parallax the apparent motion of an object caused by a shift in the position of the observer. we can use this to measure distances.
a star's angle--or more commonly, just its "parallax"-- is conventionally defined to be half its apparent shift relative to the back ground as we move from one side of the earth's surface to the other. astronomers measure parallax in arc seconds rather than degrees. the distance from the sun that a star must be to have 1 deg of parallax is 206,265 AU or 3.1 x 10^16 m or 1 parsec. for parallels seconds. one parsec is approximately 3.3 light years.
distance in parsecs = 1
parallax (in arc seconds)
the closest star to our sun is called proxima centauri
it displays the largest known stellar parallax, .76, which means that it is about 1/.76 parsecs away 1.3 p.c. or 4.3 light years.
special equipment can be used to routinely measure parallax of .o3" or less
through the use of satellites the effective range has been extended to over 100 pc
the transverse component measures a stars motion perpendicular to our line of sight-- it measures motion across the sky.
the radial component measures the stars movement along our line of sight-- toward or away from us.
the annual movement of a star across the sky, as seen from earth is called proper motion. proper motion and transverse motion describe the same components of a stars velocity. the main difference is that transverse motion is measured in linear units, such as km/sec, and proper motion, like parallax is measured in terms of angular displacement.
speckel interferometry: the use of many short-exposure images of a star, each too brief for earth's turbulent atmosphere to smear it out into a seeing disc, are combined to make a high resolution map of the star's surface
by measuring a stars angular size and knowing its distance from the sun, astronomers can determine its radius by simple geometry.
according to stefan's law, the rate at which a star emits energy into space-- the star's luminosity is proportional to the fourth power of the star's surface temperature. However luminosity must also depend on the stars surface area, because large bodies radiate more energy than small bodies having the same temperature.
luminosity ~~(is proportional to)~~ radius^2 X temperature^4
the radius-lumonisity-temperature relationship is important because it demonstrates that knowledge of a stars luminosity and temperature can yield an estimate of its radius.
radius ~~(proportional to)~~ the square root of (luminosity)
temperature^2
giants are having a radius between 10 and 100 times that of the sun. ex. Mira, a 3000K red giant
supergiants larger stars with solar radii ranging up to 1000 solar radii in diameter
sirus A is the brightest star in the night sky.
dwarf refers to any star that has a radius comparable to or smaller than that of the sun.
because any 24000K object glows bluish-white Sirus B is known as a white dwarf.
the radius range for the vast majority of stars is form .01 solar radii to 100 time the radius of the sun.
luminosity is and intrinsic property of a star--it does not depend on the location or the motion of the observer. It is sometimes referred to as the star's absolute brightness. however, when we look at a star, we see not its luminosity, but rather its apparent brightness--the amount of energy striking unit area of some light sensitive surface or device per unit time.
apparent brightness is a function of the distance a light source is from us this can be represented by the equation: apparent brightness ~~(porprtional to)~~ luminosity
distance^2
determining a stars luminosity is a two fold task:
first astronomers must determine the star's apparent brightness (using CCD, or other instruments)
second the star's distance must be measured (parallax or other means)
the luminosity can then be found using the inverse square law.
magnitude scale: used to categorize stars by their brightness. modern astronomers have modified and extended the scale.: in this scale lower numbers denote a greater apparent brightness, and higher numbers denote a lower apparent brightness
a change of five in magnitude on the scale is said to correspond exactly to a factor of 100 in apparent brightness
because the scale uses apparent brightness rather than absolute numbers on the scale are referred to as apparent magnitudes
stars can have magnitudes that are not whole numbers ex. 4.5
magnitudes of any number are allowed.
to compare intrinsic, or absolute properties of stars, however astronomers imagine looking at all stars from a distance of 10pc. a star's absolute magnitude is its apparent magnitude when it is placed at a distance of 10pc from an observer. because distance is fixed in this definition, absolute magnitude is a measure of a star's absolute brightness and luminosity.
astronomers can determine a star's surface temperature by measuring its apparent brightness (radiation intensity) at several frequencies, then matching the observations to the appropriate black-body curve. the theoritical curve that best fits the sun describes a 5800K emitter.
because the black body curve is so well understood, astronomers can measure a stars temperature using as few as two measurements at selected wavelengths. this is accomplished by using filter in telescopes that block out all radiation except that with in a specific wavelength range.
it is possible to reconstruct an entire black body curve on the basis of those two measurements because only one curve will can be drawn through both measured points.
stellar colors and temperatures:
(surface color
temp)
30,000 K Electric blue
20,000 Blue
10,000 White
7,000 Yellow-white
6,000 Yellow
4,000 Orange
3,000 Red
the differences among the colors of stars are due almost entirely to differences in temp. not physical composition
strong absorption lines are not seen in the spectra of extremely hot stars because the atoms are ionized and there for do not have electrons to move.
astronomers classify stars according to surface temp:
using letters: O, B, A, F, G, K, M.
