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%astro-ph/0505244
\documentclass[10pt,preprint2]{aastex}
\usepackage{epsf}

\newcommand{\mjb}{mJy~beam$^{-1}$}
\newcommand{\jb}{Jy~beam$^{-1}$}
\newcommand{\kms}{km~s$^{-1}$}
\newcommand{\et}{et~al.}
\newcommand{\muG}{$\mu$G}
\newcommand{\evcm}{eV~cm$^{-3}$}
\newcommand{\ergs}{ergs~s$^{-1}$}


\shortauthors{LaRosa \et\/}  \shorttitle{Weak Magnetic Field GC Region}
\begin{document}

\title{Evidence for a Weak Galactic Center Magnetic Field from 
  Diffuse Low Frequency Nonthermal Radio Emission}

\author{T.~N.~LaRosa\altaffilmark{1}, C.~L. Brogan\altaffilmark{2},
S.~N.~Shore\altaffilmark{3}, T.~J..~Lazio\altaffilmark{4},
N.~E.~Kassim\altaffilmark{4}, \& M.~E.~Nord\altaffilmark{4,5}}

Sciences, Kennesaw State University, 1000 Chastain Rd., Kennesaw, GA
30144; ted@avatar.kennesaw.edu}


\altaffiltext{2}{Institute for Astronomy, 640 North A`ohoku Place, Hilo, HI 96720; cbrogan@ifa.hawaii.edu.}


\altaffiltext{3}{Dipartimento di Fisica ``Enrico Fermi'', Universit\`a di Pisa
  and INFN, Sezione di Pisa, largo B. Pontecorvo 3, I-56127 Pisa 
Italy; shore@df.unipi.it}


\altaffiltext{4}{Remote Sensing Division, Naval Research Laboratory,
Washington DC 20375-5351; Joseph.Lazio@nrl.navy.mil; 
Namir.Kassim@nrl.navy.mil; Michael.Nord@nrl.navy.mil}

\altaffiltext{5}{Department of Physics and Astronomy,
University of New Mexico, Albuquerque, NM 8713}

\begin{abstract}

New low frequency 74 and 330 MHz observations of the Galactic center
(GC) region reveal the presence of a large-scale ($6\arcdeg\times
2\arcdeg$) diffuse source of nonthermal synchrotron emission.  A
minimum energy analysis of this emission yields a total energy of
$\sim (\phi^{4/7}f^{3/7})\times 10^{52}$ ergs and a magnetic field
strength of $\sim 6(\phi/f)^{2/7}$ \muG\/, (where $\phi$ is the proton to
electron energy ratio and $f$ is the filling factor of the synchrotron
emitting gas).  The equipartition particle energy density is
$1.2(\phi/f)^{2/7}$ \evcm\/, a value consistent with cosmic ray data.
However, the derived magnetic field is several orders of magnitude
below the 1 mG field commonly invoked for the GC.  The shorter
electron radiation lifetimes in such a strong field requires that
energy be resupplied to the source at an implausibly high rate.
Furthermore, a strong magnetic field implies an abnormally low GC
cosmic ray energy density.  We conclude that the mean magnetic field 
in the GC region must be weak, of order 10 \muG\/ (at least on 
size scales $\ga 125\arcsec$).

\end{abstract}

\keywords {ISM:Galactic Center --- radio continuum}


\section{INTRODUCTION}

An outstanding question in Galactic Center (GC) studies is the origin,
strength, and role of magnetic fields in the region.  Large scale
filamentary non-thermal structures (two dozen confirmed), with lengths
of up to tens of parsecs, have been observed in the vicinity of the GC
for over the last two decades (e.g. Morris \& Serabyn 1996, and
references therein; Lang et al. 1999; LaRosa, Lazio, \& Kassim 2001;
Nord \et\/ 2004; LaRosa \et\/ 2004; Yusef-Zadeh, Hewitt, \& Cotton
2004).  The spatial distribution of the non-thermal filaments (NTFs)
is confined to within $\sim 1.5\arcdeg$ of the GC and this phenomenon
seems to be unique to the GC region. The NTFs are widely believed to
be magnetic field lines illuminated by the injection of relativistic
particles. Within the context of this picture, it has been suggested
that a pervasive, strong ($\sim 1$ mG) magnetic field must permeate
the entire GC region in order to confine the NTFs (see for example Morris \&
Serabyn 1996, and references therein).  This paper reports the
discovery of a previously unrecognized diffuse, nonthermal structure
in the GC, and shows that its properties are not consistent with a
strong, space filling magnetic field.

