Astro 101Fall 2013 -- Lecture #3

T. Howard

Using Light to Sample the Universe

wavefronts (lines of constant phase)

Plane wave

Spherical wave

Light is a mutual oscillation of electricand magnetic fields, travelling throughspace.

Light is also a stream of fundamentalparticles (photons) that can be detectedindividually.

Both interpretations are correct.

It is electromagnetic radiation.

Light from stars starts out like this …

… and reaches us like this.

Why? Because stars are very, very far away. The curved wave flattens out with distance.

But, the amount of light we can collect …(with our telescopes)

… falls off as 1/distance2

Why? Three simple reasons:

A. The total energy = amount of light is conservedB. As the light flows away from the star, that light is spread over an imaginary sphere of area 4pR2, where R is the distance from the starC. Our telescope samples only a very small part of the area of that imaginary sphere that surrounds the distant star.

distant star

Telescope(just the front aperture is shown)

We can use this to find either (a) the absolute amount of light that the staremits, or (b) its distance, if we know the other quantity.

R

Since light is a wave, it has wave properties …

Direction of wavetravel

“Amplitude” ofthe wave = heightof the Electric fieldvibration

“Wavelength” = distance between twosuccessive peaks

This defines the color of the light wave

• Most light we see with our eyes has a spread of many colors mixed• Generally, some colors stronger than others, so we see objects in different colors

• White light is a nearly uniform mix of all the colors that we can seewith our eyes

• There are many other colors (= wavelengths) that we can’t see• Our eyes just not sensitive to vibrations at those wavelengths• But, electronic detectors and telescopes can see them

So, almost all light reaches us with a spectrum

Spectrum = spread of light wavelengths, mixed in varying strengths,that reaches our eye / telescope / camera (plural = spectra)

Spectra can be continuous … (like this)

or discrete … (like this) Continuous spectra come from warm objects (everything in the Universe, almost). The color extent and intensity of the spectrum depends on the temperature of the object. This is known as thermalor blackbody radiation.

Even you are emitting thermal radiation, right now.

Example

The astronaut’s space suit is:

a. Reflecting light from its surroundings

… and …

b. Emitting infrared (thermal) radiation

(that we can’t see because our eyes aren’t sensitive to those colors)

Q: What about the light coming from the lunar surface? Which is it?Q: Is the light from the Sun thermal radiation? If so, why can we see it with our eyes? If not, what is it?

incomingsunlight

The human eye is sensitive only to the range 400 – 700 nanometers.(1 nanometer = 10-9 meter = one-billionth of a meter.)

Blue wavelengths are shorter than red wavelengths.

The visible spectrum is only a small part of the overall possibleelectromagnetic spectrum. Other regions of the spectrum correspondto …

gamma rays (very short)x-rays (pretty short wavelengths)UV (ultraviolet, shorter than visible blue light)infrared or IR (long wavelengths, beyond the visible)radio waves (longer than infrared)

The visible spectrum

400 nm 700 nm

3x1025 1024 1023 1022 1021 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 109 108 107 106 105 104 103

Frequency [Hz]

Wavelength [m]

10-18 10-17 10-16 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105

Infrared

RadioGamma Rays

UVX-rays

400 nm[0.4 microns]

4000 Angstroms

700 nm[0.7 microns]

7000 Angstroms

1 10 100Wavelength [microns]

Visible

MWIR3-5 microns

LWIR8-12 microns

VLWIRNIR< 2 microns

Cellphones(AMPS, USDC)

850 MHzBroadcast TV

60 MHz

Shortwave10 MHz

X-band10 GHz

1 eV1.24 microns

e- e+ annihilation0.511 MeV

Broadcast AM0.8 MHz

UV “A” 320-400 nmUV “B” 290-320 nm

Electromagnetic Radiation

Medical x-rays0.1 - 0.5 Angstroms

frequency [Hz]

wavelength [m]

Peak Dayresponse570 nm

PeakDark response

510 nm

micron = mm = 10-6 mnanometer = nm = 10-9 mAngstrom = 10-10 m

Photon energy: E = hn = hc/l

ln = c

Peak of Cosmic MicrowaveBackground (CMB)

[T =2.736 K]

2900K 290K 29KTemperature of Blackbodywith Peak emission at l

Light of a certain color also has a characteristic frequency

Frequency = number of waves passing an arbitrary location (anyconvenient reference point) per second.

