Ute Lisenfeld
\altaffilmark{1} Michael Dahlem
\altaffilmark{2} \& Matthias Ehle\altaffilmark{3}
We study the relation between radio halos, the energy input by supernovae in the disk and the galaxy mass. We find that both the energy input by supernovae as well as the galaxy mass are important parameters for understanding the formation of radio halos. Galaxies with a high energy input by supernovae per star forming area and a low galaxy mass generally possess radio halos whereas galaxies with the opposite characteristics do not. %This relation suggests that there is a threshold below which radio %halos cannot form depends not only on the energy input per area but also %on the galaxy mass. Furthermore, there is a tentative correlation between the observed scale height and the expected height in a simple gravitational approximation. %We do not expect to have a clear threshold in energy input per SF %area, because at least galaxy mass must play a role as well.
radiohalos.tex
%% Version 3/21/02

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Kluwer Proceedings Sample, ProcSamp.tex
%%
%% Kluwer Academic Press
%%
%% Prepared by Amy Hendrickson, TeXnology Inc., July 1999.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%
%% LaTeX2e 
%% Uncomment documentclass, 
\documentclass{kapproc} % Computer Modern font calls

\def\lesssim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}}
\def\gtrsim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$>$}}}}
\newcommand{\energyinput}{$\dot{E}/A_{\rm SF}$}

%% and, optionally, one or more 
%%   of the \usepackage commands below:

%%%%%
%% If you use a font encoding package, please enter it here, i.e.,
%  \usepackage{T1enc}

%%%%%
%  If you have MathTimes and MathTimesPlus fonts, you
%  may uncomment the line below and use them, but you are
%  not obligated to do so, and most authors do not have
%  these fonts. (You may need to edit m-times.sty to make the
%  font names match those on your system)

%  You must have the MathTimes fonts for this to work. They may be
%  purchased from the Y&Y company, http://www.YandY.com.

% \usepackage[mtbold,noTS1]{m-times}

%%%%%
% PostScript font calls
%
% If you use the procps PS font file, you may need to edit it
% to make sure the font names match those on your system. See
% the top of the procps.sty file for more info.

\usepackage{procps} 

%%%%%
% Style for inserting .eps files and rotating illustrations or tables

% possible options for graphicx:
% [dvips], [xdvi], [dvipdf], [dvipsone], [dviwindo], [emtex], [dviwin],
% [pctexps],  [pctexwin],  [pctexhp],  [pctex32], [truetex], [tcidvi],
% [oztex], [textures]

\usepackage[dvips]{graphicx}

%%%%%%%%%%%%%%%%%%%%%
%% LaTeX209, 
%  Uncomment only one below, comment out similar commands above
%  \documentstyle{kapproc} % Computer Modern fonts
%  \documentstyle[procps]{kapproc} %For PostScript fonts
%  (The m-times.sty works only with LaTeX2e)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Commands You Can Set or Change to Customize Your Book Format: ===>>>

% Running heads:
% ==============

%  Uncomment to make chapter title on left hand page
%  and section title on right hand page
\chapsectrunningheads


% Section heads:
% ==============

%%%
% \chaptersection % will use chapter.section form for section heads.

%%%
% Uncomment to make section heads appear in
%                    both upper and lower case.
\upperandlowercase

% \useuppercase % Uncomment to make section and subsection heads 
                %  appear in uppercase.

%%%
% How many levels of section head would you like numbered?
% 0= no section numbers, 1= section, 2= subsection, 3= subsubsection
\setcounter{secnumdepth}{1}

% Table of Contents:
% ==================
% How many levels of section head would you like to appear in the
%  Table of Contents?
%  0= chapter titles, 1= section titles, 2= subsection titles, 
%  3= subsubsection titles.

\setcounter{tocdepth}{1}

% Equation numbering:
% ===================

%%%
% \nochapequationnumber % will result in equation numbers that are (1)

%%%
% \sectionequationnumber % will result in equation numbers that are (1.1)
                         % and renumber for each section

% Default for kapproc is (equation number)

% Theorem numbering:
% ==================
% \nochaptheoremnumber % will make the theorem type environments number
       % only with the theorem number. 
       % Default is only theorem number for kapproc.

% Footnotes/Endnotes:
% ===================

% Default is endnotes that appear at the end of the chapter, above
% the references, or whereever \notes is written.

%%%
% To change footnotes to appear at bottom of page uncomment:
 \let\footnote\savefootnote

%%%
% Uncomment if you want footnotetext to appear at the bottom of the page:
%\let\footnotetext\savefootnotetext

%%%
% Uncomment if you want a ruled line above the footnote.
\let\footnoterule\savefootnoterule

% Bibliography Style Settings:
% ============================
% Choose either kluwerbib or normallatexbib:

%%%
\kluwerbib % will produce this kind of bibliography entry:

%  Anderson, Terry L.,...
%    continuing bib entry here

%  \cite{xxx} will print without brackets around the citation.
% \bibliographystyle{kapalike} % should be used when you use \verb+\kluwerbib+.

