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At least 37 records · Page 2

Development of a Multivariable Parametric Cost Analysis for Space-Based Telescopes

Over the past 400 years, the telescope has proven to be a valuable tool in helping humankind understand the Universe around us. The images and data produced by telescopes have revolutionized planetary, solar, stellar, and galactic astronomy and have inspired a wide range of people, from the child who dreams about the images seen on NASA websites to the most highly trained scientist. Like all scientific endeavors, astronomical research must operate within the constraints imposed by budget limitations. Hence the importance of understanding cost: to find the balance between the dreams of scientists and the restrictions of the available budget. By logically analyzing the data we have collected for over thirty different telescopes from more than 200 different sources, statistical methods, such as plotting regressions and residuals, can be used to determine what drives the cost of telescopes to build and use a cost model for space-based telescopes. Previous cost models have focused their attention on ground-based telescopes due to limited data for space telescopes and the larger number and longer history of ground-based astronomy. Due to the increased availability of cost data from recent space-telescope construction, we have been able to produce and begin testing a comprehensive cost model for space telescopes, with guidance from the cost models for ground-based telescopes. By separating the variables that effect cost such as diameter, mass, wavelength, density, data rate, and number of instruments, we advance the goal to better understand the cost drivers of space telescopes.. The use of sophisticated mathematical techniques to improve the accuracy of cost models has the potential to help society make informed decisions about proposed scientific projects. An improved knowledge of cost will allow scientists to get the maximum value returned for the money given and create a harmony between the visions of scientists and the reality of a budget.

Dollinger, Courtnay↗

Large Space Optics: From Hubble to JWST and Beyond

If necessity truly is the mother of invention, then advances in lightweight space mirror technology have been driven by launch vehicle mass and volume constraints. In the late 1970 s, at the start of Hubble development, the state of the art in ground based telescopes was 3 to 4 meter monolithic primary mirrors with masses of 6000 to 10,000 kg - clearly too massive for the planned space shuttle 25,000 kg capability to LEO. Necessity led Hubble to a different solution. Launch vehicle mass constraints (and cost) resulted in the development of a 2.4 meter lightweight eggcrate mirror. At 810 kg (180 kg/m2), this mirror was approximately 7.4% of HST s total 11,110 kg mass. And, the total observatory structure at 4.3 m x 13.2 m fit snuggly inside the space shuttle 4.6 m x 18.3 m payload bay. In the early 1990 s, at the start of JWST development, the state of the art in ground based telescopes was 8 meter class monolithic primary mirrors (16,000 to 23,000 kg) and 10 meter segmented mirrors (14,400 kg). Unfortunately, launch vehicles were still constrained to 4.5 meter payloads and 25,000 kg to LEO or 6,600 kg to L2. Furthermore, science now demanded a space telescope with 6 to 8 meter aperture operating at L2. Mirror technology was identified as a critical capability necessary to enable the next generation of large aperture space telescopes. Specific telescope architectures were explored via three independent design concept studies conducted during the summer of 1996 (1). These studies identified two significant architectural constraints: segmentation and areal density. Because the launch vehicle fairing payload dynamic envelop diameter is approximately 4.5 meters, the only way to launch an 8 meter class mirror is to segment it, fold it and deploy it on orbit - resulting in actuation and control requirements. And, because of launch vehicle mass limits, the primary mirror allocation was only 1000 kg - resulting in a maximum areal density of 20 kg/m2. At the inception of JWST in 1996, such a capability did not exist. A highly successful technology development program was initiated resulting in matured and demonstrated mirror technology for JWST (2, 3). Today, the JWST 6.5 meter primary mirror has an areal density of 25 kg/m2 for a total mass of 625 kg or 9.6% of the total JWST observatory mass of 6,500 kg. Looking into the future, science requires increasing larger collecting apertures. Ground based telescopes are already moving towards 30+ meter mirrors. The only way to meet this challenge for space telescopes is via even lower areal density mirrors or on-orbit assembly or larger launch vehicles (4). The planned NASA Ares V with its 10 meter fairing and 55,000 kg payload to L2 eliminates this constraint (5).

