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PHE-15

ASTRONOMY AND

ASTROPHYSICS





Astronomy and Astrophysics 3+(

ȝɀɃ Bachelor of Sciences (B.Sc)

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stronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Babylonians, Greeks, Indians, Egyptians, Chinese, Maya, and many ancient indigenous peoples of the Americas. In the past, astronomy included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars. Nowadays, professional astronomy is often said to be the same as astrophysics. Professional astronomy is split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects. Astronomy is one of the few sciences in which amateurs play an active role. This is especially true for the discovery and observation of transient events. Amateur astronomers have helped with many important discoveries, such as finding new comets. The book "Astronomy and Astrophysics (PHE-15)" is written especially in question & answer format to provide students the instant gratification of a correct answer. In this book, we have tried to solve all possible questions from the exams’ point of view. Solutions of previous years’ question papers have also been included to help students to understand the unique examination structure. We hope that this book would not be only a favourite study material for the students but also can be a nice resource for teaching. An attempt has been carefully made to present this book more useful and meet the requirements and challenges of the course prescribed by Indian Universities. We wish you a successful and rewarding career ahead. Feedback in this regard is solicited. – GPH Panel of Experts

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Block-1

Basics of Astronomy

Unit-1 Unit-2 Unit-3 Unit-4

Astronomical Scales Basic Concept of Positional Astronomy Astronomical Techniques Physical Principles

Block-2

The Solar System and the Stars

Unit-5 Unit-6 Unit-7 Unit-8

The Sun The Solar Family Stellar Spectre and Classification Stellar Structure

Block-3

From Stars to our Galaxy

Unit-9 Unit-10 Unit-11 Unit-12

Star Formation Nucleosynthesis and Stellar Evolution Compact Stars The Milky Way

Block-4

Astronomy and Astrophysics

Unit-13 Unit-14 Unit-15

Galaxies Active Galaxies Large Scale Structure and the Expanding Universe







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㻌 Chapter-1

Astronomical Scales..................................……………………....…1

Chapter-2

Basic Concept of Positional Astronomy...........…………...…....15

Chapter-3

Astronomical Techniques ...……………………………..……..31

Chapter-4

Physical Principles...................…………………………….……41

Chapter-5

The Sun...............................................………………………..……49

Chapter-6

The Solar Family............................………………………………65

Chapter-7

Stellar Spectre and Classification..............................………..…..83

Chapter-8

Stellar Structure............…………………..............………………97

Chapter-9

Star Formation........................................................………………117

Chapter-10

Nucleosynthesis and Stellar Evolution.....……………............133

Chapter-11

Compact Stars.........................................……………………..…151

Chapter-12

The Milky Way.…………………………………………..........169

Chapter-13

Galaxies.……………….……….....................................................185

Chapter-14

Active Galaxies.………………………………….............….…199

Chapter-15

Large Scale Structure and the Expanding Universe.......……211

Appendix Tables...................................................................………………….............223

(1) December 2017 ............................................................................................................243 (2) June 2018 .......................................................................................................................245 (3) December 2018 ............................................................................................................247 (4) June 2019 (Solved).......................................................................................................249 (5) December 2019 (Solved)............................................................................................252



Astronomical Scales

1

1

Astronomical Scales ,QWURGXFWLRQ 



S

tudents interpret reality from their perspective of the world around them. As a result, their everyday thinking about space and time is often limited to local conditions; often at most perhaps hundreds of kilometres or decades of years. Vast distances and times are central ideas in ‘the changing Earth and its place in space’. However, these ideas are very difficult for students to grasp. This has very important implications for their learning of ideas about distances in space or very long spans of time. A light year is the distance that light travels in one year. The light from the sun takes about eight minutes to reach the Earth because it is only a relatively short astronomical distance (about 149 million km) away. The light from distant astronomical objects takes so long to get to us that we see these objects as they appeared a long time ago. Our solar system is one of many that make up our galaxy, the Milky Way. Our galaxy has a diameter of close to 100,000 light years and contains between 200 – 400 billion stars, which vary in size and brightness and are distributed throughout the galaxy. Our galaxy is one of probably more than one hundred billion galaxies that make up the universe. Some distant galaxies are so far away that their light takes several billion years to reach Earth.

Fundamentals Astronomy of Computer and Astrophysics Networks [BCS-0 [PHE E-15] 041]

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Q1. Give some deefinitions about the astronomical scales. Ans. Some definitio ons about the astronomical scales are as follows: x

Astronom mical Unit: 1 AU = 1.5 x 1011m is the mean distan nce between the Sun and the Earth. The distances in the so olar system arre measured in this unit.

x

Light Yeear: 1 ly = 9.5 x 1015 m = 6.32 x 104 AU is the distan nce travelled by light in one year. The distance to stars and galax xies are measu ured in this unit.

x

Parsec: 1 pc = 3.26 Ly = 2.062 x 105AU = 3.08 x 1016 m is the distance at which the radius of Earth’s orbit subtends an an ngle of 1”.

