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NASA NTRS2005

Using Cloud-to-Ground Lightning Climatologies to Initialize Gridded Lightning Threat Forecasts for East Central Florida

Each morning, the forecasters at the National Weather Service in Melbourn, FL (NWS MLB) produce an experimental cloud-to-ground (CG) lightning threat index map for their county warning area (CWA) that is posted to their web site (http://www.srh.weather.gov/mlb/ghwo/lightning.shtml) . Given the hazardous nature of lightning in central Florida, especially during the warm season months of May-September, these maps help users factor the threat of lightning, relative to their location, into their daily plans. The maps are color-coded in five levels from Very Low to Extreme, with threat level definitions based on the probability of lightning occurrence and the expected amount of CG activity. On a day in which thunderstorms are expected, there are typically two or more threat levels depicted spatially across the CWA. The locations of relative lightning threat maxima and minima often depend on the position and orientation of the low-level ridge axis, forecast propagation and interaction of sea/lake/outflow boundaries, expected evolution of moisture and stability fields, and other factors that can influence the spatial distribution of thunderstorms over the CWA. The lightning threat index maps are issued for the 24-hour period beginning at 1200 UTC (0700 AM EST) each day with a grid resolution of 5 km x 5 km. Product preparation is performed on the AWIPS Graphical Forecast Editor (GFE), which is the standard NWS platform for graphical editing. Currently, the forecasters create each map manually, starting with a blank map. To improve efficiency of the forecast process, NWS MLB requested that the Applied Meteorology Unit (AMU) create gridded warm season lightning climatologies that could be used as first-guess inputs to initialize lightning threat index maps. The gridded values requested included CG strike densities and frequency of occurrence stratified by synoptic-scale flow regime. The intent is to increase consistency between forecasters while enabling them to focus on the mesoscale detail of the forecast, ultimately benefiting the end-users of the product. Several studies took place at the Florida State University (FSU) and NWS Tallahassee (TAE) for which they created daily flow regimes using Florida 1200 UTC synoptic soundings and CG strike densities from National Lightning Detection Network (NLDN) data. The densities were created on a 2.5 km x 2.5 km grid for every hour of every day during the warm seasons in the years 1989-2004. The grids encompass an area that includes the entire state of Florida and adjacent Atlantic and Gulf of Mexico waters. Personnel at the two organizations provided this data and supporting software for the work performed by the AMU. The densities were first stratified by flow regime, then by time in 1-, 3-, 6-, 12-, and 24-hour increments while maintaining the 2.5 km x 2.5 km grid resolution. A CG frequency of occurrence was calculated for each stratification and grid box by counting the number of days with lightning and dividing by the total number of days in the data set. New CG strike densities were calculated for each stratification and grid box by summing the strike number values over all warm seasons, then normalized by dividing the summed values by the number of lightning days. This makes the densities conditional on whether lightning occurred. The frequency climatology values will be used by forecasters as proxy inputs for lightning prObability, while the density climatology values will be used for CG amount. In addition to the benefits outlined above, these climatologies will provide improved temporal and spatial resolution, expansion of the lightning threat area to include adjacent coastal waters, and potential to extend the forecast to include the day-2 period. This presentation will describe the lightning threat index map, discuss the work done to create the maps initialized with climatological guidance, and show examples of the climatological CG lightning densities and frequencies of occurren based on flow regime.

Lambert, Winnie↗
NASA NTRS2000

Analysis of Complexity Evolution Management and Human Performance Issues in Commercial Aircraft Automation Systems