Stahl, H. Philip↗

Hubble Space Telescope First Servicing Mission Prelaunch Mission Operation Report

The Hubble Space Telescope (HST) is a high-performance astronomical telescope system designed to operate in low-Earth orbit. It is approximately 43 feet long, with a diameter of 10 feet at the forward end and 14 feet at the aft end. Weight at launch was approximately 25,000 pounds. In principle, it is no different than the reflecting telescopes in ground-based astronomical observatories. Like ground-based telescopes, the HST was designed as a general-purpose instrument, capable of using a wide variety of scientific instruments at its focal plane. This multi-purpose characteristic allows the HST to be used as a national facility, capable of supporting the astronomical needs of an international user community. The telescope s planned useful operational lifetime is 15 years, during which it will make observations in the ultraviolet, visible, and infrared portions of the spectrum. The extended operational life of the HST is possible by using the capabilities of the Space Transportation System to periodically visit the HST on-orbit to replace failed or degraded components, install instruments with improved capabilities, re-boost the HST to higher altitudes compensating for gravitational effects, and to bring the HST back to Earth when the mission is terminated. The largest ground-based observatories, such as the 200-inch aperture Hale telescope at Palomar Mountain, California, can recognize detail in individual galaxies several billion light years away. However, like all earthbound devices, the Hale telescope is limited because of the blurring effect of the Earth s atmosphere. Further, the wavelength region observable from the Earth s surface is limited by the atmosphere to the visible part of the spectrum. The very important ultraviolet portion of the spectrum is lost. The HST uses a 2.4-meter reflective optics system designed to capture data over a wavelength region that reaches far into the ultraviolet and infrared portions of the spectrum.

Source record↗

Characterizing GEO Titan IIIC Transtage Fragmentations using Ground-Based and Telescopic Measurements

In a continued effort to better characterize the geosynchronous orbit (GEO) environment, NASA's Orbital Debris Program Office (ODPO) utilizes various ground-based optical assets to acquire photometric and spectral data of known debris associated with fragmentations in or near GEO. The Titan IIIC Transtage upper stage is known to have fragmented four times. Two of the four fragmentations were in GEO while the Transtage fragmented a third time in GEO transfer orbit. The forth fragmentation occurred in low Earth orbit. To better assess and characterize these fragmentations, the NASA ODPO acquired a Titan Transtage test and display article previously in the custody of the 309th Aerospace Maintenance and Regeneration Group (AMARG) in Tucson, Arizona. After initial inspections at AMARG demonstrated that it was of sufficient fidelity to be of interest, the test article was brought to NASA Johnson Space Center (JSC) to continue material analysis and historical documentation. The Transtage has undergone two separate spectral measurement campaigns to characterize the reflectance spectroscopy of historical aerospace materials. These data have been incorporated into the NASA Spectral Database, with the goal of using telescopic data comparisons for potential material identification. A Light Detection and Ranging (LIDAR) system scan also has been completed and a scale model has been created for use in the Optical Measurement Center (OMC) for photometric analysis of an intact Transtage, including bidirectional reflectance distribution function (BRDF) measurements. An historical overview of the Titan IIIC Transtage, the current analysis that has been done to date, and the future work to be completed in support of characterizing the GEO and near GEO orbital debris environment will be discussed in the subsequent presentation.

Cowardin, Heather↗

Characterizing GEO Titan IIIC Transtage Fragmentations Using Ground-Based and Telescopic Measurements

In a continued effort to better characterize the Geosynchronous Orbit (GEO) environment, NASA's Orbital Debris Program Office (ODPO) utilizes various ground-based optical assets to acquire photometric and spectral data of known debris associated with fragmentations in or near GEO. The Titan IIIC Transtage upper stage is known to have fragmented four times. Two of the four fragmentations were in GEO while a third Transtage fragmented in GEO transfer orbit. The forth fragmentation occurred in Low Earth Orbit. In order to better assess and characterize these fragmentations, the NASA ODPO acquired a Titan Transtage test and display article previously in the custody of the 309th Aerospace Maintenance and Regeneration Group (AMARG) in Tucson, Arizona. After initial inspections at AMARG demonstrated that the test article was of sufficient fidelity to be of interest, the test article was brought to JSC to continue material analysis and historical documentation of the Titan Transtage. The Transtage has been subject to two separate spectral measurement campaigns to characterize the reflectance spectroscopy of historical aerospace materials. These data have been incorporated into the NASA Spectral Database, the goal being to enable comparison with telescopic data and potential material identification. A LIDAR scan has been completed and a scale model has been created for use in the Optical Measurement Center for photometric analysis of an intact Transtage, including a BRDF. An historical overview of the Titan IIIC Transtage, the current analysis that has been done to date, and the future work to be completed in support of characterizing the GEO and near GEO orbital debris environment will be discussed in the subsequent presentation.

