arXiv subjects

Kazushi Sakamoto

Publications and source records attributed to Kazushi Sakamoto.

At least 37 records · Page 2Linked to original sources

arXiv2018

Dusty Superwind from a Galaxy with a Compact Obscured Nucleus: Optical Spectroscopic Study of NGC 4418

We report our optical spectroscopic study of the nucleus and its surrounding region of a nearby luminous infrared galaxy NGC 4418. This galaxy has been known to host a compact obscured nucleus, showing distinct characteristics such as a very compact ($\sim 20$ pc) sub-mm and mid-infrared core and dusty circumnuclear region with massive molecular gas concentration. We detected dusty superwind outflow at $\gtrsim 1$ kpc scale along the disk semiminor axis in both shock-heated emission lines and enhanced interstellar Na D absorption. This superwind shows basic characteristics similar to those of the prototypical superwind in the starburst galaxy M82, such as a kpc-scale extended structure of gas and dust along the disk minor axis, outflowing components (multiphase gas and dust), physical conditions of the ionized gas, and monotonically blueshifting radial velocity field with increasing distance from the nucleus on the front side of the superwind. We also detected a moderately extinct starburst population in the SDSS nuclear spectrum with the burst age of $\simeq 10$ Myr and stellar mass of $\simeq 1\times 10^7\ M_\mathrm{\odot}$. It is powerful enough to drive the superwind within the dynamical age of the superwind ($\simeq 10$ Myr). On the basis of comparison between this starburst--superwind scenario and the observations in terms of the burst age, stellar mass, infrared luminosity, and obscuration in the optical bands, we argue that this superwind-driving starburst is separate from the sub-mm core even if the core is a very young star cluster. Therefore, this galaxy hosts both the enshrouded compact core and the superwind-driving circumnuclear starburst.

astro-ph.GA↗

arXiv2018

ALMA Astrochemical Observations of the Infrared-Luminous Merger NGC 3256

In external galaxies, molecular composition may be influenced by extreme environments such as starbursts and galaxy mergers. To study such molecular chemistry, we observed the luminous-infrared galaxy and merger NGC 3256 using the Atacama Large Millimeter/sub-millimeter Array. We covered most of the 3-mm and 1.3-mm bands for a multi-species, multi-transition analysis. We first analyzed intensity ratio maps of selected lines such as HCN/HCO$^+$, which shows no enhancement at an AGN. We then compared the chemical compositions within NGC 3256 at the two nuclei, tidal arms, and positions with influence from galactic outflows. We found the largest variation in SiO and CH$_3$OH, species that are likely to be enhanced by shocks. Next, we compared the chemical compositions in the nuclei of NGC 3256, NGC 253, and Arp 220; these galactic nuclei have varying star formation efficiencies. Arp 220 shows higher abundances of SiO and HC$_3$N than NGC 3256 and NGC 253. Abundances of most species do not show strong correlation with the star formation efficiencies, although the CH$_3$CCH abundance seems to have a weak positive correlation with the star formation efficiency. Lastly, the chemistry of spiral arm positions in NGC 3256 is compared with that of W 51, a Galactic molecular cloud complex in a spiral arm. We found higher fractional abundances of shock tracers, and possibly also higher dense gas fraction in NGC 3256 compared with W 51.

astro-ph.GA↗

arXiv2017

Fast, Collimated Outflow in the Western Nucleus of Arp 220

We present the first spatially and spectrally resolved image of the molecular outflow in the western nucleus of Arp\,220. The outflow, seen in HCN~(1--0) by ALMA, is compact and collimated, with extension $\lesssim$ 120\,pc. Bipolar morphology emerges along the minor axis of the disk, with redshifted and blueshifted components reaching maximum inclination-corrected velocity of $\sim\,\pm$\,840\,km\,s$^{-1}$. The outflow is also seen in CO and continuum emission, the latter implying that it carries significant dust. We estimate a total mass in the outflow of $\geqslant$\,10$^{6}$\,M$_{\odot}$, a dynamical time of $\sim$\,10$^{5}$\,yr, and mass outflow rates of $\geqslant55$\,M$_{\odot}$\,yr$^{-1}$ and $\geqslant\,15$\,M$_{\odot}$\,yr$^{-1}$ for the northern and southern lobes, respectively. Possible driving mechanisms include supernovae energy and momentum transfer, radiation pressure feedback, and a central AGN. The latter could explain the collimated morphology of the HCN outflow, however we need more complex theoretical models, including contribution from supernovae and AGN, to pinpoint the driving mechanism of this outflow.

