\section{Introduction}

The High Altitude Water Cherenkov (HAWC) observatory is a survey instrument capable of
expanding the catalog of TeV $\gamma$-ray sources, and of
monitoring most of the objects in this catalog for flaring activity.
The HAWC observatory will not only detect new sources,
but will also promptly initiate campaigns of
multi-messenger observations.

The main objectives of the HAWC collaboration are to contribute to the study of
the origin of cosmic rays via its observations of $\gamma$-rays up to 100~TeV from discrete sources and the Galactic plane,
to understand particle acceleration in astrophysical jets using HAWC's wide field of view and high duty factor observations of transient sources (such as $\gamma$-ray bursts and supermassive black holes), and
to explore new TeV physics via HAWC's unbiased survey of
the sky.

The deployment of water Cherenkov detectors started in Summer 2011,
and $1/3$ of the final array was already completed by the time of this conference.
We present in this paper the design of the observatory, the current status of the deployment,
and the first results using data taken with a small fraction of the final layout.

\section{Design and operation of HAWC}
The HAWC design builds upon the experience with the Milagro detector.
Milagro was the first generation of $\gamma$-ray detectors using the water Cherenkov technology.
Instead of the double layer of PMTs used in Milagro,
the HAWC design utilizes a single deep layer of PMTs with a wider separation.
This configuration gives HAWC a much larger active area than Milagro for the same photo-cathode area.
Another important different with respect to Milagro is that instead of a big pond
the HAWC observatory consists of a large array of water Cherenkov detectors (WCDs).

The structural support of the detectors is provided by corrugated steel tanks of $7.3$~m diameter.
There is a light-tight plastic bladder inside each tank.
Bladders are filled with ultra-pure water to a level of $4.5$~m.
There are four upward-facing, baffled photomultiplier tubes (PMTs) in each WCD anchored to the bottom of the tank.
Three of the four PMTs
are $8"$ hemispherical \texttt{Hamamatsu R5912} (previously used in the Milagro experiment)
spaced $6$~ft from the center of the tank.
The fourth PMT, positioned in the center, is a high quantum-efficiency $10"$ PMT designed to increase the efficiency of the observatory to low-energy showers.
We show a simulation of a single air-shower muon penetrating one of the WCDs in Fig.~\ref{fig:wcd}.
 \begin{figure}[!htb]
  \centering
  \includegraphics[width=0.425\textwidth]{Single_tank_pictures.png}
  \caption{Simulation of a 1~GeV muon (red line) passing through a HAWC detector and emitting Cherenkov light (green lines). The layout of the four PMTs is shown, and the human silhouette provides the scale of the water Cherenkov detectors.}
  \label{fig:wcd}
 \end{figure}

The HAWC observatory will consist of an array of 300 WCDs to observe particles from air showers.
Hence, the observatory will comprise 1200 PMTs in total.
The optical isolation of the PMTs between detectors will reduce the noise rate.
This is an important consideration at high altitude due to the larger flux of low energy cosmic rays.

Before the deployment of the production detectors, we tested the design and concept at the site with a small engineering prototype.
The prototype array was called VAMOS and consisted of six WCDs.
We show in Fig.~\ref{fig:layout} the layout of the HAWC array and the 6-tank VAMOS prototype.
(The seventh tank in the prototype was used for water storage.)
The empty area in the center of the array is the location of the central electronics building.
Readout cables will run from the central building to the WCDs via the channel which runs from west to east across the array.
WCDs are being deployed in a dense pattern that, when completed,
will provide $62\%$ coverage of the $135$~m $\times150$~m instrumented area.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.45\textwidth]{hawc_layout}
  \caption{Relative positions of the 300 water Cherenkov detectors (blue circles) that will comprise the HAWC array. The positions of the tanks in the VAMOS prototype are also shown (green circles).}
  \label{fig:layout}
 \end{figure}

As a wide field of view instrument, the HAWC observatory is well suited to address the open question of cosmic-ray origins
through the measurement of diffuse and extended TeV $\gamma$-ray emission from large-scale areas in our Galaxy.
HAWC will provide an unbiased survey of a large portion of the Northern Hemisphere down to regions close to the Galactic center
at energies above $100$~GeV.
We show in Fig.~\ref{fig:sensimap} the sky visible to the HAWC observatory and the
dependence with declination of the detector sensitivity.
The HAWC data will allow for the study of diffuse emission from large areas along the Galactic plane
and from structures such as the Fermi bubbles.

 \begin{figure*}[!hbt]
  \centering
  \includegraphics[width=0.8\textwidth]{HAWC_sensitivity}
  \caption{The sky coverage of the HAWC observatory in Galactic coordinates. The detector sensitivity is shown in the gray bands as a function of declination.
  Sources of very high energy $\gamma$-rays are from the TeVCat online catalogue~\cite{bib:TeVCat}.}
  \label{fig:sensimap}
 \end{figure*}

\subsection{Laser calibration}
The relative times between the signals in the PMT channels
have to be calibrated with nanosecond precision over the full dynamic range of the PMTs
to properly reconstruct the arrival directions of the primary particles.
The response time of a PMT and electronics depends on the light intensity striking on the PMT.
A laser calibration system was designed to accurately measure the relative timing among the PMT channels.
Short ($300$~ps) laser pulses with varying intensities are sent into every WCD through optical splitters, switches, and optical fibers.
The time between the laser shot and the PMT signal is recorded to correct for the dependence on the light intensity.
A time residual study is also performed to improve the angular reconstruction.
The time residual is the difference between a fitted air shower front and the PMT readout time.
This systematic time offset is then accounted for in an iterative shower reconstruction procedure to improve the determination of the incoming direction of the primary particle.
In Ref.~\cite{bib:Hugo} we present the first results of the timing calibration curves and time residual studies.

As the laser calibration system provides intensities from $0.1$~photo-electrons (PEs) to over $1000$~PEs,
the charge calibration of all PMTs is also obtained using the laser pulses,
and it further improves the angular resolution of measured arrival directions.
In Ref.~\cite{bib:Robert} we describe the design and performance of the laser calibration system.
We show in Fig.~\ref{fig:calib}
the improvement in the geometrical reconstruction of air showers due to the (time and charge) calibration.
These effects are verified using the measurement of the shadow that the moon produces in the flux of cosmic rays.
The results that we show in Fig.~\ref{fig:calib} are
based on data collected with a partial array of 30 WCDs.