\section{OBSERVATIONS AND RESULTS}

We have used the Very Large Array\footnote{The Very Large Array and
the Green Bank Telescope are facilities of the National Radio
Astronomy Observatory operated under a cooperative agreement with the
National Science Foundation} (VLA) in all 4 configurations to image
the Galactic center region at 74 MHz.  The resulting image presented
in Figure 1a has a resolution of $125\arcsec$, an rms noise of $\sim
0.2$ \jb\/, and a dynamic range of $\sim 200$.  The details of the 74
MHz data reduction are discussed more throughly in Brogan \et\/ (2003;
2005).  This is the highest resolution and sensitivity image of the
Galactic center region at frequencies below 300 MHz yet created. Even
so, the data used to make Figure 1a were tapered to provide surface
brightness sensitivity optimized to the large scale emission which is
the focus of this paper. Future improvements in ionospheric
calibration offer the opportunity to achieve the full resolving power
of the VLA at 74 MHz, and to produce a map more suited to studying
smaller, discrete sources.

\begin{figure}[bth!]
\centering 
\epsfxsize=7.8cm \epsfbox{larosa_fig1.eps}
\caption{(a) VLA image of the Galactic center at 74 MHz with $125\arcsec$ 
resolution. (b) GBT image of the Galactic center at 330 MHz with $40\arcmin$ 
resolution (beam is shown in lower right). (c) Background subtracted GBT 
image of the Galactic center region (beam is shown in lower right). Some of 
the brighter emission and free-free absorption sources are indicated on 
(a). }
\end{figure}

A wide range of discrete emission and thermal absorption features are
evident in the 74 MHz image (Brogan \et\/ 2003; 2005), as well as a
large scale region of diffuse emission surrounding Sgr~A and extending
$\ell\pm 3\arcdeg$ in longitude and $b\pm 1\arcdeg$ in latitude.  At a 
distance of 8 Kpc this angular scale corresponds to a region 840 by 280 pc.  
Interestingly, none of the NTFs are detected in the 74 MHz image, and 
away from known supernova remnants, the emission is quite smooth. The
extent of the large scale low frequency structure is well matched in
size to that of the Central Molecular Zone (CMZ); the region
surrounding the Galactic center where the molecular gas density,
temperature, and velocity dispersion is high (see Brogan et al. 2003;
Morris \& Serabyn 1996).  We hereafter refer to the low frequency
structure as the Galactic center DNS (Diffuse Nonthermal Source).  The
even larger scale, smooth Galactic background is resolved out of this
image due to the spatial filtering afforded by the interferometer;
only structures smaller than $\sim 5.5\arcdeg$ (the angular scale
corresponding to the shortest baseline) down to the resolution limit
of $125\arcsec$ are sampled.  Although the size of the DNS is
comparable to the largest angular scale to which our measurements are
sensitive, two of its characteristics strengthen our confidence that
it is a distinct source: (1) the strong thermal absorption in the
vicinity of the GC itself (Fig. 1a) effectively segregates the DNS
into two pieces, each of which is considerably smaller than
$5.5\arcdeg$, and (2) the DNS is also detected in higher frequency
(330 MHz) single dish data (see below).

