\contentsline {chapter}{\numberline {1}Introductory stuff}{4}
\contentsline {section}{\numberline {1.1}Introduction }{4}
\contentsline {section}{\numberline {1.2}Galaxy formation model}{7}
\contentsline {chapter}{\numberline {2}Some results}{11}
\contentsline {section}{\numberline {2.1}Evolution of the Ly$\alpha $ luminosity function}{11}
\contentsline {section}{\numberline {2.2}Observable properties of Ly$\alpha $ emitters }{16}
\contentsline {subsection}{\numberline {2.2.1}Ly$\alpha $ equivalent widths}{16}
\contentsline {subsection}{\numberline {2.2.2}Broad-band magnitudes}{21}
\contentsline {subsection}{\numberline {2.2.3}Sizes of Ly$\alpha $ emitters}{24}
\contentsline {section}{\numberline {2.3}Predicted physical properties of Ly$\alpha $ emitters }{26}
\contentsline {subsection}{\numberline {2.3.1}Halo masses}{27}
\contentsline {subsection}{\numberline {2.3.2}Clustering bias}{27}
\contentsline {subsection}{\numberline {2.3.3}Stellar masses}{29}
\contentsline {subsection}{\numberline {2.3.4}Metallicities}{30}
\contentsline {subsection}{\numberline {2.3.5}Star formation rates}{31}
\contentsline {subsection}{\numberline {2.3.6}UV continuum luminosities}{31}
\contentsline {section}{\numberline {2.4}The abundance of Ly$\alpha $ emitters at $z>7$}{32}
\contentsline {chapter}{\numberline {3}More complicated stuff}{38}
\contentsline {section}{\numberline {3.1}Some equations}{38}
\contentsline {section}{\numberline {3.2} table}{39}
\contentsline {chapter}{\numberline {4}Final stuff}{41}
\contentsline {section}{\numberline {4.1}Conclusions}{41}