The main components of the HAWC laser calibration system are installed and operational at the site in Mexico.
Calibration runs are performed regularly without adding significant dead time.
The experience gained from a WCD prototype in Colorado, and the
systematic time residuals derived from shower fits made it possible to calibrate the HAWC data even before calibration
results for all individual PMT channels were available.
Both charge and timing calibrations significantly improve the reconstruction of the arrival directions of air showers.
The network of optical fibers  will continue to grow together with the HAWC array,
The dedicated laser system provides the regular calibration of all PMTs to guarantee a stable performance of the array.

 \begin{figure*}[!ht]
  \centering
  \includegraphics[width=0.5\textwidth]{noCalibration}%
  \includegraphics[width=0.5\textwidth]{fullCalibration}
  \caption{Significance maps of air shower event directions centered on the position of the moon, where $\alpha =$ event right
ascension $(RA) -$ moon $RA + 180^{\circ}$ and $\delta =$ event declination $-$ moon declination. The map on the left side is based on reconstructions
with all pulse charges set to $1$~photoelectron and no timing calibration. The map on the right side was produced with full charge and
timing calibrations included.
The time and charge calibrations are explained in Refs.~\cite{bib:Hugo,bib:Robert}.}
  \label{fig:calib}
 \end{figure*}

\subsection{Site and deployment status}

The HAWC observatory is being built at an altitude of 4,100~m at the Sierra Negra volcano in the state of Puebla, Mexico.
This altitude corresponds to an atmospheric depth of $\sim640$~g$/$cm$^2$.
This closer proximity to the shower maximum allows, in comparison to Milagro,
twice as many particles in a shower at the same energy, and a lower energy threshold.
The HAWC site is located at 19$^\circ$ North and $97^\circ$ West.
This allows for observations of $2/3$ of the sky (restricting observations to within 45$^\circ$ of the local zenith),
including a significant overlap with the HESS survey of the Galactic plane, and with the fields of view of IceCube and VERITAS.
HAWC will have considerable daily exposure to the Crab, Geminga, Mrk~$421$, Mrk~$501$, and the Cygnus region.
HAWC will also be able to reach the Galactic Center at $46^\circ$ from the zenith.

Installation work started at the HAWC site in Spring 2010 with the deployment of the
VAMOS engineering prototype~\cite{bib:VAMOS}.
This prototype array consisted of six WCDs with a total of 36 PMTs.
The location of the prototype array with respect to the HAWC array can be seen in Fig.~\ref{fig:layout}.
We operated the VAMOS prototype array between September, 2011 and June, 2012.
We present a more detailed description of the prototype and the first results in Ref.~\cite{bib:VAMOS}.
The experience with this prototype was useful to validate working at the high altitude site, but
also to optimize and finalize the design of the different components of the WCDs.

The deployment of WCDs at the HAWC site started in March, 2012.
By August, 2012 we started operating the first 30 WCDs.
This sub-array, referred to as HAWC-30, has a comparable area to the Milagro experiment.
We used an average calibration for the events recorded with HAWC-30.
The laser calibration system~\cite{bib:Robert} started running at the HAWC site in Summer 2013.
We show in Fig.~\ref{fig:status} the status of the HAWC array by May, 2013.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.45\textwidth]{arrayon2013_05_16}
  \caption{Status of the deployment of the HAWC array on May 16, 2013. The
cleared area indicates the size of the completed instrument, $\sim$22,000~m$^2$.}
  \label{fig:status}
 \end{figure}

We started taking data with an array of 95 WCDs (HAWC-95) on June 12, 2013.
We show in Fig.~\ref{fig:hawc95} an event with signal in all operational WCDs on the first day of HAWC-95 operation.
In this conference we present results using data from the VAMOS, HAWC-30, and HAWC-95.

 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.4\textwidth]{hawc95event.png}
  \caption{First 95-detector (341-PMT) event recorded with HAWC on June 12, 2013.}
  \label{fig:hawc95}
 \end{figure}

Full operation of HAWC-111 started in September, 2013.
Currently, the PMTs are being calibrated in situ, and we use the calibration curves corresponding to each individual PMT.
The HAWC-250 array is on schedule for completion in August, 2014,
and full HAWC observatory will be completed by the end of 2014.

We described in more detail
the HAWC site, the site infrastructure, layout and platform, and the design and construction of the WCDs
in Ref.~\cite{bib:Ibrahim}.

\section{Sensitivity to $\gamma$-ray sources}

The design of the HAWC observatory combines the Milagro water Cherenkov technology with a high altitude site.
Re-deploying the existing Milagro photomultiplier tubes (PMTs) and electronics in a different configuration
at an altitude of 4,100~m will lead to a sensitivity increase of a factor of $\sim15$ over Milagro.
This improvement is due to the higher altitude, the increased physical area, and the optical isolation of the PMTs.
As a result, the HAWC detector will see a $5\sigma$ signal from the Crab Nebula in a single $4$-hr transit
(compared to $\sim5$ months for Milagro)
while maintaining this sensitivity over $2\pi$~sr.

We show in Fig.~\ref{fig:sensitivity} the differential sensitivity of HAWC as a function of energy.
The HAWC observatory will be used to study particle acceleration in Pulsar Wind
Nebulae, Supernova Remnants, Active Galactic Nuclei and $\gamma$-ray Bursts.
We describe in Ref.~\cite{bib:Jordan} how the sensitivity and its uncertainty are calculated.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.5\textwidth]{Sensitivity_vs_energy}
  \caption{Differential sensitivity per quarter decade of HAWC for 1 and 5 years (and 1 year of HAWC-100) is shown compared to other existing and future IACTs.
  Note that the sensitivity of HAWC (and Fermi-LAT) is for a sky survey while it is for 50 hours on a source for IACTs.}
  \label{fig:sensitivity}
 \end{figure}

The Cygnus region is an extremely active star forming region with a
wealth of $\gamma$-ray sources such as pulsar wind nebulae, young star
clusters, and binary systems.
Observations from radio to TeV
energies have revealed diffuse emission and a variety of objects
such as molecular clouds, star clusters, and pulsars.
The Milagro experiment
detected two extended sources in the TeV regime (MGRO\,J2019+37 and J2031+41) along
with hints of correlated GeV emission in the region.
The HAWC observatory will have better angular and energy resolution, and one order of magnitude more sensitivity than the
Milagro experiment at similar energies.
Thus, data from HAWC will allow us to resolve the TeV emission from this region to study the morphology of the sources,
and also to improve the spectral measurements to investigate the origins of the emission in this region.
We present in Ref.~\cite{bib:Michelle} the sensitivity of the HAWC observatory to the Cygnus region.

Measurements of the very high energy diffuse $\gamma$-ray emission are an excellent probe of cosmic-ray acceleration, propagation, and density distribution at different locations within our Galaxy.
At TeV energies, the Milagro collaboration reported a significant enhancement of diffuse emission with respect to models of the Cygnus region
and the inner Galaxy.
Measuring the diffuse and extended emission in our Galaxy with better sensitivity will help us understand these enhancements,
put tighter constraints on Galactic cosmic-ray emission, and also
distinguish between hadronic and leptonic acceleration and propagation models.
We present in Ref.~\cite{bib:Petra} the sensitivity of the HAWC array to Galactic diffuse $\gamma$-ray emission under different model assumptions.

We also present in Ref.~\cite{bib:Crab} our observations of the Crab Nebula using data from HAWC-30, including observations during the flare in March 2013.
We expect to observe 7$\sigma$ with each transit of the Crab using the full HAWC array.
We will measure the TeV flux of the Crab to better than 20\% for each day of the year,
enabling long-term studies of the Crab at TeV energies.