Cowardin, H.↗

Reverberation Mapping of Markarian

The Seyfert 1 galaxy Markarian 335 will be the subject of a massive spectroscopic monitoring program during the final episode of IUE (International Ultraviolet Explorer) operations. This program, which is being undertaken by the International AGN (Active Galactic Nucleus) Watch consortium, will produce approximately 750 SWP spectra over a 75-day program, and will serve as the cornerstone for a closely coordinated multiwavelength effort involving XTE (X-ray Timing Explorer), HST (Hubble Space Telescope), and ground-based telescopes. The primary purpose of this program is to characterize the geometry and kinematics of the broad emission-line region by reverberation mapping. On behalf of the consortium, we are requesting funds to process these data, to perform the preliminary analysis, and to prepare the data for publication.

Peterson, Bradley M.↗

First Stars and Galaxies, the Roadmap Ahead: Observation

A complete observational understanding of the first stars and galaxies will require four facilities: JWST, 30m ground-based telescopes, ALMA, and the SKA. Each provides complementary capabilities. JWST is our best hope for looking to very high redshift. 30m-class ground-based telescopes provide sensitivity to the rest-frame ultraviolet with high-resolution imaging and high-resolution NIR spectroscopy, possibly reaching as far as z approx.15. They will also allow us to study stellar populations in nearby galaxies and examine the fossil record of the first stars. ALMA will image the redshifted dust continuum emission from evolving galaxies out to z approx.10. The SKA will do cosmic tomography, mapping the process of reionization.

Gardner, Jonathan P.↗

Balloon-Borne Observations of the Polarization of the Cosmic Microwave Background

This final report is confined to the sub-contract to Caltech, and does not cover work at the PI institution (PI John Ruhl, Case Western Reserve University). In our original proposal, we planned to fly BOOMERANG twice, in the 2000 / 2001 and 2002 / 2003 Austral LDB seasons. The first flight was to have used a newly developed detector technology: the Polarization Sensitive Bolometer (PSB). The second flight was to have used a yet more sophisticated technology: a polarization sensitive, antenna-coupled array (CAMWA). The development of both technologies proceeded more slowly than anticipated. In the end, we were successful in developing the PSB technology to maturity, integrating it into the payload, and flying the payload once during the 2002/2003 Austral season. The payload performed well during this flight, and analysis of the data is in progress. As originally proposed, we have also continued to work on analysis of the data from the 1998 flight, and several publications have resulted. Sufficient progress has been made on the CAMWA technology that we expect to be able to field it into an instrument in 2 to 3 years. However, ground-based telescopes now appear to be a more attractive platform for CMB polarimetry, owing to the longer integration times available. We thus anticipate first implementing CAMWA on a ground-based telescope at South Pole.

Source record↗

The scaling relationship between telescope cost and aperture size for very large telescopes

Cost data for ground-based telescopes of the last century are analyzed for trends in the relationship between aperture size and cost. We find that for apertures built prior to 1980, costs scaled as aperture size to the 2.8 power, which is consistent with the precious finding of Meinel (1978). After 1980, 'traditional' monolithic mirror telescope costs have scaled as aperture to the 2.5 power. The large multiple mirror telescopes built or in construction during this time period (Keck, LBT, GTC) appear to deviate from this relationship with significant cost savings as a result, although it is unclear what power law such structures follow. We discuss the implications of the current cost-aperture size data on the proposed large telescope projects of the next ten to twenty years. Structures that naturally tend towards the 2.0 power in the cost-aperture relationship will be the favorable choice for future extremely large apertures; out expectation is that space-based structures will ultimately gain economic advantage over ground-based ones.

telescope costs↗

Ground-Based VIS/NIR Reflectance Spectra of 25143 Itokawa: What Hayabusa will See and How Ground-Based Data can Augment Analyses

Planning for the arrival of the Hayabusa spacecraft at asteroid 25143 Itokawa includes consideration of the expected spectral information to be obtained using the AMICA and NIRS instruments. The rotationally-resolved spatial coverage the asteroid we have obtained with ground-based telescopic spectrophotometry in the visible and near-infrared can be utilized here to address expected spacecraft data. We use spectrophotometry to simulate the types of data that Hayabusa will receive with the NIRS and AMICA instruments, and will demonstrate them here. The NIRS will cover a wavelength range from 0.85 m, and have a dispersion per element of 250 Angstroms. Thus, we are limited in coverage of the 1.0 micrometer and 2.0 micrometer mafic silicate absorption features. The ground-based reflectance spectra of Itokawa show a large component of olivine in its surface material, and the 2.0 micrometer feature is shallow. Determining the olivine to pyroxene abundance ratio is critically dependent on the attributes of the 1.0- and 2.0 micrometer features. With a cut-off near 2,1 micrometer the longer edge of the 2.0- feature will not be obtained by NIRS. Reflectance spectra obtained using ground-based telescopes can be used to determine the regional composition around space-based spectral observations, and possibly augment the longer wavelength spectral attributes. Similarly, the shorter wavelength end of the 1.0 micrometer absorption feature will be partially lost to the NIRS. The AMICA filters mimic the ECAS filters, and have wavelength coverage overlapping with the NIRS spectral range. We demonstrate how merging photometry from AMICA will extend the spectral coverage of the NIRS. Lessons learned from earlier spacecraft to asteroids should be considered.

