Lets get started and first talk about seemingly simple
A)Geometry
=================
In [GM08] eq. E.6 there's a mBH production rate given in terms of a flux
(S.I.1)
and certain other quantities.
(S.I.1) is a most handy term, but a also a very dangerous one - "dangerous" in terms of over-simplifying the model.
The
is an arithmetically averaged quantity, it is all the the incoming flux/"energy level" (flux/"energy interval" from experimental data respectively) added and scaled by area and time as one can take from the dimensions for stated
above [GM08] eq. E.6.
By averaging energy of discrete events like impinging UHECR, (3D-)geometrical attributes of those discrete events, namely their (3D-)unitvectors, which will here be written as
, become disregarded.
This is without any effect for the reliability of the model as long as the respective stellar body yields a perfectly spherically symetrical response to the impinging rays regardless of CR's
.
But rarely any stellar body to be considerd here is supposed to yield such a perfectly spherically symetrical response due to its magnetic field; the most prominent sample being neutron stars ("n-star"). For n-stars, this "habit" of symetrical response is considerably disturbed; neutron stars are surrounded by a most powerful magnetic field which exerts a Lorentz-Force upon the incoming, charged, CR particles. As rightfully considered in [GM08] Appendix G, this has to be taken into account for production rate calculations.
It is not to be quantified or discussed here what part of the respective loss of rate has to be credited to either deceleration of incoming particles or deflection; for neutron stars one can simply take [GM08] eq. G.8 for reference.
[GM08] eq. G.8 defines a range for polar angle , thus a double-cone shape. CR with trajectories within those cones could contribute to production rates, whereas rays outside those cones would not.
Although the bottom of [GM08] Appendix G the authors already conclude that the production rates calculated for this scenario are too small to provide sufficient rates, things are even worse because there is a wrong ansatz behind their estimation:
The factor
, [GM08] p. 85, can be used to calculate a certain rate of suppression of incoming flux. There is a hidden implication of this ansatz, namely that respective CR sources are evenly enough distributed across a virtual sphere centered at the n-star.
Based on recent Pierre Auger data, eg. [San09] it is a solid assumption that sources of UHECR are quite unevenly distributed across the virtual sphere.
N-stars, which never during their life-time had their axis pointing roughly towards a major UHECR source would likely never have had their "share" of flux [GM08] calculate, whereas n-stars with an axis roughly pointing towards major UHECR sources would have had an impinging rate which would exceed the synchroton-loss reduced rates deduced using [G&M] Appendix G.
So the question is not "What is, for a given n-star, the percentage of appropriate flux impinging from polar regions?" but
"For which n-stars is, or has been, the axis pointing exactly enough towards active UHECR source(s)?"
Over the lifetime of a n-star, the distribution of UHECR sources across a virtual sphere around a n-star will not remain constant - e.g.:
- rotation around the galactic center
- changes of the star population
- cosmic expansion
Unfortunately, those effects are difficult to quantify.
More about anisotropy, production rates and especially similar considerations for binary systems to come.
Best regards,
Solkar
Refs (BibTeX):
=============
[GM08]
@article{Giddings:2008gr,
author = "Giddings, Steven B. and Mangano, Michelangelo L.",
title = "{Astrophysical implications of hypothetical stable TeV-
scale black holes}",
year = "2008",
url = "http://arxiv.org/abs/0806.3381v2",
journal = "Phys. Rev.",
volume = "D78",
pages = "035009",
eprint = "0806.3381",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
doi = "10.1103/PhysRevD.78.035009",
SLACcitation = "%%CITATION = 0806.3381;%%"
}
[San09]
@article{Santos:2009jj,
author = "Santos, E. M. and Colaboration, for the Pierre Auger",
title = "{Anisotropy Studies with the Pierre Auger Observatory}",
year = "2009",
url = "http://arxiv.org/abs/0902.0040"
eprint = "0902.0040",
archivePrefix = "arXiv",
primaryClass = "astro-ph.HE",
SLACcitation = "%%CITATION = 0902.0040;%%"
}http://www.relativ-kritisch.de/forum/viewtopic.php?p=38816#38816
2009-10-21 | achtphasen | 08:05:31 |
| 33 comments



your seemingly simple formula is simply wrong !
We are here talking about centre of mass energies for sub-nuclear reactions and your calculations are at best for billard balls.
All that matters here (and every experiment at a collider is quoting it) is the center of mass energy per nucleon.
So for Ea* and Eb* you have to use
Z/A * 7 TeV
and the denominator is always
2m_p.
Apart from your frequent Freudian allusions to sizeI understand bookshelves are off-topic again. Fine!
I admit I don't understand much of what you try to say.even the most basic knowledge about kinetics and even consider standard methods like LT
an error which amounts to four orders of magnitude (I'm referring to your excel table).an error.
... es finden eben auch relativistische Schwerionenstoesse bei LHC Energien in der Natur statt.
The CM-energy of colliding cars is much higher than any LHC CM-energy.is not overly creative; I would have guessed you could do better...
Following your (wrong) logic,is at least funny; let me assist you a little on consolidating your prejudices:
the CM energy of the system earth-CR is in very good approximation the rest mass of the earth M_earth c^2.
But you try to bluff by multiplying the LHC CM energies by 208 and LT to fixed target gaining another factor 208, getting everything wrong by 208^2I'm not "bluffing" but deploying a Lorentz-Transformation.
The relevant degree of freedom is the nucleon and not the nucleus, CM-energy per nucleon is 5.5 TeV.So those hadrons miraculously split apart when they are in a pro-LHC argument.
obenstehender Off-Topic-Kommentar wurde auf Grund von Drohung mit ZGB, Art. 28k veröffentlicht - es wird darum gebeten, zumindest in diesem Thread auf weitergehende Themaverwässerung zu verzichten, Danke! achtphasen
Stultification & ZGB, Art. 28k Read my comment to Mr. Uebbings question.Maybe better you read my chapter "B" where I already had written that was this
Iron ions from CR colliding with another heavy ion would come closest to Pb on Pb at LHC.could be the closest resemblance (which is not overly surprising).
No,Precisely!
if I say that FeFe could come close, how could I possibly think that pp is the same ?
Anyway this is off-topicOn the contrary - you made on-topic yourself because you tried describing lead cores as just a bunch of protons by your figures.
and I leave you with your arithmetic and audience. MM