Transcript: Since light has a finite speed, three hundred thousand kilometers per second, there’s an inevitable consequence called light travel time.  In terrestrial environments light essentially travels instantly or appears to travel fast.  The finite speed of light, three hundred thousand kilometers per second, has a consequence called light travel time.  On the Earth, light essentially travels instantly.  It takes light eight minutes to reach us from the Sun, so technically we are seeing the Sun as it was eight minutes ago.  In the solar system it takes light hours to travel through the solar system.  However, the distance to nearby stars is hundreds of thousands of times larger than the size of the solar system.  Even the nearest star, Proxima Centauri, has a distance of 4.3 lightyears.  This means we see Proxima Centauri as it was four and a third years ago.  Polaris, the pole star, is at a much larger, distance 650 lightyears.  Thus, we see Polaris as it was in the 1300s.  If Polaris exploded we would not know about it until after 2600 A.D.

Light Travel Time

Transcript: Some stars in the sky, somewhat hotter than the Sun with temperatures of 5 thousand to 10 thousand Kelvin, have very low luminosities in the range of one-hundredth to one-thousandth the Sun’s luminosity.  Application of the Stephan-Boltzmann Law shows that they must be physically small with sizes less than a tenth the size of the Sun, perhaps as low as one-hundredth the size of the Sun.  These stars are called white dwarfs.

White Dwarf Stars

Transcript: Certain rare stars in the sky with either red or blue colors are extremely luminous, up to a million times the luminosity of the Sun.  Application of the Stephan-Boltzmann Law shows that their sizes must be in the range of ten to a thousand times the size of the Sun.  These exceptional stars are called supergiant stars.  Some are hot and blue, and others are cool and red.  Although in each case the color only refers to the outer nebulous atmosphere of the star, the centers are much hotter.

Super Giant Stars

Transcript: A cool main sequence star with a temperature of about three thousand Kelvin lies on the main sequence with a luminosity of about a hundredth the luminosity of the Sun and a size about a quarter the Sun’s size, but there are stars with the same temperature, or color, as the Sun that are much more luminous, up to ten thousand times the luminosity of the Sun or even more.  Betelgeuse and Antares are two well known examples.  Application of the Stephan-Boltzmann Law shows that these stars must have sizes that are several hundred times the Sun’s size.  These are called red giant stars.

Giant Stars

Transcript: As was first seen nearly a hundred years ago, when luminosities and effective temperatures are gathered for hundreds of stars near the Sun, the result is not a scatter plot.  Most stars in the H-R diagram lie on a diagonal line or track that runs from hot, luminous, and blue stars in the upper left corner down to cool, faint, and red stars in the lower right corner.  Stars with these properties are called main sequence stars.  The main sequence runs across the H-R diagram, and it represents all stars that get their energy from the fusion of hydrogen into helium.

Main Sequence Stars

Transcript: The H-R diagram is a plot of spectral class, or equivalently effective temperature, against stellar luminosity.  The Stephan-Boltzmann Law tells us that luminosity goes as a high power of the temperature, the fourth power, and this is seen in the H-R diagram where the full range of the diagram is only about a factor of 20 in temperature but a factor of 108 or a hundred million in luminosity.  Lines of constant radius can also be represented on the H-R diagram according the Stephan-Boltzmann Law.  They are diagonal lines on the diagram which tell us the difference between giant stars, main sequence stars, and dwarf stars.

HR Diagram and Stellar Size

Transcript: As a way of exploring stellar properties and understanding how stars work, in the early twentieth century two astronomers, the Danish astronomer Ejnar Hertzsprung and the American astronomer and Henry Norris Russell, experimented with plotting spectral class for stars against their luminosity.  They saw patterns in the ways stars appeared in this plot which led them towards an idea of how stars work.  This is called the H-R diagram or the Hertzprung-Russell diagram, and it’s a key tool of stellar astronomy.  In a typical H-R diagram the y-axis is luminosity, which runs from about 106 solar luminosities, or an absolute magnitude of -10, down to about 10-4 solar luminosities, an absolute magnitude of plus 15.  The x-axis is temperature, photospheric temperature, or spectral class running from O stars, traditionally plotted on the left side, at temperatures of forty thousand Kelvin down to N stars with temperatures of twenty-five hundred Kelvin.

