# p Dr.Jayanth Murthy, Indian Institute of Astrophysics,

p { margin-bottom: 0.25cm; line-height: 120%; }

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.