The apparent shift in a nearby star's position on the celestial sphere resulting from the Earth's orbit around the sun; the  motion of nearby stars among the background of more distance stars due to Earth's motion around the Sun

Example: Proxima Centauri is closer to us than other stars, and its position among the background stars changes as the Earth orbits the sun

Formed between your eyes and the object; lets your brain judge how close you are to the object

Distance to a star in parsecs

d=1/p

d=distance to stars in parasecs

p=parallax angle of star in arcseconds

precision of stellar parallax measurements is limited by angular resolution of telescope

parallax angles smaller than .01 arcsecs difficult to measure from Earth 

Brightness of stars without regard to their distances;a measure of the brightness of light from a star or other object as seen from Earth

Brightness of star indicated by a number, brightest stars were 1: example: m=+1 etc.

  Later, astronomers discovered some stars to be brighter than the original apparent magnitude (or the +1 stars) and so, negatives came into play

Sirius, the brightest star in the universe, has m=-1.44, Venus m=-4.4, Moon m=-12.6, and Sun m=-26. 

The apparent magnitude that a star would have if it were 10 parsecs from Earth

If you have one star, and another that is twice the distance from the first, the star twice the distance will be much dimmer

The gravitational attraction between two objects and the apparent brightness of a ligth source are both inversely proportional to the square of its distance

Apparent brightness decreases inversely with the square of the distance between the source and the observer

Total amount of electromagnetic power (energy emitted each second); the rate at which electromagnetic radiation is emitted from a star or object; total amount of energy emitted by a star each second

Luminosity of Sun represented by L

Luminosities range from 106L to 10-5L

Depends on stellar size and temperature

-higher luminosity, brighter an object is (smaller, or more negative a stars absolute magnitude is, the greater its luminosity)

-luminosity expressed in multiples of the Sun’s luminosity

Stars behave much like black bodies, and so surface temperatures determines their color

-Cool stars peak at long wavelengths, so they look red

-Hot stars peak at short wavelengths, so they look blue

Wien’s Law (wavelength of emitted by a blackbody varies with its temperature)

But, both are affected by absorption lines in the spectrum and extinction

The measurement of light intensities

telescope collects starlight that is then passed through one of a set of colored filters and recorded on a CCD, providing the peak of the star’s blackbody spectra, and hence the temperature of the star

                -Filters light through different radiation (such as ultraviolet , blue filters etc.)

                -Hotter stars are bright in ultraviolet-filters, dim in blue, and dimmer in yellow

                -Cool stars visible in red filters (dimmer in yellow and blue)

The study of properties of stars encoded in their spectra; determining a stars temperatures by studying its spectrum

-begin by taking the spectrum of star and then identifying and discarding spectral lines due to interstellar gas and Earth’s atmosphere---left are spectral lines  created in star’s atmosphere

                -hydrogen makes up about ¾ of a stars mass, but they don’t always show up strongly on the spectrum because the strength depends on the star’s temperature

visible hydrogen lines

-explained because balmer lines are produced when photons excite electrons in the second energy level to a higher level. Stars with higher temperatures absorb enough energy from photons to go through this process, producing the strongest balmer lines

                -but balmer lines are dim (or weak) also if the temperature exceeds 10,000 K because high-energy photons simply strip away electrons from most of the hydrogen atoms

The grouping of similar spectra into classes

types today are : OBAFGKM “Oh, Be A Fine Guy(Girl), Kiss Me!”

                -hottest are type O, M are coolest

Each Spectral type is broken into 10 temperature subranges (0 hottest, 9 coolest)

                Example: A8 is hotter than A9, which is hotter than F0

Hertzsprung-Russel Diagram or H-R diagram

Graphs of stellar lumniosity (or absolute magnitude) against surface temperature

shows surface temperature (spectral type) and luminosity are correlated, not random

bright stars near top, dim near bottom, hotter stars to the left, cooler to the right

A grouping of stars on the H-R diagram extending diagonally across the graph from hottest, brightest stars to the dimmest, coolest stars

most of the stars we see in the night time sky on the H-R diagram

extends from hot, bright, bluish stars in upper left down to cool, dim, reddish stars in lower right

number of main-sequence stars decreases with increasing temperature

                -M, K, G stars most common, O rare

A star, fusing hydorgen to helium in its core, whose surface temperature and luminosity place it on the main sequence on the H-R diagram

90% of stars

 The greater the temperature the more luminous the star

spans range from hot, bright stars to cool, dim stars.