Autoflight systems in the current generation of aircraft have been implicated in several recent incidents and accidents. A contributory aspect to these incidents may be the manner in which aircraft transition between differing behaviours or 'modes.' The current state of aircraft automation was investigated and the incremental development of the autoflight system was tracked through a set of aircraft to gain insight into how these systems developed. This process appears to have resulted in a system without a consistent global representation. In order to evaluate and examine autoflight systems, a 'Hybrid Automation Representation' (HAR) was developed. This representation was used to examine several specific problems known to exist in aircraft systems. Cyclomatic complexity is an analysis tool from computer science which counts the number of linearly independent paths through a program graph. This approach was extended to examine autoflight mode transitions modelled with the HAR. A survey was conducted of pilots to identify those autoflight mode transitions which airline pilots find difficult. The transitions identified in this survey were analyzed using cyclomatic complexity to gain insight into the apparent complexity of the autoflight system from the perspective of the pilot. Mode transitions which had been identified as complex by pilots were found to have a high cyclomatic complexity. Further examination was made into a set of specific problems identified in aircraft: the lack of a consistent representation of automation, concern regarding appropriate feedback from the automation, and the implications of physical limitations on the autoflight systems. Mode transitions involved in changing to and leveling at a new altitude were identified across multiple aircraft by numerous pilots. Where possible, evaluation and verification of the behaviour of these autoflight mode transitions was investigated via aircraft-specific high fidelity simulators. Three solution approaches to concerns regarding autoflight systems, and mode transitions in particular, are presented in this thesis. The first is to use training to modify pilot behaviours, or procedures to work around known problems. The second approach is to mitigate problems by enhancing feedback. The third approach is to modify the process by which automation is designed. The Operator Directed Process forces the consideration and creation of an automation model early in the design process for use as the basis of the software specification and training.

Vakil, Sanjay S.↗
NASA NTRS2007

Using Flow Regime Lightning and Sounding Climatologies to Initialize Gridded Lightning Threat Forecasts for East Central Florida

Each morning, the forecasters at the National Weather Service in Melbourne, FL (NWS MLB) produce an experimental cloud-to-ground (CG) lightning threat index map for their county warning area (CWA) that is posted to their web site (httl://www.srh.weather.gov/mlb/ghwo/lightning.shtml) . Given the hazardous nature of lightning in East Central Florida, especially during the warm season months of May September, these maps help users factor the threat of lightning, relative to their location, into their daily plans. The maps are color-coded in five levels from Very Low to Extreme, with threat level definitions based on the probability of lightning occurrence and the expected amount of CG activity. On a day in which thunderstorms are expected, there are typically two or more threat levels depicted spatially across the CWA. The locations of relative lightning threat maxima and minima often depend on the position and orientation of the low-level ridge axis, forecast propagation and interaction of sea/lake/outflow boundaries, expected evolution of moisture and stability fields, and other factors that can influence the spatial distribution of thunderstorms over the CWA. The lightning threat index maps are issued for the 24-hour period beginning at 1200 UTC each day with a grid resolution of 5 km x 5 km. Product preparation is performed on the AWIPS Graphical Forecast Editor (GFE), which is the standard NWS platform for graphical editing. Until recently, the forecasters created each map manually, starting with a blank map. To improve efficiency of the forecast process, NWS MLB requested that the Applied Meteorology Unit (AMU) create gridded warm season lightning climatologies that could be used as first-guess inputs to initialize lightning threat index maps. The gridded values requested included CG strike densities and frequency of occurrence stratified by synoptic-scale flow regime. The intent was to improve consistency between forecasters while allowing them to focus on the mesoscale detail of the forecast. Several studies took place at the Florida State University (FSU) and NWS Tallahassee (TAE) in which they created daily flow regimes using Florida 1200 UTC synoptic soundings and CG strike densities, or number of strikes per specified area. The soundings used to determine the flow regimes were taken at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), FL, and the lightning data for the strike densities came from the National Lightning Detection Network (NLDN). The densities were created on a 2.5 km x 2.5 km grid for every hour of every day during the warm seasons in the years 1989-2004. The grids encompass an area that includes the entire state of Florida and adjacent Atlantic and Gulf of Mexico waters. Personnel at FSU and NWS TAE provided this data and supporting software for the work performed by the AMU.