Hertzsprung-Russell Diagram

Transcript: A human lifetime is a blink of an eye compared to the age of the stars which can be hundreds of millions or billions of years.  So how is it possible for astronomers to understand the life process of a star, to see their birth, death, and life?  Consider an analogy of an intelligent ant living in a forest who lives a very short time but observes the diversity of nature.  For instance, there are tall trees and short trees, saplings, fallen logs.  Some of the falling logs have been helped by insects to decay back into Earth itself.  Could a short living intelligent ant deduce the life cycle of the forest from sapling up to tall tree, to fallen log, and then back to Earth by observations over a short period of time?  This is the situation astronomers find themselves in.

Stellar Evolution

Transcript: Classification is often an important first step towards physical understanding.  Imagine you lived in a small town and did a survey where you gathered information on every inhabitant, three pieces of information: their age, their height, and their weight.  If you plotted height against weight you would notice an obvious trend, height and weight are correlated.  Most people would fall on a particular track in a diagram of height plotted against weight.  Some combinations are never seen; you would not have someone who is 3 feet high and 300 pounds nor someone who is 6 feet high and 60 pounds.  The pattern will be telling you something.  In this case the pattern reveals age because babies obviously grow into children who grow into larger people, and so height and weight are correlated with age.  In the case of stars, a similar situation is applied because astronomers did not know the fundamental nature of stars when they first started observing them, and they used stellar classification to get a start.

Stellar Classification

Transcript: Stars are stable.  For most of their lives, fusion provides the energy source.  Even though the Sun and other stars are fusing hydrogen into helium, it does not mean that they are bombs.  The Sun will be stable for billions of years.  Stars also do not cool off.  Energy flows continuously from the core where fusion occurs to the outer cooler regions.  At every point within a stable star there’s an energy balance between two forces: the inward force of gravity and the outward pressure caused by energy release from nuclear reactions.  This balance is called hydrostatic equilibrium.

Hydrostatic Equilibrium

14. Stars 1

Transcript: A parsec is a distance unit appropriate to the study of stars.  It’s the distance that produces a parallax shift of one arcsecond.  In other words, it’s the distance where the angle subtended by the star as seen from the Earth’s orbit six months apart, spanning the orbit, is one second of arc.  One parsec equals 3.26 lightyears, so a parsec is slightly larger than a lightyear.  Astronomers also use multiples of the parsec, a thousand parsecs, which is a kiloparsec, and a million parsecs, which is a megaparsec.  The most useful thing about the parsec unit is that it corresponds to the typical distances between stars in the Milky Way Galaxy.

Parsec

Transcript: Apparent brightness does not express a star or other source of light’s true energy output.  Astronomers are more interested in absolute brightness or equivalently absolute magnitude or luminosity.  For example, we can consider a situation where the apparent brightness of a 100 watt light bulb at a distance of 100 meters is actually the same as the apparent brightness of a dim, 1 watt nightlight at a distance of 10 meters, and both of those are the same at apparent brightness as an arc lamp of 10,000 watts at a distance of a kilometer.  The three are obviously hugely different situations in terms of the intrinsic emission of light, and yet the apparent brightness of all three is the same.  This is the situation astronomers find themselves in.  Stars are not all 100 watt light bulbs, nor do they have their brightness written on them.  And so astronomers try to use absolute brightness but find that it’s a very poor reflection of true brightness or distance.

Absolute Brightness

Transcript: The vast distances to the nearest stars encourage astronomers to use a new unit of distance.  Whereas meters and kilometers work well on the Earth, and the astronomical unit is the appropriate unit for scales within the solar system, the distance scale to the stars is given as a lightyear.  A lightyear is the distance that light travels in one year.  It’s equal to about 6-million-million miles or 1016 meters.  It’s defined as the speed of light, three hundred thousand kilometers per second, times the number of seconds in a year.  Notice two things.  The lightyear is not a metric unit.  Occasionally astronomers use none metric units when they are convenient for the scales they’re dealing with, and also a lightyear is a unit of distance, not a unit of time.

