The redshift distributions for various fluxes for certain types of extragalactic radio sources is visualised from generated data from models coded by Carole Jackson of the Astrophysics department which predict redshift distributions and fluxes for the various types of populations for these extragalactic radio sources. Interesting observations are then made from the visualisations of the various types of populations and their distributions. The visualisation procedures used for this project together with the tools used are described.
Keywords: redshift distributions, flux, extragalactic radio sources, visualisation.
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IntroductionTo obtain 3D spatial information of our Universe, astronomers have investigated extragalactic radio sources which provide a unique cosmological probe for investigating the large scale structure of our Universe. To appreciate this large scale 3D structure, the redshift distributions of various extragalactic radio sources needs to be analysed. Redshift distributions and fluxes for various extragalactic radio sources obtained from models which predict these distributions can be later compared to the Sydney University Molonglo [7] Sky Survey (SUMSS) to verify our understanding of the astrophysics at large redshifts.
Extragalactic radio sources [10] are enigmatic, highly energetic, and, for a large proportion, very distant objects. Analyses of their space distribution show that the most powerful radio sources underwent a massive increase in their space density at redshift (z) around 2 to 3, where they were >1000 times more common that they are at the current epoch (z=0). This is a similar behaviour to that seen for optically-bright QSOs [13], commonly referred to as the `quasar epoch'.
Understanding the cosmic evolution of extragalactic radio sources is now a fundamental issue in cosmology: This is because these sources are found to trace the largest-scale structure of the universe, and moreover, they do so to very high redshift (z > 4). These unique properties are a direct result of the radio emission being unaffected by the intervening intergalactic medium.
However, the observed characteristics of extragalactic radio sources are diverse so that they cannot be treated as `standard candles'. The concept of a `unified scheme', which attributes differing observed characteristics to the orientation of the source to our line-of-sight, very much simplifies the problem. Adopting the `dual population' unified scheme paradigm, we attribute the observed types to just 2 underlying populations. This simplification allows us to model the cosmic evolution history of the radio source populations. From these models we can predict the redshift distribution N(z) to mJy-flux density limits [1] [2], corresponding to the sensitivity of the `new generation' radio surveys (e.g. SUMSS, NVSS & FIRST). With some further refinement and testing these N(z) can be used to translate the 2D radio surveys to 3D structure and thus reveal the development large-scale structure [3] in the Universe.
The data from these models is visualised to obtain a clear picture of the distributions for the various populations of extragalactic radio sources and allow them to be compared in a manner that is both appealing to the eye and usefull for further study. Various 2D and 3D plots were made and compared. Interesting observations from these visualisations are then described. The procedures used for the visualisation process and the tools used are also described.
Theoretical BackgroundRedshifts of extragalactic radio sources are important for study as they provide spatial information on our Universe and have relatively high fluxes compared to other wavelengths. The term redshift signifies an increase in the wavelength of the radiation received from a receding celestial body as a consequence of the Doppler effect, which results in a shift toward the long wavelength end of the spectrum. If we have v , the radial speed of approach or recession of a galaxy, then we have:
where l is the wavelength shift and c is the speed of light. The wavelength shift is easily obtained from the stellar spectral lines compared to earth laboratory measurements of the spectrum of known position lines of elements. Using the same principle applied to extragalactic radio sources, their radial velocities can be deduced by observing the radio spectral lines of various galaxies and quasars. Many interstellar molecules radiate in the radio spectrum and these can also be observed in the laboratory. We can now define redshift by the following formula:
Then we can use the definition for v to interpret the change in wavelength as a velocity Doppler shift as follows:
This formula is however valid for small z's, z < 0.1 or so. For large redshifts as in the case for this project, one must use:
Once the velocity of the celestial body has been deduced, using the famous Hubble’s law, we can deduce the distance using:
where d is the distance and H is the Hubble constant 50 < H < 70 Kms-1.Mpc-1. It should be noted that cosmologists never use velocities and instead prefer to use dimensionless z. To calculate distance d, the proper formula for d is provided below. It is now clear why obtaining and investigating redshifts of celestial bodies is very important. By gathering data for z the 3D spatial visualisation of our Universe becomes possible. Data obtained from the SUMSS and future analysis of the data will provide a unique insite of this large structure. Furthermore, by comparing models which predict the distributions of redshifts and fluxes for various galaxies and quasars with the observed data, our understanding of the astrophysics can be refined further to improve theories on extragalactic radio sources.
