Author name code: peraiah ADS astronomy entries on 2022-09-14 author:"Peraiah, Annamaneni" ------------------------------------------------------------------------ Title: Compton broadening effect on spectral line formation Authors: Peraiah, A.; Srinivasa Rao, M. Bibcode: 2013Ap&SS.343..195P Altcode: 2012Ap&SS.tmp..337P We have investigated the effects of Compton broadening due to electron scattering in an expanding stellar atmospheres. The line transfer equation is solved by including the second approximation of Edmonds (Astrophys. J. 119:58, 1954) which is due to Compton broadening and obtained the line profiles in (1) plane parallel (PP) (2) spherical (SS) atmospheres. The effect on spectral line formation is studied for different parameters like (a) optical depths (b) densities (c) frequencies (d) temperatures (e) thickness of the atmosphere and (f) expanding velocities. Various combination of the above parameters are used in computing the line profiles observed at infinity. Line profiles are compared for the above said parameters. It is noticed that the expansion of the gases in the atmosphere produces P-Cygni type profiles and at higher optical depths the line profiles change from emission to absorption with their line centers shifting to blue side in the expanding atmospheres. Title: Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV Authors: Peraiah, A.; Srinivasa Rao, M.; Varghese, B. A. Bibcode: 2011JQSRT.112..820P Altcode: 2010arXiv1011.1984P Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 KeV photon energy range. Diffuse radiation field is calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms $n, n^2$ and $\displaystyle \bigg({\frac {\partial n}{\partial x_k}}\bigg)$ where $n$ is photon phase density and $\displaystyle x_k= \bigg({\frac {h \nu} {k T_e}} \bigg) $, in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation $I^{MB}$ [1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at $\tau=0$ and reflected radiation $\tau=\tau_{max}$ are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times. Title: Radiative transfer on X-Y geometry Authors: Peraiah, A. Bibcode: 2010BASI...38..115P Altcode: A unique and non-negative solution of the radiative transfer equation in two dimensional X-Y geometry in scattering and absorbing media is presented. This solution facilitates asymmetric boundary conditions both in geometry and direction from the two boundaries of geometrical configurations such as stellar atmospheres and similar objects. Further, it allows inhomogeneities in the physical properties that occur at any point in the medium. Title: An Integral Operator Technique of Radiative Transfer in Spherical Symmetry Authors: Peraiah, A. Bibcode: 2009nrt..book..305P Altcode: No abstract at ADS Title: Transfer of resonance line radiation in advected atmospheres with partial frequency redistribution of photons Authors: Peraiah, A. Bibcode: 2004BASI...32...33P Altcode: We studied the influence of high veolcities of expansion on resonance line radiation by taking into account of aberration and advection. We used an angle averaged redistribution function RII in spherically symmetric media. Three types of media are considered. These are: (1) purely scattering medium (2) partly scattering and emission from continuum medium and (3) partly scattering and continuum and line emission medium. The spherical shells that are being used have thicknesses equal to 2, 10 and 100 times the stellar radii. The radiation field is shown in terms of teh source functions. Computations are performed in the comoving frame of the gas and the line profiles are calculated at the observer's point at infinity. The line profiles computed in the first type of medium show P Cygni characteristics and those computed in the second and third type of media show central emission and self absorption. Title: Radiative transfer in the distorted and irradiated atmospheres of close binary components Authors: Peraiah, A.; Srinivasa Rao, M. Bibcode: 2002A&A...389..945P Altcode: We studied the transfer of line radiation in the distorted and expanding atmospheres of close binary components. We assumed that the distortion of the atmosphere is caused by self rotation and tidal force exerted by the presence of the secondary component. The distortion is measured in terms of the ratio of angular velocities at the equator and pole (X), mass ratio of the two components (m2)/(m1), the ratio of centrifugal force to that of gravity at the equator of the primary (f) and ratio of the equatorial radius of the primary to the distance between the centres of gravity of the two components displaystyle (re)/(R). A seventh degree equation is obtained to describe the distorted surface in terms of the above mentioned parameters. We have used X=1 for uniform rotation throughout and used values f=0.1 and 0.5, (m2)/(m1)=1, and (re)/(R)=0.1, 0.3, and 0.5. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We used a linear law of velocity of expansion so that the density varies as r-3 where r is the radius of the star, satisfying the law of conservation of mass. We set va=0 and vb=10 mtu (mean thermal units) where va is the velocity at the surface of the primary with radius r=a(=5*E11) cm and vb is the velocity at the surface of the extended atmosphere with radius r=b(=1012) cm. We also computed lines in a static atmosphere with density changing as rho ~ r-1. We have considered a primary with an effective temperature T* and a point source of secondary with three different temperatures Tc equal to 2x 104 K, 3x 104 K, and 4x 104 K. The maximum change in line fluxes is noticed when the parameters (re)/(R) and f are changed, while the changes due to (m2)/(m1) are minimal. The expansion of the atmosphere produces P Cygni type line profiles. The incident radiation from the secondary increases the line fluxes and absorption in the centre of the line is replaced by emission. Title: An Introduction to Radiative Transfer Authors: Peraiah, Annamaneni Bibcode: 2001irt..book.....P Altcode: Preface; 1. Definitions of fundamental quantities of the radiation field; 2. The equation of radiative transfer; 3. Methods of solution of transfer equation; 4. Two-point boundary problems; 5. Principle of Invariance; 6. Discrete space theory; 7. Transfer equation in moving media: the observer frame; 8. Radiative transfer equation in the comoving frame; 9. Escape probability methods; 10. Operator perturbation methods; 11. Polarization; 12. Polarization in magnetic media; 13. Multi-dimensional radiative transfer. Title: An Introduction to Radiative Transfer: Methods and Applications in Astrophysics Authors: Peraiah, Annamaneni Bibcode: 2001irtm.book.....P Altcode: No abstract at ADS Title: Radiative transfer in the dusty, irradiated expanding atmospheres of close binary components Authors: Srinivasa Rao, M.; Peraiah, A. Bibcode: 2000A&AS..145..525S Altcode: We studied the formation of lines in the irradiated expanding dusty atmospheres of the components of close binary systems. We considered a two-level atom approximation in Non-LTE situation with complete redistribution. The thickness of the atmosphere is set to be equal to twice that of the stellar radius. Maximum expansion velocities is set to be as large as 50 mean thermal units. The isotropically scattering dust is distributed uniformly in the atmosphere. We have computed the lines using a total optical depths 104 at the line centre. The irradiation from the secondary is one, five and ten times the self radiation. The line fluxes in the line of sight are calculated by using the total source function which is the sum of the source functions due to self radiation and that due to irradiation from the secondary. The line profiles formed in dusty atmosphere are compared with those formed in dust free atmosphere. The profiles are presented for different velocities of expansion, different separations between the components and several dust optical depths. P Cygni type profiles are produced in the expanding atmosphere and the irradiation from the secondary enhances the emission in the lines. The major effect of dust on the formation of lines in the expanding atmospheres of the component of close binary is to scatter photons into the line core, among others. Title: Principles of Invariance in Radiative Transfer Authors: Peraiah, A. Bibcode: 1999SSRv...87..465P Altcode: We have reviewed the principle of invariance, its applications and its usefulness for obtaining the radiation field in semi-infinite and finite atmospheres. Various laws of scattering in dispersive media and the consequent radiation field are studied. The H-functions and X- and Y-functions in semi-infinite and finite media respectively are derived in a few cases. The Discrete Space Theory (DST) which is a general form of the Principle of Invariance is described. The method of addition of layers with general properties, is shown to describe all the properties of multiple scattering. A few