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NASA NTRS2004

CoSSIR: A New Instrument for Exploring the Utility of Submillimeter-wave Radiometry for Earth Observation

The Conical Scanning Submillimeter-wave Imaging Radiometer (CoSSIR) has been developed to study the application of submillimeter-wave radiometry for remote sensing of cirrus clouds and humidity sounding. Measurements of the global distribution of ice cloud mass and particle size are important for understanding the Earth s energy budget and for evaluating global climate models. The spatial variability and the wide variety of cloud particle shapes and sizes make ice clouds particularly difficult to measure. Ice clouds are essentially undetectable at microwave frequencies due to the low dielectric of ice and small size of the particles relative to wavelength. However, submillimeter wavelengths demonstrate significant response to the presence of ice clouds thus this frequency regime is applicable to measuring ice clouds. Another potentially viable application for submillimeter-wave radiometry is humidity and temperature sounding. The principle of sounding at submillimeter wavelengths is similar to that at microwavelengths. Submillimeter-wave radiometry has the advantage of achieving finer spatial resolution using a smaller antenna aperture which is an important consideration for spaceborne observatories. Submillimeter-wave radiometry also offers the potential of sounding over land and as a surrogate measurement for precipitation. CoSSIR is a new instrument to explore these applications. The CoSSIR is designed to fly aboard the ER-2 aircraft and its modest size (approximately 100 kg) permits it to be configured for other aircraft. A dual-axes gimbals mechanism provides conical, across-track, and along-track scanning capability. In its present configuration CoSSIR has fifteen channels between 183 GHz and 640 GHz. Three channels are centered about the 183 GHz water vapor absorption line, four channels are centered about the 380 GHz water vapor absorption line, and three dual-polarized channels are centered about the 487 GHz oxygen absorption line. Two channels are located in atmospheric windows at 220 GHz and 640 GHz. All channels are single-linear polarized with the exception of those near 487 GHz. Calibration is achieved by periodically observing two blackbody radiators; one blackbody is heated to approximately 325 K and the other is approximately 250 K during flight. Details of the instrument design as well as measurements from the Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment will be presented.

Racette, P. E.↗
NASA NTRS1990

Ultraviolet interstellar absorption toward HD 163522, a halo star at 9 kiloparsecs in the direction l = 350 deg and b = -9 deg

UV interstellar absorption line measurements obtained by the IUE satellite toward HD 163522 in the direction l = 349.6 deg and b = -9 deg are analyzed. The UV stellar spectrum of HD 163522 places the star beyond the Galactic center at a distance away from the Galactic plane of z = -1.5 kpc. An absorption-line spectrum with S/N approximately equal to 15-25 is produced. The UV interstellar absorption lines for neutral, and weakly and highly ionized gas are examined, as well as the correlation between profiles and the Galactic rotation. Simple model calculations are performed to quantitatively determine the characteristics of the profiles. The observed absorption-line profiles for Al III, Si IV, C IV, and N V are converted into plots of optical depths vs velocity. A comparison of these plots for the weak and strong member of each doublet reveals that the profiles are not strongly influenced by the presence of unresolved saturated absorption, and the optical depth profiles can therefore be directly converted into measures of N(v), the column density per km/s. The converted column densities are examined.

Savage, Blair D.↗
NASA NTRS2001

The Ionization and Metallicity of the Intervening O VI Absorber at z=0.1212 in the Spectrum of H1821+643

