Astr 8300 : Planetary Nebula Project
Analysis of Spectra of NGC 6833 and modeling using CLOUDY
1. a.) I expanded the scale and printed out the spectra at 500 Å intervals. The identified emission and absorption lines are as labeled on the hard copies.
b.) The absorption lines detected are some of the UV metal lines:
Al III (1857), Zn II (2025), Cr II (2056), Fe I (2167), Fe II (2343), Fe II (2374), Fe II (2382), Mn II (2576), Fe II (2585), Mn II (2593), Fe II (2600), Mn II (2606), Mg II doublet (2796.4, 2803.5), Ti II (3385), Fe VI (3760).
The absorption lines are due to the dust in the planetary nebula and the dust in the path along the line of sight to the nebula from earth, which captured the photons traveling through them and produced the absorption lines. The metal lines seen in absorption implies that the lines are generated in a region containing several processed elements, i.e. the interstellar and intergalactic dust where metals produced over ages in stars have become accumulated by stellar winds and several other outflow mechanism.
c.) The large scale continuum features were:
Balmer continuum: Seen in the range 3646 A. Due to the recombination of electrons from free to n = 2 level of neutral hydrogen (free – bound transition).
Paschen continuum: Seen in the range 3647 8206 A. Due to the recombination of electrons from free to n = 3 level of neutral hydrogen (free – bound transition).
Bracket continuum: Seen in the range 8207 A. Due to the recombination of electrons from free to n = 4 level of neutral hydrogen (free – bound transition).
The continuum flux is from the central star or the ionizing source at the center of the planetary nebula. This star radiates like a blackbody of a certain temperature and gives out continuous radiation, which we see as the continuum flux.
2. a.) Emission line flux of H, fnet(H) = 1.696 10–11 erg s–1 cm–2
Emission line flux of H, fnet(H) = 5.169 10–12 erg s–1 cm–2
The observed H/H flux ratio in NGC 6833 = 3.281
Expected H/H flux ratio in a Planetary Nebula = 2.8
(from Osterbrock Table [4.4], in page 84; assuming the gas to be in thermal equilibrium between 10,000 and 15,000 K, and considering Case B recombination only).
To get the reddening E(B–V):
E(B–V) = Const * [A(4861.3) – A(6562.8)] where, Const is a constant to be determined.
or, 1/Const = A(4861.3) / E(B–V) – A(6562.8) / E(B–V).
= R(4861.3) – R(6562.8)
The RHS of the above equation was found from the extinction values at 4861.3 Å (H rest wavelength) and 6562.8 Å (H rest wavelength) using the given galactic extinction curve, by interpolating between the given extinction values, using IDL code (command INTERPOL used).
Hence an estimate of Const was obtained. From this obtained Const, the observed (H/H) flux ratio was converted to E(B–V), by the following calculation.
[Remembering that expected (H/H) flux ratio = 2.8]
Doing the calculation, the resulting E(B–V) = 0.144616.
b.) The observed (reddened) spectrum of NGC 6833 was dereddened using the IDL command ‘unred’. The corrected flux (dereddened) values at each wavelength were stored in the variable ‘fcor’. Henceforth, I worked with (measured flux ratio etc.) the dereddened fluxes (fcor).
In my original spectra (reddened) I did not see any significant 2200 Å dust feature. There was pretty much continuum around 2200 Å. So when I dereddened the spectra, I did not find any significant change in any profile. Around 2200 Å (similar to the other parts of the continuum) the continuum flux increased by some approximately constant value. [See attached plots of spectra ~ 2200 Å showing the original observed spectrum and the dereddened version].
3. a.) The net fluxes of all the observed emission lines from the corrected spectrum were measured, and the corresponding line ratios w.r.t H line flux was found. The table is attached afterwards.
b.) & c.) For temperature and density diagnosis, we want specific line ratios, which depend on these quantities.
Density of electrons in the gas can be estimated in principle from [OII] 3726 / 3729 line ratio or [SII] 6716 / 6731 line ratio. But it is not possible to use these lines for the present spectra of NGC 6833.
The [OII] lines (3726 & 3729) are broad and very much close together in , hence are blended with each other. In the spectra I saw a single broad emission line profile at ~ 3727. The peak position of this broad profile indicated that the 3726 line is stronger than the 3729 line.
