Absolute magnitude
the apparent magnitude that a star would have if it were 10 parsecs from Earth
apparent magnitude
a measure of the brightness of light from a star or other object as seen from Earth
binary star
two stars revolving about each other; a double star
center of mass
the point around which a rigid system is perfectly balanced in a gravitational field; also, the point in space around which mutually orbiting bodies have elliptical orbits
close binary
a binary star whose members are separated by a few stellar diameters
eclipsing binary
a double star system in which stars periodically pass in front of each other as seen from Earth
giant star
a star whose diameter is roughly 10 or 100 times that of the Sun
Hertz sprung-Russell (H-R) diagram
a plot of the absolute magnitude or luminosity of stars versus their surface temperatures or spectral classes
initial mass function
the numbers of stars on the main sequence at all different masses
inverse-square law
the gravitational attraction between two objects is inversely proportional to the square of their separation; also, the apparent brightness of a light source is inversely proportional to the square of its distance from an observer
light curve
a graph that displays variations in the brightness of a star or other astronomical object over time
luminosity
the rate at which electromagnetic radiation is emitted from a star or other object
luminosity class
the classification of a star of a given spectral type according to its luminosity and density; the classes are supergiant, bright giant, giant, sub giant, and main sequence
main sequence
a grouping of stars on the Hertz sprung-Russell diagram extending diagonally across the grape from the hottest, brightest stars to the dimmest, coolest stars
main-sequence star
a star, fusing hydrogen to helium in its core, whose surface temperature and luminosity place it on the main sequence on the Hertz sprung-Russell diagram
mass-luminosity relation
the direct relationship between the masses and luminosities of main-sequence stars
OBAFGKM sequence
the sequence of stellar spectral classifications from hottest to coolest stars
optical double
a pair of stars that appear to be near each other but are unbound and at very different distances from Earth
photometry
the measurement of light intensities
radial-velocity curve
a plot showing the variation of radial velocity with time for a binary star or variable star
red giant
a large, cool star of high luminosity
spectral type
a classification of stars according to the appearance of their spectra
spectroscopic binary
a double star whose binary nature can be deduced from the periodic Doppler shifting of lines in its spectrum
spectroscopic parallax
a method of determining a star's distance from Earth by measuring its surface temperature, luminosity, and apparent magnitude
stellar evolution
the changes in size, luminosity, temperature, and chemical sphere resulting from Earth's orbit around the Sun
stellar parallax
the apparent shift in a nearby star's position on the celestial sphere resulting from Earth's orbit around the Sun
stellar spectroscopy
the study of the properties of stars encoded in their spectra
supergiant
a star of very high luminosity
visual binary
a double star in which the two components can be resolved through a telescope
white dwarf
a low-mass stellar remnant that has exhausted all its thermonuclear fuel and contracted to a size roughly equal to the size of Earth
Stellar parallax measurements are used in astronomy to determine which of the following properties of stars?
distance
The brightness a star would have if it were at 10 pc from Earth is called its
absolute magnitude
Measurements of a binary star system are required to determine what property of stars?
mass
A star with which of the following apparent magnitudes appears brightest from Earth?
the lowest negative number
-1.5
A star of what spectral class has the strongest (darkest) H line?
A5
Describe how the parallax method of finding a star's distance is similar to the binocular (two-eye) vision of animals.
Look at some nearby object in the room where you are. Alternately close one eye then the other and you'll notice that the object seems to move back and forth. That's the effect of parallax, in this case caused by the distance between your eyes. Sustitute
What is stellar parallax?
the apparent shift in a nearby star's position on the celestial sphere resulting from Earth's orbit around the Sun
How do astronomers use stellar parallax to measure the distances to stars?
it is triangulation
What is the difference between apparent magnitude and absolute magnitude?
Apparent Magnitude is the star's brightness as it appears from earth. Absolute magnitude is the apparent brightness of a star if viewed from a distance of 32.6 light years away.
Briefly describe how you would determine the absolute magnitude of a nearby star.
Absolute and apparent magnitude are related via the distance. For a nearby star one might measure the parallax so the formula becomes:
M = m + 5 (log_10 (p) + 1), where p is the parallax in arc seconds.
The relative magnitude is of course measured with a
What does a star's luminosity measure?
