Evolution/ Death of Low-Mass Stars

Evolution of Low-Mass Stars

  • For stars on the main sequence, luminosity is proportional to the star’s mass to the 3.5th power (L α M3.5)
  • For the Sun: original composition about 30% helium in mass –> today – 65% helium –> 5 billion years later: 100% helium
  • The total amount of hydrogen “fuel” in a star is proportional to the star’s mass; the rate of fuel use is proportional to luminosity; lifetime α mass α 1/L
  • The Sun’s main sequence lifetime is 10¹º years; its entire lifetime is 10¹º + 1/M2.5 years, where M = the star’s mass in solar masses

How Lifetime, Luminosity, and Mass Compare Among Various Spectral Types

Spectral Type  Mass (M☉)   Luminosity (L☉)  Lifetime (years)

  • O5                        60                          800,000                        3 million
  • A5                         3                                55                              4 million
  • G2                        1                                  1                             10 billion
  • M0                      0.5                           0.08                             70 billion
  • M5                      0.2                           0.01                           190 billion

Stars with masses below 0.8 M☉ have never left the main sequence and have lifetimes longer than the current age of the Universe.

Post- Main Sequence

  • Core can’t maintain its balance between gravity and pressure; gravity compresses the star to a much smaller size
  • Electron Degeneracy Pressure: halts collapse of the star
  • Core’s radius swells to several thousand km, or about the size of Earth
  • Hydrogen converts to helium at  a very rapid rate; luminosity more than 1000 times greater than before; star swells to enormous size

Red Giant

Red Giants: 50x Sun’s radius, 1000x Sun’s luminosity

  • H –> He in a shell
  • Helium core swells to the size of Earth; no fusion anymore
  • Non-burning hydrogen atmosphere
  • Helium fusion needs higher velocities and energy to overcome repulsion
  • At 100 million K, helium atoms yield carbon atoms, also known as “helium flash”
  • Triple-Alpha Process“: 4He + 4He –> 8Be; 4He + 8Be –> ¹²C
  • In half an hour, half the helium yields carbon in the core
  • Horizontal Branch Star: after the core expands and the star enters a steady phase (50-100 million years) of helium burning and becomes less luminous

    Evolution of Low-Mass Stars: H-R Diagram

  • Core contracts again, He –> C in a shell around the core; hydrogen burning shell around that layer
  • Asymptotic Giant Brand“: star moves upward toward the H-R Diagram “Red Giant” area, exceeds 10,000 L☉

*Blue-Stragglers: stars in a dense environment; when two stars collide, the core could be “rejuvenated,” giving the star extra lifetime

Planetary Nebula

Planetary Nebulae

  • The outer layers, about 20% of the star’s mass, are ejected in a strong wind
  • Gas is ionized by UV protons from hot, exposed stellar core
  • Star shines for 50,000 years before gases disperse and fade
  • About 1,000 in the Milky Way Galaxy
  • Have many shapes and sizes because of binary star systems’ different orbits, temperature, rotation, luminosity, mass

Binary System: Sirius A (brighter, Main Sequence) & Sirius B (dimmer, white dwarf)

White Dwarfs:  (0.6 – 0.7 M☉) bare core of a star often all fusion reactions ended, supported against gravity by electron degeneracy pressure; density at 1 million grams/cm³

  • e.g. Sirius A: Main Sequence, A1, -1.5; Sirius B: white dwarf, 8.5

End States: Initial Mass and White Dwarf Composition

  • >0.45 M☉: helium
  • 0.45-4 M☉: carbon, oxygen –> (Sun)
  • 4-8 M☉: oxygen, neon, magnesium

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.

Parallax

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

THREE THINGS TO CONSIDER FOR STAR CLASSIFICATION:

  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