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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 721 records · Page 40
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DOE OSTI2014

Herschel HIFI observations of O{sub 2} toward Orion: special conditions for shock enhanced emission

We report observations of molecular oxygen (O{sub 2}) rotational transitions at 487 GHz, 774 GHz, and 1121 GHz toward Orion Peak A. The O{sub 2} lines at 487 GHz and 774 GHz are detected at velocities of 10-12 km s{sup –1} with line widths ∼3 km s{sup –1}; however, the transition at 1121 GHz is not detected. The observed line characteristics, combined with the results of earlier observations, suggest that the region responsible for the O{sub 2} emission is ≅9'' (6 × 10{sup 16} cm) in size, and is located close to the H {sub 2} Peak 1 position (where vibrationally excited H{sub 2} emission peaks), and not at Peak A, 23'' away. The peak O{sub 2} column density is ≅1.1 × 10{sup 18} cm{sup –2}. The line velocity is close to that of the 621 GHz water maser emission found in this portion of the Orion Molecular Cloud, and having a shock with velocity vector lying nearly in the plane of the sky is consistent with producing maximum maser gain along the line of sight. The enhanced O{sub 2} abundance compared to that generally found in dense interstellar clouds can be explained by passage of a low-velocity C shock through a clump with preshock density 2 × 10{sup 4} cm{sup –3}, if a reasonable flux of UV radiation is present. The postshock O{sub 2} can explain the emission from the source if its line-of-sight dimension is ≅10 times larger than its size on the plane of the sky. The special geometry and conditions required may explain why O{sub 2} emission has not been detected in the cores of other massive star-forming molecular clouds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Trigonometric distance and proper motion of IRAS 20056+3350: a massive star-forming region on the solar circle

We report our measurement of the trigonometric distance and proper motion of IRAS 20056+3350, obtained from the annual parallax of H{sub 2}O masers. Our distance of D=4.69{sub −0.51}{sup +0.65} kpc, which is 2.8 times larger than the near kinematic distance adopted in the literature, places IRAS 20056+3350 at the leading tip of the Local arm and proximal to the solar circle. Using our distance, we reevaluate past observations to reveal IRAS 20056+3350 as a site of massive star formation at a young stage of evolution. This result is consistent with the spectral energy distribution of the source evaluated with published photometric data from UKIDSS, WISE, AKARI, IRAS, and the submillimeter continuum. Both analytical approaches reveal the luminosity of the region to be 2.4 × 10{sup 4} L {sub ☉}, and suggest that IRAS 20056+3350 is forming an embedded star of ≥16 M {sub ☉}. We estimated the proper motion of IRAS 20056+3350 to be (μ{sub α}cos δ, μ{sub δ}) = (–2.62 ± 0.33, –5.65 ± 0.52) mas yr{sup –1} from the group motion of H{sub 2}O masers, and use our results to estimate the angular velocity of Galactic rotation at the Galactocentric distance of the Sun, Ω{sub 0} = 29.75 ± 2.29 km s{sup –1} kpc{sup –1}, which is consistent with the values obtained for other tangent point and solar circle objects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

THE MEGAMASER COSMOLOGY PROJECT. VI. OBSERVATIONS OF NGC 6323

We present observations of the H{sub 2}O megamasers in the accretion disk of NGC 6323. By combining interferometric and spectral monitoring data, we estimate H{sub 0}=73{sub −22}{sup +26} km s{sup –1} Mpc{sup –1}, where the low strength of the systemic masers (<15 mJy) limits the accuracy of this estimate. The methods developed here for dealing with weak maser emission provide guidance for observations of similar sources, until significant increases in radio telescope sensitivity, such as anticipated from the next generation Very Large Array, are realized.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

