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Astronomy 2 > Observational Astrophysics > Flashcards

Observational Astrophysics Flashcards

1
Q

luminosity

A

energy radiated per unit time by a source

joules per second or watts

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2
Q

what is luminosity dependent on?

A

frequency (or wavelength)

objects of a particular colour radiate more power at frequencies corresponding to their colour

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3
Q

luminosity at a specific frequency (monochromatic luminosity)

A

L=L(v)

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4
Q

luminosity of a source in a frequency interval delta v centred on v0

A

L=L(v0)deltav

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5
Q

integral for luminosity

A

strictly speaking, luminosity should be the integral of L(v) dv between v0-1/2 delta v and v0+1/2 delta v

since delta v small, can approximate as L(v0)delta v

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6
Q

bolometric luminosity

A

total power by integrating across all frequencies

“energy per unit time radiated by all frequencies”

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7
Q

isotropic

A

uniform in all directions

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8
Q

what does assuming astrophysical sources are point sources that radiate isotropically allow?

A

relate luminosity to apparent brightness or flux

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9
Q

flux falls off with…

A

the square of the distance because of the surface area of a sphere increasing with the square of its radius

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10
Q

radiant flux, F

A

energy per unit time crossing a unit area perpendicular to the direction of light propagation

watts per square metre

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11
Q

flux for an isotropic point source

A

F=L/4piD^2

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12
Q

how is flux density denoted and units

A

denoted by:
F(v),S(v), Fv or Sv

unit is janksy (Jy)

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13
Q

why does flux density need to be defined

A

frequency dependent

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14
Q

if observe at frequencies v1 and v2, flux in this interval is…

A

F= integral Sv dv between v1 and v2

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15
Q

bandwidth of interval

A

delta v= v2-v1

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16
Q

mean frequency

A

v bar = 1/2(v2+v1)

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17
Q

if delta v is small or Sv is either flat or varies linearly with frequency, then

A

F=Sv bar delta v

integrated flux = flux density x bandwidth

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18
Q

solid angle

A

fraction of sky covered by an extended source

steradian (sr)

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19
Q

solid angle formula

A

omega = A/D^2

A = area
D=distance

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20
Q

solid angle of whole sky

A

4piD^2/D^2=4pi sr

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21
Q

solid angle for a spherical source

A

A=piR^2 so omega = pi(R/D)^2

show from trig that theta/2=R/D

so can be written as omega=pi(theta/2)^2

theta in radians

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22
Q

what is the need to introduce specific intensity?

A

an extended source may deliver the same flux density as a point source but is spread over a small area of the sky.

an extended source will not be equally bright across their entire projected area.

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23
Q

specific intensity

A

flux density of the source (through a plane perpendicular to the direction of the source) per unit solid angle

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24
Q

if rays arrive at an angle, the flux is

A

reduced by cos theta

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25
Q

specific intensity formula

A

Ivcos theta = dSv/d omega

small angle approx used so cos disappears

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26
Q

flux density in terms of specific intensity

A

integral of the specific intensity over the solid angle of the source

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27
Q

if Iv is constant over the source on the sky then…

A

Sv=Iv omegas

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28
Q

what does integral of specific intensity over frequency give you?

A

intensity

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29
Q

intensity has units of

A

energy per unit time per unit solid angle crossing a unit area perpendicular to the direction of propagation.

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30
Q

if Iv is constant over the frequency band then

A

I=Iv deltav

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31
Q

if we integrate intensity of all frequencies…

A

we obtain bolometric intensity

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32
Q

brightness temperature derivation

A

use taylor expansion to show exp(hv/kT)-1 is approx =hv/kT

then can plug into specific intensity equation for blackbody and rearrange for

Tb=c^2Iv/2v^2k

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33
Q

when will brightness temp correspond to the actual temp of the source

A

if its a blackbody and hv«kT

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34
Q

bolometric apparent magnitude

A

mbol=-2.5log10F+const (pogson)

vega defined to have mbol=0 so used as calibrator

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35
Q

Johnson system

A

set of standard filters from near ultraviolet to infrared

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36
Q

transmission function T

A

defines the fraction of light transmitted by the filters as a function of frequency (or wavelength)

