Classification of Stars (Unit 5)

Question 1

Definition parsec

Answer 1

the distance to an object subtending 1 second of arc to the radius of the Earth’s orbit.
(1 second of arc (arcsecond) = 1/3600 of a degree).

Question 2

Units parsec

Answer 2

pc

Question 3

Definition light year

Answer 3

Distance light travels in a vacuum in 1 year.

(number of seconds in 1 year = 365 x 24 x 60 x 60 = 3.15x107s

Question 4

Units light year

Answer 4

lyr

Question 5

Definition astronomical unit

Answer 5

The mean distance between the Earth and the Sun

Question 6

Units astronomical unit

Answer 6

AU

Question 7

Definition of absolute magnitude

Answer 7

The brightness an object would appear if it was 10 parsecs from the Earth.

Question 8

Definition of apparent magnitude

Answer 8

The brightness of an object as seen from Earth

Question 9

What is black body radiation?

Answer 9

The electromagnetic radiation emitted by an object because of its temperature

Question 10

General shape of black body curves

Answer 10

See sheet

Question 11

Definition of lambda(max)

Answer 11

The wavelength at which maximum emission occurs.

Question 12

Assumption about a star to use Wein’s displacement law (lambda max)

Answer 12

Star is acting as a black body.

Question 13

Effect of atmosphere on estimate of a star’s temperature

Answer 13

• Ozone in atmosphere preferentially absorbs UV part of spectrum
• This increases observed lambda max (longer wavelength)
• Resulting in an underestimate of the star’s temperature

Question 14

Definition of intensity

Answer 14

energy arriving every second on a 1 m2 surface orientated perpendicular to the direction of radiation

Question 15

Units of intensity

Answer 15

Wm-2

Question 16

Relation between intensity and apparent magnitude

Answer 16

Each change in magnitude of 1 (on the magnitude scale) corresponds to a change in intensity of 2.5 (actually 2.51).
So a star which has a magnitude that is 5 times brighter than another star, has an intensity which is 100 times greater (2.55 = 100).

Question 17

Inverse square law and assumptions in its application

Answer 17

the intensity I at a distance r from a star with a total power output P, is given by
Intensity I = P/(4 x pi x r2)
Inverse square law assumes that:
• no light is scattered or absorbed between source and observer
• the source can be treated as a point

Question 18

Spectral class information

Answer 18

See sheet

Question 19

How are Hydrogen Balmer lines produced?

Answer 19

• The atmosphere of the star has hydrogen atoms with electrons in the n=2 state
• Light from the star passes through the atmosphere of the star
• Electrons (at the n=2 level) are excited into higher energy states
• They can only absorb certain amounts of energy
• These certain energies are related to specific frequencies (E=hf)
• The electrons then de-excite
• The electrons may de-excite through different energy level changes
• When the electrons de-excite the light is radiated in all directions
• This means that the intensity of the light at particular frequencies is reduced, resulting in absorption lines

Question 20

Hertzsprung Russell (HR) diagram

Answer 20

See sheet

Question 21

Spectral class and magnitude of our sun

Answer 21

G5 (it’s like a, like a, like a G6 – but not a G6)

Question 22

Stellar evolution of our sun

Answer 22

• Our sun is currently a main sequence star (G5)
• As it uses up Hydrogen fuel and starts fusing Helium its core gets hotter and expands - it becomes a giant star.
• As it expands, the outer surface of Sun will cool
• Outer parts of sun are pushed away (by continued Helium fusion) to form planetary nebula.
• Leaving extremely hot but small core - it becomes a white dwarf.
• Fusion has finished and the white dwarf cools eventually to a brown dwarf.

Question 23

Neutron star composition and properties

Answer 23

Neutron stars consist of neutrons and have the density of nuclear matter

Question 24

Properties of a neutron star

Answer 24

• very dense
• powerful radio source
• spinning (usually very quickly)
• strong magnetic field
• faint

Question 25

Definition of a supernova

Answer 25

Where the absolute magnitude of a star increases rapidly and enormously due to it exploding