The data that was visualised were also categorised according to their flux values for the various galaxy and quasar types. Fluxes are another important quantity that can reveal a great deal about the nature of the galaxy or quasar because once distance is known, it’s temperature, luminosty, and other important physical information can be deduced.
At low flux density limits we are selecting high power sources and nearby sources and any low-to-moderate power sources at high z drop out of the sample. Similarly as we model data to low flux density limits (few mJys) we pick up low-power sources to moderate z (z~0.1) i.e. the starburst population. Radio powers for FRII radio galaxies and quasars range between about 1024.5 W Hz-1 sr-1 to 1028 W Hz-1 sr-1 at 1.4 GHz observed frequency. Radio powers for FRIs and BL Lacs range around 1022 to 1025.5 W Hz-1 sr-1 (watts per hertz per steradian). Starbursts have radio powers in the range around 1021 to 1023.5 W Hz-1 sr-1. Radio flux densities are measured in a unit called janskies (Jy) where 1 Jy = 10-26 W Hz-1 m-2. The relationship between radio power and flux density [4] is
where S is the radio flux density and P is the source's intrinsic radio power which both must be at the same frequency. d is proper distance defined for an Einstein de Sitter universe as follows:
the last term (1 + z)(1 - a) is called the `radio K correction', this takes its name from the equivalent optical correction factor. This term corrects for the difference between observed frequency and the rest-frame frequency of the emission, hence the (1 + z) bit. The exponent (1 - a) corrects for the radio spectrum of the source. Generally we use a = -0.7 which is the cannonical radio slope for synchrotron emission.
The redshift distribution data was categorized for various population types as follows:
FRI galaxies FRII low-excitation FRII high-excitation FRI BL Lacs FRII Quasars FRII BL Lacs Starburst galaxies
Their description follows:
FRIIs
FRII radio sources are characterised by large-scale radio morphologies which extend 100's of kpc (and out to Mpc in some cases) beyond the host galaxy. Their radio morphology comprises a core, radio jets [11], lobes and hotspots, 3C31 is an FRI while 3C219 is an FRII.
Figure 1 - 3C31 and 3C219 radio galaxies, courtesy NRAO
All the quasars are FRIIs and are generally the most powerful radio sources known (refer to the previous given radio powers at 1.4 GHz) and are found at cosmological distances (z ~ 2 - 4).
3C219 is a classical FRII - the brightest radio emission is the core and hotspots. The lobes are sharply defined and are caused by shock heating of the intergalactic medium by the relativistic plasma. High-excitation FRII radio sources have optical spectra which have strong narrow emission lines in their optical/UV spectra indicative of very active accretion processes.
Quasars [12] [8] are thought to be high-excitation FRII radio galaxies with their radio axis close to our line of sight, so that quasars are dominated by their core emission. Quasars have strong broad, as well as strong narrow emission lines in their optical/UV spectra - the broad lines arising from a region close to the accretion disk where gas is moving at very high velocities (hence the Doppler broadening of the lines).
Figure 2 - Quasar 3C175, courtesy NRAO
Low-excitation FRIIs have the same radio morphology as the high-excitation FRIIs but do not have the optical/UV emission line signature - instead their optical/UV spectra is that of a normal elliptical galaxy so that the AGN component is much weaker and is swamped by starlight.
In our evolution model for the FRII population we find that it evolves very strongly with cosmic epoch and that the degree of evolution is dependent upon radio power. Thus the most powerful FRIIs (> 1027 W Hz-1 sr-1) have space densities > 10,000 times their local (z=0) space density.