To complement our 74 MHz data, we have imaged a $15\arcdeg\times
15\arcdeg$ region centered on the GC with the Green Bank Telescope
(GBT) at 330 MHz.  The GBT data were obtained with a 20 MHz bandwidth,
1024 spectral channels, and a scanning rate that more than Nyquist
sampled the beam ($38.9\arcmin$). The GC region is bright enough at
330 MHz that attenuators are required to avoid saturating the
detectors.  The effect of this high attenuation setting was carefully
calibrated out of the flux calibration scans on 3C~286 and the
observations of the off-positions. In order to correct for the
non-zero temperature of the off-positions located at $(l,b)=(\pm
20\arcdeg,0\arcdeg)$, estimates for the sky brightness at these two
locations were estimated from the 408 MHz survey image (Haslam \et\/
1982) assuming a spectral index of $-2.7$ (Platania et al.\ 2003) and
added back to the 330 MHz image. Finally the image was converted to a
flux density scale using the observed antenna temperature of 3C286
compared to its expected brightness temperature (Ott \et\/ 1994) and
the gain of the GBT (approximately 2 K/Jy at low frequencies).

A sub-image of the resulting GBT 330 MHz image with a resolution of
$38.9\arcmin$ is shown in Figure 1b. This image includes contributions
from all of the discrete sources apparent in the high resolution VLA
330 MHz image by LaRosa \et\ (2000), the DNS, and the smooth Galactic
background synchrotron emission, with the latter contributing much of
the total flux. Thus, the Galactic background must be removed and the
discrete source contribution accounted for before the 330 MHz
properties of the DNS can be assessed.  For background subtraction we
chose a constant longitude slice free of discrete sources (and well
outside of the DNS) near $\ell=354.5\arcdeg$ and subtracted it from
every other constant longitude plane (median weight filtering was not
used since it can introduce structures on sizescales equal to the
filter).  The image resulting from this procedure is shown in Figure
1c. Despite the resolution difference, there is excellent agreement
between the diffuse structure visible in the background subtracted GBT
330 MHz image (Fig. 1c) and the 74 MHz VLA image (Fig. 1a).
  
Having established the reality of the DNS, we now estimate its
integrated 74 and 330 MHz flux and spectral index.  Due to the copious
thermal absorption at 74 MHz apparent in Fig. 1a, a simple integration
of the total flux within the DNS region is impossible. Instead, we
have used the average 74 MHz flux density at locations within the DNS
that appear free of both discrete emission sources and thermal
absorption, together with its apparent size (an ellipse of dimension
$6\arcdeg\times 2\arcdeg$) to calculate its total flux.  Using this
method we find an integrated 74 MHz flux density for the DNS of $16.2\pm 1$
kJy. This estimate is likely to be a lower limit, however, as we show
below an underestimate of the total 74 MHz flux density of the DNS does not
significantly affect our arguments regarding the weakness of the large
scale GC magnetic field.

The integrated 330 MHz flux density within the boundaries of the DNS
(Fig.  1c) is $\sim 8,000$ Jy, while the total flux density contained in
discrete sources from the VLA 330 MHz image (LaRosa \et\/ 2000) is
$\sim 1000$ Jy\footnote{The VLA 330 MHz image is not sensitive to
structures larger than $\sim 1\arcdeg$, and thus contains little or no
contribution from the Galactic background or the DNS.}.  Thus, we
estimate that the integrated 330 MHz flux density of the DNS is $\sim
7000$ Jy. Except for the immediate vicinity of the Galactic center
itself (where the {\em thermal} ionized gas density is very high), thermal
absorption effects should not be a significant effect at 330 MHz (see 
for example Nord \et\ 2004)
Combined with the lower limit to the 74 MHz DNS flux, we find that the
spectral index of the DNS must be steeper than $-0.7$ (assuming
$S_{\nu}\propto\nu^{\alpha}$) or $-2.7$ if brightness temperatures are
considered.  This value is comparable to the brightness temperature
spectral indices measured for the Galactic plane synchrotron
background emission ($-2.55$ to $-2.7$; see Platania \et\ 2003).