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37
Q

for bolometric apparent magnitude , T(v)=

A

1 at all frequencies

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38
Q

difference between the Johnson magnitudes defines a

A

colour index which gives information on the temperature of the star

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39
Q

bolometric correction

A

difference between the bolometric magnitude and the Johnson V band

measure of what fraction of light is observable in the visible band

BC=mbol-V

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40
Q

extinction

A

effect where some light is absorbed on the way to us

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41
Q

colour excess or reddening

A

Eb-v=(B-V)-(B-V)0

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42
Q

why is the sky blue

A

light encounters atmosphere

scatters light

blue scattered more than red

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43
Q

refractor

A

objective lens forms a real image of source in focal plane

eyepiece forms a real image of source

magnification (ratio of angular size of virtual image to that of source)=fobj/feye=Dobj/Deye

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44
Q

can either view a virtual image by…

A

through the eyepiece or place a detector at the focal plane

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45
Q

reflectors

A

cheaper to make and shorter

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46
Q

types of reflectors

A

newtonian
cassegrain
gregorian
ritchy-chretein

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47
Q

cassegrain and gregorian

A

both have parabolic mirrors

gregorian has concave, elliptical secondary mirror

cassegrain has a convex, hyperbolic secondary mirror

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48
Q

ritchey-chretein

A

special form of the cassegrain with two hyperbolic mirrors

free from spherical abberation at a flat focal plane so good for wide field and photographic observations

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49
Q

reflector properties

A

virtual image viewed through eyepiece

collection area of obj = pi(Dobj/2)^2

light observed through eyepiece with area=pi(Deye/2)^2

flux density increased by (Dobj/Deye)^2

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50
Q

in reflector, secondary mirror is always

A

smaller, light squished into smaller area

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51
Q

reflector solid angle

A

increase by (Dobj/Deye)^2

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52
Q

illumination, J

A

energy per second per unit area in the focal plane

same units as flux

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53
Q

energy collected per second by the telescope aperture

A

flux density x bandwidth x area

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54
Q

focal ratio

A

F=f/D

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55
Q

rewriting illumination using focal ratio

A

J approx I/F^2

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56
Q

increasing illumination…

A

reduces the time it takes the detector to collect a given number of photons.

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57
Q

increasing aperture diameter

A

+ increased illumination and better angular resolution

-more expensive to build and house

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58
Q

increase focal length

A

+ increase image size in focal length so it covers more detector pixels

-decreases illumination, requiring longer exposure times

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59
Q

photo multiplier tubes - incident photon strikes a…

A

photocathode, held at a potential of 1kV relative to the anode on the other side of a vacuum tube

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60
Q

photomultiplier tubes - what are the anode and cathode separated by?

A

a series of dynodes at successively more positive potentials

(amplification stage)

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61
Q

photomultiplier tubes - the electron emitted from the cathode is…

A

accelerated towards the first dynode where they have enough energy to release several more electrons

(repeated and a cascade of electrons reach the anode)

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62
Q

con of photomultiplier tubes

A

little directional information
(think of as single pixel) so poor imaging

quantum efficiency approx 10%

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63
Q

describe image intensifiers

A

photoelectrons emitted by cathode are accelerated down the evacuated tube by a voltage difference of around 15 kV and strike a phosphor screen, producing an image

photons emitted strike a second cathode and process repeats

intensity of image increases with each stage

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64
Q

what does image intensifiers give you

A

maintain poisson info so get a 2D image rather than a single number

think of as night vision goggles

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65
Q

quantum efficiency of image intensifiers

A

20 to 30%

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66
Q

describe a CCD

A

semiconductor array of pixels
electron released when a photon strikes the semiconductor
bias voltage draws electrons into a potential well where they are stored
stored charge read out by manipulating the bias voltage
charge moves across the CCD line by line before being read out pixel by pixel (show)
high quantum efficiency
until saturation, no of electrons stored prop to no of incident photons

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67
Q

saturation

A

point where electrons spill over

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68
Q

pros of CCDs

A

readout noise is very low
readout rate very high
quantum efficiency around 90% nowadays

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69
Q

sloan CCD array

A

6 columns of 5 CCDs
Different filter on each CCD (wavelengths from UV to IR, create false colour images)
operates in two modes

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70
Q

two modes of sloan CCD array

A

stare mode - telescope is tracking, single exposure

dirft scan mode - target takes about 1 minute to drift across on the CCD columns

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71
Q

pixel capacity

A

number of electrons that a pixel (potential well) can store

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72
Q

for long exposure, the number of electrons produced…

A

may exceed the pixel capacity

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73
Q

dynamic range

A

range over which detector response is linear

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74
Q

brightest object before saturation/ faintest object detectable is approx…

A

60dB

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75
Q

what does adding many short exposures together in software do?