FRIs
FRI radio sources again have large-scale radio morphologies which extend over 10's or 100 kpc beyond the host galaxy. Their radio powers are generally lower than those of FRIIs and it is their large-scale radio emission which characterises them as FRIs and it is not a luminosity classification. FRIs are more local sources than FRIIs and we now think that there is a transition from high-ex FRII to low-ex FRII to FRI over the Hubble time.
3C31 is a classical FRI, see Figure 1 - the brightest radio emission is near the core. The lobes are very diffuse with no hotspots. In FRIs the radio jets are thought to decelerate very close to the core which explains the much more diffuse radio structure.
BL Lac objects [5] are thought to be low-excitation FRIIs and FRIs oriented with their radio axes close to the line of sight. This explains why the optical/UV spectra of these objects is featureless - the starlight is swamped by a bright featureless continuua from the core.
In our evolution model for the FRI population we find that they are a steady-state population in that they undergo no nett evolution. This doesn't mean that individual objects don't evolve - indeed they probably dim with time but that `new' FRIs replace them so that their space density stays approximately constant.
Starbursts
Starburst galaxies have spiral hosts (unlike FRI and FRIIs which have ellipticals). They are galaxies where the radio emission arises due to the enhanced star formation rates (up to 100 solar mass star formation per year) which ups the supernova rate also. In supernova ejecta magnetic fields and high energy particles are formed which in turn leads to radio synchrotron radiation. Thus the emission from starburst galaxies is also different to the FR sources in that in starbursts the radio emission traces the spiral galaxy morphology whereas in FR sources it is from just the core and then extends way beyond the host.
The evolution of the starburst population has been derived from IRAS (infra-red surveys) and is unconstrained at large z (z~2). [6] We adopt the IRAS model which is for pure luminosity evolution of the sources out to z=2.
Figure 3 - NGC 4670, a starburst galaxy in Coma Berenices, courtesy JHU
The redshift distribution data
Two data sets were given for this project. The first data set, consisted of data from a simpler model which excluded predictions from FRII BL Lacs by having zeros instead and ommited flux distributions for the populations. This data was smaller and easier to work with and gave us practice with the visualisation procedures necessary for the second larger set. It consisted of 15000 data values subdivided as follows:
The first 1000 numbers were the redshift points, z from 0.01 to 10.00 in steps of 0.01. Then followed 7 sets of 1000 N(z)’s for each type of object listed previously for a flux density limit > 10 mJy at 843 Mhz. Then followed another set of 7 population values at a flux density limit > 1 mJy at 843 Mhz.
The second data set was the complete version and much larger consisting of 281040 data values with all redshift distributions. This dataset also had additional flux distributions for the various sources and was subdivided as follows:
The first 1000 numbers were the redshift points, z from 0.01 to 10.00 in steps of 0.01 (same as before). The next 40 numbers were the flux density points for 1.4Ghz in log10 from 0.9 to -3.0 corresponding to a range between of 8 Jy to 1 mJy. Then followed by 7 sets of 1000 N(z)’s for each 7 population type for these flux density points greater then or equal to 8 Jy. Then followed another set of 7 population values at a flux density limit greater then or equal to 6.3 Jy and less then or equal to 8 Jy This continued for 40 sets of values so that the last set was for a flux density limit greater then or equal to 1 mJy and less then 1.26 mJy.
The second data set predicted distributions at the frequency of 1.4Ghz compared to 843Mhz for the first data set, for the population mix there is little difference.
The distributions were initially plotted against redshift but for the second data set it was decided to change the redshift axis z, to look-back time t in Gyears (billion years) which describes the time at which in the past we are looking at. This is more appealing for the average reader and makes the visualisation more interesting. The look-back time data provided was calculated for the Einstein deSitter cosmology with critical density of Wo = 1.00 which means the cosmology model assumes a flat Universe and a Hubble constant of 50 Kms-1Mps-1.
