The K-band Hubble diagram of sub-mm galaxies and hyperluminous galaxies
Stephen Serjeant$^1$
Duncan Farrah$^{2}$
James Geach$^{3}$
Toshinobu Takagi$^1$
\vspace*{0.3cm}
{\LARGEAprajita Verma$^4$
Ali Kaviani$^{3}$
Matt Fox$^{3}$}
\vspace*{0.1cm}
$^1$Centre for Astrophysics \& Planetary Science
School of Physical Sciences
Canterbury
Kent CT2 7NR
UK
$^2$SIRTF Science Center
Jet Propulsion Laboratory
Pasadena
91125
USA
$^3$Astrophysics Group
Imperial College London
Blackett Laboratory
Prince Consort Road
London SW7 2BW
$^4$MPI fuer extraterrestrische Physik
Giessenbachstr. 1
D-85748
Garching
Germany
We present the $K$-band Hubble diagrams ($K-z$ relations) of sub-mm-selected galaxies and hyperluminous galaxies (HLIRGs). We report the discovery of a remarkably tight $K-z$ relation of HLIRGs, indistinguishable from that of the most luminous radiogalaxies. Like radiogalaxies, the HLIRG K-z relation at $z\stackrel{<}{_\sim}3$ is consistent with a passively evolving $\sim3L_*$ instantaneous starburst starting from a redshift of $z\sim10$. In contrast, many sub-mm selected galaxies are $\stackrel{>}{_\sim}2$ magnitudes fainter, and the population has a much larger dispersion. We argue that dust obscuration and/or a larger mass range may be responsible for this scatter. The galaxies so far proved to be hyperluminous may have been biased towards higher AGN bolometric contributions than sub-mm-selected galaxies due to the $60\mu$m selection of some, so the location on the $K-z$ relation may be related to the presence of the most massive AGN. Alternatively, a particular host galaxy mass range may be responsible for both extreme star formation and the most massive active nuclei. %The hyperluminous $K-z$ relation also makes it easier to estimate %photometric %redshifts for hyperluminous candidates. %Our data is consistent with an evolutionary connection %between the most extreme star formation and AGN activity at the sites %of the largest supermassive black holes.
BoxedEPS.tex
  %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %%
 %%%%%   BoxedEPS.tex FOR FIGURE INSERTS OF EPSF NORM  %%%%%
 %%%%%   (EPSF = Encapsulated PostScript File)
  %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %%  
 %%%  AUTHOR: Laurent Siebenmann
  %%    lcs@matups.matups.fr
  %%  
 %%%  VERSIONS: Feb 1991 -- 24 April, 1992
  %%  
 %%%  SOMMAIRE: BoxedEPS.tex d\'efinit des macro-commandes
  %%    qui permettent d'int\'egrer dans un document TeX des 
  %%    objets graphiques d\'ecrits par fichier de norme EPSF,
  %%    tout en accordant a chacun le statut d'une bo\^ite TeX ayant 
  %%    les bonnes dimensions.  La (seule!) contribution unique 
  %%    de ce fichier est de faire cela d'une fa{\c}con universelle.
  %%    C'est a dire de fa{\c}con \`a pouvoir commod\'ement 
  %%    servir avec tout pilote d'imprimante de norme 
  %%    PostScript --- malgr\'e l'absence d'une norme 
  %%    pour \special. 
  %%  
 %%%  POSTINGS: anonymous ftp 
  %%  ---  ftp 130.84.128.100 (alias rsovax.circe.fr); 
  %%  login: anonymous; password: <anything>; directory 
  %%  [anonymous.siebenmann].  This is the master copy in 1992.
  %%  
  %%  ---  ftp 129.69.1.12 (alias rusinfo.rus.uni-stuttgart.de);
  %%  login: anonymous; password: <anything>; 
  %%  directory hints .../tex/graphics/...
  %%  
 %%%% DOCUMENTATION:
  %%  --- see BoxedEPS.doc
  %%  
 %%%% ACTIVATION:
  %%    by a driver-by-driver protocol
  %%    see \SetTexturesEPSFSpecial 
  %%    and its companions below.
  %%  

 \ifx\MYUNDEFINED\BoxedEPSF
   \let\temp\relax
 \else
   \message{}
   \message{ !!! BoxedEPS %
         or BoxedArt macros already defined !!!}
   \let\temp\endinput
 \fi
  \temp
 
 \chardef\CatAt\the\catcode`\@
 \catcode`\@=11
 \chardef\C@tColon\the\catcode`\:
 \chardef\C@tSemicolon\the\catcode`\;
 \chardef\C@tQmark\the\catcode`\?
 \chardef\C@tEmark\the\catcode`\!

 \def\PunctOther@{\catcode`\:=12
   \catcode`\;=12 \catcode`\?=12 \catcode`\!=12}
 \PunctOther@

 %%temporarily suppress Plain's logging of allocations
 \let\wlog@ld\wlog 
 \def\wlog#1{\relax} 

 %% New for TOOLS
 \newif\ifIN@
 \newdimen\XShift@ \newdimen\YShift@ 
 \newtoks\Realtoks
 
 %%% New for Boxed EPSF
  %
 \newdimen\Wd@ \newdimen\Ht@
 \newdimen\Wd@@ \newdimen\Ht@@
 %
 \newdimen\TT@
 \newdimen\LT@
 \newdimen\BT@
 \newdimen\RT@
 %
 \newdimen\XSlide@ \newdimen\YSlide@ 
 %
 \newdimen\TheScale  %% secretly scale in mils: 1pt= 1mil 
 \newdimen\FigScale  %% secretly scale in mils: 1pt= 1mil 
 %
 \newdimen\ForcedDim@@

 \newtoks\EPSFDirectorytoks@
 \newtoks\EPSFNametoks@
 \newtoks\BdBoxtoks@
 \newtoks\LLXtoks@  %% useful info for Oz
 \newtoks\LLYtoks@  

  
 \newif\ifNotIn@
 \newif\ifForcedDim@
 \newif\ifForceOn@
 \newif\ifForcedHeight@
 \newif\ifPSOrigin

 \newread\EPSFile@ 
 
 %%%% MESSAGES (separate macro needed for Europe)
  %%  
  \def\ms@g{\immediate\write16}

 %%%% WORD-PROCESSING MACROS
  %%
  %%% \IN@0#1@#2@ : Is 1st exp of #1 in 1st exp of #2 ??
   %% Answer in \ifIN@
 \newif\ifIN@\def\IN@{\expandafter\INN@\expandafter}
  \long\def\INN@0#1@#2@{\long\def\NI@##1#1##2##3\ENDNI@
    {\ifx\m@rker##2\IN@false\else\IN@true\fi}%
     \expandafter\NI@#2@@#1\m@rker\ENDNI@}
  \def\m@rker{\m@@rker}

  %%%  \SPLIT@0#1@#2@  :  Split 1st exp of #2 at 1st exp of #1
   %%  \Initialtoks@ , \Terminaltoks@ will contain pieces
  \newtoks\Initialtoks@  \newtoks\Terminaltoks@
  \def\SPLIT@{\expandafter\SPLITT@\expandafter}
  \def\SPLITT@0#1@#2@{\def\TTILPS@##1#1##2@{%
     \Initialtoks@{##1}\Terminaltoks@{##2}}\expandafter\TTILPS@#2@}

 %%%% MACROS TO TRIM  \ForeTrim@0#1@ and \Trim@0#1@  
   %% result appears in \Trimtoks@
   %% LIMITATION: assume no multiple spaces to trim

  \newtoks\Trimtoks@

  %%% \ForeTrim@0#1@ trims initial space of first erpansion of #1
   %% #1 of form \the\toks0 or \mymacro
 \def\ForeTrim@{\expandafter\ForeTrim@@\expandafter}
 \def\ForePrim@0 #1@{\Trimtoks@{#1}}
 \def\ForeTrim@@0#1@{\IN@0\m@rker. @\m@rker.#1@%
     \ifIN@\ForePrim@0#1@%
     \else\Trimtoks@\expandafter{#1}\fi}
   %%\m@rker expands here to \m@@rker since spot initial,
   %% so no confusuion with \m@rker

  %%% \Trim@0#1@ trims init and terminal spaces 
   %% Same syntax.
   %% Warns if internal spaces found.
   %% 
  \def\Trim@0#1@{%
      \ForeTrim@0#1@%
      \IN@0 @\the\Trimtoks@ @%
        \ifIN@ 
             \SPLIT@0 @\the\Trimtoks@ @\Trimtoks@\Initialtoks@
             \IN@0\the\Terminaltoks@ @ @%
                 \ifIN@
                 \else \Trimtoks@ {FigNameWithSpace}%
                 \fi
        \fi
      }


  %%%% MATH MACROS (provisional)
    %% use dimen registers for reals; unit 1pt
    %% (numerical dimension arguments OK unless contrary noted)

  %%%% One needs the point token seq (pt with cat 12) USES dimen 0
   \newtoks\pt@ks
   \def \getpt@ks 0.0#1@{\pt@ks{#1}}
   \dimen0=0pt\relax\expandafter\getpt@ks\the\dimen0@

   %%% Convert dimen to "decimal multiplier"% USES dimens 0,2
  \newtoks\Realtoks% the output!
  \def\Real#1{%
    \dimen2=#1%
      \SPLIT@0\the\pt@ks @\the\dimen2@%%  lop off the points
       \Realtoks=\Initialtoks@%\showthe\Realtoks
            }

   %%% Multiplication 
      % USES dimens 0,2,4,6; preserves args; output \Product
   \newdimen\Product
   \def\Mult#1#2{%
     \dimen4=#1\relax
     \dimen6=#2%
     \Real{\dimen4}%
     \Product=\the\Realtoks\dimen6%
        }

   %%% Inverse 
     % USES dimens 0; preserves arg; output \Inverse
 \newdimen\Inverse
 \newdimen\hmxdim@ \hmxdim@=8192pt%halfmaxdimen
 \def\Invert#1{%
  \Inverse=\hmxdim@
  \dimen0=#1%
  \divide\Inverse \dimen0%
  \multiply\Inverse 8}

 %%% \Rescale#1#2#3  % USES dimens 0,2,4,6
  %%  alters dimen register #1 by ratio #2/#3 
  %%  where #2,#3 can be raw dimensions OR dimen registers
   \def\Rescale#1#2#3{% Adequate accuracy. Can improve. 
              \divide #1 by 100\relax
              \dimen2=#3\divide\dimen2 by 100 \Invert{\dimen2}% 
              \Mult{#1}{#2}%
              \Mult\Product\Inverse 
              #1=\Product}

 %%% \Scale#1 scales dimen register #1 
   %  by dimen register real \TheScale; USES dimens 0
  \def\Scale#1{\dimen0=\TheScale %
      \divide #1 by  1280 %% 1280*5120*10=1000*2^16 
      \divide \dimen0 by 5120 % 
      \multiply#1 by \dimen0 
      \divide#1 by 10   %% max size of #1 about 32000/10 pt
     }
 
 %%% SCRUNCHING BOXES AND SHIFTING CONTENTS
  %% TeX has to do this in general
  %% since some drivers do not let 
  %% one do it readily using Postscript

 \newbox\scrunchbox

 %%% \Scrunched#1 puts #1 in an hbox
  %%    then in effect zeros the dimensions of this box
 \def\Scrunched#1{{\setbox\scrunchbox\hbox{#1}%
   \wd\scrunchbox=0pt
   \ht\scrunchbox=0pt
   \dp\scrunchbox=0pt
   \box\scrunchbox}}

  %%% \Shifted@#1 puts #1 in \hbox 
   %% then locates basepoint to bottom left corner
   %% then translates ink only by \XShift@,\YShift@
   %% with Postscript convention
   %% For simplicity use only on scrunched boxes
  %\newdimen\XShift@ 
  %\newdimen\YShift@ 
 \def\Shifted@#1{%
   \vbox {\kern-\YShift@
       \hbox {\kern\XShift@\hbox{#1}\kern-\XShift@}%
           \kern\YShift@}}

  %%% \cBoxedEPSF#1 the main macro
   %%  component macros are explained in order below

 \def\cBoxedEPSF#1{{{}\leavevmode %{} fixes box mirage for \Mas
   \ReadNameAndScale@{#1}%
   \SetEPSFSpec@
   \ReadEPSFile@ \ReadBdB@x  
   %% Calculations
     \TrimFigDims@ 
     \CalculateFigScale@  
     \ScaleFigDims@
     \SetInkShift@
   \hbox{$\mathsurround=0pt\relax
         \vcenter{\hbox{%
             \FrameSpider{\hskip-.4pt\vrule}%
             \vbox to \Ht@{\offinterlineskip\parindent=\z@%
                \FrameSpider{\vskip-.4pt\hrule}\vfil 
                \hbox to \Wd@{\hfil}%
                \vfil
                \InkShift@{\EPSFSpecial{\EPSFSpec@}{\FigSc@leReal}}%
             \FrameSpider{\hrule\vskip-.4pt}}%
         \FrameSpider{\vrule\hskip-.4pt}}}%
     $\relax}%
    \CleanRegisters@ 
    \ms@g{ *** Box composed for the % 
         EPSF file \the\EPSFNametoks@}%
    }}      %% double brace for amstex \allign, \alligned, ...