\subsection{Moon shadow}

The Moon causes a detectable deficit on top of a nearly isotropic flux of cosmic rays incident at Earth.
The measurement of the angular width and position of this ``shadow" allows us to infer the accuracy of our angular reconstruction.
We show in Fig.~\ref{fig:moon} an observation of the Moon shadow using 95 days of HAWC-30 data.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.45\textwidth]{HAWCMoon}
  \caption{Skymap around the region of the Moon for 95 days of HAWC-30 data
  in Moon-centered equatorial coordinates.
  The mapping technique, simulations, background estimation, and event selection are explained in Ref.~\cite{bib:Dan}.}
  \label{fig:moon}
 \end{figure}

We report in Ref.~\cite{bib:Dan} the detection and study of the moon shadow and its deflection due to the geomagnetic field.
Both the width and center of the observed Moon shadow are consistent with the predictions obtained from simulations.
The measurement of the amount of suppressed cosmic ray flux (in a circular region of radius 5$^\circ$ around the Moon)
also matches the expectations.
We infer a point-spread function of 1.2$^\circ$ for cosmic ray data from HAWC-30
by comparing the observations with simulations.
We expect the Moon shadow position and width as well as the angular resolution of the detector to be a function of energy.
We estimate the median energy of this subset
to be $\sim3$~TeV.

As HAWC-111 starts operation in August 2013,
the observation of the Moon shadow will become a daily monitoring tool.
We will also be able to measure the angular resolution as a function of energy with the larger data set from a larger array.

\subsection{Transient events}

Observations of energy spectra of $\gamma$-ray bursts (GRBs) can provide information
about the intervening space between the burst and Earth as well as about the source itself.
The HAWC observatory will be almost two orders of magnitude more sensitive to GRBs at $100$~GeV
than the Milagro experiment due to the higher altitude.
Due to the wide instantaneous field of view ($\sim2$~sr) and large duty cycle of the HAWC observatory,
we will be able to observe the beginning of the prompt phase of GRBs without needing to slew.
We will also be able to constrain the shape and cutoff of the GRB spectra in the sub-TeV to TeV energy range,
especially in conjunction with observations from other detectors such as the Fermi satellite.

GRB~130504C is the brightest GRB that occurred in the field of view of HAWC-30 during its uptime.
A preliminary analysis using the main DAQ data for GRB 130504C shows no excess larger than $5\sigma$
in the time windows examined ($73.2$, $105.0$, and $219.6$~s).
We show in Fig.~\ref{fig:GRB} the upper limits derived from Monte Carlo simulations for a 5$\sigma$ discovery of GRB~130504C
using data from HAWC-30
(for the $105$~s time window).
This analysis will be updated to show 90\% confidence level upper limits once the data are unblinded.
The Konus-Wind spectral fit from GCN circular 14587  is also shown in Fig.~\ref{fig:GRB} for comparison.
More details on this analysis can be found on Ref.~\cite{bib:GRB}.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.45\textwidth]{Flux_limit_grb130504c}
  \caption{The $5\sigma$ upper limit on the high-energy emission from GRB~130504C imposed with HAWC-30 data.
  The $5\sigma$ sensitivity is reported rather than $90\%$ C.L.\ upper limits to allow the data to remain blinded.
  The spectral fit reported by Konus-Wind
  is shown for comparison.}
  \label{fig:GRB}
 \end{figure}

HAWC data are collected by two
acquisition systems (DAQs).
Using the main DAQ, we measure the arrival time and the time over threshold (TOT) of the PMT pulses.
This system provides us with the information to reconstruct the shower core, the arrival direction, and the lateral distribution.
This in turn helps us determine the species of primary particle and its energy.
We discuss in more detail the GRB results using the main DAQ in Ref.~\cite{bib:GRB}.

The other DAQ, the scalers system, operates in a counting mode,
and it is sensitive to $\gamma$-ray and cosmic ray
transient events that produce a sudden increase
or decrease in the counting rates with respect to those produced by atmospheric showers and noise.
We present
the analysis procedure for data
taken with the scalers DAQ,
and the first results for selected GRBs
in Ref.~\cite{bib:icrcscalers}.
Although we see no indication of emission above $10$~GeV,
GRBs like 090510 and 090902B would be significantly detected with the scalers
if they occurred at favorable zenith angles.

The sensitivity of the HAWC observatory to GRBs increases dramatically as the array grows.
We show in Ref.~\cite{bib:GRB} the effects of different GRB emission spectra on the expected sensitivity of HAWC
for several stages of the deployment.
The HAWC observatory stands an excellent chance of seeing GRBs that are detected at lower energies
even before the array gets completed by the end of 2014.

The
HAWC observatory will provide a nearly continuous, unbiased survey of TeV emission from the northern hemisphere,
which makes it ideally suited for detecting bright transient events, such as outbursts from active galactic nuclei (AGN).
We are implementing a comprehensive, online flare-monitoring program to promptly detect bright outbursts from moderate-redshift AGN.
This will provide unique opportunities to trigger follow-up observations at complimentary wavelengths.
We discuss in Ref.~\cite{bib:Asif} the various components of the flare-monitoring system.

\section{Observations of cosmic rays}

The main goal of the HAWC observatory is to study $\gamma$-rays
between $50$~GeV and $100$~TeV.
Although charged cosmic rays are the major source of background,
the distribution of the arrival directions of the cosmic rays in this energy range is of significant interest to the particle astrophysics community.
An anisotropy in the distribution of arrival directions of TeV cosmic rays has been
observed  at the $10^{-3}$ level on large ($>60^\circ$) and
small ($<20^\circ$) angular scales by multiple experiments
in both hemispheres.
The large-scale structure
is dominated by dipole and quadrupole moments and does not appear to persist
above the TeV energies.
Although many explanations have been suggested,
the origin of the observed anisotropy is not understood.

We measure the cosmic-ray anisotropy in the TeV energy range
using data
collected during the operation of HAWC-30 between January 1, 2013 and April 15, 2013.
(This corresponds to a live-time of $95$~days.)
We require a
zenith angle below $45^\circ$ and at least $15$ triggered PMTs.
The rate of air showers from cosmic rays recorded with the HAWC-30 array is $>2$~kHz.
We accumulated $2.2\times10^{10}$ well-reconstructed events during this period.
We estimate a median energy of $2$~TeV for this data set.

To search for anisotropies on small angular scales,
we compute
the amplitude of the deviations from the isotropic expectation in each pixel.
We determine
the deviations from isotropy by calculating
the relative intensities (with respect to a reference map) as a function of equatorial coordinates.
We show the measured relative intensities in Fig.~\ref{fig:crani}.
 \begin{figure*}[!hbt]
  \centering
  \includegraphics[width=0.8\textwidth]{HAWCCRAnisotropy}
  \caption{Relative intensity of the HAWC-30 cosmic-ray data produced using a time-integration window $\Delta t = 2$~hr.
The sky map of the pre-trial significances of the features in this map are shown in Ref.~\cite{bib:CRani}.}
  \label{fig:crani}
 \end{figure*}
Data have been smoothed using a $10^\circ$ top-hat function.
Our measurements are sensitive
to features smaller than $30^\circ$ in right ascension
because we use an integration time of $\Delta~t=2$~hr to generate the maps.
Due to the low latitude of the HAWC site,
these data cover a region of the sky previously unobserved by other experiments.

