Koornwinder polynomials: Difference between revisions

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{{About|black hole spin-flips|atomic spin-flips|Hydrogen line}}
If an existing Word - Press code is found vulnerable, Word - Press will immediately issue an update for that. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. * A community forum for debate of the product together with some other customers in the comments spot. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. You can easily customize the titles of the posts in Word - Press blog in a way that only title comes in the new post link and not the date or category of posts. <br><br>Luckily, for Word - Press users, WP Touch plugin transforms your site into an IPhone style theme. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. We also help to integrate various plug-ins to expand the functionalities of the web application. These four plugins will make this effort easier and the sites run effectively as well as make other widgets added to a site easier to configure. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>Minor and medium sized corporations also have a lot to obtain by shelling out in a very good website. After sending these details, your Word - Press blog will be setup within a few days. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. These frequent updates have created menace in the task of optimization. If you've hosted your Word - Press website on a shared hosting server then it'll be easier for you to confirm the restricted access to your site files. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. If you choose a blog then people will be able to post articles on your site and people will be able to make comments on your posts (unless you turn comments off). Look for experience: When you are searching for a Word - Press developer you should always look at their experience level. <br><br>This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user.  If you adored this article and you would like to receive more info concerning [http://topne.ws/BackupPlugin403045 wordpress dropbox backup] please visit our internet site. Word - Press is the most popular personal publishing platform which was launched in 2003. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.
 
[[Image:SpinFlip.jpg|thumb|Schematic diagram of a black hole spin-flip.]]
 
A '''black hole spin-flip''' occurs when the [[rotation|spin]] axis of a [[rotating black hole]] undergoes a sudden change in orientation due to absorption of a second (smaller) black hole.
Spin-flips are believed to be a consequence of [[galaxy merger]]s, when two [[supermassive black holes]] form a bound pair at the center of the merged [[galaxy]] and coalesce after emitting [[gravitational waves]].
Spin-flips are significant astrophysically since a number of physical processes are associated with black hole spins; for instance, [[relativistic jet|jets]] in [[active galaxies]] are believed to be launched parallel to the spin axes of supermassive black holes.
A change in the rotation axis of a black hole due to a spin-flip would therefore result in a change in the direction of the jet.
 
==Physics of Spin-Flips==
 
A spin-flip is a late stage in the evolution of a [[binary black hole]]. The binary consists of two black holes, with masses <math>M_1</math> and <math>M_2</math>, that revolve around their common [[center of mass]]. The total [[angular momentum]] <math> J </math> of the binary system is the sum of the angular momentum of the [[orbit]], <math>{L}</math>, plus the [[spin angular momenta]] <math>{S}_{1,2}</math> of the two holes:
 
<math>
 
\mathbf{J}_{\rm init} = \mathbf{L}_{\rm orb} + \mathbf{S}_1 + \mathbf{S}_2.
 
</math>
 
If the orbital separation is sufficiently small, emission of energy and angular momentum in the form of [[gravitational radiation]] will cause the orbital separation to drop. Eventually, the smaller hole <math>M_2</math> reaches the innermost stable circular orbit, or ISCO, around the larger hole. Once the ISCO is reached, there no longer exists a stable orbit, and the smaller hole plunges into the larger hole, coalescing with it. The final angular momentum after coalescence is just
 
<math>
 
\mathbf{J}_{\rm final} = \mathbf{S},
 
</math>
 
the spin angular momentum of the single, coalesced hole.  Neglecting the angular momentum that is carried away by gravitational waves during the final plunge—which is small<ref>Baker, J. et al. (2006), [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000096000011111102000001&idtype=cvips&gifs=yes  "Gravitational wave extraction from an inspiraling configuration of merging black holes"], ''Phys. Rev. Lett.'' '''96''', 11102.</ref> -- conservation of angular momentum implies
 
<math>
 
\mathbf{S} \approx \mathbf{L}_{\rm ISCO} + \mathbf{S}_1 + \mathbf{S}_2.
 
</math>
 
<math>S_2</math> is of order <math> (M_2/M_1)^2</math> times <math>S_1</math> and can be ignored if <math>M_2</math> is much smaller than <math> M_1</math>.  Making this approximation,
 
<math>
 
\mathbf{S} \approx \mathbf{L}_{\rm ISCO} + \mathbf{S}_1.
 
</math>
 
This equation states that the final spin of the hole is the sum of the larger hole's initial spin plus the orbital angular momentum of the smaller hole at the last stable orbit. Since the vectors <math>S_1</math> and <math> L </math> are generically oriented in different directions, <math> S </math> will point in a different direction than <math> S_1 </math> -- a spin-flip.<ref name=ME2002/>
 
The angle by which the black hole's spin re-orients itself depends on the relative size of <math> L_{\rm ISCO}</math> and <math> S_1</math>, and on the angle between them. At one extreme, if <math> S_1 </math> is very small, the final spin will be dominated by <math> L_{\rm ISCO}</math> and the flip angle can be large. At the other extreme, the larger black hole might be a maximally-rotating [[Kerr black hole]] initially. Its spin angular momentum is then of order
 
<math>
 
S_1 \approx GM_1^2/c.
 
</math>
 
The orbital angular momentum of the smaller hole at the ISCO depends on the direction of its orbit, but is of order
 
<math>
 
  L_{\rm ISCO} \approx GM_1M_2/c.
 
</math>
 
Comparing these two expressions, it follows that even a fairly small hole, with mass about one-fifth that of the larger hole, can reorient the larger hole by 90 degrees or more.<ref name="ME2002"/>
 
==Connection with radio galaxies==
 
Black hole spin-flips were first discussed<ref name="ME2002">[[David Merritt|D. Merritt]] and R. Ekers (2002), [http://adsabs.harvard.edu/abs/2002Sci...297.1310M  "Tracing black hole mergers through radio lobe morphology"], ''Science'' '''297''', 1310.</ref> in the context of a particular class of [[radio galaxy]], the [[X-shaped radio galaxy|X-shaped radio sources]]. The X-shaped galaxies exhibit two, misaligned pairs of radio lobes:  the "active" lobes and the "wings". It is believed that the wings are oriented in the direction of the jet prior to the spin-flip, and that the active lobes point in the current jet direction.  The spin-flip could have been caused by absorption of a second black hole during a [[galaxy merger]].
 
== See also ==
 
* [[Supermassive black hole]]
* [[Gravitational waves]]
* [[Radio galaxy]]
 
== References ==
 
{{Reflist}}
 
==External links==
* [http://relativity.livingreviews.org/Articles/lrr-2005-8/index.html Massive black hole binary evolution] An article on binary black holes.
* [http://www.nrao.edu/pr/2002/xmark/ Scientists Detect "Smoking Gun" of Colliding Black Holes]
 
[[Category:Radio galaxies| ]]
[[Category:Supermassive black holes]]
[[Category:Black holes]]

Latest revision as of 01:59, 25 September 2014

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