astro-ph.GA↗

arXiv2017

Resolved Structure of Arp 220 Nuclei at λ~3 mm

We analyze 3 mm emission of the ultraluminous infrared galaxy Arp 220 for spatially-resolved structure and spectral properties of the merger nuclei. ALMA archival data at ~0.05" resolution are used for extensive visibility fitting and deep imaging of continuum emission. The data are fitted well with two concentric components for each nucleus, such as two Gaussians or one Gaussian plus one exponential disk. The larger components in individual nuclei are similar in shape and extent, ~100-150 pc, to the cm-wave emission due to supernovae. They are therefore identified with the known starburst nuclear disks. The smaller components in both nuclei have about a few 10 pc sizes and peak brightness temperatures (Tb) more than twice higher than in previous single-Gaussian fitting. They correspond to the dust emission that we find centrally concentrated in both nuclei by subtracting the plasma emission measured at 33 GHz. The dust emission in the western nucleus is found to have a peak Tb ~ 530 K and a full width at half maximum of about 20 pc. This component is estimated to have a bolometric luminosity on the order of 10^{12.5} Lsun and a 20 pc-scale luminosity surface density 10^{15.5} Lsun/kpc^2. A luminous AGN is a plausible energy source for these high values while other explanations remain to be explored. Our continuum image also reveals a third structural component of the western nucleus --- a pair of faint spurs perpendicular to the disk major axis. We attribute it to a bipolar outflow from the highly inclined (i ~ 60 deg) western nuclear disk.

astro-ph.GA↗

arXiv2017

Submillimeter Array CO(2-1) Imaging of the NGC 6946 Giant Molecular Clouds

We present a CO(2-1) mosaic map of the spiral galaxy NGC 6946 by combining data from the Submillimeter Array and the IRAM 30 m telescope. We identify 390 giant molecular clouds (GMCs) from the nucleus to 4.5 kpc in the disk. GMCs in the inner 1 kpc are generally more luminous and turbulent, some of which have luminosities >10^6 K km/s pc^2 and velocity dispersions >10 km/s. Large-scale bar-driven dynamics likely regulate GMC properties in the nuclear region. Similar to the Milky Way and other disk galaxies, GMC mass function of NGC 6946 has a shallower slope (index>-2) in the inner region, and a steeper slope (index<-2) in the outer region. This difference in mass spectra may be indicative of different cloud formation pathways: gravitational instabilities might play a major role in the nuclear region, while cloud coalescence might be dominant in the outer disk. Finally, the NGC 6946 clouds are similar to those in M33 in terms of statistical properties, but they are generally less luminous and turbulent than the M51 clouds.

astro-ph.GA↗

arXiv2016

SMA Observations of the Extended CO(6-5) Emission in the Starburst Galaxy NGC253

We present observations of the $^{12}$CO(6-5) line and 686GHz continuum emission in NGC253 with the Submillimeter Array at an angular resolution of ~4arcsec. The $^{12}$CO(6-5) emission is clearly detected along the disk and follows the distribution of the lower $^{12}$CO line transitions with little variations of the line ratios in it. A large-velocity gradient analysis suggests a two-temperature model of the molecular gas in the disk, likely dominated by a combination of low-velocity shocks and the disk wide PDRs. Only marginal $^{12}$CO(6-5) emission is detected in the vicinity of the expanding shells at the eastern and western edges of the disk. While the eastern shell contains gas even warmer (T$_{\rm kin}$>300~K) than the hot gas component (T$_{\rm kin}$=300K) of the disk, the western shell is surrounded by gas much cooler (T$_{\rm kin}$=60K) than the eastern shell but somewhat hotter than the cold gas component of the disk (for similar H$_2$ and CO column densities), indicative of different (or differently efficient) heating mechansisms. The continuum emission at 686GHz in the disk agrees well in shape and size with that at lower (sub-)millimeter frequencies, exhibiting a spectral index consistent with thermal dust emission. We find dust temperatures of ~10-30K and largely optically thin emission. However, our fits suggest a second (more optically thick) dust component at higher temperatures (T$_{\rm d}$>60K), similar to the molecular gas. We estimate a global dust mass of ~10$^6$Msun for the disk translating into a gas-to-dust mass ratio of a few hundred consistent with other nearby active galaxies.

