# The effect of the partial redistribution of spectral line formation K. E. Rangarajan [Ph.D Thesis]

Material type: TextPublication details: Bangalore Indian Institute of Astrophysics 1987Description: 114pSubject(s): Online resources: Dissertation note: Doctor of Philosophy Indian Institute of Astrophysics, Bangalore 1987 Summary: The main effort of this study is concentrated on ascertaining the role of partial redistribution(PRD> functions in the process of spectral line formation. The effects of angle averaged R I' R II' RIIIa nd R V redistribution with isotropic phase function are studied. We have compared these results with those obtained using complete redistribution (CRD) . Transfer equation with plane parallel geometry is solved using the Discrete space theory technique of Grant and Hunt (1969) . Various types of boundary conditions considered. The following results are the new and important conclusions of this study. In this study, we find that for a purely scattering optically thick medium, RI function produces deeper absorption profile compared to other functions. The redistribution function R II is more coherent than Rv and R v is more coherent than R: u:x in the wings. The more non-coherent the redistribution function is, the higher would be the emergent intensity in the Doppler core. If thermal sources are present in the medium and if there is incident radiation on the lower boundary, all the redistribution functions give the same intensity, in the core. But in the wings, the more non-coherent the redistribution is, the higher would be the intensity. The presence of continuous opacity makes the spectral lines appear weak. Their effects are more pronounced compared to that of the thermal sources in the medium and are present for any type of redistribution mechanism. In high optical depth situations, the R type of redistribution allows the photons to diffuse to the line centre and increase the intensity there. In the third chapter, coherent and non-coherent electron scattering combined with complete and partial redistribution by atoms are studied for some parameterized models. Since this problem is characterized by two frequency scales, one for the atoms and the other for the electrons, two types of frequency quadrature are required to cover the effect of both the processes. Though the basic equations are solved within the framework of Discrete space theory, the frequency quadrature points, normalization, segmenting the problem into core and wing regions and the iteration procedure all follow that of Auer and Mihalas (1968). We obtain the following new result: If the coherent electron scattering is the only continuous opacity source, we find that the more non-coherent the redistribution by atoms is, the higher the value of the mean intensity in the wings for optically thick media. The non-coherent electron scattering combined with PRD fills up the core and hence one gets higher fluxes in the core compared to coherent electron scattering_ We investigate the deviation of absorption and emission profiles from each other for a two level atom with angle avera9~d redistribution functions. The corr~ct expression for the source function derived by Baschek,Mihalas and Oxenius (1981) is used to solve consistently for the emission profile and the radiation field. From this study, we get the following new and important results: The absorption and emission profiles do not deviate from each other in the Doppler core for any redistribution function even if the stimulated emission term is important. The devition of absorption and emission profiles in the wing is more for coherent type of redistribution function. R xxx redistribution gives identical absorption and emission profiles and so one can approximate RIII by CRD for all practical purposes. The effects of small macroscopic velocity fields on Ca II Hand K lines are given in chapter 5. The atomic model chosen contains the lower most five levels and the continuum. radiative transfer equation and statistical equilibrium equations are solved simultaneously using equivalent two level atom method. A schematic chromospheric type of atmosphere is considered. The emergent profiles are calculated for the systematic expanding velocities 0.0, 0.5 and 1.0 (velocities at the outer boundaries expressed in mean thermal units). We obtain the following significant results: Even though the velocities are small, they seem to affect the shapes of the H and K profiles considerably. A single peak emission instead of a double• peaked emission is obtained for the K line with v ~ 1 and p = 0.79. ( ~ = cos8 , 8 is the angle of the ray to the normal at the surface.). The small velocities do not affect the infrared triplet lines significantly.Item type | Current library | Shelving location | Call number | Status | Date due | Barcode |
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Thesis & Dissertations | IIA Library-Bangalore | General Stacks | 043:52/RAN (Browse shelf(Opens below)) | Available | 10991 |

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Doctor of Philosophy Indian Institute of Astrophysics, Bangalore 1987

The main effort of this study is concentrated on

ascertaining the role of partial redistribution(PRD> functions

in the process of spectral line formation. The effects of

angle averaged R I' R II' RIIIa nd R V

redistribution with

isotropic phase function are studied. We have compared these

results with those obtained using complete redistribution

(CRD) . Transfer equation with plane parallel geometry is

solved using the Discrete space theory technique of Grant and

Hunt (1969) . Various types of boundary conditions

considered. The following results are the new and important

conclusions of this study.

In this study, we find that for a purely scattering

optically thick medium, RI function produces deeper absorption

profile compared to other functions. The redistribution

function R II is more coherent than Rv and R v is more coherent

than R: u:x in the wings. The more non-coherent the

redistribution function is, the higher would be the emergent

intensity in the Doppler core. If thermal sources are present

in the medium and if there is incident radiation on the lower

boundary, all the redistribution functions give the same

intensity, in the core. But in the wings, the more non-coherent

the redistribution is, the higher would be the intensity. The

presence of continuous opacity makes the spectral lines appear

weak. Their effects are more pronounced compared to that of the

thermal sources in the medium and are present for any type of

redistribution mechanism. In high optical depth situations,

the R type of redistribution allows the photons to diffuse

to the line centre and increase the intensity there.

In the third chapter, coherent and non-coherent

electron scattering combined with complete and partial

redistribution by atoms are studied for some parameterized

models. Since this problem is characterized by two frequency

scales, one for the atoms and the other for the electrons, two

types of frequency quadrature are required to cover the effect

of both the processes. Though the basic equations are solved

within the framework of Discrete space theory, the frequency

quadrature points, normalization, segmenting the problem into

core and wing regions and the iteration procedure all follow

that of Auer and Mihalas (1968). We obtain the following new

result: If the coherent electron scattering is the only

continuous opacity source, we find that the more non-coherent

the redistribution by atoms is, the higher the value of the

mean intensity in the wings for optically thick media. The

non-coherent electron scattering combined with PRD fills up

the core and hence one gets higher fluxes in the core compared

to coherent electron scattering_

We investigate the deviation of absorption and

emission profiles from each other for a two level atom with

angle avera9~d redistribution functions. The corr~ct

expression for the source function derived by Baschek,Mihalas

and Oxenius (1981) is used to solve consistently for the

emission profile and the radiation field. From this study, we

get the following new and important results: The absorption

and emission profiles do not deviate from each other in the

Doppler core for any redistribution function even if the

stimulated emission term is important. The devition of

absorption and emission profiles in the wing is more for

coherent type of redistribution function. R xxx redistribution

gives identical absorption and emission profiles and so one

can approximate RIII by CRD for all practical purposes.

The effects of small macroscopic velocity fields on

Ca II Hand K lines are given in chapter 5. The atomic model

chosen contains the lower most five levels and the continuum.

radiative transfer equation and statistical equilibrium

equations are solved simultaneously using equivalent two level

atom method. A schematic chromospheric type of atmosphere is

considered. The emergent profiles are calculated for the

systematic expanding velocities 0.0, 0.5 and 1.0 (velocities

at the outer boundaries expressed in mean thermal units). We

obtain the following significant results: Even though the

velocities are small, they seem to affect the shapes of the H

and K profiles considerably. A single peak emission instead of

a double• peaked emission is obtained for the K line with v

~ 1 and p = 0.79. ( ~ = cos8 , 8 is the angle of the ray to

the normal at the surface.). The small velocities do not

affect the infrared triplet lines significantly.

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