We use high-resolution UV (ultraviolet) spectra of the radio-quiet QSO (quasi-stellar object) H1821+643 (z(sub em) = 0.297), obtained with the Space Telescope Imaging Spectrograph (STIS) and the Far Ultraviolet Spectroscopic Explorer (FUSE), to study the ionization and metallicity of an intervening O VI absorption line system at z(sub abs) = 0.1212. This absorber has the following notable properties: (1) Several galaxies are close to the sight line at the absorber redshift, including an actively star-forming galaxy at a projected distance of 144 h(sub 75)(exp -1) kpc. (2) There is a complex cluster of H I Ly(alpha) absorption lines near the O VI redshift, including at least five components spread over a velocity range of approximately 700 km s(exp -1). (3) The strongest Ly(alpha) line in the cluster appears to be composed of a mildly saturated component with a typical b-value blended with a remarkably broad component with b approximately equals 85 km s(exp -1). (4) The O VI absorption is not aligned with the strongest (saturated) H I absorption, but instead is well-aligned with the very broad component. (5) The only detected species (at the 4(sigma) level) are O VI and H I despite coverage of strong transitions of abundant elements (e.g., C II, C III, and C IV). Based on these constraints, we find that the absorption line properties can be produced in collisionally ionized gas with 10(exp 5.3) is equal to or less than T is equal to or less than 10(exp 5.6) K and -1.8 is equal to or less than [O/H] is equal to or less than -0.6. However, we find that photoionization is also viable if the pathlength l through the absorbing gas is long enough; simple photoionization models require 85 is equal to or less than l is equal to or less than 1900 kpc and -1.1 is equal to or less than [O/H] is equal to or less than -0.3. We briefly discuss how observations of X-ray absorption lines due to O VII and O VIII could be used, in principle, to break the ionization mechanism degeneracy, and we conclude with some comments regarding the nature of O VI absorbers.

Tripp, Todd M.↗
DOE OSTI2017

Multiepoch Spectropolarimetry of SN 2011fe

We present multiple spectropolarimetric observations of the nearby Type Ia supernova (SN) 2011fe in M101, obtained before, during, and after the time of maximum apparent visual brightness. The excellent time coverage of our spectropolarimetry has allowed better monitoring of the evolution of polarization features than is typical, which has allowed us new insight into the nature of normal SNe Ia. SN 2011fe exhibits time-dependent polarization in both the continuum and strong absorption lines. At early epochs, red wavelengths exhibit a degree of continuum polarization of up to 0.4%, likely indicative of a mild asymmetry in the electron-scattering photosphere. This behavior is more common in subluminous SNe Ia than in normal events, such as SN 2011fe. The degree of polarization across a collection of absorption lines varies dramatically from epoch to epoch. During the earliest epoch, a λ 4600–5000 Å complex of absorption lines shows enhanced polarization at a different position angle than the continuum. We explore the origin of these features, presenting a few possible interpretations, without arriving at a single favored ion. During two epochs near maximum, the dominant polarization feature is associated with the Si ii λ 6355 Å absorption line. This is common for SNe Ia, but for SN 2011fe the polarization of this feature increases after maximum light, whereas for other SNe Ia, that polarization feature was strongest before maximum light.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Optical and UV spectroscopy of the black hole binary candidate LMC X-1

Both further optical spectroscopy of the binary star identified with LMC X-1, obtained between 1983 and 1985, and a series of IUE UV spectra taken during a 5 day interval in 1984 are presented. The optical data are used to refine the orbital period to 4.2288 days, and improved orbital parameters are derived. The velocity of the optical emission lines is antiphased with the absorption lines and has twice the velocity amplitude. These new results support the estimates of the masses in the system given earlier. The most probable component masses are approximately 20 solar masses for the primary and near 6 solar masses (for the x-ray star), suggesting the the latter may be a black hole. The UV spectra show very weak, low-velocity stellar-wind lines. It is suggested that much of the surrounding medium is highly ionized by the X-ray flux. The 'nonwind' UV spectral lines and the UV continuum temperature are consistent with the optical data, indicating a late O type star of M(bol) = -8.5. There is a weak modulation of absorption-line strengths with orbital phase, suggestive of a lack of axisymmetry in the X-irradiation of the primary star and indicative of a fairly low orbital inclination.

Hutchings, J. B.↗
DOE OSTI2016

Communication: XUV transient absorption spectroscopy of iodomethane and iodobenzene photodissociation

Time-resolved extreme ultraviolet (XUV) transient absorption spectroscopy of iodomethane and iodobenzene photodissociation at the iodine pre-N{sub 4,5} edge is presented, using femtosecond UV pump pulses and XUV probe pulses from high harmonic generation. For both molecules the molecular core-to-valence absorption lines fade immediately, within the pump-probe time-resolution. Absorption lines converging to the atomic iodine product emerge promptly in CH{sub 3}I but are time-delayed in C{sub 6}H{sub 5}I. We attribute this delay to the initial π → σ{sup *} excitation in iodobenzene, which is distant from the iodine reporter atom. We measure a continuous shift in energy of the emerging atomic absorption lines in CH{sub 3}I, attributed to relaxation of the excited valence shell. An independent particle model is used to rationalize the observed experimental findings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The Formation and Physical Origin of Highly Ionized Cooling Gas