these stellar designations are called spectral classes.
use Oh Be A Fine Guy Kiss Me to remember them
astronomers further subdivide each class into 10 subdivisions. 0-9 the lower the # the hotter the star.
a H-R diagram plots luminosity against temperature of a graph.
expressed In solar units of luminosity. range for 10^-4 10 10^4 with the sun at
the temperatures increase to the left.
main sequence: the band of stars spanning the H-R diagram that stretches from top right to bottom left and contains most stars on the graph. can me considered normal or average
faint red M type stars (1/10th the size of the sun) are at the bottom left and bright blue O type stars are at the top right. they are about 10x the sun's size.
at one end of the H-R diagram stars are large, hot, and very luminous. Because of their size and color, they are refereed to as blue giants.
the very largest are called the blue supergiants.
at the other end, stars are small, cool, and faint. They are known as red dwarfs, they are probably the most common type of star in the sky, making up about 80%.
a white dwarf has a temperature four times that of the sun, but a luminosity much lower than that had by the sun 9% of stars.
red giants are found in the upper right hand corner of the diagram, they are relatively rare 1%, but many can be seen because they are so bright.
ninety percent of stars in our solar neighborhood lie on the main sequence.
inner planets can be radar ranged to find distance
stellar parallax can be used to distance close stars
spectroscopic parallax (refers to the whole process of using spectra to infer distances) can be used to determine the distance of further stars. a measurement of the apparent brightness of a light source, combined with some knowledge of its luminosity, can yield an estimate of its distance.
from a star's spectrum we can determine its surface temperature. If the star lies on the main sequence then there is only one possible luminosity corresponding to that temperature. this method can be used out to several thousand parsecs.
distances obtained using spectroscopic parallax are probably accurate to no more than 25%
astronomers can use spectral lines to determine weather a star lies on the main sequence. because line width is particular sensitive to density in the stellar photosphere, which is in turn closely related to luminosity. this stellar property has come to be known as luminosity class.
Ia bright supergiants
Ib Supergiants
II Bright giants
III Giants
IV Subgiants
V Main-secuence stars/dwarfs
mass and composition ultimately determine a stars position on the main sequence.
a stars mass can be measured by observing its gravitational influence on some nearby body. if we know the distance between the two we can calculate their masses.
most stars are members of multiple star systems--groups of two or more stars in orbit around one another. the majority of stars are found in binary-star systems. astronomers classify binary star systems according to their appearance from earth and the ease with which they can be observed.
visual binaries: have widely separated members bright enough to be observed and monitored separately.
spectroscopic binaries: too distant to be resolved as separate stars, but they can be indirectly perceived by monitoring the back and forth Doppler shifting of their spectral lines. in a double line spectroscopic binary, two distinct lines shift back and forth and the mass of each star can be determined. in single line systems one star is too faint for its spectrum to be distinguished. we can only see one set of lines shifting back and forth. in this situation we can only determine the combined mass of the two stars. the shifting indicates to us that the star must be in orbit around another star.
in much less common eclipsing binaries, the orbital plane of the pair of stars is almost edge on to our line of sight. in this situation, we observe a periodic decrease in starlight intensity as one member of the binary passes in front of the other. by studying the variation of the light from an eclipsing binary system-- called the binary's light curve--we can derive detailed information not only about the star's orbits and masses but also their radii. note that a star that belongs to the last category will also belong to one of the others.
with few exceptions, the main sequence stars range in mass from about .1 to 20 times the mass of the sun. the hot O and B type stars are generally 10 to 20 times more massive than our sun.
the mass of a star at its time of formation determines its position on the main sequence
as a rule of thumb, radius rises ion direct proportion to mass, whereas luminosity increases much faster--more like the cube of the mass.
stellar lifetime ~~(proportional to)~~ stellar mass
stellar luminosity
if we observe a group of stars that all lie in the same distance from us, then comparing apparent brightness is equivalent to comparing absolute brightness. Because as radiation travels to earth, the brightness of every star is reduced by the same amount according to the inverse square law.
such an easily recognizable group of stars is called a star cluster. all stars in a given cluster formed at the same time out of the same cloud of interstellar gas, and under the same environmental conditions. the only factor distinguishing star in a cluster from another is mass.
open cluster: a type of loose irregular cluster, found mainly in the strip across the sky known as the Milky Way. open clusters typically contain from a few tens to a few thousands of stars and are a few parsecs across.
globular cluster: tightly knit, roughly spherical, can contain millions of stars. over about 50pc. like open clusters the whole group is held together by gravity. these clusters lack O and B stars in fact they contain no main sequence stars with masses greater than about .8 times that of the sun. apparently globular clusters formed long ago; and the more massive stars have already exhausted their nuclear fuel. and disappeared from the main sequence. on the basis of these and other observations astronomers estimate that globular clusters are at least 10 billion years old. they contain the oldest stars in the galaxy.