%%%
%\normallatexbib %will produce bibliography entries as shown in the
                % LaTeX book

% [1] Anderson, Terry L.,
%     continuing bib entry

% \cite{xxx} will print with square brackets around the citation, i.e., [1].

% Any \verb+\bibliographystyle{}+ may be used with \verb+\normallatexbib+, but
% you should check with your editor to find the style preferred for
% your book.

% Change Brackets around Citation:
% ================================

%% Default with \kluwerbib is no brackets around citation. 
%% Default with \normallatexbib is square brackets around citation. 

% For parens around citation uncomment these:

%\let\lcitebracket(
%\let\rcitebracket)

% For square brackets around citation uncomment these:

%\let\lcitebracket[
%\let\rcitebracket]

% Draft Line:
% ===========
%  Optional, uncomment to make current time and `draft' appear at
%  bottom of page.

% \draft

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% <<== End Formatting Commands You Can Set or Change %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\articletitle
{Radio halos in star forming galaxies}

\chaptitlerunninghead{Radio halos in star forming galaxies} 
% Shorter running head title.

\author{Ute Lisenfeld,\altaffilmark{1} Michael Dahlem,\altaffilmark{2}
\& Matthias Ehle\altaffilmark{3}}


\affil{\altaffilmark{1}Instituto de Astrof\'\i sica de Andaluc\'\i a (CSIC),
Granada, Spain \ 
\altaffilmark{2} ATNF, Narrabi, Australia \
\altaffilmark{3} XMM-Newton Science Operations Centre, ESA, Madrid, Spain
}


\begin{abstract}
We study the relation between radio halos, the energy input
by supernovae in the disk and the
galaxy mass. We find that both the energy input
by supernovae as well as 
the galaxy mass are important parameters for understanding the
 formation of  radio halos.
Galaxies with a high energy input
by supernovae per star forming area and a low galaxy mass  
generally possess radio halos whereas galaxies with the
opposite characteristics do not.
%This relation suggests that there is a threshold below which radio 
%halos cannot form depends not only on the energy input per area but also
%on the galaxy mass.
Furthermore, there is a tentative correlation
between the observed scale height
and the expected height in a simple gravitational approximation.
%We do not expect to have a clear threshold in energy input per SF
%area, because at least galaxy mass must play a role as well. 


\end{abstract}

\section{Introduction}
 
There is accumulating observational evidence for the existence
of gaseous halos around disk galaxies (see \cite{det92} 1992 and 
\cite{dah97} 1997
for reviews), consisting of warm and hot ionized gas, dust,  
magnetic fields and cosmic rays (CRs), the latter two generating
the radio continuum
(synchrotron) emission. 
Theoretical models have been developed
to explain these halos, such as the galactic
fountain model (\cite{sha76} 1976), galactic chimneys 
(\cite{nor89} 1989), superwinds (\cite{hec90} 1990) and
superbubble outbreaks (\cite{mac99} 1999). All models are based on the
assumption that the energy source driving the 
formation of halos
are supernova (SN) explosions.

Observationally, it is still a matter of controversy how many and exactly
which galaxies have such halos. In order to answer this question,
we have been  observing radio halos
(\cite{dah95} 1995, \cite{dah01} 2001) in an ongoing project.
In the present paper we summarize some 
results and use existing data  to try to understand the formation of 
radio halos.


\section{Observations of radio halos}

\cite{dah01} (2001) observed a sample  of galaxies with
active star formation (SF) 
(selected with respect to the  IRAS flux ratio
between 60 and 100 $\mu$m,  $f_{60}/f_{100} \gtrsim 0.4$) 
with the VLA and the Australia Telescope Compact Array.
They fitted the radio emission perpendicular
to the disk with two exponential functions
convolved with the beam, modeling in this way a thin disk and a halo.
Radio halos were found in 6 out of 11 galaxies (55\%) with exponential scale
heights between 1.4 and 3.1 kpc.  
The high detection rate in these actively star forming
galaxies showed that SF is indeed a key factor for the
formation of radio halos. 
Possible reasons for the non-detection of halos in 5 galaxies could be:
(i) There is no radio halo. (ii) The resolution of the data is too low.
We are currently obtaining higher resolution data for some
objects. (iii) The width of the thin disk is much smaller than
the beam and therefore not resolved. 
This is supported by the fact that
for galaxies with no radio halo the apparent scale height of the
thin disk was much larger (between 1 and 2 kpc) than in galaxies
with a radio halo (less than 1 kpc).

