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STUDY OF HYDROGEN IN THE INTERSTELLAR MEDIUM

A dissertation submitted in partial fulfilment of the requirements for the award of the degree of

Master of Science

in

Physics

by

Dhanya A Saviour

(Reg.no 1647325)

Bhuvana GR

(Reg.no 1647324)

Under the Guidance of

Dr.Jayant.Murthy

Indian Institute of Astrophysics

&

Dr.Ravichandran

Professor

Department of Physics,

CHRIST UNIVERSITY,

BENGALURU-560029, INDIA

DECLARATION

We, Dhanya A Saviour and Bhuvana GR declare that the project titled ‘Study of Hydrogen in the Interstellar Medium’ is a record of original research work undertaken by us for the award of Master of Science in Physics. We have completed this study under the capable supervision of Dr.Jayanth Murthy, Indian Institute of Astrophysics, Bengaluru and Dr.Ravichandran, Deartment of Physics, Christ University, Bengaluru.

We also declare that htis report has not been submitted for the award of any other degree, diploma, associateship, fellowship or any other title. It has not been sent for any publication or presentation purpose. We hereby confirm the originality of this work ad that there is no plagiarism in any part of the dissertation.

Place: Bengaluru
Date:
Signature of the candidate
Dhanya A Saviour
(Reg.No 1647325)
Department of Physics
Christ University, Bengaluru -29

Signature of the candidate
Bhuvana GR
(Reg.No 1647324)
Department of Physics
Christ University, Bengaluru – 29

CERTIFICATE
This is to certify that the project report submitted by Dhanya A Saviour(1647325) and Bhuvana GR(1647324) titled ‘Study of Hydrogen in the Interstellar Medium’ is a record of research work carried out by them during the academic year 2017-2018 under my supervision in partial fulfilment for the award of Master of Science in Physics.
I hereby confirm the originality of the work and that there is no plagiarism in any part of the dissertation.

Place: Bengaluru
Date:
Signature of the supervisor

Dr Jyanth Murthy,
Indian Institute of Astrophysics,Bengaluru

Signature of the Head of the Deprtment

Dr.George Thomas C
Professor, HOD

Department of Physics,
Christ University, Benagluru
Internal Suervisor
Dr Ravichandran
Professor
Christ University, Bengaluru

ACKNOWLEDGEMENTS

-We would like to express our sincere gratitude to Dr Jayanth Murthy, who has been a guiding beacon and has patiently stuck with us through difficult situations.

-We would like to express our heartfilled thanks to our faculty in charge Dr Ravichandran for hi trust in our efforts and his unfetted guidance in providing an independant environment for carrying out this project.
-We would like to thank Akshaya maam ,KT Paul George Thomas sir and Blesson sir for all their ceasless support for the project that was undertaken under their guidance

-We would like to thank the Dept. Of Physics, Christ University for their dilligent support and guidance towards systematic conduction of this project.

Dhanya A Saviour
Bhuvana GR

CONTENTS
Declaration

Certificate

Acknowledgement

Abstract

Chapter 1. Introduction

Interstellar Medium
Spectral series of Hydrogen
Optical Depth
Column density
Voigt Function

Chapter 2.Theoritical Background and methodology

Line profile fitting method
Iterative process

Chapter 3.Procedure

IDL program
Voigt fit function for Lyman beta
Voigt fit function for lyman gamma

Chapter 4.Results

Tables
Spectra

Chapter 5: Conlusion and future prospects

References

List of figures

ABSTRACT

Spectral line shape describes the form of a feature, obseved in spectroscopy, corresponding to an energy change in an atom, molecule or ion. Ideal line shapes include Lorentzian, Gaussian and Voigt functions1. A knowledge of shape function is needed for spectroscopic curve fitting and deconvolution. Molecular and atomic transitions inform on the physical conditions of the absorbing source2.

A spectroscopic transition is associated with a specific amount of energy E. However, when this energy is measured by means of some spectroscopic technique, the spectroscopic line is not infinetly sharp, but has a particular shape. Numerous factors can contribute to the broadening of spectral lines.

In this work, the spectral fitting for lyman beta and lyman gamma code is presented, intended to determine spectral line parameters by their fitting to several absorption spectra recorded under different conditions. Parameters to be determined are central wavelength, line width parameter and column density.

Basic principles, capabilities and the code to determine the spectral fitting are described.

After a complex is identified, it is fitted by iteratively adding and optimizing a set of voigt profiles for a particular spectral line until the region is considered successfully fit. This requires an initial estimate of the parameters to be fit. (column density, line width parameter and b-value)

Each time a line is added, the guess parameters is based on the difference between the line complex and the fit so far. For the first line this means the initial guess is based solely on the wavelength of the line complex. The column density is given by the initial column density given in the species parameters dictionary. These values are chosen to make optimisation faster and stable by being closer to the actual value, but the final results of fitting results should not depend on them as they merely provide a starting point.