\subsection{Minimum Energy Analysis}

Using standard synchrotron theory (Moffat 1975), the minimum energy
and magnetic field are given by $U_{min}=0.5(\phi AL)^{4/7}V^{3/7}$,
and $B(U_{min})=2.3(\phi AL/V)^{2/7}$.  Here $A$ is a function of the
spectral index, $L$ is the luminosity, $V$ is the source volume, and
$\phi$ is the ratio of energy in protons compared to electrons.  Using
a 74/330 MHz spectral index of $-0.7$ and integrating from 10 MHz to
100 GHz we find a total luminosity for the DNS of $3\times 10^{36}$
\ergs\/ (we have used $S_{330}=7000$ Jy and
$S_{\nu}=S_{330}\nu^{-0.7}$ for this calculation).  If for example,
the spectral index were actually as steep as $-1.5$ the luminosity
would still be $> 10^{36}$ \ergs\/. Thus, the possibility that we have
underestimated the 74 MHz flux is unlikely to significantly impact
this analysis. Assuming that the depth of the DNS is 480 pc (the
geometric mean diameter assuming a distance of 8 kpc), the minimum
energy is $(\phi^{4/7}f^{3/7})\times 10^{52}$ ergs and the
corresponding magnetic field strength is $6(\phi/f)^{2/7}$ \muG\/,
where $f$ is the filling factor of the nonthermal emission within the
volume $V$.  With these values, the equipartition particle energy
density is $1.2(\phi/f)^{2/7}$ \evcm\/.  A filling factor as low as
1\% will only increase the derived field strength and particle density
by a factor of $\sim 4$.  A large proton to electron energy ratio of
100 could increase these estimates by another factor of $\sim 4$.
Thus, even with these extreme parameters, the magnetic field on size
scales larger than the 74 MHz beam ($125\arcsec$) must be $\la 100$
\muG\/.

The above calculation applies to the entire $6\arcdeg\times 2\arcdeg$ region 
spanned by the DNS.  However, the nonthermal filaments are found only 
in the inner $1.5\arcdeg\times 0.5\arcdeg$.  The integrated 330 MHz flux 
in this smaller region is $\sim 1000$ Jy and yields a minimum energy of 
$(\phi^{4/7}f^{3/7})\times 10^{51}$ ergs and magnetic field of 
$11(\phi/f)^{2/7}$ \muG\/.  Thus the gradient in the DNS brightness 
does not translate into a significantly larger magnetic field in the 
innermost region compared to the region as a whole.    

\section{DISCUSSION}

\subsection{Energy Requirements}

Radiative lifetimes provide an important added constraint on the
global magnetic field strength within the DNS region.  An electron
emitting at 74 MHz in a 1 mG field has an energy of $\sim 0.07$ GeV
and a synchrotron lifetime of $\sim 10^5$ years.  Therefore, the
entire DNS (with an energy of $\sim 10^{52}$ ergs) would have to be
replenished on this timescale.  The energy contained in a typical supernova remnant in particles and magnetic field is $5 \times 10^{49}$ ergs (Duric et al 1995), so that
$\sim 200$ SNe within the last $10^5$ years are required if the global
field is as high as 1 mG. The SNe rate scales with the star formation
rate, which is a factor of $\approx 250$ higher in the inner 50 pc
than in the disk (Figer et al 2004). However, even with this enhanced
star formation rate, the GC SNe rate is only about {\em one} per
$10^5$ years. Thus, only if the DNS is due to a single extreme
event (with an energy of $\sim 10^{52}$ ergs) or was formed
during a period of {\em recent} starburst could it have been generated
in the presence of a 1 mG field.  Indeed, the presence of a large
bipolar wind structure centered on the GC from dust and radio emission
studies suggests that our GC has undergone periods of more prolific
star formation in the past (see e.g.  Sofue \& Handa 1984;
Bland-Hawthorne \& Cohen 2003).  However, Bland-Hawthorne \& Cohen
(2003) estimate that the GC ``Omega Lobe'' was formed during a
starburst event $10^7$ years ago, inconsistent with the 1 mG
synchrotron lifetime.  Additionally, the agreement between the derived
DNS spectral index ($-0.7$) and that of the diffuse Galactic plane
emission suggests that the acceleration mechanism is similar. This
steep spectral index also suggests that the emission arises from a
relatively old population of electrons.

