Section 18: A Celestial Census of Stars

Celestial Ceneus

basically a survey or count of celestial objects in the universe — like stars, planets, galaxies, nebulae, and other cosmic bodies → looks at different types number and distributions 

Stellar Masses:

Determined through looking at binary star systems 

1. Visual

1. Spectroscopic

2. Eclipsing

Ranges for masses

• Stars: 1/12 < m < 250 

• BROWN Dwarfs: 1/100 < m < 1/12

  • Considered failed stars

• Planets: m < 1/100 

Binary Star Systems

• a system of two stars orbiting a common center of mass

Visual method for determining mass

Both stars can be directly seen through a telescope as two separate points of light

Spectroscopic method for determining mass

Stars are too close to be resolved visually, but their spectral lines show Doppler shifts as they move toward or away from us

• Shows two spectral line movements 

Eclipsing method for determining mass

The orbital plane is edge-on to our line of sight, so the stars pass in front of each other, causing brightness variations

• Looks similar to the transit graph

Mass-Luminosity Relationship

• More massive a star the more luminous: L ~ M^3.9 

• Stellar Mass Calculations: Newton’s Versions of Kepler’s third law

• D³= (M₁+ M₂)P²

  • D = semimajor axis of the orbit of one with respect to the other in AU 

  • P = period with which they go around each other in years

  • M₁+M₂ = Both masses are non-negligable and its their sum 

Barycentre/ Centre of mass

• The point about which the stars will orbit

  • The star with the higher mass will be closer to the barycentre and move with a slower velocity

Stellar Radii Ranges

• Fainter stars are smaller than brighter stars

Star Sizes by Occultations

1. An occultation occurs when a larger object passes in front of a smaller, more distant object, temporarily blocking its light 

• Measure the time it takes for the star’s light to disappear and reappear

• Using the speed of the occulting object the stars angular diameter can be calculated 

  • By measuring the distance to the star its size can be measured

Star Sizes by Eclipsing Binaries

A binary star system where the orbital plane is aligned so that one star passes in front of the other as seen from Earth → causing a periodic dips in brightness

• Primary Eclipse: Brighter star is partially or fully blocked → largest dip in brightness.

• Secondary Eclipse: Dimmer star is blocked → smaller dip.

• Contacts: 

  • First Contact: Beginning of brightness drop.

  • Second Contact: Smaller star fully hidden (total eclipse starts).

  • Third Contact: Smaller star starts to reappear (total eclipse ends).

  • Fourth Contact: Eclipse fully over, brightness returns to normal.

• T₂ - t₁ = second contact to first contact time

• T₃ - t₁ = third contact to first contact time

Star Sizes by Stefan-Boltzmann Law:

1. Luminosity and Temperature of a star

• L=4πR²σT⁴

  • Rewritten as:

  • Need luminosity from apparent brightness and distance (flux) and temperature from colour index (B-V) or spectral type 

HR Diagrams

the relationship between a star's luminosity and its surface temperature

• Axes

  • X-axis: Surface temperature (hot → cold from left to right or vice versa depending on convention)

  • Y-axis: Luminosity (brightness) increases upward

 

Observations from HR diagrams

1. Classification of the star

2. Determine its evolutionary stage

3. Estimate size

4. Estimate Temperature 

5. Estimate luminosity

• Mass determines a Star’s positions on the HR Diagrams: 

• Higher mass → hotter and more luminous → top-left

  • O, B, A

• Medium Stars

  • F and G

• Lower mass → cooler and dimmer → bottom-right

  • K and M

Main Sequence

•  A diagonal band from top-left (hot, luminous) to bottom-right (cool, dim)

  • This band is where 90% of stars lie showing a strong correlation 

    • Where they spend most of their lives

  • These stars eventually become giants/ supergiants

1. Spectral Class vs luminosity

• Giants/Supergiants: Above this main sequence → large radius and very luminous however they have cooler surfaces 

  • Tend to become white dwarfs later on 

  • Around 10% of stars

• White dewars: Below the main sequence → Small radii but have high temperatures with lower luminosities 

  • Better seen in UV