Astronomical Observatory: Cool Images

Astr212 Spring 2005

M42 Orion Nebula, Andrew Butler, honors project

Purpose:
The purpose of this project was to determine how the dust grains in the nebula dim the starlight that we see from Earth.

Properties of the Orion Nebula:
The Orion Nebula is about 1600 light-years away, which is 10.3 million times the distance between the Earth and the sun. This is equivalent to about 25 quadrillion miles! The dimensions of the image are 9.0 × 8.3 light-years.

The Orion Nebula is actually at the front of what is called a giant molecular cloud (GMC) complex. These GMC’s contain molecular hydrogen, which is two hydrogen atoms bound together in a single compound. The center of the Orion Nebula contains massive, hot, blue stars whose temperatures range from roughly 10,000 K to 40,000 K, which translates to a range of 18000° F to 72000° F. This is roughly 2.5 to 7 times the temperature of the sun. These hot stars also heat up the surrounding nebula to 10,000 K and emit enough energy to eject the single electron in the hydrogen atoms surrounding the stars (this process is called ionization). After the electrons have been ejected, most of them will recombine with the ionized hydrogen. When this happens, the electrons eventually emit light of a characteristic wavelength of 656.2 billionths of a meter, which corresponds to red light (an image made at this wavelength is shown below). This is the cause of the red color that is visible in the vicinity of the blue stars in the color image above. Regions in space that emit this characteristic wavelength, called H-alpha, are labeled HII regions. The Orion Nebula is just one of many HII regions in the Milky Way galaxy. Astronomers have even observed HII regions in other galaxies.

In addition to emitting beautiful red light, the Orion Nebula is a place of active star formation. The ultraviolet radiation from the blue stars causes the surrounding HII region to expand into the molecular cloud, which compresses it. This process of gas compression is what makes stars form – if enough mass is initially present, that mass will be significantly contracted, giving rise to stronger gravitational attraction and more kinetic energy to fuse the mass into stars. Astronomers theorize that a recent wave of compression triggered a new generation of star birth in the nebula, which appear as small, faint, red dots in the bottom half of the color image.

Not only does the Orion Nebula contain hydrogen, but it is also surrounded by dust grains, which dim the starlight that we see from Earth, a phenomenon called extinction. The visible effects of these dust grains can be seen in the dark lanes that seem to be cutting into the nebula. These dark lanes are so dense that they block a large majority of the visible light that hits them. Amazingly, the grains that make up the dust clouds are much smaller than common household dust – the smallest dust grains have a radius of around 2 millionths of a meter! They are called polycyclic aromatic hydrocarbons. Even though the dust grains absorb a lot of visible light, they do not absorb nearly as much light of longer wavelengths, such as infrared light. In fact, the currently-forming stars in the nebula (the small, red dots in the image) can only be seen through an infrared filter, which can “see” through the dust in the nebula to reveal the stars that are blocked by dust.

Additional information on and images of the Orion Nebula can be found at the SEDS web site, and a "fly-through" movie of the Orion Nebula was made by the San Diego Supercomputing Center.

Scientific Analysis:

Images in the B and V filters (blue and green) were used to compare how much the dust had dimmed the starlight in each filter. The process of photometry, which converts the pixel values in the images to actual magnitudes of the stars, was used in both filters for four different stars in various parts of the nebula to map the column density of the dust in the different regions of the nebula. The column density is the number of dust particles along the length of a hypothetical cylinder, which stretches from Earth to the star of interest, per unit area of that cylinder. One reference star with a known apparent magnitude (GSC 4774:805 with Vobs = 12.81 and Bobs = 13.92), found in the SIMBAD Astronomical Database, was used to calculate the magnitudes of the other stars in the V and B filters. The Hillenbrand et al paper was used to find the spectral type of each star. Then, using the stellar data in An Introduction to Modern Astrophysics, the expected B – V color for each star’s spectral type and luminosity class were found (luminosity classes were assumed – see notes on table below). The expected B–V is the difference between the absolute magnitudes in the B and V filters, respectively, for each star. For stars GSC 4774:834 and SAO 132343, B–V had to be interpolated between two values because the table did not list their specific spectral types. Taking the difference between the observed Bobs–Vobs and the expected B–V allowed the calculation of A_B – A_V, the difference in extinction between the two filters. Another equation, R = A_V/(A_B – A_V), gave A_V (R was assumed to be 3.1, a typical value for most interstellar regions). From this, A_V = (1.086)t was used to find the optical depth, t. Optical depth is defined as the fraction of the incoming radiation that is absorbed by a cylindrical column of length l and cross-sectional area s_tot = Ns, where N is number of particles in the column (whatever they are) and s is the cross-sectional area of each particle. Each dust particle was assumed to be a sphere with a radius of 0.2 µm (a common value).

Using the equation t = snl, where n is the number of particles per unit volume and l is the length of the cylindrical column, the column density (nl) of dust in the Orion Nebula could be found. The average density of the material between the Earth and the star (the volume density) could also be calculated by dividing the column density by the distance to the star.

To find the distances to each star of interest, the following equation was used:
r = (10 pc)[10^{(V – MV – AV)/5}], where r is the distance, V is the measured apparent magnitude, M_V is the absolute magnitude (found by looking it up for each star’s spectral type), and A_V is the extinction. These distances were used to get a more accurate calculation for the volume density than would be possible by just assuming the stars were all located at the distance of the nebula.