 
 \def\tBoxedEPSF#1{\setbox4\hbox{\cBoxedEPSF{#1}}%
     \setbox4\hbox{\raise -\ht4 \hbox{\box4}}%
     \box4
      }

 \def\bBoxedEPSF#1{\setbox4\hbox{\cBoxedEPSF{#1}}%
     \setbox4\hbox{\raise \dp4 \hbox{\box4}}%
     \box4
      }

  \let\BoxedEPSF\cBoxedEPSF% default setting

  %% Some compatibility with BoxedArt.tex
   %
   \let\BoxedArt\BoxedEPSF

  %% Some compatibility with Sweet-teX
   %
  \def\gLinefigure[#1scaled#2]_#3{%
        \BoxedEPSF{#3 scaled #2}}
    
  %% Some compatibility with Rokicki's dvips
   %
  \let\EPSFbox\bBoxedEPSF \let\EPSFfile\bBoxedEPSF
  
  \def\EPSFxsize{\afterassignment\ForceW@\ForcedDim@@}
      \def\ForceW@{\ForcedDim@true\ForcedHeight@false}
  
  \def\EPSFysize{\afterassignment\ForceH@\ForcedDim@@}
      \def\ForceH@{\ForcedDim@true\ForcedHeight@true}


 %%% \ReadNameAndScale@#1
  %
 \def\ReadNameAndScale@#1{\IN@0 scaled@#1@% DOUBLE BARRELED
   \ifIN@\ReadNameAndScale@@0#1@%
   \else \ReadNameAndScale@@0#1 scaled\DefaultMilScale @
   \fi}
  
 \def\ReadNameAndScale@@0#1scaled#2@{% HELPER MACRO
    \let\OldBackslash@\\%
    \def\\{\OtherB@ckslash}%
    \edef\temp@{#1}%
    \Trim@0\temp@ @%
    \EPSFNametoks@\expandafter{\the\Trimtoks@ }%
    \FigScale=#2 pt%
    \let\\\OldBackslash@
    }
 
 \def\SetDefaultEPSFScale#1{%
      \global\def\DefaultMilScale{#1}}

 \SetDefaultEPSFScale{1000}


 %%% \ReadEPSFile@
  %
 \def \SetBogusBbox@{%
     \global\BdBoxtoks@{ BoundingBox:0 0 100 100 }%
     \global\def\BdBoxLine@{ BoundingBox:0 0 100 100 }%
     \ms@g{ !!! Will use placeholder !!!}%
     }

 {\catcode`\%=12\gdef\P@S@{%!}} %% %! min sign of PS file

 \def\ReadEPSFile@{%\show\EPSFSpec@%
     \openin\EPSFile@\EPSFSpec@
     \relax  %necessary to prevent precocious expansion of \ifeof
  \ifeof\EPSFile@
     \ms@g{}%
     \ms@g{ !!! EPS FILE \the\EPSFDirectorytoks@
       \the\EPSFNametoks@\ WAS NOT FOUND !!!}
     \SetBogusBbox@
  \else%\fi
   \begingroup%%
   \catcode`\%=12\catcode`\:=12\catcode`\!=12
   \catcode`\G=14\catcode`\\=14\relax% 14 is comment
   \global\read\EPSFile@ to \BdBoxLine@%\show\BdBoxLine@
   \IN@0\P@S@ @\BdBoxLine@ @%
   \ifIN@ %% %! accepted as %!PS so do BdBox search!!
     \NotIn@true
     \loop   
       \ifeof\EPSFile@\NotIn@false 
         \ms@g{}%
         \ms@g{ !!! BoundingBox NOT FOUND IN %
            \the\EPSFDirectorytoks@\the\EPSFNametoks@\ !!! }%
         \SetBogusBbox@
       \else\global\read\EPSFile@ to \BdBoxLine@
       %\show\BdBoxLine@
       \fi
       \global\BdBoxtoks@\expandafter{\BdBoxLine@}%
       \IN@0BoundingBox:@\the\BdBoxtoks@ @%
       \ifIN@\NotIn@false\fi%
     \ifNotIn@\repeat
   \else
         \ms@g{}%
         \ms@g{ !!! \the\EPSFNametoks@\ not PS!\  !!!}%
         \SetBogusBbox@
   \fi
  \endgroup\relax
  \fi
  \closein\EPSFile@ 
   }


  %%% \ReadBdB@x
   % Rmk For simplicity 0 not used in syntax 
   %  of \ReadBdB@x@,  \ReadBdB@x@@ 
  \def\ReadBdB@x{% PART 0
   \expandafter\ReadBdB@x@\the\BdBoxtoks@ @}
  
  \def\ReadBdB@x@#1BoundingBox:#2@{% PART 1
    \ForeTrim@0#2@%
    \IN@0atend@\the\Trimtoks@ @%
       \ifIN@\Trimtoks@={0 0 100 100 }%
         \ms@g{}%
         \ms@g{ !!! BoundingBox not found in %
         \the\EPSFDirectorytoks@\the\EPSFNametoks@\space !!!}%
         \ms@g{ !!! It must not be at end of EPSF !!!}%
         \ms@g{ !!! Will use placeholder !!!}%
       \fi%% cf \SetBogusBbox@
    \expandafter\ReadBdB@x@@\the\Trimtoks@ @%
   }
    
  \def\ReadBdB@x@@#1 #2 #3 #4@{% PART 2
      \Wd@=#3bp\advance\Wd@ by -#1bp%
      \Ht@=#4bp\advance\Ht@ by-#2bp%
       \Wd@@=\Wd@ \Ht@@=\Ht@ %% useful info for Clark
       \LLXtoks@={#1}\LLYtoks@={#2}%% useful info for Oz
      \ifPSOrigin\XShift@=-#1bp\YShift@=-#2bp\fi 
     }

  %%% \SetEPSFDirectory 
   %
   \def\G@bbl@#1{}
   \bgroup
     \global\edef\OtherB@ckslash{\expandafter\G@bbl@\string\\}
   \egroup

  \def\SetEPSFDirectory{%  Part 1
           \bgroup\PunctOther@\relax
           \let\\\OtherB@ckslash
           \SetEPSFDirectory@}

 \def\SetEPSFDirectory@#1{% Part 2
    \edef\temp@{#1}%
    \Trim@0\temp@ @%  result in \Trimtoks@
    \global\toks1\expandafter{\the\Trimtoks@ }\relax
    \egroup
    \EPSFDirectorytoks@=\toks1
    }

  %%% \SetEPSFSpec@
 \def\SetEPSFSpec@{%
     \bgroup
     \let\\=\OtherB@ckslash
     \global\edef\EPSFSpec@{%
        \the\EPSFDirectorytoks@\the\EPSFNametoks@}%
     \global\edef\EPSFSpec@{\EPSFSpec@}%
     \egroup}
   

 %%% \TrimFigDims@ 
  % 
 \def\TrimTop#1{\advance\TT@ by #1}
 \def\TrimLeft#1{\advance\LT@ by #1}
 \def\TrimBottom#1{\advance\BT@ by #1}
 \def\TrimRight#1{\advance\RT@ by #1}

 \def\TrimBoundingBox#1{%
   \TrimTop{#1}%
   \TrimLeft{#1}%
   \TrimBottom{#1}%
   \TrimRight{#1}%
       }

 \def\TrimFigDims@{%
    \advance\Wd@ by -\LT@ 
    \advance\Wd@ by -\RT@ \RT@=\z@
    \advance\Ht@ by -\TT@ \TT@=\z@
    \advance\Ht@ by -\BT@ 
    }


 %%% \CalculateFigScale@
  %
  \def\ForceWidth#1{\ForcedDim@true
       \ForcedDim@@#1\ForcedHeight@false}
  
  \def\ForceHeight#1{\ForcedDim@true
       \ForcedDim@@=#1\ForcedHeight@true}

  \def\ForceOn{\ForceOn@true}
  \def\ForceOff{\ForceOn@false\ForcedDim@false}
  
  \def\epsfxsize{\afterassignment\ForceW@\ForcedDim@@}
      \def\ForceW@{\ForcedDim@true\ForcedHeight@false}
  
  \def\epsfysize{\afterassignment\ForceH@\ForcedDim@@}
      \def\ForceH@{\ForcedDim@true\ForcedHeight@true}
  
  \def\CalculateFigScale@{%
            %Have default \FigScale or read \FigScale
     \ifForcedDim@\FigScale=1000pt% %% start afresh
           \ifForcedHeight@
                \Rescale\FigScale\ForcedDim@@\Ht@
           \else
                \Rescale\FigScale\ForcedDim@@\Wd@
           \fi
     \fi
     \Real{\FigScale}%
     \edef\FigSc@leReal{\the\Realtoks}%
     }
   
  \def\ScaleFigDims@{\TheScale=\FigScale
      \ifForcedDim@
           \ifForcedHeight@ \Ht@=\ForcedDim@@  \Scale\Wd@
           \else \Wd@=\ForcedDim@@ \Scale\Ht@
           \fi
      \else \Scale\Wd@\Scale\Ht@        
      \fi
      \ifForceOn@\relax\else\global\ForcedDim@false\fi
      \Scale\LT@\Scale\BT@  %%%\Scale\Wd@\Scale\Ht@
      \Scale\XShift@\Scale\YShift@
      }
      
  %%% \ShowReservedBoxes
   %%  shows (prints) corrected scaled and positioned
   %%  bounding boxes; for diagnostics
  %%% \HideReservedBoxes makes them invisible again
   %%
 \def\HideReservedBoxes{\global\def\FrameSpider##1{\null}}
 \def\ShowReservedBoxes{\global\def\FrameSpider##1{##1}}
 \let\HideDisplacementBoxes\HideReservedBoxes  %% some synonyms
 \let\ShowDisplacementBoxes\ShowReservedBoxes
 \let\HideFigureFrames\HideReservedBoxes
 \let\ShowFigureFrames\ShowReservedBoxes
  \ShowDisplacementBoxes
 
  %%% \hSlide#1, \vSlide#1
   %%
 \def\hSlide#1{\advance\XSlide@ by #1}
 \def\vSlide#1{\advance\YSlide@ by #1}
 
  %%% \SetInkShift@, \InkShift@#1
   %%
  \def\SetInkShift@{%
            \advance\XShift@ by -\LT@
            \advance\XShift@ by \XSlide@
            \advance\YShift@ by -\BT@
            \advance\YShift@ by -\YSlide@
             }
   %
  \def\InkShift@#1{\Shifted@{\Scrunched{#1}}}
 
  %%% \CleanRegisters@
   %
  \def\CleanRegisters@{%
      \globaldefs=1\relax
        \XShift@=\z@\YShift@=\z@\XSlide@=\z@\YSlide@=\z@
        \TT@=\z@\LT@=\z@\BT@=\z@\RT@=\z@
      \globaldefs=0\relax}

 %%% Special syntax for several drivers. The macros 
  %% \SetTexturesEPSFSpecial  %% Textures 
  %% \SetUnixCoopEPSFSpecial %% dvi2ps early unix 
  %% \SetBetcholsheimEPSFSpecial %% dvi2ps by S.P.Betcholsheim
  %% \SetLisEPSFSpecial %% dvi2ps by Tony Lis
  %% \SetRokickiEPSFSpecial  %% dvips by Tom Rokicki
  %% \SetOzTeXEPSFSpecial  %% OzTeX by Andrew Trevorrow
  %% \SetOzTeXPreviewedEPSFSpecial %% OzTeX >= 1.42 by Andrew Trevorrow
  %% \SetPSprintEPSFSpecial %% PSprint by Andrew Trevorrow
  %% \SetArborEPSFSpecial  %% ArborTeX DVILASER/PS
  %% \SetClarkEPSFSpecial %% dvitops by James Clark
  %% \SetDVIPSoneEPSFSpecial %% DVIPSONE of Y&Y 
  %% \SetBeebeEPSFSpecial %% DVIALW by N. Beebe
  %% \SetNorthlakeEPSFSpecial %% Northlake Software
  %% \SetStandardEPSFSpecial %% Nonexistant: Placebo below
  %% These macros adapt to various drivers roughly
  %% by (re-)defining the macro \EPSFSpecial#1#2, where
  %% #1 = EPS file pathname (use \\ for the letter backslash)
  %% #2 = scale in mils 
  %% Be wary of using strange characters in pathnames!
 
