AST 2002 Chapter Notes - Chapter 12: Open Cluster, Fusion Power, Solar Mass
Chapter 12: Surveying the Stars
12.1 Properties of Stars
• All stars have a lot in common with the sun.
• All form in great clouds of gas and dust, and each begins its life with roughly the
same chemical composition as the Sun: about three quarters hydrogen and one
quarter helium (by mass), with no more than about 2% consisting of elements
heavier than helium.
• Stars are not all the same; they differ in size, age, brightness, and temp.
How do we measure stellar luminosities?
• Brightness of a star depends distance as well as how much light it actually emits.
• When talking about how bright stars look in our sky, we are referring to apparent
brightness; the amount of power (energy per second) reaching us per unit area.
• When talking about how bright stars are in absolute sense, regardless of distance,
we are talking about luminosity, the total amount of power that a star emits into
space.
• A star’s apparent brightness in the sky depends on both its true light output, or
luminosity, and its distance from us.
• Apparent brightness of a star or any light object obeys an inverse square law with
distance, much like the inverse square law that describes the force of gravity.
• If we viewed the Sun from twice Earth’s distance, it would appear dimmer by a
factor of 2^2=4. If viewed from 10 times Earth’s distance, it would appear
10^2=100 times dimmer.
• The amount of light received per unit area decreases with increasing distance by
the square of the distance, thereby obeying an inverse square law.
• Inverse square law leads to a very simple and important formula relating the
apparent brightness, luminosity, and distance of any light source, called the
inverse square law for light.
• Apparent brightness= luminosity/ (4pi x distance^2)
• Doubling the distance to a star would decrease its apparent brightness by a factor
of 2^2 or 4.
• The units of apparent brightness are watts per square meter.
• We can always determine a star’s apparent brightness by carefully measuring the
amount of light per square meter we receive from the star.
• Then we can use the inverse square law to calculate a star’s luminosity if we can
first measure its distance, or to calculate a star’s distance if we know its
luminosity.
• Most direct way to measure a star’s distance is with stellar parallax, the small
annual shifts in a star’s apparent position caused by Earth’s motion around the
sun.
• Astronomers measure stellar parallax by comparing observations of a nearby star
made 6 months apart.
• The nearby star appears to shift against the background of more distant stars
because we are observing it from two opposite points of Earth’s orbit.
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• We can calculate the star’s distance if we know the precise amount of the star’s
annual shift due to parallax. Meaning measuring the angle p, which we call the
star’s parallax angle.
• Angle would be smaller if the star were farther away, meaning that more distant
stars have smaller parallax angles.
• Real stellar parallax angles are very small: even the nearest stars have parallax
angles of less than 1 arcsecond, well below the approximately 1-arcminute
angular resolution of the naked eye.
• The distance to an object with a parallax angle of 1 arcsecond is 1 parsec (pc),
which is equivalent to 3.26 light years.
• If we measure the parallax angle p in arcseconds, the star’s distance d in parsecs is
d=1/p; we just multiply by 3.26 to convert from parsecs to light-years.
• A star with a parallax angle p=1/10 arcsecond is 10 parsecs away, or 10 x 3.26=
32.6 light-years.
• Kiloparsecs (1000 parsecs), megaparsecs (1 million parsecs)
• We can measure the distance to a nearby star by observing how its apparent
location shifts as Earth orbits the Sun.
• If we know a star’s distance from its parallax angle, we can calculate its
luminosity with the inverse square law for light.
• Parallax measurements are the key to all other distance measurements in the
universe, because astronomers have used parallax measurements of the distances
of nearby stars to learn general properties of stars.
• Usually state stellar luminosity in comparison to the Sun’s luminosity. Lsun
• Stars come in a wide range of luminosities, with our sun somewhere in the
middle.
• Dimmest stars have luminosities 1/10,000 times that of the Sun (10^-4 Lsun)
while the brightest are about 1 million times as luminous as the Sun (10^6 Lsun)
• Dim stars more common than bright stars.
• Even though the sun is in the middle of the range of stellar luminosities, it is
brighter than the vast majority of stars in our galaxy.
