Photometric Distances

Photometric distances are used for almost all astronomical objects. These distances are calibrated by geometric methods using parallax and proper motion, which is why the geometrical methods were given a week of class time.

Photometric methods depend on knowing the luminosity of an object, which is the power it radiates. Examples:
1. A 100 watt incandescent bulb radiates 100 watts, 95 in infrared, 5 in visible light.
2. A 20 watt flourscent bulb radiates 5 watts, all in visible light.
3. The sun radiates 4 * 10E26 watts, meaning 10 to the 25th power. This is such a large number that we just call it one solar luminosity, or L(sun).
4. A supernova at peak luminosity radiates billions of L(sun).

The brightness of an object is an intuitive concept, but the units may not be. The brighter object illuminates a given area with more power than a dimmer object. The unit of brightness is watts/square meter.

Consider a star at the center of a sphere of radius d. The brightness at any place on the sphere is its luminosity/(area of the sphere), or  luminosity/4*pi*d(squared). The formula just tells us that the brightness of a star depends directly on its luminosity, and inversly on the square of its distance.

If the distance is what we want to discover, as in Astronomy and Cosmology, we need objects of known luminosity. Such objects are called standard candles. The distance squared is proportional to the luminosityand inversely proportional to the measured brightness. The distance is proportional to the square root of (luminosity/brightness). That is what we call a photometric distance.

Any photometric method is labeled by the type of standard candle used, whose luminosity is determined in different ways. Otherwise, they're all one method. We have considered four so far:

1. Main sequence stars if a known color. (Works in clusters, where we know which stars are on the main sequence.)
2. Cepheid variables of a known period. Works for "nearby" galaxies.
3. Type II supernovas. (See also here.) Works by measuring the temperature of the expanding photosphere, and calculating its radius over time from its Doppler velocity toward us. The temperature and area yield the luminosity.
4. Type Ia supernovas. These are self similar, and with care can be really accurately calibrated. We do need (and have) a set in galaxies whose distances are accurately known.