 %% Textures, Blue Sky Research, Barry Smith
 \def\SetTexturesEPSFSpecial{\PSOriginfalse%\PSOrigintrue
  \gdef\EPSFSpecial##1##2{\relax
    \edef\specialthis{##2}%
    \SPLIT@0.@\specialthis.@\relax
    %\showthe\Initialtoks@
    \special{illustration ##1 scaled
                        \the\Initialtoks@}}}
 
  %% Unix : dvi2ps by:  Mark Senn, Stephan  Bechtolsheim,  
   % Bob  Brown, Richard, Furuta, James Schaad, 
   % Robert  Wells, Norm Hutchinson, Neal Holtz.
   % Introduced by B. Horn <bkph@ai.mit.edu>
  \def\SetUnixCoopEPSFSpecial{\PSOrigintrue % Please test!
   \gdef\EPSFSpecial##1##2{%
      \dimen4=##2pt% convert real to dimen
      \divide\dimen4 by 1000\relax
      \Real{\dimen4}%dimens 0,2 used here
      \edef\Aux@{\the\Realtoks}%  
      %%convert dimen to real
      \special{psfile=##1\space 
        hscale=\Aux@\space
        vscale=\Aux@}}}

  %% dvi2ps by S.P. Bechtolsheim,
   % implantations? ; dates?; availability?
   % Introduced by B. Horn <bkph@ai.mit.edu>; please test!!
  \def\SetBechtolsheimEPSFSpecial{\PSOrigintrue 
   \gdef\EPSFSpecial##1##2{%
      \dimen4=##2pt% convert real to dimen
      \divide\dimen4 by 1000\relax
      \Real{\dimen4}% dimens 0,2 used here
      \edef\Aux@{\the\Realtoks}%  
      %%convert dimen to real
      \special{ps: psfiginit}%
      \special{ps: literal 1 1 0 0 1 1 startTexFig
           \the\mag\space 1000 div \Aux@\space mul 
           \the\mag\space 1000 div \Aux@\space mul scale}%
      \special{ps: include  ##1}%
      \special{ps: literal endTexFig}%
        }}

  %% dvi2ps by Tony Lis,
   % implantations? ; dates?; availability?
   % Introduced by B. Horn <bkph@ai.mit.edu>; please test!!
  \def\SetLisEPSFSpecial{\PSOrigintrue 
   \gdef\EPSFSpecial##1##2{%
      \dimen4=##2pt% convert real to dimen
      \divide\dimen4 by 1000\relax
      \Real{\dimen4}% dimens 0,2 used here
      \edef\Aux@{\the\Realtoks}%  
      %%convert dimen to real
      \special{pstext="1 1 0 0 1 1 startTexFig\space
           \the\mag\space 1000 div \Aux@\space mul 
           \the\mag\space 1000 div \Aux@\space mul scale}%
      \special{psfile=##1}%
      \special{pstext=endTexFig}%
        }}

  %% dvips by Tom Rokicki; driver in portable C 
   % This driver improves on dvi2ps; its Postscript
   % output is thee times as compact as that 
   % produced by dvi2ps
   % Introduced by W.D. Neumann <neumann@mps.ohio-state.edu>
  \def\SetRokickiEPSFSpecial{\PSOrigintrue 
   \gdef\EPSFSpecial##1##2{%
      \dimen4=##2pt% convert real to dimen
      \divide\dimen4 by 10\relax
      \Real{\dimen4}% dimens 0,2 used here
      \edef\Aux@{\the\Realtoks}%  
      %%convert dimen to real
      \special{psfile="##1"\space 
        hscale=\Aux@\space
        vscale=\Aux@}}}

  \def\SetInlineRokickiEPSFSpecial{\PSOrigintrue 
   \gdef\EPSFSpecial##1##2{%
      \dimen4=##2pt% convert real to dimen
      \divide\dimen4 by 1000\relax
      \Real{\dimen4}% dimens 0,2 used here
      \edef\Aux@{\the\Realtoks}%  
      %%convert dimen to real
      \special{ps::[begin] 1 1 0 0 1 1 startTexFig\space
           \the\mag\space 1000 div \Aux@\space mul 
           \the\mag\space 1000 div \Aux@\space mul scale}%
      \special{ps: plotfile ##1}%
      \special{ps::[end] endTexFig}%
        }}

  %% OzTeX (all versions; no preview), by AndrewTrevorrow, 
  \def\SetOzTeXEPSFSpecial{\PSOriginfalse % artifice; see below
  \gdef\EPSFSpecial##1##2{%note order
     \special{##1\space 
       ##2 1000 div \the\mag\space 1000 div mul
       ##2 1000 div \the\mag\space 1000 div mul scale
       \the\LLXtoks@\space neg 
       \the\LLYtoks@\space neg translate
             }}} 
  
 %%  OzTeX (beta versions 1.41-2), by Andrew Trevorrow
 %  complete public domain TeX for Macintosh
 %  Send 10 UNFORMATTED 800K disks 
 %  with return postage 
 %  Peter Abbott, Computing Service, 
 %  Aston University, Aston Triangle, Birmingham B4 7ET
 \def\SetOzTeXPreviewedEPSFSpecial{\PSOrigintrue
 \gdef\EPSFSpecial##1##2{%
 \dimen4=##2pt%% convert real to dimen
 \divide\dimen4 by 1000\relax
 \Real{\dimen4}%% dimens 0,2 used here
 \edef\Aux@{\the\Realtoks}%% convert dimen to real
 \special{epsf="##1"\space scale=\Aux@}%
 }} 

 %% PSprint,  by AndrewTrevorrow for VaX VMS
  % diagnosed and tested 2-91 by Max Calviani 
  % <ISICA@ASTRPD.infn.it>
  \let\SetPSprintEPSFSpecial\SetOzTeXEPSFSpecial
  \let\SetPsprintEPSFSpecial\SetOzTeXEPSFSpecial

 %% DVILASER/PS driver originally written by David Fuchs
  % marketed and supported by ArborTeXt  535 W. William St.
  % Suite 300, Ann Arbor, MI 48103, U.S.A
  % (313) 996-3566 (313) 996-3573
  % help@arbortext.com, Andrew Dobrowolski
 \def\SetArborEPSFSpecial{\PSOriginfalse % check!
   \gdef\EPSFSpecial##1##2{%
     \edef\specialthis{##2}%
     \SPLIT@0.@\specialthis.@\relax % suppress decimals (nec!)
     \special{ps: epsfile ##1\space \the\Initialtoks@}}}

 %% dvitops, (c) James Clark <jjc@jclark.uucp>
  % public domain; distributed by UK TeX Archive
  % computers: unix, msdos, vms, primos and vm/cms,
  % (introduced by S. Ratz <spqr@uk.ac.southampton.ecs>)
 \def\SetClarkEPSFSpecial{\PSOriginfalse % please test!
   \gdef\EPSFSpecial##1##2{%
     \Rescale {\Wd@@}{##2pt}{1000pt}%
     \Rescale {\Ht@@}{##2pt}{1000pt}%
     \special{dvitops: import 
           ##1\space\the\Wd@@\space\the\Ht@@}}}

 %% DVIPSONE, for PC compatibles
  % Y&Y, 106 Indian Hill, Carlisle MA 01741, USA
  % (508) 371-3286
  % (introduced by B. Horn <bkph@ai.mit.edu>)
  \let\SetDVIPSONEEPSFSpecial\SetUnixCoopEPSFSpecial
  \let\SetDVIPSoneEPSFSpecial\SetUnixCoopEPSFSpecial

 %% DVIALW by N. Beebe, public domain, charge $100 
  % DVI Driver Distribution, Center for Scientific Computing,
  % Department of Mathematics, 220 South Physics Building,
  % University of Utah, Salt Lake City, UT 84112, USA
  % (introduced by B. Horn <bkph@ai.mit.edu>)
  \def\SetBeebeEPSFSpecial{%please test!
   \PSOriginfalse% 
   \gdef\EPSFSpecial##1##2{\relax
    \special{language "PS"
      literal "##2 1000 div ##2 1000 div scale
      position = "bottom left",
      include "##1"}}}
  \let\SetDVIALWEPSFSpecial\SetBeebeEPSFSpecial

 %% Northlake software
  \def\SetNorthlakeEPSFSpecial{\PSOrigintrue
   \gdef\EPSFSpecial##1##2{%
     \edef\specialthis{##2}%
     \SPLIT@0.@\specialthis.@\relax % suppress decimals (nec!)
     \special{insert ##1,magnification=\the\Initialtoks@}}}


 \def\SetStandardEPSFSpecial{%
   \gdef\EPSFSpecial##1##2{%
     \ms@g{}
     \ms@g{%
       !!! Sorry! There is still no standard for \string%
       \special\ EPSF integration !!!}%
     \ms@g{%
      --- So you will have to identify your driver using a command}%
     \ms@g{%
      --- of the form \string\Set...EPSFSpecial, in order to get}%
     \ms@g{%
      --- your graphics to print.  See BoxedEPS.doc.}%
     \ms@g{}
     \KillEPSFSpecial
     }}

  \def\KillEPSFSpecial{\gdef\EPSFSpecial##1##2{}}

  \SetStandardEPSFSpecial %% currently gives warning
 
 \let\wlog\wlog@ld %%restore logging 

 \catcode`\:=\C@tColon
 \catcode`\;=\C@tSemicolon
 \catcode`\?=\C@tQmark
 \catcode`\!=\C@tEmark

 \catcode`\@=\CatAt

  \endinput

%%%%%%%%%%%% ASCII Character test
 %
 %       Upper case letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ
 %       Lower case letters: abcdefghijklmnopqrstuvwxyz
 %                                   Digits: 0123456789
 % Square, curly, angle braces, parentheses: [] {} <> ()
 %           Backslash, slash, vertical bar: \ / |
 %                              Punctuation: . ? ! , : ;
 %          Underscore, hyphen, equals sign: _ - =
 %                Quotes--right left double: ' ` "
 %"at", "number" "dollar", "percent", "and": @ # $ % &
 %           "hat", "star", "plus", "tilde": ^ * + ~
 %
 %%%%%%%%%%%%%%%%%%%%%%%%
 %
 % Une seule erreur de transmission peut empoisoner un programme!
 %
 % A single transmission error can poison a whole program.
 %
 %%%%%%%%%%%%%%%%%%%%%%%%

kz.tex
\documentclass{mn2e}
\usepackage{epsfig}

\usepackage{graphicx}
%\usepackage{epstopdf}
%\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `basename #1 .tif`.png}

\newif\ifAMStwofonts
\AMStwofontstrue


\title[The K-band Hubble diagram of sub-mm galaxies and 
hyperluminous galaxies]
{The K-band Hubble diagram of sub-mm galaxies and 
hyperluminous galaxies}
\author[Serjeant, et al.]
  {Stephen Serjeant$^1$, Duncan Farrah$^{2}$, 
James Geach$^{3}$, Toshinobu Takagi$^1$, 
\vspace*{0.3cm}\\
{\LARGE\rm 
Aprajita Verma$^4$, Ali Kaviani$^{3}$, 
Matt Fox$^{3}$}\\
\vspace*{0.1cm}\\
$^1$Centre for Astrophysics \& Planetary Science, School of Physical
Sciences, University of Kent, Canterbury, Kent CT2 7NR, UK\\
$^2$SIRTF Science Center, Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, 91125, USA\\
$^3$Astrophysics Group, Imperial College London, Blackett Laboratory,
Prince Consort Road, London SW7 2BW\\
$^4$MPI fuer extraterrestrische Physik, Giessenbachstr. 1, D-85748,
Garching, Germany
}
\date{Received 2003}
\pubyear{2003}


\begin{document}

%\input /Users/cpp/chris/IC-ASTRO-F/MP/IRCsurvey/IRCpaper/paper/july30paper/BoxedEPS.tex
%\SetEPSFDirectory{/Users/cpp/chris/IC-ASTRO-F/MP/IRCsurvey/IRCpaper/paper/july30paper/}