Light Year

Transcript: Nearly 2,000 years ago Ptolemy's Almagest, a compendium of astronomical information, contained catalogs of star names.  Ancient knowledge was brought to Europe by Arab astronomers who gave names to many of the brightest stars in the sky.  The Arab article is al and so we have Algol, Aldebaran, Altair, Alcor, and others.  Other stars were named from myths and legends and are often given names associated with the constellation in which they reside.  Thus, Alpha Centauri is the first star named in the Centaur constellation; Delta Scuti is the fourth star named in the shield constellation.  Other catalogs exist too; T Tauri is the twentieth variable star in the constellation the bull.  Astronomers name fainter stars by their coordinates and are given numbers rather than names, and despite what you may read in some parts of the popular press, it’s not possible to exclusively buy a star name.  Star names are given by the International Astronomical Union.

Star Names

Transcript: Almost all of the world’s energy comes from non-renewable sources or fossil fuels.  These energy sources took 300 million years to aggregate on the Earth, originating with solar energy and living organisms.  We have significantly depleted them in only one hundred years.  Modern energy usage is very inefficient; the United States wastes energy equivalent to $300 billion a year.  The standard modes of energy use are also inefficient.  An incandescent light is only five percent efficient, the internal combustion engine only ten percent efficient.  However, clean and efficient energy sources do exist.  They are cosmic fuels.  The first is solar energy itself.  Solar cell technology has now improved to the point where solar cells are about fifty percent efficient which is ten times more efficient than an incandescent light bulb.  Fuel cells is the other possible technology.  Fuel cells create energy from hydrogen, the ultimate cosmic fuel, the most abundant element in the universe and a clean energy source.  Fuel cells are also approaching fifty percent in their efficiency.

Cosmic Energy Sources

Transcript: Most stars are very different in chemical composition from you, or I, or the material on the Earth.  The Sun for example, of every 10 thousand atoms has 74 hundred hydrogen atoms, 24 hundred helium atoms, and 150 or so corresponding to all the other elements in the periodic table; for example, there are only three carbon atoms, two nitrogen atoms, and five oxygen atoms out of that 10 thousand.  Contrast that with human material which of course is mostly water.  Out of every 10 thousand atoms in the human body 62 hundred are hydrogen, 11 hundred carbon, 200 nitrogen, and 25 hundred oxygen; only two are helium.  Humans have vastly more carbon, nitrogen, and oxygen than typical stellar material.

Stellar Composition

Transcript: The way astronomers observe and calibrate the apparent brightness of something is through the technique of photometry.  Photometry allows astronomers to measure the number of photons per second coming from an astronomical source in some specified wavelength range or pass band that’s defined by a filter.  A filter is simply a colored piece of glass sitting above the CCD detector in a telescope that isolates a narrow range of wavelength.  CCD detectors are sensitive to a wide range of wavelengths, and so the pass band must be specified by a separate optical element.  Most photometry is done at optical and near infrared wavebands, so some of these wavebands are beyond the sensitivity of the human eye.  The traditional wavebands are named after letters that do not follow the alphabet, they exist for historical reasons.  In the optical bands we have U, B, V, R, and I at 350, 450, 550, 700, and 850 nanometers, and in the near-infrared the J, H, and K pass bands at 1.25 microns, 1.65 microns, and 2.2 microns.  Relative brightness in absolute units is then determined by measuring bright stars where the absolute brightness has been measured by spacecraft.

Photometry

Transcript: The first direct estimate of stellar distances used geometry.  In 1838, Friedrich Bessel measured the parallax of the bright star 61-Cygni.  This is the seasonal shift in the apparent position of the star on the sky relative to more distant stars as the Earth travels its orbit of the Sun.  The shift was only 0.6 seconds of arc, a very small effect, which is in part why it took two hundred years of telescopic observations before parallax to any star was measured.  Here, however, was finally a direct measure of the distance to the stars showing that the stars were indeed hundreds of thousands of times further away than the Sun itself.  The formal equation that gives the distance to the stars in terms of parallax is that the distance in astronomical units is roughly two hundred thousand divided by the parallax angle in arcseconds, or the distance in parsecs equals one over the parallax angle.

