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	<title>Comments on: Pulsar SMASH!</title>
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	<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/</link>
	<description>I am an astronomer, writer, and skeptic. I likes reality the way it is, and I aims to keep it that way. My real name is Phil Plait, and I run the Bad Astronomy blog.</description>
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		<title>By: DrFlimmer</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-2/#comment-126587</link>
		<dc:creator>DrFlimmer</dc:creator>
		<pubDate>Sat, 18 Oct 2008 11:44:46 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126587</guid>
		<description>@ Ivan

Thanks a lot! My english is improving but there are still many errors - so correction always helps. And &quot;enaugh&quot; is a word I&#039;m spelling wrong many times, I don&#039;t know why.....

@ Tom Marking

I have no &quot;real&quot; answer for you, but I think that most neutron stars have masses of about 2 solar masses or more. I don&#039;t know if it&#039;s impossible to have a neutron star lighter than the earth, but I think this is VERY unlikely.</description>
		<content:encoded><![CDATA[<p>@ Ivan</p>
<p>Thanks a lot! My english is improving but there are still many errors &#8211; so correction always helps. And &#8220;enaugh&#8221; is a word I&#8217;m spelling wrong many times, I don&#8217;t know why&#8230;..</p>
<p>@ Tom Marking</p>
<p>I have no &#8220;real&#8221; answer for you, but I think that most neutron stars have masses of about 2 solar masses or more. I don&#8217;t know if it&#8217;s impossible to have a neutron star lighter than the earth, but I think this is VERY unlikely.</p>
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		<title>By: Tom Marking</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-2/#comment-126551</link>
		<dc:creator>Tom Marking</dc:creator>
		<pubDate>Sat, 18 Oct 2008 02:08:42 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126551</guid>
		<description>@DrFlimmer &quot;The Chandrasekhar limit is for electron degeneracy which does not apply for neutron stars but for white dwarfs.&quot;

If anyone knows, are there any known cases of binary pulsars where the combined mass of the two pulsars is less than 2.8 solar masses?  Also, what would determine the lower limit for the mass of a neutron star?  Could you have one with the mass of the earth or smaller?</description>
		<content:encoded><![CDATA[<p>@DrFlimmer &#8220;The Chandrasekhar limit is for electron degeneracy which does not apply for neutron stars but for white dwarfs.&#8221;</p>
<p>If anyone knows, are there any known cases of binary pulsars where the combined mass of the two pulsars is less than 2.8 solar masses?  Also, what would determine the lower limit for the mass of a neutron star?  Could you have one with the mass of the earth or smaller?</p>
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		<title>By: IVAN3MAN</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-2/#comment-126528</link>
		<dc:creator>IVAN3MAN</dc:creator>
		<pubDate>Fri, 17 Oct 2008 23:27:52 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126528</guid>
		<description>@ DrFlimmer

I&#039;ve being doing some more checking and, yes, you&#039;re right, but you have misspelled a couple of words more than once in your posts: it should be &lt;i&gt;weird&lt;/i&gt;, not &quot;weired&quot;, and it should be &lt;i&gt;enough&lt;/i&gt;, not &quot;enaugh.&quot; :) 

Excuse me for being a nitpicker, but I used to be a proofreader -- old habits die hard!

The &quot;upper mass limit&quot; that you mentioned, this is known as the &lt;b&gt;Tolman-Oppenheimer-Volkoff (TOV) limit&lt;/b&gt;; there is some speculation that a &lt;b&gt;quark star&lt;/b&gt; might be created if it has a density of between 2 to 3 solar masses, but any star of over 5 solar masses will inevitably collapse due to gravitational forces forming a black hole.</description>
		<content:encoded><![CDATA[<p>@ DrFlimmer</p>
<p>I&#8217;ve being doing some more checking and, yes, you&#8217;re right, but you have misspelled a couple of words more than once in your posts: it should be <i>weird</i>, not &#8220;weired&#8221;, and it should be <i>enough</i>, not &#8220;enaugh.&#8221; <img src='http://blogs.discovermagazine.com/badastronomy/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' />  </p>
<p>Excuse me for being a nitpicker, but I used to be a proofreader &#8212; old habits die hard!</p>
<p>The &#8220;upper mass limit&#8221; that you mentioned, this is known as the <b>Tolman-Oppenheimer-Volkoff (TOV) limit</b>; there is some speculation that a <b>quark star</b> might be created if it has a density of between 2 to 3 solar masses, but any star of over 5 solar masses will inevitably collapse due to gravitational forces forming a black hole.</p>
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		<title>By: Tom Marking</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-2/#comment-126525</link>
		<dc:creator>Tom Marking</dc:creator>
		<pubDate>Fri, 17 Oct 2008 23:17:14 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126525</guid>
		<description>@Ian &quot;That complicates the angular momentum calculation.&quot;