\input BoxedEPS.tex
\SetEPSFDirectory{./}

\SetRokickiEPSFSpecial
\HideDisplacementBoxes

\label{firstpage}

\maketitle


\begin{abstract}
We present the $K$-band Hubble diagrams ($K-z$ relations) of
sub-mm-selected galaxies and hyperluminous galaxies (HLIRGs). 
We report the discovery of a remarkably tight $K-z$ relation
of HLIRGs, 
indistinguishable from that of the most luminous radiogalaxies.
Like radiogalaxies, the HLIRG K-z relation at $z\stackrel{<}{_\sim}3$
is consistent with a passively evolving 
$\sim3L_*$ instantaneous starburst starting from a redshift of $z\sim10$. 
In contrast, many sub-mm selected galaxies are $\stackrel{>}{_\sim}2$
magnitudes fainter, and the population has a much larger
dispersion. We argue that dust obscuration and/or a larger mass range 
may be responsible for this scatter. 
The 
galaxies so far proved to be hyperluminous may have been biased
towards higher AGN bolometric contributions than sub-mm-selected galaxies 
due to the $60\mu$m
selection of some, so the location on the $K-z$ relation
may be related to the presence of the most massive AGN. Alternatively,
a particular host galaxy 
mass range may be responsible for both extreme star formation and the
most massive active nuclei. 
%The hyperluminous $K-z$ relation also makes it easier to estimate
%photometric 
%redshifts for hyperluminous candidates. 
%Our data is consistent with an evolutionary connection
%between the most extreme star formation and AGN activity at the sites
%of the largest supermassive black holes. 
\end{abstract}

\begin{keywords}
cosmology: observations - 
galaxies: evolution - 
galaxies:$\>$formation - 
galaxies: star-burst - 
infrared: galaxies - 
submillimetre 
\end{keywords}

\section{Introduction}\label{sec:introduction}
Hyperluminous galaxies (HLIRGs, $L>10^{13}L_\odot$, as distinct from
the less-luminous ultraluminous population with $L=10^{12-13}L_\odot$), 
were first identified from follow-ups of the IRAS mission
(e.g. Kleinmann et al. 1988, Rowan-Robinson et al. 1991). 
Gravitational lensing was found to be responsible for some of 
the extreme
luminosity of at least one HLIRG, IRAS F10214+4724 
(Graham \& Liu 1995, Serjeant et
al. 1995, Broadhurst \& Lehar 1995, Eisenhardt et al. 1996), but 
subsequent HST imaging of more HLIRGs showed no further lens
candidates (Farrah et al. 2002a). The morphologies were 
found to be diverse, from interacting to quiescent. 
Although active nuclei have been found in all HLIRGs to date, the
enormous gas and dust masses (e.g. Downes et al. 1993, Clements et
al. 1992, Farrah et al. 2002b) are indicative of violent, possibly
bolometrically-dominant, star formation. 
By fitting multi-wavelength photometry of HLIRGs, several authors
have found comparable bolometric contributions from star formation and
active nuclei in many HLIRGs 
Hyperluminous galaxies appear to be a population of 
galaxies undergoing their major star formation episode (Rowan-Robinson
2000), but at an epoch in which AGN activity is also present
(e.g. Rowan-Robinson 2000, Farrah et al. 2002b, Verma et  
al. 2002). 
The sub-mm detections of radiogalaxies (Archibald et al. 2001)
and quasars (e.g. Priddey et al. 2003) further
supported a link between violent star formation and AGN activity,
though quasar-heated dust has also been raised as a possibility
(Willott et al. 2002). In this paper we will present further evidence
for a link between AGN activity and extreme star formation, using the
$K$-band Hubble diagram. 

The tight dispersion in the 
$K$-band Hubble diagram ($K-z$ relation) of radiogalaxies
has long been held to suggest a high
formation epoch for radiogalaxy hosts (Lilly \& Longair
1984). Redshifted emission line contributions (Eales \& Rawlings 1993)
complicate the interpretation at redshifts $z>2$, but largely 
only for the most
luminous radiogalaxies (e.g. Jarvis et al. 2001). The current
consensus is that the tight $\pm0.5$ magnitude 
dispersion in the radiogalaxy $K-z$
relation persists at $z>2$, and is still consistent with a passively
evolving stellar population with a formation
epochs at $z>2.5$. There is also a weak correlation of $K$-band
luminosity with radio luminosity at any epoch (e.g. Willott et
al. 2003) which has been attributed to mutual correlations with
central nuclear black hole masses. 
Furthermore, the host galaxies of radio-loud AGN tend to be restricted
to a more luminous population than their radio-quiet counterparts
(Dunlop et al. 2003a), suggesting that it is only the most massive
($>10^9M_\odot$) nuclear black holes which give rise to radio-loud
AGN. Finally, the similarity of the $K$-band morphologies of
sub-mm-selected galaxies to those of high-$z$ radiogalaxies, the high
star formation rates in sub-mm galaxies (sufficient to assemble a
giant elliptical in $\sim10^8$ years), and the presence of radio-loud
AGN in local ellipticals has suggested to some authors that both
high-$z$ radiogalaxies and sub-mm selected galaxies are the
progenitors of the most massive spheroids (e.g. Dunlop 2002, Scott et
al. 2002). 

%K-z relation of radiogalaxies: original discovery; use as 
%redshift estimator; dispersion at high redshift; latest news. 
%Interpretation as high-z Magorrian. 

%Discovery of HLIRGs: IRAS F15307, IRAS F10214 and the subsequent
%discovery of lensing; review of what we've done ourselves; starburst
%dominance or AGN dominance. 
%Suggestions of a link between hyperluminous activity and AGN by
%Michael, the Oxford group and the Edinburgh group. 


In this paper we report the discovery of a remarkably tight $K-z$
relation of HLIRGs, and the surprising lack of a tight $K-z$ relation
for coeval sub-mm-selected galaxies.  
Section \ref{sec:method} describes the compilation
of $K$-band magnitudes, and the $K-z$ relations are presented in
section \ref{sec:results}. Section \ref{sec:discussion} places the
results in the context of other high-$z$ populations, and discusses
the physical implications and possible applications of this relation. 
Throughout this paper, ``quasars'' are taken to mean objects with
broad ($\stackrel{>}{_\sim}2000$ km s$^{-1}$) unpolarised emission
lines, regardless of the presence or absence of a host galaxy in
imaging data, and we assume $\Omega_{\rm M}=0.3$,
$\Omega_\Lambda=0.7$ and 
$H_0=70$ km s$^{-1}$ Mpc$^{-1} = 100h$ km s$^{-1}$ Mpc$^{-1}$.  
In this cosmology, a minority of the 
hyperluminous galaxy compilation of
Rowan-Robinson (2000) slip just below the hyperluminous threshold, and
others attain hyperluminous status, 
but for consistency with previous works we restrict ourselves to this
compilation. This choice does not affect the results in this paper. 

\section{Method}\label{sec:method}
 
\begin{table}
\begin{tabular}{llllll}
Name             & $z$ & $\log_{10}L_{\rm bol}$ & $K$ & Aper & Notes\\
IRAS F00235+1024 & 0.58 & 13.15 & 17.19 & $3''$ & (4)\\  %SB=AGN
SMM J02399-0136   & 2.803 & 13.08 & 18.79 & $3''$ & (1,7)\\ %
4C41.17         & 3.8  & 13.12 & 19.6  & $4''$ & (11)\\ %
IRAS 09104+4109  & 0.44 & 13.24 & 15.41 & $3''$ & (4)\\ % 
%IRASF10026+4949 & 1.12 16.85  Q  Farrah
%IRASF10119+1429 & 1.55 16.37  Q  Farrah
%LBQS1220+0939   & 0.68 17.54  Q  Farrah
%IRASF14218+3854 & 1.21 17.21  Q  Farrah
%B2 0902+343      & 3.391 & 12.89 & 19.9 & $4''$ & (6)\\ % 
IRAS F10214+4724 & 2.286 & 13.54 & 20.10 & $\sim3''$ & (2,9)\\ %SB=AGN
IRAS F12514+1027 & 0.30 & 13.00 & 13.48 & $10''$ & (5)\\ %
SMM J14011+0252 & 2.55 & 13.18 &  18.71 & $3''$ & (3,7)\\
IRAS F15307+3252 & 0.93 & 13.50 & 16.59 & $2''$ & (10)\\
FFJ1614+3234    & 0.710 & 13.07 & 16.6  & $3''$ &  (8)\\ %SB dominated
\end{tabular}
\caption{\label{tab:kmags}
K-band magnitudes for non-quasar hyperluminous galaxies of
Rowan-Robinson (2000). Following Dunlop et al. (2003) we neglect the
corrections between $K'$, $K$ and $K_{\rm s}$ as these are smaller
than the typical photometric errors ($\sim0.1-0.2$ magnitudes). 
Bolometric luminosities are taken from Farrah et al. (2003), Farrah et
al. (2002b) and Rowan-Robinson (2000). 
Notes: (1) corrected for $\times1.3$ lens
magnification factor; (2) corrected for emission line contribution and
$\times10$ magnification factor; (3) corrected for $\times2.8$ lens
magnification; (4) photometry from the data of 
Farrah et al. 2003 (note that those authors used slightly different
photometric apertures); (5) photometry
from 2MASS (Cutri et al. 2003); (6) photometry from Eisenhardt \&
Dickinson 1992; 
(7) photometry from  
Smail, Ivison, Blain \& Kneib 2002b; 
(8) photometry from Stanford et al. 2000; 
(9) photometry
from Graham \& Liu 1995; 
(10) photometry from Liu et al. 1996; 
(11) photometry from Graham et al. 1994
}
\end{table}

% 00235 R<22 (not on APM)
% 02399 R=21.2/mag = 21.48
% 4C41.17 R=21.7
% 09104 R=17.6
% 0902 V=22.5
% 10214 B=21.5/mag = 26.5
% 12514 R=17.34
% 14011 R=21.3/mag = 22.4
% 15307 R=19.03
% 1614 R=18.89
%
%



\begin{table}
\begin{tabular}{lllll}
Name             & $z$ & $K$ & Aper & Notes\\
SMMJ02399-0134 & 1.06  & 17.29 & $3''$ & (7)\\
SMMJ02399-0136 & 2.803 & 18.79 & $3''$ & (7)\\
CUDSS10A       & 0.550 & 17.11 & $3''$ & (16)\\
LH850.11       & 2.610 & $>$20.6 & $4''$ & (13,21)\\
LH850.12       & 2.698 & $>$20.6 & $4''$ & (13,21)\\
LH850.15       & 2.429 & $>$20.4 & $4''$ & (13,21)\\
LH850.18       & 3.699 & $>$20.4 & $4''$ & (13,20)\\
HDF850.4       & 0.475 & 18.14 & $6''$ & (14,20)\\
HDF850.6       & 0.884 & 19.85 & $6''$ & (14,20)\\
HDF850.8       & 1.355 & 19.69 & total & (15,20)\\
SMMJ14011+0252 & 2.55  & 18.71 & $3''$ & (7)\\
CUDSS14F       & 0.660 & 16.81 & $3''$ & (16)\\
N2850.1        & 0.840 & 19.48 & $4''$ & (13,20)\\
N2850.4        & 2.376 & 18.43 & $4''$ & (13,20)\\
N2850.8        & 1.189 & 18.15 & $4''$ & (13,20)\\
SMMJ17142+5016 & 2.39  & 21.80 & total & (12)\\
\hline
SMMJ00266+1708 & 2.0-5.0 & 23.45 & $3''$ & (7,19)\\
SMMJ09429+4658 & 2.1-4.5 & 20.15 & $3''$ & (7,19)\\
LH850.1        & 2.0-3.0 & 19.8 & $4''$ & (13,19)\\
LH850.3        & 1.2-3.5 & 18.86 & $4''$ & (13,19)\\
LH850.8        & 2.4-5.2 & 18.82 & $4''$ & (13,19)\\
HDF850.1       & 3.5-4.7 & 23.5 & $1''$ & (17,19)\\
SMMJ14099+0252 & 2.6-5.1 & 21.44 & $3''$ & (7,19)\\
CUDSS14.1      & 2.0-4.6 & 19.55 & $4''$ & (18,19)\\
\end{tabular}
\caption{\label{tab:kmags_scuba}
K-band magnitudes for sub-mm selected galaxies with spectroscopic
redshifts or $\geq3$ band photometric redshifts. Notes as table
\ref{tab:kmags}, and in addition: (12) from Smail et al. 2003 and
Keel et al. 2002, and corrected for emission line contributions; (13)
from Ivison et al. 2002; (14) Barger et 
al. 2000; (15) Fernandez-Soto et al. 1999; (16) Lilly et al. 1999; 
(17) from Dunlop et al. 2003, photometric aperture is small but source
is not significantly more extended, and no account taken of lensing;
(18) Gear et al. 2000; (19) Aretxaga et al. 2003; (20) Serjeant et
al. 2003; (21) Chapman et al. 2003. Non-sub-mm selected
galaxies (e.g. HR10) that are nevertheless detected in sub-mm
photometry are excluded from this table. 
}
\end{table}


