Characteristics of Stars

Mass of a Star

• The mass of a star is the hardest for astronomers to determine and it can only be found based on the gravitational forces and interactions with nearby stars.

• We can calculate the mass of an object if we know Kepler’s constant for it (from his 3rd Law), although we won’t do it in this course. (It's sometimes done in grade 12 physics).

• Masses are typically expressed as a multiple of our Sun (Msun or M

, where "" being the astronomical symbol

for the Sun) rather than in kg. This allows us to get a better idea of how big the star we're dealing with is.

Apollo: Greek God of the Sun 2

Star Colour

• When a chunk of iron is heated, it glows orange, then yellow, white, and blue as it gets progressively hotter.

• Similarly, the colour of a star is directly related to its surface temperature.

Cooler stars (which are still over 1000oC) appear to be reddish

Mid temperatures stars appear white/yellow

High temperatures stars appear bluish white.

• This property of things to glow certain colours regardless of their material is called blackbody radiation (and is a significant part of quantum physics).

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Blackbody Radiation

• The curves on the graphs below show how much energy of each radiation type is given off depending on the temperature of the star.

• The cooler star on the left emits more energy with longer wavelengths (the red end of the visible spectrum), so it will appear red in colour.

• The mid temperature star in the middle appears yellowish white because it gets a nice blend of all of the colours of the rainbow. (Note: White light is made of all colours blended together.)

• The hot star on the right emits more energy with shorter wavelengths (the blue end of visible spectrum), so it appears to be blue in colour.

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Peak Radiation Curve

The hotter the star, the more the peak of the curve moves to

the left (higher energy radiation types).

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Wien's Law

• Although we'll do the details later, I think you can see that we can determine the surface temperature of a star by just knowing its colour!

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Spectral Classes

• The colour of a star (and thus it's temperature) determines which spectral class it belongs to.

• All starts of the same spectral class have similar properties, although size isn't one of those.

• You can remember it as “Oh Be A Fine Girl/Guy... Kiss Me!

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• An H-R Diagram showing star distributions. More on this later!

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Apparent Magnitude

• This is how bright the star seems to be when viewed from Earth.

• This has NOTHING to do with the actual brightness of a star.

• For instance, you know that the flashlight in your hand may not be as bright as a spotlight that's 25 metres away, but when you shine it in your face, it seems brighter because it's closer.

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• Although it seems backwards, the smaller the magnitude, the brighter the star.

• Some of the brighter stars in the sky (other than our sun) have a magnitude of 1.

• The faintest stars that can be seen with the unaided eye have a magnitude of about 6.

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• By definition, a magnitude 1 star is 100 times brighter than a magnitude 6.

• Each magnitude is about 2.5 times brighter than the magnitude next to it. – (2.55 100)

• Some stars have negative magnitudes. The apparent magnitude of the sun is -26.7 (about 120 billion times brighter than magnitude 1)

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Luminosity

• Luminosity is the amount of electromagnetic energy (visible light, UV, ultraviolet, etc) that the star gives off per second. We can measure this in watts, just like a light bulb.

• While a typical light bulb gives off 100 watts, the sun gives off about somewhere around 3.85x1026, or 385,000,000,000,000,000,000,000,000 watts!

• Larger stars are more luminous than smaller stars.

• Hotter stars are more luminous than cooler stars. 13

Absolute Magnitude

• The absolute magnitude of a star is how bright the star would be if it was 10 parsecs away from Earth.

• A parsec is a distance (we'll get to it shortly!)

• This allows us to fairly compare the brightness of different stars with each other.

The observer in this picture sees the apparent magnitude... both stars seem to have the same brightness.

We can see from the picture that B is brighter than A. We compare the stars with both of them

at the same distance from us. 14

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Radius of a Star

• The radii of stars varies far more than the masses do.

• Unlike solid planets, whose size is determined by the amount of matter that makes them, the size of a star is determined by its internal (core) temperature more than anything else.

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• The size of a star is stable when the force of gravity pulling the surface towards the centre is balanced with the pressure pushing outwards from internal heat.

• Gravity = Heat Pressure Size is Stable

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Gravity Heat Pressure

• If the temperature increases (which happens as the star fuses heavier elements) the outward force increases while the inward force stays the same.

• This makes the star start to grow.

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• Once the forces are in equilibrium again, the star is at its new stable size.

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Same Mass

VERY Different Radii!

Smaller Mass

Larger Radius

Finding the Radius from Luminosity and Temperature

• Most stars appear as a single point of light in the sky, and the radius, with a few exceptions, can’t be measured directly.

• The radius can be determined from its temperature and luminosity using the Stefan-Boltzmann Law.