astro-ph.GA↗

arXiv2015

Infrared and X-Ray Evidence of an AGN in the NGC 3256 Southern Nucleus

We investigate signs of Active Galactic Nucleus (AGN) in the luminous infrared galaxy NGC 3256 at both infrared and X-ray wavelengths. NGC 3256 has double, the Northern and Southern, nuclei (hereafter, N and S nuclei, respectively). We show that the Spitzer IRAC colors extracted at the S nucleus are AGN-like, and the Spitzer IRS spectrum is bluer at <6um than at the N nucleus. We built for the S nucleus an AGN-starburst composite model with a heavily absorbed AGN to successfully reproduce not only the IRAC and IRS specrophotometries at ~3arcsec but also the very deep silicate 9.7um absorption observed at 0.36" scale by Diaz-Santos et al. We found a 2.2um compact source at the S nucleus in a HST NICMOS image and identified its unresolved core (at 0.26" resolution) with the compact core in previous mid-infrared observations at comparable resolution. The flux of the 2.2umm core is consistent with our AGN spectral energy distribution model. We also analyzed a deeper than ever Chandra X-ray spectrum of the unresolved (at 0.5" resolution) source at the S nucleus. We found that a dual-component power-law model (for primary and scattered ones) fits an apparently very hard spectrum with a moderately large absorption on the primary component. Together with a limit on equivalent width of a fluorescent Fe-K emission line at 6.4 keV, the X-ray spectrum is consistent with a typical Compton-thin Seyfert 2. We therefore suggest that the S nucleus hosts a heavily absorbed low-luminosity AGN.

astro-ph.GA↗

arXiv2014

High-Resolution Radio Continuum Measurements of the Nuclear Disks of Arp 220

We present new Karl G. Jansky Very Large Array radio continuum images of the nuclei of Arp 220, the nearest ultra-luminous infrared galaxy. These images have both the angular resolution to study detailed morphologies of the two nuclei that power the system and sensitivity to a wide range of spatial scales. At 33 GHz, and with a resolution of 0".081 x 0".063 (29.9 x 23.3 pc), we resolve the emission surrounding both nuclei and conclude that is mostly synchrotron in nature. The spatial distributions of radio emission in both nuclei are well described by exponential profiles. These have deconvolved half-light radii of 51 and 35 pc for the eastern and western nuclei, and they match the number density profile of radio supernovae observed with very long baseline interferometry. This similarity might be due to the fast cooling of cosmic rays electrons caused by the presence of a strong (~ mG) magnetic field in this system. We estimate high luminosity surface densities of $\mathrm{Σ_{IR} \sim 4.2^{+1.6}_{-0.7} \times 10^{13}}$ (east) and $\mathrm{\sim 9.7^{+3.7}_{-2.4} \times 10^{13}~(west)~L_{\odot}~kpc^{-2}}$, and star formation rate surface densities of $\mathrm{Σ_{SFR} \sim 10^{3.7\pm0.1}}$ (east) and $\mathrm{\sim 10^{4.1\pm0.1}~(west)~M_{\odot}~yr^{-1}~kpc^{-2}}$. These values, especially for the western nucleus are, to our knowledge, the highest luminosity and star formation rate surface densities measured for any star-forming system. Despite these high values, the nuclei lie below the dusty Eddington limit in which radiation pressure is balanced only by self-gravity. The small measured sizes also imply that the nuclei of Arp 220 are only transparent in the frequency range ~ 5 to 350 GHz. Our results offer no clear evidence that an active galactic nucleus dominates the emission from either nucleus at 33 GHz.

astro-ph.GA↗

arXiv2014

A Luminous Infrared Merger with Two Bipolar Molecular Outflows: ALMA and SMA Observations of NGC 3256