In order to base our present  study
on a larger number of galaxies, we use, in addition to the 11 galaxies
from \cite{dah01} (2001), data for
6 galaxies described in \cite{dah95} (1995), 
%These include 3 galaxies
%with prominent radio halos (NGC 891 and NGC 4631, possesing 
%the prototype radio halos and NGC 4666, a galaxy with a superwind REF)
%as well as 3 very quiscient galaxies with no detectable radio halo.
as well as for
3 galaxies from \cite{irw99} (1999) who 
observed 16 edge-on galaxies searching for radio halos.
Their analysis of the radio emission is different
from ours and involves a ranking of the visibility of 
extended emission based on different criteria.
%In order to allow comparison to our data, 
We include only those galaxies for which
their VLA D-array data does not  show evidence
of emission beyond their modelled thin disk (their Fig. 1),
a  robust criterion that is similar
to the one used in the rest of the sample. 
 



\section{Understanding radio halos}

From theoretical considerations we expect that the formation of
radio halos depends (at least) on the following 
factors.

1) According to all models (see above) 
a fundamental parameter is the energy input  by SN explosions 
into the interstellar  medium.
\cite{dah95} (1995) showed that radio halos do not form above the
entire disk, but only out to radial distances where SF
takes place. Therefore, 
the relevant parameter is expected to be
the energy input by SNe per SF disk area, \energyinput.

2) The energy input from SNe allows material to be lifted above the
disk against the gravitational potential determined by the
mass of the galaxy. Therefore, the mass of the galaxy is expected to
play an important 
role.

3)  CR electrons have
a limited life-time due to inverse Compton and synchrotron
energy losses. The observed steepening of the synchrotron spectrum
with increasing distance from the disk (e.g. \cite{hum91} 1991)
is due to these energy losses
and shows that they are indeed important.
These energy losses limit the distance to which CR electrons
can travel and therefore the size of radio halos.
In the present work, we do
not take into account CR energy losses, because it would 
require a detailed knowledge of the distribution
of the energy density of the radiation field, $U_{\rm rad}$, (determining
the inverse Compton losses) and the magnetic field structure (causing the
synchrotron losses and emission and determining the CR propagation).
Qualitatively, we expect CR energy losses
to decrease the range of observed scale heights because galaxies with a 
high surface brightness (implying a high SF rate and thus a high
\energyinput) also possess a high $U_{\rm rad}$
causing important inverse Compton losses.


\begin{figure}[ht]
\centerline{\includegraphics[width=6.cm]{lisenfeld_fig1a.ps}
\includegraphics[width=6.cm]{lisenfeld_fig1b.ps}}
\caption{The energy input by SNe per SF area as a function of
the IRAS flux ratio between  60 and 100
$\mu$m, $f_{60}/f_{100}$ {\bf (left)},
and the dynamical mass of a galaxy, $M_{\rm dyn}$(HI), calculated from 
the HI linewidth {\bf (right)}. 
As a measure for the energy input by SNe we use the 
radio continuum emission as described
in \cite{dah95} (1995). 
%The SF area is calculated from the radius of the
%radio emission in the disk, assuming circular symmetry. 
%The filled symbols denote galaxies with a detected
%radio halo and the open symbols those with none.
}
\end{figure}


Fig. 1 (left) shows the dust temperature (measured as $f_{60}/f_{100}$),
which is an empirical measure for the SF activity,
as a function of the energy input by SNe per SF area.
There is a rough correlation between both quantities and a 
trend for radio halos to be found in galaxies with a high dust temperature,
respectively a high \energyinput.
A similar conclusion was drawn from the smaller sample used in
\cite{dah01} (2001) and by \cite{ros03} (2003) for a sample
of 74 edge-on galaxies observed in H$\alpha$.


Fig. 1 (right) shows \energyinput \
versus the dynamical mass of a galaxy.
There is a clear division between galaxies with and without
a halo: Galaxies with a low mass
and a high energy input (lower right side) have radio halos whereas 
galaxies with a high mass and a low energy input 
(upper left side) do not. 
This shows that the
galaxy mass plays an important role in the formation of radio halos.
%\cite{dah95} (1995) and \cite{ros03} (2003)
%concluded  that a threshold in dE/dt per surface area 
%exists below which no radio halos can form. However, Fig. 1 (left) shows
%that such a threshold should also take into account 
%galaxy mass.

 
\begin{figure}[ht]
\centerline{\includegraphics[width=6.cm]{lisenfeld_fig2.ps}}
{\caption{The observed exponential scale height of the radio halos
versus the expected height
in the approximation described in the text.
For the galaxies without a detected radio halo from \cite{irw99} (1999)
and \cite{dah95} (1995) we adopted an arbitrary but
realistic upper limit of 1 kpc. For the galaxies from \cite{dah01}
(2001) without a detected radio halo we adopted 
the measured scale height of the thin disk as an upper limit.}}
\end{figure}