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• An approximation of the star’s radius is determined using the formula:

L ≈ R2T4

L is the luminosity of the star, in Watts (W)

R is the radius of the star in metres (m)

T is the surface temperature of the star in Kelvin (K)

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• Ratios are normally used to compare the values used in the equation to the Sun.

L/L

= (R/R

)2(T/T

)4

• We can rearrange this to be (trust my math):

R/R

= (T

/T)2(L/L

)0.5

Note: An exponent of 0.5 is the same as a square root.

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Example: Betelgeuse (a fairly large star) has a surface temperature of 3500 K and a luminosity of about 60,000 times that of the Sun. What is the radius of Betelgeuse?

Solution:

R/R

= (T /T)2(L/L )0.5

R/R

= (5800/3500)2(60,000)0.5

R/R

= (2.746)(244.95)

R/R

= 673

R = 673 R

• Therefore Betelgeuse has a radius that is about 670 times larger than the Sun.

Note: An exponent of 0.5 is the same as a square root.

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T

= 5500 oC ≈ 5800 K

Distances to Stars

• AU's are great for measuring distances within a solar system, but are a little too small for measuring the distances between stars.

1 AU = 1.5 x 1011 m

• Light years (the distance that light travels in a year) work better, but still aren't the unit preferred by astronomers.

1 LY = 9.46 x 1015 m (just over 63,000 AU)

(3.00 x 108 m/s)(3.15 x 107 seconds) = 9.46 x 1015 m

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• A parsec is short for a "parallax second".

• It is the distance to a star that experiences a parallax angle of 1 arcsecond as viewed from Earth as it orbits the sun.

– 1 arcsecond is 1/60th of a arcminute.

– 1 arcminute is 1/60th of a degree.

• This means that 1 arcsecond is 1/3600th of a degree.

• A parsec works out to be about 3.26 light years.

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Parallax

• Close your right eye. Hold out your arm and hold up your thumb so that it covers an object in the distance.

• Now close your left eye and look at the location of your thumb with the right eye. It looks like your thumb moved.

• The location of your thumb changed relative to the background because of the different angles you are viewing it from. This is called the parallax of an object.

• Neither your thumb not the distant object moved... you're just looking at them both from a different perspective.

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Measuring Parallax

• The parallax angle can be measured by comparing the displacement of a star relative the background stars when the Earth is on opposite sides of the Sun (in January and June).

• This tends to work better on closer stars (less than a few hundred parsecs) since those that are too far away are the background stars themselves

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• Hal Jordan (who used to be Green Lantern) became a Super Villain named Parallax.

• He's seen here standing behind Kyle Rayner (a newer Green Lantern).

• There's a superhero for nearly ever scientific concept... gotta love it!

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Finding the Distance to a Star using Parallax

• To calculate the distance using parallax the following formula can be used:

d = 1/p

p is the parallax angle measured in arcseconds (1/3600th of a degree)

d is the distance in parsecs

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Example:

Calculate the distance (in light years) to the star Vega which has a parallax angle of 0.129 arcseconds.

Solution:

d = 1/0.129 d = 7.75 parsecs

To convert parsecs to light years multiply by 3.26.

d = 7.75 parsec x 3.26 light years/parsec d = 25.3 light years

• So Vega is 25.3 light years from Earth.

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Finding the Distance to a Star using Absolute and Apparent Magnitude

• Unlike the parallax calculation, the absolute magnitude and apparent magnitude could be used to calculate the distance to distant stars (greater than a few hundred parsecs).

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• If you know the Absolute and Apparent Magnitudes, you can find the distance with the formula:

d = 10(m - M + 5)/5

• d is the distance (in parsecs)

• m is the apparent magnitude

• M is the absolute magnitude

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Example:

The absolute magnitude of Betelgeuse (a bright star in the Orion constellation) is determined to be -5.14 and has an apparent magnitude of 0.45. Calculate the distance to Betelgeuse. Solution:

d = 10(m - M + 5)/5 d = 10(0.45 - (-5.14) + 5)/5 d = 10(10.59)/5 d = 102.118 d = 131 parsecs

• Therefore the distance to Betelgeuse is 131 parsecs.

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Finding the Distance to a Star using Cepheid Variable Stars

• Cepheid variable stars are special stars that dim and brighten repeatedly, with a regular period.

• They are typically 5 to 20 solar masses.

• Typical classical cepheids pulsate with periods of a few days to months, and their radii change by several million kilometers (30% of their size) in the process.

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• By knowing the period of dimming/brightening, the absolute magnitude can be calculated and substituted into the formula as in the example we did for Betelgeuse.

• Note: We won't go into the details of how a cepheid variable works or into calculating the absolute magnitude using this method.

• If you'd like to know more, talk to my good friend Dr. Google...

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The same cepheid star at its dim / bright points.

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