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At least 1,009 records · Page 56

Flash Mixing on the White-Dwarf Cooling Curve: Understanding Hot Horizontal Branch Anomalies in NGC 2808

We present an ultraviolet color-magnitude diagram (CMD) spanning the hot horizontal branch (HB), blue straggler, and white dwarf populations of the globular cluster NGC 2808. These data, obtained with the Space Telescope Imaging Spectrograph (STIS), demonstrate that NGC 2808 harbors a significant population of hot subluminous HB stars, an anomaly only previously reported for the globular cluster omega Cen. Our theoretical modeling indicates that the location of these subluminous stars in the CMD, as well as the high temperature gap along the HB of NGC 2808, can be explained if these stars underwent a late helium-core flash while descending the white dwarf cooling curve. We show that the convective zone produced by such a late helium flash will penetrate into the hydrogen envelope, thereby mixing hydrogen into the hot helium-burning interior, where it is rapidly consumed. This phenomenon is analogous to the "born again" scenario for producing hydrogen-deficient stars following a late helium-shell flash. The flash mixing of the envelope greatly enhances the envelope helium and carbon abundances that, in turn, leads to a discontinuous increase in the HB effective temperatures. We argue that the hot HB gap is associated with this theoretically predicted dichotomy in the HB properties. Moreover, the changes in the emergent spectral energy distribution caused by these abundance changes are primarily responsible for explaining the hot subluminous HB stars. Although further evidence is needed to confirm that a late helium-core flash can account for the subluminous HB stars and the hot HB gap, we demonstrate that an understanding of these stars requires the use of appropriate theoretical models for their evolution, atmospheres, and spectra.

Brown, Thomas M.↗

Cloud Cover Increase with Increasing Aerosol Absorptivity: A Counterexample to the Conventional Semidirect Aerosol Effect

We reexamine the aerosol semidirect effect using a general circulation model and four cases of the single-scattering albedo of dust aerosols. Contrary to the expected decrease in low cloud cover due to heating by tropospheric aerosols, we find a significant increase with increasing absorptivity of soil dust particles in regions with high dust load, except during Northern Hemisphere winter. The strongest sensitivity of cloud cover to dust absorption is found over land during Northern Hemisphere summer. Here even medium and high cloud cover increase where the dust load is highest. The cloud cover change is directly linked to the change in relative humidity in the troposphere as a result of contrasting changes in specific humidity and temperature. More absorption by aerosols leads to larger diabatic heating and increased warming of the column, decreasing relative humidity. However, a corresponding increase in the specific humidity exceeds the temperature effect on relative humidity. The net effect is more low cloud cover with increasing aerosol absorption. The higher specific humidity where cloud cover strongly increases is attributed to an enhanced convergence of moisture driven by dust radiative heating. Although in some areas our model exhibits a reduction of low cloud cover due to aerosol heating consistent with the conventional description of the semidirect effect, we conclude that the link between aerosols and clouds is more varied, depending also on changes in the atmospheric circulation and the specific humidity induced by the aerosols. Other absorbing aerosols such as black carbon are expected to have a similar effect.

Perlwitz, Jan↗

New Perspective on Electron Transfer through Molecules

Motivated by experiments which display unusual length and temperature effects for electron transfer in the nanometer length regime, we propose a new approach for describing long range electron transfer (ET) processes through molecules. We posit that the electron reorganization in the molecules (e.g., the electronic polarization of a macromolecule or organic film by an applied electric potential, or the injected charge generating a dipole moment) should be included in the description. We numerically solve a one-dimensional model for the electron transport, which includes electron-electron interactions explicitly; and we show that it generates a power law distance dependence for electron similar to that observed in experiments. The model does not include vibrations explicitly and should be consistent with the weak temperature dependences observed experimentally. This approach emphasizes the need to treat the electronic changes in the molecule(s) more explicitly to understand the behavior.