Lambert, Winifred↗
NASA NTRS2006

Using Flow Regime Lightning and Sounding Climatologies to Initialize Gridded Lightning Threat Forecasts for East Central Florida

Each morning, the forecasters at the National Weather Service in Melbourne, FL (NWS MLB) produce an experimental cloud-to-ground (CG) lightning threat index map for their county warning area (CWA) that is posted to their web site (http://www.srh.weather.gov/mlb/ghwo/lightning.shtml) . Given the hazardous nature of lightning in East Central Florida, especially during the warm season months of May September, these maps help users factor the threat of lightning, relative to their location, into their daily plans. The maps are color-coded in five levels from Very Low to Extreme, with threat level definitions based on the probability of lightning occurrence and the expected amount of CG activity. On a day in which thunderstorms are expected, there are typically two or more threat levels depicted spatially across the CWA. The locations of relative lightning threat maxima and minima often depend on the position and orientation of the low-level ridge axis, forecast propagation and interaction of sea/lake/outflow boundaries, expected evolution of moisture and stability fields, and other factors that can influence the spatial distribution of thunderstorms over the CWA. The lightning threat index maps are issued for the 24-hour period beginning at 1200 UTC each day with a grid resolution of 5 km x 5 km. Product preparation is performed on the AWIPS Graphical Forecast Editor (GFE), which is the standard NWS platform for graphical editing. Currently, the forecasters create each map manually, starting with a blank map. To improve efficiency of the forecast process, NWS MLB requested that the Applied Meteorology Unit (AMU) create gridded warm season lightning climatologies that could be used as first-guess inputs to initialize lightning threat index maps. The gridded values requested included CG strike densities and frequency of occurrence stratified by synoptic-scale flow regime. The intent is to improve consistency between forecasters while allowing them to focus on the mesoscale detail of the forecast, ultimately benefiting the end-users of the product. Several studies took place at the Florida State University (FSU) and NWS Tallahassee (TAE) in which they created daily flow regimes using Florida 1200 UTC synoptic soundings and CG strike densities, or number of strikes per specified area. The soundings used to determine the flow regimes were taken at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), FL, and the lightning data for the strike densities came from the National Lightning Detection Network (NLDN). The densities were created on a 2.5 km x 2.5 km grid for every hour of every day during the warm seasons in the years 1989-2004. The grids encompass an area that includes the entire state of Florida and adjacent Atlantic and Gulf of Mexico waters. Personnel at FSU and NWS TAE provided this data and supporting software for the work performed by the AMU.

Lambert, Winifred↗
NASA NTRS2016

The Impact of New Trends in Satellite Launches on Orbital Debris Environment

The main goal of this study is to examine the impact of new trends in satellite launch activities on the orbital debris environment and collision risk. Starting from the launch of the first artificial satellite in 1957, space borne technology has become an indispensable part of our lives. More than 6,000 satellites have been launched into Earth orbit. Though the annual number of satellites launched stayed flat for many decades, the trend has recently changed. The satellite market has been undergoing a major evolution with new space companies replacing the traditional approach of deploying a few large, complex and costly satellites with an approach to use a multitude of smaller, less complex and cheaper satellites. This new approach creates a sharp increase in the number of satellites and so the historic trends are no longer representative. As a foundation for this study, a scenario for satellite deployments based on the publicly announced future satellite missions has been developed. These constellation-deploying companies include, but are not limited to, Blacksky, CICERO, EROS, Landmapper, Leosat, Northstar, O3b, OmniEarth, OneWeb, Orbcomm, OuterNet, PlanetIQ, Planet Labs, Radarsat, RapidEye Next Generation, Sentinel, Skybox, SpaceX, and Spire. Information such as the annual number of launches, the number of orbital planes to be used by the constellation, as well as apogee, perigee, inclination, spacecraft mass and area were included or approximated. Besides the production of satellites, a widespread ongoing effort to enhance orbital injection capabilities will allow delivery of more spacecraft more accurately into Earth orbits. A long list of companies such as Microcosm, Rocket Lab, Firefly Space Systems, Sierra Nevada Corporation and Arca Space Corporation are developing new launch vehicles dedicated for small satellites. There are other projects which intend to develop interstages with propulsive capabilities which will allow the deployment of satellites into their desired orbits beyond the restrictions of the launch vehicle used. These near future orbital injection technologies are also covered in the developed scenario. Using the above-mentioned background information, this study aims to examine how the orbital debris environment will be affected from the new dynamics of the emerging space markets. We developed a simulation tool that is capable of propagating the objects in a given deployment scenario with variable-sized time-steps as small as one second. Over the course of the run, the software also detects collisions; additional debris objects are then created according to the NASA breakup model and are fed back into the simulation framework. Examining the simulation results, the total number of particles to accumulate in different orbits can be monitored and the number of conjunctions can be tracked to assess the collision risks. The simulation makes it possible to follow the short- and long-term effects of a particular satellite or constellation on the space environment. Likewise, the effects of changes in the debris environment on a particular satellite or constellation can be evaluated. It is authors hope that the results of this paper and further utilization of the developed simulation tool will assist in the investigation of more accurate deorbiting metrics to replace the generic 25-year disposal guidelines, as well as to guide future launches toward more sustainable and safe orbits.

