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By carefully measuring the line profiles the rates of expansion for the N II and Halpha envelope were determined. This data was then put together with the low resolution data to create a model shown below. I should stress that this is my own interpretation of the data that I have acquired here and you may wish to consider its validity for yourself.

The model shows a slice through the nebula along the line of the slit, so this image represents depth through the nebula with the bottom receding edge being furthest from the observer. The left hand side corresponds to the left side of the slit image.

Top spectral row, left side of slit image.
Middle spectral region.
Bottom spectral row, right side of slit image.
In the diagram above there is no sharpe transition between the high and low density nitrogen regions intended but rather a gradual transition. The terms high and low are intended as relative rather than absolute. What I am trying to indicate is a compression with the "slow" velocities and higher densities on the RHS relative to the LHS. The question this model raises is why is the distribution of nitrogen like this?

If we consider the nitrogen rich regions as the equator, then you might explain the thinner region about the poles with higher velocity winds in this region, both during the AGB phase (precursor to the planetary nebula phase, slower winds) and during the planetary nebular (PN) phase (much high velocities), spreading the nitrogen further and more evenly over time. If the material at the equator were not dispersed as greatly during the AGB stage, then there would be regions of higher density nitrogen that could be compressed in the PN phase. The question that I am then left with is "why should there be winds with greater velocity in the polar region if this is what is happening" ?

If we look at our Sun, it is known that there are holes in the corona at the poles and that the solar wind is almost twice that found emminating from the equator. The wind at the poles is about 800km/s, and although it is not known why there should be two components to the solar wind like this, it has been suggested that it is to do with the magnetic field lines and that at the poles the field lines extend out into space. If something like this was happening during the AGB phase of the star that created M57, this could explain the distribution of the gasses seen in the nebula.

Another question that I find interesting is "why is the chemical composition enriched in nitrogen in some regions"? My best thoughts on this at the moment are that these nitrogen enriched clouds were produced during the AGB phase where the star is shedding mass. This suggests that at some point the outer layer that was being shed was high in nitrogen relative to the other elements that can be observed in the above data. It would be interesting to be able to measure the ratio of carbon and oxygen to nitrogen in these clouds but I am not sure how or if I could do this yet. There does seem to be differentiation in the nitrogen and oxygen data shown above.

This all raises more questions than I have answers for, but it does keep the mind active!

The next step in this study was to obtain spectral data in high resolution mode with a 2400g/mm grating. So far I have only manage a single 900s exposure of M57 in this mode in the N II, Halpha region. By time I have everything set up and calibrated M57 is getting very close to the roof of my home and that coupled with a lack of clear nights is very frustrating.

Below is an image to show the position of the slit adjacent to the colour picture of M57. The spectrum was taken on 21 September 2010.

The above data was subsequently corrected for the instrument response using Vega as the reference star. The traces were then normalized. The resulting intensity scales are currently arbitrary units. As can be seen by the change in the plots, my camera has a greater sensitivity in the red than the blue region of the spectrum.
The next set of graphs show plots of the ratio of the H_alpha / H_beta across the nebula.
The data was then extracted by element and the mean intensity plotted against pixel position, which can then be converted into arcsec if desired. This data is shown below.
The comparison of each of the profiles is interesting. Of note is the sharper, more intense nature of the RHS (right hand side) over the LHS. This would suggest that the density of the gas on the RHS is greater. One thing to remember when looking at data like this is that the shorter wavelengths represent higher energy emissions which in turn require higher energy excitation radiation to create the excited species in the first place. The source of the energetic radiation comes from the very hot central star in the form of high energy (UV) photons. This UV radiation , as well as creating excited states can also knock electrons out from atoms to form ions. These electrons can go on to recombine with other ions to form excited states, which when they relax back down towards the ground state generate emission lines. The O2+ emission line at 5007A requires much higher energy photons than the N+ emission line at 6583A to create it. This leads to a situation where the O2+ emission tends to tail off faster than N+ emission because the average radiation / particle energy drops as you move outwards through the nebula.

In the colour pictures, the green colour largely comes from the O2+ emission lines and the red colour at the very edges can be seen to largely come from the N+ emission lines.