We report ALMA and SMA observations of the luminous infrared merger NGC 3256, the most luminous galaxy within z=0.01. Both of the two merger nuclei separated by 5" (0.8 kpc) on the sky have a compact concentration of molecular gas, i.e., nuclear disks with Sigma_mol > 10^3 Msun pc^-2. The one at the northern nucleus is face-on while the southern nuclear disk is almost edge-on. The northern nucleus is more massive and has molecular arcs and spiral arms around. The high-velocity molecular gas previously found in the system is resolved to two molecular outflows associated with each of the two nuclei. The molecular outflow from the northern nuclear disk is part of a starburst-driven superwind seen nearly pole on. Its maximum velocity is >750 km/s and its mass outflow rate is estimated to be > 60 Msun/yr for a conversion factor N_{H_2}/I_{CO(1-0)}=1x10^20 cm^-2/(K km/s). The outflow from the southern nucleus is a highly collimated bipolar molecular jet seen nearly edge-on. Its line-of-sight velocity increases with distance out to 300 pc from the southern nucleus. Its maximum de-projected velocity is ~2000 km/s for the estimated inclination and should exceed 1000 km/s even allowing for its uncertainty. The mass outflow rate is estimated to be >50 Msun/yr for this outflow. There are possible signs that this southern outflow has been driven by a bipolar radio jet from an AGN that became inactive very recently. The sum of these outflow rates, although subject to the uncertainty in the molecular mass estimate, either exceeds or compares to the total star formation rate in NGC 3256. The feedback from nuclear activities in the form of molecular outflows is therefore significant in the gas consumption budget, and hence evolution, of this luminous infrared galaxy. (abridged)

astro-ph.GA↗

arXiv2013

Submillimeter Interferometry of the Luminous Infrared Galaxy NGC 4418: A Hidden Hot Nucleus with an Inflow and an Outflow

We have observed the nucleus of the nearby luminous infrared galaxy NGC 4418 with subarcsec resolution at 860 and 450 micron for the first time to characterize its hidden power source. A ~20 pc (0.1") hot dusty core was found inside a 100 pc scale concentration of molecular gas at the galactic center. The 860 micron continuum core has a deconvolved (peak) brightness temperature of 120-210 K. The CO(3-2) peak brightness temperature there is as high as 90 K at 50 pc resolution. The core has a bolometric luminosity of about 10^{11} Lsun, which accounts for most of the galaxy luminosity. It is Compton thick (N_H >~ 10^{25} cm^{-2}) and has a high luminosity-to-mass ratio ~500 Lsun/Msun as well as a high luminosity surface density 10^{8.5+-0.5} Lsun pc^{-2}. These parameters are consistent with an AGN to be the main luminosity source (with an Eddington ratio about 0.3) while they can be also due to a young starburst near its maximum L/M. We also found an optical color (reddening) feature that we attribute to an outflow cone emanating from the nucleus. The hidden hot nucleus thus shows evidence of both an inflow, previously seen with absorption lines, and the new outflow reported here in a different direction. The nucleus must be rapidly evolving with these gas flows.

astro-ph.CO↗

arXiv2012

High-Resolution Sub/millimeter Observations of Mergers and Luminous Galaxy Nuclei

I present recent high-resolution submillimeter and millimeter observations of molecular gas and dust in some mergers, luminous galaxy nuclei, and possible mergers. Such observations tell us the behavior and properties of interstellar medium in merger nuclei. For example, the gas sometimes makes a mini disk around the remnant nucleus, feeds starburst and/or a massive black hole there, hides such a power source(s) by enveloping it, and is blown out by the embedded power source. Even when the power source is completely enveloped and hidden we can still constrain its physical parameters and nature from high-resolution (sub)millimeter observations. The observables include gas motion such as rotation (hence dynamical mass) and inflow/outflow, luminosity and luminosity density of the embedded nucleus, and mass, temperature, density, chemical composition, and (sometimes unusual) excitation conditions of gas.