New Space↗
NASA NTRS2012

Science Benefits of Onboard Spacecraft Navigation

Primitive bodies (asteroids and comets), which have remained relatively unaltered since their formation, are important targets for scientific missions that seek to understand the evolution of the solar system. Often the first step is to fly by these bodies with robotic spacecraft. The key to maximizing data returns from these flybys is to determine the spacecraft trajectory relative to the target body-in short, navigate the spacecraft- with sufficient accuracy so that the target is guaranteed to be in the instruments' field of view. The most powerful navigation data in these scenarios are images taken by the spacecraft of the target against a known star field (onboard astrometry). Traditionally, the relative trajectory of the spacecraft must be estimated hours to days in advance using images collected by the spacecraft. This is because of (1)!the long round-trip light times between the spacecraft and the Earth and (2)!the time needed to downlink and process navigation data on the ground, make decisions based on the result, and build and uplink instrument pointing sequences from the results. The light time and processing time compromise navigation accuracy considerably, because there is not enough time to use more accurate data collected closer to the target-such data are more accurate because the angular capability of the onboard astrometry is essentially constant as the distance to the target decreases, resulting in better "plane-of- sky" knowledge of the target. Excellent examples of these timing limitations are high-speed comet encounters. Comets are difficult to observe up close; their orbits often limit scientists to brief, rapid flybys, and their coma further restricts viewers from seeing the nucleus in any detail, unless they can view the nucleus at close range. Comet nuclei details are typically discernable for much shorter durations than the roundtrip light time to Earth, so robotic spacecraft must be able to perform onboard navigation. This onboard navigation can be accomplished through a self- contained system that by eliminating light time restrictions dramatically improves the relative trajectory knowledge and control and subsequently increases the amount of quality data collected. Flybys are one-time events, so the system's underlying algorithms and software must be extremely robust. The autonomous software must also be able to cope with the unknown size, shape, and orientation of the previously unseen comet nucleus. Furthermore, algorithms must be reliable in the presence of imperfections and/or damage to onboard cameras accrued after many years of deep-space operations. The AutoNav operational flight software packages, developed by scientists at the Jet Propulsion Laboratory (JPL) under contract with NASA, meet all these requirements. They have been directly responsible for the successful encounters on all of NASA's close-up comet-imaging missions (see Figure !1). AutoNav is the only system to date that has autonomously tracked comet nuclei during encounters and performed autonomous interplanetary navigation. AutoNav has enabled five cometary flyby missions (Table!1) residing on four NASA spacecraft provided by three different spacecraft builders. Using this software, missions were able to process a combined total of nearly 1000 images previously unseen by humans. By eliminating the need to navigate spacecraft from Earth, the accuracy gained by AutoNav during flybys compared to ground-based navigation is about 1!order of magnitude in targeting and 2!orders of magnitude in time of flight. These benefits ensure that pointing errors do not compromise data gathered during flybys. In addition, these benefits can be applied to flybys of other solar system objects, flybys at much slower relative velocities, mosaic imaging campaigns, and other proximity activities (e.g., orbiting, hovering, and descent/ascent).

