ASTRO 2233 TOPICS IN ASTRONOMY AND ASTROPHYSICS...
Transcript of ASTRO 2233 TOPICS IN ASTRONOMY AND ASTROPHYSICS...
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ASTRO 2233
TOPICS IN ASTRONOMY AND ASTROPHYSICS
Fall 2008
Lectures 1 & 2
Telescopes
August 28 & September 2, 2008
Don Campbell
ARECIBO RADIO TELESCOPE
D = 300 m => Res = 20 arcsec at λ = 3 cm
EARLY GREEK ASTRONOMY:
Obliquity of Earth - Angle between plane of the Sun’s motion in the sky (the
ecliptic) and the plane of Earth’s equator.
Known in the 6th century BCE – measured angle differences for
shadows at the summer (northern) soltice and the winter soltice
≈ 470 - Tropic of Cancer +23.50; tropic of Capricorn -23.50
Eratosthenes (276 – 194 BCE) measured angle difference of 11/83 of a circle
= 470 43’
Real value NOW = 460 26’ – has decreased by ~15’ since antiquity
ECLIPTIC and the ZODIAC:
Looking from Earth, Sun moves in the Ecliptic plane – defined by Lunar
eclipses since you can’t see the stars around the Sun.
Ecliptic plane lies in the Zodiac – the constellations through which the
Sun and planets pass during a year.
Babylonian astronomers knew about the Zodiac in the 6th century BCE,
Greeks in the 5th century.
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“Because of the precession of the equinoxes, the vernal equinox moves
through all the constellations of the Zodiac over the 26,000 year precession
period. Presently the vernal equinox is in the constellation Pisces and is
slowly approaching Aquarius. This is the origin of the "Age of Aquarius"
celebrated in the musical Hair: a period when according to astrological
mysticism and related hokum there will be unusual harmony and
understanding in the world. We could certainly use a dose of harmony and
understanding in this old world; unfortunately, it is unlikely to come because
of something as irrelevant as the position of the vernal equinox with respect
to the constellations of the Zodiac. “ (Unknown author)
The Dawning of the Age of Aquarius (Almost)
Celestial coordinates
- Right Ascension (RA) and
Declination (δ or Dec)
PRECESSION => RA and δ
coordinate frame rotates with
26,000 yr period => must
specify year with RA and δ
e.g. 2,000 coordinates (common)
DISTANCES
Astronomical Unit (AU): Mean distance from Earth to the Sun (149.598 106 km)
Light year: Distance light travels in one year (9.5 1012 km) (vel. of light = 3 105 km s-1)
Parsec: Distance at which 1.0 AU subtends 1 arc sec (= 2 105 AU ~ 3.26 light years)
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THE APPARENT MAGNITUDE BRIGHTNESS SCALE
Logarimithmic since the sensitivity of the eye to brightness is logarithmic
Inverted scale – all the fault of the Greeks.
Greeks set brightest star to have
brightness of ~1
Dimmest observable star to have
brightness of ~6
Suppose we have two stars with
apparent magnitudes m1 and m2.
We can calculate the ratio of their
brightnesses b1 and b2 by the formula:
m1 - m2 = -2.5 log (b1 / b2)
Let's compare Sirius, the brightest star
visible in the night sky, to the Sun.
(-1.5) - (-26.8) = -2.5 log bSirius / bSun
log bSirius / bSun = -10.1
bSirius / bSun = 10-10.1 = 7.9 x 10-11
bSirius / bSun = 1/13,200,000,000.
Sirius appears 13,200,000,000 times
fainter than the Sun.
But Sirius is actually more luminous than
the Sun. It is just much more distant.
Apparent magnitudes of some familiar objectsFor the apparent brightness, we usually use the apparent magnitude, conventionally written as m.