astro-ph.CO↗

arXiv2011

Star-forming Cloud Complexes in the Central Molecular Zone of NGC 253

We report 350 and 230 GHz observations of molecular gas and dust in the starburst nucleus of NGC 253 at 20-40 pc (1"-2") resolution. The data contain CO(3-2), HCN(4-3), CO(2-1), 13CO(2-1), C18O(2-1), and continuum at 0.87 mm and 1.3 mm toward the central kiloparsec. The CO(2-1) size of the galaxy's central molecular zone (CMZ) is measured to be about 300 pc x 100 pc at the half maximum of intensity. Five clumps of dense and warm gas stand out in the CMZ at arcsecond resolution, and they are associated with compact radio sources due to recent massive star formation. They contribute one third of the CO emission in the central 300 pc and have 12CO peak brightness temperatures around 50 K, molecular gas column densities on the order of 10^{4} Msun pc^{-2}, gas masses on the order of 10^{7} Msun in the size scale of 20 pc, volume-averaged gas densities of n(H2) ~ 4000 cm^{-3}, and high HCN-to-CO ratios suggestive of higher fractions of dense gas than in the surrounding environment. It is suggested that these are natal molecular cloud complexes of massive star formation. The CMZ of NGC 253 is also compared with that of our Galaxy in CO(2-1) at the same 20 pc resolution. Their overall gas distributions are strikingly similar. The five molecular cloud complexes appear to be akin to such molecular complexes as Sgr A, Sgr B2, Sgr C, and the l=1.3deg cloud in the Galactic center. On the other hand, the starburst CMZ in NGC 253 has higher temperatures and higher surface (and presumably volume) densities than its non-starburst cousin.

astro-ph.CO↗

arXiv2010

Vibrationally Excited HCN in the Luminous Infrared Galaxy NGC 4418

Infrared pumping and its effect on the excitation of HCN molecules can be important when using rotational lines of HCN to probe dense molecular gas in galaxy nuclei. We report the first extragalactic detection of (sub)millimeter rotational lines of vibrationally excited HCN, in the dust-enshrouded nucleus of the luminous infrared galaxy NGC 4418. We estimate the excitation temperature of T_vib ~ 230 K between the vibrational ground and excited (v_2=1) states. This excitation is most likely due to infrared radiation. At this high vibrational temperature the path through the v_2=1 state must have a strong impact on the rotational excitation in the vibrational ground level, although it may not be dominant for all rotational levels. Our observations also revealed nearly confusion limited lines of CO, HCN, HCO+, H13CN, HC15N, CS, N2H+, and HC3N at lambda ~ 1 mm. Their relative intensities may also be affected by the infrared pumping.

astro-ph.CO↗

arXiv2009

P-Cygni Profiles of Molecular Lines toward Arp 220 Nuclei

We report ~100 pc (0.3") resolution observations of (sub)millimeter HCO+ and CO lines in the ultraluminous infrared galaxy Arp 220. The lines peak at two merger nuclei, with HCO+ being more spatially concentrated than CO. Asymmetric line profiles with blueshifted absorption and redshifted emission are discovered in HCO+(3-2) and (4-3) toward the two nuclei and in CO(3-2) toward one nucleus. We suggest that these P-Cygni profiles are due to ~100 km/s outward motion of molecular gas from the nuclei. This gas is most likely outflowing from the inner regions of the two nuclear disks rotating around individual nuclei, clearing the shroud around the luminosity sources there.

astro-ph.GA↗

arXiv2008

SMA CO(J=6-5) and 435 micron interferometric imaging of the nuclear region of Arp 220

We have used the Submillimeter Array (SMA) to make the first interferometric observations (beam size ~1") of the 12CO J=6-5 line and 435 micron (690 GHz) continuum emission toward the central region of the nearby ULIRG Arp 220. These observations resolve the eastern and western nuclei from each other, in both the molecular line and dust continuum emission. At 435 micron, the peak intensity of the western nucleus is stronger than the eastern nucleus, and the difference in peak intensities is less than at longer wavelengths. Fitting a simple model to the dust emission observed between 1.3 mm and 435 micron suggests that dust emissivity power law index in the western nucleus is near unity and steeper in the eastern nucleus, about 2, and that the dust emission is optically thick at the shorter wavelength. Comparison with single dish measurements indicate that the interferometer observations are missing ~60% of the dust emission, most likely from a spatially extended component to which these observations are not sensitive. The 12CO J=6-5 line observations clearly resolve kinematically the two nuclei. The distribution and kinematics of the 12CO J=6-5 line appear to be very similar to lower J CO lies observed at similar resolution. Analysis of multiple 12CO line intensities indicates that the molecular gas in both nuclei have similar excitation conditions, although the western nucleus is warmer and denser. The excitation conditions are similar to those found in other extreme environments, including M82, Mrk 231, and BR 1202-0725. Simultaneous lower resolution observations of the 12CO, 13CO, and C18O J=2-1 lines show that the 13CO and C18O lines have similar intensities, which suggests that both of these lines are optically thick, or possibly that extreme high mass star formation has produced in an overabundance of C18O.