Frequency and wavelength are inversely related:

Longer wavelength = lower frequency = slower vibrationsShorter wavelength = higher frequency = faster vibrations

Most of the time, in this class, we will talk about wavelength ratherthan frequency. But if you specify one, you know the other.The energy of the light is also related to wavelength and frequency.

Some typical wavelengths, temperatures, and frequencies

Object Temperature Wavelength or frequency

Dental narrow line near 5 nmX-rays

Sun 5700 K Peak at about 500 nm

Your skin about 70F Peak at about 10000 nm = 10 microns

WiFi signal narrow signals at 2.4 GHz or 5 GHz (approx.)

1 GHz = 109 waves/sec.

AM Radio 530 – 1070 kHz wavelength 280 – 560 m

What about discrete spectra ?

• Narrow, well-defined spectral lines are phenomena caused by energy transitions in individual atoms or molecules

• These narrow lines correspond to specific light energies• Both atoms and molecules can exist in many possible energy states• Only certain energy states are physically possible (“allowed”)• So, the transition of an atom or molecule from energy state 1 to energy state 2 has a fixed energy difference

• That difference is characteristic of the atom or molecule• The energy either absorbs light of a certain color, or emits energy of a certain color

Low High energy High Low energy (absorbs light) (emits light)

Spectroscopy and Atoms

How do we know:

- Physical states of stars, e.g. temperature, density.

- Chemical make-up and ages of stars, galaxies

- Masses and orbits of stars, galaxies, extrasolar planets

- expansion of universe, acceleration of universe.

All rely on taking and understanding spectra: spreading out radiationby wavelength.

Types of Spectra and Kirchhoff's (1859) Laws

1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). Produced by a hot opaque solid, liquid, or dense gas.2. "Emission line" spectrum - bright at specific wavelengths only. Produced by a transparent hot gas.3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines. Produced by a transparent cool gas absorbing light from a continuous spectrum source.

The pattern of lines is a fingerprint of the element (e.g. hydrogen, neon) in the gas.

For a given element, emission and absorption lines occur at the same wavelengths.

Sodium

The Particle Nature of Light

On microscopic scales (scale of atoms), light travels as individual packets of energy, called photons. (Einstein 1905).

cphoton energy is proportional toradiation frequency:

E n (or E )1l

example: ultraviolet photons are more harmful than visible photons.

The Nature of Atoms

The Bohr model of the Hydrogen atom (1913):

_

+proton

electron

"ground state"

_

+

an "excited state"

Ground state is the lowest energy state. Atom must gain energy to move to an excited state. It must absorb a photon or collide with another atom.

But, only certain energies (or orbits) are allowed:

__

_

+

The atom can only absorb photons with exactly the right energy to boost the electron to one of its higher levels.

(photon energy αfrequency)

a few energy levels of H atom

When an atom absorbs a photon, it moves to a higher energy state briefly

When it jumps back to lower energy state, it emits a photon - in a random direction

Other elements

Helium Carbon

neutron proton

Atoms have equal positive and negative charge. Each element has its own allowed energy levels and thus its own spectrum. Number of protons defines element. Isotopes of element have different number of neutrons.

Ionization

+

Hydrogen

_

++

Helium

"Ion"

Two atoms colliding can also lead to ionization. The hotter the gas, the more ionized it gets.

_

_

Energetic UV Photon

Atom

Energetic UV Photon

So why do stars have absorption line spectra?

Simple case: let’s say these atoms can only absorb green photons. Get dark absorption line at green part of spectrum.

hot (millions of K), dense interiorhas blackbody spectrum,gas fully ionized

“atmosphere” (thousandsof K) has atoms and ionswith bound electrons

Stellar SpectraSpectra of stars differ mainly due to atmospheric temperature (composition differences also important).

“hot” star

“cool” star

So why absorption lines?

.. .

.

.

..

..

..

cloud of gas

The green photons (say) get absorbed by the atoms. They are emitted again in random directions. Photons of other wavelengths go through. Get dark absorption line at green part of spectrum.