examples of the application of DST such as polarization, line formation in expanding stellar atmospheres, etc., and a numerical analysis of DST are presented. Other developments in the theory of radiative transfer are briefly described. Title: A series of theoretical line profiles formed in the irradiated expanding atmospheres of close binary components Authors: Peraiah, A.; Srinivasa Rao, M. Bibcode: 1998A&AS..132...45P Altcode: We studied the effects of irradiation on the line formation in the expanding atmospheres of the components of close binary systems. We considered a two-level atom approximation in Non-LTE situation. The thickness of the atmosphere is assumed to be twice that of the stellar radius. Expansion velocities are assumed to be as large as 50 mean thermal units. We have computed the lines using total optical depths 10(3) , 10(4) and 10(5) at the line centre. The irradiation from the secondary is assumed to be one, five and ten times the self radiation. The line fluxes in the line of sight are calculated by using the total source function which is the sum of the source functions due to self radiation and that due to irradiation. We notice that the expansion of the medium produces P Cygni type profiles and the irradiation enhances the emission in the lines although the equivalent widths reduce considerably. Figures 1(1-6), 2(1-30), 3(1-8), 4(1-8), 5(1-6) and 6(1-8) are available in electronic form at the http://www.edpsciences.com Title: Radiative transfer - Chandrasekhar - and after Authors: Peraiah, A. Bibcode: 1996BASI...24..397P Altcode: No abstract at ADS Title: Linear Polarization in Close Binaries Authors: Parman, S. K.; Peraiah, A. Bibcode: 1993icpc.proc..171P Altcode: 1993IAUCo.132..171P No abstract at ADS Title: Effects of Aberration and Advection on Line Formation Authors: Peraiah, A. Bibcode: 1991ApJ...380..212P Altcode: The effects of inclusion of the aberration and advection terms in the equation of the line transfer are studied. Spherical shells whose ratios of outer (B) to inner (A) radii (B/A) are 2, 5, and 10 and with line-center optical depths 500, 1300, and 1350 are considered. The velocities of expansion of the medium are set at 1000, 2000, 3000, 4000, and 5000 km/s. The line source functions and the corresponding profiles of lines are calculated. The individual and combined effects of the transverse and radial velocity gradients, and those of aberration and advection in plane-parallel and spherically symmetric geometries on the line source functions and the emerging line profiles are considered. It is found that large effects are generated in the radiation field when these physical mechanisms are taken into account in the transfer of the line radiation. The method for various velocity laws was tested and found to be stable. Title: The effects of non-coherent electron scattering on spectral line formation Authors: Rangarajan, K. E.; Mohan Rao, D.; Peraiah, A. Bibcode: 1991MNRAS.250..633R Altcode: Spectral line profiles from a plane-parallel homogeneous atmosphere have been calculated for the complete and partial redistribution mechanisms (CRD and PRD) including coherent and noncoherent electron scattering. It is found that in all the cases where the electron scattering coefficient is more than the continuous absorption coefficient, there are measurable changes in the spectral line profiles. In such situations, the PRD profiles have more emission hump compared to CRD profiles in the intermediate frequency range. Extended wings and additional broadening of the line profiles are obtained for the case of noncoherent electron scattering compared to coherent electron scattering. These results have implications in the derivation of physical properties (for example, microturbulent velocities) of stellar atmospheres from spectral lines. Title: Aberration and Advection Effects in Expanding Spherically Symmetric Shells Authors: Peraiah, A. Bibcode: 1991ApJ...371..673P Altcode: The extreme outer layers of supernovae, novae, AGN, QSOs, and many supergiant stars are known to be in rapid expansion or contraction. In this paper, aberration and advection effects in a spherical medium scattering radiation isotropically and coherently are investigated. The shells are assumed to be moving radially with velocities of 1000, 2000, 3000, 4000, and 5000 km/s. A solution of the radiative transfer equation is presented. The changes in mean intensities are dependent on the geometrical and optical thickness and in particular depend on the ratio T/(B/A), where T is the maximum optical depth and B and A are the outer and inner radii of the spherical shell, respectively. Title: Effects of Aberration and Advection on Line Transfer in Plane Parallel Geometry Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1991BASI...19....9P Altcode: We have investigated the effects of aberration and advection on line formation in a plane-parallel medium. We have considered velocities of the order of V = l000, 2000, 3000, 4000, 5000 km s-1 in a plane parallel medium in which the line centre optical depths are 500 and 1200. We consider a two-level atom approximation and find that the line source (SL) changes considerably depending on the optical depth, and SL for V = 0 km s-1 differ from that at V = 5000 km s-1 by a factor of 103. Title: Polarization in binaries Authors: Barman, S. K.; Peraiah, A. Bibcode: 1991BASI...19...37B Altcode: Theoretical models are computed for estimating linear polarization from the extended dusty outer layers of the components of a close binary system whose surfaces are distorted by rotation and mutual tidal effects. Plane-parallel layers of the dusty atmospheres of the components are assumed. A wavelength-dependent scattering coefficient and a Rayleigh phase function is used in solving the equation of radiative transfer. Polarization increases with decreasing wavelength and increasing particle size. Polarization for uniform rotation is larger than that for nonuniform rotation. Polarization for single stars is always less than that for a binary component, dependent on the position of the observer. Title: Radiative Transfer with Compton Scattering in Spherically Symmetric Shells Authors: Peraiah, Annamaneni; Varghese, Baba A. Bibcode: 1990PASJ...42..675P Altcode: We have solved the equation of radiative transfer with Compton scattering in spherically symmetric shells. The specific intensity was expanded by a Taylor series and the first three terms were retained in solving the transfer equation. We assumed optical depths of 2 and 5 in a spherical shell whose outer radii (B) and inner radii (A) are in the ratio of 2 and 5. Multiple Compton scattering redistributes the initial energy over a range of 1 to 10 Compton wavelengths. A good fraction of the incident radiation is transferred across the shell, the radiation being redistributed in wavelength, the percentage of which depends on the optical thickness of the medium. Title: Abhyankar - the Scientist Authors: Peraiah, A. Bibcode: 1990BASI...18..119P Altcode: No abstract at ADS Title: Radiation transfer in fast moving fluids Authors: Peraiah, A. Bibcode: 1990BASI...18..149P Altcode: Various factors influencing the formation of spectral lines are described, emphasizing the physics of stellar atmospheres. Broadening mechanisms, photon or partial frequency redistribution, the role of chemical species are briefly addressed. Emphasis is given to a discussion of geometrical and dynamical aspects, including plane parallel and spherical symmetry, the rest and the comoving frames, and aberration and advection. Title: Effects of stimulated emission on radiative transfer with partial redistribution. Authors: Rangarajan, K. E.; Mohan Rao, D.; Peraiah, A. Bibcode: 1990A&A...235..305R Altcode: The authors study the non-LTE line transfer with stimulated emission. Stimulated emission is important for red transitions in hot stars and infrared transitions in cool stars. The authors investigate the deviation of the absorption and emission profiles from each other for a two-level atomic model with the line scattering described by the angle-averaged redistribution functions. The partial redistribution formalism has been used while solving the radiative transfer equation. The correct expression for the source function derived by Baschek, Mihalas and Oxenius (1981) has been employed to obtain the emission profile and the radiation field. From this study, the authors have obtained the following results: the redistribution function RIII gives the emission profile same as that of the absorption profile (like complete redistribution) in the core and also in the wings but with a small enhancement at the intermediate frequency points whether stimulated emission is present or not. The emergent emission profile is different from the absorption profile by several factors in the wings for RII. Title: Effect of the Time Spent by the Photon in the Absorbed State on the Time-dependent Transfer