astro-ph↗

arXiv2008

SMA Imaging of CO(3-2) Line and 860 micron Continuum of Arp 220 : Tracing the Spatial Distribution of Luminosity

We used the Submillimeter Array (SMA) to image 860 micron continuum and CO(3-2) line emission in the ultraluminous merging galaxy Arp 220, achieving a resolution of 0.23" (80 pc) for the continuum and 0.33" (120 pc) for the line. The CO emission peaks around the two merger nuclei with a velocity signature of gas rotation around each nucleus, and is also detected in a kpc-size disk encompassing the binary nucleus. The dust continuum, in contrast, is mostly from the two nuclei. The beam-averaged brightness temperature of both line and continuum emission exceeds 50 K at and around the nuclei, revealing the presence of warm molecular gas and dust. The dust emission morphologically agrees with the distribution of radio supernova features in the east nucleus, as expected when a starburst heats the nucleus. In the brighter west nucleus, however, the submillimeter dust emission is more compact than the supernova distribution. The 860 micron core, after deconvolution, has a size of 50-80 pc, consistent with recent 1.3 mm observations, and a peak brightness temperature of (0.9-1.6)x10^2 K. Its bolometric luminosity is at least 2x10^{11} Lsun and could be ~10^{12} Lsun depending on source structure and 860 micron opacity, which we estimate to be of the order of tau_{860} ~ 1 (i.e., N_{H_2} ~ 10^{25} cm^{-2}). The starbursting west nuclear disk must have in its center a dust enshrouded AGN or a very young starburst equivalent to hundreds of super star clusters. Further spatial mapping of bolometric luminosity through submillimeter imaging is a promising way to identify the heavily obscured heating sources in Arp 220 and other luminous infrared galaxies.

astro-ph↗

arXiv2006

Detection of CO Hotspots Associated with Young Clusters in the Southern Starburst Galaxy NGC 1365

We have used the Submillimeter Array for the first interferometric CO imaging toward the starburst-Seyfert nucleus of the southern barred spiral galaxy NGC 1365, which is one of the four galaxies within 30 Mpc that have L_{8-1000micron} >= 10^{11} Lsun. Our mosaic maps of 12CO, 13CO, and C18O (J=2-1) emission at up to 2" (200 pc) resolutions have revealed a circumnuclear gas ring and several CO clumps in the central 3 kpc. The molecular ring shows morphological and kinematical signs of bar-driven gas dynamics, and the region as a whole is found to follow the star formation laws of Kennicutt. We have found that some of the gas clumps and peaks in CO brightness temperature, which we collectively call CO hotspots, coincide with the radio and mid-infrared sources previously identified as dust-enshrouded super star clusters. This hotspot-cluster association suggests that either the formation of the most massive clusters took place in large molecular gas concentrations (of Sigma_{mol} ~10^{3} Msun/pc^2 in 200 pc scales) or the clusters have heated their ambient gas to cause or enhance the CO hotspots. The active nucleus is in the region of weak CO emission and is not associated with distinctive molecular gas properties.

astro-ph↗

arXiv2006

Elevation angle dependence of the SMA antenna focus position

We report the measurement results and compensation of the antenna elevation angle dependences of the Sub-millimeter Array (SMA) antenna characteristics. Without optimizing the subreflector (focus) positions as a function of the antenna elevation angle, antenna beam patterns show lopsided sidelobes, and antenna efficiencies show degradations. The sidelobe level increases and the antenna efficiencies decrease about 1% and a few %, respectively, for every 10 degrees change in the elevation angle at the measured frequency of 237 GHz. We therefore obtained the optimized subreflector positions for X (azimuth), Y (elevation), and Z (radio optics) focus axes at various elevation angles for all the eight SMA antennas. The X axis position does not depend on the elevation angle. The Y and Z axes positions depend on the elevation angles, and are well fitted with a simple function for each axis with including a gravity term (cosine and sine of elevation, respectively). In the optimized subreflector positions, the antenna beam patterns show low level symmetric sidelobe of at most a few %, and the antenna efficiencies stay constant at any antenna elevation angles. Using one set of fitted functions for all antennas, the SMA is now operating with real-time focusing, and showing constant antenna characteristics at any given elevation angle.

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