Yes, it does.  If you intend to correctly model pulsar formation you will need a supercomputer, and even then, you are likely to be wrong because we don&#039;t have a good model.  For example, the EOS (Equation Of State) for neutron stars which links temperature, density, pressure, etc. together is pretty much not known to any high degree of accuracy.  Also, angular momentum is not conserved since mass is ejected from the star during the supernova event.</description>
		<content:encoded><![CDATA[<p>@Ian &#8220;That complicates the angular momentum calculation.&#8221;</p>
<p>Yes, it does.  If you intend to correctly model pulsar formation you will need a supercomputer, and even then, you are likely to be wrong because we don&#8217;t have a good model.  For example, the EOS (Equation Of State) for neutron stars which links temperature, density, pressure, etc. together is pretty much not known to any high degree of accuracy.  Also, angular momentum is not conserved since mass is ejected from the star during the supernova event.</p>
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		<title>By: Tom Marking</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-2/#comment-126521</link>
		<dc:creator>Tom Marking</dc:creator>
		<pubDate>Fri, 17 Oct 2008 22:59:20 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126521</guid>
		<description>&quot;But why does it only emit gamma rays? Hey, good question. I don’t know the answer (and the press release doesn’t say, in fact). I suspect the answer right now is, we don’t know.&quot;

Isn&#039;t the radiation from pulsars synchrotron radiation caused by charged particles rotating around magnetic fields.  The frequency of emission is:

Freq = B * q / (2 * pi * m)

B is the magnetic field strength in teslas
q is the charge of the particle in coulombs
m is the mass of the particle in kilograms

So for very high frequency radiation such as gamma rays the magnetic field is intense.  The region where B is very large is close to the magnetic poles of the pulsar.  X-rays will be generated farther out.  Ultraviolet radiation still farther out, visible light even farther, and so on.  Now, because the magnetic field lines curve around the geometry may be such that the gamma ray emitting region is aligned with our line of sight but the visible light emitting region is not.

Or another alternative is that the gamma ray emitting region has lots of charged particles which allow it to emit strongly whereas the visible light emitting region is relatively depleted in charged particles.  So there are lots of explanations that could explain the data.  Finding out which explanation is correct is, of course, more tricky.</description>
		<content:encoded><![CDATA[<p>&#8220;But why does it only emit gamma rays? Hey, good question. I don’t know the answer (and the press release doesn’t say, in fact). I suspect the answer right now is, we don’t know.&#8221;</p>
<p>Isn&#8217;t the radiation from pulsars synchrotron radiation caused by charged particles rotating around magnetic fields.  The frequency of emission is:</p>
<p>Freq = B * q / (2 * pi * m)</p>
<p>B is the magnetic field strength in teslas<br />
q is the charge of the particle in coulombs<br />
m is the mass of the particle in kilograms</p>
<p>So for very high frequency radiation such as gamma rays the magnetic field is intense.  The region where B is very large is close to the magnetic poles of the pulsar.  X-rays will be generated farther out.  Ultraviolet radiation still farther out, visible light even farther, and so on.  Now, because the magnetic field lines curve around the geometry may be such that the gamma ray emitting region is aligned with our line of sight but the visible light emitting region is not.</p>
<p>Or another alternative is that the gamma ray emitting region has lots of charged particles which allow it to emit strongly whereas the visible light emitting region is relatively depleted in charged particles.  So there are lots of explanations that could explain the data.  Finding out which explanation is correct is, of course, more tricky.</p>
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		<title>By: Ian</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-1/#comment-126501</link>
		<dc:creator>Ian</dc:creator>
		<pubDate>Fri, 17 Oct 2008 21:20:09 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126501</guid>
		<description>Thanks Tom, although I think I wasn&#039;t clear enough.  The problem I ran into when I tried it was that the sun&#039;s rotation isn&#039;t homogeneous; its period varies from 25-35 days depending on latitude, and it also appears to rotate faster at the core than at the surface (source: Wikipedia).  That complicates the angular momentum calculation.  Your estimate is probably correct to within an order of magnitude, though, and I guess I&#039;ll have to be satisfied with that.</description>
		<content:encoded><![CDATA[<p>Thanks Tom, although I think I wasn&#8217;t clear enough.  The problem I ran into when I tried it was that the sun&#8217;s rotation isn&#8217;t homogeneous; its period varies from 25-35 days depending on latitude, and it also appears to rotate faster at the core than at the surface (source: Wikipedia).  That complicates the angular momentum calculation.  Your estimate is probably correct to within an order of magnitude, though, and I guess I&#8217;ll have to be satisfied with that.</p>
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		<title>By: DrFlimmer</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/comment-page-1/#comment-126495</link>
		<dc:creator>DrFlimmer</dc:creator>
		<pubDate>Fri, 17 Oct 2008 21:01:54 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2008/10/16/pulsar-smash/#comment-126495</guid>
		<description>@ kappapavonis and Tom Marking