We present a simple model that explains the origin of warm, diffuse gas seen primarily as highly ionized absorption-line systems in the spectra of background sources. We predict the observed column densities of several highly ionized transitions such as O vi, O vii, Ne viii, N v, and Mg x, and we present a unified comparison of the model predictions with absorption lines seen in the Milky Way disk, Milky Way halo, starburst galaxies, the circumgalactic medium, and the intergalactic medium at low and high redshifts. We show that diffuse gas seen in such diverse environments can be simultaneously explained by a simple model of radiatively cooling gas. We show that most such absorption-line systems are consistent with being collisionally ionized, and we estimate the maximum-likelihood temperature of the gas in each observation. This model satisfactorily explains why O vi is regularly observed around star-forming low- z L* galaxies, and why N v is rarely seen around the same galaxies. We further present some consequences of this model in quantifying the dynamics of the cooling gas around galaxies and predict the shock velocities associated with such flows. A unique strength of this model is that while it has only one free (but physically well-constrained) parameter, it nevertheless successfully reproduces the available data on O vi absorbers in the interstellar, circumgalactic, intragroup, and intergalactic media, as well as the available data on other absorption lines from highly ionized species.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Trident: A Universal Tool for Generating Synthetic Absorption Spectra from Astrophysical Simulations

Hydrodynamical simulations are increasingly able to accurately model physical systems on stellar, galactic, and cosmological scales; however, the utility of these simulations is often limited by our ability to directly compare them with the data sets produced by observers: spectra, photometry, etc. To address this problem, we have created trident, a Python-based open-source tool for post-processing hydrodynamical simulations to produce synthetic absorption spectra and related data. trident can (i) create absorption-line spectra for any trajectory through a simulated data set mimicking both background quasar and down-the-barrel configurations; (ii) reproduce the spectral characteristics of common instruments like the Cosmic Origins Spectrograph; (iii) operate across the ultraviolet, optical, and infrared using customizable absorption-line lists; (iv) trace simulated physical structures directly to spectral features; (v) approximate the presence of ion species absent from the simulation outputs; (vi) generate column density maps for any ion; and (vii) provide support for all major astrophysical hydrodynamical codes. trident was originally developed to aid in the interpretation of observations of the circumgalactic medium and intergalactic medium, but it remains a general tool applicable in other contexts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Scaling Relations of Starburst-driven Galactic Winds

Using synthetic absorption lines generated from 3D hydrodynamical simulations, we explore how the velocity of a starburst-driven galactic wind correlates with the star formation rate (SFR) and SFR density. We find strong correlations for neutral and low ionized gas, but no correlation for highly ionized gas. The correlations for neutral and low ionized gas only hold for SFRs below a critical limit set by the mass loading of the starburst, above which point the scaling relations flatten abruptly. Below this point the scaling relations depend on the temperature regime being probed by the absorption line, not on the mass loading. The exact scaling relation depends on whether the maximum or mean velocity of the absorption line is used. We find that the outflow velocity of neutral gas can be up to five times lower than the average velocity of ionized gas, with the velocity difference increasing for higher ionization states. Furthermore, the velocity difference depends on both the SFR and mass loading of the starburst. Thus, absorption lines of neutral or low ionized gas cannot easily be used as a proxy for the outflow velocity of the hot gas.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Ultraviolet studies of the interstellar gas

Sounding-rocket and satellite UV observations of interstellar gas clouds are reviewed with major attention given to Copernicus observations of interstellar absorption lines. Analysis of typical absorption-line data is outlined, and observations are reviewed for atomic hydrogen as well as interstellar H2, HD, and CO molecules. Investigations of atomic abundances in H I regions are summarized, measurements of atomic deuterium abundances in the interstellar gas are examined, and the properties of ionized interstellar gas are described. Theoretical analyses of the physical state of the interstellar gas are summarized with respect to ionization by energetic radiation, cool H I clouds, and the intercloud medium. The data obtained thus far are shown to indicate mean temperatures of about 80 K, particle densities between 10 and 1000 per cu cm, and a depletion of heavy elements that becomes greatly enhanced with increasing condensation temperature for those H I regions with strong H2 lines.