Why emission lines?

.

..

...

hot cloud of gas

- Collisions excite atoms: an electron moves to a higher energy level

- Then electron drops back to lower level

- Photons at specific frequencies emitted.

Molecules

Two or more atoms joined together.

They occur in atmospheres of cooler stars, cold clouds of gas, planets.

Examples

H2 = H + HCO = C + OCO2 = C + O + ONH3 = N + H + H + H (ammonia)CH4 = C + H + H + H + H (methane)They have

- electron energy levels (like atoms) - rotational energy levels - vibrational energy levels

Molecule vibration and rotation

Types of Spectra

1. "Continuous" spectrum - radiation over a broad range of wavelengths(light: bright at every color).

3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines.

2. "Emission line" spectrum - bright at specific wavelengths only.

Kirchhoff's Laws (1859)1. A hot, opaque solid, liquid or dense gas produces a continuous spectrum.

2. A transparent hot gas produces an emission line spectrum.

3. A transparent, cool gas absorbs wavelengths from a continuous spectrum, producing an absorption line spectrum.

Doppler shifts

● Happens for all wave phenomena:

sound => change of pitch

light => change of wavelength (or color)

where V is the velocity of the emitting source (m/s), c is the speed of light (m/s).

Redshift if receding, blueshift (negative sign) if approaching.

Spectral lines are used to measure Doppler shift => gives us information about the motion of an object.

Example Doppler shift

● A spectral line normally seen at 400nm is shifted to 401nm due to relative motion of the source. What is the velocity of the source? Is it approaching or receding?

We've used spectra to find planets around other stars.

Star wobbling due to gravity of planet causes small Doppler shift of its absorption lines.

Amount of shift depends on velocity of wobble. Also know period of wobble. This is enough to constrain the mass and orbit of the planet.

Now 800 + extrasolar planets known. Here are the first few discovered.

Final note: the Sun’s surface temperature of about 5800 K produces peak emission at 500 nm.

Sun is not yellow-green! What’s going on?

The Earth’s atmosphere scatters short wavelength blue light more efficiently than red light. Sun appears redder because blue light scattered away into the sky. Sun even appears red at sunset.

Telescopes

Telescopes

● Basic function of a telescope: extend human vision– Collect light from celestial object– Focus light into an image of the object

● Human eye works from 400 – 700 nm or so and uses a lens to form an image on the retina. Astronomical objects emit at much larger range of wavelengths, and can be very faint!

Optical telescopes

Kinds of optical telescopes– Refractor – uses a lens that light passes through, to

concentrate light. Galileo’s telescope was a refractor.

Large objective lens at the front of the telescope forms theimage, the eyepiece lens at the back of the telescope magnifiesthe image for the observer.

Focal length, f, is distance from the lens to the focal point.

Problem with refractors: big diameterobjective lens means huge telescope!Tube here is 64 ft, biggest lens ever was 40 inches in diameter.

Solution: use concave mirror, not lens, to focus light. Reflecting telescope.Reflector – uses a mirror (shape is conic section– typically parabolic). Big, modern research telescopes are reflectors.

Eye

ObjectiveEyepiece

Observing with Your Eye vs. Telescope Photography

ObjectiveDetector(or film)

Q: Why the difference?A: Because your eye has

its own “detector” inside (the retina)

Eyepiece providesmagnification

Your eye lens focuses thelight onto the retina

Aligning the Telescope Axes … It Makes a Difference

“Alt-Az” mounting :Vertical axis (sweep around horizon)Horizontal axis (up and down)

Problem:Stars (& moon, etc.)drift throughImage as Earth rotatesNo good forPhotography,Spectroscopy

“Equatorial” mounting :Main axis is parallel to Earth N-S axisOther axis goes up and down in ;atitude

Advantage:Clock motorturns the telescopeto match the Earthrotation, so longexposures possible

X !!

100 inch Telescope, Mt. Wilson Observatory

A small amateur telescope

Reflector advantages● Mirrors can be large, because they can be

supported from behind.● Largest single mirror built: 8.4 m diameter for

the Large Binocular Telescope

● There are 10 m telescopes, but in segments

Reasons for using telescopes● Light gathering power: LGP area, or D2 Main

reason for building large telescopes!

