exam 2 Flashcards
Luminosity
total amount of energy at all wavelengths that a star emits per
second.– absolute brightness - is a property of the star. It is a measure of the total
power radiated from the star (wattage). Absolute brightness does not change with distance.
apparent brightness (luminosity/distance^2)
the amount of a star’s energy that reaches a given area each
second here on Earth– how bright a star appears to be. This depends on the
distance away and the absolute brightness.
For two stars of the same apparent brightness, the star closer to the Sun will generally have
. a lower luminosity
Magnitude Scale
Magnitude 1 stars are 100 times brighter than magnitude 6 stars.
Thus each division on the magnitude scale changes brightness by about a
factor of 2.5.
Apparent Magnitudes
Use of telescopes to see brighter and fainter
objects has expanded the scale.
Note - negative apparent
magnitudes are brighter!
Changing the distance of a star by a factor of 10
decreases it brightness by a factor of 100 - thus
increases it apparent magnitude by 5 units.
Magnitude equation
apparent magnitude- absolute magnitude = 5log(distance/10 parsecs)
A star has an apparent magnitude 10.0 and an absolute magnitude 2.5.
How far away is it? How does its luminosity compare to the Sun’s?
10-2.5=5log(distance/10)->10^1.5=distance/20-> 316
Which of the following quantities do you need in order to calculate a star’s luminosity?
apparent brightness & distance to the star
Colors of Stars
Stars are not all the same color because they do not all have identical
temperatures. the hottest stars have temperatures of over 40,000 K, and the
coolest stars have temperatures of about 2000 K. Our Sun’s
surface temperature is about 6000 K
Stellar Spectra
more informative than blackbody curves Measuring colors is only one way of analyzing starlight. Another way
is to use a spectrograph to spread out the light into a spectrum
O B A F G K M
Using Stellar Spectra
Analyzing the spectrum, we can infer:
* Star size
* Composition
* Radial velocity
* Rotation
Stellar Spectra - size
A giant star has a large, extended photosphere, thus the gas will have a low
density, therefore, the pressure in the photosphere will be low as well!
A star with a lower-pressure photosphere shows
narrower spectral lines than a star of the same
temperature with a higher-pressure photosphere
More atoms are ionized in a giant star than in a
star like the Sun with the same temperature, and
ionized atoms have different spectra from atoms
that are neutral.
Stellar Spectra - composition
Absorption lines of a majority
of the known chemical
elements have now been
identified in the spectra of
the Sun and stars. If we see
lines of iron in a star’s
spectrum, for example, then
we know immediately that
the star must contain iron.
Stellar Spectra - velocity
Doppler effect of spectral lines yields clues about the relative velocity of the star
We should see all the spectral lines of
moving stars shifted toward the red end of
the spectrum if the star is moving away
from us, or toward the blue (violet) end if it
is moving toward us
proper motion
proper motion, is transverse: that is, across our line of
sight.
Stellar Spectra - rotation
We can also use the Doppler effect to measure how fast a star rotates
If an object is rotating, then one of its sides is approaching us while the
other is receding rotating toward us are shifted to shorter
wavelengths and the lines in the light from the
opposite edge of the star are shifted to longer
wavelengths.
A stellar census
there are
many more lowluminosity (and hence low
mass) stars than highluminosity ones. Only three of
the stars in our local
neighborhood
Measuring stellar masses
The mass of a star - how much material it contains - is one of its most important
characteristics
binary stars
The first binary star was discovered in 1650. About half the stars are binary
stars, two stars that orbit each other,
bound together by gravity. Masses of
binary stars can be calculated from
measurements of their orbits can be seen with
a telescope is called a visual
binary. but which spectroscopy
shows really to be a double star, is
called a spectroscopic binary.
Masses of binaries
We can estimate the masses of binary star systems using Newton’s
reformulation of Kepler’s third law
Mass-Luminosity relation
The more massive stars are generally also the more luminous The mass-luminosity
relation reads:
L ∝ M^3.9
A binary star system:
Is composed by two stars
Is held together by gravity
Is useful to find the mass of the component stars
Is not always visually detectable
Stellar size
observe the dimming of light that occurs
when the Moon passes in front of a star Accurate sizes for a large number of stars come
from measurements of eclipsing binary star
systems: stars that are lined up in such a way
that, when viewed from Earth, each star passes
in front of the other during every revolution
Radiation law:
Another method for measuring star diameters makes use of the StefanBoltzmann law for the relationship between energy radiated and temperature
Most nearby stars are roughly the size of the Sun, with typical diameters of
a million kilometers or so. Faint stars are generally smaller than more
luminous stars. However, there are some dramatic exceptions to this
simple generalization.