You are both right that there is that threshold of 1.4 solar masses. But it doesn&#039;t apply to neutron stars because there is a BIG difference in the formation process between a neutron star and a white dwarf which is limited by the Chandrasekhar limit. 
Also during a type-B-Supernova (or core-collapse-supernova as those guys are called, too, when neutron stars or black holes form) things are really weired, so there is no need for a neutron star to be &quot;so massive&quot;.

If a core of a star burns out of fuel, that is it burns silicium to iron (not to mention that this process only takes few days - very short time!!), then iron-core finally collapses in a very short amount of time (some milli-seconds). The pressure is so high that the electrons are pressed into the protons to form a neutron and send out a neutrino. Although neutrinos do not interact very willingly with matter the density of the surrounding material is high enaugh that the cross section of neutrino-partical-interaction is rather big. So the neutrinos crash into the surrounding material and blow it off - the supernova explodes and leaves behind the degenerated core containing only neutrons. 
But the degeneracy depends on neutrons and not on electrons which means that we have another upper mass limit, but not a lower limit. A neutron star can actually be lighter than 1.4 solar masses due to the different formation processes.

The Chandrasekhar limit is for electron degeneracy which does not apply for neutron stars but for white dwarfs. Those guys form rather non-violent compared to a supernova. If a light-weight star (like the sun) runs out of fuel the core contracts (very slowly ;) ) and settles finally when the electrons degenerate. The outer layers of the star have been shed throughout the lifetime of the star leaving behind the core. 

I hope I got these things right ;) I didn&#039;t looked it up, but this is what I remembered.

I still think it is amazing. Gravitation is always known to be &quot;weak&quot;, the weakest force at all. But finally it can overcome everything else if you don&#039;t pay attention ;)</description>
		<content:encoded><![CDATA[<p>@ kappapavonis and Tom Marking</p>
<p>You are both right that there is that threshold of 1.4 solar masses. But it doesn&#8217;t apply to neutron stars because there is a BIG difference in the formation process between a neutron star and a white dwarf which is limited by the Chandrasekhar limit.<br />
Also during a type-B-Supernova (or core-collapse-supernova as those guys are called, too, when neutron stars or black holes form) things are really weired, so there is no need for a neutron star to be &#8220;so massive&#8221;.</p>
<p>If a core of a star burns out of fuel, that is it burns silicium to iron (not to mention that this process only takes few days &#8211; very short time!!), then iron-core finally collapses in a very short amount of time (some milli-seconds). The pressure is so high that the electrons are pressed into the protons to form a neutron and send out a neutrino. Although neutrinos do not interact very willingly with matter the density of the surrounding material is high enaugh that the cross section of neutrino-partical-interaction is rather big. So the neutrinos crash into the surrounding material and blow it off &#8211; the supernova explodes and leaves behind the degenerated core containing only neutrons.<br />
But the degeneracy depends on neutrons and not on electrons which means that we have another upper mass limit, but not a lower limit. A neutron star can actually be lighter than 1.4 solar masses due to the different formation processes.</p>
<p>The Chandrasekhar limit is for electron degeneracy which does not apply for neutron stars but for white dwarfs. Those guys form rather non-violent compared to a supernova. If a light-weight star (like the sun) runs out of fuel the core contracts (very slowly <img src='http://blogs.discovermagazine.com/badastronomy/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' />  ) and settles finally when the electrons degenerate. The outer layers of the star have been shed throughout the lifetime of the star leaving behind the core. </p>
<p>I hope I got these things right <img src='http://blogs.discovermagazine.com/badastronomy/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' />  I didn&#8217;t looked it up, but this is what I remembered.</p>
<p>I still think it is amazing. Gravitation is always known to be &#8220;weak&#8221;, the weakest force at all. But finally it can overcome everything else if you don&#8217;t pay attention <img src='http://blogs.discovermagazine.com/badastronomy/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' /> </p>
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