Dark Matter in Spiral Galaxies

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Поисковые слова: heart nebula

This is a small research project suitable for undergraduate Astronomy and Physics students. It was put together by Dr Helmut Jerjen from the Research School of Astronomy and Astrophysics (ANU). Please send me an e-mail if you are planning to do this project. I would be delighted to hear more about your own results. Enjoy and have fun!

ROTATION CURVE: When studying spiral galaxies it is invariably found that the stellar rotational velocity in the disk remains constant, or "flat", with increasing distance away from the galactic center. This result is highly counterintuitive since, based on Newton's law of gravity, the rotational velocity would steadily decrease for stars further away from the galactic center. Analogously, inner planets within the Solar System travel more quickly about the Sun than do the outer planets (e.g. the Earth travels around the sun at about 100,000 km/hr while Saturn, which is further out, travels at only one third this speed). One way to speed up the outer planets would be to add more mass to the solar system, between the planets. By the same argument the flat galactic rotation curves seem to suggest that each galaxy is surrounded by significant amounts of dark matter. It has been postulated, and generally accepted, that the dark matter would have to be located in a massive, roughly spherical halo enshrouding each galaxy.

DARK MATTER: it is a kind of matter that does not produce detectable amounts of light but it does have a noticeable gravitational effect. Astronomers are not sure what the dark matter is made of. Possibilities range from large things like planets, brown dwarfs, white dwarfs, black holes to huge numbers of small things like WIMPS, neutrinos or other particles that have not been seen in our laboratories yet. To understand the nature of dark matter is one of the central research activities in astronomy today.
The rotation speed of the stars in galaxies is found NOT to decrease with increasing distance from the galactic center (see emission lines in the spectrum), implying that the overall mass distribution of the galaxy is different from the light distribution. The mass must continue to increase: since the rotation speed satisfies v^2=GM/r, where M is the mass within radius r, we infer that M increases proportionally to r.

MATERIAL: astronomical data visualization software like ds9, IRAF, galaxy spectra

METHOD

Your colleague from the European Southern Observatory sent you a set of spectra for the galaxy NGC6810 obtained at the 3.5m New Technology Telescope. The 2-D CCD spectra can be downloaded here . The slit of the spectrograph was centred on the galaxy and aligned parallel to its major axis. On the CCD each row corresponds to a spectrum of the target galaxy at a specific location along the major axis.

NGC6810_[1-4].fits:
You will notice five prominent S-shaped emission lines when you display one of the spectra. The task is to analyse one of them to derive the rotation curve of the galaxy. The first group of three emission lines are (from left to right) [NII] @ 6548 A, H_alpha @ 6563 A, and [NII] @ 6584 A. The two emission lines on the right are [SII] @ 6712 A and 6731 A. Please note that the quoted wavelengths are rest frame wavelengths. From these numbers work out the spectral resolution of the spectrum (along the x-axis).

Consider the 2-D spectrum to be a landscape image. Every pixel has a position (x-y coordinates) and a height (ie. the amount of flux at pixel x, y). Select a suitable emission line. Display the spectrum in IRAF (display spectrum.fits) - run imexam (imexam) - put cursor onto the position you want to measure the center of the spectral line - press j-key. This will fit a Gaussian curve to the spectrum along the x-axis and gives you for each row (y) the x-value where the height (z) of that emission line reaches its maximum. Record all the x, y, z coordinates in a file. (Note: To improve the signal-to-noise in the first data set you may want to combine the four images using the imcombine command in IRAF.)

After you obtained all the technical information you need to convert them into physical quantities by using a pixel scale along the y-axis of 0.166 arcsec/pix (1st set), 0.267 arcsec/pix (2nd set) on the sky and the spectral resolution as you have calculated before.

Analysing a NeAr-lamp spectrum, your colleague calibrated the galaxy spectrum and found that the rest frame x-coordinate of the H_alpha line for the 1st set is at pixel 1686.3 ([NII] @ 6584A is at 1702.5). The number for the 2nd set are: H_alpha is at pixel 581.0. Calculate the redshift of the galaxy, generate the apparent and true (inclination corrected) rotation curve of the galaxy. Use the HST image of NGC6810 (NGC6810_WFPC2_606.fits) to estimate the inclination. What is the maximum rotation velocity and the total amount of mass (including dark matter) in the galaxy as a function of radius.

RESULTS: compare your findings with the results reported in the literature.

Now use the acquired knowledge and analyse the Echelle spectrum of ESO240-G011. The brightest emission line spectrum is from H_alpha. Slit width is 330 arcsec.

Images and data credits: the galaxy spectrum and the data for the rotation curve were kindly made available by Erwin de Blok.
Comments and feedback: jerjen@mso.anu.edu.au
Last update: August, 2007