PHYS 3380 - Astronomy Homework Set #5 10/01/14 Due 10/08/14 Chapter 7 Review questions 4 and 5...

PHYS 3380 - Astronomy

Homework Set #510/01/14

Due 10/08/14

Chapter 7

Review questions 4 and 5Problems 1, 5, and 7Learning to Look 1

Extra Problem

1. A star’s continuous spectrum peaks at 700 nm and has a luminosity of 3 solar luminosities. What is its temperature? What is its radius?


Kirchhoff’s Laws of Radiation

First Law. A luminous solid, liquid or gas, such as a light bulb filament, emits light of all wavelengths thus producing a continuous spectrum of thermal radiation.

Second Law. If thermal radiation passes through a thin gas that is cooler than the thermal emitter, dark absorption lines are superimposed on the continuous spectrum. The gas absorbs certain wavelengths. This is called an absorption spectrum or dark line spectrum.

Third Law. Viewed against a cold, dark background, the same gas produces an emission line spectrum. It emits light of discrete wavelengths. This is called an emission spectrum or bright line spectrum.

.



So what astronomical body has this spectrum?


Starlight

Produced in photosphere - outer surface of star

- photons produced by gases deep inside star - absorbed before they can escape- low-density gas above photosphere too thin to emit significant quantities of light- photosphere dense enough to emit copious quantities of light - thin enough to allow them to escape

The spectrum of a star is an absorption spectrum

- denser layers of photosphere produce continuous - blackbody spectrum- gases in stellar atmosphere absorb specific wavelengths - form

dark absorption lines

PHYS 3380 - Astronomy Solar Spectrum

Each of the 50 slices covers 60 angstroms, for a complete spectrum across the visual range from 4000 to 7000 angstroms.


Balmer Temperature

Hydrogen emits photons in infrared, visible, and ultraviolet wavelengths - series named after scientists that studied them and came up with equation that calculated frequency of each

- Paschen - infrared- Balmer - visible- Lyman - ultraviolet

Balmer series only lines emitted by astronomical objects visible from Earth’s surface - produced by electrons in second energy level


Strength of Balmer lines gives more accurate estimation of stellar temperature

- produced by electrons in second energy level- if star is cool - most electrons in ground state

- can’t absorb photons in Balmer series - weak absorption

- if star is hot - electrons excited to high energy levels, even ionized

- few hydrogen atoms have electrons in second energy level - weak absorption

- absorption strongest at medium temperatures where most electrons in second energy level

Strength of lines of other elements also dependent on temperature -

can be used together to get accurate estimate of temperature


Spectral classes of stars - based on stellar temperature

Spectral Intrinsic Effective Class color temperature*

O electric blue 38,000B blue 30,000A blue white 10,800F yellow white 7,240G yellow 5,920K orange 5,240M red 3,920

*For the hottest spectral type in class, such as A0 in class A.

Each class is divided into 10 subgroups labeled 0 - 9. For example, B0 (hottest), or B9 (coolest) in class B.


Spectral Type Classification System

O B A F G K MOh Be A Fine Girl/Guy, Kiss Me!

50,000 K 3,000 K Temperature

Other stellar classes have be added as new stars types are discovered.

Class "W" stars are very hot stars known as "Wolf-Rayet"

Stars."R", "N", "S" stars are cool stars with particular types of molecular

bands.

"L" stars - brown dwarfs - are possibly not truly stars at all, in the sense

that they may not have nuclear reactions at their cores.


Stellar spectra - hottest stars at top, coolest stars at bottom- strongest Balmer absorption - A0


Digital spectra usually represented by line graphs of intensity vs wavelength

Hottest stars at top, coolest at bottom


The Doppler Effect


Sound

Each circle represents the crests of sound waves going in all directions from the train whistle. The circles represent wave crests coming from the train at different times, say, 1/10 second apart. If the train is moving, each set of waves comes from a different location. Thus, the waves appear bunched up in the direction of motion and stretched out in the opposite direction.

The Doppler Effect - Wavelength Shift Due to Motion.


Doppler Shift for Light

We get the same effect for light as for sound.

PHYS 3380 - Astronomy The Doppler Effect

1. Light emitted from an object moving towards you will have its wavelength shortened.

2. Light emitted from an object moving away from you will have its wavelength lengthened.

3. Light emitted from an object moving perpendicular to your line-of-sight will not change its wavelength.

BLUESHIFT

REDSHIFTREDSHIFT


v c

=

The amount of spectral shift tells us the velocity of the object:


The Doppler shift only tells us part of the object’s full motion - the radial part or the part directed toward or away from us.