A

prevents bleeding effect

76
Q

systematic errors which need to be eliminated from CCD observations

A

Bias
Dark (thermal) current
response factor

77
Q

Bias

A

signal from the CCD due to residual charge in the CCD and readout noise rather than photons

think of as electron already in the bucket so offset

78
Q

how to measure bias

A

taking an exposure of zero seconds followed by read out the CCD chip

79
Q

dark (thermal) current

A

signal from electrons produced in the absence of light due to thermal emission in the CCD

will vary pixel to pixel but grow over time

80
Q

response factor

A

signal readout from each pixel differs from the true signal due to variations in the sensitivity across the CCD

non uniform response in the CCD

for pixel at (x,y) can model this distortion by response factor r(x,y)

81
Q

what can r(x,y) be estimated from

A

a flat field observation: an exposure for a uniform light source for which the ‘true’ signal should be uniform

*new flat field required each observing session since irregularities (eg dust) can very

82
Q

relation between systematic effects

A

signal measured from pixel = true signal x response factor + bias at pixel + dark current from pixel

83
Q

what is r(x,y) prop to?

A

flat field signal - bias at pixel - dark current

84
Q

sensitivity of an instrument or detector

A

the smallest signal that it can measure which is clearly not noise

85
Q

noise

A

random signal from another undesired source

86
Q

how to measure reliability of an observation

A

SNR

expected signal level / expected noise level

87
Q

minimum SNR

A

not trusted unless at least 3

(preferably much higher)

88
Q

signal can be easily detected after background subtracted because…

A

SNR is large

S is large compared to N

89
Q

low SNR

A

signal, background and noise have comparable sizes

difficult to estimate the amount of background to subtract

90
Q

what is fluctuation in no of photons expected in given time interval

A

uncertainty

91
Q

axioms for counting photons

A
  1. photons arrive independently in time
  2. average photon arrival rate is constant
92
Q

if observed photons satisfy axioms, then

A

number of photons observed will follow a poisson distribution

93
Q

expectation value of the number photons

A

E(N)-<N>=Rtau</N>

N=no of photons
mean photon arrival rate is R per second
tau = exposure time

94
Q

series of observations - wouldn’t expect exactly the same no of photons for each. Instead…

A

average number of photon counts

<N>=R_tau
</N>

95
Q

as Rtau increase, shape of poisson distribution

A

becomes more symmetric

tends towards a normal/gaussian distribution

96
Q

variance of N

A

measure of the spread of the distribution

= mean squared standard deviation of N from <N></N>

97
Q

for a poisson distribution, var(N)=

A

R_tau

98
Q

estimate of the photon rate

A

R hat = No of obs/tau

99
Q

quote our experimental estimate of the mean no of photons in tau as

A

Nobs +/- sqrt (Nobs)

since standard deviation is sqrt(Nobs)

100
Q

total noise variance

A

found by adding together all the individual sources

sigma total ^2 = sigma poisson ^2 + sigma other ^2 +…

101
Q

sources of poisson noise

A

fluctuations in the photon count from the sky
dark current: thermal fluctuations in a CCD

102
Q

no of photons collected is…

A

total energy collected by detector / hv0

total energy = FAT = SvA deltav tau

103
Q

correcting for combined quantum efficiency of telescope and detector

A

Ntot= n SvA delta v tau/h vo

n is fraction of photons that produce response in the detector

104
Q

maximise SNR

A

bigger telescope
larger observing time
large bandwidth

105
Q

when the noise of dominated by counting statistics of photons, the sensitivity of a telescope…

A

only increases with the square root of the aperture’s area

106
Q

in radio astronomy, noise is often dominated by

A

noise in the receiver electronics

107
Q

when noise of dominated by detector electronics, the sensitivity of the telescope…