For Wo > 1, the Universe contains enough mass/energy that it’s self gravity will halt the expansion and pull everything back together in a Big Crunch. For Wo < 1, the Universe will expand forever. To date, neither observation nor theory suggest Wo is greater or equal to 1 and it is most likely that we live in an open Universe, ie forever expanding after the Big Bang. However this project will assume Wo = 1.00 to keep it manageable given our time constraints and will ignore observations made earlier this year which give Wo as low as 0.2 or 0.3 [9]. From this model we have:
Age of the Universe = 13.037239840799 Gyrs
Look back time data
The Visualisation
1. The first data setThe first data set was a simpler and much smaller version of the second data set and allowed us to learn the necessary visualisation procedures and ideas more easily. The ideas learnt here were then applied to the second and substantially larger data set. The various plots below are mostly test plots and for more accurate plots, please refer to the second data set where the results are more interesting.
The redshift distribution data described above needed to be graphed with N(z) versus z for each flux limit of 10mJy and 1mJy. To visualise the distributions for the various type of objects and to be able to compare their distributions at a glance, it was decided to plot all the N(z) versus z graphs for each object next to one another separated slightly with a 3D view of all the graphs plotted. Futhermore standard 2D plots were made to confirm the 3D plots and to obtain a better quantitative view of the data. We initially considered to plot the N(z) axis using a log axis, however there was a problem with AVS's log axis feature which didn't seem to work so FRI galaxies for example is very large compared to the other populations. Later for the second data set we decided to use a linear axis for N(z) and noting that the highest value shown is not necessarily the top value.
Figure 4 - 2D graph for S >10 mJy
The software packages used for the visualisation were AVS 5, Advanced Visualisation System [15], AVS Express, Photoshop together with various utilities such as image format conversion. These software packages had enough features to cater for our needs. AVS field files were written to read the N(z) values for each population types for both seven sets and the redshift points. The networks in AVS were then created to handle the data and provide visual aids in graphing the data and provide a display of all the plots in series with a perspective view. A sample of the field files used and the AVS network used can be found in the Appendix.
To obtain 2D plots of the data, an AVS 5 module which caters for plotting 2D graphs was used and all the populations were plotted versus redshift. To obtain 3D plots of the data, it was found that AVS Express had more flexibility for our needs and had a module for ribbon plots which was ideal for our purpose. A description of the modules used in the AVS Express network and their purpose follows:
Figure 5 - AVS Express network to render the ribbons
Read field module: These modules read in the data from the data file and follow the instructions given in our field files. Combine comp: this module takes components from two different fields to make a new n component field. This was required to generate the ribbon plots which required colour values to be added to the data to obtain colour. Scale: This module simply scales any axis values and is usefull for making very small values visible on the plot. Ribbon plot: This generates the ribbons for each population type and was convenient way of plotting the data for this data set. Uviewer3D: This module is required to view the 3D plot.
It was necessary to write a perl script to generate sets of 1000 colour values (for each population type) to give the ribbons differentiating colour. This scipt can be found in the Appendix.
Figure 6 - 3D ribbon plots of the redshift distributions
For the 3D ribbon plots, it was decided to make an animation of the ribbons progressing towards higher redshift making a nice animation of the distributions and clearly descibring their interelationship. We found it important that we gain the experience on generating animated visualisations because the public more and more expects dynamic visualisations on TV or video for example. For example the weather man’s 3D animated weather view on the channel 7 news is much more appealing and descriptive then the other channel’s weather maps. To make an animation of the ribbons progressing towards higher redshift, it was decided to use AVS Express and the network is similar for our previous static ribbon plot, but here a loop generator was used to provide different croping values for the ribbons over time. This produces an animation of the ribbons progressing over time towards z = 10. A module was also used to provide different numbered write image files.
To save the animation for further viewing, it is necessary to save each individual frames by using a write image module in AVS Express then compile the images into a MPEG, QuickTime, RealVideo, AVI, video file using various utilities available. However, one needs to also use another loop module to give the file names individual incremented numbers such as video001.jpg, video002.jpg and so on such that the write image module doesn't overwrite the same picture. We then saved the animation to a Quick Time, QT movie and video cassette for playback on TV to gain some experience in producing visualisations for TV and to gain some video production experience which is very important today as many people only have VCRs and do not have web access.