Fig. 1.1 x

dius:1 RΌ = 7 x 108 m is the unit equivalent to the rad dius Solar Rad of the sun n, in which the radii of stars and other celestial objeects is measurred. Eg: Sirius has radius 2RΌ.

x

Solar Mass: 1 MΌȱ= 2 x 1030 kg is the unit equivalent to the mass m of the sun n, in which the mass of other stars and celestial objeects is measurred. Eg: Milky Way Galaxy has mass ~ 1011 MΌȱ.

x

Luminossity: It is the energy emitted per unit time; units = ergs/s, W W. Luminosity is directly proportional to fourth pow wer of tempeerature and surface area. The luminosity of a stellar object is a measure of the intrinsic brightness of a star.

x

b

x

L 4S r 2

It is exprressed in the units of solar luminosity LΌ. 1 LΌ= 4 x 10 W = 4 x 1033 erg/s .

26

x

Apparen nt Brightness/Radiant Flux: It is the energy passsing through aarea perpendicular to the line-of-sight per unit time.. Its measurem ments depend on luminosity and distance of the sou urce 2 from the point of observation. Unit: erg/s/cm .

Astronomical Scales

x

3

Parallax: It is theshift apparent of nearby objects with respect to backgrou und as observer moves. Parallax is measured in arca a seconds. Expression for parallax: p (radians) Observing the d object fro om points A and B, we can compute the distance to it from ang gle “p” and the length of the baseline.

Fig. 1.2 Q2. Explain the A Apparent Magnitude Scale. Ans. The apparent brightness of a star as measured by the human eye (or human perception n) defines the stellar magnitude scale. This iss a logarithmic scale. Greek astronomer Hipparchus introduced the old magnitude scale: b brightest stars have a magnitude m = 1, the faintest, m = 6. A variation of 1 in the magnitude scale corresponds to a factorr of 2.512 in brightness,, because (2.512)5= 100. For Example, the pole star has h an apparent magniitude +2.3 and the star Altair has apparent magnitu ude 0.8 which means Alltair is about 4 times brighter than Polaris.

Fig. 1.3 Dimmer stars have higher apparent magnitudes. These are apparrent magnitudes, becausse they are related to the apparent brightness (i.e. th hey

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have no information about the total output of energy from a star). The relationship between apparent magnitude and apparent brightness is: b1   m1  m2 b 2.512 which translates to m1  m2  2.5log10 1 b2 b2 Modern magnitude scale is extended in both directions. The larger magnitude on negative scale indicates higher brightness while the larger positive magnitude indicates the faintness of an object. Q3. What is Absolute Magnitude? What is the relationship between absolute and apparent magnitude? ›ȱ Derive an expression for the distance modulus. Ans. The absolute magnitude of a star (M) is the apparent magnitude the star would have if it were at a distance of 10 parsec. The apparent magnitude scale is distance independent. Therefore, this scale has no information about how luminous stars are. Thus, the absolute magnitude scale was introduced to characterize the luminosity (L) / intrinsic brightness of stars by including the distance. L M 1  M 2  2.5log10 1 L2 The absolute magnitude of the star can be related to apparent magnitude. Let us consider a star at d pc with magnitude m, luminosity or intrinsic brightness L and apparent brightness or radiant flux b1. When the same star is placed at a distance of 10 pc from the place of observation, then its magnitude would be M and corresponding apparent brightness b2. If the apparent magnitude of a star is m and its absolute magnitude is M (its real brightness), then the distance to the star, d in parsecs, is given by:

b2 b1 where b

b2 b1

100  m  M /5 L , Since Luminosity is constant for a star, 4S r 2

§ d pc · ¨ ¸ © 10 pc ¹

2

Astronomical Scales

5

The differencce between apparent magnitude (m) and absollute magnitude (M) is a measure of difference, called the distance modulus

mM

§d · 5 log110 ¨ ¸ © 10 ¹

m  M 5log110  d  5 M m  5  5llog10  d Q4. Describe thee method used to measure astronomical distancces. State its limittations. ›ȱ Explain how Parallax Method is used to measure astronomiical distances. Staate its limitations. Ans. A nearby starr would change position on the sky relative to disttant background stars. Observing the star from different points, we can c nce compute the parallaax angle and length of the baseline and hence, distan to the star. For meeasuring the distance to the nearest star, a very lo ong baseline is required, much greater than the Earth’s diameter. The T diameter of the Earth’s orbit is chosen as the baseline and two t d SE observations at an interval of six months is taken. tan T wh here distance dSE is the average diistance between Sun and Earth i.e. 1 AU. Since, tan T # T

Distance (pc)= =

1AU

T

Parallax ( T ) iis measured in arc-seconds and 1 Parsec is the distan nce at which 1 AU subttends an angle of 1 arc sec. 1 Distance (pc) = Parallax

Fig. 1.4

Fundamentals Astronomy of Computer and Astrophysics Networks [BCS-041] [PHE-15]

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For example, the star Alpha Centauri has a parallax of 0.77” so the distance is 1/0.77, which is equal to 1.3 pc. Some limitations are there to this method. Parallax becomes smaller as distance to a star increases and parallax cannot be measured to be better than 0.02” from the ground which gives less than distance of 50 parsecs. Q5. Discuss the motion of a star. Ans. All the celestial objects are on relative motion with respect to one another. The stars appear fixed to the sky but these are in constant motion. The great distances to the stars means that their apparent motions across the sky are very small during a human lifetime. The motion of a star can be resolved along two directions: x

Motion along the line of sight of the observer is called radial motion.

x

Motion perpendicular to the line of sight of the observer is called proper motion.