Table \ref{tab:kmags} lists the $K$ magnitudes for all non-quasar
hyperluminous galaxies in the compilation of Rowan-Robinson (2000), 
except IRAS F14481+4454 and IRAS F14537+1950 for which no data is
available. Several quasar HLIRGs have optical host galaxy
measurements (e.g. Farrah et al. 2002a), but we exclude these on the
grounds that the $K$-band nuclear contribution will
differ. 
%Nevertheless, the hyperluminous quasars IRAS F10026+4949 and
%IRAS F14218+3845 have nuclear components enhancing the $I$-band fluxes
%by $2.1$ and $1.5$ magnitudes respectively, which if applied to the
%$K$-band 
%fluxes reported by Farrah et al. (2003) would place them well within
%the locus of the narrow-line HLIRGs discussed below. 

There are great difficulties with associating $14''$ resolution
sub-mm blank-field survey galaxies with
sources at other wavebands (e.g. Serjeant et al. 2003), especially
given the non-Poissonian distribution of these and other populations
(e.g. Almaini et al. 2003). 
Most claimed spectroscopic redshifts 
report spectroscopic evidence of star formation (e.g. Chapman et
al. 2003), but one should note that 
there are precedents for
identifications of sub-mm sources changing with the advent of new data
(e.g. Dunlop et al. 2003b, Serjeant et al. 2003, Smail et al. 1999). 
%The $16$ sources with published $K$
%magnitudes or limits are from the SCUBA 8mJy survey
%(Scott et al. 2002, Fox et al. 2002, Ivison et al. 2002), the
%cluster lens survey (Smail et al. 2002b), the signposts survey
%(Smail et al. 2003) and the SCUBA-HDF survey (Serjeant et al. 2003,
%Hughes et al. 1998). 
%We also use the $\geq3$ band photometric redshifts of sub-mm selected
%galaxies of Aretxaga et
%al. (2003). 
The $K$ magnitudes of all published sub-mm galaxies with spectroscopic
redshifts are listed in table \ref{tab:kmags_scuba}. We also include
galaxies with $\geq3$ band photometric redshifts, though the accuracy
of these redshifts will depend on how closely the high-$z$ population
resembles local templates (yet to be determined). 

In addition to HLIRGs and sub-mm galaxies, 
we have compiled comparative data from the
literature on other, ostensibly related populations. 
%We opt not
%to use photometric redshift estimates from the radio:sub-mm spectral
%index (Yun \& Carilli 2002, Carilli \& Yun 2000a,b, Dunne et al. 2000)
%because of the problems with the cross-identifications, and the 
%additional uncertainty that the far-infrared:radio relation holds at
%all redshifts. 
We use the photometry and redshifts of non-quasar Chandra sources
from the Hubble Deep Field North Chandra $1$ megasecond catalogue
of Barger et al. (2002), which is an improvement on the inhomogeneous
compilations available to Willott et al. (2001). We also use the
$K$-band photometry and spectral classifications 
of ultraluminous infrared galaxies of Kim et al. (2002) and Veilleux
et al. (2002). 
%$\gamma$-ray burst host galaxies from Le Floch
%et al. (2003). 
Finally, we use the radiogalaxy photometry compilation in Willott et
al. (2003). 
Because the 3CRR flux limit remains
close to the radio $L_*$ ($L_*$(radio)), 3CRR radio galaxies lie at
$\sim3-4L_*$(radio) 
(Willott et al. 2003) at all redshifts. Note also that 3CRR sources
are also the highest luminosity  
radio sources in the Hubble volume at $z<2$. 

\section{Results}\label{sec:results}

\begin{figure}
\centering
\ForceWidth{5in}
\hSlide{-1.8cm}
\vspace*{-1cm}
\BoxedEPSF{kz1.ps}
\vspace*{-1cm}
\caption{\label{fig:kz1}$K$-band Hubble diagram of non-quasar
hyperluminous galaxies (filled circles), 3CRR radiogalaxies (open
triangles), 6CE radiogalaxies (open squares), and sub-mm selected
galaxies with spectroscopic redshifts (large open
circles). The 
hyperluminous radiogalaxy 4C41.17 (also the highest redshift HLIRG) is
plotted with a  
slightly smaller symbol, to distinguish it from the other HLIRGs. 
%Radiogalaxy photometry is from the compilation in 
%Willott et al. (2003), HLIRG
%photometry is given in table \ref{tab:kmags}, and sub-mm galaxy 
%data is from
%Ivison et al. (2002) and Chapman et al. (2003). 
B2 0902+343 is excluded because it
is not clear whether the sub-mm flux is thermal, Downes et al. 1996.
Note that two sub-mm selected galaxies are also hyperluminous.
Also plotted are: a no evolution curve (short dash), instantaneous
starburst at $z=10$ followed by passive stellar evolution (full line),
$z=5$ starburst (long dash) and $z=3$ starburst, from Willott et
al. (2003). Also plotted are obscured starburst models of Takagi et
al. (2003): age $t/t_0=2$, compactness $\Theta=0.4$ (dash-dot) and
$\Theta=0.5$ (dash-dot-dot-dot). All models are for a
$3L_*(K)$ galaxy.}
\end{figure}

Figure \ref{fig:kz1} shows the $K-z$ relation of HLIRGs, compared to
that of bright radio sources from the 3CRR survey (Laing et al. 1983)
and 6CE survey 
(Eales et al. 1997). Willott et al. (2003) quotes a fit to the
radiogalaxy $K-z$ 
relation of 
\begin{equation}
K_{pred}=17.37 + 4.53\log_{10}(z) - 0.31(\log_{10}(z))^2 .
\end{equation}
3CRR has dispersion around this relation of only $\pm0.5$
magnitudes. The HLIRGs are statistically indistinguishable from the
3CRR radiogalaxies: a Kolmogorov-Smirnov test of the distributions of
$K-K_{pred}$ of HLIRGs and 3CRR radiogalaxies rejects the null
hypothesis of same distributions at only $23\%$ 
confidence.
\footnote{Although this test is only asymptotically
distribution-free, we 
verified the test in this case with a bootstrap analysis. We randomly 
selected $10$ 3CRR radiogalaxies, and compared $K-K_{pred}$ for this
subset against the remainder. By repeating this, we found that the
confidence levels returned  
are well-represented by a uniform distribution on the interval $[0,1]$
as required.} 
%Excluding HLIRGs which are radiogalaxies does not affect
%this conclusion ($23\%$ confidence of rejecting the null hypothesis). 
(We have excluded the hyperluminous radiogalaxy 4C41.17 from this test,
though its magnitude is consistent with the $K-z$ relation of other
HLIRGs table \ref{tab:kmags}). 

Curiously 
however, the same cannot be said of sub-mm selected galaxies, also
plotted in  
figure \ref{fig:kz1}. Even assuming the $K$-band limits are obtained
for these galaxies, the distributions are still dissimilar at $99.98\%$
confidence. Figure \ref{fig:kz2} shows the HLIRG $K-z$ relation in the
context of other potentially 
related populations. 
%sub-mm selected galaxies with $\geq3$-band photometric redshifts
%(Aretxaga et al. 2003), 
%%$\gamma$-ray burst host galaxies
%%(Le Floch et al. 2003),
%Chandra HDF-N $1$Ms sources (Barger et al. 2002), and
%ultraluminous infrared galaxies (Kim et al. 2002, Veilleux et
%al. 2002). 
%%from 6C* (Jarvis et al. 2001a,b), 7CI+II (Willott et
%%al. 2003) and 7CIII (Lacy et al. 2000), though these lie in almost the
%%same region as 6CE (see Willott et al. 2003). 
Note that the
photometric redshifts of three sub-mm selected galaxies and at least
$5$ with spectroscopic redshifts place them
securely away from the radiogalaxy locus. 

Neither the sub-mm galaxies nor the HLIRG samples from Rowan-Robinson
2000 are spectroscopically 
complete. Could this selection bias cause our HLIRG $K-z$ relation? In
a sample with a flux limit at two wavelengths, correlating the
luminosity at one wavelength with that at 
the other is essentially a distance vs. distance correlation
(e.g. Serjeant et al. 1998). However
this cannot be the cause of our HLIRG $K-z$ relation because 
(a) the apparent $K$ magnitudes 
are not well-represented by a $K$ flux limit: the magnitude histogram of
table \ref{tab:kmags} is more or less uniform from $K\sim13$ to
$K>20$; (b) more importantly, the optical selection ($R$ or $B$)
shows no greater evidence for clustering around a particular apparent
magnitude. If Malmquist bias (distance vs. distance correlations) 
were responsible, we would expect {\it more} clustering
around a particular apparent magnitude in the optical, compared to
the $K$-band. As discussed in Rowan-Robinson 2000,
there are probably 
optically-fainter HLIRGs still to be found in the IRAS database, and
our results make very specific predictions for their K magnitudes. 
However, if an as-yet-undiscovered selection effect results in the
undiscovered HLIRGs having fainter $K$ magnitudes, this would change
the results of this study. 

In both figure \ref{fig:kz1} and \ref{fig:kz2} we overplot passive
stellar evolution tracks of a $3L_*(K)$ galaxy
(where $L_*(K)$ is the K-band $L_*$) for an instantaneous starburst at
$z=10$, $z=5$, and $z=3$, as well as a no-evolution curve, as derived
by Willott et al. (2003), and two obscured starburst models of Takagi
et al. (2003).  We adopt $M_*(K)=-24.5$ in accordance with
the recent determination by Huang et al. (2003). We refer to the
passively evolving curve starting from a $z=10$ instantaneous
starbust, normalised to $M(K)=-24.5$ at zero redshift, as $K_*(z)$. 

\section{Discussion}\label{sec:discussion}

\begin{figure}
\centering
\ForceWidth{5in}
\hSlide{-1.8cm}
\vspace*{-1cm}
\BoxedEPSF{kz2.ps}
\vspace*{-1cm}
\caption{\label{fig:kz2}
$K$-band Hubble diagram for HLIRGs (filled circles; 4C41.17 has
smaller symbol), sub-mm galaxies
with spectroscopic redshifts (large open circles) 
%the populations and models shown in figure
%\ref{fig:kz1}, and in addition 
%$\gamma$-ray burst host galaxies ($+$)
%from Le Floch et al. (2003),
%sub-mm selected sources with 
or photometric redshifts from detections in
$\geq3$ bands (large diamonds), 
%from Aretxaga et al. 2003,
non-quasar ultraluminous infrared galaxies ($\times$), 
%from Kim et al. 2003 and
%Veilleux et al. 2003, 
and Chandra HDF-N $1$Ms non-quasar 
sources ($+$) from Barger et al. (2002). 
%radiogalaxies from 6C* (open downward
%triangles), 
%7CI+II (open diamonds) and 7CIII (open upward triangles).
%Radiogalaxy photometry is from the compilation in Willott et al. (2003). 
Chandra source photometry assumes $HK'-K=0.13+0.05(I-K)$ where
$I$-band photometry is available, and $HK'-K=0.3$ otherwise (Barger et
al. 2002). 
For clarity we omit the 
radiogalaxies. The same models are plotted as figure \ref{fig:kz1}. 
}
\end{figure}

The difference between the HLIRG and sub-mm galaxy $K-z$ relations is
all the more puzzling given our discovery that some HLIRGs would have
comparable sub-mm fluxes to sub-mm-selected galaxies, if redshifted to
$z\sim3$ (Farrah et al. 2002b), including two of the HLIRGs in the
present paper. Given a template spectral energy
distribution with a sufficiently warm colour temperature, many of the
sub-mm-selected galaxies could have bolometric luminosities
approaching $10^{13}L_\odot$. 
Five of the ten HLIRGs in this paper were selected at
$60\mu$m, and two of the remainder were discovered by 
follow-ups of radiogalaxies, either of which may have introduced a
bias towards high AGN bolometric 
contributions. 
If so, this would suggest that the position on the
$K-z$ relation may be related to the presence of the most massive
AGN.  A prediction of this interpretation is that the multi-wavelength
data on sub-mm galaxies from SIRTF (e.g. Lonsdale et al. 2003) should
find an anticorrelation between $K-K_*$ magnitudes and the bolometric
contributions in the mid-infrared. 