Vilas, Faith↗

Far UV camera/spectrograph

In March 1610, Galileo Galilei reported the first use of a telescope to view mountains and maria on the Moon. On April 21, 1972, the Apollo 16 commander pointed a somewhat more complex optical instrument at the Earth from the Moon and obtained several remarkable photographs showing atmospheric rather than surface features. The optical part of the far UV camera (aperture, 7.5 cm) was not much larger than Galileo's telescope. Like his, this instrument was also pointed at other celestial objects that Galileo viewed, including the Milky Way and Jupiter, and the Large Magellanic Cloud (LMC), which is not visible from Italy. More important, the far UV camera/spectrograph recorded light in the invisible band of wavelengths between 50 and 160 nm, approximately one-third the wavelength that can penetrate the atmosphere of the Earth to ground-based telescopes. As described in more detail in this section, these UV observations from the Moon allow study of the entire atmosphere of the Earth and the geocorona. The photographs show hydrogen and other gases in the solar wind and interplanetary media, and they provide new data on stars, nebulae, and galaxies much farther away. When used as a spectrograph, the instrument distributes the light it receives according to wavelength, and the resulting spectrum shows bright lines or gaps known to be characteristic of various gases, such as hydrogen (H), helium (He), oxygen (O), nitrogen (N), and neon (Ne). If a gas cloud is hot, the atoms are excited and the spectrum shows bright emission lines; if it is cool, the atoms absorb light, leaving gaps or absorption lines. The far UV camera is blind to ordinary visible light; for that reason, the photographs show very few of the stars mapped by ground-based telescopes. Only the very-high-temperature (blue) stars of spectral classes O, B, and possibly A (temperatures from 50000 ° down to 10000°K) are expected to be recorded. Image blackness or density on the negatives also depends on the brightness of the star, which astronomers measure in an inverted logarithmic scale of magnitudes. A star of 6 magnitudes (mag.) can barely be seen with the unaided eye. An 11-mag. star is 100 times fainter, and a 12-mag. star is 2.5 times fainter yet. The faintest star recorded by the far UV camera is at least 11 mag., which is called the limiting magnitude.

George R. Carruthers↗

Experimentally-Derived Bidirectional Reflectance Distribution Function Data in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and zenith angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper discusses the validation of experimental BRDF and phase function approximations produced in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is imaged and the subsequent experimental functions are scrutinized to confirm that they correspond to an object that has an isotropic luminance. With the image processing algorithm validated, test objects with varying optical properties are then imaged to confirm that the produced photometric functions are both unique and repeatable. Once the validation is complete, the OMC will be used to evaluate a subset of fragments from a hypervelocity impact test of a mock-up satellite and assess the appropriate phase function and size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Orbital Debris Program Office (ODPO)↗

Experimentally-Derived Phase Function Approximations in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and elevation angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper presents the initial BRDF and phase function approximations for various fragments/targets acquired in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is used as a baseline for initial size estimation calculations and phase function comparisons. Spacecraft materials and fragments from hypervelocity laboratory impact tests are also presented to compare against the current assumed Lambertian phase function used for size estimates. This paper presents the preliminary phase function analysis and plan forward to utilize a laboratory-based phase function to improve the current optical size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Hostetler, J.↗

Synoptic planetary imaging with the LST high-resolution camera

The value of synoptic imaging of the planets is illustrated. Advantages of the large space telescope, as compared with ground based telescopes, planetary orbiters, and flybys are discussed. Desirable LST camera parameters and observing strategies are considered from the standpoint of synoptic imaging.

Baum, W. A.↗

Astronomical studies of the major planets, natural satellites and asteroids using the 2.24 m telescope

Ground based detection of east-west asymmetries in the Jovian torus, three dimensional models of the plasma conditions in the Jovian torus, rotational variations in methane band images of Neptune, Io's rapid flickering, thermophysical models, the diameters and albedos of the satellites of Uranus from radiometric observations, the diameters of Pluto and Triton, standard stars are discussed.