of Radiation Authors: Rao, D. Mohan; Rangarajan, K. E.; Peraiah, A. Bibcode: 1990ApJ...358..622R Altcode: The time-dependent transfer equation is derived for a two-level atomic model which takes both bound-bound and bound-free transitions into account. A numerical scheme is proposed for solving the monochromatic time-dependent transfer equation when the time spent by the photon in the absorbed state is significant. The method can be easily extended to solve the problem of time-dependent line formation of the bound-free continuum. It is used here to study three types of boundary conditions of the incident radiation incident on a scattering atmosphere. The quantitative results show that the relaxation of the radiation field depends on the optical depth of the medium and on the ray's angle of emergence. Title: Equivalent widths of hydrogen Lyman alpha line in an expanding spherical atmosphere Authors: Peraiah, A.; Ingalgi, M. F. Bibcode: 1990JApA...11..209P Altcode: The profiles of hydrogen Lyman-alpha line in an expanding spherical atmosphere containing dust and gas were calculated. The variation of equivalent widths with velocities of expansion of the atmosphere, together with the amount of dust present in the medium is being investigated. Curves of growth have been drawn for different velocities and dust optical depths. Title: Radiative transfer with Compton scattering in plane parallel geometry Authors: Peraiah, A. Bibcode: 1990JApA...11..193P Altcode: The equation of radiative transfer with Compton scattering is solved. The specific intensity has been expanded by Taylor series with respect to wavelength and the first three terms have been retained in solving the transfer equation. It is noted that, in a medium stratified in plane parallel layers, the multiple Compton scattering redistributes the initial energy over a range of 3 to 5 Compton wavelengths. A good fraction of the incident radiation is transferred across the layer with redistribution in wavelength, the actual value depending on the optical thickness of the medium. Title: Effects of dust on equivalent widths of spectral lines formed in expanding spherically symmetric shells Authors: Peraiah, A.; Ingalgi, M. F. Bibcode: 1990BASI...18...17P Altcode: A study is made of the effects of the presence of dust and radial expansion of the spherical shells around stars on the equivalent widths of the lines formed in such shells. A non-LTE, two-level atom approximation is considered, and it is assumed that the dust scatters isotropically; 30 shells and an optical depth of 300 are considered. Two types of expanding shells are treated: with velocity gradients and without velocity gradients. Depending upon the parameters used, the equivalent widths change considerably. Title: The Effects of Aberration and Advection in Plane-Parallel and Absorbing Media Authors: Peraiah, A. Bibcode: 1989Ap&SS.159..339P Altcode: We have calculated the changes that would occur in mean intensity due to the presence of aberration and advection terms in radiative transfer equation. We have considered an absorbing medium with velocities 1000, 2000, 3000, 4000, and 5000 km s-1 (β-0.0033, 0.017, where β=V/C,V is the velocity of the medium andC is the velocity of the light). Calculations have been done in a comoving frame with monochromatic radiation field. We have calculated the deviation in mean intensity defined asbar J = \{ [J(V = 0) - J(V > 0)]/J(V = 0)], whereJ is the mean intensity. We have taken two types of absorbing media (1) with a source of constant emission and (2) with emission source. As the emission decreases as 1/n 2 wheren is the number of layer, wheren=1 corresponds to τmax and n=N corresponds to τ=0 We find that for a total optical depth of one, the maximum change is about 2% whenB(r)=1 and about 6%, whenB(r)∝1/n 2 whereB(r) is the Planck function. When the optical depth increases to 5 the maximum change in the case of the constant source function falls to 1.5%, where as in the other case in which the Planck function changes as 1/r 2 the maximum changes remains at 6%. Further increase of the optical depth will reduce the changes to less than 2%. The amplification factor in the case of the Planck function varying as 1/r 2 is more than when the emission sources are constant. Title: Effects of Aberration and Advection in a Partially Scattering Medium Authors: Peraiah, A.; Srinivasa-Rao, M. Bibcode: 1989BASI...17...14P Altcode: We have investigated the effects of aberration and advection terms, which are of order ν/c (where ν is the velocity of gas and C is the velocity of light) on the solution of the radiative transfer equation. We have employed a plane-parallel medium which is moving with velocities 1000, 2000, 3000, 4000 or 5000 km s-1 (β = 0.0033, - 0.07 where (β = ν/c). The calculations have been done in the fluid frame, with monochromatic radiation field. We introduce emission sources inside the medium. We assume equal contribution from internal emission and from isotropic and coherent scattering to the radiation field. We have estimated the effects of aberration and advection on the mean intensities and on outward fluxes for different velocities and different optical depths. The effects are found in terms of the mean intensity barJ { = [J(ν = 0) - J(ν > 0)] × 100/J (ν = 0) and the outward flux barF { = [F(ν = 0) - F(ν > 0)] × 100/F (V = 0)}. We set ω (albedo for single scattering) equal to 0.5 and the Planck function equal to B(n) == 1 (case i) and B(n) ∼ 1/n2 (case ii). In case (i), the values of barJ and barF are not spectacular and the maximum changes are in the range of 2 to 3%. In case (ii) the changes are in the range of 5 to 6%. Title: On the coronal lines λ5303 Å and λ6374 Å Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1989SoPh..124...53P Altcode: We present theoretical calculations of the observed coronal emission line profiles of FeXIV (5303 Å) and Fex (6374 Å) ions, which are observed at the time of total solar eclipse. Baumbach's relation (Allen, 1973) of electron density has been employed to compute the full width at half maximum FWHM. We have employed several other electron density distributions and found that the calculated differences in the FWHM are within 0.5% of one another. We have used the ion densities Ni/NE given by Jordan (1969). To explain the observed FWHM, we have assumed that the corona is expanding spherically symmetrically with a velocity of one or two mean thermal units and no turbulence is included. With these highly simplified assumptions, we have reproduced qualitatively the profiles and FWHM's of the above lines. However, to explain quantities of FWHM's, we should take into account the inhomogeneities in the structure of the corona. It is thus shown, that turbulence is not necessary to explain the observed FWHM. Title: Some physical processes influencing the polarization of continuum and line radiation Authors: Nagendra, K. N.; Peraiah, A. Bibcode: 1987A&A...181...71N Altcode: Some physical mechanisms which affect the continuum and line polarization are studied. The physical conditions of the plasma selected for this purpose represent different astrophysical situations of interest, particularly the magnetic stars. The pure absorption polarization transfer equation is solved individually taking these effects into account. Title: Aberration and Advection Effects in a Plane-parallel Medium in Motion Authors: Peraiah, A. Bibcode: 1987ApJ...317..271P Altcode: The effects of aberration and advection terms in the fluid-frame steady-state radiative-transfer equation are evaluated by means of numerical computations for plane-parallel media moving at velocities 1000, 2000, 3000, 4000, and 5000 km/s. A monochromatic radiation field, no internal emission, and coherent isotropic scattering are assumed; the results are presented graphically and briefly characterized. The inclusion of aberration and advection is shown to produce substantial changes in the mean intensities and outward fluxes, even when time dependency is neglected. Application of the results to models of light propagation through the rapidly expanding outer layers of supergiants, novae, supernovae, QSOs, etc. is recommended. Title: Effects of dust on the formation of lines in an expanding spherical medium Authors: Peraiah, A.; Varghese, B. A.; Rao, M. S. Bibcode: 1987A&AS...69..345P Altcode: A series of line profiles formed in a spherically symmetric and radially expanding atmosphere in which dust is present are computed, assuming that the dust scatters radiation isotropically. Two cases of dust distribution are employed: (1) uniform distribution of dust throughout the medium and (2) density increasing with radius. The density and the velocity of expansion of the gaseous component are assumed to satisfy the equation of continuity for a model of a two-level atom in a non-LTE approximation with complete redistribution. The calculations are done in the comoving frame of the fluid and