%In order to investigate the role of energy input and galaxy mass
%for the properties of radio halos further,
Fig. 2  shows the observed exponential scale heights  of the radio emission
versus the expected height in the simple approximation  
that the energy  input per mass
is proportional to \energyinput, that
energy losses of CR electrons are neglected and that the gravitational
potential is described by that of an infinite disk. With these
assumptions,
the expected height of the radio halo is proportional to 
\energyinput \ per mass surface density.
%A rough correlation is visible between both quantities.
% 
A trend is visible in the sense that
large radio halos are present in galaxies
with high values of (\energyinput) per mass surface density
whereas galaxies with no 
radio halos have a low values.
%(\energyinput)/($M_{\rm dyn}$(HI)r$_{25}$). 
%
This indicates that -- although more detailed modelling taking into
account CR propagation is necessary for a  full understanding 
-- the energy input by SNe  and the
galaxy mass are important parameters to understand 
%not only the existence but also the height of radio halos.
the properties of radio halos.
 
\begin{acknowledgments}
UL is partially supported
by the  Spanish MCyT  Grant  AYA 2002-03338 and
Junta de Andalucia (Spain).
\end{acknowledgments}


\begin{chapthebibliography}{}


\bibitem[Dahlem]{dah97} 
Dahlem, M., 1997, PASP, 109, 1298
\bibitem[Dahlem et al.]{dah95} Dahlem, M., Lisenfeld, U., 
Golla, G., 1995, ApJ, 444, 119
\bibitem[Dahlem et al.]{dah01} Dahlem, M., Lazendic,  J.S., 
Haynes, R.F., Ehle, M., 
Lisenfeld, U., 2001, A\&A, 374, 42
\bibitem[Dettmar]{det92} Dettmar, R.-J., 1992, Fund. Cosm. Phys., 15, 143 
\bibitem[Heckman et al.]{hec90} Heckman, T. M., Armus, L., Miley, G. K.,
1990, ApJS, 74 833
\bibitem[Hummel et al.]{hum91} Hummel, E., Dahlem, M., van der Hulst, J.M.,
Sukumar, S., 1991, A\&A, 246, 10
\bibitem[Irwin et al.]{irw99} Irwin, J.A., English, J., Sorathia, B., 
1999, AJ, 117, 2102
\bibitem[MacLow \& Ferrara]{mac99} MacLow, M., Ferrara, A., 1999, ApJ, 513, 142
\bibitem[Norman \& Ikeuchi]{nor89} Norman, C.A., Ikeuchi, S., 1989, ApJ, 
345, 372
\bibitem[Rossa \& Dettmar]{ros03} Rossa, J., Dettmar, R.-J., 2003, A\& A,
406, 493
\bibitem[Shapiro \& Fields]{sha76} Shapiro, P.A., Fields, G.B., 1976,
ApJ, 205, 762
\end{chapthebibliography}

\end{document}



astro-ph0310458.extracted_bib
\bibitem[Dahlem]{dah97} 
Dahlem, M., 1997, PASP, 109, 1298

\bibitem[Dahlem et al.]{dah95} Dahlem, M., Lisenfeld, U., 
Golla, G., 1995, ApJ, 444, 119

\bibitem[Dahlem et al.]{dah01} Dahlem, M., Lazendic,  J.S., 
Haynes, R.F., Ehle, M., 
Lisenfeld, U., 2001, A\&A, 374, 42

\bibitem[Dettmar]{det92} Dettmar, R.-J., 1992, Fund. Cosm. Phys., 15, 143 

\bibitem[Heckman et al.]{hec90} Heckman, T. M., Armus, L., Miley, G. K.,
1990, ApJS, 74 833

\bibitem[Hummel et al.]{hum91} Hummel, E., Dahlem, M., van der Hulst, J.M.,
Sukumar, S., 1991, A\&A, 246, 10

\bibitem[Irwin et al.]{irw99} Irwin, J.A., English, J., Sorathia, B., 
1999, AJ, 117, 2102

\bibitem[MacLow \& Ferrara]{mac99} MacLow, M., Ferrara, A., 1999, ApJ, 513, 142

\bibitem[Norman \& Ikeuchi]{nor89} Norman, C.A., Ikeuchi, S., 1989, ApJ, 
345, 372

\bibitem[Rossa \& Dettmar]{ros03} Rossa, J., Dettmar, R.-J., 2003, A\& A,
406, 493

\bibitem[Shapiro \& Fields]{sha76} Shapiro, P.A., Fields, G.B., 1976,
ApJ, 205, 762