Spitzer, L., Jr.↗
NASA NTRS2021

On the Impact of an Intermediate Duration X-ray Burst on the Accretion Environment in IGR J17062-6143

We report on a spectroscopic analysis of the X-ray emission from IGR J17062−6143 in the after-math of its June 2020 intermediate duration Type I X-ray burst. Using the Neutron Star Interior Composition Explorer, we started observing the source three hours after the burst was detected with MAXI/GSC, and monitored the source for the subsequent twelve days. We observed the tail end of the X-ray burst cooling phase, and find that the X-ray flux is severely depressed relative to its historic value for a three day period directly following the burst. We interpret this intensity dip as the inner accretion disk gradually restoring itself after being perturbed by the burst irradiation. Superimposed on this trend we observed a 1.5 d interval during which the X-ray flux is sharply lower than the wider trend. This drop in flux could be isolated to the non-thermal components in the energy spectrum, suggesting that it may be caused by an evolving corona. Additionally, we detected a 3.4 keV absorption line at 6.3σsignificance in a single 472 s observation while the burst emission was still bright. We tentatively identify the line as a gravitationally redshifted absorption line from burning ashes on the stellar surface, possibly associated with 40Ca or 44Ti.

Peter Bult↗
NASA NTRS2021

A variable magnetic disc wind in the black hole X-ray binary GRS 1915+105?

Context. GRS 1915+105 being one of the brightest transient black hole binaries (BHBs) in the X-rays offers a unique testbed for the study of the connection between accretion and ejection mechanisms in BHBs. In particular, this source can be used to study the accretion disc wind and its dependence on the state changes in BHBs. Aims. Our aim is to investigate the origin and geometry of the accretion disc wind in GRS 1915+105. This study will provide a basis for planning future observations with the X-ray Imaging Spectroscopy Mission (XRISM), and may also provide important parameters for estimating the polarimetric signal with the upcoming Imaging X-ray Polarimetry Explorer (IXPE). Methods. We analysed the spectra of GRS 1915+105 in the soft ϕ and hard χ classes using the high-resolution spectroscopy offered by Chandra HETGS. In the soft state, we find a series of wind absorption lines that follow a non-linear dependence of velocity width, velocity shift, and equivalent width with respect to ionisation, indicating a multiple component or stratified outflow. In the hard state we find only a faint Fe XXVI absorption line. We model the absorption lines in both the states using a dedicated magneto-hydrodynamic (MHD) wind model to investigate a magnetic origin of the wind and to probe the cause of variability in the observed line flux between the two states. Conclusions. The MHD disc wind model provides a good fit for both states, indicating the possibility of a magnetic origin of the wind. The multiple ionisation components of the wind are well characterised as a stratification of the same magnetic outflow. We find that the observed variability in the line flux between soft and hard states cannot be explained by photo-ionisation alone but is most likely due to a large (three orders of magnitude) increase in the wind density. We find the mass outflow rate of the wind to be comparable to the accretion rate, suggesting an intimate link between accretion and ejection processes that lead to state changes in BHBs.

A. Ratheesh↗
NASA NTRS1991

Large-scale gas dynamical processes affecting the origin and evolution of gaseous galactic halos

Observations of galactic halo gas are consistent with an interpretation in terms of the galactic fountain model in which supernova heated gas in the galactic disk escapes into the halo, radiatively cools and forms clouds which fall back to the disk. The results of a new study of several large-scale gas dynamical effects which are expected to occur in such a model for the origin and evolution of galactic halo gas will be summarized, including the following: (1) nonequilibrium absorption line and emission spectrum diagnostics for radiatively cooling halo gas in our own galaxy, as well the implications of such absorption line diagnostics for the origin of quasar absorption lines in galactic halo clouds of high redshift galaxies; (2) numerical MHD simulations and analytical analysis of large-scale explosions ad superbubbles in the galactic disk and halo; (3) numerical MHD simulations of halo cloud formation by thermal instability, with and without magnetic field; and (4) the effect of the galactic fountain on the galactic dynamo.

