<?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>S0185-11012015000200005</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Approximate analytic solutions for the ionization structure of a dusty Strömgren sphere]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Raga]]></surname>
<given-names><![CDATA[A. C.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lora]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Ciencias Nucleares ]]></institution>
<addr-line><![CDATA[México Distrito Federal]]></addr-line>
<country>México</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Ruprecht-Karls-Universitat Heidelberg Astronomisches Rechen-Institut Zentrum für Astronomie der Universität Heidelberg]]></institution>
<addr-line><![CDATA[Heidelberg Baden-Wurttemburg]]></addr-line>
<country>República Federal Alemana</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2015</year>
</pub-date>
<volume>51</volume>
<numero>2</numero>
<fpage>187</fpage>
<lpage>195</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012015000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012015000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012015000200005&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Presentamos un modelo de balance global de "esfera de Strömgren" para el caso de regiones HII polvorientas. De este modelo, obtenemos prescripciones para el radio exterior de las nebulosas en función del radio de Strömgren R S (de la nebulosa correspondiente libre de polvo) y del espesor óptico del polvo. También obtenemos una nueva solución analítica aproximada para el problema de transporte radiativo, dando formas analíticas para la fracción de ionización en función del radio. Estas soluciones se comparan con los resultados obtenidos del análisis de esfera de Strömgren. Nuestros resultados pueden ser usados para evaluar bajo qué condiciones la presencia de polvo puede tener un efecto importante sobre las estructuras de regiones HII.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[We present a global balance "Strömgren sphere" approach for the case of dusty HII regions. From this model, we obtain prescriptions for the outer radius of the nebulae as a function of the Strömgren radius R S (of the corresponding dust-free nebula) and the dust optical depth. We also obtain a new, approximate analytic solution for the radiative transfer problem, giving analytic forms for the ionization fraction as a function of radius. These solutions are compared with the results obtained from the Strömgren sphere approach. Our results can be used to evaluate under what conditions the presence of dust can have an important effect on the structures of HII regions.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[ISM]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  	    <p align="center"><font face="verdana" size="4"><b>Approximate analytic solutions for the ionization structure of a dusty Str&ouml;mgren sphere</b></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="center"><font face="verdana" size="2"><b>A. C. Raga<sup>1</sup> and V. Lora<sup>2</sup></b></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><sup><i>1</i></sup> <i>Instituto de Ciencias Nucleares, Universidad Nacional Aut&oacute;noma de M&eacute;xico, Ap. 70&#45;543, 04510</i> <i>D.F., M&eacute;xico.</i> (<a href="mailto:raga@nucleares.unam.mx">raga@nucleares.unam.mx</a>).</font></p>  	    <p align="justify"><font face="verdana" size="2"><sup><i>2</i></sup><i>&nbsp;Astronomisches Rechen&#45;Institut, Zentrum f&uuml;r Astronomie der Universit&auml;t Heidelberg, M&uuml;nchhofstr.</i> <i>12&#45;14, 69120 Heidelberg, Germany.</i> (<a href="mailto:vlora@ari.uni&#45;heidelberg.de">vlora@ari.uni&#45;heidelberg.de</a>).</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2">Received February 26 2015.    <br> 	Accepted May 11 2015.</font></p>  	    ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>RESUMEN</b></font></p>  	    <p align="justify"><font face="verdana" size="2">Presentamos un modelo de balance global de "esfera de Str&ouml;mgren" para el caso de regiones HII polvorientas. De este modelo, obtenemos prescripciones para el radio exterior de las nebulosas en funci&oacute;n del radio de Str&ouml;mgren <i>R<sub>S</sub></i> (de la nebulosa correspondiente libre de polvo) y del espesor &oacute;ptico del polvo. Tambi&eacute;n obtenemos una nueva soluci&oacute;n anal&iacute;tica aproximada para el problema de transporte radiativo, dando formas anal&iacute;ticas para la fracci&oacute;n de ionizaci&oacute;n en funci&oacute;n del radio. Estas soluciones se comparan con los resultados obtenidos del an&aacute;lisis de esfera de Str&ouml;mgren. Nuestros resultados pueden ser usados para evaluar bajo qu&eacute; condiciones la presencia de polvo puede tener un efecto importante sobre las estructuras de regiones HII.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>ABSTRACT</b></font></p>  	    <p align="justify"><font face="verdana" size="2">We present a global balance "Str&ouml;mgren sphere" approach for the case of dusty HII regions. From this model, we obtain prescriptions for the outer radius of the nebulae as a function of the Str&ouml;mgren radius <i>R<sub>S</sub></i> (of the corresponding dust&#45;free nebula) and the dust optical depth. We also obtain a new, approximate analytic solution for the radiative transfer problem, giving analytic forms for the ionization fraction as a function of radius. These solutions are compared with the results obtained from the Str&ouml;mgren sphere approach. Our results can be used to evaluate under what conditions the presence of dust can have an important effect on the structures of HII regions.</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Key Words:</b> ISM: HII regions.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmaa/v51n2/v51n2a5.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2"><b>ACKNOWLEDGMENT</b></font></p>  	    <p align="justify"><font face="verdana" size="2">We acknowledge support from the CONACyT grants 61547, 101356, 101975 and 167611 and the DGAPA&#45;UNAM grants IN105312 and IG100214. We acknowledge an anonymous referee for comments which lead to the discussion in &sect; 5.