p and Dr.Ravichandran, Deartment of Physics, Christ University,

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STUDY OF HYDROGEN IN THE
INTERSTELLAR MEDIUM

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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.