later transformed to a point at infinity. Title: Transmission and reflection operators of radiative transfer equation with aberration and advection terms. II - Line radiation in spherical symmetry Authors: Peraiah, A. Bibcode: 1987BASI...15...70P Altcode: A formal solution of the equation of radiative transfer is presented with aberration and advection terms corresponding to the lines included. The operators of reflection and transmission in a radially expanding spherically symmetric shell are derived. This solution is valid in a medium moving with velocity v such that v/c is about 0.0167. Complete or partial frequency redistribution of photon frequencies can be incorporated if desired. Title: Transmission and Reflection Operators of Radiative Transfer Equation with Aberration and Advection Terms - Part One - Monochromatic Radiation Field with Spherical Symmetry Authors: Peraiah, A. Bibcode: 1987BASI...15....1P Altcode: Integration of the radiative transfer equation, with the aberration and advection terms included, is described, assuming coherent and isotropic scattering. The operators of transmission and reflection derived in this paper are applicable to situations in which v/c = 0.0167 where v and c are the velocities of the gas and light respectively. These operators can be applied to a spherically symmetric medium in which matter scatters or absorbs and emits monochromatic radiation. Title: An Integral Operator Technique of Radiative Transfer in Spherical Symmetry Authors: Peraiah, A. Bibcode: 1987nrt..book..305P Altcode: No abstract at ADS Title: Effects of Temperature and Velocity Gradients on Doppler Widths Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1986Ap&SS.126..295P Altcode: We have investigated how the gradients of temperature and expansion velocities will change the emergent profiles from an extended medium in spherical symmetry. Variation of the source function and expansion velocities are assumed. The following variations of temperature are employed:

(1)

T(r) ; T0 (isothermal case)

(2)

T(r) ; T0(r/r0)1/2

(3)

T(r) ; T0(r/r0)-1

(4)

T(r) ; T0(r/r0)-2

(5)

T(r) ; T0(r/r0)-3 The profiles calculated present an interesting feature of broadening. Title: Relativistic effects on radiative transfer equation: order of magnitude study. Authors: Peraiah, A. Bibcode: 1986KodOB...5..141P Altcode: The author has analyzed how the high gas velocities which are observed in objects such as the atmospheres of supergiant stars, novae, supernovae, accretion discs around high density objects would change the coefficients of different terms in the transfer equation which is solved in a comoving frame. Velocities as low as 5000 km s-1 are enough to show the relativistic effects in different terms in the transfer equation. It is suggested that the relativistic effects must be taken into account in almost all the cases where the line profiles are studied in the expanding atmospheres. Title: Discretization of the equation of radiative transfer with Compton scattering. Authors: Peraiah, A. Bibcode: 1986KodOB...5...61P Altcode: The author has attempted to solve the equation of radiative transfer by including Compton and inverse Compton scattering. He expanded the specific intensity by Taylor series. The resulting equation has been discretized for obtaining the solution. Title: Integral operator technique of line transfer. Authors: Peraiah, A. Bibcode: 1986KodOB...5..113P Altcode: The author presents details of a new technique of obtaining a numerical solution of the radiative transfer equation in spherical symmetry in a polychromatic system. He employed the integral operators together with an interpolation formula of the specific intensity defined on radius-angle-frequency grid. The author finds that the method is quite stable and employs a large stepsize in all the variables on the grid. Title: Some Aspects of the Solution of Vector Transfer Equation in a Magnetized Medium Authors: Nagendra, K. N.; Peraiah, A. Bibcode: 1985Ap&SS.117..121N Altcode: A simplification of the numerical method of solving the vector transfer equation, given earlier by Nagendra and Peraiah (1985a), is described for problems which involve only absorption. This allows us to attempt to solve under realistic conditions and with reduced computing efforts, the important problems of polarization of light emerging from magnetized stars. For the purpose of illustration, the equations described are used for solving the continuum and Zeeman line transfer problems. Title: Numerical solution of the radiative transfer equation in a magnetized medium Authors: Nagendra, K. N.; Peraiah, A. Bibcode: 1985MNRAS.214..203N Altcode: A numerical method of solution based on the discrete space theory of radiative transfer as applied to the transfer problems in an anisotropic medium is discussed. Two simple applications, namely the scattering in the atmosphere of a hot magnetic white dwarf and in a plasma slab immersed in a superstrong magnetic field are discussed. The normal wave transfer equations for the scattering and absorption of radiation are used for this purpose. The solutions are compared with those obtained for the non-magnetic Thomson scattering in the same media. A comparative study is made of the normal wave and Stokes vector equations for a Zeeman active gas. Title: Radiative transfer equation in spherical symmetry Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1985ApJ...290..411P Altcode: A numerical solution of the radiative transfer equation in spherically symmetric geometry is presented using integral operators within the framework of the discrete space theory and expressing the specific intensity in terms of the nodal values of the radius-angle mesh. The solution obtained satisfies the following tests: (1) the invariance of the specific intensity in a medium in which radiation is neither absorbed nor emitted, (2) the continuity of the solution in both angle and radial distribution, (3) a numerical proof showing the uniqueness of the solution, and (4) the condition of zero net flux in a scattering medium with one boundary having a specular reflector, and global conservation of energy. The solution is found to satisfy the above tests to the machine accuracy. Title: Solution of Radiative Transfer Equation with Spherical Symmetry in Partially Scattering Medium Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1985Ap&SS.108...67P Altcode: We have solved the equation of radiative transfer in spherical symmetry with scattering and absorbing medium. We have set the albedo for single scattering to be equal to 0.5. We have set the Planck function constant throughout the medium in one case and in another case the Planck function has been set to vary asr -2. The geometrical extension of the spherical shell has been taken as large as one stellar radius. Two kinds of variations of the optical depth are employed (1) that remains constant with radius and (2) that varies asr -2. In all these cases the internal source vectors and specific intensities change depending upon the type of physics we have employed in each case. Title: P Cygni type profiles. Authors: Peraiah, A.; Srinivasa Rao, M. Bibcode: 1985KodOB...5...45P Altcode: The authors present a series of P Cygni type profiles of spectral lines computed by employing different velocity laws of expansion in a spherically symmetric atmosphere. A comparison has been made with those of Beals classification. They have employed the line transfer equation in comoving frame in certain test cases, to obtain the source function which is being used to calculate the profiles observed at infinity. Title: Radiative transfer equation in spherically-symmetric non-scattering media. Authors: Peraiah, A.; Varghese, B. A. Bibcode: 1984Ap&SS.107..177P Altcode: We solved the equation of radiative transfer in spherically-symmetric shells with arbitrary internal sources. We integrated the equation of transfer on the discrete grid of angle and radius given by [μj-1, μj] [ri-1, ri]. The size in the angle coordinates is determined by the roots of a quadrature formula where as the size in the radial coordinate is determined by the non-negativity of the reflection and transmission operators. We considered two cases of variation of the Planck function. (1) Constant throughout the medium and (2) varying as 1/r 2. We find that in the inner shells, the radiation directed toward the centre of the sphere is more than that directed away from the centre of the sphere. In the outer shells the converse is true. Title: The interaction principle in radiative transfer. Authors: Peraiah, A. Bibcode: 1984Ap&SS.105..209P Altcode: We describe the interaction principle which is of fundamental importance to the theory of radiative transfer in one-, two-, and three-dimensional geometry. We also describe the practical difficulties associated with this principle in these geometries. Title: Polarization of Continuum Radiation in Magnetic Atmospheres Authors: Nagendra, K. N.; Peraiah, A. Bibcode: 1984Ap&SS.104...61N Altcode: A numerical solution is presented for the problem of continuum radiative transfer in a magnetoactive medium. The continuum opacities are calculated in the presence of a strong magnetic field (H=107 G) typical of magnetic white dwarfs. The L.T.E. pure absorption model is assumed for calculating the polarized radiation field emitted by a realistic model atmosphere in the plane parallel approximation. The wavelength dependence of the linear and circular polarizations are calculated for both uniform and dipole field configurations. Title: Effects of partial frequency redistribution functions R(II), R(III) and R(V) on source functions Authors: Mohan Rao, D.; Rangarajan, K. E.; Peraiah, A. Bibcode: 1984JApA....5..169M Altcode: The effects of partial frequency redistribution on the formation of spectral lines have been studied. The angle-averaged R(II), R(III) and R(V) types of redistribution with isotropic phase function have been considered. Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S/L/(R/V/) lies below S/L/(R/III/) but above S/L/(R/II/) in the line wings. Title: Reflection effect in close binaries. Authors: Peraiah, A. Bibcode: 1984bims.symp...27P Altcode: The author describes an initial attempt of how the radiation field is calculated from the irradiated surface of the component in a binary system. Title: Discrete space theory of radiative transfer. Authors: Peraiah, A. Bibcode: 1984mrt..book..281P Altcode: 1984mrt..conf..281P This contribution describes a general numerical method for solving the equation of radiative transfer in inhomogeneous media with curved geometries. The method is based on the interaction principle and the star product algorithm. It is applied to line formation in expanding media. Title: Reflection effect in close binaries. IV. Limb darkening of the reflected radiation incident from an extended surface of the secondary. Authors: Peraiah, A.; Rao, M. S. Bibcode: 1983JApA....4..175P Altcode: The law of limb darkening has been calculated when the atmosphere of the primary component is illuminated by the extended surface of the secondary component in a binary system. The specific intensities calculated at infinity show marked changes when the plane-parallel approximation is replaced by the assumption of spherical symmetry. The middle portions of the illuminated surface reflect maximum radiation while the innermost and outermost layers show lesser amount of reflected radiation. Title: Reflection Effect in Close Binaries. V. Effects of reflection on spectral line formation Authors: Peraiah, A.; Rao, M. S. Bibcode: 1983JApA....4..183P Altcode: The effects of reflection on the formation of spectral lines is investigated. The authors have assumed a purely scattering atmosphere and studied how the equivalent widths change due to irradiation from the secondary. Generally, the flux in the lines is increased at all frequency points, the cores of the lines receiving more flux than the wings. Moreover, the proximity of the secondary component changes the equivalent widths considerably. The further away the secondary is from the primary the higher are the equivalent widths. Title: Density dependence of the line source functions in scattering media. Authors: Peraiah, A. Bibcode: 1983Ap&SS..95..117P Altcode: We have calculated source functions in a scattering medium in which the density changes according to the law ofN e (r)∼r n wheren takes the value from -3 to +3(1) andN e (r) is the electron density. We have assumed that the media consist of electrons and we have also considered a geometrically extended media in which the outer radii are 2, 3, 5 times the inner radius. The source functions obtained are completely due to electron scattering. It is found that the source function varies considerably for different variations of density changes fromn=-3 to +3. In the case of density variation withn=-3 and -2, the source functions do not increase with optical depth considerably, but whenn=-1, 0, they rise slowly with the increase in optical depths and whenn=1 to 3 there is a steep rise in the source functions with the optical depth increasing towards the center of the star. Title: Reflection effect in close binaries. III - Distribution of radiation incident from an extended source Authors: Peraiah, A. Bibcode: 1983JApA....4..151P Altcode: The effects of irradiation from an extended surface of the secondary component on the atmosphere of the primary are studied. Consideration is given to an isothermal and purely scattering medium. The resultant radiation field due to irradiation from an extended surface and self-radiation is different from that due to irradiation from a point source and self-radiation. In the case of the point source the middle layers of the exposed part of the atmosphere show maximum reflection, while in the former case the reflection gradually decreases from the center of the component towards the surface of the outermost layers of the atmosphere. The reflection effect appears to be strongly dependent on the density distribution of the electrons. Title: Reflection effect in close binaries. II - Distribution of emergent radiation from the irradiated component along the line of sight Authors: Peraiah, A. Bibcode: 1983JApA....4...11P Altcode: The author has calculated the effects of irradiation from a point source observed at infinity. Plane-parallel approximation and spherically-symmetric approximations are employed in calculating the self-radiation field for the sake of comparison. It is found that there are considerable changes in the radiation received at infinity between the approximation of plane-parallel stratification and spherical symmetry. Title: Effects on partial prequency redistributionR II on the level population ratios in a resonance line Authors: Peraiah, A.; Nagendra, K. N. Bibcode: 1983Ap&SS..90..237P Altcode: Angle-averaged partial frequency redistributionR II has been employed in obtaining a simultaneous solution of radiative transfer equation in the comoving frame and the statistical equilibrium equation for a non-LTE two level atom. We have obtained the ratios of population densities of the upper and lower levels of the resonance line of PV by utilizing the data given in Bernacca and Bianchi (1979). Line source functions are also obtained for different types of variations of density and velocity of the expanding gases. We have considered the atmosphere to be 11 times as thick as the stellar radius. The first iteration was started by putting the density of the upper level (N 2) equal to zero. However, the convergent solution shows a substantial increase inN 2 although it is still much less than the equilibrium value. The line source function and the ratio of the densities of the particles in the upper and lower levels fall sharply from a maximum at τ=τmax to minimum at τ=0. We have studied the scattering integralint {_{ - infty }^{ + infty } J_x φ _x } dx and found that this quantity also varies quite similar to the ratioN 2/N 1 and the line source functionS L. Title: Radiative Transfer Effects due to Curvature and Expansion in a Dusty Planetary Nebulae Authors: Peraiah, A. Bibcode: 1983IAUS..103..516P Altcode: No abstract at ADS Title: Limb darkening due to the incidence of a parallel beam of radiation. Authors: Peraiah, A. Bibcode: 1983KodOB...3..120P Altcode: The author has investigated how the radiation is distributed from the centre to the limb when the atmosphere receives a parallel beam of radiation from infinity. He considers a purely reflecting surface at the bottom of the atmosphere when the outer layers are illuminated uniformly from all directions. The atmosphere under question is half the radius of the star itself. Although the extension of the atmosphere is quite small the differences in the laws of limb darkening are considerable. The differences are further accentuated when the radiation is assumed to be totally reflected from the bottom of the atmosphere. The situation can be very similar to that of a planetary atmosphere. Title: Reflection effect in close binaries. I - Distribution of radiation from a point source Authors: Peraiah, A. Bibcode: 1982JApA....3..485P Altcode: The radiation field along an irradiated surface of a component in a binary system is calculated. The source of irradiation is assumed to be a point source. This is done primarily to understand easily how the incident radiation will get changed after it is being scattered by the atmosphere. It is noticed that the maximum radiation comes from intermediate points of the atmosphere, the reason being that here there exists the combined radiation due to the star and incident radiation from the point source outside the star although both are diluted. Title: On the Balmer progression in the expanding shell of PLEIONE Authors: Peraiah, A. Bibcode: 1982JApA....3..297P Altcode: The Balmer progression in velocities seen in Pleione