INITIAL FRAGMENTATION IN THE INFRARED DARK CLOUD G28.53−0.25

To study the fragmentation and gravitational collapse of dense cores in infrared dark clouds (IRDCs), we have obtained submillimeter continuum and spectral line data as well as multiple inversion transitions of NH{sub 3} and H{sub 2}O maser data of four massive clumps in IRDC G28.53−0.25. Combining single-dish and interferometer NH{sub 3} data, we derive a rotation temperature of G28.53. We identity 12 dense cores at a 0.1 pc scale based on submillimeter continuum, and obtain their physical properties using NH{sub 3} and continuum data. By comparing the Jeans masses of cores with the core masses, we find that turbulent pressure is important for supporting the gas when 1 pc scale clumps fragment into 0.1 pc scale cores. All cores have a virial parameter that is smaller than 1 if we assume an inverse squared radial density profile, suggesting they are gravitationally bound, and the three most promising star-forming cores have a virial parameter that is smaller than 1 even when taking the magnetic field into account. We also associate the cores with star formation activities revealed by outflows, masers, or infrared sources. Unlike what previous studies have suggested, MM1 turns out to harbor a few star-forming cores and is likely a progenitor of a high-mass star cluster. MM5 is intermediate while MM7/8 are quiescent in terms of star formation, but they also harbor gravitationally bound dense cores and have the potential for forming stars, as in MM1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

THE MEGAMASER COSMOLOGY PROJECT. VII. INVESTIGATING DISK PHYSICS USING SPECTRAL MONITORING OBSERVATIONS

We use single-dish radio spectra of known 22 GHz H{sub 2}O megamasers, primarily gathered from the large data set observed by the Megamaser Cosmology Project, to identify Keplerian accretion disks and to investigate several aspects of the disk physics. We test a mechanism for maser excitation proposed by Maoz and McKee (1998), whereby population inversion arises in gas behind spiral shocks traveling through the disk. Though the flux of redshifted features is larger on average than that of blueshifted features, in support of the model, the high-velocity features show none of the predicted systematic velocity drifts. We find rapid intra-day variability in the maser spectrum of ESO 558−G009 that is likely the result of interstellar scintillation, for which we favor a nearby (D ≈ 70 pc) scattering screen. In a search for reverberation in six well-sampled sources, we find that any radially propagating signal must be contributing ≲10% of the total variability. We also set limits on the magnetic field strengths in seven sources, using strong flaring events to check for the presence of Zeeman splitting. These limits are typically 200–300 mG (1σ), but our most stringent limits reach down to 73 mG for the galaxy NGC 1194.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Sgr B2(N): A bipolar outflow and rotating hot core revealed by ALMA

We present the results of SiO (2 − 1) and SO{sub 2} (12{sub 4,8}--13{sub 3,11}) line observations of Sgr B2(N) made with the Atacama Large Millimeter/submillimeter Array at an angular resolution of ∼2″. Our analysis of the SiO and SO{sub 2} line emission reveals a bipolar molecular outflow in an east–west direction whose driving source is located at K2. In addition, the SO{sub 2} line core shows a north–south velocity gradient most probably indicating a hot core of molecular gas rotating around K2. Fractional abundances of SO{sub 2} and SiO (X(SO{sub 2}) and X(SiO), respectively) in the outflowing molecular gas are derived from comparisons with the C{sup 18}O emission. Assuming an excitation temperature of 100 ± 50 K, we calculate X(SO{sub 2}) = 2.3{sub −0.4}{sup +2.6} × 10{sup −8} and X(SiO) = 1.2{sub −0.1}{sup +0.1} × 10{sup −9}. The outflow from Sgr B2(N) K2 is characterized as a young (5 × 10{sup 3} yr) and massive (∼2000 M{sub ⊙}) but moderately collimated (∼60°) outflow. We also report a possible detection of the SiO (v=2,J=2--1) maser emission from the position of K2. If confirmed, it would make Sgr B2(N) the fourth star-forming region associated with SiO masers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