We present in Ref.~\cite{bib:CRani} the results of the search for anisotropy on large and small angular scales
using data from HAWC-30.
We also compare the observed anisotropy with previous measurements of the northern and southern skies.
Several prominent features are visible in the sky map, notably the regions of
excess flux at $\alpha=60^\circ$ and $\alpha=120^\circ$.
There are of the order of $10^5$ independent pixels in the sky map, and after
accounting for trial factors only these two regions of excess are significant at a level larger than $5\sigma$.
These hot spots correspond to the $10^\circ$--~$20^\circ$ regions of cosmic ray excess previously observed by Milagro
and ARGO.
We also note that
regions of excess are associated with neighboring deficits in the cosmic ray flux.
We cannot currently rule out the possibility that the deficit regions are artifacts of the analysis
rather than real features in the residual cosmic ray flux.

\subsection{Solar events}

Although one of the primary purposes of the HAWC collaboration
is to study
sources of high energy $\gamma$-rays,
the counting rate of the HAWC observatory will be sensitive to cosmic rays with energies above the
geomagnetic cutoff of the site ($\sim 9$~GV).
In particular, we will be able to detect solar energetic particles
and the effect of coronal mass ejections on the galactic cosmic rays.
This effect is known as Forbush Decreases (FDs).
We present in Ref.~\cite{bib:Lara}
the capabilities of the HAWC observatory to observe
solar energetic events,
and the observation of an FD in the data from HAWC-30.

We show in Fig.~\ref{fig:FD} the observation of an FD in the data from the engineering prototype VAMOS using the main DAQ.
We describe the analysis of data from both the main DAQ and the scalers system, and the corrections due to atmospheric effects
in Ref.~\cite{bib:Mario}.
The observation of this transient event in the data from VAMOS is in very good agreement with
neutron monitors located in Mexico City and the South Pole.
 \begin{figure}[!ht]
  \centering
  \includegraphics[width=0.475\textwidth]{FD_VAMOS_TDC}
  \caption{Comparison between the counting rate of the main DAQ system of the VAMOS prototype (in magenta for 2-edge hits and in green for 4-edge hits),
  the Mexico City Cosmic Rays Observatory (in black), and the McMurdo station (in brown) during a Forbush decrease.
  The  magnetic rigidity cutoffs are $9$~GV, $8.2$~GV, and $0.3$~GV, respectively.}
  \label{fig:FD}
 \end{figure}

\section{Fundamental physics with HAWC}

The high energy coverage of the HAWC observatory
enable us to study fundamental physics beyond the Standard Model.
The large field of view of the observatory will also allow detailed studies of cosmologically significant backgrounds and
intergalactic magnetic fields.
We describe in this section the sensitivity of the HAWC observatory to dark matter, cosmology, and fundamental physics.

Each WCD holds $\sim$200,000 liters of ultra-pure water.
Thus, the completed HAWC array will be a $60$~kton detector.
Its flat geometry also provides more effective area for a given volume.
These features of the HAWC array give us the opportunity to search for exotic particles.
One interesting example is the Q-balls that are predicted by several supersymmetric theories.
Q-balls are very massive, sub-relativistic particles that can have a large baryon
number and can be stable since their creation in the early universe.
They are also an appealing candidate for the dark matter of the universe,
but their large masses imply that their flux is very low.
The HAWC observatory has a flexible DAQ system that
allows us to search for Q-balls traversing the detector.
For this purpose, a dedicated trigger algorithm for non-relativistic species was designed and implemented.
We show in Fig.~\ref{fig:Qballs} the sensitivity to Q-balls for one year of data of
the full HAWC array in comparison to established limits and a theoretical prediction.
For this limit we assume that background triggers can be removed after reconstruction.
This is possible with a more restrictive event selection in the trigger algorithm.
We describe the fundamentals of Q-balls, and the dedicated trigger algorithm in Ref.~\cite{bib:Peter}.
\begin{figure}[!ht]
  \centering
  \includegraphics[width=0.475\textwidth]{QBallSens}
  \caption{Estimated flux upper limit to Q-balls using one year of data of the HAWC observatory (assuming no background) compared to current limits.
  The solid line indicates what can be done with the current Q-ball trigger algorithm while the dashed line indicates cross sections which could be accessible with a new saturation trigger.
  The blue lines on the right show expectations from theory.
  Details about this analysis can be found in Ref.~\cite{bib:Peter}.}
  \label{fig:Qballs}
 \end{figure}

A growing body of evidence exists supporting the existence of Dark Matter (DM), yet its particle nature remains a mystery.
Weakly-interacting massive particles (WIMPs) with a mass ranging from $10$~GeV to $10$~TeV are a popular candidate to explain
the particle nature of DM.
A WIMP hypothesis is compelling as it naturally explains the density of DM observed,
and such particles are expected in some solutions to the gauge hierarchy problem.
WIMPs could annihilate into Standard Model particles and produce high energy photons via various processes.
Detecting such high energy photons would provide an indirect detection of the DM particle mass.

The HAWC observatory can set
stringent limits of indirect detection of WIMP candidates above $100$~GeV
due to its large effective area, excellent angular resolution, efficient gamma-hadron separation, and large duty cycle.
We show in Fig.~\ref{fig:Segue1} the preliminary limits on DM candidate velocity weighted cross-section
as a function of the DM mass for observations of Segue~1.
We use data collected with HAWC-30 ($82.8$~days) in this analysis.
These represent the most stringent limits available above $20$~TeV.
We also show the predicted sensitivity of the HAWC observatory after completion in 2014.
\begin{figure}[!ht]
  \centering
  \includegraphics[width=0.5\textwidth]{Segue1}
  \caption{The preliminary sensitivity on $\left<\sigma\ v\right>$ vs.\ $M_\chi$ in the annihilation channels
  $\chi \bar\chi \rightarrow  \tau \bar\tau$ and $\chi \bar\chi \rightarrow  b \bar b$ from observations of Segue~1
  with HAWC-30 ($82.8$~days), and the expected sensitivity for the HAWC observatory (1~year)
  compared to the
  current limits from Fermi-LAT (24~months) and VERITAS (50~hours).}
  \label{fig:Segue1}
 \end{figure}

We present in Ref.~\cite{bib:Pat}
these preliminary limits for various DM annihilation channel hypotheses.
As we continue deployment, the sensitivity of the HAWC array will increase due to improvements in effective area, angular resolution,
and $\gamma/$hadron separation.
Observations with the HAWC observatory on DM dominated objects such as Segue~1 will provide competitive limits on
masses above $1$~TeV.