and other shell stars is investigated without undertaking the complicated calculations of non-LTE radiative transfer and hydrodynamics of the shells. The equations of the conservation of mass and momentum are simultaneously solved using assumptions which simplify the calculations of the solution. The radiation pressure due to the lines and continuum are examined. It is found qualitatively that the high excitation Balmer lines of hydrogen are formed in a region where the velocity gradients are high and therefore these lines show high radial velocities. Title: Effects of Partial Frequency Redistribution on the Level Population Densities in a Resonance Line Authors: Peraiah, A.; Rao, D. M. Bibcode: 1981Ap&SS..80..437P Altcode: We have obtained a simultaneous solution of the statistical equilibrium equation for a non-LTE two-level atom and the radiative transfer equation in the comoving frames by employing the angle-averaged partial frequency redistribution.R i with isotropic scattering. In the first iteration we have set the population density of the upper level equal to zero and allow it to be populated in the subsequent iterations. The solution converges within two to four iterations. The process of iteration is terminated when the ratios of population densities in two successive iterations at each radial point, attain an accuracy of 1%. The effects of partial frequency redistribution is to increase the population density of the upper level. Radial gas motions do not seem to have significant effects, although in highly extend geometries, velocity gradients change the population densities considerably. Title: Optical depth effects on the formation of spectral lines in rotating and expanding spherical atmospheres Authors: Peraiah, A.; Raghunath, G.; Nagendra, K. N. Bibcode: 1981JApA....2..277P Altcode: The effect of high optical depths and large rotational velocities on the spectral lines in rotating and radial expanding spherical shells is investigated. It is assumed that the outer radius of the shell is three times the inner radius and that there are no velocity gradients in the shell; the radial optical depths are 10, 50, 100, and 500. The shell rotates with velocities varying as 1/p, where p is the perpendicular distance from the axis of rotation. Two expansion (radial) velocities, V = 0 and V = 10 mean thermal units, are considered, with maximum rotational velocities of 0, 5, 10, and 20. In the shell with no radial motions, symmetric lines with emission in the wings were obtained for rotational velocities = 0 and 5, while for rotational velocities greater than or equal to 10, symmetric absorption lines were formed. Lines with central emission were obtained in the case of an expanding shell. Title: Effects of redistribution with dipole scattering on line source functions Authors: Peraiah, A.; Rangarajan, K. E. Bibcode: 1981JApA....2..245P Altcode: The partial frequency redistribution function for zero natural line width and dipole scattering is used to obtain a simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of an expanding gas. A non-LTE, two-level atom in an expanding spherical medium is considered, and the population ratio of the two levels, N2/N1, is calculated. The upper level population (N2), initially set equal to zero, is found to be enhanced significantly from its initial value. Variation in the velocity gradient had little effect on the N2/N1 ratio when the geometrical thickness of the medium was three or ten times the stellar radius; when the thickness was increased to twenty times the central radius, however, the velocity gradients changed this ratio considerably in the region where log T is less than or equal to two, T being the total optical depth. Title: Radiative Transfer in the Co-Moving Frame Authors: Peraiah, A. Bibcode: 1981Ap&SS..77..243P Altcode: Solution of line-transfer equation in the co-moving frame, obtained on the basis of discrete space theory, has been employed to calculate the lines emerging from a rapidly expanding stellar atmosphere. The solution is found to be highly stable for large velocities of expansion with both positive and negative velocity gradients. We have presented profiles of spectral lines that are translated along the line of sight of the observer at infinity. We have treated a Non-LTE two-level atom in a medium scattering isotropically with line and continuum emission. P Cygni-type profiles noticed in a purely scattering medium. Title: Photon escape probabilities in expanding atmospheres Authors: Peraiah, A.; Rangarajan, K. E.; Rao, D. M. Bibcode: 1981JApA....2...81P Altcode: A comparison of mean number of scatterings and escape probabilities has been made in isotropic scattering and dipole scattering by using the angle-averaged partial frequency redistribution function. The equations of radiative transfer and statistical equilibrium have been solved simultaneously in a spherically symmetric expanding atmosphere. Two cases of atmospheric extension where the ratios of outer to inner atmospheric radii are 3 and 10 have been treated. It is found that the partial frequency redistribution gives a larger mean number of scatterings compared to that given by complete redistribution. Velocities tend to reduce the mean number of scatterings and increase the mean escape probabilities. Title: Effects of velocities on Ca II H and K lines. Authors: Rangarajan, K. E.; Mohan Rao, D.; Peraiah, A. Bibcode: 1981KodOB...3...75R Altcode: With a chosen model atmosphere, the authors find double peaked emission for H and K lines in the static medium. The results show that the systematic velocity fields do play a significant role in determining the shape of the H and K profiles. Title: Transient solution of equations of hydrodynamics in gas clouds. Authors: Peraiah, A. Bibcode: 1981KodOB...3...86P Altcode: The author presents numerical results of transient phenomena in incompressible fluids. This has been obtained by solving the equations of conservation of momentum, energy and mass. Title: Formation of spectral lines with the redistribution function RI along the line of sight. Authors: Peraiah, A. Bibcode: 1981KodOB...3...84P Altcode: The author studies the formation of spectral lines at infinity with the redistribution function RI. The radial optical depths considered are .5, 5, 10, 50 and 100. A linear law of velocity is assumed in these calculations. Profiles clearly show the P Cygni nature of asymmetry. Title: An Iterative Simultaneous Solution of the Equations of Statistical Equilibrium and Radiative Transfer in Comoving Frame Authors: Peraiah, A. Bibcode: 1980JApA....1..101P Altcode: No abstract at ADS Title: Effects of High Velocities on Photoionization Lines Authors: Peraiah, A.; Raghunath, G. Bibcode: 1980JApA....1..113P Altcode: No abstract at ADS Title: Comoving Frame Calculations of Spectral Lines formed in Rapidly Expanding Media with the Partial Frequency Redistribution Function for Zero Natural Line Width Authors: Peraiah, A. Bibcode: 1980JApA....1....3P Altcode: Comoving frame calculations have been used to compute the spectral lines formed in rapidly expanding spherical media. We have employed the angle-averaged partial frequency redistribution function R(I) with a two-level atom model in non-LTE atom approximation. A linear velocity law increasing with radius has been employed with maximum velocity at tau=o being set equal to 30 mean thermal units. It is found that one obtains almost symmetric emission line profiles at large velocities similar to those found in quasars. Title: Lines formed in Rotating and Expanding Atmospheres Authors: Peraiah, A. Bibcode: 1980JApA....1...17P Altcode: Spectral lines formed in a rotating and expanding atmosphere have been computed in the frame of the observer at infinity. Two kinds of velocity laws are employed: (i) a uniform radial velocity of the gas and (ii) velocity increasing with radius (i.e. velocity gradients). The atmosphere has been assumed to be rotating with constant velocity. We have considered maximum radial and rotational velocities to be 10 and 3 thermal units respectively in an atmosphere whose geometrical thickness is 10 times the stellar radius. The total radial optical depth at line centre is taken to be about 100. In all cases, Doppler profile and a source function which is varying as 1/r**2 have been used. Generally, the lines are broadened when rotation is introduced. However, when radial motion is also present, broadening becomes asymmetic and the red emission and blue absorption are enhanced. Title: Effects of high radial velocities on line transfer in extended atmospheres Authors: Peraiah, A. Bibcode: 1980AcA....30..525P Altcode: The equation of radiative transfer in a comoving frame has been solved for rapidly expanding gaseous medium in spherically symmetric extended stellar atmospheres. A non-LTE two-level atom with Voigt profile function is assumed. The comoving terms in the radiative transfer are discretized