The Sheth & van de Weygaert 2004 paper (http://arxiv.org/abs/astro-ph/0311260) shows a plot of number density of voids of a given radius (figure 8, bottom left), but does not give details on its derivation. I am struggling to arrive at the correct formula from the one given on the previous page in the paper (equation 6). If anyone has done this before, or is feeling particularly bored this week, I would really appreciate some help with the derivation.
Article A hierarchy of voids: Much ado about nothing
Chris, if you send an email to Rien van de Weygaert as per his email address given in the paper (just below the title or at the bottom of the first page) he may be able to send you some notes. He has lectured on this and may have something that clarifies it.
I'll tell him to expect a message from you (I share his office on occasion). He's on LinkedIn but not currently active on ResearchGate.
Thanks for your reply Bernard. I have since used the formulation given in Jennings, Li & Hu (2013), equation [10]. This produces a similar form for the abundance as seen in van de Weygaerts paper. If this is the incorrect approach I would greatly appreciate his clarification.
Thank you again for your reply
Article The abundance of voids and the excursion set formalism
Great!
I would nevertheless suggest contacting Rien since he almost certainly will have studied that and he will also be interested in what you are doing. He's a highly constructive person.
With our student at the time, Erwin Platen, we did a number of things with regard to voids, including the Watershed Void Finder (WVF) which in the "Amsterdam tests" proved far more effective than all others except perhaps Marc Neyrink's VOBOZ which gave similar results.
We also tested voids using WVF found in N-body models against the "Much ado .." model, but we did not publish that in its entirety (we did publish a thing on void shapes).
The "Much ado .." paper was a great paper.
Interesting subject - much more work to be done!
You can reach me directly at 'bernard at astrag.demon.co.uk' - I am hibernating away from my Institute while I try to finish my book on cosmology.
Thanks for the help and advice!
I am currently doing some background research for a summer placement on voids; specifically looking at the most extreme examples. The 'Much ado' paper is fantastic, with a thorough explanation of the two barrier problem. A later paper by Sheth entitled 'More ado about nothing' also expands on the formalism, clearing up some of the uncertainty in defining the size / shape / existence of those voids encapsulated within larger overdensities.
From my reading so far I have begun to tentatively conclude that the ZOBOV Voronoi Tesselation algorithm is the most accurate and natural void finding algorithm. However, beyond this the multitude of excursion set forms, and the different means in which the dark matter underdensity is related to the halo underdensity, and then to the galaxy underdensity, is quite intimidating! The paper by Elise Jennings et al. makes a compelling case for assuming a constant volume fraction and allowing the number density of voids to decrease as per hierarchical merging, however concrete comparisons with galaxy catalogues is apparently still beyond reach.
If you have any suggestions or advice on which path of models to take for a current study this would be greatly appreciated. I will email Dr. Van De Weygaert as advised.
Many thanks, and best wishes on completing your book. I look forward to reading it in the future.
Article A hierarchy of voids: More ado about nothing
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