NEWLY IDENTIFIED EXTENDED GREEN OBJECTS (EGOs) FROM THE SPITZER GLIMPSE II SURVEY. I. CATALOG

We have produced a catalog containing 98 newly identified massive young stellar object (MYSO) candidates associated with ongoing outflows (known as extended green objects, or EGOs). These have been identified from the Spitzer Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) II data set and our new identifications increase the number of known EGOs to {approx}400 in our Galaxy, adding to the {approx}300 previously identified EGOs reported by Cyganowski et al. from the GLIMPSE I survey. The high detection rate ({approx}70%) of 95 GHz class I methanol masers achieved in a survey toward 57 of these new EGOs with the Mopra 22 m radio telescope demonstrates that the new EGOs are associated with outflows. Investigations of the mid-infrared properties and physical associations with other star formation tracers (e.g., infrared dark clouds, class I and II methanol masers, and millimeter Bolocam Galactic Plane Survey sources) reveal that the newly identified EGOs are very similar in nature to those in the sample of Cyganowski et al. All of the observational evidence supports the hypothesis that EGOs correspond to MYSOs at the earliest evolutionary stage, with ongoing outflow activity, and active rapid accretion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

NEWLY IDENTIFIED EXTENDED GREEN OBJECTS (EGOs) FROM THE SPITZER GLIMPSE II SURVEY. II. MOLECULAR CLOUD ENVIRONMENTS

We have undertaken a survey of molecular lines in the 3 mm band toward 57 young stellar objects using the Australia Telescope National Facility Mopra 22 m radio telescope. The target sources were young stellar objects with active outflows (extended green objects (EGOs)) newly identified from the GLIMPSE II survey. We observe a high detection rate (50%) of broad line wing emission in the HNC and CS thermal lines, which combined with the high detection rate of class I methanol masers toward these sources (reported in Paper I) further demonstrates that the GLIMPSE II EGOs are associated with outflows. The physical and kinematic characteristics derived from the 3 mm molecular lines for these newly identified EGOs are consistent with these sources being massive young stellar objects with ongoing outflow activity and rapid accretion. These findings support our previous investigations of the mid-infrared properties of these sources and their association with other star formation tracers (e.g., infrared dark clouds, methanol masers and millimeter dust sources) presented in Paper I. The high detection rate (64%) of the hot core tracer CH{sub 3}CN reveals that the majority of these new EGOs have evolved to the hot molecular core stage. Comparison of the observed molecular column densities with predictions from hot core chemistry models reveals that the newly identified EGOs from the GLIMPSE II survey are members of the youngest hot core population, with an evolutionary time scale of the order of 10{sup 3} yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

CATALOG OF OBSERVED TANGENTS TO THE SPIRAL ARMS IN THE MILKY WAY GALAXY

From the Sun's location in the Galactic disk, one can use different arm tracers (CO, H I, thermal or ionized or relativistic electrons, masers, cold and hot dust, etc.) to locate a tangent to each spiral arm in the disk of the Milky Way. We present a master catalog of the astronomically observed tangents to the Galaxy's spiral arms, using different arm tracers from the literature. Some arm tracers can have slightly divergent results from several papers, so a mean value is taken—see the Appendix for CO, H II, and masers. The catalog of means currently consists of 63 mean tracer entries, spread over many arms (Carina, Crux-Centaurus, Norma, Perseus origin, near 3 kpc, Scutum, Sagittarius), stemming from 107 original arm tracer entries. Additionally, we updated and revised a previous statistical analysis of the angular offset and linear separation from the mid-arm for each different mean arm tracer. Given enough arm tracers, and summing and averaging over all four spiral arms, one could determine if arm tracers have separate and parallel lanes in the Milky Way. This statistical analysis allows a cross-cut of a Galactic spiral arm to be made, confirming a recent discovery of a linear separation between arm tracers. Here, from the mid-arm's CO to the inner edge's hot dust, the arm halfwidth is about 340 pc; doubling would yield a full arm width of 680 pc. We briefly compare these observations with the predictions of many spiral arm theories, notably the density wave theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