in the framework of the discrete space theory of Grant. These terms are simply reduced to a tri-diagonal matrix. The boundary conditions for the frequency derivative can be introduced through the elements of the first and last rows of this matrix. This seems to be quite stable for arbitrary velocities in the medium. Maximum velocities up to 60 units of mean thermal velocities have been considered. Title: Lines formed in a slowly expanding thin spherical shell. Authors: Peraiah, A.; Raghunath, G.; Nagendra, K. N. Bibcode: 1980KodOB...3...30P Altcode: The authors have investigated how an optically thin spherical shell with small velocities change the profiles and equivalent widths of the lines. They have employed several types of variations in density, velocity of expansion and source functions. In all the cases they find that the line centres are shifted to the blue side almost in proportion to the velocity of expansion. The shells moving with constant velocities shift the line centre the most, irrespective of the density variation. The velocity gradients shift the line centre the least. Title: Flux vector splitting of the inviscid radiation gas dynamic equations. Authors: Peraiah, A. Bibcode: 1980KodOB...3...49P Altcode: The author has analysed various schemes for the iterative simultaneous solution of the inviscid gas dynamic equations. He considers the problem from the point of view of the stellar atmospheres. The difference between conservative and quasi-conservative systems has been analysed by using the flux vector splitting process. The radiation pressure in the atmosphere (due to continuum and resonance lines) has been included in flux vector splitting analysis to obtain best difference schemes. Title: Rotational effects on line source function. Authors: Peraiah, A.; Raghunath, G. Bibcode: 1980KodOB...3...21P Altcode: The effects of rotation are investigated on the source functions in an expanding atmosphere. The authors have considered a non-LTE two-level atom in an extended atmosphere. They have also made use of von Zeipel's theorem in giving the incident radiation at τ = τmax. Uniform rotation is assumed and the values of the ratios of the centrifugal force and gravity force at the equator are taken to be 0.1, 0.4, 0.8 corresponding to a uniform rotational velocity of 1, 4 and 8 mtu. It is found that rotation will dilute the radiation field which is similar to the effects of expansion. Title: Simultaneous solution of radiative transfer equation in the comoving frame and the statistical equilibrium equation with complete redistribution. Authors: Peraiah, A. Bibcode: 1980KodOB...3...17P Altcode: Complete redistribution with Voigt profile function has been employed in obtaining the simultaneous solution of line transfer and the statistical equilibrium equation for a non-LTE two level atom in an extended stellar atmosphere expanding with spherical symmetry. Title: Line Formation in Spherical Media with Partial Frequency Redistribution. II. Expanding Media with Redistribution Function RI Authors: Peraiah, A. Bibcode: 1979Ap&SS..63..267P Altcode: Lines formed in a differentially expanding atmosphere have been calculated by using the angle averaged redistribution functionR I (Hummer, 1962). We have compared these lines, in a few cases, with those formed by complete redistribution in the observer's frame of reference. We have considered an atmosphere whose ratios of inner to outer radii are 2 and 10, and it is assumed that the gas in the atmosphere is expanding uniformly with a maximum velocity of 3 mean thermal units. We have presented lines formed in spherical symmetry and those obtained by integrating over the apparent disc. Three types of physical situations are considered with a 2-level atom with non-LTE approximation (1) ɛ=10-4, β=10-4, (2) ɛ=10-4, β=0 and (3) ɛ=β=0, where ɛ is the probability per scatter that a photon is destroyed by collisional de-excitation, and β is the ratioKc/Kl of absorption in the continuum per unit frequency interval to that in the line centre. It is found that there are noticeable differences between the profiles formed by partial redistribution (PRD) and complete redistribution (CRD). The profiles integrated over the stellar disc from the first type of the media are box type with flat top, which are similar to those observed in WC stars and those from the second type of media show emission peaks on red and blue sides with emission on the red side larger than the one on the blue side. The profiles from the third type of media with pure scattering, show some emission on the red side and deep absorption on the blue side. Large geometrical extensions of the atmosphere and higher gas velocities seem to enhance these two effects. Title: Formation of the hydrogen Lyman alpha line in expanding spherical planetary nebulae. Authors: Wehrse, R.; Peraiah, A. Bibcode: 1979A&A....71..289W Altcode: The radiation field in the hydrogen Lyman-alpha line is calculated for an optically thick nebula, which is in uniform or accelerated expansion (velocity increasing to the surface). The radiative-transfer equation is solved for a spherical configuration using the discrete space theory with partial redistribution. The computations were performed for a nebula with a ratio of outer to inner radius of 3.3 and an optical depth at line center of about 1000. Velocities up to 26 km/s are considered. In all cases strongly asymmetric profiles are found with a high emission peak at the red side of the line center and a low one at the blue side. Inside the nebula the mean intensities are much smaller than in the static case. The calculations also show that the transverse velocity gradients induced by the sphericity are very important. Title: RII partial frequency redistribution function and its effects on the formation of lines in expanding spherical atmospheres. Authors: Peraiah, A. Bibcode: 1979KodOB...2..203P Altcode: No abstract at ADS Title: Solution of the radiative transfer equation in spherically symmetric media with spherical harmonic approximation. Authors: Peraiah, A. Bibcode: 1979KodOB...2..230P Altcode: No abstract at ADS Title: Comoving frame calculations with Lorentz profiles in radially expanding media. Authors: Peraiah, A.; Raghunath, G. Bibcode: 1979KodOB...2..240P Altcode: No abstract at ADS Title: Radiation pressure in resonance lines. Authors: Peraiah, A. Bibcode: 1979KodOB...2..260P Altcode: No abstract at ADS Title: Formation of the Hydrogen Lyman ~ Line in Expanding Spherical Nebulae with Dust Authors: Peraiah, A.; Wehrse, R. Bibcode: 1978A&A....70..213P Altcode: Summary. The radiation field in the hydrogen Ly line is calculated for a dust fflled spherical gaseous nebula. It is assumed that the nebula with a ratio of inner to outer radius of 3.3 has an optical depth at the line center of about 1000 and is either static or expands uniformly with 26 km s '. For the solution of the radiative transfer equation the discrete space theory with partial redistribution is used. It is found that the dust gives only rise to small changes if it purely scatters. However, if it absorbs it is very effective in reducing the mean intensities j in the whole nebula, e.g. for an optical depth in the dust of =1 decreases J by about a factor of 7. The results also show that for dust filled nebulae the effects of velocities are of minor importance in contrast to dust-free configurations. Key words: gaseous nebulae - dust - H Ly line - spherical radiative transport - expansion Title: Line Formation in Spherical Media with Partial Frequency Redistribution I: Solution of the Line Transfer Authors: Peraiah, A. Bibcode: 1978Ap&SS..58..189P Altcode: The effects of partial redistribution of frequency on the formation of spectral lines in a static and spherically symmetric media have been investigated. The partial redistribution functionsR I andR II (Hummer, 1962) have been employed to calculate the lines for a two-level atom in non-LTE in a spherically symmetric medium with homogenous physical characteristics whose ratiosB/A (of outer to inner radii) are equal to 2 and 10. These results are compared with those formed in a plane-parallel medium withB/A=1. Two types of atmosphere are treated: (1) a pure scattering medium with ɛ=0 and β=0, and (2) an atmosphere with a constant source of emission ɛ=10-4 and β=0, where ɛ is the probability per scatter that a photon will be destroyed by collisional de-excitation and β is the ratioK c/K l of opacity due to continuous absorption per unit interval of frequency to that in the line. Lines formed in complete redistribution also have been calculated for the sake of comparison, and the total optical depth in all cases has been taken to be 103 at the line centre. Vast differences have been found between the lines formed by complete and partial redistribution functions (which, for the sake of simplicity, we shall hereafter refer to as CRD and PRD, respectively). In the case of a purely