To compile the individual frames to a QT movie, we used an utility called mediaconvert which provides all the facilities to do this. To save to video, we used the sophisticated facilities at Vislab which can record to video cassette whatever is on the screen. We simply played the QT movie and the video was saved to video casette for playback on TV. It should be noted that one needs to be carefull with colour when used on TV because video on TV is of less quality then on computer monitors, the colour red for example doesn't come out to well and many colours get lost. One needs to be carefull of the colour palette used before exporting to TV video and if necessary reduce or select which colors get exported to videocasette. For professional quality visualisation presentations on video, one should have introduction frames and various other special effects such as labelling on certain frames. Ideally our video would have shown the z values dynamically as the ribbons progress towards higher redhshift. These can easily be done with digital video production software such as Adobe Premiere and is relatively straightforward. Due to time constraints, we didn't pursue this further.
The video below can be viewed with Apple's QuickTime plugin, available for download at the top of this webpage. QT movies are a convenient medium for viewing video over the web and is very popular.
Figure 7 - Testing QT digital video output of the animated ribbons of the redshift distributions data1.mov (230 Kb); data1.mpg (158 Kb)
The use of VRML [14] has allowed 3D data to be visualised easily by anyone on the web and is often used to visualise 3D models online and experience virtual worlds. We decided to use VRML to convert some of the 3D graphs and surface contours into VRML models so anyone on the web can view the redshift distributions at any angle or view. This provides some flexibility compared to static pictures of the distributions which show them only from one angle point of view. It gives the viewer the freedom to explore the redshift distributions and gain a better visualisation of the data. The use of VRML to exchange scientific data that needs to be visualised in 3D can be very usefull and we thought it was necessary that we gain experience in this area.
To convert the redshift distribution 3D plots to VRML files, an AVS module which exports to VRML format was used and provides the facility to convert any geometry to VRML. Since our 3D plots were already meshes, this was relatively straightforward. However, in AVS5 we found that the module only exports to VRML 1.0 and the exported VRML world was very dark even with added lights in AVS. An equivalent network was created in AVS Express which had a VRML 2.0 export module and provided much better results with good lighting of the model and colours. All VRML models of the distributions were done with AVS Express and a typical network is shown below.
Figure 8 - AVS Express network to output to VRML2
The local area ops module is equivalent to the AVS5 module which takes the maximum in a given area and as such smooths the surface. The downsize module reduces the amount of data used to render the surface and as such makes the VRML model more manageable. Surf plot is equivalent to Field to mesh in AVS5 which converts geometry to a mesh which can be viewed by the Uviewer, AVS Express' geometry viewer.
To view VRML worlds, one needs to install the Cosmo player plugin which is a VRML2 browser and works with Netscape (downloadable form the top of this webpage). The downsized VRML model below is for FRII low excitation in the second data set.
Figure 9 - Testing the VRML 2 export capability of AVS Express FRIILowexc.wrz (6 Kb); FRIILowexc.wrl (44Kb)
We also used VRML for the second set of data with the surface contour plots which provide more interesting information on the distributions. One of the major problems we encountered with exporting the redshift distribtions to VRML is that the conversion from the AVS meshes to VRML is very inefficient, generating enormous VRML files of the order of several Megabytes. It is necessary to downsize the data and optimize the final VRML file to approximate the surface otherwise the end user is faced with a very long download time and very slow display frame rate. To deal with this problem, we reduced the number of polygons and faces in the VRML geometry. The less segments and faces a VRML model has, the faster it will display on the computer.
One can also delete hidden faces in the VRML model which cannot be seen by the viewer reducing further the number of segments and faces in the geometry. One can also reduce the digits of precision that the VRML model uses to tell the computer where to display the polygons and faces, this facility is provided for in the AVS Express VRML export module. Finally, the VRML file can be gzipped from a test.wrl VRML file to test.wrl.gz compressed VRML file. This was then renamed to test.wrz which is now commonly used for compressed VRML files. Gzip is a standard compression utility on UNIX systems and since VRML files are ASCII files, it compresses VRML files very well. Cosmo player automatically recognizes these files and we compressed all our VRML files to make them as small as possible.