Reasons for using telescopes, cont.

● Magnification: angular diameter as seen through telescope/angular diameter on sky: m=fobj/feyepiece

– Typical magnifications 10 to 100

● Resolution: The ability to distinguish two objects very close together. Angular resolution:

= 2.5 x 105 l/D, where is angular resolution of telescope in arcsec, l is wavelength of light, D is diameter of telescope objective, both typically in meters.

Two light sources with angular separation much larger thanangular resolution vs. equal to angular resolution

Detectors

Quantum Efficiency = how much light they respond to:– Eye 2%– Photographic emulsions 1-4%– CCD (Charge coupled device) 80%

● Can be used to obtain images or spectra

Photographic film CCD

Same telescope, same exposure time!

● Spectrographs: light spread out by wavelength, by prism or “diffraction grating”

Radio Telescopes● Problems – low photon energies, long l

– Remember = 2.5 x 105 l/D

● Single Dish: need big diameter to get decent resolution.

● Can also design clever shapes of reflectors, which minimize unwanted radio waves bouncing off feed legs into receiver

● The Green Bank Telescope

● Reflecting surface shouldn’t have irregularities that are larger than 1/16 of wavelength being focussed – are radio or optical telescopes easier to construct in terms of surface accuracy?

● But, wavelength is large – how do we get good

resolution?● Interferometers – e.g., VLA

Use interference of radio waves to mimic the resolution of a telescope whose diameter is equal to the separation of the dishes

Aperture Synthesis

-- Combine signals from multiple apertures.

-- Control the optical (or radio) path length from each aperture so that the signals act as if they were reflected from a single larger, filled aperture.

-- Computers, high accuracy time reference, and specialized signal processing reconstruct an image.

● Our own telescope: the Long Wavelength Array

● Far larger than the VLA. “Stations” of 256 antennas, to be spread across NM

● Square Kilometer Array, currently being designed, will be 50 times collecting area of VLA, with baselines to 1000’s km

Optical-mm Telescope sites

● Site requirements– Dark skies (avoid light pollution)– Clear skies– Good “seeing”, stable atmosphere

● High, dry mountain peaks are ideal observatory sites, for optical to cm

Earth at night

● Adaptive Optics – use a wavefront sensor and a

deformable mirror to compensate for deformations of incoming wave caused by the Earth’s atmosphere.

Telescopes in spacePros – above the atmospheric opacity so can work

at l impossible from ground, above turbulence, weather, lights on Earth

Con – expensive!

The Hubble Space Telescope (HST)

Wide Field Camera 3

Cosmic Origins Spectrograph

• In 1996, researchersat the Space TelescopeScience Institute usedthe Hubble to make avery long exposure ofa patch of seeminglyempty sky.

Q: What did they find?

A: Galaxies “as far as the eye can see …”

(nearly everything inthis photo is a galaxy!)

40 hour exposure

JWST (James Webb Space Telescope)

Mirror 6.5 m, segmented(current) Expected launch 2018

Spectral range: 0.6 – 28 microns

Science instruments:

NIR Camera (0.6 – 5 um) [U. Ariz.]NIR Spectrograph (0.6 – 5 um) [ESA]Mid-IR Instrument (5 – 28 um) camera + spectrograph [Consortium]Fine Guidance Sensor [Canadian Space Agency]

● Hubble Space Telescope. 2.4 m mirror, 115nm – 1 micron

● Successor: JWST. 6.5 m mirror, 600 nm – 28 microns

Spitzer aperture: D = 0.85m, f/12Be lightweight mirror, T < 5.5 K

Cooling: Liquid He

Wavelength coverage: -- Imaging 3 – 180 microns -- Spectroscopy 5 – 40 microns -- Spectrophotometry 50 -100 microns

73[Davi10]

Kepler Instrument

21 x 2 Focal Plane Arrays

KeplerSpacecraft

95 M pixels

FOV: 105 deg2

Photometeraccuracy: 0.0001

Chandra X-ray telescope

The sky at different wavelengths

Visible

Infrared

Gamma ray

Radio(neutralhydrogen)

X-ray