The [SII] lines (6716 & 6731) are very weak in the present spectra. They are almost buried in the continuum. There is only a tiny bump around 6731, so it can be concluded that 6731 is stronger than 6716. So by estimating their flux ratio (somehow) can we just get an approximate limit on the density, but not the correct value.
So I used [OIII] 4959, 5007, 4363 lines and [NII] 6548, 6583, 5755 lines to get the estimates of temperature & density. Ratio of [OIII] and [NII] lines give relation between temperature (T) & density (Ne), as following:
These relations are taken from eqns (5.4) and (5.5) of Osterbrock.
Henceforth I found the T and Ne estimate in the following way. Measuring the flux ratio of the corresponding [OIII] lines in the dereddened spectra, I plotted Ne vs. T, taking T as the independent variable and expressing Ne (from [OIII] ratio) in terms of T. Similarly I also measuring the flux ratio of the corresponding [NII] lines, and plotted Ne (from [NII]) vs. T, taking T as independent variable and expressing Ne in terms of T. The point where these 2 curves intersect give the required value of Ne and T for the gas in the planetary nebula. I did this using IDL code (as attached). From the point of intersection of the 2 curves (explained above) I obtained the estimates as:
Temperature, T ~ 12,600 K
Density, Ne ~ 5.9 104 g cm–3
d.) I did not detect any high ionization line, e.g. He II, Ne V. So the ionization state for the planetary nebula NGC 6833 must be low.
This implies that the temperature of the central star must not be very high, ~ 50,000 K or less (and the radiation is not energetic enough to produce high ionization species).
4. a.) I tried to generate CLOUDY model to match the line ratios observed from NGC 6833. Here I briefly describe the method that I used.
The input parameters of CLOUDY are the following and these were set to the given values.
Sphere: Geometry of the cloud was taken as Spherical.
Filling factor: = 0.3, was kept fixed.
Abundances of various elements in the nebula: I did not set any value; they were set at their default values in CLOUDY.
Optical depth / Column Density of gas between us and NGC 6833: I did not set any value, it was at the default.
Density of the gas, nH: This was set at the gas density obtained in part (3.c.) from observed line ratio, i.e. nH = Ne .
Radius of the Planetary Nebula / Distance of the front end of the nebula from the central star: I found this radius (r) from given data.
Given: Angular diameter of NGC 6833, = 0.8 arcsec.
Distance to NGC 6833, D = 4750 Pc.
Diameter of the nebula, 2r (a.u.) = D (Pc) (arcsec)
r = ( 4750 0.8 / 2 ) a. u. = 1900 a. u. = 1900 1.496 1013 cm = 2.8424 1016 cm.
I started with the standard T and L values for a typical CLOUDY model input (T = 100,000 K, log10 L = 38). Then I saw the output lines that the model gave, their ratios with H; and compared them with the observed ratios in the spectra taken. The aim was to get within 50% match of the net flux in the strong lines for the model output and the observed spectra, by judiciously giving the model input parameters. But effectively I changed only L and T, which changed the ionization fraction of the gas.
First I saw the kinds of lines CLOUDY output gave and compared them with the strong lines from the spectra. The model gave several He II lines, which I did not find in the spectra. This implied that in the model the central star (at T = 100,000 K) was too hot, and the flux is ionizing most of the He, so that He II lines are seen. But the actual star in NGC 6833 is probably not so hot, as it does not give any He II in emission. So the 1st modification was to decrease the temperature of the central star, so that I do not see appreciable He II lines in CLOUDY output. I kept on decreasing T (keeping log10 L fixed at 38 initially, but later varied L too), making sure that the ratios of other major lines (the Balmer lines, [OIII], [NII], [OII], [OI], He I etc) also did not deviate too much from the observed value. At ~ 50,000 – 55,000 K, the HeII lines decreased to a significant degree compared to H, so that I concluded that no He II comes out of the model, at such low temperature.
However, to get a consistent match with the other observed line ratios also, I had to change the ionizing luminosity too along with temperature; and the process is painful. If I decreased T too much, He II lines became totally absent (more consistent with observation), but then some of the other line ratios were also coming down compared to observation, so I could not decrease the temperature as desired.
