Stellar Properties

Stars: Stellar Properties

Stars are balls of gas held together by force of gravity and generate energy and light by nuclear fusion.

A star’s “color,” or wavelength gives information on:

  1. Temperature
  2. Composition
  3. Conditions
  4. Motion (Doppler Shift)
  5. Classification Scheme

What to Measure and How to Classify Stars:

  1. Spectroscopy
    • To determine composition
      • Absorption line produced when an electron absorbs a photon; emission line produced when an electron emits a photon
      • Dual nature of light: light behaves as waves (electromagnetic waves) or as particles (photons)
      • High energy electromagnetic waves are high energy photons, low energy electromagnetic waves are low energy photons
      • Energy of a photon defined by: E = hf, where h is Planck’s constant (h = 6.63 x 10 ^ – 34 joules sec) and f is the frequency of the electromagnetic wave
      • Three Types of Spectra:
        • Continuous Spectrum: appears as a rainbow spectrum
        • Emission Spectrum: appears as distinct color lines, characteristic of chemical elements
        • Absorption Spectrum: appears as black lines on a rainbow background, reverse of emission spectrum
    • To determine temperature
      • All objects give off thermal radiation
      • Peak wavelength corresponds to maximum intensity of radiation
      • Peak wavelength of electromagnetic radiation is related to temperature
      • Wien’s Law: W = 0.00290/T
      • As temperature increases, wavelength decreases
      • The hotter an object, the bluer the radiation
    • To determine density
      • The thicker the spectral line, the greater the abundance of the chemical element present
    • To determine motion
      • Doppler shift of spectral lines
      • Red Shift = moving away
      • Blue Shift = moving closer
    • To determine distance
      • Measured in light years (ly) – distance light travels in one year and parsecs (pc) – one parsec is 3.26 light years
      • Parallax: the only direct measure of stellar distance, the angle across the sky that a star seems to move with respect to a background of distant stars) between two observation points at the ends of a baseline of one astronomical unit (A.U.); a star one parsec from Earth has a parallax of one arc second
  2. Brightness
    • Apparent Brightness
      • Affected By: absolute (true) brightness, distance, intervening space, Earth’s atmosphere, and eyes’ visual response
      • Measured by apparent magnitude “m,” relative brightness as seen on Earth; brightest star (m=1) to faintest (m=6); a 1st magnitude star is 100 times brighter than a 6th magnitude star
    • Absolute Brightness
      • Measured by absolute magnitude “M”
      • The magnitude of a star observed from a distance of 10 parsecs (1 parsec = 3.26 light years)
      • Stars further than 10 parsecs would “appear” brighter; M increases
      • Stars closer than 10 parsecs would “appear” dimmer; M decreases
    • m-M = 5 log (r/10)
  3. Distances
    • Distance as the primary factor in the decrease of stellar brightness as perceived on Earth, used to determine absolute brightness
    • Inverse Square Law: the intensity of light varies inversely with the square of the star’s distance from the Earth
  4. Mass and Size
    • MASS: For binary stars, both the period of revolution of one star orbiting the other and the distance between the two stars can be measured
    • SIZE: Diameters of stars can be determined from temperature and luminosity (calculated from absolute brightness) =>  L  =   σ  T^4  A, where L = luminosity, σ = distance, T = temperature, and A = absolute brightness
  5. Classification Scheme
    • Spectral Types: O, B, A, F, G, K, M; subtypes 0 to 9 (e.g. B1, A4, G2, and M0)
    • O stars are more than 10 times hotter than M stars
    • Developed by Annie Jump Cannon in the late 1800’s
  6. H-R Diagram: to study evolutionary tracks

Stars Under a Microscope

Stars are held by gravity and shine because of the nuclear fusion reactions (fusing light nuclei into heavier nuclei, e.g. hydrogen atoms –> helium atoms) occurring in their cores. Luminosity and lifetime depend entirely on the star’s mass. Stars are composed of mainly hydrogen and helium, with trace amounts of other elements. Stars end their lives when they have exhausted their available nuclear fuel. Their final end states of stellar evolution are different and depend on mass.

OBSERVING STARS: Stars are so far away that they appear as infinitesimally tiny “points” of light.

What Do Astronomers Measure in Stars?

  • Brightness: Is the star constant or variable over time?
  • Spectrum: temperature and chemical composition
  • Color: temperature
  • Motion and Doppler Shift
  • Distance (measuring can be very difficult)

HOW MEASURING DISTANCE TO STARS IS IMPORTANT: Distance and magnitude can determine the star’s luminosity, or how much energy it’s generating and emitting. Distance to stars also determines the structures of galaxies. Then, measuring distances to galaxies can also determine the structure of the universe.


MEASURING DISTANCE USING PARALLAX: Parallax is the apparent movement of a distant object when viewing from two different lines of sight. For example, hold out your thumb at arm’s length and close your right eye. Now, open your right eye and close your left eye. See the difference? Astronomers use distance the object “moved” and the angle from Earth and the object’s two different locations to determine the distance to that object. Earth’s motion acts as a baseline to measure the distance of a nearby star. As Earth moves around the Sun, a nearby star will appear to move slightly relative to distant background stars.