Alternatively, the HLIRG $K-z$ relation may be intrinsic, rather than
the product of a subtle AGN bias. 
All of the galaxies currently {\it proved} to be hyperluminous
currently lie on a tight $K-z$ relation, including those selected in
the sub-mm. 
Also, radiative transfer models of the Rowan-Robinson (2000) HLIRGs do
not find the AGN to be bolometrically dominant in all cases
(e.g. Verma et al. 2002, Farrah et al. 2002b). 
There is
no prima facie reason to suppose that HLIRGs should necessarily follow
the radiogalaxy $K-z$ relation. 
For example, the 
obscured high-redshift AGN detected by Chandra are not found with similar
$K$ magnitudes to radiogalaxies (or HLIRGs, figure \ref{fig:kz2}),
which Willott et al. (2001) 
argued was due to the Chandra sources hosting smaller mass nuclear black
holes. 
However, the relative number densities
of radiogalaxies and HLIRGs lend plausibility to a physical link
between the populations, or at least a common progenitor. 
Rowan-Robinson (2000) lists $16$ HLIRGs with $z\leq1$, implying a
lower limit to the $z\leq1$ HLIRG number density of
$\geq3\times10^{-10}h^3$Mpc$^{-3}$, and also 
estimates
that only $\sim10-20\%$ of HLIRGs have been identified to date.
These number densities are comparable to the 
$z\leq1$ number
density of 3CRR radio galaxies ($1.1\times10^{-9}h^3$Mpc$^{-3}$) and
significant compared to $z\leq1$ 3CRR active galaxies as a whole
($2.5\times10^{-9}h^3$Mpc$^{-3}$). Notably, both HLIRGs and 3CRR are
the most luminous in the Hubble volume of their class. 

This does not necessarily imply that radiogalaxies and HLIRGs must be
the most massive galactic systems in the Hubble volume. Huang et
al. (2003) measured the space density of $10L_*(K)$ galaxies 
to be
$2.1\times10^{-8}h^3$Mpc$^{-3}$ at $z<0.4$. 
These galaxies are $2.5$ magnitudes brighter than the HLIRG and
radiogalaxy host galaxies, and $\sim10\times$ more numerous than
radio-loud AGN. However, the space density of $>10L_*(K)$ galaxies has
not been determined at higher redshifts. 

There is 
evidence in figure \ref{fig:kz3} that infrared luminosity scales with
host luminosity, in a manner reminiscent of the trend of host
luminosity with radio lobe luminosity in radiogalaxies (Willott et
al. 2003). The difference in the mean $K-K_*$ for the
$1-3\times10^{12}L_\odot$ and $>10^{13}L_\odot$ bins is significant
at $99.6\%$ confidence using Student's T statistic, though the objects
in these bins span 
different redshifts, so differential evolution may also be a factor
(e.g. Serjeant et al. 1998). Samples of infrared-luminous galaxies
spanning a narrow range in redshift, but a wide range in luminosity,
are needed to test this relationship definitively. Such samples may
become available with the advent of SIRTF. 

If radiogalaxy and HLIRG activity is both short lived and rare (in the
sense that a $5L_*(K)$ galaxy has a low probability of ever hosting a
radiogalaxy or HLIRG), then the lack of $>10L_*(K)$ HLIRGs might be
explained by the finite size of the volume surveyed so far for 
HLIRGs. 
If we assume that $K$-band galaxies in the range $0.5-5L_*(K)$ are the
hosts of short-lived HLIRG activity with $10^{13-14}L_\odot$, and we
interpolate from the  
$K$-band luminosity function (Huang et al. 2003) 
keeping the HLIRG duty cycle constant, 
then the space density of $10^{14-15}L_\odot$ galaxies should be
around a factor of $\sim1000$ lower. 
%``\"{U}ber-luminous'' 
%galaxies with luminosities $>10^{15}L_\odot$ in
%the Hubble volume. 
This is, of course, only a toy model: the $K$-band
luminosity function is unlikely to 
keep the same shape at all redshifts, the luminosities may not scale
with the host galaxy masses, and the duty cycle assumptions
may be ill-founded, but this does raise the interesting question of
the existence of still more extreme 
%%``\"{U}ber-luminous'' 
populations of infrared galaxies. 
Source count models differ widely in their predictions at these
luminosities (Pearson 2001, Rowan-Robinson 2001). 
Whether such systems do in fact exist may be
testable with the next generation of sub-mm/mm-wave survey
facilities, such as SCUBA-2 (Holland et al. 2003) or the LMT (Baars et
al. 1998). 

%The only population of objects currently known to be more luminous
%than HLIRGs is $\gamma$-ray bursts. 
%Figure \ref{fig:kz2} shows that 
%the host galaxies of $\gamma$-ray
%bursts are under-luminous, as reported by Le Floch et al. (2003), 
%rather than being found in the most massive
%(and potentially the most violently star forming) galaxies, or even in
%$\sim L_*(K)$ systems which dominate the comoving stellar mass. 

In short, there are plausible precedents for
abundant populations of galaxies with evidence of dust-enshrouded AGN,
extreme luminosities and/or large stellar masses, which are 
many times more luminous in $K$, or 
many times less luminous, than HLIRGs. 
The fact that these populations
do not host HLIRG activity suggests 
that the similarity of the HLIRG and radiogalaxy 
$K-z$ relations is due to a direct physical link between the two
phenomena, such as an evolutionary connection, or a common progenitor
population. 
Alternatively, the position of HLIRGs on the $K-z$ relation may be
solely related to the presence of the most massive AGN (see above),
for which a key test is whether the SIRTF detects hyperluminous
AGN activity in sub-mm selected galaxies. 


\begin{figure}
\centering
\ForceWidth{5in}
\hSlide{-1.8cm}
\vspace*{-2cm}
\BoxedEPSF{kz3.ps}
\vspace*{-1cm}
\caption{\label{fig:kz3}
$K$-band luminosity relative to $L*$ ($z=10$ starburst model), plotted
against bolometric 
luminosity. HLIRGs: filled circles; ultraluminous galaxies: crosses. 
%Hyperluminous galaxies from Rowan-Robinson (2000) are
%plotted as filled circles, and ultraluminous galaxies from Kim et
%al. (2002) and Veilleux et al. (2002) are plotted as crosses. 
Also plotted are the mean $K-K_*$ values in binned luminosity ranges
(horizontal lines). 
The standard deviation is $\sim\pm0.6$ magnitudes in each bin, and the
errors on the means are plotted as vertical lines. 
Note that for our cosmology, some of the Rowan-Robinson (2000)
compilation slip just below the HLIRG threshold, and one of
the ultraluminous galaxies becomes HLIRGs. For consistency with
previous work, we restrict our HLIRGs to the Rowan-Robinson (2000)
compilation, but as can be seen from this figure this choice does not
affect our conclusions. 
}
\end{figure}

Surprisingly, sub-mm galaxies have a very different distribution in
the $K-z$ plane. 
%The evidence for their divergence from the radiogalaxy $K-z$
%relation is currently based on only two outlier galaxies (or more if
%the $K$-band limits are not obtained). 
This is contrary to the result of Dunlop (2002) 
due to the subsequent increase in (ostensibly) reliable spectroscopic
redshifts.  
%used radio:sub-mm photometric redshifts to 
%place sub-mm sources on the $K-z$ relation, and found a good agreement
%with radiogalaxies. His sample is similar to ours, except that we
%have excluded LH850.1, CUDSS14A and ELAIS N2850.2 as these lack
%spectroscopic redshifts, and we have the benefit of new spectroscopic
%redshifts since the Dunlop (2002) study (Chapman et al. 2003). 
The spectroscopic redshift of ELAIS N2850.1 
is anomalous compared to its radio:sub-mm ratio, which led Chapman et
al. (2002) to suggest that the system may be lensed. Placing the
system at higher redshift may well restore ELAIS N2850.1 to closer to
the locus of the radiogalaxy $K-z$ relation. 
Nevertheless, several photometric or spectroscopic 
redshifts place sub-mm
galaxies away from 
the radiogalaxy $K-z$ relation (figure \ref{fig:kz2}). 
%Aretxaga et al. (2003)
%lists photometric redshifts of sub-mm selected galaxies based on
%detections in at least $3$ passbands. Eight of these still lack a
%spectroscopic redshift, but of these three are clear outliers 
%on the $K-z$ plane on the basis of their photometric redshifts
%(HDF850.1, SMMJ00266+1708, SMMJ14099+0252). 
Plausibly, these may represent separate populations; there is no
reason to suppose that sub-mm selected galaxies represent a single
homogeneous population of objects (e.g. Dannerbauer et al. 2002), as
with Extremely Red Objects (e.g. Smail et al. 2002a). 
%Our 
%data in figure \ref{fig:kz2} is consistent with a heavily obscured
%sub-population. 

One possibility is that some sub-mm galaxies are less massive systems;
another is that 
not all of them  
are the progenitors of the most massive ellipticals
(Efstathiou \& Rowan-Robinson 2003,
Kaviani et al. 2003) but rather are cool cirrus-dominated objects. 
Alternatively, some sub-mm galaxies may be heavily extinguished even
in the observed-frame $K$-band. 
Such an interpretation is physically plausible: figures \ref{fig:kz1}
and \ref{fig:kz2}  
show the predictions of such a model from 
Takagi et al. 2003. 

%The similarity of the $K$-band morphologies of at least
%some sub-mm selected galaxies and radiogalaxies has been argued to 
%suggest a common
%connection with the assembly of the most massive ellipticals (Lutz et
%al. 2001), as has the similarity of the comoving number densities of
%sub-mm selected galaxies, extremely red objects at $z\sim1.5$, and
%present-day $2-3L_*$ ellipticals (Scott et al. 2002). The clustering
%of sub-mm galaxies will be a powerful test of this interpretation (van
%Kampen et al. in prep.) and others 
%(Efstathiou \& Rowan-Robinson 2003,
%Kaviani et al. 2003). 

%Our HLIRG 
%data is also consistent with models in which the dust responsible
%for the far-infrared emission in HLIRGs is almost entirely 
%heated by the active
%nucleus (Willott et al. 2002). While radiative transfer models 
%of our HLIRGs typically suggest comparable contributions from
%starburst and active nucleus (e.g. Rowan-Robinson 2000), at
%least half the sample is starburst-dominated and only two have AGN
%contributions which models imply exceed the starburst (IRAS 09104+4109
%and IRAS F10214+4724, though differential lensing may play a role in the
%latter, Lacy et al. 1998). Another problem of quasar-heated dust
%models in HLIRGs is 
%that every HLIRG so far
%has shown some evidence of an active nucleus, but 
%not every radio-loud AGN
%has hyperluminous far-infrared emission. This might be explained by
%variations in the dust content and distribution in active nuclei, and
%in the central black hole masses and Eddington ratios, but
%at the cost of a natural explanation for the similarity of HLIRG and
%radiogalaxy $K-z$ relations. Notably, at least $50\%$ of
%normal galaxies also show evidence of active nuclei (Ho et al. 1997),
%without requiring these nuclei to be bolometrically dominant. 