The image below indicates which stars were studied, and the table below indicates the results. It is notable that SAO 132343, a young blue star that is in the nebula and the farthest away from Earth, has the least extinction (see note for explanation of negative value). This must mean that its light is reaching Earth through a gap in the dust lanes. GSC 4774:810 is a young white star somewhat in front of the nebula. It has a large column density but a relatively small volume density. GSC 4774:834 is located even further in front of the nebula than GSC 4774:810, yet it has higher extinction and column density (the highest, in fact). Finally, GSC 4774:805 is a cool star in the foreground. Its extinction and column density are less than those for GSC 4774:810 and GSC 4774:834, which makes sense because it is closer to Earth than those stars.

The average value for the volume density (7.2 × 10^-13 cm^-3) was about 3.5 times greater than a typical value in the plane of the Milky Way (2 × 10^-13 cm^-3).

Table Notes:
† The stars had no data for their luminosity class and were assumed to be main sequence stars of class V.
^‡The units for distance are in parsecs (pc), which is a more convenient unit to use in astronomy than units such as miles. 1 pc = 3.26 light-years.
^× The negative values for the extinction, column density, and volume density of SAO 132343 are due to the uncertainties in its calculated magnitudes in the V and B filters (there are uncertainties in the magnitudes for the other stars as well, but the extinctions for those stars weren’t close enough to zero to place the values below zero). Since our calculated uncertainties for all the stars were no greater than ±0.02 magnitudes, it’s reasonable to say that SAO 132343 has virtually zero extinction, column density, and volume density.
* For these stars, the Hillenbrand et al paper gave a range of spectral types (G0-G2 and K0-K2). Spectral types G1 and K1 were assumed for these stars.

Image Dimensions:

The original images for each separate field were 14.5 × 21.5 arcminutes (vertical × horizontal). When mosaicked, the final uncropped image was 29 × 21.5 arcminutes (the vertical dimension was doubled because two fields were added on top of the other). The cropped image had dimensions of about 21.3 × 17.7 arcminutes. This corresponds to approximately 10 × 8.2 light-years.

North field: (J2000 coordinates 5h 35m 29.0s -5° 12’ 56.0”)

Processing details:
To calibrate the images, a dark, a flat, and a bias image were used. After calibrating the data, the images taken in each filter and in each field were combined using the “combine” function (median) in Maxim. Then, the images in each filter and each field were mosaicked together using the “mosaic” function to create complete images of the entire field in each filter. Since the exposure times in the north field were longer than in the south field, the north field images had to be scaled down so that when the mosaics were made, the whole image had the correct level of brightness. This was done using the “scale factor” function in the “pixel math” menu in Maxim. Essentially, this reduced the amount of pixel counts in the north field images in each filter by a factor that equaled the ratio of the exposure time in the north field to the exposure time in the south field. After this was done, the narrow R mosaic was subtracted from the H-alpha (Ha) mosaic because the Ha filter lets in the Ha emission from the glowing hydrogen gas in the nebula and the stars in the field. Since the narrow R filter only lets in a range of red wavelengths that excludes the Ha wavelength, subtracting the narrow R mosaic from the Ha mosaic gave only the Ha emission in the nebula. This had to be done so an accurate picture of the Ha emission in the nebula could be displayed. The resultant Ha – R mosaic was added to the I mosaic so that all the stars hidden by the dust plus the Ha emission of the nebula could be seen. In order to equalize the brightness levels and to display as much information as possible, the I image was increased by a factor of three because the nebula in the Ha part of the spectrum was about three times as bright as the infrared part. This was the red component of the final image. In addition, the V filter mosaic was used for the green component and the B filter mosaic for the blue component. They were combined in the following proportion: R = 0.65, V = 1.78, B = 7.5. These values provided an equal balance between all the colors (they were adjusted until all the stars looked white on average). Then the gamma function was set to a value of 0.45 in order to display the bright and faint structures of the nebula at the same time. The highest and lowest pixel values were adjusted so the background noise and graininess could be eliminated (min=140, max=5000). This completed the final color image. For the H-alpha image, the mosaics had to scaled by the same method described above in order to get the correct brightness for the whole image, and the gamma function was set to 0.5 with a minimum pixel value of 35 and maximum pixel value of 12000.

Sources:

Ask Dr. Math. 11 Feb. 1997. 29 Apr. 2005

Astronomy Picture of the Day. Eds. Robert Nemiroff and Jerry Bonnell. 21 Apr. 1998. NASA / Goddard Space Flight Center. 27 Apr. 2005

Carroll, Bradley W., and Dale A. Ostlie. An Introduction to Modern Astrophysics. Reading, MA: Addison-Wesley Publishing Company, Inc, 1996. Section 12.1.

Cummings, Karen, Priscilla W. Laws, Edward F. Redish, and Patrick J. Cooney. Understanding Physics: Part 2. Hoboken, NJ: John Wiley & Sons, Inc, 2004.

Hillenbrand, Lynne A. et al. "On the Stellar Population and Star-Forming History of the Orion Nebula Cluster." (1997) Astronomical Journal 113, 1733

Kutner, Marc L. Astronomy: A Physical Perspective. Cambridge, United Kingdom: Cambridge University Press, 2003. Sections 6.2, 14.2.1, 14.2.3, 15.1, 15.6.1, 15.7.

Nadeau, David R., Carter Emmart, and C R. O'Dell. Volume Visualization of the Orion Nebula. 2002. The San Diego Supercomputer Center and the American Museum of Natural History Hayden Planetarium. 4 May 2005

SIMBAD Astronomical Database. Centre de Données astronomiques de Strasbourg. 27 Apr. 2005

Smith, Gene. Gene Smith's Astronomy Tutorial: The Interstellar Medium. 26 Apr. 1999. University of California, San Diego; Center for Astrophysics and Space Sciences. 5 May 2005.

Temperature of the Sun. Ed. Harold Myron. Argonne National Laboratory, Division of Educational Programs. 5 May 2005