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Astronomy 2 Session 2011-12

Observational Astrophysics10 Lectures, starting September 2011

Lecture notes:http://physci.moodle.gla.ac.uk

Dr. Eduard Kontar

Kelvin Building, room 615, ext 2499

Email: Eduard (at) astro.gla.ac.uk

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Course aim: Observational Astrophysics 2 forms a bridge

between Levels 1 and 3, consolidating the elementarymaterial covered in Astronomy 1 and introducing more

advanced concepts in preparation for Honours.

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Books to read:

Astronomical Observations, Walker - rather simpleoverview of modern instrumentation, biased to theoptical.

Observational Astrophysics, Smith Instrumentationand descriptions of stars and galaxies etc.High Energy Astrophysics vol. 1, Longair Useful forDetectors and A3/4.

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Learning objectives:

Section 1 Ideas of Astrophysical Measurements : astrophysicalobservations, units, Luminosity, Flux, intensitySection 2 Detectors and telescopes: optical,

X-ray and gamma-ray detectors, radio telescopesSection 3 Optical detectors : photographic plates,photomultipliers, image intensifies, Charged, Coupled Devices(CCDs)

Section 4 Sensitivity, uncertainties and noise: Poissonstatistics,standard deviation, background, telescope designSection 5 Observations through the atmosphere: diffraction

grating, spectral resolution, slit spectrometersSection 6 Spectroscopy: spectra and spectral resolving powerSection 7 Resolution and interferometry: diffraction, Airydisk, angular resolution

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What we can observe?Particles:o Cosmic Rays

o Neutrinoso Neutrons

o Solar particles

Electromagnetic emission

o Optical range/EUV/infra-red

o Radio waves

o X-rays and gamma-rays

In-situ measurements of electric/magnetic fields

Gravitational Waves?

1. Ideas of Astrophysical Measurements

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Ideas of Radiant Energy

Astrophysical observations are almost always of light(i.e. electromagnetic radiation)

Historically, it was mainly the optical (visible) part of the E-M spectrum

that was used:-

nm700nm400 ( )m10nm1 -9=

( )m101 10

=BLUE RED

1.

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Nowadays observations are carried out from gamma rays

to radio

Remember

nm01.0

cm10

hc

hE ==

=cFrequency (Hz)

Speed of light-18 ms10998.2 =

Energy (J or eV)

( )J10602.1eV1 -19= Plancks constantJs10626.6

34

=

(1.1)

(1.2)

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= energy radiated per unit time by a source in the

frequency interval centred on

In A1 you met the concept of

Luminosity = energy radiated per unit time by a source

Unit = Watts (Joules per second)

In general, luminosity is dependent on wavelength or frequency.

i.e. astrophysical objects generally dont radiate the same amount

of energy at all frequencies.

Hence we write

and

)(LL =

Sometimes referred to as

Monochromatic luminosity

)( 0L

0

(1.3)

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Strictly speaking we should write the luminosity as the integral

but provided is small we can approximate by

Sometimes we consider instead luminosity as a function of

wavelength, i.e.

Relating and is rather trivial.

( See A2 Theoretical Astrophysics notes! )

Bolometric Luminosity = energy per unit time radiated atall frequencies (wavelengths)

+

210

21

0

)( dL )( 0L

)(LL =

)(L )(L

dLdLL

==00

bol )()(Note: Luminosity isan intrinsicproperty

of a source

(1.4)

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Usually we assume that astrophysical sources radiate isotropically (i.e.

uniformly in all directions). This allows us to relate their luminosity totheir apparent brightness which decreases with distance, according to

the inverse-square law.

Apparent brightness falls off with the square of the distance, becausesurface area of a sphere increases with the square of the radius

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As with luminosity, in general we need to work with a measure

of flux which is frequency dependent. We thus define

Flux Density = energy per unit time, per unit frequency,

crossing a unit area perpendicular to the

direction of light propagation

Astronomers use a special unit for flux density

Jy is a common unit of measurement in radio, microwave and infra-red

astronomy. It is less common in optical astronomy, although it has become

more widely used in recent years.

(Jy)Jansky1HzmW10

-1-226

=

Usually denoted by or)(F S

(1.6)

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Suppose we observe in frequency interval

Define bandwidth (also known as bandpass, or passband)

And the mean frequency

If is small or is either flat,

or varies linearly with frequency, then

Integrated Flux =2

1

dSF

12 =

( )2121 +=

S = SF

Integrated flux = flux density x bandwidth

21

(1.7)

(1.8)

(1.9)

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Example

The radio source Cygnus A has a flux density of 4500 Jy. How much energy

is incident on a radio telescope, of diameter 25m, which observes Cygnus A

for 5 minutes over a bandwidth of 5 MHz?