In contrast, the synchrotron lifetime in a 10 \muG\/ field is $10^8$
years. With this longer lifetime, the $\sim 200$ SNe required to power
the DNS are entirely consistent with the enhanced GC SNe rate ($10^5$
year/SNe).  This scenario for the generation of the DNS is also
consistent with the diffuse soft X-ray emission from the GC region.
Muno \et\/ (2004) report the presence of diffuse hard (kT$\sim 8$ keV)
and soft (kT$\sim 0.8$ keV) X-ray emission from the inner 20 pc. The
soft component requires input of the energy equivalent of one SNe
every $10^5$ years, in good agreement with the rate required to
explain the DNS.  The hard component is more difficult to
explain with this injection rate (requiring $\sim 1$ SNe per 3000
years), but Muno et al. suggest that a significant fraction of the hard
emission may arise from unresolved cataclysmic variables and other
compact objects, so that the high implied rate may be overestimated.


\subsection{Constraints on GC Cosmic Ray Energy Density}

By construction, the minimum energy procedure constrains the field and
particle energies together but they can also be analyzed separately.
The peak 330 MHz brightness of the DNS in the inner $1.5\arcdeg\times 0.5\arcdeg$ is $\sim 1000$ \jb\/.  Assuming a 1 mG magnetic
field, this brightness requires a cosmic ray (CR) electron energy
density of 0.04 \evcm\/.  In contrast, the energy density of electrons
in the local interstellar medium is a factor of 5 larger (0.2
\evcm\/ Webber 1998).  Thus, unless the electron energy density in the
GC region is significantly lower than that in other parts of the
Galaxy, a 1 mG field is inconsistent with the 330 MHz data.

The cosmic ray energy density in a particular region is determined by
the local balance between CR production and escape rates. In the disk,
particles escape with a typical turbulent diffusion velocity of order
10-15 \kms\/ (e.g., Wentzel 1974).  In contrast, it is likely that
particles in the GC region escape much more rapidly due to strong
winds of order a few thousand \kms\/ (see e.g.  Suchkov, Allen, \&
Heckman 1993; Koyama \et\/ 1996).  However, since the production rate
scales with the SNe rate, which exceeds that of the disk by a factor
of $\sim 250$ in the GC region, the higher escape rate in the GC could
be balanced by the higher production rate.  Thus the cosmic ray energy
density in the Galactic center region may well be similar to that
measured in the disk.  Unfortunately, no direct {\em measurements} of
the GC cosmic ray energy density currently exist. There are, however,
a number of indirect indicators that can be used to constrain its
properties.

Diffuse $\gamma$-ray emission in our Galaxy is produced by the
interaction of high energy cosmic rays with interstellar material, as
well as a relatively uncertain contribution from unresolved compact
sources (e.g. pulsars, X-ray binaries, etc.). Thus, $\gamma$-ray
emission can be expected to peak where the cosmic ray density is high,
the gas density is high, or there is a high concentration of compact
objects. Recent re-analysis of all available EGRET data toward the GC
region by Mayer-Hasslewander \et\/ (1998) suggest a number of
pertinent conclusions: (1) the level of $\gamma$-ray emission within
the DNS region is entirely consistent with that predicted by models of
the Galactic disk (Hunter \et\/ 1997) with the exception of a $\la
0.6\arcdeg$ radius region of enhanced emission centered on the GC
itself. (2) Taking into account newer estimates of the GC gas mass,
this finding disputes earlier claims that there is a {\em deficit} of
cosmic rays toward the GC region (e.g. Blitz 1985). (3) No excess is
observed toward the SgrB, SgrC, or SgrD molecular cloud complexes as
might be expected if gas density played a large role in the GC
$\gamma$-ray emissivity.  (4) The spectrum of the {\em excess} GC
$\gamma$-ray emission is significantly harder than that of the
Galactic disk, and most likely arises from the GC radio arc and/or
compact objects like pulsars.