The HLIRG $K-z$ relation could be used to estimate redshifts of
HLIRG candidates, as was the early 
practice for radiogalaxies (e.g. Dunlop \&
Peacock 1990). Based on the 3CRR radiogalaxy $K-z$ relation, the $K$
magnitude is sufficient to determine the redshift of HLIRGs 
to better than $\pm10\%$ in $(1+z)$ at all redshifts, provided the
systems are indeed hyperluminous and are not quasars. Regarding 
the hyperluminous quasars in Farrah et al.
(2003), we can predict that the
hyperluminous quasar LBQS 1220+0939 should be 
dominated by the host galaxy
flux in $K$, while the hyperluminous quasar 
IRAS F10119+1429 should be 
dominated by the nuclear component in $K$. The remaining cases in
Farrah et al. (2003) should be intermediate between these two cases. 

Only two of the known non-quasar HLIRGs lack $K$-band photometry, so
further tests of the HLIRG $K-z$ relation using HLIRGs discovered to
date must rely on 
sub-arcsecond near-infrared imaging of hyperluminous quasar hosts. 
Alternatively, both SIRTF and ASTRO-F will have sensitive $L$ and $M$-band
cameras, which can further reduce the contribution from the active
nucleus by sampling closer to the rest-frame $K$-band. 

\section{Acknowledgements}
We would like to thank Chris Willott for kindly supplying the 
stellar evolution curves, and the anonymous referee for very 
helpful
suggestions, including the possibility that an AGN bias in the
Rowan-Robinson (2000) sample may be related to their position on the
$K-z$ relation. 
This research was supported by PPARC grant PPA/G/0/2001/00116, and
Nuffield Foundation grant NAL/00529/G. 
This publication makes use of data products from the Two Micron All
Sky Survey, which is a joint project of the University of
Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National
Aeronautics and Space Administration and the National Science
Foundation. This research made use of the NASA/IPAC Extragalactic
Database (NED) which is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration. 

\begin{thebibliography}{}

\bibitem{} Almaini, A., et al., 2003, MNRAS 338, 303
\bibitem{} Aretxaga, I., Hughes, D.H., Chapin, EL., Gazta\~{n}aga, E.,
Dunlop, J.S., Ivison, R.J., 2003, MNRAS 342, 759
\bibitem{} Archibald, E.N., Dunlop, J.S., Hughes, D.H., Rawlings, S.,
Eales, S.A., Ivison, R.J., 2001, MNRAS 323, 417
\bibitem{}
Baars, J.W.M., Carrasco, L., Schloerb, F.P., 1998, Bulletin of the
American Astronomical Society, vol. 31, p. 840
%\bibitem[\protect\citename{Dickinson et al. }2001]{dickinson01}
%Dickinson M.,  et al., 2001, BAAS, 198, 2501 
%\bibitem{} Elbaz, D., et al., 1999, A\&A 351, L37
\bibitem{} Barger, A.J., Cowie, L.L., Richards, E.A., 2000, AJ 119, 2092 
\bibitem{} Barger, A., Cowie, L.L., Bradt, W.N., Capak, P., Garmire,
G.P., Hornschemeier, A.E., Steffen, A.T., Wehner, E.H., 2002, AJ 124, 1839
\bibitem{} Broadhurst, T., Lehar, J., 1995, ApJ 450, L41
%\bibitem{} Carilli, C.L., \& Yun, M.S., 2000a, ApJ 530, 618
%\bibitem{} Carilli, C.L., \& Yun, M.S., 2000b, ApJ 539, 1024
\bibitem{} Chapman, S.C., Smail, I., Ivison, R.J., Blain, A.W., 2002,
MNRAS 335, L17
%\bibitem{} Chapman, S.C., Smail, I., Ivison, R.J., Helou, G., Dale,
%D.A., Lagache, G., 2002, ApJ 573, 66 %%% FIRBACK
\bibitem{} Chapman, S.C., Blain, A.W., Ivison, R.J., Smail, I.R.,
2003, Nature 422, 695
\bibitem{} Clements, D.L., Rowan-Robinson, M., Lawrence, A.,
Broadhurst, T., McMahon, R., 1992, MNRAS 256, 35P
\bibitem{} Cutri, R.M., et al., 2003, Explanatory Supplement to the
2MASS All Sky Data Release, IPAC
\bibitem{} Dannerbauer, H., Lehnert, M.D., Lutz, D., Tacconi, L.,
Bertoldi, F., Carilli, C., Genzel, R., Menten, K., 2002, ApJ 573, 473
\bibitem{} Downes, D., Solomon, P.M., Radford, S.J.E., 1993, ApJ 414, L13
\bibitem{} Downes D., Solomon P. M., Sanders D. B., Evans A. S., 1996,
A\&A, 313, 91  
\bibitem{}
Dunlop, J.S., 2002, in 
%{\it A New Era In Cosmology}, 
ASP conference
proceedings vol. 283, eds. T. Shanks and N. Metcalfe, San Fransisco:
Astronomical Society of the Pacific (astro-ph/0203183) 
\bibitem{} Dunlop, J.S., \& Peacock, J.A., 1990, MNRAS 247, 19
\bibitem{} Dunlop, J.S., McLure, R.J., Kukula, M.J., Baum, S.A.,
O'Dea, C.P., Hughes, D.H., 2003a, MNRAS 340, 1095
\bibitem{} Dunlop, J.S., et al., 2003b, MNRAS submitted (astro-ph/0205480)
\bibitem{} Dunne, L., Clements, D.L., Eales S.A., 2000, MNRAS 319, 813
\bibitem{} Eales, S.A., \& Rawlings, S., 1993, ApJ 411, 67
\bibitem{} Eales, S.A., Rawlings, S., Law-Green, J.D.B., Cotter, G.,
Lacy, M., 1997, MNRAS 291, 593
\bibitem{} Efstathiou, A., \& Rowan-Robinson, M., 2003, MNRAS 343, 322
\bibitem{} Eisenhardt, P., \& Dickinson, M., 1992, ApJ 399, L47
\bibitem{} Eisenhardt, P., Armus, L., Hogg, D.W., Soifer, B.T.,
Neugebauer, G., Werner, M.W., 1996, ApJ 461, 72
\bibitem{}
Farrah, D., Verma, A., Oliver, S., Rowan-Robinson, M., McMahon, R.,
2002a, MNRAS 329, 605
\bibitem{} Farrah, D., Serjeant, S., Efstathiou, A., Rowan-Robinson,
M., Verma, A., 2002b, MNRAS 335, 1163
%\bibitem{} Farrah, D., Afonso, J., Efstathiou, A., Rowan-Robinson, M.,
%Fox, M., Clements, D., 2003a, MNRAS 343, 585
\bibitem{}
Farrah, D., Geach, J., Fox, M., Serjeant, S., Oliver, S., Verma, A.,
Kaviani, A., Rowan-Robinson, M., 2003, MNRAS submitted
\bibitem{} Fernandez-Soto, A., Lanzetta, K.M., Yahil, A., 1999, ApJ
513, 34 
\bibitem{} Fox, M.J., et al., 2002, MNRAS 331, 817
\bibitem{} Gear, W.K., Lilly, S.J., Stevens, J.A., Clements, D.L.,
Webb, T.M., Eales, S.A., Dunne, L., 2003, MNRAS submitted
(astro-ph/0007054) 
%\bibitem{} Graham, J.R., \& Dey, A., 1996, ApJ 471, 720
\bibitem{} Graham, J.R., \& Liu, M.C., 1995, ApJ 449, L29
\bibitem{} Graham, J.R., et al., 1994, ApJ, 420, L5
\bibitem{}
Ho, L.C., Filippenko, A.V., Sargent, W.L.W., 1997, ApJS, 112, 315
\bibitem{}
Holland, W.S., Duncan, W., Kelly, B.D., Irwin, K.D., Walton, A.J.,
Ade, P.A.R., Robson, E.I., 2003, in Millimeter and Submillimeter
Detectors for Astronomy, eds. T.G. Phillips and J. Zmuidzinas,
Proceedings of the SPIE, vol. 4855, pp. 1-18
\bibitem{} Huang, J.S., Glazebrook, K., Cowie, L.L., Tinney, C., 2003,
ApJ 584, 203
\bibitem{} Hughes, D.H., et al., 1998, Nature 394, 241
%\bibitem{} Ivison, R.J., Smail, I., Barger, A.J., Kneib, J.-P., Blain,
%A.W., Owen, F.N., Kerr, T.H., Cowie, L.L., 2000, MNRAS 315, 209
\bibitem{} Ivison, R.J., et al., 2002, MNRAS 337, 1
\bibitem{} Jarvis, M.J., Rawlings, S., Eales, S.A., Blundell, K.M.,
Croft, S., McLure, R.J., Willot, C.J., 2001, MNRAS 326, 1585
%\bibitem{} Jarvis, M.J., et al., 2001b, MNRAS 326, 1563
\bibitem{} Kaviani, A., Haehnelt, M.G., Kauffmann, G., 2003, MNRAS
340, 739
\bibitem{} Keel, W.C., Wentao, W., Waddington, I., Windhorst, I.,
Pascarelle, S.M., 2002, AJ 123, 3041
\bibitem{} Kim, D.-C., Veilleux, S., Sanders, D.B., 2002, ApJS 143, 277
\bibitem{} Kleinmann, S.G., Hamilton, D., Keel, W.C., Wynn-Williams,
C.G., Eales, S.A., Becklin, E.E., Kuntz, K.D., 1988, ApJ 328, 161
\bibitem{} Lacy, M., Rawlings, S., Serjeant, S., 1998, MNRAS 299, 1220
%\bibitem{} Lacy, M., Bunker, A.J., Ridgway, S.E., 2000, AJ 120, 68
\bibitem{} Laing, R.A., Riley, J.M., Longair, M.S., 1983, MNRAS 204,
151 
%\bibitem{} Le Floch, E., et al 2003, A\&A 400, 499
\bibitem{} Lilly, S.J., Longair, M.S., 1984, MNRAS 211, 833
\bibitem{} Lilly, S.J., Eales, S.A., Gear, W.K.P., Hammer, F., Le
F\'{e}vre, O., Crampton, D., Bond, J.R., Dunne, L., 1999 ApJ 518, 641
\bibitem{} Liu, M.C., Graham, J.R., Wright, G.S., 1996, ApJ 470, 771
%\bibitem{} Lutz, D., et al., 2001, A\&A 378, L70
\bibitem{} Lonsdale, C., et al., 2003, PASP 115, 897
\bibitem[\protect\citename{Pearson }2001]{cpp01a}Pearson, C.P., 2001,
MNRAS 325, 1511 
\bibitem{} Priddey, R.S., Isaak, K.G., McMahon, R.G., Omont, A., 2003,
MNRAS 339, 1183
\bibitem{} Rowan-Robinson, M., et al., 1991, Nature 351, 719
\bibitem{} Rowan-Robinson, M., 2000, MNRAS 316, 885
\bibitem{} Rowan-Robinson, M., 2001, ApJ 549, 745
\bibitem{} Scott, S., et al., 2002 MNRAS 331, 817
\bibitem{} Serjeant, S., Lacy, M., Rawlings, S., King, L.J., Clements,
D.L., 1995, MNRAS 276, L31
\bibitem{} Serjeant, S., Rawlings, S., Lacy, M., Maddox, S.J., Baker,
J.C., Clements, D., Lilje, P., 1998, MNRAS 294, 494
\bibitem{} Serjeant, S., et al., 2003, MNRAS in press
\bibitem{} Smail, I., Ivison, R.J., Kneib, J.-P., Cowie, L.L., Blain,
A.W., Barger, A.J., Owen, F.N., Morrison, G., 1999, MNRAS 308, 1061
\bibitem{} Smail, I., Owen, F., Morrison, G.E., Keel, W.C., Ivison,
R.J., Ledlow, M.J., 2002a, ApJ 581, 844
\bibitem{} Smail, I., Ivison, R.J., Blain, A.W., Kneib, J.-P., 
2002b, MNRAS 331, 495
\bibitem{} Smail, I., Ivison, R.J., Gilbank, D.G., Dunlop, J.S., Keel,
W.C., Motohara, K., Stevens, J.A., 2002, ApJ 583, 551
\bibitem{} Stanford, S.A., Stern, D., van Breugel, W., De Breuk, C., 
2000, ApJS 131, 185
\bibitem{} Takagi, T., Arimoto, N., Hanami, H., 2003, MNRAS 340, 813
\bibitem{} Veilleux, S., Kim, D.-C., Sanders, D.B., 2002, ApJS 143, 315
\bibitem{} Verma, A., Rowan-Robinson, M., McMahon, R., Efstathiou, A.,
2002, MNRAS 335, 574
\bibitem{}
Willott, C.J., et al., 2001, in Recent results of XMM-Newton and
Chandra, XXXVIth Recontres de Moriond, XXIst
Moriond Astrophysics Meeting, eds. D.M. Neumann \& J.T.T. Van. 
(astro-ph/0105560)
\bibitem{}
Willott, C.J., Rawlings, S., Archibald, E.N., Dunlop, J.S., 2002,
MNRAS 331, 435
\bibitem{}
Willott, C.J., Rawlings, S., Jarvis, M.J., Blundell, K.M., 2003, MNRAS
339, 173