Shapiro, Paul R.↗
DOE OSTI2016

The spectroscopic foundation of radiative forcing of climate by carbon dioxide

The radiative forcing (RF) of carbon dioxide (CO 2 ) is the leading contribution to climate change from anthropogenic activities. Calculating CO 2 RF requires detailed knowledge of spectral line parameters for thousands of infrared absorption lines. A reliable spectroscopic characterization of CO 2 forcing is critical to scientific and policy assessments of present climate and climate change. Our results show that CO 2 RF in a variety of atmospheres is remarkably insensitive to known uncertainties in the three main CO 2 spectroscopic parameters: the line shapes, line strengths, and half widths. We specifically examine uncertainty in RF due to line mixing as this process is critical in determining line shapes in the far wings of CO 2 absorption lines. RF computed with a Voigt line shape is also examined. Overall, the spectroscopic uncertainty in present-day CO 2 RF is less than 1%, indicating a robust foundation in our understanding of how rising CO 2 warms the climate system.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2004

The Properties and the Evolution of the Highly Ionized Gas in MR 2251-178

We present the first XMM-Newton observations of the radio-quiet quasar MR 2251-178 obtained in 2000 and 2002. The EPIC-pn spectra show a power-law continuum with a slope of Gamma = 1.6 at high energies absorbed by at least two warm absorbers (WAs) intrinsic to the source. The underlying continuum in the earlier observation shows a soft excess at low X-ray energies which can be modeled as an additional power-law with Gamma = 2.9. The spectra also show a weak narrow iron K alpha emission line. The high-resolution grating spectrum obtained in 2002 shows emission lines from N VI, O VII, O VIII, Ne IX, and Ne X, as well as absorption lines from the low-ionization ions of O III, O IV, and O V, and other confirmed and suspected weaker absorption lines. The O III - O V lines are consistent with the properties of the emission line gas observed as extended optical (O III) emission in this source. The signal-to-noise of the 2000 grating data is too low to detect any lines. We suggest a model for the high-resolution spectrum which consist of two or three warm-absorber (WA) components. The two-components model has a high-ionization WA with a column density of 10(exp 21.5)-10 (exp 21.8) sq cm and a low-ionization absorber with a column density of 10(exp 20.3) sq cm. In the three-components model we add a lower ionization component that produces the observed iron M-shell absorption lines. We investigate the spectral variations in MR 2251-178 over a period of 8.5 years using data from ASCA, BeppoSAX, and XMM-Newton. All X-ray observations can be fitted with the above two power laws and the two absorbers. The observed luminosity variations seems to correlate with variations in the soft X-ray continuum. The 8.5 year history of the source suggests a changing X-ray absorber due to material that enters and disappears from the line-of-sight on timescales of several months. We also present, for the first time, the entire FUSE spectrum of MR 2251-178. We detect emission from N III, C III, and O VI and at least 4 absorption systems in C III, H I, and O VI, one at -580 km/s and at least 3 others which are blended together and form a wide trough covering the velocity range of 0 to -500 km/s. The general characteristics of the UV and X-ray absorbers are consistent with an origin in the same gas.

Kaspi, Shai↗
NASA NTRS1995

The Local Ly(alpha) Forest: Association of Clouds with Superclusters and Voids

The Goddard High Resolution Spectrograph aboard the Hubble Space Telescope was used with the G160M grating to obtain high-resolution (6.2 A) spectra of three very bright active galactic nuclei located behind voids in the nearby distribution of bright galaxies (i.e., CfA and Arecibo redshift survey regions). A total of eight definite (greater than or equal to 4 sigma) Ly(alpha) absorption lines were discovered ranging in equivalent width from 26 to 240 mA at Galactocentric velocities 1740-7740 km/s. Of these eight systems, we locate seven in supercluster structures and one, in the sight line of Mrk 501 at 7740 km/s, in a void. In addition, one of two tentative (3-4 sigma) Ly(alpha) absorption lines are found in voids. Thus, the voids are not entirely devoid of matter, and not all Ly(alpha) clouds are associated with galaxies. Also, since the path lengths through voids and superclusters probed by our observations thus far are nearly equal, there is some statistical evidence that the Ly(alpha) clouds avoid the voids. The nearest galaxy neighbors to these absorbing clouds are 0.45-5.9 Mpc away, too far to be physically associated by most models. The lower equivalent width absorption lines (W(sub lambda) less than or equal to 100 mA) are consistent with random locations with respect to galaxies and may be truly intergalactic, similar to the bulk of the Ly(alpha) forest seen at high z. These results on local Ly(alpha) clouds are in full agreement with those found by Morris et al. (1993) for the 3C 273 sight line but are different from the results for higher equivalent width systems where closer cloud-galaxy associations were found by Lanzetta et al. (1994). Pencil-beam optical and 21 cm radio line observations of the area of sky surrounding Mrk 501 fail to find faint galaxies near the velocities of the Ly(alpha) clouds in that sight line. Specifically, for the 'void absorption' system at 7740 km/s, we find no galaxy at comparable redshift to the absorber within 100 h(sub 75)(sup -1) kpc (H(sub 0) = 75 h(sub 75) km/s Mpc(sup -1)) with an absolute magnitude of B less than or equal to - 16 and no object with H I mass greater than or equal to 7 x 10(exp 8) h(sub 75)(sup -2) M(solar) within 500 h(sub 75)(sup -1) kpc. Thus, neither a faint optical galaxy nor a gas-rich, optically dim or low surface brightness galaxy is present close to this absorber.

