<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012017000200020</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An Approximate Analytic Solution and Stability Criterion for the Logatropic Sphere]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lizano]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Raga]]></surname>
<given-names><![CDATA[A. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez-Ramírez]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,UNAM Instituto de Radioastronomía y Astrofísica ]]></institution>
<addr-line><![CDATA[Morelia Michoacán]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Ciencias Nucleares ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<volume>53</volume>
<numero>2</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012017000200020&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012017000200020&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012017000200020&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT A logatropic equation of state (in which the pressure is proportional to the logarithm of the gas density) has been used in models of molecular clouds to mimic turbulent pressure. We explore solutions of the associated logatropic Lane-Emden equation, describing the hydrostatic equilibrium of a self-gravitating sphere with a logatropic equation of state. We present approximate analytic solutions for the small radius behavior of the non-singular solution, and for its large radius convergence to the singular solution. Combining a &#8220;small radius&#8221; and a &#8220;large radius&#8221; solution, we obtain an analytic approximation to the full, non-singular solution. Using both an exact (numerical) and the approximate analytic solution, we apply Bonnor&#8217;s stability criterion, and determine the stability of the non-singular solution of the logatropic, self-gravitating sphere.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Una ecuación de estado logatrópica (en la que la presión es proporcional al logaritmo de la densidad del gas) ha sido empleada en modelos de nubes moleculares para imitar una presión turbulenta. Exploramos soluciones a la correspondiente ecuación de Lane-Emden logatrópica, que describe el equilibrio hidrostático de una esfera autogravitante con una ecuación de estado logatrópica. Presentamos soluciones analíticas aproximadas para el comportamiento a radios pequeños de la solución no singular, y para su convergencia a radios grandes a la solución singular. Combinando soluciones para &#8220;radios pequeños&#8221; y para &#8220;radios grandes&#8221;, obtenemos una aproximación analítica completa para la solución no singular. Usando la solución exacta (numérica) y la solución analítica aproximada, aplicamos el criterio de estabilidad de Bonnor, y determinamos la estabilidad de la solución no singular de una esfera logatrópica autogravitante.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[equation of state]]></kwd>
<kwd lng="en"><![CDATA[ISM: clouds]]></kwd>
<kwd lng="en"><![CDATA[stars: formation]]></kwd>
</kwd-group>
</article-meta>
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