Autonomy↗
NASA NTRS2016

MarCO: Interplanetary Mission Development on a CubeSat Scale

Shortly after JPL’s Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission launches, separates, and commences its cruise phase, two CubeSats will deploy from the launch vehicle’s upper stage and begin independent flight to Mars (Fig. 1). During InSight’s entry, descent, and landing (EDL) sequence, these twin Mars Cube One (MarCO) spacecraft will fly 3,500 km above the Martian surface, recording and relaying InSight UHF radio data to the Deep Space Network (DSN) on Earth1. MarCO is a twin CubeSat mission developed by the NASA Jet Propulsion Laboratory (JPL) to accompany the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) Mars mission lander. MarCO's primary mission objective is to launch with InSight and independently fly to Mars to serve as a communications relay during InSight's entry, descent, and landing (EDL) phase. MarCO represents a new type of deep space mission: CubeSats at Mars. Building on the development of JPL's first interplanetary CubeSat project, the Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment (INSPIRE), MarCO further refined the approach to hardware, software, and ground architecture development to solve the challenges of quickly building low-budget spacecraft to fly to Mars. The greatest constraint, beyond others typical of CubeSat missions, was time. The duration between MarCO's conception to completion of spacecraft assembly was less than two years - an unprecedented schedule for any planetary mission to date. Through necessity, MarCO has built on previous experience, procedures, systems, and development methodologies, defining a new niche for supporting larger primary missions. The MarCO spacecraft are poised to write a new chapter in deep space exploration. Originally slated to launch and reach Mars in 2016, the InSight mission schedule subsequently slipped to 2018. During the original landing of InSight, Earth would not be in view, and no orbiter around Mars would have been in position to both receive UHF EDL data and simultaneously relay it back to Earth. It was from this obstacle that MarCO was conceived. Regardless of any changes to InSight’s 2018 EDL configuration geometry, MarCO is still expected to fly and serve in the same capacity as originally designed: the first CubeSat mission to Mars. CubeSats have historically been firmly in the domain of universities and small companies. As first conceived, they served as a platform upon which to teach all aspects of the space mission lifecycle. JPL took on this mission type with Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment2 (INSPIRE), moving the concept into a new domain: deep space. Building from the INSPIRE platform and lessons learned, MarCO addressed new challenges in the domain of planetary missions: independent interplanetary flight and navigation, integration with a large-scale mission, long-distance and long-delay communication, short development time, and a small development team. Of these, the greatest constraint was schedule: only 18 months passed from conception of mission concept until delivery of fully assembled and tested flight hardware. Careful selection of mission team, along with extensive use of off-the-shelf equipment, and streamlining automated processes, was essential. This achievement represents the next step in the evolution of CubeSats beyond low-Earth orbit.

Werne, Thomas↗
NASA NTRS1993

Brief summary of the evolution of high-temperature creep-fatigue life prediction models for crack initiation

The evolution of high-temperature, creep-fatigue, life-prediction methods used for cyclic crack initiation is traced from inception in the late 1940's. The methods reviewed are material models as opposed to structural life prediction models. Material life models are used by both structural durability analysts and by material scientists. The latter use micromechanistic models as guidance to improve a material's crack initiation resistance. Nearly one hundred approaches and their variations have been proposed to date. This proliferation poses a problem in deciding which method is most appropriate for a given application. Approaches were identified as being combinations of thirteen different classifications. This review is intended to aid both developers and users of high-temperature fatigue life prediction methods by providing a background from which choices can be made. The need for high-temperature, fatigue-life prediction methods followed immediately on the heels of the development of large, costly, high-technology industrial and aerospace equipment immediately following the second world war. Major advances were made in the design and manufacture of high-temperature, high-pressure boilers and steam turbines, nuclear reactors, high-temperature forming dies, high-performance poppet valves, aeronautical gas turbine engines, reusable rocket engines, etc. These advances could no longer be accomplished simply by trial and error using the 'build-em and bust-em' approach. Development lead times were too great and costs too prohibitive to retain such an approach. Analytic assessments of anticipated performance, cost, and durability were introduced to cut costs and shorten lead times. The analytic tools were quite primitive at first and out of necessity evolved in parallel with hardware development. After forty years more descriptive, more accurate, and more efficient analytic tools are being developed. These include thermal-structural finite element and boundary element analyses, advanced constitutive stress-strain-temperature-time relations, and creep-fatigue-environmental models for crack initiation and propagation. The high-temperature durability methods that have evolved for calculating high-temperature fatigue crack initiation lives of structural engineering materials are addressed. Only a few of the methods were refined to the point of being directly useable in design. Recently, two of the methods were transcribed into computer software for use with personal computers.