After the parameters for a line are optimized for the first time, the optimization parameters are then used for the initial guess on subsequent iterations with more lines.

The complex is considered successfully fit when the sum of squares of the difference between the generated fit and the desired fit (chi square minimum)error is the least3.

STUDY OF HYDROGEN IN THE INTERSTELLAR MEDIUM

INTRODUCTION:
The interstellar medium is the matter and radiation that exists in the space between the stars in a galaxy. This matter includes gas in ionic, atomic and molecular form, as well as dust and cosmic rays. It fills the interstellar space and blends into the surrounding intergalactic space.
By mass, 99% of ISM is gas in any form, and 1% is dust. Of the gas, 91% of of atoms are hydrogen and 9% are helium. The interstellar gas is typically found in two forms:
-cold clouds of neutral atomic or molecular hydrogen
-hot ionised gas near hot young stars.
Hydrogen is the most abundant element in the universe. Spectroscopic studies of the sun ,stars and gaseous nebulae reveal that these objects comprise of approximately 85% by mass, of hyrogen. This composition is likewise accepted to be the illustrative of the general interstelar medium, although it much hard to quantify4.

Under the cold, unexcited conditions of the ISM, atomic and molecular hydrogen do not absorb in the ordinary visible and IR wavelength ranges. Their resonance absorption lie in the far UV. Therefore these resonance absorption lines, will reveal directly the number of atoms in the line of sight to the star used as a backgroung source5.

Hydrogen is the simplest of all atoms and its properties and spectrum have been the best determined, both experimentally and theoretically. We will concern here primarily with Lyman beta and Lyman gamma lines.
Absorption spectroscopy is a spectroscopic technique that measaure absorption of radiation as a function of wavelength. Absorption line reveals abundant information about the intervening medium.
The shape of spectral features, namely absorpton lines, is determined by the abundance of various elements or compounds and the pressure and temperature of environment. Spectral data can be used to determine abundances.
The Voigt function is essential in order to correctly model the profiles of absorption lines imprinted in the spectra by intervening absorption systems. In this work we present a simple analytic approximation to the Voigt function can be modelled for an arbitary range in wavelength, column densities up to 1022 cm-2 context of absorption line profiles at a given line of sight.

The voigt function is a convolution of gaussian and lorentzian.

Voigt damping parmeter a and the offset frequency u:

where,

where v0 is the line center frequency and the doppler width is given by,

The line profile is defined as’

The continuum obtained by the voigt fit spectra gives optical depth which in turn gives column density6.

Optical depth is essentially a measure of much light is absorbed in a medium, which is a measure of decreased photon intensity relative to the assumed continuum. The relation between absorption line and column density is given as

tau(v)=(pi e2)/(mec) f phi0 Na(v)

where f is the oscillator strength and lambda0 is the central wavelength,and the rest all are constants.
The oscillator strength measures the strength of transition and is dependand on the observed wavelength. Thus for every absorption line, the column density and apparant optical depth as functions of wavelength are related through a constant(which is dependant on the oscillator strength and central wavelength).

Column density of hydrogen is the number of units of hydrogen in the given line of sight7.

Methodology:
Line profile fitting:
We obtained oscillator strength and transition rate of Lyman beta(1026) and Lyman gamma(973) values of each from Morton paper(1991). For each line there were three free parameters, the line center V0, the line width parameter b in kms-1 and the column density N in cm-2.
Since data quality is sufficient, it was feasable to determine abundance of hydrogen through line profile fitting procedure using IDL. This was accomplished through an iterative process with guess(trivial) values for column density, the velocity dispersion (b value), and the velocities of the observed cloud components are adopted and the synthetic line profile is calculated. Then adjustments are made in the input paramaters until the best fit to the observed profile is achieved.
A variation on the profile-fitting technique is to reconstruct the continuum by determining the optical depth as a function of wavelength offset from the line center, the multiplying the observed profile by exp(tau), where tau is the optical depth. The column density is then adjusted until the reconstructed continuum is level.
For diffuse clouds H1 is usually the dominant form of hydrogen. Atomic and molecular hydrogen have numerous transitions in the vacuum ultraviolet, which can be exploited in order to derive hydrogen column densities. In typical reddened lines of sight, the atomic hydrogen lines(the lyman series) are very strongly saturated and thus are candidates for profile reconstruction method of column density determination. Atomic hydrogen is nearly always sufficiently abundant for the principal lines (lyman )to be damped and therefore well-suited to continuum reconstruction(e.g Bohlin 1975). In lines of sight having significant total gas column densities(of order 10^20/cm^2 or greater). The molecular hydrogen bands are usually strong enough to be damped and therefore analysed by profile fitting/continuum recnstruction method8.