Galactic center molecular clouds have significantly higher
temperatures, densities, and turbulent velocities than their disk
counterparts (i.e. the CMZ; Morris \& Serabyn 1996;
Rodr{\'{\i}}guez-Fern{\' a}ndez \et\/ 2004). In the past, heating by a
larger than average CR energy flux has been invoked to explain the
high temperatures of the GC clouds (Suchkov \et\/ 1993). More
recently, a number of studies have shown that the required heating can
be produced by turbulent dissipation, shear due to the intense GC
gravitational potential, and large scale shocks (see for example
Rodr{\'{\i}}guez-Fern{\' a}ndez \et\/ 2004; G\"usten, \& Philipp
2004).  Moreover, recent observations of the GC region in infrared
transitions of H$_3^+$ by Goto \et\/ (2002) suggest that the GC CR
ionization rate ($\zeta$) is consistent with that of the disk
$\zeta\sim 3\times 10^{-17}$ s$^{-1}$cm$^{-3}$. It has also been
suggested that an enhanced GC CR density might reveal itself through
enhanced abundances of Lithium and Boron. These atoms can be formed
through spallation reactions between cosmic rays and the ISM.
Lubowich, Turner, \& Hobbs (1998) have searched the GC region for
hyperfine-structure lines of neutral Li and B with no success.  From
their detection upper limits, these authors suggest that the GC cosmic
ray energy density cannot exceed the disk value by more than a factor
of 13.

Together these results ranging from $\gamma$-ray emission to the
non-detection of Lithium and Boron provide strong circumstantial
evidence that the GC cosmic ray energy density is similar to that of
the Galactic disk.


\section{CONCLUSIONS}

Utilizing new 74 and 330 MHz observations, we have discovered a new
Galactic Center feature, the diffuse nonthermal source (DNS).  The DNS
is extended along the Galactic plane with a size of $\sim
6\arcdeg\times 2\arcdeg$ and a spectral index steeper than $-0.7$. A
minimum energy analysis of the DNS requires that any \emph{pervasive}
magnetic field must be weak, of order 10 \muG\/ (and almost certainly
$\la 100$ \muG\/).  This field strength is two orders of magnitude
less than the commonly cited value of 1 mG inferred from the
assumption that the NTFs are tracing a globally organized magnetic
field.  We find that the minimum energy required to fuel the DNS can
be supplied by the enhanced star formation, and hence supernova,
rate within the Galactic center region.

The low global GC region magnetic field derived from this work is
supported by a number of other lines of evidence.  First, particle
emission lifetimes in a 1 mG field, $\sim 10^5$ years, are shorter
than any plausible replenishment timescale for a long-lived
source. Second, if the global GC field strength is 1 mG then the
observed emission would imply a very low GC CR energy
density. However, EGRET $\gamma$-ray observations (Mayer-Hasslewander
\et\/ 1998; Hunter \et\/ 1997) indicate a GC CR energy density
consistent with that measured in the Galactic disk. Light element (Li
and B) abundance upper limits, $H_3^+$ detections, and consideration
of molecular cloud heating are also all consistent with a normal
Galactic plane cosmic ray energy density in the GC.

This weak field picture is substantially different from the canonical
one that has emerged over the past two decades for the ``Galactic
center magnetosphere'' (e.g. Morris \& Serabyn 1996; G\"usten, \&
Philipp 2004) wherein the entire Galactic center
region (approximately bounded by the CMZ) has a globally organized
strong magnetic field of order 1 mG.  Together, the radio and
$\gamma$-ray data yield a GC cosmic ray energy density and magnetic field
strength that are comparable to their
disk values.  Any departures in the energetics from the disk values result from the enhanced level of star formaing and associated activity at the Galactic center, an even more extreme version of which may be the nuclear starburst in M82 (Odegard and Seaquist 1991).  It is important to note that our analysis
constrains the average magnetic field strength on size scales larger
than our 74 MHz resolution of $125\arcsec$ and {\em does not} preclude
locally strong magnetic fields on smaller sizescales.
         
\acknowledgments
Basic research in radio astronomy at the NRL is supported by the
Office of Naval Research.  SNS thanks P. Caselli and D. Galli for
discussions.  TNL thanks the INFN/Pisa for travel support.


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