PHYS 3380 - Astronomy Spectral Line Shapes

In classical picture of the atom as the definitive view of the formation of spectral lines:

- spectral lines should be delta functions of frequency - appear as infinitely sharp black lines on stellar spectra

However, many processes tend to broaden these lines - lines develop a characteristic shape or profile

- quantum mechanical effects - natural or radiation broadening- according to Heisenberg's uncertainly principle, product of the uncertainty in the measurement of energy, ΔE, and time Δt is:

- results in a natural spread of photon energies around the spectral line. The longer an excited state exists (Δt), the narrower the line width so that metastable states can have very narrow lines.- intrinsic to atom itself - natural width ~0.001 - 0.00001 nm

€

EΔt ≥h

2π


- Zeeman effect-the splitting of a spectral line into several components in the presence of a static magnetic field. - used by astronomers to measure the magnetic field of the Sun and other stars

- collisions with neighboring particles-potential of charged particles interacts with that of the atomic nucleus which binds the orbiting electrons. - perturbs the energy levels of the atom in a time-dependent fashion - broadens the spectral line.

- motions of the atoms giving rise to the line- macroscopic - highly ordered, i.e. stellar rotation -microscopic - random, i.e., thermal motions, turbulence

- Doppler broadening

Spectral Line Broadening


Collisional Broadening

Occurs when atoms absorb or emit photons while colliding with other atoms, ions, or electrons

- potential of charged particles interacts with that of the atomic nucleus which binds the orbiting electrons. - perturbs the energy levels of the atom - can absorb slightly wider range of wavelengths- dependent on temperature and density of gas

Balmer 434.0 nm line (H) from two A1 stars (same temperature)

- differences in width due to differences in density of gas


Doppler Broadening

Caused by motions of individual atoms in gas- some moving towards observer (blueshift), some moving away (redshift)- some moving faster, some moving slower- broadens spectral line- dependent on temperature

Cool gas Hot gas


Measuring Rotational Velocity

Doppler shift can be used to tell us how fast an object is rotating: As an object rotates, light from side rotating toward us is blueshifted - light from side rotating away from us is redshifted. Spectral lines appear wider - the faster it rotates, the wider are the spectral lines.


Extrasolar Planets

• Planets which orbit other stars are called extrasolar planets.

• Over the past century, we have assumed that extrasolar planets exist, as evidenced from our science fiction.

• We finally obtained direct evidence of the existence of an extrasolar planet in the year 1995.– A planet was discovered in orbit around the star 51 Pegasi.

• To date:– 1746 Confirmed Planets around 1065 Stars – 453 Systems with Multiple Planets – 4,229 Kepler Candidates


Detecting Extrasolar Planets

• Can we actually make images of extrasolar planets?– No, this is very difficult to do.

• The distances to the nearest stars are much greater than the distances from a star to its planets. – The angle between a star and its planets, as seen from Earth, is too

small to resolve with our biggest telescopes.

• A star like the Sun would be a billion times brighter than the light reflected off its planets.

• As a matter of contrast, the planet would be lost in the glare of the star.

• Improved techniques of interferometry may solve this problem someday.

Detection Methods

Astrometry - precisely measure star's position in the sky and observe the ways in which that position changes over time - gravitational influence of the planet causes the star to move in a tiny orbit about common center of mass

Radial velocity or Doppler method - variations in the speed with which the star moves towards or away from Earth deduced from the displacement in the parent star's spectral lines due to the Doppler effect. By far the most common detection method.

Pulsar timing - slight anomalies in the timing of observed radio pulses used to track changes in the pulsar's motion caused by the presence of planets.

Transit method - observed brightness of the star drops by a small amount as a planet crosses in front of its parent star's disk.

Gravitational microlensing - gravitational field of a star acts like a lens, magnifying the light of a distant background star. Possible planets orbiting the foreground star cause detectable anomalies in the lensing event light curve.

Detection Methods

Circumstellar disks - disks of space dust are detected because dust absorbs ordinary starlight and re-emits it as infrared radiation. Features in dust disks may suggest the presence of planets.

Eclipsing binary – planet detected by finding variability in light curve minima as it goes back and forth - most reliable method for detecting planets in binary star systems.

Orbital phase – observing planetary orbital phases - depends on inclination of the orbit. By studying orbital phases scientists can calculate particle sizes in the atmospheres of planets.

Polarimetry - stellar light becomes polarized when it interacts with atmospheric molecules, which could be detected with a polarimeter. So far, one planet has been studied by this method.



Doppler shift allows detection of slight motion of star caused by orbiting planet


Determining Star’s Velocity Animation


A plot of the radial velocity shifts forms a wave.

–Its wavelength tells you the period and size of the planet’s orbit.

–Its amplitude tells you the mass of the planet.

Doppler shift in spectrum of star 51 Pegasi - shows presence of large planet with orbital period of about 4 days.


Determining Planet Mass and Orbit Animation


Remember - Doppler shift only tells us radial motion. If plane of orbit perpendicular to our line of sight - no shift seen. If we view it from edge on, maximum Doppler shift seen. Orbit generally tilted at some angle - star’s full speed not measured. So mass derived from Doppler technique is minimum possible. If changing velocity and varying position in sky measured (as in one case - Gliese 876) orbital tilt can be determined and mass measured accurately. Gliese 876 is only about 15 LY away.

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PHYS 3380 - Astronomy Homework Set #5 10/01/14 Due 10/08/14 Chapter 7 Review questions 4 and 5...

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