F = σT^4
The H-R Diagram
H–R diagram plots stellar luminosity versus surface temperature.
With just a few stars plotted, no relationships (groups) are obvious.
However, when many stars are plotted…
vertical axis:
Luminosity in solar units (L⦿)
L⦿=3.9E26 W
horizontal axis:
Surface Temperature (K)
and
Spectral Class
T⦿~6000 K, G2
The H-R Diagram
The darkened curve is called the main
sequence, as this is where most stars are. the white dwarf region;
these stars are hot but not very luminous, as
they are quite small. Clearly, the brightest stars in the sky appear
bright because of their enormous
luminosities, not their proximity. *90 percent of stars lie on
the main sequence
* 9 percent are red giants
* 1 percent are white dwarfs
What are the two most important intrinsic properties for classifying stars?
luminosity and surface temperature
Measuring Distances
The “distance ladder” depicts
methods depending on how far
away the object is. Use triangles (parallax).Bounce E&M radiation off the object
parallax
Apparent motion of object against distant background from
two vantage points. Determining the Parallactic Angle( )
Use telescope to measure shift.
Determine from half of measured shift
Use s=1 AU for baseline
How many radians in 60 degrees?
pi/3
parsec
parsec = d=1/theta(arc second)
If the parallax of a star is measured to be 0.1 seconds of arc, its distance is
10 parsecs d=(1/0.1)
How big is a parsec?
Find the distance d (parsec) for an angle of 1” using a baseline of 1 AU. parsec = 3.11 × 10^16 m
1 pc = 3.3 ly
Recall Earth is ~ 8 light-minutes from the Sun
Spectroscopic Parallax
1) measure the apparent magnitude and spectral
class (temperature) without knowing distance.
2) assume the star lies on the main sequence - this
gives absolute magnitude (luminosity).
3) apply inverse square law to determine distance.
The width of spectral lines determines a stars luminosity class.
Spectral Class - which lines are present gives temperature.
(OBAFGM)
The widths of the absorption line depend on
the pressure in the stellar atmosphere.
Spectral Class - which lines are present gives temperature.
(OBAFGM)
a denser atmosphere creates broader
absorption lines
The atmospheres of red giants are less dense than
main sequence stars which are less dense than white
dwarfs. So pressure (line width) gives me radius.
Stellar Luminosity Classes
Well developed spectral analysis system differentiates star classes.
luminosity ∝ radius^2 × temperature^4
For stars with the same temperature - the line width can
give radius which leads to a determination of luminosity.
Variable stars
Some stars are seen to vary in brightness and, for this reason, are
called variable stars.
Variable stars
Figure out the intrinsic
luminosity, compare it to the
observed brightness, and find
the distance!
overlay of same field of view -
shifted to compare pairs of stars
Variable stars have a known
relationship between
period of variation and
intrinsic luminosity!
The variability of these stars comes from a dynamic balance between gravity and
pressure – they have large oscillations (in size) around stability.
Oscillations is size produce
oscillations in luminosity!
Light Curve
A graph that shows how the brightness of a variable star changes with time is
called a light curve - The maximum is the point of the light curve where the star has its
greatest brightness; the minimum is the point where it is faintest. If the
light variations repeat themselves periodically, the interval between
the two maxima is called the period of the star.
RR Lyrae stars
All such stars have
essentially the same luminosity curve, with
periods from 0.5 to 1 day. stars all have about the same
luminosity; knowing their apparent
magnitude allows us to calculate the
distance.
Cepheid variables:
Cepheid
periods range from about 1 to 100
days. have a luminosity that is
strongly correlated with the period of
their oscillations; once the period is
measured, the luminosity is known and
we can proceed as above.
Distance Ladder
Measuring variable stars luminosity via
the light-curve time period expands
our ability to measure distances out
to 25 Mpc (83 million ly)