\end{thebibliography}



\end{document}





astro-ph0310661.extracted_bib
\begin{thebibliography}{}

\bibitem{} Almaini, A., et al., 2003, MNRAS 338, 303
\bibitem{} Aretxaga, I., Hughes, D.H., Chapin, EL., Gazta\~{n}aga, E.,
Dunlop, J.S., Ivison, R.J., 2003, MNRAS 342, 759
\bibitem{} Archibald, E.N., Dunlop, J.S., Hughes, D.H., Rawlings, S.,
Eales, S.A., Ivison, R.J., 2001, MNRAS 323, 417
\bibitem{}
Baars, J.W.M., Carrasco, L., Schloerb, F.P., 1998, Bulletin of the
American Astronomical Society, vol. 31, p. 840
%\bibitem[\protect\citename{Dickinson et al. }2001]{dickinson01}
%Dickinson M.,  et al., 2001, BAAS, 198, 2501 
%\bibitem{} Elbaz, D., et al., 1999, A\&A 351, L37
\bibitem{} Barger, A.J., Cowie, L.L., Richards, E.A., 2000, AJ 119, 2092 
\bibitem{} Barger, A., Cowie, L.L., Bradt, W.N., Capak, P., Garmire,
G.P., Hornschemeier, A.E., Steffen, A.T., Wehner, E.H., 2002, AJ 124, 1839
\bibitem{} Broadhurst, T., Lehar, J., 1995, ApJ 450, L41
%\bibitem{} Carilli, C.L., \& Yun, M.S., 2000a, ApJ 530, 618
%\bibitem{} Carilli, C.L., \& Yun, M.S., 2000b, ApJ 539, 1024
\bibitem{} Chapman, S.C., Smail, I., Ivison, R.J., Blain, A.W., 2002,
MNRAS 335, L17
%\bibitem{} Chapman, S.C., Smail, I., Ivison, R.J., Helou, G., Dale,
%D.A., Lagache, G., 2002, ApJ 573, 66 %%% FIRBACK
\bibitem{} Chapman, S.C., Blain, A.W., Ivison, R.J., Smail, I.R.,
2003, Nature 422, 695
\bibitem{} Clements, D.L., Rowan-Robinson, M., Lawrence, A.,
Broadhurst, T., McMahon, R., 1992, MNRAS 256, 35P
\bibitem{} Cutri, R.M., et al., 2003, Explanatory Supplement to the
2MASS All Sky Data Release, IPAC
\bibitem{} Dannerbauer, H., Lehnert, M.D., Lutz, D., Tacconi, L.,
Bertoldi, F., Carilli, C., Genzel, R., Menten, K., 2002, ApJ 573, 473
\bibitem{} Downes, D., Solomon, P.M., Radford, S.J.E., 1993, ApJ 414, L13
\bibitem{} Downes D., Solomon P. M., Sanders D. B., Evans A. S., 1996,
A\&A, 313, 91  
\bibitem{}
Dunlop, J.S., 2002, in 
%{\it A New Era In Cosmology}, 
ASP conference
proceedings vol. 283, eds. T. Shanks and N. Metcalfe, San Fransisco:
Astronomical Society of the Pacific (astro-ph/0203183) 
\bibitem{} Dunlop, J.S., \& Peacock, J.A., 1990, MNRAS 247, 19
\bibitem{} Dunlop, J.S., McLure, R.J., Kukula, M.J., Baum, S.A.,
O'Dea, C.P., Hughes, D.H., 2003a, MNRAS 340, 1095
\bibitem{} Dunlop, J.S., et al., 2003b, MNRAS submitted (astro-ph/0205480)
\bibitem{} Dunne, L., Clements, D.L., Eales S.A., 2000, MNRAS 319, 813
\bibitem{} Eales, S.A., \& Rawlings, S., 1993, ApJ 411, 67
\bibitem{} Eales, S.A., Rawlings, S., Law-Green, J.D.B., Cotter, G.,
Lacy, M., 1997, MNRAS 291, 593
\bibitem{} Efstathiou, A., \& Rowan-Robinson, M., 2003, MNRAS 343, 322
\bibitem{} Eisenhardt, P., \& Dickinson, M., 1992, ApJ 399, L47
\bibitem{} Eisenhardt, P., Armus, L., Hogg, D.W., Soifer, B.T.,
Neugebauer, G., Werner, M.W., 1996, ApJ 461, 72
\bibitem{}
Farrah, D., Verma, A., Oliver, S., Rowan-Robinson, M., McMahon, R.,
2002a, MNRAS 329, 605
\bibitem{} Farrah, D., Serjeant, S., Efstathiou, A., Rowan-Robinson,
M., Verma, A., 2002b, MNRAS 335, 1163
%\bibitem{} Farrah, D., Afonso, J., Efstathiou, A., Rowan-Robinson, M.,
%Fox, M., Clements, D., 2003a, MNRAS 343, 585
\bibitem{}
Farrah, D., Geach, J., Fox, M., Serjeant, S., Oliver, S., Verma, A.,
Kaviani, A., Rowan-Robinson, M., 2003, MNRAS submitted
\bibitem{} Fernandez-Soto, A., Lanzetta, K.M., Yahil, A., 1999, ApJ
513, 34 
\bibitem{} Fox, M.J., et al., 2002, MNRAS 331, 817
\bibitem{} Gear, W.K., Lilly, S.J., Stevens, J.A., Clements, D.L.,
Webb, T.M., Eales, S.A., Dunne, L., 2003, MNRAS submitted
(astro-ph/0007054) 
%\bibitem{} Graham, J.R., \& Dey, A., 1996, ApJ 471, 720
\bibitem{} Graham, J.R., \& Liu, M.C., 1995, ApJ 449, L29
\bibitem{} Graham, J.R., et al., 1994, ApJ, 420, L5
\bibitem{}
Ho, L.C., Filippenko, A.V., Sargent, W.L.W., 1997, ApJS, 112, 315
\bibitem{}
Holland, W.S., Duncan, W., Kelly, B.D., Irwin, K.D., Walton, A.J.,
Ade, P.A.R., Robson, E.I., 2003, in Millimeter and Submillimeter
Detectors for Astronomy, eds. T.G. Phillips and J. Zmuidzinas,
Proceedings of the SPIE, vol. 4855, pp. 1-18
\bibitem{} Huang, J.S., Glazebrook, K., Cowie, L.L., Tinney, C., 2003,
ApJ 584, 203
\bibitem{} Hughes, D.H., et al., 1998, Nature 394, 241
%\bibitem{} Ivison, R.J., Smail, I., Barger, A.J., Kneib, J.-P., Blain,
%A.W., Owen, F.N., Kerr, T.H., Cowie, L.L., 2000, MNRAS 315, 209
\bibitem{} Ivison, R.J., et al., 2002, MNRAS 337, 1
\bibitem{} Jarvis, M.J., Rawlings, S., Eales, S.A., Blundell, K.M.,
Croft, S., McLure, R.J., Willot, C.J., 2001, MNRAS 326, 1585
%\bibitem{} Jarvis, M.J., et al., 2001b, MNRAS 326, 1563
\bibitem{} Kaviani, A., Haehnelt, M.G., Kauffmann, G., 2003, MNRAS
340, 739
\bibitem{} Keel, W.C., Wentao, W., Waddington, I., Windhorst, I.,
Pascarelle, S.M., 2002, AJ 123, 3041
\bibitem{} Kim, D.-C., Veilleux, S., Sanders, D.B., 2002, ApJS 143, 277
\bibitem{} Kleinmann, S.G., Hamilton, D., Keel, W.C., Wynn-Williams,
C.G., Eales, S.A., Becklin, E.E., Kuntz, K.D., 1988, ApJ 328, 161
\bibitem{} Lacy, M., Rawlings, S., Serjeant, S., 1998, MNRAS 299, 1220
%\bibitem{} Lacy, M., Bunker, A.J., Ridgway, S.E., 2000, AJ 120, 68
\bibitem{} Laing, R.A., Riley, J.M., Longair, M.S., 1983, MNRAS 204,
151 
%\bibitem{} Le Floch, E., et al 2003, A\&A 400, 499
\bibitem{} Lilly, S.J., Longair, M.S., 1984, MNRAS 211, 833
\bibitem{} Lilly, S.J., Eales, S.A., Gear, W.K.P., Hammer, F., Le
F\'{e}vre, O., Crampton, D., Bond, J.R., Dunne, L., 1999 ApJ 518, 641
\bibitem{} Liu, M.C., Graham, J.R., Wright, G.S., 1996, ApJ 470, 771
%\bibitem{} Lutz, D., et al., 2001, A\&A 378, L70
\bibitem{} Lonsdale, C., et al., 2003, PASP 115, 897
\bibitem[\protect\citename{Pearson }2001]{cpp01a}Pearson, C.P., 2001,
MNRAS 325, 1511 
\bibitem{} Priddey, R.S., Isaak, K.G., McMahon, R.G., Omont, A., 2003,
MNRAS 339, 1183
\bibitem{} Rowan-Robinson, M., et al., 1991, Nature 351, 719
\bibitem{} Rowan-Robinson, M., 2000, MNRAS 316, 885
\bibitem{} Rowan-Robinson, M., 2001, ApJ 549, 745
\bibitem{} Scott, S., et al., 2002 MNRAS 331, 817
\bibitem{} Serjeant, S., Lacy, M., Rawlings, S., King, L.J., Clements,
D.L., 1995, MNRAS 276, L31
\bibitem{} Serjeant, S., Rawlings, S., Lacy, M., Maddox, S.J., Baker,
J.C., Clements, D., Lilje, P., 1998, MNRAS 294, 494
\bibitem{} Serjeant, S., et al., 2003, MNRAS in press
\bibitem{} Smail, I., Ivison, R.J., Kneib, J.-P., Cowie, L.L., Blain,
A.W., Barger, A.J., Owen, F.N., Morrison, G., 1999, MNRAS 308, 1061
\bibitem{} Smail, I., Owen, F., Morrison, G.E., Keel, W.C., Ivison,
R.J., Ledlow, M.J., 2002a, ApJ 581, 844
\bibitem{} Smail, I., Ivison, R.J., Blain, A.W., Kneib, J.-P., 
2002b, MNRAS 331, 495
\bibitem{} Smail, I., Ivison, R.J., Gilbank, D.G., Dunlop, J.S., Keel,
W.C., Motohara, K., Stevens, J.A., 2002, ApJ 583, 551
\bibitem{} Stanford, S.A., Stern, D., van Breugel, W., De Breuk, C., 
2000, ApJS 131, 185
\bibitem{} Takagi, T., Arimoto, N., Hanami, H., 2003, MNRAS 340, 813
\bibitem{} Veilleux, S., Kim, D.-C., Sanders, D.B., 2002, ApJS 143, 315
\bibitem{} Verma, A., Rowan-Robinson, M., McMahon, R., Efstathiou, A.,
2002, MNRAS 335, 574
\bibitem{}
Willott, C.J., et al., 2001, in Recent results of XMM-Newton and
Chandra, XXXVIth Recontres de Moriond, XXIst
Moriond Astrophysics Meeting, eds. D.M. Neumann \& J.T.T. Van. 
(astro-ph/0105560)
\bibitem{}
Willott, C.J., Rawlings, S., Archibald, E.N., Dunlop, J.S., 2002,
MNRAS 331, 435
\bibitem{}
Willott, C.J., Rawlings, S., Jarvis, M.J., Blundell, K.M., 2003, MNRAS
339, 173

\end{thebibliography}