The radial velocity of a star is how fast it is moving directly towards or away from us. Radial velocities are measured using the Doppler Shift of the star's spectrum: x

Star moving towards Earth: Blue shift

x

Star moving away from Earth: Redshift

x

Star moving across our line of sight: No Shift

In all cases, the radial velocity is independent of distance. Proper Motion is the apparent angular motion of a star across the sky with respect to more distant stars.Typical proper motion is ~0.1 arcsec/year and largest: 10.25 arcsec/year (Barnard's Star). The effect of proper motion builds over time. It is measured over an interval of 20 to 30 years. The amount of proper motion shown by a star depends upon its distance. The proper motion is denoted by μ. For a distance d from the Earth, it is related to transverse velocity as follows:

proper motion= Or,

P=

transverse velocity distance of the star

vT where vΌȱis the transverse velocity. Hence, vT r

Pr

Astronomical Scales

7

More distant stars tend to have smaller Proper Motions. However, it could be a nearby star moving directly away or towards us. Such stars will have no proper motion. Space velocity of star is given by the sum of radial velocity vector and the proper motion vector. If two stars have the same space velocity and move perpendicular to the line of sight, the one with the larger proper motion will be nearer. Sun itself is not stationary. The space velocity vector of a star is corrected by subtracting from the velocity vector of the sun and the corrected velocity vector is called peculiar velocity. Q6. Using Stefan-Boltzmann law of radiation, obtain the ratio of radii of two stars in terms of their surface temperatures and absolute magnitudes. Ans. From Stefan-Boltzmann Law of radiation, ...(i) F VT 4 where F is the radiant flux from the surface of the object, V , Stefan’s constant and T is the surface temperature of the star. Luminosity, ...(ii) L 4S R 2 F where R is the radius of the star. Using (i), L 4S R 2V T 4 Let there be two stars of radii R1 and R2 and surface temperature T1 and T2 respectively. The ratio of Luminosities of these two stars: 2

L1 L2

§ R1 · § T1 · ¨ ¸ ¨ ¸ © R2 ¹ © T2 ¹

4

Also,

L2 L1

100 

M1  M 2 /5

where, M1 and M2 are the absolute magnitudes. Therefore, 2

4

§ R1 · § T1 · 0.4 M1  M 2 ¨ ¸ ¨ ¸ 10 R T © 2¹ © 2¹ Q7. What is a binary system? Using Kepler’s law, find the mass of a binary system. Ans. Two stars revolving about each other form a binary system. If the orbits of two stars are such that the stars pass in front of each other as

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Fundamentals Astronomy of Computer and Astrophysics Networks [BCS-0 [PHE E-15] 041]

seen by an observeer, then the light from the group dips periodically. The T periodic dip reveaals the binary nature of stars and gives informattion about their luminossities and sizes.

Fig. 1.5 To find the mass of a binary system we need to apply Kepler's Law ws. If we adapt them fo or a binary system where the masses of the compon nent stars are similar, theen: x

ௗThe starss orbit each other in elliptical orbits, with the centree of mass (or barycentre) as one common focus.

x

The line b between the stars (the radius vector) sweeps out eq qual areas in eequal periods of time. 3.ௗThe square of a star's periiod, T, is direectly proportional to the cube of its average distan nce 2 3 from the centre of system mass, r: T v r

Fig. 1.6

Astronomical Scales

mA rA r

9

mB rB

rA  rB , rB

r  rA

mA rA

mB ( r  rA )

mA rA

mB r  mB rA

? rA

mB r  m A  mB

rA

mB r M

The forces acting on each star are balanced, that is the gravitational force equals the centripetal force. So,

FG

FC

or

GmA mB r2

mA v 2 rA

v is the orbital speed of A which can be calculated from the period T

2S rA T Gm  2B r v=

4S 2 rA T2 mB r Subsitute rA M 2 Gm 4S mB r  2B r T 2M 4S 2 r 3 M GT 2 4S 2 r 3  m A  mB GT 2 Q8. Describe methods to estimate temperature of a star. Ans. A star's surface temperature can be determined from its spectrum or colour. The Stars produce a spectrum, which is a close approximation to a blackbody spectrum. Therefore, it is possible to fit in Planck’s curve to the observed data at temperature T. This temperature determines the colour of the star.

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