36 MATERIALS SCIENCE↗

An extrasolar extreme-ultraviolet object. II - The nature of HZ 43

A variety of data are presented concerning the spectrum, distance, temperature, and evolutionary state of the hot white dwarf HZ 43, the first extrasolar object to be detected in the EUV band. The data include spectrophotometry of the star and its red dwarf companion (HZ 43B), a trigonometric parallax for the star, its tangential velocity, and results of soft X-ray and EUV observations. The main conclusions are that: (1) the spectrum of HZ 43A is that of a hot DAwk star, (2) HZ 43B is a dM3.5e star, (3) the distance of the system is about 65 pc, (4) the tangential velocity is not atypical of white dwarfs, and (5) the stellar energy distribution of HZ 43A is well fitted by a black body with an effective temperature of approximately 110,000 K. Evolutionary implications of the existence of an object as hot as HZ 43A are briefly considered, and it is suggested that the progenitors of hot DA stars must include objects hotter than spectral type sdB, with logical possibilities being nuclei of planetary nebulae and sdO stars.

Margon, B.↗

New model atmospheres for very cool white dwarfs with mixed H/He and pure He compositions

New model atmosphere calculations for very cool white dwarfs with mixed H/He and pure He compositions are presented. The hydrogen-rich models incorporate improved cross section calculations of the collision-induced absorption by molecular hydrogen due to collisions with H2, H, and He. The effects associated with variations in the effective temperature (T(sub eff) greater than or equal to 4000 and less than or equal to 10,000 K), the surface gravity (log g greater than or equal to 7.5 and less than or equal to 9.5), and the chemical composition (N(He)/N(H) greater than or equal to O and less than or equal to 100) are investigated. Results from earlier calculations are confirmed qualitatively, but a more detailed comparison reveals large quantitative deviations. Cool white dwarfs with mixed H/He chemical compositions are shown to be easily recognizable from their predicted strong infrared flux deficiency. Pure helium model calculations are described as well. These include a modified version of the recently developed equation of state of D. Saumon and G. Chabrier. Nonideal effects brought about by various equations of state are explored in detail. For the purpose of this analysis, a model of pressure ionization based on an accurate description of the interactions in a mostly atomic helium fluid is developed. The effects of pressure ionization are shown to be the most important issue in the model calculations. A critical discussion of previous generations of pure helium model calculations is presented. Finally, broadband color indices are provided for the complete model grid.

Bergeron, P.↗

Chromospheres of the active dwarf binaries EQ Pegasi and Xi Bootis

Ultraviolet spectroscopic measurements of the M dwarf binary EQ Peg and the G8 V star Xi Boo A have been made with the International Ultraviolet Explorer satellite. High-temperature emission lines (N V, C IV, Si IV) are present with similar strengths in both stars. The surface fluxes of chromospheric and transition-region lines are enhanced relative to those of normal main-sequence stars and are comparable to those observed in solar active regions. If inhomogeneities are present, the surface fluxes may be markedly higher than the derived values. It is likely that the emission observed from EQ Peg was not the result of major flare activity; however, the quiescent radiative losses observed in the ultraviolet are comparable to the time-averaged optical flare losses. The similarity of the line emissions of active dwarfs of diverse spectral types suggests that the character of the transition region is independent of the stellar effective temperature.

Hartmann, L.↗

Prediction of Transition-State Scaling Relationships and Universal Transition-State Vibrational and Entropic Correlations for Dehydrogenations

Linear scaling relationships (LSRs) and Brønsted–Evans–Polanyi (BEP) or transition-state scaling (TSS) relations aid with the prediction of electronic energies. However, temperature effects and pre-exponentials are often taken as constants across metal surfaces or a homologous series. Vibrational scaling relationships (VSRs) offer a way to determine such parameters. Transition-state VSRs (TSVSRs) between local minima and transition states of AH X (A = C, N, O) surface diffusions correlate with BEP relations and broaden to thermochemical property scaling. Using density functional theory, we extend TSVSRs to AHX dehydrogenation reactions on transition-metal surfaces, relating vibrational modes of local minima to transition states. We first predict the slopes of the TSS relations by incorporating bond angles using the Slater–Koster structure factors and hybridization through crystal orbital overlap population analysis and energy overlap integrals between adsorbates and metal surfaces. Additionally, we uncover universal thermochemical property scaling, enabling the estimation of entropies and temperature corrections to enthalpies across a homologous series. Here, we demonstrate both significant vibrational corrections in reactions with low intrinsic electronic barriers and considerable variation in the pre-exponential of a simple dehydrogenation reaction across metals and AH X adsorbates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling heat exchange characteristics of long term space operations: Role of skin wettedness and exercise