A star whose diamter is roughly 10 to 100 times that of the Sun

A star of very high luminosity; a star even bigger than a giant star

make up top of the H-R diagram 

combined with giant stars make up less than 1% of the stars in our vicinity 

 very bright and very large stars across the range of temperatures

A low-mass stellar remnant that has exhausted all its thermonuclear fuel and contracted to a size roughly equal to the size of the Earth

stars that are hot, dim, and tiny compared to the sun.

roughly the size of earth, can only see with the aid of telescope

only remnants of stars

A dark line in a continuous spectrum created when photons are removed from the continuum

Studying absorption lines more accurate than luminosity and temperatures because absorption lines are affected by density and pressure of the gas in a star’s atmosphere, both of which determined what type of star it is

Most stars approximately the size of the sun

The classification of a star of a given spectral type according to its luminosity and desnity; the classes are super giant, bright giant, giant, subgiant, and main sequence

categorizes stars by their type (roman numerals I-V)

                -super giants Ia and Ib

                Giants : II III IV

                Main sequence stars V

                -white dwarfs don’t get a category because they are not creating enough energy by fusion

1; observe star’s apparent magnitude and spectral type

2. from spectrum, determine what luminosity class the star belongs to

3. spectrum also provides absolute magnitude

4. Use distance-magnitude relationship to determine distance of star

 Finding absolute magnitude and luminosity from the H-R diagram

Downfalls:

  -limited in accuracy because of the spread of stars in each luminosity

                -limited in that spectra of distant stars become increasingly hard to determine

                -errors of 10% are common

But can be used for stars at much farther distances than those by stellar parallax

Stellar Mass

How to Find it

-In order to find stellar mass, the star must be orbiting something else

                -must use Newton’s 3^rd law to determine this

                -2/3 of stars in our solar system orbit another star

When two stars appear to be in the same location, but are in fact nowhere near each other...they simply lie in the same direction from Earth

-Mainly can only determine if a star is a binary if it is close to Earth, or if the stars are separated by a great distance

But spectroscopy can help!

                -on spectrum of a binary star, strong absorption lines of say, helium, may appear along with strong lines for titanium. Both cannot be true of one star, because titanium (common in cooler stars) would not be present if the star were hot enough to produce helium, indicating binary stars!

A double star in which the two components can be resolved through a telescope; both stars can be seen through the telescope

The sum of masses = the cube of semimajor axis

                                                The square of the orbital period

Heavier star closer to the center of mass

                M1 + M2 =a^3/P^2

P=orbital period

M1 and M2= two masses of stars

A= length of semimajor axis of the ellipse

Trend: More massive a star is, the more luminous

Demonstrate that the main sequence on the H-R diagram is a progression of mass as well as in luminosity and surface temperature; the direct relationship between the masses and luminosities of the main-sequence stars

Hot, bright, bluish stars in upper left are the most massive main-sequence stars

Dim, cool, reddish stars in lower right corner are smallest

But spectroscopy can help!

                -on spectrum of a binary star, strong absorption lines of say, helium may appear along with strong lines for titanium. Both cannot be true of one star, because titanium (common in cooler stars) would not be present if the star were hot enough to produce helium, indicating binary stars!

Spectroscopy can also determine movements of stars orbiting each other because of Doppler shift

                -approaching source has shorter wavelengths  (blue)

                -receding source has longer wavelengths (red)

                -the greater the speed, the greater the shift

Radial Velocity: The portion of an object's velocity parallel to the line of sight

Radial Velocity Curve: A plot showing the variation of radial velocity with time for a binary star or variable star; displays orbital velocities of stars in spectroscopic binary

Radial Motion/Velocity

Detected when the stars cannot be resolved as two distinct images

                -apparent magnitude of the image dims each time one star blocks out part of the other

Can be used to determine stellar atmospheres…

if close enough, stars affect each other –big star might give some of its mass to the smaller star etc.

Closest stars measured using parallax

Parallax is only accurate for the nearest ~120,000 stars (out of 200 billion in Milky Way)

1 parsec = 1 parallax arcsec~ 3.26 light years

Transverse (Proper) Motion

The higher the temperature, the greater the luminosity

The larger the star, the greater the luminosity