AURORAL RADIO EMISSION FROM STARS: THE CASE OF CU VIRGINIS

CU Virginis is a rapidly rotating Magnetic Chemically Peculiar star with at present unique characteristics as a radio emitter. The most intriguing one is the presence of intense, 100% circularly polarized radiation ascribed to a cyclotron maser. Each time the star rotates, this highly beamed emission points two times toward the Earth, like a pulsar. We observed CU Vir in 2010 April with the Expanded Very Large Array in two bands centered at 1450 and 1850 MHz. We covered nearly the whole rotational period, confirming the presence of the two pulses at a flux density up to 20 mJy. Dynamical spectra, obtained with unprecedented spectral and temporal sensitivity, allow us to clearly see the different time delays as a function of frequency. We interpret this behavior as a propagation effect of the radiation inside the stellar magnetosphere. The emerging scenario suggests interesting similarities with the auroral radio emission from planets, in particular with the Auroral Kilometric Radiation from Earth, which originates at few terrestrial radii above the magnetic poles and was only recently discovered to be highly beamed. We conclude that the magnetospheres of CU Vir, Earth, and other planets, maybe also exoplanets, could have similar geometrical and physical characteristics in the regions where the cyclotron maser is generated. In addition, the pulses are perfect 'markers' of the rotation period. This has given us for the first time the possibility to measure with extraordinary accuracy the spin-down of a star on or near the main sequence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

FIRST RESULTS FROM A 1.3 cm EXPANDED VERY LARGE ARRAY SURVEY OF MASSIVE PROTOSTELLAR OBJECTS: G35.03+0.35

We have performed a 1.3 cm survey of 24 massive young stellar objects (MYSOs) using the Expanded Very Large Array. The sources in the sample exhibit a broad range of massive star formation signposts including infrared dark clouds (IRDCs), ultra-compact H II (UC H II) regions, and extended 4.5 {mu}m emission in the form of extended green objects (EGOs). In this work, we present results for G35.03+0.35 which exhibits all of these phenomena. We simultaneously image the 1.3 cm NH{sub 3} (1,1) through (6,6) inversion lines, four CH{sub 3}OH transitions, two H recombination lines, plus continuum at 0.05 pc resolution. We find three areas of thermal NH{sub 3} emission, two within the EGO (designated as the NE and SW cores) and one toward an adjacent IRDC. The NE core contains a UC H II region (CM1) and a candidate hyper-compact H II region (CM2). A region of non-thermal, likely masing NH{sub 3} (3,3) and (6,6) emission is coincident with an arc of 44 GHz CH{sub 3}OH masers. We also detect two new 25 GHz Class-I CH{sub 3}OH masers. A complementary Submillimeter Array 1.3 mm continuum image shows that the distribution of dust emission is similar to the lower-lying NH{sub 3} lines, all peaking to the NW of CM2, indicating the likely presence of an additional MYSO in this protocluster. By modeling the NH{sub 3} and 1.3 mm continuum data, we obtain gas temperatures of 20-220 K and masses of 20-130 M{sub sun}. The diversity of continuum emission properties and gas temperatures suggests that objects in a range of evolutionary states exist concurrently in this protocluster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

PROTOSTELLAR OUTFLOW HEATING IN A GROWING MASSIVE PROTOCLUSTER

The dense molecular clump P1 in the infrared dark cloud complex G28.34+0.06 harbors a massive protostellar cluster at its extreme youth. Our previous Submillimeter Array observations revealed several jet-like CO outflows emanating from the protostars, indicative of intense accretion and potential interaction with ambient natal materials. Here, we present the Expanded Very Large Array spectral line observations toward P1 in the NH{sub 3} (J,K) = (1,1), (2,2), (3,3) lines, as well as H{sub 2}O and class I CH{sub 3}OH masers. Multiple NH{sub 3} transitions reveal the heated gas widely spread in the 1 pc clump. The temperature distribution is highly structured; the heated gas is offset from the protostars, and morphologically matches the outflows very well. Hot spots of spatially compact, spectrally broad NH{sub 3} (3,3) emission features are also found coincident with the outflows. A weak NH{sub 3} (3,3) maser is discovered at the interface between an outflow jet and the ambient gas. These findings suggest that protostellar heating may not be effective in suppressing fragmentation during the formation of massive cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