Question 26

Light curve of a type 1a supernova

Answer 26

See sheet

Question 27

Definition of a black hole

Answer 27

an object whose escape velocity is greater than the speed of light

Question 28

Properties of a black hole

Answer 28

* Large gravitational field strength | * Nothing, including light, can escape

Question 29

Definition event horizon

Answer 29

``` The boundary (or surface) where the escape velocity equals the speed of light Schwarzschild radius, Rs, on formula sheet is the radius of the event horizon ```

Question 30

What is at the centre of galaxies?

Answer 30

Super massive black holes

Question 31

How are type 1a supernovae used as standard candles to determine distances

Answer 31

* All type 1a supernovae have the same peak absolute magnitude (M). * Apparent magnitude, m, (of supernovae) can be measured * Distance to galaxy, d, (supernova) can be calculated using m-M=5log(d/10).

Question 32

Controversy surrounding accelerating universe

Answer 32

* The absolute magnitude of type 1a supernova is known, so they can be used as standard candles * Using m-M=5log(d/10) the distance to the galaxy can be calculated * Supernovae are very bright so they can be seen in very distant galaxies * It has taken billions of years for the light from the most distant galaxies to reach Earth; these supernovae were therefore produced when the Universe was young * Measurement of red shift (to measure velocity) and use of Hubble’s Law shows that these supernovae are fainter than expected * This indicates that the Universe is expanding faster now than when the supernovae exploded as the light has had to travel further to reach us than expected by a constant rate of expansion.

Question 33

What is causing accelerating expansion of universe?

Answer 33

Dark energy

Question 34

Binary star system

Answer 34

Two stars orbiting a common centre of mass

Question 35

Eclipsing binary star system

Answer 35

Binary star system whose orbit lies in same plane as the line of sight from the Earth (so one star passes in front of the other as observed from Earth)

Question 36

Light curve from binary star system

Answer 36

See sheet

Question 37

Explain light curve from binary star system

Answer 37

* Brightest magnitude (3.30) occurs when both stars can be seen. * First (smaller) dip (3.45) occurs when brighter star is in front of dimmer star. * Second (large) dip (3.60) occurs when dimmer star is in front of brighter star.

Question 38

Definition of Doppler effect

Answer 38

Change in wavelength (of em radiation) due to relative velocity between observer and source

Question 39

How can Doppler effect be used to calculate relative velocity?

Answer 39

• From spectrum obtain change in wavelength, lambda, for a spectral line • Using known wavelength measured on Earth, lambda, • Calculate v from lambda/lambda = v/c

Question 40

Assumption for Doppler equation

Answer 40

v

Question 41

Definition of red shift

Answer 41

Increase in wavelength (of em radiation) due to relative recessive velocity between observer and source

Question 42

Interpretation of red shift in terms of expanding universe

Answer 42

Hubble observed that: • (virtually) all galaxies are red shifted – means they are moving away from us (and each other) • the more distant galaxies have greater red shifts – meaning more distant galaxies are travelling faster • Hubble discovered that the (recessional) velocity of a galaxy was directly proportional to its distance.

Question 43

Estimation of age of universe

Answer 43

* If in time, t, a galaxy has moved a distance, d, at velocity v, then * as , v = d/t, t = d/v * But from Hubble’s Law, v = Hd * Time (age of Universe) = d/v = d/Hd = 1/H

Question 44

Assumption for estimating age of Universe from Hubble’s Law

Answer 44

Hubble’s constant, H, has been constant since the Big Bang.

Question 45

Features of Big Bang

Answer 45

* Expanding universe * from an extremely hot and dense single point * Suggest about 15 billion years ago (from Hubble’s constant) * “explosion” – creation of space/matter and time

Question 46

Evidence for Big Bang

Answer 46

Redshift of distant galaxies • In keeping with Hubble’s law (see Hubble observations above). • Hubble’s law can be used to age universe. Cosmological microwave background radiation • If Universe is about 15 billion years old and has been expanding and cooling since Big Bang. • would estimate temperature of “empty space” to be a few Kelvin after this time. • black body curve of “empty space” corresponds to temperature of about 2.7 Kelvin (appropriate max) • consistent with temperature universe would have cooled to after 15 billion years Relative abundance of Helium and Hydrogen • short time after Big Bang universe hot enough to fuse matter • Hydrogen fused to form Helium • Universe continued to expand, and cool • making fusion of helium into heavier elements impossible • creating predicted ratio of 3:1 (Hydrogen to Helium) • consistent with observation of matter in Universe.

Question 47

Properties of quasars

Answer 47

* Originally identified as strong radio sources (though now known to emit at all parts of em spectrum) * They have very large red shifts (and hence large distance from Hubble’s law) * They are very faint (dim apparent magnitudes) * They are very small (about size of a solar system) * Application of m-M=5log(d/10), using d calculated from Hubble’s law, suggests they are the brightest objects in the universe (same absolute magnitude as several galaxies put together) * Now believed to be super massive black holes at centre of active galaxies * Most distant measurable objects.