The problems of heat exchange during rest and exercise during long term space operations are covered in this report. Particular attention is given to the modeling and description of the consequences of requirement to exercise in a zero-g atmosphere during Space Shuttle flights, especially long term ones. In space environments, there exists no free convection therefore only forced convection occurring by movement, such as pedalling on a cycle ergometer, augments required heat dissipation necessary to regulate body temperature. The requirement to exercise at discrete periods of the day is good practice in order to resist the deleterious consequences of zero-gravity problems and improve distribution of body fluids. However, during exercise (ca. 180 to 250W), in zero-g environments, the mass of eccrine sweating rests as sheets on the skin surface and the sweat cannot evaporate readily. The use of exercise suits with fabrics that have hydrophobic or outwicking properties somewhat distributes the mass of sweat to a larger surface from which to evaporate. However, with no free convection, increased skin wettedness throughout the body surface induces increasing thermal discomfort, particularly during continuous exercise. This report presents several alternatives to aid in this problem: use of intermittent exercise, methods to quantify local skin wettedness, and introduction of a new effective temperature that integrates thermal stress and heat exchange avenues in a zero-g atmosphere.

Gonzalez, Richard R.↗

Hot HB Stars in Globular Clusters: Physical Parameters and Consequences for Theory: The Second Parameter Pair M 3 and M 13 - VI

We present the results of spectroscopic analyses of hot horizontal branch (HB) stars in M 13 and M 3, which form a famous "second parameter" pair. F rom the spectra and Stromgren photometry we derived - for the first time in M 13 - atmospheric parameters (effective temperature and surface gravity). For stars with Stromgren temperatures between 10,000 and 12,000 K we found excellent agreement between the atmospheric parameters derived from Stromgren photometry and those derived from Balmer line profile fits. However, for cooler stars there is a disagreement in the parameters derived by the two methods, for which we have no satisfactory explanation. Stars hotter than 12,000 K show evidence for helium depletion and iron enrichment, both in M 3 and M 13. Accounting for the iron enrichment substantially improves the agreement with canonical evolutionary models, although the derived gravities and masses are still somewhat too low. This remaining discrepancy may be an indication that scaled-solar metal-rich model atmospheres do not adequately represent the highly non-solar abundance ratios found in blue HB stars affected by diffusion. We discuss the effects of an enhancement in the envelope helium abundance on the atmospheric parameters of the blue HB stars, as might be caused by deep mixing on the red giant branch or primordial pollution from an earlier generation of intermediate mass asymptotic giant branch stars. Key words. Stars: atmospheres - Stars: evolution - Stars: horizontal branch - Globular clusters: individual: M 3 - Globular clusters: individual: M 13

Moehler, S.↗

Effect of Measurement Temperature on Electrical Cable Frequency Domain Reflectometry Response

In nuclear power plants, electrical cables are exposed to stressors, such as elevated temperature and radiation. Evaluation of the effect of stressors on the lifetime of electrical cables can be conducted using offline electrical reflectometry techniques, such as frequency domain reflectometry (FDR). However, recent work has raised the concern that FDR measurements at temperatures higher than ambient may diminish or reduce the response due to stressors, potentially leading to incorrect predictions of electrical cable damage and lifetime. In this work, we explore the FDR response of an electrical cable exposed to an oven-based thermal stressor up to 140°C, including both ramping up and ramping down temperature. It was observed that, for both the oven entrance and exit, an increase in the FDR measurement temperature led to a decrease in the FDR reflection coefficient. In particular, it was found that the reflection coefficient at the oven entrance decreased from the ambient measurement by approximately 7%, 22%, and 36% at a temperature of 60°C, 100°C, and 140°C, respectively.