A SCALING RELATION BETWEEN MEGAMASER DISK RADIUS AND BLACK HOLE MASS IN ACTIVE GALACTIC NUCLEI

Several thin, Keplerian, sub-parsec megamaser disks have been discovered in the nuclei of active galaxies and used to precisely determine the mass of their host black holes. We show that there is an empirical linear correlation between the disk radius and the black hole mass. We demonstrate that such disks are naturally formed by the partial capture of molecular clouds passing through the galactic nucleus and temporarily engulfing the central supermassive black hole. Imperfect cancellation of the angular momenta of the cloud material colliding after passing on opposite sides of the hole leads to the formation of a compact disk. The radial extent of the disk is determined by the efficiency of this process and the Bondi-Hoyle capture radius of the black hole, and naturally produces the empirical linear correlation of the radial extent of the maser distribution with black hole mass. The disk has sufficient column density to allow X-ray irradiation from the central source to generate physical and chemical conditions conducive to the formation of 22 GHz H{sub 2}O masers. For initial cloud column densities {approx}< 10{sup 23.5} cm{sup -2} the disk is non-self-gravitating, consistent with the ordered kinematics of the edge-on megamaser disks; for higher cloud columns the disk would fragment and produce a compact stellar disk similar to that observed around Sgr A* at the galactic center.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

QUASI-QUIESCENT RADIO EMISSION FROM THE FIRST RADIO-EMITTING T DWARF

Radio detections of ultracool dwarfs provide insight into their magnetic fields and the dynamos that maintain them, especially at the very bottom of the main sequence, where other activity indicators dramatically weaken. Until recently, radio emission was only detected in the M and L dwarf regimes, but this has changed with the Arecibo detection of rapid polarized flares from the T6.5 dwarf 2MASS J10475385+2124234. Here, we report the detection of quasi-quiescent radio emission from this source at 5.8 GHz using the Karl G. Jansky Very Large Array. The spectral luminosity is L{sub {nu}} = (2.2 {+-} 0.7) Multiplication-Sign 10{sup 12} erg s{sup -1} Hz{sup -1}, a factor of {approx}100 times fainter than the Arecibo flares. Our detection is the lowest luminosity yet achieved for an ultracool dwarf. Although the emission is fully consistent with being steady, unpolarized, and broad band, we find tantalizing hints for variability. We exclude the presence of short-duration flares as seen by Arecibo, although this is not unexpected given estimates of the duty cycle. Follow-up observations of this object will offer the potential to constrain its rotation period, electron density, and the strength and configuration of the magnetic field. Equally important, follow-up observations will address the question of whether the electron cyclotron maser instability, which is thought to produce the flares seen by Arecibo, also operates in the very different parameter regime of the emission we detect, or whether instead this ultracool dwarf exhibits both maser and gyrosynchrotron radiation, potentially originating from substantially different locations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

EVIDENCE OF A HADRONIC ORIGIN FOR THE TeV SOURCE J1834-087

We report on the discovery of compact, narrow OH line emission from the hydroxyl molecule at 1720 MHz toward the extended TeV source J1834-087. The origin of this high energy emission is unknown; it could be powered by one or more candidate neutron stars (leptonic) or by cosmic rays interacting with dense gas (hadronic). The OH emission is detected near the center of J1834-087, coincident with the radio continuum of the supernova remnant W41, and the radial velocity of the line is the same velocity as a giant molecular cloud along the line of sight. We argue that the OH is maser emission stimulated by the interaction of the W41 shock with the molecular cloud. The known correlation between {gamma}-ray bright supernova remnants and OH masers favors a hadronic interpretation for this high energy emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A HOT MOLECULAR CIRCUMSTELLAR DISK AROUND THE MASSIVE PROTOSTAR ORION SOURCE I