A

increases in proportion to its aperture

108
Q

when is it not true that increasing bandwidth increases SNR

A

if source only emits over a narrow frequency

will just increase noise without increasing any signal

109
Q

line profile

A

specific intensity or flux density as a function of frequency

shape of line profile characterised by a measure of its width

110
Q

why is spectroscopy important

A

allows us to deduce many physical characteristics of planets, stars and galaxies

111
Q

learn about chemical elements from

A

frequency

112
Q

learn about chemical abundances from

A

relative intensities

113
Q

learn about bulk velocity from

A

frequency

114
Q

learn about temp, pressure, gravity from

A

line width

115
Q

learn about spread of velocities from

A

line width

116
Q

learn about magnetic and electric fields from

A

‘fine structure’ in lines

eg Zeeman splitting

117
Q

spectral resolving power

A

characterises effectiveness of filter or any spectroscopy instrumentation

R=vo/delta v = lambda0/delta lambda

118
Q

useful spectral resolving power

A

approx 10^5 or higher

ie sensitive to Doppler shifts of a few km/s

119
Q

much higher spectral resolving powers can be achieved by…

A

using a prism or diffraction grating

120
Q

difference in prism and diffraction grating dispersing light

A

prism disperses blue light more strongly than red light

diffraction grating disperses red light more strongly than blue light

121
Q

for diffraction grating with light incident at right angles, diffracted light has an intensity maximum when path difference satisfies

A

asin theta = n lambda

a = spacing between grating lines (not number of grating lines)
n = order of the maximum

122
Q

if light is incident at an oblique (not perpendicular) angle…

A

maxima occurs at pd which satisy

a(sin theta + sin alpha)=n lambda

123
Q

how to get expression for angular dispersion

A

differentiating maxima expressions

124
Q

how can higher angular resolution be achieved

A

large n
small a and/or large theta

125
Q

linear dispersion

A

when focal length taken into account

dx=fdtheta

126
Q

relationship between linear and angular dispersion

A

linear dispersion = f x angular dispersion

127
Q

intensity profile from a monochromatic light source diffracted by an infinite diffraction grating

A

a series of infinitely thin peaks equally spaced in sin theta

128
Q

grating with N rules

for the mth opening, phase difference with 0th opening is

A

m (2pi/lambda) a sin theta

129
Q

what limits the resolving power of a diffraction grating

A

the finite width of the peak

130
Q

we can only resolve two lines if they are…

A

separated by at least their width

R=lambda/delta lambda= Nn

131
Q

key features of a spectrometer design

A

aperture - slit - collimating lens - grating - focussing lens - detector

(in that order)

132
Q

collimating lens

A

diverging rays become parallel again

133
Q

after grating, individual colours…

A

parallel

eg all red rays are parallel

134
Q

slit cuts out

A

unwanted light

135
Q

angular size at collimating lens defines

A

range of angles entering the grating

136
Q

diameter of the collimating lens

A

approx the width of the grating so little light is lost

137
Q

focussing lens will produce a diffraction pattern that

A

spreads out the light over a width around lambda/Dfocus

138
Q

we want lambda/Dfocus < lambda/Dgrating so

A

Dfocus > D grating

139
Q

light from a distance point source arrives at a telescope as

A

plane waves which are diffracted as they pass through circular aperture

140
Q

can work out airy disc pattern depending on

A

size of aperture and wavelength of incident light

141
Q

resolving power - simplified 1D analysis

A

integrate diffraction pattern across a slit of width D

consider light emerging the aperture at theta to axis

142
Q

the diffracted signal at an angle theta is obtained by

A

integrating e^i2pi theta x/lambda

from x=-D/2 to x=D/2

143
Q

sinc x

A

sin x /x

maximum at x=0 and zeros occur at x=+/-mpi

144
Q

when light from two point sources observed, telescope will produce

A

image that is combination of the diffraction pattern of each of the stars

airy discs would overlap if they are too close

145
Q

we regard two stars as resolvable if

A

central max of diffraction pattern of one star coincides with first min of other

angular sep satisfies theta min = 1.22lambda/D

146
Q

if we observe a point source which is not monochromatic, observed intensity is

A

integral of intensity pattern at each observed wavelength

147
Q

combined intensity pattern washes out

A

the side lobes and the secondary maxima are not visible

148
Q

diffraction blurs point sources over an angle

A

theta is approx lambda/D

149
Q

for an extended source, each point of the source is

A

blurred by the diffraction pattern which we call the point spread function (PSF)

150
Q

convolved

A

we say the source function is convolved with the PSF

151
Q

rayleigh criterion defines

A

theoretical angular resolving power of a telescope

152
Q

diffraction limited

A

if we resolve features down to the rayleigh criterion

153
Q

for small telescopes of aperture a few cms, the diffraction limit is

A

larger than the typical size of the seeing disc so these telescopes are not limited by seeing

154
Q

for ground based optical telescopes, D>1m, diffraction limit

A

is much smaller than the seeing disc

so theoretical angular resolving limit is not achieved and we say that its seeing limited