After doing a set of trial and errors with the L value, I got reasonably close match of the ratios at log10 L ~ 37 – 38.
I tried to do more fine–tuning of the L and T values. Changing T in some directions changed some lines favorably, but ratios for other lines went worse. e.g. to have the correct ratios for [OIII] had to increase T, but then the ratios for [OII] & [OI] went worse.
After messing around with the parameters for a long time; finally I think I have the T & L, within acceptable limits which gives within 50 % match of the line ratios. The final input parameters are: (copied from CLOUDY output).
*********************************> Cloudy 94.00 <****************************
* title Planetary Nebula *
* radius 16.4537 *
* hden 4.77085 *
* blackbody temp=55000 lumin=37.5 *
* filling factor 0.3 *
* sphere *
* print last iter *
*********************************> Log(U): -1.48 <******************
Radius of the Planetary Nebula, log10 (r) = 16.4537.
Density of gas, log10 (nH) = 4.77085
Tstar = 55,000 K
Luminosity, log10 L = 37.5
b.) I have included the final CLOUDY output line ratios in the table along with the observed ratios, indicating if there is a within 50 % match of the ratios for each line.
c.) The lines that are still not matched well and some speculative reasons are as following. In general some usual measurement and observation errors can be attributed to the mismatch.
Some temporary error (random noise generated) in the process of taking the spectra.
Analysis error: As all the line fluxes were obtained by the procedure ‘feature’ that is based on rough eye estimate seeing the profile, there will be finite chances of making human error here.
Some lines were blended with other surrounding lines, so the flux measurement for those lines was not very accurate.
Some lines were broadened so that they blended with some surrounding lines.
If I try to give reasons specific for each line, then the following can be stated.
OIII] 1661, 1666 – the multiplets were blended and hence there were errors in measuring the net fluxes.
NIII] 1750 – Actually a blended multiplet, so difficult to measure net flux accurately.
CII] 2326 – Very weak line, difficult to measure flux.
H15 3712 – Weak line, error in measuring flux.
[OII] 3727 – 3726 blended with 3929, so errors.
[SII] 4070 – Error in measurement of observed flux, as weak line.
[OIII] 4363 – Instrumental or Human error.
Ar IV 4711 – Weak line, error in measuring net flux.
[Ar III] 7135 – T too low to produre Ar III.
[Ar III] 7751 – T too low; observed profile broad & blended ; measurement probably not correct.
d.) I studied the spectra of the Planetary nebula NGC 6833, obtained by HST (FOS), in order to determine some of the physical conditions going on in this nebula and characterize the central star of the nebula. I used IDL and CLOUDY for the analysis.
The spectra (1574 Å to 8498 Å) cover the optical wavelength range and extend to some UV. It consisted of the Blamer and Paschen continuum. There were several emission lines, the most strong ones being: [OIII] 5007 4959, H (6563), H(4861), etc. Some metallic absorption lines could be seen too. The reddening for the nebula was worked out to be E(B–V) = 0.146 (using standard Galactic reddening curve). From line ratios of [OIII] and [NII] the temperature of the gas in the nebula was estimated to be T ~ 12,600 K, and the gas density, Ne ~ 5.9 104 g cm–3. NGC 6833 is probably a low ionization planetary nebula, as we do not see lines of highly ionized species in its spectra.
Then I tried to generate CLOUDY model to match this spectrum. I got reasonable close match of almost all strong emission lines, with temperature of central star, Tstar = 55,000 K, and Luminosity, log10 L = 37.5.
Planetary nebulae are regions of ionized gases around hot stars. From the emission and absorption lines seen in spectra, we can model the physical processes going on in the nebula. We can also try to characterize the ionizing source, i.e. the central hot star from the spectral line characteristics seen. For this we can use photoionization codes like CLOUDY, as was done in this project. But because of several limitations in the observation and analysis methods, and the numerous theoretical assumptions done to develop the code model, we do not get a match of model with observation so easily.
In principle there are several ways to model the physical conditions in a cloud of gas from the spectral line seen. But when comes to the real life application of these theories, several problems come up like: blending of lines with each other, broadening and other turbulence effects etc. I saw several of them while studying the lines of NGC 6833. So we will have to be more clever and design many new different ways to study the nature so that we are successful at the end.