• Some astronomy resources describe brightness’s and luminosities of stars by
using the ancient magnitude system devised by the Greek astronomer Hipparchus.
• Hipparchus designated the brightest stars in the sky as first magnitude, the next
brightest as second magnitude, and so on.
• The faintest visible stars were magnitude 6.
• We now call this type of designation an apparent magnitude because it describes
how bright a star appears in the sky.
• The magnitude scale runs backwards, as a larger apparent magnitude means a
dimmer apparent brightness.
• A star of magnitude 4 is dimmer than a star of magnitude 1.
• Each difference of 5 magnitudes is defined to represent a factor of exactly 100 in
brightness.
• EX: a magnitude 1 star is 100 times as bright as a magnitude 8 star.
• Stars can have fractional apparent magnitudes and a few bright stars have
apparent magnitudes less than 1- which means brighter than magnitude 1.
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• The brightest star in the night sky, Sirius, has an apparent magnitude of -1.46
• Modern magnitude system defines absolute magnitude as a way of describing
stellar luminosity.
• Star’s absolute magnitude is the apparent magnitude it would have if it were at a
distance of 10 parsecs (32.6 light-years) from Earth.
• Sun’s absolute magnitude is about 4.8, meaning that the sun would have an
apparent magnitude of 4.8 if it were 10 parsecs away from us- bright enough to be
visible but not conspicuous on a dark night.
How do we measure stellar temperatures?
• Second fundamental property of a star is its surface temperature.
• Only surface temperature is directly measurable; interior temperatures are inferred
from mathematical models of stellar interiors.
• Measuring surface temperature is somewhat easier than measuring luminosity,
because the star’s distance does not affect the measurement.
• We determine surface temperature from either the star’s color or its spectrum.
• Stars come in almost every color of the rainbow
• Just by looking at the color of the star tells us about the surface temperature.
• Red stars are cooler than blue stars.
• Stars come in different colors because they emit thermal radiation.
• Thermal radiation spectrum depends only on the surface temperature of the object
that emits it.
• Astronomers can measure surface temperature fairly precisely by comparing a
star’s apparent brightness in two different colors of light.
• EX: by comparing the amount of blue light and red light coming from Sirius,
astronomers can measure how much more blue light it emits than red light.
• Thermal radiation spectra have a distinctive shape, this difference between blue
and red light output allows astronomers to calculate a surface temperature.
• A star’s spectral lines provide a second way to measure its surface temperature.
• Interstellar dust can affect the apparent colors of stars, temperatures determined
from spectral lines are generally more accurate than temperatures determined
from colors alone.
• Stars displaying spectral lines of highly ionized elements must be fairly hot,
because it takes a high temperature to ionize atoms.
• Stars displaying spectral lines of molecules must be relatively cool, because
molecules break apart into individual atoms unless they are at relatively cool
temperatures.
• Types of spectral lines present in star’s spectrum provide a direct measure f the
star’s surface temp.
• Astronomers classify stars according to surface temps by assigning a spectral
type, determined from the spectral lines present in the star’s spectrum.
• Hottest stars, with bluest colors, are called spectral type 0, followed in order of
declining surface temp by spectral types B, A, F, G, K, and M.
• OBAFGKM, “Oh Be A Fine Girl, Kiss Me!”
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Document Summary
If we viewed the sun from twice earth"s distance, it would appear dimmer by a factor of 2^2=4. If viewed from 10 times earth"s distance, it would appear. 10^2=100 times dimmer: the amount of light received per unit area decreases with increasing distance by the square of the distance, thereby obeying an inverse square law. 32. 6 light-years: kiloparsecs (1000 parsecs), megaparsecs (1 million parsecs, we can measure the distance to a nearby star by observing how its apparent location shifts as earth orbits the sun. K to less than 3000 k, corresponding to the sequence of spectral types. Obafgkm: all stars are made primarily of hydrogen and helium and that a star"s surface temperature determines the strength of its spectral lines. How do we measure stellar masses: mass is harder to measure than surface temp or luminosity, most dependable method for weighing a star relies on newton"s version of.