155
Q

resolving power - more exact 2D analysis

A

integrate the diffraction pattern over a circular aperture of diameter D

156
Q

earth’s atmosphere is opaque to EM radiation apart from

A

two windows, one in optical band and another in radio band

157
Q

model of the atmosphere as series of parallel slabs

A

slab thickness dl
intensity I incident perpendicular to slab

dI=-Ikdl where k=absorption coefficient

158
Q

optical depth

A

Iobs=I0e^-t

159
Q

if t=0

A

atmosphere transparent Iobs=I0

160
Q

if t«1

A

atmosphere optically thin I obs approx=I0

161
Q

if t>1

A

atmosphere optically thick
Iobs«I0

162
Q

observing stat at zenith angle theta

path length through slab of thickness dl=

A

dl/cos theta = dlsec theta

163
Q

refraction - approach of modelling atmosphere as plane-parallel slabs and light incident at theta valid for

A

angles less than 60 degrees
for larger angles, need to account for Earth’s curvature

164
Q

air molecules, dust and water vapour all

A

scatter light

effect depends on the size of the scattering particle

165
Q

particle size a, where a»λopt

A

particles scatter all wavelengths equally

atmospheric water droplets fall into this category, why clouds appear white

166
Q

scattering for particle sizes a approx= λopt

A

scattering strength prop. to 1/λ

why cigarette smoke has bluish tinge

167
Q

scattering for particle size a«λopt

A

scattering strength prop. to 1/λ^4 so blue light strongly scattered

rayleigh scattering

why daytime sky is blue and red at sunset when blue scattered out of line of sight

168
Q

scattering is anisotropic and

A

light from the sky is polarised

169
Q
A
169
Q

loss of intensity due to scattering

A

dI=-Isigmadl

170
Q

what is scintillation

A

‘twinkling’of starlight caused by turbulence in the atmosphere

air cells of varying density and refractive index are continually passing through the line of sight to the star changing the illumination

171
Q

cells deflect the light from a point source over a

A

seeing disk (angular radius approx 3arcsec)

172
Q

if telescope aperture is such that D is approx r0(typical scale of the cells)

A

see rapid variations in positions and brightness of the image as individual cells move across the line of sight

173
Q

if telescope aperture is such that D»r0

A

image formed from many cells added together

average brightness of image approx constant but rapid variations in position, size and shape of seeing disk

174
Q

radio astronomy affected by scintillation, not from atmosphere but from

A

turbulence in the interstellar medium and the interplanetary medium

typical size of cells much larger

175
Q

extremely high energy gamma ray detectors

A

energy >10^12 eV
do not detect these photons directly but see effect they have on atmosphere
they collide with atoms to create shower of subatomic particles
produces cherenkov radiation

176
Q

high energy gamma rays

A

E=100mEv
need to get above most of atmosphere to detect
photons produce positron-electron pairs
track path through spark chambers

177
Q

low energy gamma rays and x-rays
1keV<E<20keV

A

use propoetional counter: tube filled with gas
xray ionises gas atom and liberates an electron
electron accelerates towards anode, ionsing more atoms

leads to cascade of electrons

178
Q

low energy gamma rays and x-rays
E>20 keV

A

x-rays would pass straight through gas

instead used solid state detector or scintillation counter

x-ray enters and ionises atom, electron excites other electrons, impurity atoms capture electrons

captures lead to bright flahses detected by photomultiplier

179
Q

we can image x-rays using

A

grazing incidence optics

series of nested surfaces of high conducting material
x-rays reflected for large incidence angles

180
Q

UV and optical wavelenghts

A

1eV<E<100eV

CCDs cooled to reduce thermal noise

181
Q

near infrared wavelengths

A

0.04eV<E<1eV

CCD technology using semiconductors with appropriate band gap so that weak NIR photons can still eject electrons to produce current

182
Q

far infrared wavelengths

A

10^-3eV<E<4x10^-3eV

too weak for CCDs but too high frequency for radio techniques

bolometer measures temp increase in crystlas when struck by photons

183
Q

radio wavelengths

A

E<10^-4eV

treat as wave

radio waves detected by antenna where changing EM field induces a current

pre-amplifier produces voltage prop. to the current

184
Q

radio antennas

A

chooses direction of observation
collects radiation
converts radiation into AC signal

185
Q

radio receiver

A

amplifies the signal by gain factor
selects frequency and bandwidth
processes and records signals

186
Q

radio - availability of phase information means

A

radio observations can be combined from different telescopes

Astronomy 2 (4 decks)

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