2. The second data set
The second data set required plots of N(z) versus z versus S (flux) with surface contours following the distributions. This data set was a substantially larger set and required new field files to be written to read in the flux distributions, the amount of data meant that much finer distributions plots can be obtained with no population types ommited. It was decided first to plot the distributions as surface contours and a colormap was given to the surfaces to appreciate their height for N(z).
A perl scipt was written to parse the large data file into 7 smaller data files for each of the populations, this script can be found in the Appendix. An AVS5 network was then wired up to plot a population type using the data file generated by the perl script and a surface contour was obtained by using a local area operations module which took the maximum for N(z) at a certain local area, this smoothed out the contour from many peaks to a more gradual surface. The same network was then cloned with different field files and the surface contours for each of the populations follows:
Figure 10 - Distributions for FRI galaxies
Figure 11 - Distributions for FRII low-excitation
Figure 12 - Distributions for FRII high-excitation
Figure 13 - Distributions for FRI BL Lacs
Figure 14 - Distributions for FRII Quasars
Figure 15 - Distributions for FRII BL Lacs
Figure 16 - Distributions for Starburst galaxies
Having done this, it was decided to place each of these surface contours next to oneanother such that it was easier to compare the distributions between the various populations. Once all the networks for the seven populations were brought together, three plots were made, one for a top view of all seven population surface contours next to oneanother, and two perspective 3D views of the surface contours showing clearly the height for N(z). It was decided to separate the populations into two plots for these views, one for low N(z) values and one for very high N(z) values. This was necessary to plot the surface contours without loosing detail in the surfaces and without using a log axis for N(z). These three plots are the highlight of our project and as such are displayed at the top of this report.
The network to produce these plots is shown below. This essentially uses the same networks used for the surfaces above but combined into a single network:
Figure 17 - AVS5 network to render the combined 3D plots and top view
Most of the modules used above are similar to the previous networks explained earlier. Note that it was decided to use the color range from the FRII Quasars because this provided the better color range for the other plots. In the color legend it was then necessary to mention that the highest N(z) is acutally a lower bound.
We attempted to make a flythrough of the 3D plots and make a VRML model of the combined set. However due to problems with AVS Express' capability to import AVS 5 netorks and lack of time, it was decided to move on. Although AVS Express is supposed to be backward compatible with AVS 5, we found that for most AVS 5 networks this wasn't so and it is necessary to make an entirely new network using AVS Express modules. The top and perspective 3D surfaces of the surface contours provided the visualisation required for this project so this wasn't a problem.
We did however decide to make an animation of the ribbons for this data set similar to the first one for all the flux ranges. Using the same procedure as for the first animation, we obtained the following animation for N(z) increasing towards higher redshift z=10.
Figure 18 - MPEG video of the redshift distributions for the second data set data2.mpg (450 Kb)
The ribbons plots above are given as follows: Dark blue: FRII BL Lacs; Light Blue: FRII Quasars; Yellow: FRI Low excitation; Red: FRI High excitation. The other population ribbons didn't reveal much information and were ommited from the plots. This digital video file is larger then our first animated ribbons and for this animation we decided to save it in MPEG which has a somewhat more superior compression scheme then QT but is lossy and hence reduces download time.
Discussion
The visualisations produced for this project show a wide range of redshift and flux distributions for the various population types. However upon close inspection of the distributions one can notice that the FRII low-excitation, FRII high excitation, FRII Quasars and FRII BL Lacs (call then group A) share similar distributions and characteristics in their surface contours. They have relatively low N(z) surfaces compared to FRI galaxies, FRI BL Lacs and starburst galaxies (call them group B) which have relatively high peaks at low redshifts.