It is possible to measure the electron temperature and density across a nebula if sufficient lines are identified for an ion such as OIII. Unfortunately I was unable to find suitable sets, for example I could not find the OIII signal at 4363A. I calculated that it would be 0.00002 units above background on the adjacent plots from a literature value of the temperature. This would require much longer exposures if I was to see it, at this stage I am not sure how long an exposure it would take to see.

The N+ distribution relative to the O2+ is interesting in that it is different on the left and right. It looks like the density is greater on the right, particularly on the edge of slice B (a sharp edge to the nebula or perhaps radiation bound) with a more diffuse tail off on the left side.

The interesting thing here is that there is not a linear relationship between the Halpha and Hbeta emissions. If the conditions changed uniformly across the nebula moving outward from the central star, you might expect there to be a direct relationship between the Halpha and Hbeta lines with the plots being symmetrical either side of the central axis. The intensity of the emission lines reflect the populations in the different energy levels. The fact that there is not an apparent direct relationship or symmetry suggests that the predominant excitation and relaxation processes that establish the Halpha and Hbeta excited state populations changes across the nebula i.e. that the environment is changing.

At the outer edges the Hbeta decreases, in the ring the Halpha is higher and the Hbeta is dropping. In the central part the Hbeta emission to Halpha is constant. The central region is the easiest to explain, the radiation is intense and the gas density is lower so direct UV excitation processes dominated. As you move further out from the central star, the gas density increases, there is a consequential decrease in the available high energy photons, lower energy photons are still available directly from the star and through photon release from high energy excited ions. These lower energy photons can still give rise to an excited state that will produce a Halpha emission. It is also possible that as the density of the nebula increases that there is an increase in the partial transfer of energy from excited species through non-radiative processes that increases the population of lower energy excited species which can give rise to Halpha emission.

This project is to study the Ring Nebula (M57) in Lyra. On the C14 with the spectroscope it is a fairly easy target with reasonable data possible in 35minutes. This means that a number of slices can be taken and differences in the spectra observed across the nebula. The spectra were first printed out as shown for the slice A2 with mean intensity against wavelength. Where there was doubt as to whether the signal was noise or real it is quite easy to verify by looking at the raw spectra shown immediately below where the ring structure across the slit shows up. The sky sodium doublet at 5890A & 5896A can easily be seen running from top to bottom showing a very different distribution to the lines from M57 itself.

The data here is presented with my own interpretation. This is not my field of expertise, stellar gas cloud spectroscopy is some way from a synthetic chemistry lab, so the reader is advised to make their own assessments on how accurate the statements are.

Luminance data taken from the colour image in the above diagrams. Plot showing pixel intensity on z axis against x,y pixel positions.

The luminance filter allows all the visible wavelengths through, so is a combination of all the wavelengths recorded in the spectra above. As can be seen, the general pattern is as expected with the right side being more intense than the left, while the left side is broader.

It should be remembered that this is a plot of intensity from a flat picture, so the 3D structure does not represent the 3D structure of the ring. The data has also not been corrected for instrument response.

Of interest is that it is not smooth, there are variations in intensity which, when viewed in combination with the spectral data above can be seen to reflect variations in gas density and composition. It is hard to see how this would occur otherwise. The two peaks in the centre are stars, one is the central nebula star and the other is a background star that is coincidental to our line of sight.

Slit 61 arcsec from the star at the top. C14, QSI 532 camera, Bin 1x1, slit 24um, grating 2400 g/mm, R=17534, dispn = 0.0873 A/pixel, single exposure of 900s.

The image on the right shows the N II (6548A), Halpha (6563A) and N II (6583) lines from left to right. Because this was a single exposure it was not possible to remove the cosmic ray strike across the Halpha or the hot pixel at the top of the first N II line. Fortunately the N II (6583) line which is the most interesting was clean.

The N II line clearly shows both red shift and blue shift components and from this the rates of expansion can be calculated. In comparison to the N II line, the Halpha can be seen to be much more evenly spread.

Some plots of this data can be seen below:

Date 2/9/2010
Date 2/9/2010
Date 2/9/2010
Date 31/8/2010
Date 2/9/2010