5 magnitudes = 100
N.B. Magnitude differences can change depending on the wavelength
ABSOLUTE MAGNITUDE (M) = APPARENT MAGNITUDE (m) IF OBJECT WAS AT A DISTANCE OF 10 PARSECS
M = 5 + m - 5log (d)
where d = dist of object in parsecs
ONE PARSEC = DISTANCE AT WHICH 1 AU SUBTENDS AN ANGLE OF 1.0 ARCSEC
We are probably nearing the limit of all we can
know about astronomy.- Simon Newcomb, astronomer, 1888
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Ionospheric absorption
Interstellar
absorption Atmospheric absorption
• BEFORE 1950’s OBSERVATIONAL ASTRONOMY USED ONLY OPTICAL TELESCOPES – 200 inch PALOMAR TELESCOPE COMPLETED 1948
• FIRST RADIO ASTRONOMICAL TELESCOPES IN 1950’s
• FIRST SPACE BASED TELESCOPES/MISSIONS IN 1960’s
Infrared, UV, x-rays, γ-rays
• VERY LARGE ARRAY (VLA) 1976 – Synthesis radio telescope
• COSMIC BACKGROUND EXPLORER 1989 – Cosmic Microwave Background
• HUBBLE SPACE TELESCOPE 1990
• 10 m KECK TELESCOPE 1993
• CHANDRA X-RAY SATELLITE 1999
• SPITZER INFRARED TELESCOPE FACILITY (SIRTF) Aug 25 2003
1770’s Charles Messier compiled list of 100 “fuzzy” or diffuse non-stellar objects (nebulae) in the sky – Messier objects
1864 – General Catalogue of Nebulae by John Herschel
1888 – New General Catalogue (NGC numbers) by J. Dreyer
Some of these nebulae showed spiral structure – debate raged until 1920 as to whether these nebulae were in our galaxy or external to it.
Issue resolved by Edwin Hubble in 1922 using new 100 inch Mt Wilson telescope in California using Cepheid variables as standard candles.
New and better telescopes allow problems to be solved.
ATMOSPHERIC ABSORPTION
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Sky brighness temperature and atmospheric transmission over Cerro
Chajnantor (near ALMA site in Chile) with 1 mm of precipitable water
overhead and over the VLA site in New Mexico with 4 mm of precipitable
water overhead.
Cerro Chajnantor, Chile site ~5,600 m
CCAT – Cornell-Caltech sub-mm telescope
Galileo Galilei (1564 (?) – 1642
Galileo’s telescope –
about 2 cm effective
aperture
2009
– 400 YEARS OF ASTRONOMICAL TELESCOPES
ORBITS: Confirmation of the heliocentric model of the solar system
Galileo (1609 and 1610)
- Observed that Venus showed “phases” like the Moon
- not possible on the epicycle model
- Discovered the Jovian (Galilean) satellites
- clearly in orbit about Jupiter – mini-solar system
Jupiter and its moons (1609)
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ELECTROMAGNETIC WAVES
Oscillating electric and magnetic fields that propagate with a velocity;
v = (ε µ)-1/2 where ε = the electric permittivity
µ = the magnetic permeability
For a vacuum: v = c = (ε0 µ0)-1/2 = 2.997 108 ms-1 ≈ 3 108 ms-1
where ε0 & µ0 are the values for a vacuum
Image courtesy of W. Blake, U. Rochester
In vacuum c = λ x ν
where λ = wavelength
ν = frequency
In 1864 James Clerk Maxwell derived a set of equations – Maxwell’s
equations – which showed the relationship between electric and magnetic
fields
=> a propagating electromagnetic wave in a vacuum
- a very new concept!!
Propagation in a Dielectric (non-conducting) material – e.g. glass
v = (ε µ)-1/2 ms-1 and, for a vacuum, c = (ε0 µ0)-1/2 ms-1
Substituting: v = c x (ε0 µ0)1/2 / (ε µ)1/2
= c/n where n = the refractive index = (ε µ)1/2 / (ε0 µ0)1/2
For Earth’s atmosphere at radio wavelengths n ≈ 1.0003 - mainly due to H20 vapor
For non magnetic materials: n ≈ (ε/ε0)1/2 since µ ≈ µ0 (almost all materials)
Plane and Spherical Wavefronts and Huygens’ Principle
Plane
wavefront
Spherical
wavefront
Point source will generate a spherical wavefront.