In astronomy, luminosity is the total amount of energy emitted by a star, galaxy, or other astronomical object per unit time. It is related to the brightness, which is the luminosity of an object in a given spectral region. In SI units luminosity is measu
How does the magnitude scale "background" from what common sense dictates?
Magnitude scale runs backward = a larger apparent magnitude means a dimmer apparent brightness
Does the star Betelgeuse, whose apparent magnitude is m = +0.5, look brighter or dimmer to us than the star Pollux, whose apparent magnitude is m = +1.1?
Brighter
How and why is the spectrum of a star related to its surface temperature?
The spectrum of a star is related to its surface temperature in at least two ways, (i) through its overall colour, changing from "red" to "blue," etc. as it gets hotter, and (ii) the particular pattern of "spectral lines" observed in its own spectrum. The
What is the primary chemical component of most stars?
Helium
A star of which spectral type has the strongest Na 1 absorption lines? At approximately what wavelength is this line normally found?
K has the strongest Na 1 absorption lines. This line is normally found in 5890 wavelength.
Why does a G2 star have many more absorption lines that a B0 star?
Atoms near the outer edge of a B0 star are highly ionized. Atoms in a G2 star still have most of their electrons. Electrons changing energy states in bound-bound transitions are what cause absorption lines.
How can observations of a visual binary lead to information about the masses of its stars?
If they're visual, then we can estimate the distance between them. If we know the distance, then we can calculate each stars' mass, by observing the period of orbit, and by seeing how much a smaller star makes the larger star oscillate by it's gravitation
What is a radial-velocity curve? What kinds of stealer systems exhibit such curves?
Radial velocity is simply the component of velocity in the line of sight. A radial velocity curve is just a graph of this as a function of time. The systems which exhibit radial velocity curves are systems of 2 or more stars orbiting each other, where the
What is the difference between a single-line and a double-line spectroscopic binary?
A single-line spectroscopic binary results from one of the stars being too faint to
contribute to the spectrum we see. All the spectral lines in this system move together. In a
double-line spectroscopic binary, we can see lines from both stars. Since one
What is meant by the light curve of an eclipsing binary? What sorts of information can be determined from such a light curve?
One measures and graphs the intensity of the light over time. When the binary elements are aligned, you see less light as one is hiding all or part of the other. This can directly show the period of their mutual revolution, and also give hints as to their
What is the mass-luminosity relation? To what kind of stars does it apply?
The mass-luminosity relationship is quite basic: The more massive the star, the greater the luminosity. This applies only to main-sequence stars, however. As a star evolves off the main sequence, its luminosity varies greatly, first increasing tremendousl
Parallax method
used for the measurement of the distance to nearby stars
Spectroscopic method
used for determining the distance to faraway stars
Stellar evolution
uses observational properties of stars
Science by Starlight
- By analyzing starlight, astronomers can determine the masses of stars, their temperatures, and their compositions.
- It is possible to determine the stances of stars and their velocities toward or away from us.
The Realm of the Stars
- Proxima Centauri, the closest star to Earth other than the Sun, is about 25 trillion miles away in the constellation Centaurus.
- Light rays from this star require over four years to travel to Earth.
The Stellar Parallax Effect
- The positions of stars close to Earth appear to change relative to the faraway background stars as the Earth orbits around the Sun.
- Analogous Effect: The retrograde motion of planet Mars with respect to the stars.
* Proxima Centauri and Sirius are amo
Determining Distance by Parallax
As the Earth orbits the Sun, stars appear to shift their position against the background of more distant stars.
Determining Distance by Stellar Parallax
- A star's parallax angle p is equal to the angle between Sun and Earth as seen from the star.
* The farther the star is from us, the smaller the parallax angle.
- The distance d to the star (measured in parsecs) is equal to the inverse of the parallax an
Astronomer's Toolbox
Definition of Parsec: One parsec is the distance at which two objects that are one AU apart appear to subtend an angle of one arc-second.
* The formula for stellar distances is:
d [parsec] = 1/p [arcsec]
* Since 1 pc = 3.26 light years or
1 pc = 206,265 A
First Parallax Measurement
In 1838: Friedrich Wilhelm Bessel measures the parallax angle of star 61 Cygni. Its parallax is found to be 1/3 arctic. The star's distance hence is about 3 parsec.
