# STELLAR SURFACE TEMPERATURES

Q. How do we determine the surface temperatures of stars?

• Ultra-cheap trick: "Say, that star looks a little bit redder than the Sun so its surface temperature must be less than 5800K"

• Cheap Trick: Disperse the light from a star ("take a spectrum"), find the wavelength at which you have the most radiation, then apply Wien's Law. Wien's Law lets us quantify the color-temperature relationship but Wien's Law gives temperatures for objects with Planck-like spectra. Stars don't quite have Planck spectra because of the absorption lines, flux redistribution and other complications like that.

• One of the two ways it is really done - measure colors: The basic idea - for Planck spectra (from solid objects), the ratio of the light in two different color filters unambiguously gives the temperature of the objects. The relationship between color and surface temperature is just a little more complicated however and needs to be calibrated using computer models.

Cooler objects will have redder colors. So, at the crudest level we can simply sort them out by color with the red stars being the coolest and the blue stars being the hottest. To the extent that Stellar spectra look like blackbodies, the temperature of a star can also be measured amazingly accurately by recording the brightness in two different filters.

To get a stellar temperature:

1. Measure the brightness of a star through two filters and compare the ratio of red to blue light.

2. Compare to the spectra of computer models of stellar spectra of different temperature and develop an accurate color-temperature relation.

• Besides the fact that the spectra of stars are not quite Plank spectra, there is a another problem which is that there is stuff between the stars. This stuff is dust and it has properties similar to the upper atmosphere of the Earth - Blue light is more effectively scattered than Red light. This is called "interstellar reddening". So...

• Most stars APPEAR redder than they really are. This means that if we use colors to estimate temperatures, then we will always measure stars to be cooler than their real temperatures.

• Stars of a given Luminosity appear fainter than you would calculate given the distance and inverse sqaure law.

These things lead to all sorts of confusion.

## Fortunately we have Spectral Types

A long time ago, astronomers recognized that different stars had dramatically different absorption lines in their spectra. Some had strong absorption lines due to Hydrogen and little else, some had no Hydrogen lines and many lines due to Iron, Calcium and other elements. The different spectral types were assigned letters with type "A" having the strongest Hydrogen absorption lines, type "B" the next strongest, and so on down the alphabet (skipping lots of letters for various reasons).

One COULD conclude that these stars had different chemical compositions, but the strong correlations between the presence of various lines and a star's color suggested the underlying cause was Atomic physics.

### Here's how it works:

Think about the absorption lines caused when a gas of Hydrogen atoms absorbs photons with an energy that corresponds to an electron jumping from the 1st excited state to the 2nd excited state in the H atom. This photon has a wavelength of 636.5 nm (remember? H ).

For this to happen, there must be some H atoms in the gas with their electrons in the 1st excited state.

Suppose we are talking about the atmosphere of a star.

• For stars with LOW surface temperatures, the atoms and molecules in the atmosphere are on average not flying around as fast as in a hotter gas. This means:

• There will be fewer energtic collision between atoms that could knock electrons into excited states and
• essentially all the H atoms have their electrons in the ground state so even if there are many H atoms, there will be no tell-tale absorptions at 636.5nm.

• For stars with HIGH surface temperature, the atoms in the atmosphere are flying around very quickly.

• Now there are many energetic collisions but
• a large fraction of the H atoms are ionized with no chance of producing absorption lines.

• Or, for stars with just the right surface temperature such that collisions continuously populate the 1st excited state with electrons, there will be LOTS of photons caught that bump the electrons to the 2nd excited level and there will be strong H-absorption lines.

- So a lack of hydrogen absorption lines in a star does not necessarily mean the star's atmosphere is devoid of Hydrogen, it could also mean that the star has a low or very high surface temperature.

- These temperature effects are far and away the most important things when determining spectral types. This can be turned around and we can use spectral types to assign surface temperatures for stars.

- One very nice thing about the spectral type of a star is that the spectral type doesn't change as you add more and more dust between the Earth and a star.

Q. Suppose you measure two stars with identical Spectral Type but Star X is much redder than Star Z. What do you conclude? The colors of Star X have been strongly affected by interstellar reddening.

Once it was recognized that differences in spectral type were due mostly to differences in temperatures of the stars the spectral sequence was reordered by temperature. This has led to lots of dumb mnemonic devices to remember the following sequence:

## Spectral type and distance

Now we can see how to extend the distance ladder to beyond the ~100 parsecs that we get from Trigonometric parallax. This is a technique called Spectroscopic Parallax.

1. Take a spectrum of a star.

2. Find the closest match in spectral type among the nearby stars.

3. Assume that the nearby and distant object are the same sort of star, specifically the same Luminosity.

4. Now compare the apparent brightness and luminosity, apply the inverse square law and you have the distance.

Hold it! What about dust? If the distant star has a redder color than its nearby spectral-type match, the color difference tells you how much dust there is along the line-of-sight and we can calculate how much of the dimming is due to dust and how much is due to distance.