PROCEDURE:

-We observed the spectra of O and B type stars obtained by FUSE satellite, Lyman beta(1026 A) and Lyman gamma(972 A) absorption lines are fitted by Voigt fit profile using IDL program MPFIT which is a user supplied function where the user supplies data points by adjusting a set of parameters.
Voigt fit is used to fit the data set as it is dominated by the Lorentzian at the wings and Gaussian at its center. The function is normalised.
Every absorption line we normalised required a continuum estimate in the surrounding wavelength region. The quality of this estimate varied from throughout the data set. Once the continuum is established, the spectra is fitted using voigt fit. The voigt fit measurements were taken by approximating the absorption lines as voigt functions. The main purpose of this was to establish a clear velocity for each line (to help resolve mutiple components). In order to measue column density, the spectrum was converted to optical depth profile. The profile could be then integrated (with corret central wavelength and oscillator strength)to derive column density.
The line profile method that is used for a particular target, for every absorptin line would have an approximated continuum. This allowed for integration of every line to determine column density based on that particulr line. Taking average of these is simply the most logical and simple way to derive a column density along the given line of sight. Different guess values of column density is varied so that chi2 would be minimised8.
In the absorption line fitting there are three parameters :
-Line center A

-Line width parameter b in kms-1
-Column density of hydrogen N in cm-2

The program used to fit the lines of lyman beta and gamma are:

For lyman beta

Program:

$cat linfit/voigtfit.pro
FUNCTION voigtfit1,wave,par,gamma
gamma=1.897e08
f=0.079120
;wave: wavelength in Angstroms
;a = GAMMA/(4*PI*DELTA_VD)
;DELTA_VD = V0/C * B
;u = (NU – NU0)/DELTA_VD
;NU = C/LAMBDA
;phi(a, u) = H(a, u)/DELTA_VD/SQRT(PI)
;
;par(0) = LAMBDA0 in A
;par(1) = B in km/s
;par(2) = N in cm-2
c_km = 3.e5; Wavelength of light in km/s
c_ang = 3.e18; speed of light in A/s
nu = c_ang/wave
nu0 = c_ang/par(0)
delta_vd = nu0*par(1)/c_km
a = gamma/(4*!pi*delta_vd)
u = (nu – nu0)/delta_vd
phi1 = voigt(a, u)/delta_vd/sqrt(!pi)
tau1=(2.654e-02*par(2)*f*phi1)

;2nd component
c_km = 3.e5; Wavelength of light in km/s
c_ang = 3.e18; speed of light in A/s
nu = c_ang/wave
nu0 = c_ang/par(3)
delta_vd = nu0*par(4)/c_km
a = gamma/(4*!pi*delta_vd)
u = (nu – nu0)/delta_vd
phi2 = voigt(a, u)/delta_vd/sqrt(!pi)
tau2=(2.654e-02*par(5)*f*phi2)

prof = exp(-(tau1 +tau2));Output
return,prof
END

For Lyman gamma:

Program:

For Lyman gamma:

$cat linfit/voigtfit.pro
FUNCTION voigtfit2,wave,par,gamma
gamma=8.127e07
f=0.029
;wave: wavelength in Angstroms
;a = GAMMA/(4*PI*DELTA_VD)
;DELTA_VD = V0/C * B
;u = (NU – NU0)/DELTA_VD
;NU = C/LAMBDA
;phi(a, u) = H(a, u)/DELTA_VD/SQRT(PI)
;
;par(0) = LAMBDA0 in A
;par(1) = B in km/s
;par(2) = N in cm-2
c_km = 3.e5; Wavelength of light in km/s
c_ang = 3.e18; speed of light in A/s
nu = c_ang/wave
nu0 = c_ang/par(0)
delta_vd = nu0*par(1)/c_km
a = gamma/(4*!pi*delta_vd)
u = (nu – nu0)/delta_vd
phi1 = voigt(a, u)/delta_vd/sqrt(!pi)
tau1=(2.654e-02*par(2)*f*phi1)

;2nd component
c_km = 3.e5; Wavelength of light in km/s
c_ang = 3.e18; speed of light in A/s
nu = c_ang/wave
nu0 = c_ang/par(3)
delta_vd = nu0*par(4)/c_km
a = gamma/(4*!pi*delta_vd)
u = (nu – nu0)/delta_vd
phi2 = voigt(a, u)/delta_vd/sqrt(!pi)
tau2=(2.654e-02*par(5)*f*phi2)

prof = exp(-(tau1 +tau2));Output
return,prof
END

RESULT:

REFERENCE:

1

Donal C. Morton. (1991) “Atomic data for resonance absorption lines. I, Wavelength longward of the lyman limit”, National Research Council of Canada

Boulanger, F.; Cox, P.; Jones, A. P. (2000). “Course 7: Dust in the Interstellar Medium”. In F. Casoli; J. Lequeux; F. David. Infrared Space Astronomy, Today and Tomorrow. p.251.

Ferriere, K. (2001), “The interstellar Environment of our galaxy”, Reviews of modern Physics, 73(4): 1031-1066.

Jeffrey G Magnum (2015),”How to Calculate Molecular Column Density”,

CONCLUSIONS:
The last few years have seen remarkable new discoveries concerning the concentration of atomic and molecular hydrogen in the ISM.