scattering medium, a small amount of emission is observed in the wings for all cases of scattering functions in the spherical medium as a result of the combined effects of curvature and physical scattering. In the scattering medium, more photons are scattered into the cores of the lines by PRD than in the case of CRD. The lines formed in the medium with internal sources show emission in all cases with small absorption in the cores, except those lines formed by the angle-dependent PRD functions which again depend on the geometrical extension of the medium. Title: Formation of the H Lyalpha line in an expanding spherical planetary nebula with dust. Authors: Wehrse, R.; Peraiah, A. Bibcode: 1978BASI....6...50W Altcode: No abstract at ADS Title: On negative intensities in discrete space theory in spherical medium. Authors: Peraiah, A. Bibcode: 1978KodOB...2..180P Altcode: No abstract at ADS Title: Effects of partial frequency redistribution with dipole scattering on the formation of spectral lines in expanding media. Authors: Peraiah, A. Bibcode: 1978KodOB...2..115P Altcode: No abstract at ADS Title: Geometry effects on the formation of the hydrogen Ly alpha line in planetary nebulae. Authors: Peraiah, A.; Wehrse, R. Bibcode: 1977A&A....61..719P Altcode: Summary. In order to study the effects of sphericity on the radiative transfer in the hydrogen Ly oc line of planetary nebulae, the radiation field in this line is calculated for static pure hydrogen models with ratios of outer to inner radiis approximately equal to 2,4 and 8. For r0 r 2 the transfer equation is also solved in plane parallel approximation for comparison. Both reflecting and open inner boundaries are considered. The transfer equation has been solved in the framework of the discrete space theory. In the spherical calculations the profiles of the emergent radiation are not found to be very different in their shapes (one from another) while there are large differences in the internal radiation fields. Substantial changes occur for most quantities, when the spherical approximation is replaced by the plane parallel one. Key words: spherical radiative transfer hydrogen Ly cc planetary nebulae Title: Linear Polarization from Rotating Extended Atmospheres of Stars Authors: Peraiah, A. Bibcode: 1976A&A....46..237P Altcode: Summary. Linear polarization from the extended atmospheres of rotating stars has been calculated. Two types of atmospheres have been considered: (1) the atmospheres of early type supergiants with electron scattering (Thomson scattering) and (2) the atmospheres of late type supergiants with scattering due to H2 molecules (Rayleigh scattering). In both cases, the density at any point in. the atmosphere is assumed to vary as the inverse square of the distance from the centre of the star. In the latter type of atmosphere, the wavelength dependence of linear polarization has been calculated and it appears to be in accordance with the observational result (Kruszeski et al., 1968; Dyck and SandfordII, 1971) that the polarization increases with decreasing wavelength. It is also shown that, in the case of an electron scattering atmosphere, polarization always increases with the size of the atmosphere, while this need not be so in the case of an atmosphere with molecular scattering. Keywords: linear polarization extended atmospheres atmospheres of supergiant stars - Thomson scattering - Rayleigh scattering Title: Numerical solution of radiative transfer equation in extended spherical atmospheres with Rayleigh phase function. Authors: Peraiah, A. Bibcode: 1975A&A....40...75P Altcode: No abstract at ADS Title: Curvature Effects in Extended Stellar Atmospheres - Absorption and Scattering Authors: Peraiah, A. Bibcode: 1973Ap&SS..23..159P Altcode: The numerical solution of radiative transfer equation including curvature with both absorption and scattering has been developed in the frame work of Discrete Space Theory. Two cases have been considered: (A) irradiation of the atmosphere at τ=T and (B) no irradiation on either side of the atmosphere. Isotropic scattering has been assumed. It is found that the emergent luminosities (defined by ∫r 2 I(r, μ) đμ) from scattering dominated atmospheres are smaller than those from absorption dominated atmospheres. Title: Temperature Difference between Pole and Equator of the Sun Authors: Peraiah, A. Bibcode: 1973SoPh...30...29P Altcode: No abstract at ADS Title: Curvature effects in extended stellar atmospheres — Pure absorption Authors: Peraiah, A. Bibcode: 1973Ap&SS..21..223P Altcode: The effects of curvature in an atmosphere with pure absorption are investigated. Numerical solution of the transfer equation has been obtained in the framework of the Discrete Space Theory of Radiative Transfer. Two cases have been considered: (a) the atmosphere is irradiated at the bottom and there is no incident radiation at the top of the atmosphere; and (b) no radiation is incident on either side of the atmosphere. It is found that the thermal sources inside the atmosphere dominantly influence the emergent radiation and this is very much so, in the spherical case and for large optical thickness. The emergent luminosities increase with the geometrical thickness although the emergent specific intensities are reduced and the former seems to be because of the larger surface area and later seems to be because of the effects of curvature. Title: Spectral line formation in extended atmospheres-II Authors: Peraiah, A. Bibcode: 1973MNRAS.162..321P Altcode: Line profiles have been computed for a model of two-level atom both for plane parallel and spherically symmetric geometry assuming both LTE and non-LTE. Title: Numerical solution of the radiative transfer equation in spherical shells. Authors: Peraiah, A.; Grant, I. P. Bibcode: 1973JIMA...12...75P Altcode: No abstract at ADS Title: Effect of atmospheric curvature on spectral line profiles in extended stellar atmospheres. Authors: Peraiah, A.; Grant, I. P. Bibcode: 1972css..conf..211P Altcode: 1971css..conf..211P No abstract at ADS Title: Spectral line formation in extended stellar atmo-spheres Authors: Grant, L. P.; Peraiah, A. Bibcode: 1972MNRAS.160..239G Altcode: A method of numerical solution of the equation of radiative transfer for spectral line formation in extended spherically symmetric stellar atmospheres is described. A simple Non-LTE two-level atom model is assumed. Results are presented for the cases b/a 2 where a is the inner and b the outer radius of the atmosphere. Title: Theoretical Light Changes in Close Binaries Authors: Peraiah, A. Bibcode: 1970A&A.....7..473P Altcode: A general expression for the gravity darkening of the tidally and non-uniformly rotating Roche components of close binary systems has been derived. This expression has been used to ealculate the temperatures and spectral distributions on the surfaces of these components and to compute their luminosities with limb-darkening taken into account. The effects of uniform and non-uniform rotation have been considered together with a few cases of synchronous rotation. The distributions, especially that of temperature are relatively insensitive to the amount of non-uniformity of the rotation. The laws of darkening tend to converge as the mass ratio increases. The results for synchronous rotation of the components a not very different from those found for nonsynchronous systems. Luminosities can be reduced by as much as 40 to 50 percent of the total luminosities in different directions depending upon the line of sight. Title: Gravity Darkening in the Components of Close Binary Systems Authors: Peraiah, A. Bibcode: 1969A&A.....3..163P Altcode: The variation of temperature and brightness on the surface of the components of close binary systems has been investigated taking account of non-uniform rotation and tidal effects of the other component considered as mass pomt. The equations for such surfaces had been developed in terms of the mass ratio of the two components (m3/m1); ratio of the equatorial radius of the primary to the distance between the centers of gravity of the two components (re/B); ratio of centrifugal to gravity forces at the equator (1); and the ratio of angular velocities at the equator and the pole (x). When these equations are used to compute the temperature and brightness distributions by using different values for the above mentioned parameters, it has been observed that temperature and brightness fall very rapidly between 45 colatitude and the equator. Higher temperatures tend to reduce gravity darkening due to tidal effect. The fall in brightness is steeper than that of temperature. These results are compared with those of Ireland by putting m3 = 0. Title: Apsidal Motion in Close Binary Systems Authors: Peraiah, A. Bibcode: 1966ZA.....64...27P Altcode: No abstract at ADS Title: Rotation of the Components in Close Binary Systems Authors: Peraiah, A. Bibcode: 1965ZA.....62...48P Altcode: No abstract at ADS