Jefferies, J. T.↗

Direct imaging of planetary systems with a ground-based radio telescope array

The National Radio Astronomy Observatory's proposed Millimeter Array (MMA) will bring unprecedented sensitivity, angular resolution, and image dynamic range to the millimeter wavelength region of the spectrum. An obvious question is whether such an instrument could be used to detect planets orbiting nearby stars. The techniques of aperture synthesis imaging developed for centimeter wavelength radio arrays are capable of producing images whose dynamic ranges greatly exceed the brightness ratio of a solar-type star and a Jupiter-like planet at sub-millimeter or millimeter wavelengths. The angular resolution required to separate a star and planet at a few pc distance can be obtained with baselines of several km. The greatest challenge is sensitivity. At the highest possible observing frequencies (approximately 300 GHz for typical high, dry sites, and approximately 900 GHz from the Antarctic plateau), the proposed MMA will be unable to detect the thermal emission from a Jupiter-like planet a few pc away. An upgraded MMA operating near 300 GHz with twice the currently proposed number of antennas, a 20% fractional bandwidth, and improved receivers could detect Jupiter at 4 pc in a few months. Building such an array on the Antarctic plateau and operating at approximately 900 GHz would allow Jupiter at 4 pc to be detected in approximately one day of observing time.

Jones, Dayton L.↗

Ultraviolet Broad Absorption Features and the Spectral Energy Distribution of the QSO PG 1351+641

We present a moderate-resolution (approximately 20 km/s) spectrum of the broad-absorption line QSO PG 1351+64 between 915-1180 angstroms, obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE). Additional low-resolution spectra at longer wavelengths were also obtained with the Hubble Space Telescope (HST) and ground-based telescopes. Broad absorption is present on the blue wings of C III lambda977, Ly-beta, O VI lambda-lambda-1032,1038, Ly-alpha, N V lambda-lambda-1238,1242, Si IV lambda-lambda-1393,1402, and C IV lambda-lambda-1548,1450. The absorption profile can be fitted with five components at velocities of approximately -780, -1049, -1629, -1833, and -3054 km/s with respect to the emission-line redshift of z = 0.088. All the absorption components cover a large fraction of the continuum source as well as the broad-line region. The O VI emission feature is very weak, and the O VI/Ly-alpha flux ratio is 0.08, one of the lowest among low-redshift active galaxies and QSOs. The ultraviolet continuum shows a significant change in slope near 1050 angstroms in the restframe. The steeper continuum shortward of the Lyman limit extrapolates well to the observed weak X-ray flux level. The absorbers' properties are similar to those of high-redshift broad absorption-line QSOs. The derived total column density of the UV absorbers is on the order of 10(exp 21)/s, unlikely to produce significant opacity above 1 keV in the X-ray. Unless there is a separate, high-ionization X-ray absorber, the QSO's weak X-ray flux may be intrinsic. The ionization level of the absorbing components is comparable to that anticipated in the broad-line region, therefore the absorbers may be related to broad-line clouds along the line of sight.

Zheng, W.↗

Ultraviolet Broad Absorption Features and the Spectral Energy Distribution of the QSO PG 1351+64

We present a moderate-resolution (approximately 20 km s(exp -1) spectrum of the mini broad absorption line QSO PG 1351+64 between 915-1180 A, obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE). Additional low-resolution spectra at longer wavelengths were also obtained with the Hubble Space Telescope (HST) and ground-based telescopes. Broad absorption is present on the blue wings of C III (lambda)977, Ly(beta), O VI (lambda)(lambda)1032,1038, Ly(alpha), N V (lambda)(lambda)1238,1242, Si IV (lambda)(lambda)1393,1402, and C IV (lambda)(lambda)1548,1450. The absorption profile can be fitted with five components at velocities of approximately -780, -1049, -1629, -1833, and -3054 km s(exp -1) with respect to the emission-line redshift of z = 0.088. All the absorption components cover a large fraction of the continuum source as well as the broad-line region. The O VI emission feature is very weak, and the O VI/Ly(alpha) flux ratio is 0.08, one of the lowest among low-redshift active galaxies and QSOs. The UV (ultraviolet) continuum shows a significant change in slope near 1050 A in the restframe. The steeper continuum shortward of the Lyman limit extrapolates well to the observed weak X-ray flux level. The absorbers' properties are similar to those of high-redshift broad absorption-line QSOs. The derived total column density of the UV absorbers is on the order of 10(exp 21) cm(exp -2), unlikely to produce significant opacity above 1 keV in the X-ray. Unless there is a separate, high-ionization X-ray absorber, the QSO's weak X-ray flux may be intrinsic. The ionization level of the absorbing components is comparable to that anticipated in the broad-line region, therefore the absorbers may be related to broad-line clouds along the line of sight.

Zheng, W.↗