Point source at “infinity” (a large distance) will give a plane wave or
use a lens
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Huygens principle: “Each point on a wavefront may be considered a point
source of secondary waves – wavelets. After time ∆t the new location of the
wavefront is the envelope – or tangent surface – to these secondary wavelets.”
Reflection and Refraction:
Reflection: θr = θi
Refraction: n1 sin θi = n2 sin θt
Refractive index
n1
n2
Refraction is just the application
of Huygens principle and the
different propagation velocities
in the two media.
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For small angles sinθ = θ and First Null is at θ = λ/a radians
Plane wave incident on a slit Fraunhofer Diffraction Pattern
I(θ) = I0 [sin (πaθ/λ)/ (πaθ/λ)]2
HOW DO TELESCOPES WORK?
For circular apertures first null is at 1.22 λ/a
Intensity at the focal point as telescope
scans a “point” source of radio waves
Single or a few
pixels only at cm
wavelengths
Telescope
resolution ~ λ/D
radians RESOLUTION = λ/D radians1 rad = 2 105 arcsec
At optical wavelengths 10 cm diameter gives ~ 1 arcsec resolution
Hubble Space Telescope: 90 cm aperture => 0.1 arcsec at 0.6 µm
Earth based telescopes: Atmospheric turbulence limits resolution to, at
the very best, about 0.25 arcsec.
Adaptive optics a partial solution
100 m radio telescope at a wavelength of 10 cm gives ~ ??
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Achromatic lenses invented by
Fraunhofer ~1815 – solved the
problem
Lenses produce chromatic aberration: light of different
wavelengths comes to focus at different points.
OPTICAL TELESCOPESFUERTES OBSERVATORY
12 inch diameter refractor
Joseph van Fraunhofer 1787 - 1824
Fraunhofer Diffraction Patterns
Fraunhofer lines in the solar spectrum
Fraunhofer achromatic lenses
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Resolution: The minimum angle at which two point sources of light (or
radio waves) can be distinguished. Very close to λ/D
Field of View: Solid angle over which a telescope can focus an incoming
plane wave – dependent on ratio of focal length to diameter – F/D ratio
Number of independent pixels over the field of view ≈ FOV x D2/λ2
e.g. FOV = 1 square degree; resolution = 1 arcsec
Number of pixels ≈ 107 ≈ # of pixels in a good digital camera.
N.B. Single dish radio telescopes typically have 1 to a few pixels
WE WANT MORE!
200 inch
PALOMAR
TELESCOPE
Gemini North 8 m telescope on Mauna
Kia showing the Cassegrain focus.
SEEING!
Japanese 8 m Subaru telescope on Mauna Kia, Hawaii showing
Nasmyth focus
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KECK 10m TELESCOPES
D = 10 m => res = 0.01 arc sec at 0.5 µm
(Earth’s atmosphere is the limit on the res.)
Planned Large Optical/IR TelescopesExpected 2015 to 2020
OWL – European
Overwhelmingly
Large Telescope
40 m diameter
Thirty meter telescope (TMT)
Caltech/California project
HUBBLE SPACE TELESCOPE
D = 2.4 m => resolution = 0.04 arcsec at λ = 0.5 µm
JAMES WEBB SPACE TELESCOPE
D = 6 m
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Large Synoptic Survey Telescope
(LSST)
PanSTARRS 1.8 m telescope
LARGE BINOCULAR TELESCOPE
Mt Graham, Arizona
SPITZER INFRARED TELESCOPE CHANDRA X-RAY TELESCOPE
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LASER INTERFEROMETER GRAVITATIONAL OBSERVATORY (LIGO) AT HANFORD, WA
AND LIVINGSTON, LOUISIANA