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Optical depth (astrophysics)

About: Optical depth (astrophysics) is a research topic. Over the lifetime, 1007 publications have been published within this topic receiving 33744 citations.


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TL;DR: The authors studied the evolution of the ionization state of the intergalactic medium (IGM) at the end of the reionization epoch using moderate-resolution spectra of a sample of 19 quasars at 5.74 5.7.
Abstract: We study the evolution of the ionization state of the intergalactic medium (IGM) at the end of the reionization epoch using moderate-resolution spectra of a sample of 19 quasars at 5.74 5.7: the GP optical depth evolution changes from τ ~ (1 + z)4.3 to (1 + z)11, and the average length of dark gaps with τ > 3.5 increases from 80 comoving Mpc. The dispersion of IGM properties along different lines of sight also increases rapidly, implying fluctuations by a factor of 4 in the UV background at z > 6, when the mean free path of UV photons is comparable to the correlation length of the star-forming galaxies that are thought to have caused reionization. The mean length of dark gaps shows the most dramatic increase at z ~ 6, as well as the largest line-of-sight variations. We suggest using dark gap statistics as a powerful probe of the ionization state of the IGM at yet higher redshift. The sizes of H II regions around luminous quasars decrease rapidly toward higher redshift, suggesting that the neutral fraction of the IGM has increased by a factor of 10 from z = 5.7 to 6.4, consistent with the value derived from the GP optical depth. The mass-averaged neutral fraction is 1%-4% at z ~ 6.2 based on the GP optical depth and H II region size measurements. The observations suggest that z ~ 6 is the end of the overlapping stage of reionization and are inconsistent with a mostly neutral IGM at z ~ 6, as indicated by the finite length of the dark absorption gaps.

1,420 citations

Journal ArticleDOI
TL;DR: In this paper, the delta-Eddington approximation was used to calculate monochromatic radiative fluxes in an absorbing-scattering atmosphere, by combining a Dirac delta function and a two-term approximation, which overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions.
Abstract: This paper presents a rapid yet accurate method, the “delta-Eddington” approximation, for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. By combining a Dirac delta function and a two-term approximation, it overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. Comparisons of delta-Eddington albedos, transnmissivities and absorptivities with more exact calculations reveal typical differences of 0–0.022 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo and phase function asymmetry. Delta-Eddington fluxes are in error, on the average, by no more than 0.5%0, and at the maximum by no more than 2% of the incident flux. This computationally fa...

1,075 citations

Journal ArticleDOI
TL;DR: In this article, a two-phase accretion disk model with thermal Comptonization is presented, with emphasis on thermal Comptonisation as the basic mechanism for producing the X-ray power-law continuum of Seyfert galaxies within the framework of the inner emission region.
Abstract: Attention is given to a two-phase accretion disk model, with emphasis on thermal Comptonization as the basic mechanism for producing the X-ray power-law continuum of Seyfert galaxies within the framework of the new picture of the inner emission region. A substantial fraction, f, of the gravitational power is assumed to be dissipated via buoyancy and reconnection of the magnetic fields in a hot tenuous 'corona' surrounding the disk's main body. Coupled thermal balance equations for the two phases yield the temperature of the hot phase and the slope of the Comptonized component self-consistently as a function of f and tau, the optical depth of the hot phase. It is found that for f approximately equal to 1 and tau less than 1, the temperature of the hot phase adjusts so as to maintain alpha approximately equal to 1. For small tau the temperature of the hot phase is sufficient for the production of electron-positron pairs to be important. Pair production contributes to the optical depth and limits the maximum temperature allowed.

951 citations

Journal ArticleDOI
TL;DR: In this paper, a multiline UV pumping model was proposed to compare the effect of self-shielding on the overall fluorescent efficiency of the photodissociation front, including the effects of line overlap.
Abstract: The structure of stationary photodissociation fronts is revisited. H_2 self- shielding is discussed, including the effects of line overlap. We find that line overlap is important for N(H_2) > 10^{20} cm^{-2}. We compute multiline UV pumping models, and compare these with simple analytic approximations for the effects of self-shielding. The overall fluorescent efficiency of the photodissociation front is obtained for different ratios of chi/n_H (where chi characterizes the intensity of the incident UV) and different dust extinction laws. The dust optical depth tau_{pdr} to the point where 50% of the H is molecular is found to be a simple function of a dimensionless quantity phi_0 depending on chi/n_H, the rate coefficient for H_2 formation on grains, and the UV dust opacity. The fluorescent efficiency of the PDR also depends primarily on phi_0 for chi 10^4K, but shows some sensitivity to the v-J distribution of newly-formed H_2. The 1-0S(1)/2-1S(1) and 2-1S(1)/6-4Q(1) intensity ratios, the ortho/para ratio, and the rotational temperature in the $v$=1 and $v$=2 levels are computed as functions of the temperature and density, for different values of chi and n_H. We apply our models to the reflection nebula NGC 2023. We are best able to reproduce the observations with models having chi=5000, n_H=10^5 cm^{-3}.

766 citations

Journal ArticleDOI
TL;DR: In this article, a multiline UV pumping model was proposed to compare the effect of self-shielding on the overall fluorescent efficiency of the photodissociation front, including the effects of line overlap.
Abstract: The structure of stationary photodissociation fronts is revisited. H_2 self- shielding is discussed, including the effects of line overlap. We find that line overlap is important for N(H_2) > 10^{20} cm^{-2}. We compute multiline UV pumping models, and compare these with simple analytic approximations for the effects of self-shielding. The overall fluorescent efficiency of the photodissociation front is obtained for different ratios of chi/n_H (where chi characterizes the intensity of the incident UV) and different dust extinction laws. The dust optical depth tau_{pdr} to the point where 50% of the H is molecular is found to be a simple function of a dimensionless quantity phi_0 depending on chi/n_H, the rate coefficient for H_2 formation on grains, and the UV dust opacity. The fluorescent efficiency of the PDR also depends primarily on phi_0 for chi 10^4K, but shows some sensitivity to the v-J distribution of newly-formed H_2. The 1-0S(1)/2-1S(1) and 2-1S(1)/6-4Q(1) intensity ratios, the ortho/para ratio, and the rotational temperature in the $v$=1 and $v$=2 levels are computed as functions of the temperature and density, for different values of chi and n_H. We apply our models to the reflection nebula NGC 2023. We are best able to reproduce the observations with models having chi=5000, n_H=10^5 cm^{-3}.

548 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202182
202060
201952
201856
201765