Spencer, Mychal P.↗

EX-111 Thermal Emission from Hot White Dwarfs: The Suggested He Abundance-Temperature Correlation. EX-112: The Unique Emission Line White Dwarf Star GD 356

Progress in the EXOSAT data analysis program is reported. EXOSAT observations for four white dwarfs (WD1031-115, WD0004+330, WD1615-154, and WD0109-264) were obtained. Counting rates were unexpectedly low, indicating that these objects have a substantial amount of x-ray absorbing matter in their photosheres. In addition, soft x-ray pulsations characterized by a 9.25 minute cycle were discovered in the DA white dwarf V471 Tauri. A residual x-ray flux from the K dwarf companion can be seen during the white dwarf eclipse at orbital phase 0.0. Pronounced dips in the soft x-ray light curve occur at orbital phases 0.15, 0.18, and 0.85. The dips may be correlated with the triangular Lagrangian points of the binary orbit. Smaller dips at phases near the eclipse may be associated with cool loops in the K star corona. Data for the white dwarf H1504+65 was also analyzed. This object is particularly unusual in that its photoshere is devoid of hydrogen and helium. Finally, existing data on the white dwarf Sirius B were analyzed to see what constraints from other data can be placed on the properties of this star. Interrelationships between radius, rotational velocity, and effective temperature were derived.

Shipman, H. L.↗

Model Stellar Atmospheres and Real Stellar Atmospheres and Status of the ATLAS12 Opacity Sampling Program and of New Programs for Rosseland and for Distribution Function Opacity

I discuss errors in theory and in interpreting observations that are produced by the failure to consider resolution in space, time, and energy. I discuss convection in stellar model atmospheres and in stars. Large errors in abundances are possible such as the factor of ten error in the Li abundance for extreme Population II stars. Finally I discuss the variation of microturbulent velocity with depth, effective temperature, gravity, and abundance. These variations must be dealt with in computing models and grids and in any type of photometric calibration. I have also developed a new opacity-sampling version of my model atmosphere program called ATLAS12. It recognizes more than 1000 atomic and molecular species, each in up to 10 isotopic forms. It can treat all ions of the elements up through Zn and the first 5 ions of heavier elements up through Es. The elemental and isotopic abundances are treated as variables with depth. The fluxes predicted by ATLAS12 are not accurate in intermediate or narrow bandpass intervals because the sample size is too small. A special stripped version of the spectrum synthesis program SYNTHE is used to generate the surface flux for the converged model using the line data on CD-ROMs 1 and 15. ATLAS12 can be used to produce improved models for Am and Ap stars. It should be very useful for investigating diffusion effects in atmospheres. It can be used to model exciting stars for H II regions with abundances consistent with those of the H II region. These programs and line files will be distributed on CD-ROMs.