  • the star’s parallax = 1/2 the angular shift of the star over one year
  • parsec = parallax second of arc
  • 1 parsec = the distance to a star whose parallax angle is one arcsecond
  • 1 parsec = 3.26 light years
  • 1 parsec = 3.08 x 1016 meters
  • distance (in parsecs) = 1/parallax angle (in arcseconds) –> d = 1/p
*Note: Parsec is NOT a unit of time, but a unit of distance! Arcminutes and arcseconds are NOT units of time, but units of rotation.

All stars have parallaxes smaller than 1 arcsecond. The nearest star, Proxima Centauri has a parallax of o.77 arcseconds and a distance of 1.3 parsecs. Parallaxes can be measures to 200 parsecs from ground-based telescopes. The GAIA Mission (2013), if launched successfully, will allow astronomers to measure 20 micro-arcseconds, or distances to 1 billion stars!

APPARENT MAGNITUDE: Apparent magnitude is how bright a star appears from Earth. On a logarithmic scale, a magnitude 1 star is 100 times brighter than a magnitude 6 star. Brighter stars have smaller magnitudes. The brightest star in the night sky is Sirius at -1.5. The faintest objects detected by the Hubble telescope are magnitude 30. Photometry is measuring the apparent brightness of an object.

Comparing Two Stars’ Apparent Magnitudes with an Equation

m2-m1 = -2.5 log10 (b2/b1)

  • m2 and m1 = apparent magnitudes of two stars
  • b2 and b1 = fluxes of two stars (flux is the amount of light energy received per unit of time per unit of area)

Apparent Magnitude Comparison

  • The Sun = -26.8
  • Full Moon = -12.6
  • Sirius = -1.5
  • Naked Eye (faintest objects) = +6
  • Hubble telescope (faintest objects) = +30

ABSOLUTE MAGNITUDE: Absolute magnitude is the actual luminosities of stars. The Sun has an absolute magnitude of 4.83.

Calculating Absolute Magnitude

m-M = -5 + 5 log10 (d/10 parsecs)

  • m = apparent magnitude
  • M = absolute magnitude
  • d = distance in parsecs

FILTERS & COLORS: Telescopes have filters that isolate specific wavelength regions of the wavelength. The most common filter is UBVRI. Different filters corresponds to different brightness. The ratio of brightness through two different filters correspond to the star’s color. The star’s color also determines the star’s temperature. The ratio between the star’s brightness through two different filters, such as the B and V filters, would be bB/bV.

(B-V) = (mB-mV) = -2.5 log10(bB-bV)

  • The B-V color index depends on the surface temperature of the star

The zeropoints are defined by the star Vega. Vega is 10,000 K and Vega’s color index for any filter combination is 0.

Stellar Spectra

STELLAR SPECTRUM: A star’s spectrum is close to a black-body (an ideal physical body that absorbs all electromagnetic waves) curve, with absorption lines imprinted on it by elements in the star’s photosphere. From the late 1800s to the early 1900s, Harvard College Observatory employed women to observe, map, and define all stars in the sky. When the observers disagreed on the classification of these stars, Annie Jump Cannon invented the spectral sequence base on the strength of stars’ Balmer absorption lines (Hα). Star with the strongest Hα lines were spectral type “A”, and the next strongest were type “B.” Later, however, some letters were removed. The astronomers discovered that the strength of Hα lines depends on the stars’ surface temperatures and stars with temperatures of 10,000 K have the strongest Hα lines. The sequence was then re-arranged in decreasing temperature, resulting in: O, B, A, F, G, K, and M. An acronym to remember the spectral types is “OBa Fine Girl/Guy, Kiss Me.” The subtypes range from 0 –> 9, with subtype 0 as the hottest and 9 the coolest.

Spectral Types and Corresponding Temperatures

  • O = >25,000 K
  • B = 11,000 K – 25,000 K
  • A = 7,500 K – 11,000 K
  • F = 6,000 K – 7,500 K
  • G = 5,000 K – 6,000 K
  • K = 3,800 K – 5,000 K
  • M = 2,200 K – 3,800 K
  • L, T = <2,200 K

* Spectral Types L and T are the recently discovered brown dwarfs, or stars too small for nuclear fusion

In addition to the spectral type and the subtype, each star also has a class. For example, the Sun is G2V (V means main sequence star). While a M0 main sequence star may have 0.6 R☉ and 0.06 L☉, a M0 red giant star will have 40 R☉ and 300 R☉.

RADIUS: The Sun’s radius is 696,000 km, or 1 R☉. A Red Giant is 50 – 100 R☉. A White Dwarf is about   0.01 R☉.

MASS: The Sun’s mass is 1.989 x 10³º kg, or 1 M☉. 1 M☉ is 330,000 times Earth’s mass. Masses of stars range from 0.08 M☉ to over 100 M☉.

H-R Diagram: Majority of Stars in the Main Sequence; Very Few Stars as Red Giants or White Dwarfs

H-R DIAGRAM: The Hertzsprung-Russell (Color-Magnitude) Diagram  organizes the stars into a plot graph, based on color (spectral type)/ temperature and luminosity/ absolute magnitude.

  • Main Sequence: normal stars in their prime of life fusing hydrogen into helium
  • Red Giants: late-stage stars swollen to enormous size, sued up all fuel
  • White Dwarfs: the “dead” star cores

* ☉ = solar units; L = luminosity; R = radius; M = mass


  1. Mass: star’s evolution, location on main sequence, where is it in its lifetime
  2. Age: different locations in the H-R Diagram
  3. Chemical Composition/ Metallicity: abundance of metals