Stocke, John T.↗
NASA NTRS1979

IUE observations of the quasar 3C 273

IUE observations indicate that the spectrum of 3C 273 is similar to that of other large-redshift quasars. There is a large excess of flux in the range 2400 A to 5300 A, which encompasses the Balmer jump region but which does not appear to be explainable by Balmer emission. The intensity ratio of Lyman-alpha to H-beta is 5.5, in agreement with other measures and a factor 6 smaller than the recombination value. The only absorption lines in the spectrum are due to our Galaxy. There is marginal evidence for a depression of the continuum shortward of the Lyman-alpha emission line, but the errors are too large to warrant any conclusion that 3C 273 has a rich absorption-line spectrum such as that seen in large-redshift quasars. The absence of emission and absorption lines of Fe II leads to the conclusion that resonance fluorescence probably produces the visual Fe II emission lines.

Boggess, A.↗
NASA NTRS2001

The Lyman-Alpha Forest in the Lensed Quasar Q0957+561 and the Characteristic Dimension of the Absorbing Clouds

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and 9 were obtained with the Hubble Space Telescope Faint Object Spectrograph (FOS) at five equally spaced epochs, one every two weeks. We confirm the flux variability of the quasar's Lyman-alpha and 0 VI emission lines reported by Dolan et al. (1995) in IUE spectra. The fluxes in these lines vary on a time scale of weeks in the observer's rest frame, independently of each other and of the surrounding continuum. The individual spectra of each image were co-added to investigate the properties of the Lyman-alpha forest along the two lines of sight to the quasar. Absorption lines having equivalent width W > 0.3 A in the observer's frame not previously identified by Michalitsianos et al. (1997) as interstellar lines, metal lines, or higher order Lyman lines were taken to be Ly-alpha forest lines. The existence of each line in this consistently selected set was then verified by its presence in two archival FOS spectra with -1.5 times higher signal to noise than our co-added spectra. Ly-alpha forest lines with W > 0.3 A appear at 41 distinct wavelengths in the spectra of the two images. one absorption line in the spectrum of image A has no counterpart in the spectrum of image B and one line in image B has no counterpart in image A. Based on the separation of the lines of sight over the redshift range searched for Ly-forest lines, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a distance R = 160 (+120, -70)/ h(sub 50) kpc in the simplified model where the absorbers are treated as spherical clouds and the characteristic dimension, R, is the radius. (We adopt H(sub 0) = 50 h(sub 50) km/s/ kpc, q(sub 0) = 1/2, and lambda = 0 throughout the paper.) The 95% confidence interval on R extends from (50 - 950)/h(sub 50) kpc We show in the Appendix that the fraction of Ly-alpha forest lines that appear in only one spectrum can be expressed as a rapidly converging power series in 1/r, where r the ratio of the radius of the cloud to the separation of the two lines of sight at the redshift of the cloud. This power series can be rewritten to give r in terms of the fraction of Ly-forest wavelengths that appear in the spectrum of only one image. A simple linear approximation to the solution that everywhere agrees with the power series solution to better than 0.8% for r > 2 is derived in the Appendix.

Dolan, Joseph↗