Populations in group A share a common trench like characteristic in their surface contours. The trench or valley in group A goes from higher to lower redshift and towards higher flux densities. The surface contours for the FRII low and high excitation populations and the top view of the combined plots show this clearly. The trench means there is a gap of these populations along the redshift and flux density values that these trenches follow and hence less extragalactic radio sources can be expected to be found at these redshifts and fluxes. To find out why they share this common trench like characteristic one would need to go in the Fortran code that the models used to generate the redshift/flux distribution data and look at the astrophysics used behind the modeling process and determine what physical characteristics populations of group A have in common. Apart from being FRIIs, it is not clear at first glance why there would be a gap in N(z) along these trenches and why they have very similar shapes.
Group B on the other hand have very large peaks for N(z) and high flux densities. Their large peaks for N(z) means their populations are in relatively high numbers compared to populations in group B even though their areas viewed from top of the plots is less. Their flux densities decreases sharply with increasing redshift. From the starburst plot, we can see that these galaxies are relatively closeby with high flux densities compared to the other populations.
One needs to do compare these distributions with astronomical surveys and look at similarities between these distributions to determine whether they agree with the observed data. Astronomers code models of various astronomical objects using current astrophysics that is understood and compare the data from models with observed data from observatories. This comparaison process of the visualisation of the model and observed data is very important because models can then be refined and the astrophysics can be better understood. Unfortunetly due to time constraints, we didn't pursue this further.
Conclusion
This project visualised redshift distribution and flux data for various extragalactic radio sources obtained from models and from these distributions interesting observations and comparaisons were made between the populations. The various tools and procedures used during the visualisation process were described and various visualisation mediums were used to bring the data from obscure numbers in a data file to easy to understand visual displays of the distributions. This project has shown that current tools for effective visualisations of scientific data have reached maturity and that the effect visualisations of data such as these should be standard for all research data.
Acknowledgements
We wish to thank the staff at Sydney Vislab for their invaluable assistance and support they have given us throughout this project and in particular, we would like to thank Daniel Mitchell of Sydney Vislab for his help with AVS together with good ideas he gave us in the visualisation process.
References
[1] Jackson C.A., Wall J.V.: 1998, The Redshift Distribution of Extragalactic Radio Sources, IAP Conf
[2] Jackson C.A., Wall J.V.: 1998, Testing models of radio source space density evolution with the SUMS survey, IAP Conf
[3] Zeilik M., Gregory S.A., Smith E.: 1992, Introductory Astronomy & Astrophysics, 3rd edition, Saunders College Publishing, 439
[4] Kraus J.D.: 1988, Radio Astronomy, 2nd edition, Cygnus-Quasar Books, 3-7
[5] Smith C.R.: 1995, Observational Astrophysics, Cambridge University Press, 322
[6] Pascarelle S.M., Windhorst R.A., Keel W.C., Odewahn S.C.: 1996, Sub-galactic clumps at a redshift of 2.39 and implications for galaxy formation, Nature, 45
[7] Mills B.Y.: 1985, Astronomy at the Molonglo Radio Observatory, Proc. ASA(1), 72
[8] Blundell K.M., Garringtom S.T.: 1996, Evidence for a Black hole in a radio-queit Quasar nucleus, The Astrophysical Journal 486, L91
[9] Adams F.C., Laughlin G.: 1998, The Future of the Universe, Sky and Telescope Aug. 98, 32
[10] The brightest extragalactic radio sources (all sky map)
[11] Jets in nearby FRII galaxies
[12] Surveys for High Redshift Quasars
[13] 2dF QSO Redshift Survey
[14] The VRML Repository - Sydney Vislab Mirror Site
[15] The International AVS Centre
Appendix
A: Typical AVS5 field file used for the first data set for the 2D graphs
B: Typical AVS Express field file to make the 3D ribbons for the first data set
C: AVS Express field file to read the colour values which are assigned to the ribbons
D: AVS Express network for the data1 ribbons
E: Perl script used to sort data2 populations into separate data files
F: AVS5 network used to test the output to VRML
Copyright © 1998 Paul Titze
