Observational Methods Flashcards
Cosmic rays
High energy particles from space (supernovae, sun etc) detected at high altitude
Most atrononomical information is deduced from
Observations of EM radiation
EM waves
Oscillating electric and magnetic fields
Travel at c
C=v lambda
Or considered particles, E=hf
Atmospheric windows
Only certain parts of the EM spectrum can be viewed from the ground
Some parts completely opaque
Radio window completely transparent
Atmospheric windows - Main bands
Visible ~300-1100nm
Microwave/radio 10^-2 - 10m
Parts of infrared also observed from Earth
Effect of the Atmosphere
Gamma and x-rays absorbed by atoms and nuclei
UV mostly absorbed by O2 and O3
IR absorbed in different bands by H2O and CO2
Radio>10m blocked by charged particles in ionosphere
Luminosity
Power radiated by an object
Bolometric luminosity
Refers to power radiated at all wavelengths
Lbol= integral between 0 and infinity of Lmono d labda
Monochromatic luminosity
Measured over a small wavelength window
Power
Shaded area of curve monochromatic L x d lambda
Total power = integral (area under whole graph)
Flux
Power radiated per unit area received a distance d from an object (units Wm^-2)
F=L/4pid^2 (=L/ area)
Monochromatic flux
Exactly the same but using monochromatic luminosity in equation instead
Magnitude
Describes an object’s brightness
Apparent magnitude, m
How bright an object appears
Absolute magnitude, M
Intrinsic brightness of an object
Sirius
Brightest star in sky has m=-1.46
Apparent magnitude zero point
Apparently brighter star has smaller apparent magnitude than fainter star
m=0 point chosen to be vega
Apparent magnitude of sun
-27
Parallax
Difference in apparent position when an object is viewed along different lines of sight
Annual parallax
Difference in apparent position when a star is viewed from Earth and from the sun
Earth’s orbit gives different viewing positions
Calculate annual parallax from positions 6 months apart
Equation for annual parallax
Draw triangle to get tanP=SE/d = 1au/d
Since p very small, tanP~sinP~P (in rad)
So P~ 1au/d
Parsec
The distance at which an object has a parallax of one second of arc
Need P in radians
Absolute magnitude
Compares luminosities accounting for distance
M is the apparent magnitude a star would have at a distance of 10 parsecs
Two functions of telescopes
Make objects appear brighter and bigger
Collect a lot of light to enable faint objects to be seen and magnify objects to allow detail to be resolved
As astronomical objects very far away, light arrives at Earth
In essentially parallel rays
Convex lens
Brings parallel rays to focus at focal distance
Light ray passing through the centre is undeviated
Basic refracting telescope
Consists of primary/objective lens and an eyepiece lens
Lens separated by the sum of their focal lens
Exit pupil, d
Diameter occupied by outgoing light rays
Light collecting function
Light from large area, diameter D, collected into smaller area, diameter d
Magnification
Increase of the apparent angular size of an object
Ratio of of angular size of image when viewed through eyepiece to the actual angular size of the object
Or ratio of focal lengths of the objective and eyepiece
magnification=alpha e/ alpha o
Angular size
When object close, it subtends a large angle at the telescope
Far away object subtends a smaller angle
Tan alpha o
h/fo
Tan alpha e
h/fe
Large primary lens or small eyepiece gives
High magnification
For visual use, exit pupil should be
< or = diameter of dilated pupil of eye (~8mm)
Telescope size
Refers to diameter of objective/primary optic
Telescope speed
F0/D
F/10 or f-ten means F0/D=10
Fast lens gatherers more light in a shorter time and can have a shorter shutter speed
Is F/10 or F/22 faster
F/10
Light collection
Larger diameter collects more light
Larger area collects more power
Collected power
W=FA
for telescope of circular aperture of diameter D, A=pi(D/2)^2
Number of collected photons per second
nph=W/Ephoton
Ephoton=hf
Limiting magnitude
Apparent magnitude of the faintest object which can be observed through the telescope
Calculated via Pogsen’s equation mlim=6+5log10D/deye
Naked eye can detected stars of approximately
m=6 and below
Diffraction
Bending of wave passing through an aperture or around an object
Cross section through diffraction pattern from circular aperture
Central maximum contains 84% of the light - airy disk
First minima occurs at angular distance of 1.22lambda/D from centre
Two adjacent stars produce
Overlapping diffraction patterns
Stars far apart can be easily resolved
Close together start to overlap
At some point can just be resolved, any closer cannot separate
Can typically resolve stars if
Maximum of one overlaps the first minimum of the other
a~1.22 lambda/D
a=theoretical angular resolution=angular resolving power=Rayleigh’s criterion
Useful guide but depends on the eyesight of the observer
Angular resolution of a means
Object with angular separation > or = a can be resolved
Why not all light entering telescope reaches detector
Absorption of light in glass
Absorption/scattering by mirror/lens surface (dirt, bubbles, surface roughness)
Telescope transmission T
Fraction of incident light which reaches detector