Primordial black holes (PBHs) are hypothetical objects that formed from extreme densities of matter
that were present during the early universe.
PBHs with large enough initial masses
could be bursting high energy particles,
including very high energy $\gamma$-rays.
The HAWC observatory
will be an important tool to
either detect a PBH burst or set stringent new limits on the PBH burst rate.
We present in Ref.~\cite{bib:Tilan} the sensitivity of the HAWC observatory to PBH bursts according to the Standard Model.

Lorentz invariance is believed to be a fundamental symmetry.
The observation of a Lorentz invariance violation (LIV) would revolutionize our view of  the universe and probe physics
at energy scales not attainable with manmade accelerators.
The combination of extreme distance, high energy emission,
and short duration
makes GRBs an ideal laboratory to search for LIV.
We discuss in Ref.~\cite{bib:Lukas} the current limits on LIV and
the potential to study possible deviations of the speed of photons from $c$.
We will be able to set competitive limits on the scale of LIV
using GRB observations with the HAWC observatory.

The intergalactic magnetic field (IGMF),
presumed to exist in the void regions between galaxy clusters,
may play a role in galaxy formation, contain information about conditions in the early universe,
and influence the trajectories of cosmic rays of extragalactic origin.
Recent studies have attempted to measure the IGMF by searching for its influence on the cascades
produced when very high energy gamma rays from blazars interact with the extragalactic background light (EBL).
The HAWC observatory
will provide unbiased observations of the average fluxes from blazars and
accurate measurements of the attenuation of $\gamma$-rays due to interactions with the EBL.
We present in Ref.~\cite{bib:Tom} the capabilities of the HAWC observatory to contribute to measurements of the IGMF
from the observations of the delayed secondary flux following a bright blazar flare.

\section{Conclusions and outlook}

Deployment of the HAWC array
started in March 2012.
After only six months we were already operating an array of 30 WCDs with a size comparable to the Milagro experiment.
The modularity of the observatory allows us to take data during deployment as the WCDs are instrumented and verified as they are placed into the data stream.
We present at this conference the first results on
the observation of the shadow of the moon, the observation of small-scale and large-scale angular
clustering of TeV cosmic rays, the measurement of transient
solar events, the observation of Forbush decreases,
upper limits on high energy emission from GRBs,
the observation of the Crab Nebula,
a program to monitor AGN flares,
and the sensitivity of the observatory to
Q-balls, primordial black holes, Lorentz invariance violation, and
the indirect detection of dark matter.
We will have approximately one year of data from HAWC-111 for Summer 2014.
At the next ICRC in The Netherlands, we will have the first results from the full HAWC array,
one order of magnitude more sensitive than its predecessor.

\vspace*{0.5cm}
\footnotesize{{\bf Acknowledgment:}{We acknowledge the support from the U.S.\ National Science Foundation; U.S.\ Department of Energy Office of High-Energy Physics; The Laboratory Directed Research and Development program of Los Alamos National Laboratory; Consejo Nacional de Ciencia y Tecnolog\'{\i}a, M\'exico; Red de F\'{\i}sica de Altas Energ\'{\i}as, M\'exico; DGAPA-UNAM, M\'exico; and the University of Wisconsin Alumni Research Foundation.}}


\section{Introduction}\label{section:intro}

Radio galaxies are some of the brightest objects in the radio sky and as such have been widely studied for several decades (e.g.\ \citealt{1974MNRAS.167P..31F,1980ARA&A..18..165M,1995PASP..107..803U}). Powerful radio galaxies mainly fall into two distinct morphological classes; the luminous edge-brightened Fanaroff and Riley type-II sources (FRII; \citealt{1974MNRAS.167P..31F}), and the more centrally-brightened less luminous FRI sources. The vast majority of the observed flux in these sources come from the large lobes and jets, which can extend for up to several Mpc (for an overview see \citealt{1991bja..book...52M}), whilst the emission from their cores typically only make up a few percent of the total emission. The core prominence differs between the two morphological classes, with FRI sources tending to have a higher fraction of their total flux density coming from the core \citep{1997MNRAS.284..541M,2014MNRAS.437.3405L}. Several studies suggest that there is a relationship between the core power and the total power of a source (e.g.\ \citealt{1990A&A...227..351D,1988A&A...199...73G}), with core fraction decreasing exponentially with increasing source luminosity. Physically, the emission from the core can be considered as a measure of the instantaneous jet power, while the extended emission traces the past jet activity. The contribution of the core to the total emission can therefore provide valuable information about the activity of the central engine and the duty cycle of a source.
In order to fully understand the role that cores play we need to study both individual sources and the statistical properties of larger samples across a range of redshifts and luminosities.

Recent studies of lower power ($L_{1.4~\rm GHz} < 10^{25} \rm W \, Hz^{-1}$) radio galaxies in the local universe ($z \sim 0.1$) have shown that the majority of these sources lack the powerful extended emission characteristic of the classical FRI and FRII sources, and have a higher proportion of their emission originating from their cores. For example, \citet{2014MNRAS.438..796S} found that more than two-thirds of the local radio galaxy population selected at 20~GHz were compact radio galaxies (with linear sizes less than $\sim 15$~kpc). \citet{2005MNRAS.362....9B} studied 2215 radio galaxies in both FIRST and SDSS with $L_{1.4~\rm GHz} \sim 10^{22} - 10^{26} \rm W\, Hz^{-1}$ and found that 80 per cent of the sample are unresolved in FIRST (therefore have angular sizes less than 5~arcsec, corresponding to $\sim 15$~kpc).  A pilot study of 12 of the \citeauthor{2005MNRAS.362....9B} sources using high-resolution VLA data at 1.4, 4.5 and 7.5~GHz by \citet{2015A&A...576A..38B} showed that 11 of the 12 sources studied show a compact morphology, with emission extending at most to $3$~kpc. These compact radio galaxies have been referred to as `FR0' sources. \citet{2016MNRAS.462.2122W} studied a sample of faint radio galaxies at higher redshifts ($z \sim 1$) selected from the Tenth Cambridge (10C; \citealt{2011MNRAS.415.2708D,2011MNRAS.415.2699F,2016MNRAS.457.1496W}) survey at 15.7 GHz. They used 610-MHz GMRT observations to investigate the morphology of the sample and found that the bulk of the sources are radio galaxies which lack extended emission on arcsec-scales, suggesting that this compact radio galaxy population may be significant at higher redshifts. There is therefore mounting evidence for a population of radio galaxies with a deficit of extended emission compared to classical FRI and FRII radio galaxies. Almost all of these compact radio galaxies have $L_{1.4~\rm GHz} < 10^{25} \rm W\, Hz^{-1}$ and they are most numerous at $L_{1.4~\rm GHz} < 10^{24} \rm W\, Hz^{-1}$, they therefore overlap classical FRI sources in luminosity.