Halford, Gary R.↗
NASA NTRS2018

On the 2018 Outburst of the Accreting Millisecond X-Ray Pulsar Swift J1756.9-2508 As Seen with NICER

We report on the coherent timing analysis of the 182 Hz accreting millisecond X-ray pulsar SwiftJ1756.92508during its 2018 outburst as observed with the Neutron Star Interior Composition Explorer (NICER). Combiningour NICER observations with Rossi X-ray Timing Explorer observations of the 2007 and 2009 outbursts, we alsostudied the long-term spin and orbital evolution of this source. We find that the binary system is well describedby a constant orbital period model, with an upper limit on the orbital period derivative of Pb < 7.4 ´ 10-13 ss1.Additionally, we improve upon the source coordinates through astrometric analysis of the pulse arrival times,finding R.A.=17h56m57 18±0 08 and decl.=25°0627 8±3 5, while simultaneously measuring thelong-term spin frequency derivative as n = -7.3 ´ 10-16 Hzs1. We briefly discuss the implications of thesemeasurements in the context of the wider population of accreting millisecond pulsars. We reported on the coherent timing analysis of the 2018 outburst of Swift J1756 as observed with NICER. Consistent with analyses of the previous outbursts (Krimm et al. 2007b; Patruno et al. 2010), we find that the X-ray pulsations have energy dependent amplitudes; the fractional amplitude of the fundamental increases with energy, whereas the fractional amplitude of the harmonic shows a slight decline with energy. This energy dependent behavior is not unusual in AMXPs (Patruno & Watts 2012) and can be interpreted in terms of the thermal emission from the stellar hotspot and reprocessing in the accretion column (e.g., Gierliński et al. 2002; Ibragimov & Poutanen 2009). The pulse arrival times of the 2018 outburst are well described by a timing model consisting of a circular orbit with a constant spin frequency. The pulse phases with respect to this model do not show spurious residuals with time or orbital phase, and no evidence is found that the pulse arrival times exhibit an additional delay associated with passing through the gravitational well of the companion star (Shapiro delay). We note, however, that the expected Shapiro delay is given as (Shapiro et al. 1971) Equation (5) where Φ is the orbital phase, G is the gravitational constant, c is the speed of light, and i is the inclination. Even for the maximum allowed companion mass, ${M}_{C}=0.030\,{M}_{\odot }$ (Krimm et al. 2007b, but see Section 4.2 for more details) and an inclination of 90°, the largest delay we can expect is only 4 μs. As this time-delay is smaller than the uncertainty on our phase residuals by nearly two orders of magnitude (see Figure 1), we are not sensitive to Shapiro delays in Swift J1756. Comparing our measurements for the 2018 outburst with those of the 2007 and 2009 outbursts as observed with RXTE, we analyzed the long-term evolution of this source. We found that the binary system is consistent with having a constant orbital period and that the pulsar shows a spin frequency derivative of $\dot{\nu }=-7.3\times {10}^{-16}\,\mathrm{Hz}\,{{\rm{s}}}^{-1}$. 4.1. Spin-down Evolution The long-term spin frequency derivative measured in Swift J1756 is of the same order as the spin frequency derivatives measured in other AMXPs (Hartman et al. 2008; Patruno 2010; Riggio et al. 2011). This frequency change is most likely driven by the neutron star's loss of rotational energy. If so, then the spin-down luminosity is given as Equation (6) where I represents the neutron star moment of inertia. The long-term spin-down of a neutron star is usually assumed to be dominated by the braking torque associated with a spinning magnetic field. Assuming this mechanism is responsible for the observed spin-down in Swift J1756, we can compute the magnetic dipole moment as (Spitkovsky 2006) Equation (7) where α is the misalignment angle between the rotational and magnetic poles. Considering α = 0°–90°, we then find a magnetic field strength of $B\simeq (4\mbox{--}6)\times {10}^{8}$ G at the stellar magnetic poles. This magnetic field strength estimate is in line with those obtained for other accreting millisecond pulsars (see Mukherjee et al. 2015 and references therein). 