- Parallax angles smaller than about 0.01 arctic are difficult to measure from Earth-based
Apparent Magnitude
Hipparchus: Introduction of the Magnitude Scale - The classification of stars according to their apparent brightness or apparent magnitude (m).
* Apparent Magnitude measures the brightness of stars as they appear to an observer on Earth, without regard to
Apparent Magnitude Scale
Astronomers have extended the magnitude scale to include negative numbers:
- A star 2.5 times brighter than a first magnitude star has apparent magnitude m= 0.
- A star 2.5 x 2.5 times brighter than a first-magnitude star has apparent magnitude m = -1.
Si
Absolute Magnitude
Apparent brightness is affected by the distance of stars from Earth: The closer of two identical stars appears brighter than the star farther away.
- Apparent magnitude depends on a star's distance from Earth.
- Absolute magnitude is independent of a star
Inverse-Square Law
Because light spreads out as it moves away from the source, the apparent brightness of the source decreases according to
The Inverse-Square Law:
Intensity ? 1/(Distance)2
Example: The relative intensity of Sunlight in the Solar System.
Absolute Magnitude Scale
For a meaning comparison of the brightness of stars at different distances, astronomers define the absolute magnitude: The absolute magnitude M or a star is equal its apparent magnitude m, if that star is viewed from a distance of 10 parsecs.
- Absolute m
Stellar Luminosities
Absolute and apparent magnitudes use the same counterintuitive scale: The brighter the star, the smaller its magnitude.
- Alternative measure: Since stars are essentially blackbodies, their brightness and absolute magnitudes are directly related to the to
Starlight
The analysis of stellar spectra allows astronomers to determine many details such as surface temperature, chemical composition, luminosity, and radial and rotational motion.
* Observational Astronomy:
- Astrometry: the precise measurement of stellar posit
Stellar Colors and Temperatures
- The most common colors of stars: red, orange, yellow, white, and blue
* Physical Description of Stellar Radiation:
- Stars are nearly-perfect blackbodies -> Star colors reveal star temperatures.
- Red stars are relatively cool (surface temperatures arou
Temperature and Color
The relation between star color and temperature of the star surface.
* The peak of the intensity curve determines each star's apparent color.
Stellar Spectra and Temperatures
Stellar surface temperatures can also be determined by spectroscopy.
* Recall: The spectral lines result from the absorption of starlight by gases in the star's atmosphere.
- Some stellar spectra show prominent absorption lines of hydrogen.
- Some exhibit
Classification of Stars by Stellar Spectra
Stars with similar spectra are grouped into certain classes or spectral types.
* Classification Scheme of the late 1800s: Stars assigned letter from A through P (depending on the strength of the Balmer hydrogen lines in the star's spectrum).
*Classificati
Types of Stars and the Hertz sprung - Russell Diagram
Around 1911, astronomers Ejnar Hertz sprung and Henry Norris Russell noticed:
- Interesting patterns emerge when the luminosities of stars are plotted against the stars' surface temperatures.
- Equivalently, similar interesting patterns emerge when the st
Hertz sprung - Russell Diagram
Stellar luminosities vs. Spectral type
- Corresponding absolute magnitudes and surface temperatures are listed at the right and top of the graph.
- The data points are grouped, revealing that luminosity and spectral type are correlated.
Bright stars: At t
Determining Star Sides from the Hertz sprung - Russell Diagram
The dashed diagonal lines indicate regions of constant stellar radius.
* For fixed stellar radius: As the surface temperature increases (moving from right to left on the diagram), the star's luminosity increases (corresponding to an upward move on the dia
Luminosity Classes
Astronomers find it convenient to subdivide the stars on the Hertz sprung - Russell Diagram into regions called luminosity classes.
- Subdivisions permit finer distinctions between giants and supergiants.
- Luminosity Classes Ia & Ib: Encompass the superg
The Spectroscopic Parallax Method
Information on Spectral Type and Luminosity Class of a Star ?Determination of the Star's Distance from Earth!
(1) Measure the star's apparent magnitude and spectral type.
(2) From its spectrum determine the star's luminosity class.
(3) From the luminosity
11-10 Binary Stars provide information about stellar masses
Double star - a pair of stars located at nearly the same position in the night sky
optical doubles (sometimes called apparent binaries) - double stars that do not physically close together; they just happen to lie in the same direction
- Through a telesco