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>REFERENCES</b></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">Binette, L., Wang, J., Villar&#45;Mart&iacute;n, M., Martin, P. G., Magris, C. G. 1993, ApJ, 414, 535</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448153&pid=S0185-1101201500020000500001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Draine, B. T. 2011, ApJ, 732, 100</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448154&pid=S0185-1101201500020000500002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Dyson, J. E., Williams, D. A. 1980, "The Physics of the Interstellar Medium", Manchester University Press, Manchester</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448155&pid=S0185-1101201500020000500003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Franco, J., Tenorio&#45;Tagle, G., Bodenheimer, P. 1990, ApJ, 349, 126</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448156&pid=S0185-1101201500020000500004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Haro&#45;Corzo, S. A. R., et al. 2007, ApJ, 662, 145</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448157&pid=S0185-1101201500020000500005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Hollenbach, D. J., Tielens, A. G. G. M. 1999, RvMP, 71, 173</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448158&pid=S0185-1101201500020000500006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Krumholz, M. R., McKee, C. F., Tumlinson, J. 2008, ApJ, 689, 865</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448159&pid=S0185-1101201500020000500007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Kurtz, S. 2005, in Massive star birth, a crossroads of astrophysics, eds. Cesaroni R. et al. (Cambridge: Cambridge Univ. Press), 111</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448160&pid=S0185-1101201500020000500008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Morisset, C. et al. 2002, A &amp; A, 386, 558</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448161&pid=S0185-1101201500020000500009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Petrosian, V., Silk, J., Field, G. B. 1972, ApJ, 177, L69</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448162&pid=S0185-1101201500020000500010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify"><font face="verdana" size="2">Raga, A. C. 2015, RMxAA, in press</font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">Sternberg, A., Le Petit, F., Roueff, E., Le Bourlot, J. 2014, ApJ, 790, 10</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448164&pid=S0185-1101201500020000500011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Str&ouml;mgren, B. 1939, ApJ, 89, 526</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448165&pid=S0185-1101201500020000500012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">Vasconcelos, M. J., Cerqueira, A. H., Raga, A. C. 2011, A &amp; A, 527, 86</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=7448166&pid=S0185-1101201500020000500013&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Binette]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Villar-Martín]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Martin]]></surname>
<given-names><![CDATA[P. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Magris]]></surname>
<given-names><![CDATA[C. G.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>1993</year>
<volume>414</volume>
<page-range>535</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Draine]]></surname>
<given-names><![CDATA[B. T.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>2011</year>
<volume>732</volume>
<page-range>100</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dyson]]></surname>
<given-names><![CDATA[J. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Williams]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Physics of the Interstellar Medium]]></source>
<year>1980</year>
<publisher-loc><![CDATA[Manchester ]]></publisher-loc>
<publisher-name><![CDATA[Manchester University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Tenorio-Tagle]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Bodenheimer]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>1990</year>
<volume>349</volume>
<page-range>126</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Haro-Corzo]]></surname>
<given-names><![CDATA[S. A. R.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>2007</year>
<volume>662</volume>
<page-range>145</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hollenbach]]></surname>
<given-names><![CDATA[D. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Tielens]]></surname>
<given-names><![CDATA[A. G. G. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[RvMP]]></source>
<year>1999</year>
<volume>71</volume>
<page-range>173</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Krumholz]]></surname>
<given-names><![CDATA[M. R.]]></given-names>
</name>
<name>
<surname><![CDATA[McKee]]></surname>
<given-names><![CDATA[C. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Tumlinson]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>2008</year>
<volume>689</volume>
<page-range>865</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kurtz]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Cesaroni]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Massive star birth, a crossroads of astrophysics]]></source>
<year>2005</year>
<page-range>111</page-range><publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge Univ. Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Morisset]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[A & A]]></source>
<year>2002</year>
<volume>386</volume>
<page-range>558</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Petrosian]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Silk]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Field]]></surname>
<given-names><![CDATA[G. B.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>1972</year>
<volume>177</volume>
<page-range>L69</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sternberg]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Le Petit]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Roueff]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Le Bourlot]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>2014</year>
<volume>790</volume>
<page-range>10</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Strömgren]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[ApJ]]></source>
<year>1939</year>
<volume>89</volume>
<page-range>526</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vasconcelos]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cerqueira]]></surname>
<given-names><![CDATA[A. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Raga]]></surname>
<given-names><![CDATA[A. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[A & A]]></source>
<year>2011</year>
<volume>527</volume>
<page-range>86</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