The SKA Simulated Skies is a suite of simulations of the radio and sub-millimetre universe; one part is a semi-empirical simulation of the extra-galactic radio continuum sky developed by \citet{2008MNRAS.388.1335W,2010MNRAS.405..447W} which we will refer to as S$^3$. It covers a $20 \times 20$~deg$^2$ sky area out to a redshift of 20, containing 320 million radio components and extending down to a flux density limit of 10~nJy at 151, 610~MHz, 1.4, 4.86 and 18~GHz. It encapsulated our best understanding of the radio sky in 2010 and therefore serves two main purposes: it allows this understanding to be tested against newer observations, and it can be used to optimise the design of telescopes and radio surveys, such as the Square Kilometre Array. It is widely used by the community for both these purposes, see e.g.\ \citet{2015aska.confE..18J,2015aska.confE..83M,2015aska.confE..69S}.

Sources in S$^3$ are split into six distinct source types which are treated differently: radio-quiet AGN, radio-loud AGN (which are split into FRI and FRII sources and GHz-peak spectrum (GPS) sources), quiescent star-forming and star-bursting galaxies. The radio-loud AGN in the simulation are drawn from the 151 MHz luminosity function derived by \citet{2001MNRAS.322..536W}, which consists of low- and high-luminosity components whose luminosity function have different functional forms. These low- and high-luminosity components are crudely identified as FRI and FRII sources respectively. The morphologies and spectra of the two populations are then modelled differently and the morphological parameters are tuned to fit the observed source counts at $S > 1$~mJy over a range of frequencies from 151~MHz through to 18~GHz. A small number of GPS sources are included by introducing a spectral turnover in the relevant source spectra.
Throughout this paper, `FRI sources' refer to sources classified as FRI sources in the simulation (note that FR0 sources are not represented in this model).

At 18~GHz the majority of the simulated sources with $S_{18~\rm GHz} > 0.5$~mJy are radio-loud AGN, with FRI sources making up 71 per cent followed by FRII sources with 13 per cent, while the remaining source types only contribute a few per cent each. This is broadly consistent with recent work by \citet{2015MNRAS.453.4244W} who studied a sample of sources selected at 15.7~GHz from the 10C sample and found that $> 90$ out of a sample of 96 sources with $S_{15.7~\rm GHz} > 0.5$~mJy are radio galaxies, while star-forming galaxies make a negligible contribution to the population. (Although note that the majority of the radio galaxies in the \citealt{2015MNRAS.453.4244W} 10C sample seem to lack the extended emission typical of FRI/FRII sources, even in lower-frequency, 5~arcsec resolution imaging.)

One type of observation that can easily be compared to S$^3$ is a radio source count. The 1.4-GHz source counts derived from the simulation are consistent with the observed counts down to at least the $\muup$Jy-level, unsurprisingly as the model was originally set up to match the counts at this frequency. At higher frequencies (e.g.\ 18~GHz), however, S$^3$ fails to reproduce the observed counts. The 18-GHz counts derived from the simulation under-predict the counts from the Ninth Cambridge (9C; \citealt{2003MNRAS.342..915W,2010MNRAS.404.1005W}) and 10C surveys by a factor of two below 10~mJy. Other leading high-frequency models (e.g.\ \citealt{2005A&A...431..893D,2011A&A...533A..57T}) also significantly under-predict the number of sources at faint flux densities, indicating that the faint, high-frequency source population is not well characterised. As the cores of radio galaxies play a more significant role at higher frequencies due to their flat spectral shape, this suggests that the core emission, which is directly related to the instantaneous jet power, may be poorly modelled in the simulations of these populations.

The spectral index of a radio galaxy can provide information about the relative contributions of the core and the extended structure to the total emission; the extended lobes tend to have steep spectra ($\alpha > 0.5$) because the predominant emission mechanism is optically-thin synchrotron, while the core emission has a much flatter spectrum ($\alpha < 0.5$) due to the superposition of many synchrotron self-absorbed spectra from the base of the jet (e.g.\ \citealt{1979ApJ...232...34B}). Radio galaxies which are more core-dominated therefore tend to have flatter spectra than those dominated by extended emission.
\citet{2013MNRAS.429.2080W} compared the spectral index distributions of a sample of 10C sources with a comparable sample selected from the S$^3$ simulation and found that they were significantly different; there are essentially no sources in the simulated sample with $\alpha < 0.3$\footnote{The convention $S \propto \nu^{-\alpha}$ for flux density $S$, frequency $\nu$ and spectral index $\alpha$ is used throughout this work.} while 40 per cent of the 10C sample have $\alpha^{15.7~\rm GHz}_{0.61~\rm GHz} < 0.3$.  This is probably because the spectra of the FRI sources, which dominate the simulated sample and are assumed to have steep spectra, are not modelled correctly. In particular, their cores are known to be more dominant than is assumed in the simulation (e.g.\ \citealt{2014MNRAS.437.3405L}).  This is discussed in more detail in Section~\ref{section:source_mod}.

The failure to model the spectra of the FRI radio galaxies in S$^3$ implies that the structures of these sources are not well known. Spectral ageing, which occurs as the synchrotron electrons lose energy over time, causes the spectra of the extended lobes to steepen with time.

As the vast majority of the faint radio galaxies in the simulation are classified as FRI sources, in this work we probe how these sources are modelled in order to better understand this population. We focus on reproducing the statistical properties of the population at high frequencies ($\sim 15$ GHz) as this is where the simulation fails. In this work we introduce more significant cores into the FRI sources, as it is known that the core fraction ($S_{\rm core}/S_{\rm tot}$, where $S_{\rm core}$ is the flux density originating from the core and $S_{\rm tot}$ is the total flux density of the source) is higher than assumed in the simulation (e.g.\ \citealt{2015A&A...576A..38B}), to investigate the extent to which this improves the simulation by comparing with recent high-frequency observations. The radio data used to in this work are discussed in Section~\ref{section:radio_data}. The changes made to the FRI sources are described in Section~\ref{section:source_mod} and the results are discussed in Section~\ref{section:discussion}. The conclusions are then presented in Section~\ref{section:conclusions}.

\section{Radio data used}\label{section:radio_data}

The 10C survey is the deepest high-frequency ($\gtrsim 10$~GHz) radio survey to date, so is the most appropriate dataset to use to test any model or simulation of the source population making up the faint ($ \lesssim 50$~mJy), high-frequency radio sky. It was observed with the Arcminute Microkelvin Imager (AMI; Zwart et al., 2008) Large Array in Cambridge, UK, and consists of a total of 27~deg$^2$ complete to 1~mJy in 10 different fields and a further 12~deg$^2$ complete to 0.5~mJy contained within these fields. It has recently been extended down to 0.1~mJy in two fields \citep{2016MNRAS.457.1496W}. The properties of a complete sample of nearly 100 sources in one of the fields with extensive multi-wavelength data available have been studied in detail by \citet{2013MNRAS.429.2080W,2015MNRAS.453.4244W,2016MNRAS.462.2122W}, using lower-frequency radio data along with near- and far-infrared, optical and X-ray data. The key results of relevance to this work are that essentially all ($\geq 96$~per cent) of the sources are radio galaxies, and they have flatter spectra and are more numerous than the simulation predicts.