For multiple lenses or mirrors Ttot=T1xT2x…
Typical values for telescope transmission
T=0.75 for mirrors
T=0.9 for lenses
Single s
Energy arriving at detector for an observation time delta t
S=FATdelta t
But detectors not 100% efficient so quantum efficiency, n, added to equation
For photons of equal energy, no of photons detected
N=S/hf = FATn delta t/ hf
Noise (statistical uncertainty)
Present whenever we measure a signal
Can arise from source, telescope and detector, concentrate on noise from source being observed
Poisson noise
Associated with random processes such as radioactive decay and emission of photons from source
Mean emission rate N
Fluctuations around mean, for large number of random, independent events typical variation is root N
So signal to noise ratio is SNR=N/ root N = root N
Relative error can be greatly reduced when
Large number of photons are measured
Why build telescopes on mountain tops
To avoid atmospheric distortion of light
Atmosphere refractive index (density)
Changes in space and time
Atmospheric flow, turbulence
Refraction of rays in atmosphere gives random deviations
Scintillation
Variations of flux entering telescope, brightness variations
Seeing
Variations in apparent direction of origin of light
Seeing value refers to average size of image
0.5” is very good
Two types of telescope
Refractor, primary optic is a lens
Reflector, primary optic is a mirror
Chromatic aberration
Different wavelengths being focussed at different positions
Spherical aberration
Paraxial rays which hit lens at different distances from optical axis are focused at different distances
Corrected by using aspherical lenses
Disadvantages of refractors
Chromatic aberration
Spherical aberration for spherical lenses
Lenses are heavy
Require very uniform glass
Largest practical size for refractor is ~1m diameter
Reflectors
Use a mirror as primary optic
Ideal shape - concave paraboloid
Focus all wavelengths to single point
Parabolic mirror
Preferable to spherical but highly susceptible to astigmatism, leads to spread in image position if rays not exactly paraxial
Newtonian reflector
Concave primary to focus light, flat secondary folding mirror to divert light to focal point outside telescope
Cassegrain reflector
Concave primary, convex secondary, reflecting light through a gap in the primary
Allows long focal length, high magnification telescope
Schmidt-Cassegrain reflector
Primary mirror is spherical
Refracting Schmidt correct plate used to compensate for spherical aberration
Gregorian reflector
Primary mirror is concave paraboloid
Real image is formed before light reaches secondary mirror
At secondary mirror, rays diverging so it is concave to further focus them
Hubble Space Telescope
Benefit of being above atmosphere seeing effects so get very clear images
James Webb Space Telescope
Primary mirror with 18 hexagonal mirror segments
Near and mid infrared imaging and spectroscopy
Disadvantages of secondary mirrors
Loss of light (some of aperture blocked)
Diffraction around secondary mirror and holder leading to image distortion
Active optics
Primary mirror can change shape due to mechanical stress and thermal expansion/contraction
Slow changes of order 1s or longer
Large mirrors only possible with active optics
Monitor mirror shape/image quality
Apply corrections via mechanical actuators which change mirror shape
Largest mirror practical to avoid sagging under own weight
About 8m
Segmentation critical to allow very large mirrors
Adaptive optics
Corrects for rapid (millisecond timescale) effects of seeing
Process for adaptive optics
Beam splitter directs some light to a wavefront sensor
Wavefront sensor analyses wavefront
Wavefront analysis used to calculate correction
Corrections applied to a deformable ‘adaptive mirror’
Corrections aim to make wavefronts more planar, improving image quality
Shack Hartmann wavefront sensor
Light focussed by an array of small lenses onto a position sensitive detector
Actual image positions are compared to the plane wave case to measure wavefront distortion
Guide star
Often the target if observation is too faint to properly measure wavefront distortion
Nearby guide star monitored instead- light has followed similar path through atmosphere
Artificial guide star
Where bright, nearby star not available
Lasers used to produce light source in atmosphere
Eg: Rayleigh guide star, near UV, use backscattering from high in atmosphere to measure wavefront distortion
Sodium: 587nm laser used to excite sodium atoms high in atmosphere, creating glow
Chemical photography
Photographic plates used in the past
Still provides best spatial detail and largest formats
Entirely superseded by electronic detectors which rely on photo electric effect
Photo electric effect
Photon striking alkali metal or semiconductor can eject photon if Ep>wf
Eelectron=Ep-wf
Quantum efficiency of material
n=no of ejected electrons/no of incident photons
CCDs
Charge coupled devices are sensors which are spatially sensitive to photons
Semiconductor chips utilise photoelectric effect
Array of pixels to provide position sensitivity
How CCDs work
Incident photon hits CCD pixel, photon ejects electron from its place in semiconductor lattice
