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The Webfooted Astronomer - July 2000

## Interstellar Dust and Its Effect on Starlight

By Dave Irizarry

INTERSTELLAR dust and gas are abundant in our galaxy and affect the way a star appears. In this article, we will look at the effect dust can have on stellar magnitude, distance estimates, and color. The average distribution of dust within our galaxy is on the order of one dust particle per million cubic meters. Although this sounds like an insignificant amount, interstellar dust makes up about 1% of the interstellar matter, and significantly reduces light received from distant sources.

Interstellar dust can have the following effects on starlight:

• Diminished light received from stars
• A reddening of the light

Under ideal (no dust) circumstances, the relationship between apparent magnitude, absolute magnitude, and distance can be expressed by the distance modulus formula:

m-M = 5 log d – 5

where m is apparent magnitude, M is absolute magnitude, and d is the distance in parsecs

This formula does not suffice, however, if dust intervenes between the observer and the object observed.

When a star is observed through interstellar dust, the apparent magnitude m increases (the object appears dimmer). Therefore, the derived distance d will also increase, resulting in an inflated distance estimate.

To compensate for this, you should add a factor to the distance modulus equation to allow for dimming due to dust. The new distance modulus formula now becomes the following:

m-M = 5 log d – 5 + Av

where m is apparent magnitude, M is absolute magnitude, and d is the distance in parsecs, and Av
is the absorption at visible wavelengths.

First, astronomers determine the color excess of a star, which represents how much "redder" a star appears for a standard star of that type. This is accomplished by first finding a star's observed color index (magnitude measured at a blue wavelength minus magnitude measured at visible wavelength, a.k.a B-V).

This measured color index is then compared to the intrinsic color index of the typical star of that type. This intrinsic color index can be deduced from the spectral properties of the star. By subtracting the observed color index from the intrinsic color index, you get a quantity called color excess (CE).

Shorter (blue light) wavelengths are scattered more effectively by interstellar dust than are longer wavelengths (red light). The such extinction is inversely proportional to the wavelength of light. Thus the more distant a star is, the redder it will appear. In our galaxy, the average absorption at visible wavelengths was found to be approximately 3.2 times CE.

Therefore, if you take a B-V reading and calculate CE, you can more accurately calculate the distance to a star.

There's one caveat: dust can be more concentrated in some directions, so the 3.2 times CE factor should only be taken as an average value.