Star Properties: Color, Spectra, Distance & Magnitude

Characterizing Stars

• Distances to nearby stars can be measured directly; distances to farther stars are determined indirectly.
• Astronomers use the observed properties of stars to base their models of stellar evolution
• Astronomers analyze starlight to determine a star's temperature and chemical composition.
• The total energy emitted by stars and their surface temperatures are related.
• Stars are categorized into different classes.
• Binary star systems have variety and importance in astronomy.
• Astronomers calculate stellar masses.

Using Parallax to Determine Distance

• Eyes change the angle between sight lines when looking at objects at different distances.
• Eyes adjust for the parallax of things and this helps in determining distances to objects
• The parallax of objects is analogous to how astronomers determine the distances to objects in space.
• As Earth orbits the Sun, a nearby star appears to shift its position against distant stars.
• A star's parallax angle (p) equals the angle between the Sun and Earth as seen from the star.
• The closest star, other than the Sun, would be about 5 km (3.2 mi) away if the stars were drawn to the correct scale.
• The closer a star, the greater the parallax angle p.
• The distance to a star in parsecs is found by taking the inverse of the parallax angle p in arcseconds: d = 1/p.

Luminosity and Magnitude

• Luminosity is the amount of energy a star emits each second, it differs from brightness as more luminous stars appear brighter.
• Greek astronomers like Hipparchus (2nd century BCE) and Ptolemy (90-168 CE) classified stars by evaluating their apparent brightness relative to each other.
• Apparent magnitude (m) measures a star's brightness as seen from Earth.
• Absolute magnitude (M) measures a star's true brightness and relates directly to its luminosity.
• Absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc
• Absolute magnitudes can be calculated from a star's apparent magnitude and distance from Earth.

Apparent Magnitude Scale

• Several stars appear in and around the constellation Orion and are labeled with their names and apparent magnitudes
• The brightnesses of objects in the sky have magnitudes between m = -1.44 (Sirius) and about m = +6.0 for stars visible without aid
• CCD photography through telescopes may allow for the detection of stars and objects as faint as m = +31.5.
• Pluto's apparent magnitude ranges from +13.7 to +16.3, depending on its distance from Earth; its average is +15.1.

The Inverse-Square Law

• The same radiation from a light source illuminates an ever-increasing area as distance increases.
• Brightness decreases following an inverse-square law.
• Tripling the distance from a light source reduces the brightness by a factor of 9.
• A car is seen at distances of 10 m, 20 m, and 30 m; this illustrates the inverse-square law in action

Radiation Laws Revisited

• Wien's law: the peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature.
• The higher the temperature, the shorter the peak wavelength; intensities of radiation emitted at various wavelengths are depicted as a blackbody curve.
• The Stefan-Boltzmann law: a hotter blackbody emits more radiation at every wavelength than a cooler one.
• The Stefan-Boltzmann law determines how much brighter (luminosity) a hotter star is versus a cooler star.

Temperature and Color

• The diagrams show the relationship between a star's color and surface temperature.
• The intensity of light emitted by stars is plotted against wavelength.
• The location of each star's intensity curve's peak determines the apparent color of its visible light.
• Ultraviolet extends to 10 nm.

The Spectra of Stars with Different Surface Temperatures

• The spectral types are indicated on the right side of each spectrum shown with varying temperatures
• The hydrogen Balmer lines are strongest in stars that have a temperatures of about 10,000 K, called A-type stars.
• Cooler G- and K-type stars show numerous atomic lines caused by different elements, indicating temperatures from 4000 to 6000 K.
• Titanium oxide (TiO) molecules cause several of the broad, dark bands in the spectrum of the coolest M-type stars, which exist only if the temperature is less than 3700 K
• A Roman numeral I after a chemical symbol indicates that a neutral atom causes the absorption line.
• A numeral II indicates that atoms that have each lost one electron cause the absorption line.