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Solid Angle

Stars can be regarded as point sources

Angular diameter of the Sun =

Angular diameter of Betelgeuse =

o533.0

o000014.0

(barely) resolvablewith HST

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We use solid angle as measure of the fraction of the sky covered (or

subtended) by an extended source.

Unit of solid angle

= steradian (sr)

Consider a source of

projected area at

distance

Whole sky = sr

D

AreaA

4

D

Solid angle2

D

A=(1.10)

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For a spherical source, of radius

Projected area,

Thus

But

So

D

AreaA

2RA =

2

= D

R

DR2=

Angular diameter of

source, in radians

2

2

=

(1.11)

(1.12)

(using ) tan

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Need to be careful about units

In Eq. (1.12) angular diameter must be in radians, but is often measured in

degrees (or arcminutes / arcseconds)

Examples

Calculate solid angle subtended by the Sun

ang. diam. =

Calculate solid angle subtended by globular cluster NGC 6093

ang. diam. = 8.9 arcmin

o533.0

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But many other objects (e.g. galaxies, nebulae) are extended sources.

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Specific Intensity

An extended source (e.g. a galaxy) may deliver the same flux density as a

point source (e.g. a star) but spread over a small area of the sky.

Also, as can be seen clearly forNGC 6093, an extended source

will not be equally bright across

its entire projected area.

We need to introduce a new

quantity to describe this variation

in brightness. It is usually

referred to as specific intensity

or (particularly in the context of

galaxies) as surface brightness

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( ) = dddAIL nrbol

)

,

(1.13)

(1.14)

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Relating Specific Intensity and Flux Density

Consider an extended source of projected area

Flux density from = energy received per unit time, per unit frequency

SA

D

Source, ofarea

SA

1m2 atthe Earth

1dA

2dA

1d

2d

SA

( ) ( ) K++= 2222211111 ,,,, ddAIddAI rr

(1.15)

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For a distant source we can assume that

Thus

But, if is measured in metres, then

So we can write

=== ddd K21

( ) ( )[ ] ++= ddAIdAIS K22221111 ,,,, rr

= ddAISA

(1.16)

2

1

D

d = (1.17)

=

=

SSAA D

dAI

D

dAIS22

1

(1.18)

Solid angle of area element on

the source as seen from the Earth

dA

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Hence

Flux density = integral of specific intensity over the

solid angle of an extended source

If is constant over the projected area of the source, then

=

S

SdIS

(1.19)

I

SIS = (1.20)

from Eq. (1.5)2

DS 2 DS from Eq. (1.10)

Specific intensity isindependent of distance

( constant along rays )

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Example

For a blackbody of temperature,

Blackbody radiation is isotropic (i.e. specific intensity doesnt depend on

direction)

At a given frequency, depends only on

We can use the measured to define a temperature

Recall effective temperature from A1Y Stellar course

T

( )[ ]1-1-2-

2

3

srHzWm1exp

2

=kT

hc

hv

I (1.21)

T

I

I

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Wiens Law

3max 109.2 =T

in min K

Tv10

max 106=in Kin Hz

(1.22)

(1.23)

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hlog

log

I

2 I

maxlog h

We can make a similar definition, common in radio astronomy:

Brightness temperature

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At typical radio frequencies and temperatures

Hence

We define

Note that we can always define a brightness temperature, but it will onlycorrespond to the actual temperature if the source is approximately a black

body and

We can make a similar definition, common in radio astronomy:

Brightness temperature

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The quasar 3C123 has an angular diameter of 20 arcsec, and emitsa flux density of 49 Jy at a frequency of 1.4 GHz.

Calculate the brightness temperature of the quasar.

Example

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The Magnitude System

While many modern astrophysical observations are made in terms of flux

density, optical astronomy has mainly retained the magnitude system,

which is based on a logarithmic scale (See A1 handout).

Bolometric apparent magnitude

Need to calibrate via standard stars. e.g. Vega defined to have

bolometric apparent magnitude zero

const.Flog5.2 10bol +=m

Vega

10bolF

Flog5.2=m

Radiant flux (over all frequencies)

(1.26)

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VBVEA 1.3

V-band extinctionColourexcess

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VBBEA 1.4

B-band extinctionColourexcess

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Example

The star Merope in the Pleiades is observed to have apparent

magnitudes B = 4.40 and V = 4.26

The V band extinction affecting this observation is estimated to be0.2 magnitudes.

Estimate the true colour index of Merope