasin D and nocodazole, suggesting that intact microtubules can stabilize cell form when the microfilament lattice is partially compromised. The physiological relevance of the cytoskeleton and cell shape in hepatocyte physiology was highlighted by the finding that a short exposure (6 hour) of cells to nocodazole resulted in production of smaller cells 42 hours later that exhibited enhanced production of a liver-specific product (albumin). These data demonstrate that spreading and flattening of the entire cell body is not driven directly by net polymerization of either microfilaments or microtubules.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Cell Biology↗

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗

Transmission Of Power Via Combined Laser Beams

Laser Diode Array (LDA) appears to be most efficient means of transferring power from Earth to satellites and between satellites, in terms of mass and size, of various laser configurations. To form large-scale-array amplifier (LSAA), element LDA's must generate well-defined diffraction-limited beams. Coherent matching of phases among LDA's enables system to generate good beam pattern in far field over thousands of kilometers. By passing beam from master laser through number of LDA amplifiers simultaneously, one realizes coherence among amplified output beams. LSAA used for transmission of power with efficiency of approximately 80 percent into receiver of moderate size at 5,000 km. Also transmits data at high rates by line-of-sight rather than fiber optics.

Kwon, Jin H.↗

Simultaneous X-ray and optical observations of the flaring X-ray source, Aquila A-1

During the summer of 1978 the recurrent transient X-ray source, Aquila X-1, underwent its first major outburst in two years. The results of extensive observations at X-ray and optical wavelengths throughout this event, which lasted for approximately two months are presented. The peak X-ray luminosity was approximately 1.3 times that of the Crab and exhibited spectral dependent flickering on timescales approximately 5 minutes. The observations are interpreted in terms of a standard accretion disk model withparticular emphasis on the similarities to Sco X-1 and other dward X-ray systems, although the transient nature of the system remains unexplained. It was found that Aquila X-1 can be described adequately by the semi-detached Roche lobe model and yields a mass ratio of less than or approximate to 3.5.

Bowyer, C. S.↗