Kurucz, Robert L.↗

The interstellar medium in the starburst regions of NGC 253 and NGC 3256

We discuss observations of the (C II) 158 micrometers, (O I) 63 micrometers, (Si II) 35 micrometers, (O III) 52,88 micrometers, and (S III) 33 micrometers fine-structure transitions toward the central 45 seconds of the starburst galaxies NGC 253 and NGC 3256. The (C II) and (O I) emission probably originates in photodissociated gas at the surfaces of molecular clouds, although a small (less than or approximately 30%) contribution to the (C II) flux from H II regions cannot be ruled out. The (O III) and (S III) lines originate in H II regions and the (Si II) flux is best explained as originating in H II regions with some contribution from photodissociation regions (PDRs). The gas phase silicon abundance is nearly solar in NGC 253, which we interpret as evidence for grain destruction in the starburst region. We find that the photodissociated atomic gas has densities approximately 10(exp 4)/cu cm and temperature 200-300 K. About 2% of the gas is in this phase. The thermal gas pressure in the PDRs, P(PDR)/k approximately 1-3 x 10(exp 6) K/cu cm, might represent the 'typical' interstellar gas pressure in starburst systems. The Far Ultraviolet (FUV) radiation fields illuminating the clouds are 10(exp 3)-10(exp 4) stronger than the local Galactic FUV field and come from the contribution of many closely packed O and B stars. For the central 250 pc of NGC 253, we find that the H II gas has an average density n(sub e) is approximately 400/cu cm. This corresponds to a thermal pressure P(H II)/k approximately 7 x 10(exp 6) K/cu cm which is approximately P(PDR)/k, suggesting that the ionized gas is in pressure equilibrium with the photodissociated gas at the surfaces of molecular clouds. The H II gas fills a significant fraction, approximately 0.01-0.3, of the volume between the clouds. The effective temperature of the ionizing stars in NGC 253 is greater than or approximately 34,500 K; 2 x 10(exp 5) O7.5 stars would produce the observed Lyman countinuum photon luminosity. The average separation between the stars is approximately 3 pc. Applying the simple model for the interstellar medium in galactic nuclei of Wolfire, Tielens, & Hollenbach (1990), we find the molecular gas in the central regions of NGC 253 and NGC 3256 to be distributed in a large number (5 x 10(exp 3) to 5 x 10(exp 5)) of small (0.5-2 pc), dense (approximately 10(exp 4)/cu cm) clouds (or alternatively 'thin-flattened' structures) with volume filling factors 10(exp -3) to 10(exp -2), very different from the local Interstellar Medium (ISM) of the Galaxy. We suggest a self-consistent scenario for the ISM in NGC 253 in which clouds and H II gas are in pressure balance with a supernova-shocked, hot 1-3 x 10(exp 6) K, low-density (approximately 10(exp 4)/cu cm), all pervasive medium. A feedback mechanism may be indicated in which the pressure generated by the supernovae compresses the molecular clouds and triggers further massive star formation. The similarity of ISM parameters deduced for NGC 253, NGC 3256, and M82 (Lord et al. 1993) suggests that the ISM properties are independent of the luminosity of the starburst or the triggering mechanism, but are rather endemic to starburst systems. The starburst in NGC 3256 appears to be a scaled-up version of the NGC 253 and M82 starbursts.

Carral, P.↗

WISEA J041451.67-585456.7 and WISEA J181006.18-101000.5: The First Extreme T-type Subdwarfs?

We present the discoveries of WISEA J041451.67−585456.7 and WISEA J181006.18−101000.5, two low-temperature (1200–1400 K), high proper motion T-type subdwarfs. Both objects were discovered via their high proper motion (>0farcs5 yr(exp -1)); WISEA J181006.18−101000.5 as part of the NEOWISE proper motion survey and WISEA J041451.67−585456.7 as part of the citizen science project Backyard Worlds; Planet 9. We have confirmed both as brown dwarfs with follow-up near-infrared spectroscopy. Their spectra and near-infrared colors are unique among known brown dwarfs, with some colors consistent with L-type brown dwarfs and other colors resembling those of the latest-type T dwarfs. While no forward model consistently reproduces the features seen in their near-infrared spectra, the closest matches suggest very low metallicities ([Fe/H] ≼ −1), making these objects likely the first examples of extreme subdwarfs of the T spectral class (esdT). WISEA J041451.67−585456.7 and WISEA J181006.18−101000.5 are found to be part of a small population of objects that occupy the “substellar transition zone,” and have the lowest masses and effective temperatures of all objects in this group.

T subdwarfs↗

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↗

New Fracture Diagnostic Tool for Unconventionals: High-Resolution Distributed Strain Sensing via Rayleigh Frequency Shift during Production in Hydraulic Fracture Test 2