Parallax Distance

Transcript: The magnitude scale is defined in such a way as a magnitude difference of five magnitudes corresponds to a factor of a hundred in apparent brightness.  Two and a half magnitude difference corresponds to a factor of 10 in apparent brightness.  Lower numbers in the magnitude scale are brighter, which is of course the opposite of a scale set by the number of photons per second.  Zero on the magnitude scale is defined by the bright star Vega.  The magnitude scale can be illustrated by some magnitude differences and corresponding brightness ratios of typical situations.  Two bright stars that are identical, seen at the same distance, have a magnitude difference of zero; their brightnesses are equal.  Magnitude difference of one, or a factor of 2.5 in apparent brightness, is the minimum difference visible by eye between stars in the night sky.  Magnitude difference of 4, or a brightness ratio of 40, corresponds to the limit of the naked eye relative to binoculars.  Magnitude difference of 5, or a factor of 100, is a range between the brightest and the faintest stars in the sky.  A factor of 104, or 10 magnitudes, is the ratio between the full moon and Mars.  Fifteen magnitudes, or a factor of 106 in apparent brightness, is the ratio between the brightest star and Pluto.  Twenty magnitudes, or 108 in apparent brightness, is the limit between binocular vision and the Hubble Space Telescope, and twenty-five magnitudes, 1010 in apparent brightness ratio, is the ratio between the Sun and the brightest star in the night sky.

The Magnitude Scale

Transcript: Apparent magnitude or apparent brightness must be specified at a particular wavelength.  Stars have different colors or different energy distributions, so the apparent brightness depends on the wavelength of observation.  Traditionally, astronomy is done by eye, and the detector was the visual detector which is the wavelength sensitivity of the human eye peaking somewhere in the green part of the visual spectrum.  This is called visual apparent brightness or visual magnitude.  Professional astronomers have, however, more carefully defined the wavelength scales that they use when measuring astronomical objects.  They’ve used filters to isolate relatively small ranges of wavelengths, and they define magnitudes or apparent brightness in terms of those narrow wavelength ranges.

Visual Magnitude

Transcript: We can use relative brightness to show how bright various objects in the night sky are compared to the limits of technologies we use to observe the sky.  In units where Vega, the bright star, is one unit of apparent brightness, the Sun is 40 billion times brighter.  The full moon is 100 thousand times brighter than Vega, and for reference a 100 watt light bulb at a distance of 100 meters is 27,700 times brighter than Vega.  Venus at its brightest is about 60 times brighter than the star Vega, Mars 12 times brighter, and Jupiter about 4 times brighter.  The bright star Sirius is 3.5 times brighter than Vega.  The limit of observation in cities with the naked eye, in units where Vega is one, is 0.025.  That is, that we can see 40 times fainter than Vega.  In a remote rural area the limit may be ten times less than that, 400 times fainter than Vega.  Neptune on the same scale in the same units is 0.0008, a thousand times fainter than the bright star Vega.  The limit of binoculars is about 6 timse 10-6 in these units, 100 thousand times fainter than the bright stars, and the limit of the Hubble Space Telescope in the same relative units is 3 times 10-12.  The Hubble Space Telescope can see about a trillion times fainter than the brightest star in the sky.

Relative Brightness

Transcript: The apparent brightness of the Sun is a factor of 1010 or 10 billion times brighter than the brightest stars in the night sky like Vega, or Canopus, or Sirius.  If we assume that the Sun and the stars are intrinsically the same type of object, that is they emit the same number of photons per second, we can use the inverse square law to say what the relative distance is to the stars and the Sun is.  It must be a factor of the square-root of 1010 or 105. The stars are therefore roughly 105 or 100 thousand times further away than the Sun is from us.  That’s 105 times 108 or 1013 kilometers, 10 trillion kilometers, or about a third of a parsec.  Thus, this simple assumption gives us a rough estimate of the huge distance to the stars.  We can compare the Sun and the stars directly through the medium of an equivalent light bulb of 100 watts.  The Sun is like a 100 watt light bulb at a distance of 3 inches from your eye, very intense, don’t ever try that, whereas the brightest stars in the night sky are like 100 watt light bulbs at a distance of about 9 kilometers.  That is a reading light at a distance of 5 miles.  This gives a sense of the enormous range of apparent brightness between the Sun and even the nearest stars.

Stars as Suns

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