The spectral indices of these sources were studied using 610~MHz GMRT data \citep{2008MNRAS.387.1037G,2010BASI...38..103G} and 1.4~GHz WSRT data \citep{2012rsri.confE..22G}, along with FIRST and NVSS (both at 1.4~GHz). The large resolution difference between the 10C survey (beam size 30~arcsec), and some of the other surveys means that care needs to be taken when calculating the spectral indices. To minimise the effects of these issues, contour maps of the sources in the higher-resolution surveys (e.g.\ the GMRT survey) are examined by eye and images are smoothed to a comparable resolution to the 10C survey. Full details of these methods used for each of the different surveys are given in Section 3.2 of \citet{2013MNRAS.429.2080W}.

The morphologies of the sources were investigated using 610~MHz GMRT data with a resolution of $6 \times 5$~arcsec \citep{2008MNRAS.387.1037G,2010BASI...38..103G}; the majority of the sources are compact of these scales, with 67 per cent classified as compact, 19 per cent classified as FRI or FRII sources and the remaining 14 per cent showing some signs of extended emission \citep{2016MNRAS.462.2122W}.

The two main data products used in this paper to compare to the simulation are the 10C source counts, which are presented in \citet{2011MNRAS.415.2708D} and extended in \citet{2016MNRAS.457.1496W} and the spectral index distribution, which is derived and discussed in \citet{2013MNRAS.429.2080W} and extended in \citet{2017MNRAS.464.3357W}.

\section{Modifying the FRI sources}\label{section:source_mod}

In S$^3$, each FRI source is modelled as consisting of a compact core component and two extended lobes, based on observations of high-flux density FRIs. The core component is modelled as having some spectral curvature, meaning that while the core spectra are flat at low frequencies, between 1.4 and 18 GHz they are relatively steep, with a mean spectral index of 0.60; the extended emission is assumed to have a constant spectral index of 0.75. The contribution of the core to the total 1.4-GHz flux density is small, with a distribution which peaks at a core fraction, $x$, where $x = S_{\rm core}/S_{\rm tot}$ ($S_{\rm core}$ is the flux density originating from the core and $S_{\rm tot}$ is the total flux density of the source) of $2.5 \times 10^{-3}$. This means that the overall spectral shape of the FRI sources, which make up the majority of sources in the simulation with $S_{18~\rm GHz} = 1$~mJy, is steep with a mean spectral index of 0.73.

There is evidence that the core prominence of FRI sources is higher than assumed by the model; for example \citet{2015A&A...576A..38B} find a core fraction ranging from 0.05 to 0.9. There is also evidence that at higher frequencies ($\nu > 10$~GHz) the spectra of the lower power sources are flatter than assumed by the simulation.
\citet{2013MNRAS.429.2080W} studied the properties of a sample of 10C sources and showed that the spectra of sources selected at 15~GHz are much flatter than this, with a median spectral index between 610-MHz and 15.7-GHz of 0.36 for sources with $S_{15.7~\rm GHz} \sim 1$~mJy (see \citealt{2013MNRAS.429.2080W} for a full discussion of the spectral indices of the observed and simulated samples). We suspect that this discrepancy between S$^3$ and the observations arises because the cores of these lower power sources are in fact more dominant, and have flatter spectra, than the simulation assumes.

\begin{figure}
\centerline{\includegraphics[width=\columnwidth]{FRI_spectrum-crop.pdf}}

\caption{Example radio spectra of an FRI source in the modified catalogue. The source has $L_{1.4~\rm GHz} = 10^{24}~\rm W\, Hz^{-1}$ and a core fraction $x = 0.31$ at 1.4~GHz. The core and lobe components are shown separately, and have spectral indices of 0.0 and 0.75 respectively.}\label{fig:FRI_spectrum}
\end{figure}

\begin{figure}
\centerline{\includegraphics[width=\columnwidth]{core_frac_1b-crop.pdf}}
\caption{Fraction, $x$, of the total 1.4-GHz flux density attributed to the core as a function of 1.4-GHz luminosity for three different values of core spectral index.}\label{fig:core_frac}
\end{figure}

In order to test this theory, we have added a flat-spectrum core component to the FRI sources in S$^3$. We have assumed that a fraction $x$ of the total 1.4-GHz flux density is in the core, and assigned the core component a spectral index between 1.4 and 15.7~GHz of $\alpha_{\rm c}$. The extended emission, which accounts for the remainder of the flux density at 1.4 GHz, is given a spectral index of 0.75 (consistent with optically-thin synchrotron emission, in the same way as in the original simulation). (Note that, in reality, spectral ageing will cause the lobes of many sources to have steeper spectra at high frequencies. We make no attempts to include this effect here, leaving it for future work, but note that it would mean that our additional core components should be considered as lower limits as including this effect would cause a larger core component to be required. This is discussed in more detail in Section~\ref{section:discussion}.)
We then calculate a revised 15.7-GHz flux density for each FRI source, and use this to produce a revised 15.7-GHz source count. An example radio spectrum for a modified source is shown in Fig.~\ref{fig:FRI_spectrum}.

In order to fit the observed source counts across the full range of flux densities, a higher core fraction is required for the lower luminosity sources than for the higher luminosity sources. To achieve this we modelled the core fraction as a step function which depends on 1.4-GHz luminosity. We therefore had three parameters in our model: the core fraction required at low luminosities ($x_{\rm l}$), the core fraction required at high luminosities ($x_{\rm h}$), and the break in luminosity ($b$) where the change between the two core fractions occurs, as demonstrated in equation~\ref{eqn:core_frac}:

\begin{equation}
x = \left\{
\begin{array}{llc}
x_{\rm l} & \textrm{for} & L_{1.4~\rm GHz} \leq b \\
x_{\rm h} & \textrm{for} & L_{1.4~\rm GHz} > b.\\
\end{array}\right.
\label{eqn:core_frac}
\end{equation}

\noindent We tried more complicated models where rather than a step function we had a gradually decreasing core component but found that the data did not warrant the inclusion of extra parameters.