Fiber Optic monitoring in unconventional reservoirs has proven to be an invaluable diagnostic tool for assessing both near-wellbore stimulation effectiveness and to help describe the far-field frac geometries created by hydraulic fracture stimulation. Unfortunately, gaining any detailed qualitative and quantitative understanding of the near-wellbore frac geometry or cluster/stage productivity during production via Fiber Optic (FO) has proven to be more difficult, particularly in wells producing liquids. A new FO diagnostic method, Distributed Strain Sensing based on Rayleigh Frequency Shift (DSS-RFS), first demonstrated for oil and gas applications in the Hydraulic Test Site 2 (HFTS2) provides new insights about the characteristics of near-wellbore-region (NWR) during production. DSS-RFS is different from other FO strain measurements because it relies on accurate measurement of frequency shifts of Rayleigh backscattered spectrum obtained by scanning the fiber with a coherent optical time-domain reflectometer with a range of laser frequencies using a tunable-wavelength laser system. Changes in strain are measured with an extremely high spatial resolution of 20 cm and with high signal-to-noise ratios over long distances. In HFTS2, strain changes for the entire wellbore have been measured twice during scheduled shut-in and reopening operations (February 2020 and September 2020). After removing temperature effects, consistent strain changes have been observed at the location of most perforation clusters. These are caused by near wellbore fracture aperture changes due to pressure increases during shut-in within the near-wellbore fracture network. The strain-change patterns from the DSS-RFS during shut-in correlate very well with the location of clusters and allow for the definition of extending intervals with positive strain signals at each cluster and slightly compressing intervals with negative strain signals between the clusters and in the non stimulated intervals. The locations of the measured positive strain peaks also show good correspondence to DAS acoustic intensity measurements acquired during the stimulation. The geometry and magnitude of the strain changes differ significantly between the two tested completion designs in the same well. During shut in and reopening each cluster exhibit its own strain-change / pressure path. In addition, the September 2020 dataset also revealed the existence of small but measurable strain changes as consequence of pressure decline during production. These strain changes also correlate well with the presence of producing clusters, but the strain-rate signals are opposite to that obtained during shut-in and reopening operations. Although Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/2-21URTC/D021S031R002/2477551/urtec-2021-5408-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5408 2 we are still in the early stages of exploring the potential of this novel FO technique, we believe that the highly detailed information contained in the measurement of strain changes using DSS-RFS during production can significantly improve our understanding of near-wellbore hydraulic fracture characteristics and the relationships between stimulation and production from unconventional oil and gas wells.

04 OIL SHALES AND TAR SANDS↗

Formation and evolution of luminous supersoft X-ray sources

Luminous supersoft X-ray sources, with characteristic luminosities of approximately 10(exp 38) ergs/s and temperatures, kT, of approximately 35 eV, have been established as a new and distinct class of X-ray source through recent Roentgen Satellite (ROSAT) observations. Several possible physical models have been proposed for these sources. One promising scenario (van den Heuvel et al. 1992) involves mass transfer, which is unstable on a thermal timescale, from a main-sequence or subgiant donor star onto the surface of a white dwarf. For a narrow range of accretion rates, steady nuclear burning of the accreted matter can take place. This process can provide the high luminosities and the correct range of temperatures observed in the supersoft sources. However, given the limited range of mass transfer rates that are consistent with this phenomenon, it is far from obvious that a sufficient population of such systems exists in galaxies such as our own, M31, and the Magellanic Clouds, in order to account for the large number of supersoft sources which can be inferred from present observations. This work addresses the population question in detail, through a Monte Carlo simulation of the formation and evolution of such systems, which starts with zero-age primordial binaries. In order to evolve into close binary systems which contain a white dwarf component and a companion transferring mass at a rate within the requisite narrow range, a binary system must undergo a specific progression of evolutionary steps. We find that a sufficient subset of our initial binaries evolve to become systems with the requisite properties, so that they can account for the population of supersoft sources that is inferred from observations. In particular, we find that there should be more than 1000 systems in the Galaxy today with properties that very closely match those of the observed supersoft sources. From our models, we find expected luminosities, white dwarf effective temperatures, and orbital periods in the ranges of 10(exp 37) - 10(exp 38) ergs/s, (1-5) x 10(exp 5) K, and 8 hr-1.4 days, respectively. The masses of the white dwarf and donor star are expected to lie in the range of 0.7-1.05 solar mass and 1.3-2.7 solar mass. Finally, we discuss the role that supersoft X-ray sources may play as the progenitors of Type Ia supernovae, and estimate the rate of production via this channel.

Rappaport, S.↗