The Spectral Sequence

• Spectral Class O: blue-violet color, temperature 50,000-30,000 K, with ionized helium as a spectral line
• Spectral Class B: blue-white color, temperature 30,000-11,000 K, with helium and some hydrogen spectral lines
• Spectral Class A: white color, temperature 11,000-7500 K, with strong hydrogen and some ionized metals as spectral lines
• Spectral Class F: yellow-white color, temperature 7500-5900 K, with hydrogen, ionized metals, calcium, and iron as spectral lines
• Spectral Class G: yellow color, temperature 5900-5200 K, with both neutral and ionized metals, and ionized calcium as spectral lines
• Spectral Class K: orange color, temperature 5200-3900 K, shows spectral lines for neutral metals
• Spectral Class M: red-orange color, temperature 3900-2500 K, shows titanium oxide and some neutral calcium spectral lines

Classifying the Spectra of Stars

• The Harvard College Observatory developed the modern classification scheme for stars in the late nineteenth century.
• Female astronomers led by Edward C. Pickering and Williamina Fleming analyzed hundreds of thousands of spectra.
• Annie Jump Cannon, Margaret Harwood, Cecilia Payne, and others contributed to the classification of stars.
• Social conventions prevented most female astronomers from using research telescopes or receiving comparable salaries.

A Hertzsprung-Russell Diagram

• On an H-R diagram, stellar luminosities are plotted against their spectral types.
• Each data point on the graph represents a star whose luminosity and spectral type have been determined.
• Luminosity and spectral type are correlated, resulting in groupings on the H-R diagram.
• Main-sequence stars fall along a curve; giants are to the right, supergiants are at the top, and white dwarfs are below.
• Absolute magnitudes and surface temperatures are sometimes used instead of luminosities and spectral types.

The Types of Stars and Their Sizes

• Stellar luminosities are plotted against surface temperatures.
• Dashed diagonal lines indicate stellar radii.
• Hotter stars glow more intensely and are more luminous for stars of the same radius.
• Main-sequence, giant, supergiant, and white dwarf stars occupy specific regions of the H-R diagram.
• The Sun is a middle-of-the-road star, being intermediate in luminosity, surface temperature, and radius.

Stellar Size and Spectra

• Supergiant stars have low-density, low-pressure atmospheres with narrow spectral absorption lines.
• Main-sequence stars have denser, higher-pressure atmospheres with broad absorption lines.
• These spectra are from two B8 stars with a surface temperature of 13,400 K, but different radii and luminosities.
• The stars: B8 supergiant Rigel (luminosity 58,000 L☉) in Orion and B8 main-sequence star Algol (luminosity 100 L☉) in Perseus.

Luminosity Classes

• H-R diagrams are divided into regions allowing distinctions between giants and supergiants.
• Luminosity classes Ia and Ib are supergiants; II, III, and IV are giants of different brightness.
• Luminosity class V indicates main-sequence stars.
• White dwarfs lack a luminosity class, as they do not create energy by fusion.

Spectrographic Parallax

• Astronomers observe a distant star's apparent magnitude and spectrum.
• They figure out what spectral class the star belongs to by looking at the spectrum.
• This is the same as finding the surface temperature
• The spectrum also reveals the star's luminosity class, that is, whether it is a supergiant, giant, or main-sequence star.
• Combining the temperature and the luminosity class determines the star's location on the H-R diagram. Then its absolute magnitude can be read.
• The star's distance can then be calculated using apparent and absolute magnitudes in the distance-magnitude relationship.

Stellar Mass

• The mass of each star determines how strongly it compress and heat its interior, therefore creating light and electromagnetic radiation by thermonuclear fusion.
• Stellar masses cannot be found by examining isolated stars.
• A star's mass is determined by its gravitational effects, using Newton's law of gravity.
• Most stars near the solar system are members of systems where two stars orbit each other.

Binary Stars

• A pair of stars close together in the night sky is a double star.
• Some double stars are not physically close; these optical doubles only appear in the same direction from Earth.
• Other double stars are true binary stars, where two stars orbit a common center of mass.
• Visual binaries are systems where both stars can be seen, enabling astronomers to plot their orbits.
• Spectroscopic binaries are detected from the periodic shift of their spectral lines due to the Doppler effect.
• Eclipsing binaries are systems with orbits viewed nearly edge-on, causing one star to eclipse the other.
• Binary light curves are studied to get information about stars in an eclipsing binary

A Binary Star System

• Double stars account for about one-third of the objects referred to as "stars” in the Milky Way Galaxy.
• The Mizar system in Ursa Major contains binary stars with about 0.01 arcsec separation.
• The relative positions of stars are shown with images and plots over half their star's orbital period.
• The orbital motion of the two stars and their orbits are evident, and either star may be fixed in some plots.
• Mizar A and its dimmer companion are bound to another binary pair, Mizar B and its dimmer companion.

Center of Mass of a Binary Star System

• In a binary system, two stars orbit a common center of mass in elliptical orbits, each on opposite sides of the orbital path, preventing collision.
• The center of mass is a balance point much like a fulcrum on a seesaw, with the heavier child (more massive star) located nearest.