We report new Atacama Large Millimeter/Submillimeter Array (ALMA) observations of a circumstellar disk around Source I in Orion KL, an archetype of massive protostar candidates. We detected two ortho-H{sub 2}O lines at 321 GHz (10{sub 2,} {sub 9}-9{sub 3,} {sub 6}) and 336 GHz (ν{sub 2} = 1, 5{sub 2,} {sub 3}-6{sub 1,} {sub 6}) for the first time in Source I. The latter one is in a vibrationally excited state at the lower state energy of 2939 K, suggesting evidence of hot molecular gas close to Source I. The integrated intensity map of the 321 GHz line is elongated along the bipolar outflow while the 336 GHz line map is unresolved with a beam size of 0.''4. Both of these maps show velocity gradients perpendicular to the bipolar outflow. The velocity centroid map of the 321 GHz line implies a spatial and velocity structure similar to that of vibrationally excited SiO masers tracing the root of the outflow emanating from the disk surface. In contrast, the 336 GHz line is most likely emitting from the disk midplane with a diameter of 0.''2 (84 AU) as traced by radio continuum emission and a dark lane devoid of the vibrationally excited SiO maser emission. The observed velocity gradient and the spectral profile of the 336 GHz H{sub 2}O line can be reconciled with a model of an edge-on ring-like structure with an enclosed mass of >7 M{sub ☉} and an excitation temperature of >3000 K. The present results provide further evidence of a hot and neutral circumstellar disk rotating around Source I with a diameter of ∼100 AU scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

IRAS 16547–4247: A NEW CANDIDATE OF A PROTOCLUSTER UNVEILED WITH ALMA

We present the results of continuum and {sup 12}CO(3-2) and CH{sub 3}OH(7-6) line observations of IRAS 16547–4247 made with the Atacama Large Millimeter/submillimeter Array (ALMA) at an angular resolution of ∼0.''5. The {sup 12}CO(3-2) emission shows two high-velocity outflows whose driving sources are located within the dust continuum peak. The alignment of these outflows does not coincide with that of the wide-angle, large-scale, bipolar outflow detected with the Atacama Pathfinder Experiment in previous studies. The CH{sub 3}OH(7-6) line emission traces an hourglass structure associated with the cavity walls created by the outflow lobes. Taking into account our results together with the position of the H{sub 2}O and class I CH{sub 3}OH maser clusters, we discuss two possible scenarios that can explain the hourglass structure observed in IRAS 16547–4247: (1) precession of a biconical jet, (2) multiple, or at least two, driving sources powering intersecting outflows. Combining the available evidence, namely, the presence of two cross-aligned bipolar outflows and two different H{sub 2}O maser groups, we suggest that IRAS 16547–4247 represents an early formation phase of a protocluster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Radiative transfer effects in primordial hydrogen recombination

The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of cosmic microwave background anisotropies. Lyman transitions, in particular the Lyman-{alpha} line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have already been computed in other works. In this paper, we compute the impact of some radiative transfer effects that were previously ignored, or for which previous treatments were incomplete. First, the effect of Thomson scattering in the vicinity of the Lyman-{alpha} line is evaluated, using a full redistribution kernel incorporated into a radiative transfer code. The effect of feedback of distortions generated by the optically thick deuterium Lyman-{alpha} line blueward of the hydrogen line is investigated with an analytic approximation. It is shown that both effects are negligible during cosmological hydrogen recombination. Second, the importance of high-lying, nonoverlapping Lyman transitions is assessed. It is shown that escape from lines above Ly{gamma} and frequency diffusion in Ly{beta} and higher lines can be neglected without loss of accuracy. Third, a formalism generalizing the Sobolev approximation is developed to account for the overlap of the high-lying Lyman lines, which is shown to lead to negligible changes to the recombination history. Finally, the possibility of a cosmological hydrogen recombination maser is investigated. It is shown that there is no such maser in the purely radiative treatment presented here.

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