4.2. Orbit Evolution The observed long-term binary evolution of Swift J1756 is consistent with this source having a constant orbital period and a lower limit on the evolutionary timescale of Equation (8) Binary evolution theory predicts that systems of this type evolve due to angular momentum loss through gravitational radiation (Kraft et al. 1962; Rappaport et al. 1982; Verbunt 1993). For conservative mass transfer, the binary period derivative is given by di Salvo et al. (2008), Equation (9) where MNS is the neutron star mass, $q={M}_{C}/{M}_{\mathrm{NS}}$ is the binary mass ratio, and −1/3 < n < 1 is the mass–radius index of the companion star. Depending on the source inclination, Krimm et al. (2007b) derived a companion mass of ${M}_{C}\,=0.007\mbox{--}0.022\,{M}_{\odot }$ for a neutron star mass of 1.4 ${M}_{\odot }$. For a neutron star mass of 2.2 ${M}_{\odot }$, the allowed range increased to ${M}_{C}=0.009\mbox{--}0.030\,{M}_{\odot }$. In both cases, they assumed an upper limit on the inclination of i < 85°, motivated by the fact that Swift J1756 does not show eclipses in its light curve. Accounting for the extreme cases of stellar masses and n, the binary may either be contracting or expanding. In either case, however, the rate of change is limited to $| {\dot{P}}_{b}| \lesssim 7\times {10}^{-14}$ s s−1, which is well below the upper limit obtained in this work. Although the binary evolution timescale we obtain for Swift J1756 is consistent with theory, it is worth noting that this is not generally true for low-mass X-ray binaries (see Patruno et al. 2017, for a comprehensive discussion). The AMXP SAX J1808.4–3658, in particular, has been found to evolve on a much shorter timescale, with a first derivative on the orbital period of $3.5\times {10}^{-12}$ s s−1 (Hartman et al. 2008; Patruno et al. 2012; Sanna et al. 2017a). Two models have been proposed to explain this discrepancy: highly nonconservative mass transfer due to irradiation of the companion star by the pulsar (di Salvo et al. 2008; Burderi et al. 2009), and spin–orbit coupling in the companion star (Hartman et al. 2008, 2009). While the latter depends on the companion star, and may vary from source to source, the former should operate in all AMXPs (see also Patruno 2017; Sanna et al. 2017c), including Swift J1756. The spin-down luminosity impinging on the companion star can be estimated as Equation (10) where ${\dot{E}}_{\mathrm{abl}}$ is the ablation luminosity, RL2 is the Roche lobe radius of the companion (Eggleton 1983), and a the binary separation. The irradiation fraction is $f={\dot{E}}_{\mathrm{abl}}/{\dot{E}}_{\mathrm{sd}}$, which, accounting for the range of allowed neutron star and companion masses, evaluates to f = 0.15%–0.35%. The associated mass loss for the companion is given by Equation (11) such that, assuming an efficiency of η = 100%, ${\dot{M}}_{C}\,\sim -3\times {10}^{-10}\,{M}_{\odot }$ yr−1. The effect of this mass loss on the orbital period follows through the relation (Frank et al. 2002) Equation (12) giving a period derivative due to mass loss of ${\dot{P}}_{b,\mathrm{ML}}\,=5\times {10}^{-12}$ s s−1. This value is well above our limit on the period derivative. Hence, in order for this mechanism to be consistent with our observations of Swift J1756, the efficiency at which the companion star converts the incident luminosity into mass loss must be η < 15%. This value is very different from the 40% required in SAX J1808.4–3658 (Patruno et al. 2016) and is instead in line with the <5% efficiency determined for IGR J00291+5934 (Patruno 2017). This work was supported by NASA through the NICER mission and the Astrophysics Explorers Program, and made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC). P.B. was supported by an NPP fellowship at NASA Goddard Space Flight Center. D.A. acknowledges support from the Royal Society.

Bult, Peter↗