Bias voltage draws electron into a ‘well’, held until it is read out
More photons on pixel will result in more electrons stored in well
After exposure, collected electrons read out for analysis
What does it mean by read out
Voltage applied
Electrons move pixel to pixel
All e move right, third row to transfer register
Move step down, first reading
Another step down, next reading
Pixels in CCDs
Usually 5-10 micro m squares
Size of CCD is around 4cm side length (found by square rooting total no of pixels and multiply by size of each pixel)
CCDs are
Sensitive in optical band
Stable
Quick to read out
Linear
Must be cooled to reduce dark current (e emitted by random thermal fluctuations)
Limited in size
Photomultiplier
Photons incident on photocathode, liberating electron
E accelerated to another electrode held at higher potential
Collision liberates several e, accelerated to next electrode etc
Generates pulses of charge at anode
Cold hydrogen
Emits at wavelength 21cm due to transition of the neutral ground state
Passes easily through atmosphere
21cm radio observations used to map structures
Angular resolution of single radio telescope is
Rayleigh’s criterion
For radio wavelengths >0.01m angular resolution poor
Antennae
Used to transmit or receive radio waves
Simplest is metal rod
Electric field of radio wave makes e oscillate producing voltage which can be detected
Angular resolution of antennae described by
Beam
The angle of the cone within which a source is detected
1 Jansky (Jy)
10^-26 W/m^2/Hz
Waveguides
Simple antenna has poor angular resolution and low sensitivity
Improve sensitivity by waveguides which re-radiate any energy falling onto them towards the dipole and a reflector behind antenna
How to see high resolution images from radio telescopes
Arrays of antennae and dishes used together in an interferometer configuration to improve angular resolution
Interferometers
Parallel rays arrive at two antennae separated by D
Signals combined at receiver
pd=l=Dsin theta
Constructive interference when integer multiple n lambda
Small angle approx when source close to zenith
As source moves across sky it’s position is tracked and interferometric signal
oscillates as an interference pattern is mapped out
Angular resolution is precision with which position can be measured delta theta = delta n lambda/D
X rays emitted by
Very hot gases
Thermal Bremsstrahlung radiation
Galactic clusters forming from merging of galaxies/groups of galaxies
In falling matter collides with existing gas and is heated, leading to x ray emission
Crab Nebula
Remnant of core collapse supernova
Pulsar at centre
X ray interaction with matter
High photon energy tend to penetrate matter
Refractive index of many materials is close to 1 in X-ray band
Not deviated much and eventually absorbed without much change in direction
Can scatter easily rather than reflect at normal incidence
Grazing incidence
X-rays can be reflected at grazing incidence
Large angle of incidence
X-ray mirrors
Nearly parallel to incoming rays
X-rays can be focused by first reflecting from parabolic mirror then from hyperbolic mirror
Problem with X-ray telescopes and mirrors
Not much collecting area compared to an optical telescope, particularly serious as X-ray flux tends to be low
Solution for X-ray telescopes and mirrors
Many cylindrical nested mirrors
Problem: Until recently could only use grazing incidence optics, lambda >0.1nm
Shorter wavelength, imperfections/roughness of mirror’s surfaces is a problem, defects similar size to wavelength
New multilayer optical coatings
Allow higher energy x-rays to be imaged
Alternating coatings layers of tungsten/silicon or platinum/silicon carbide used
Collimating optics/ Fourier grid
Alternative to focussing optics for x-ray imaging
Simplest technique - a collimator restricts viewing angle to locate origin of x-rays
Modulation collimator
Two arrays of wire grids allow only x-rays from narrow strips of sky to be detected
Coded aperture
A mask/collimator which transmits some X-rays in a pattern is placed in front of the detector
The position/ shape of the pattern allows reconstruction of the source direction
CCDs for X-rays
Due to high energy of X-ray photons, one X-ray can liberate many electrons
No of e proportional to photon energy
Read out identifies location of X-ray on grid and energy of X-ray
X-rays of particular energy emitted from particular atoms can be identified - very useful
Micro channel plate
Plates with small channels- micron scale glass tubes coated to emit electrons when struck by x-rays
Electrons accelerated by voltage to hit second array of tubes
Collisions with walls of tubes produce more e, causes large pulse of e at anode
Wire grid allows position sensitivity
CHANDRA - high resolution camera
Micro channel plates coated to emit electrons when struck by x-rays
Electrons accelerated down tube by voltage, emitting more electrons from collisions with tube walls
Crossed wire grid detects signal and allows position of x-ray to be determined
CHANDRA - advanced CCD imaging spectrometer
Array of CCDs
Can measure energy of every detected photon
Map x-rays produced by different elements