We allowed the three parameters in our core fraction model to vary in the following ranges: $1.0 \times 10^{-5} < x_{\rm h} < 0.1$, $0.1 < x_{\rm l} < 0.7$ and $1.0 \times 10^{22} < b < 1.0 \times 10^{28}$ and fix the core spectral index $\alpha_{\rm c}$. We then compared the simulated 15.7-GHz source count produced by each set of values to the observed source counts from the 9C, 10C and 10C ultra-deep surveys \citep{2010MNRAS.404.1005W,2011MNRAS.415.2708D,2016MNRAS.457.1496W} and used a simple chi-squared minimisation to select the best-fitting values. We repeated this process for different values of $\alpha_{\rm c}$ to produce a best-fit core fraction model for each value of core spectral index. The core spectral index and the core fraction are degenerate; the same result can be achieved by using a steeper core spectrum and a larger core fraction as by using a flatter spectrum and a smaller core fraction. To illustrate this, we found the best fit core fraction model using three different values of $\alpha_{\rm c}$; $-0.1$, 0.0 and 0.1. With more data it would be possible to investigate models in which the spectral index is related to the core fraction, but for the present study we just highlight this degeneracy. The core fraction found to best fit the observed counts in each case is tabulated in Table~\ref{tab:core_frac} and shown in Fig.~\ref{fig:core_frac}.

\begin{table}
\caption{Parameters of the core fraction function required to best fit the observed source counts assuming different core spectral indices ($\alpha_{\rm c}$). $x_{\rm l}$ and $x_{\rm h}$ are the core fractions at low and high luminosities respectively, and $b$ is the break in luminosities, as described by Equation~\ref{eqn:core_frac}.}\label{tab:core_frac}
\smallskip
\centering
\begin{tabular}{dccc}\hline
\dhead{$\alpha_{\rm c}$} & $x_{\rm l}$ & $x_{\rm h}$ & $b$ \\
 & & &(W / Hz) \\ \hline
-0.1 & 0.23 & $3.6 \times 10^{-4}$ & $1 \times 10^{25}$\\
0.0  & 0.31 & $4.8 \times 10^{-4}$ & $1 \times 10^{25}$\\
0.1  & 0.42 & $6.4 \times 10^{-4}$ & $1 \times 10^{25}$\\
\hline
\end{tabular}
\end{table}

\begin{figure}
\centerline{\includegraphics[width=\columnwidth]{sc_modified-crop.pdf}}
\caption{15.7~GHz Euclidean-normalised source counts. The red pluses ($+$) and crosses ($\times$) show the total source counts for the modified and original S$^3$ respectively. The dotted lines show the original S$^3$ counts split up into the different source populations used in the simulation, and the dot-dashed line shows the modified count for the FRI sources only (the only population modified here). The source counts from the 9C, 10C and 10C ultra-deep surveys are shown by the dashed line.}\label{fig:counts_18}
\end{figure}

The 15.7-GHz source counts resulting from the modified catalogue are shown in Fig.~\ref{fig:counts_18}, along with the observed counts from the 9C and 10C surveys and the original simulated counts. It is clear from this figure that the source counts from the modified simulation are a much better fit to the observed counts than those from the original catalogue.  The 4.8-GHz source counts, shown in Fig.~\ref{fig:counts_4}, are only slightly modified by the addition of the flat-spectrum cores, and are still consistent with the observations (compiled by \citealt{2010A&ARv..18....1D}).

\begin{figure}
\centerline{\includegraphics[width=\columnwidth]{4ghz_counts-crop.pdf}}
\caption{4.8-GHz source counts from the original and modified simulation. Observed counts, compiled from several different studies by \citet{2010A&ARv..18....1D} are also shown.}\label{fig:counts_4}
\end{figure}

The median integrated spectral index as a function of flux density is shown in Fig.~\ref{fig:alpha}. In the original catalogue this was a particularly poor match to the observations; almost all sources in the simulation selected at 18~GHz had a spectral index of $\sim 0.75$, while the observed sample showed a much wider range of spectral indices. In particular, the observed sample contained a large proportion of flat-spectrum sources, which were totally missing from the simulation \citep{2013MNRAS.429.2080W,2017MNRAS.464.3357W}. The spectral index distribution from the modified simulated catalogue is clearly a much better match to the observations at 15~GHz.

\begin{figure}
\centerline{\includegraphics[width=\columnwidth]{alpha-crop.pdf}}
\caption{Median spectral index as a function of 15.7-GHz flux density. The median spectral index from the modified S$^3$ (assuming a core spectral index of 0.0) is shown as red `$\times$', while the observed median spectral index from the 10C and 10C ultra-deep surveys \citep{2013MNRAS.429.2080W,2017MNRAS.464.3357W} are shown in blue. }\label{fig:alpha}
\end{figure}

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

The model presented in Section~\ref{section:source_mod} demonstrates one simple way in which S$^3$ can be altered to fit the observations; we have shown that by adding a flat-spectrum core component to the FRI sources with 1.4-GHz luminosities $ < 10^{25} \rm W \, Hz^{-1}$, the observed source counts and spectral index distributions can be reproduced.

As discussed in Section~\ref{section:intro}, there is growing evidence in the literature for a significant population of radio galaxies with $L_{1.4~\rm GHz} < 10^{25} \rm W \, Hz^{-1}$ which lack significant extended emission, both in the local universe \citep{2014MNRAS.438..796S} and at higher redshifts \citep{2016MNRAS.462.2122W}, particularly in samples selected at higher frequencies. This is consistent with our result that a significant core fraction is required in lower-luminosity sources to reproduce the observed high-frequency source count and spectral index distribution. The more core-dominated `FRI sources' in the modified simulation could well be equivalent to the compact (FR0) sources found in several recent surveys; the surface brightness of any extended emission could be too low to be detected in the observations, causing them to appear compact. \citet{2016MNRAS.tmp.1528S} modelled the emission from three VLBI-detected AGN and found that the predicted lobe surface brightness was too low to be detected in current surveys with the VLA and LOFAR, explaining why these sources appear compact. In fact, \citet{2015A&A...576A..38B} found that the only distinguishing factor between FR0 and FRI sources was the higher core dominance in FR0 sources; the two classes had very similar spectroscopic nuclear and host properties (e.g\ black hole mass, colour, emission line ratio).

As shown in Fig.~\ref{fig:core_frac}, we have found that a significant core fraction is only required for sources with $L_{1.4~\rm GHz} < 10^{25} \rm W \, Hz^{-1}$; most of the FR0 sources in \citet{2014MNRAS.438..796S} and \citet{2015A&A...576A..38B} have luminosities below this value, so this is consistent with the scenario described above. Assuming a core spectral index of 0.0, we have found that a core fraction of 0.31 is required for the lower luminosity sources; the core dominance in the \citeauthor{2015A&A...576A..38B} FR0 sample ranges from 0.05 to 0.86, broadly consistent with the value found here, but the small sample size and large range makes it difficult to make a meaningful comparison. \citet{2014MNRAS.437.3405L} modelled the decelerating relativistic jets in ten low-luminosity ($L_{1.4~\rm GHz} \sim 10^{24} \rm W \, Hz^{-1}$) FRI sources selected from the 3CR and B2 samples. They found a range of core fractions, varying from 0.01 to 0.5. This indicates that a large spread of values are possible, depending on a variety of different factors, such as environment, jet speed and orientation angle with respect to the observer.

For the powerful sources, with $L_{1.4~\rm GHz} > 10^{25} \rm W \, Hz^{-1}$, we have found that a core fraction of $5 \times 10^{-4}$ is required to match the observed source counts (again, assuming a core spectral index of 0.0). This is significantly smaller than has been found for bright sources in several observational studies. For example, \citet{2011MNRAS.417..184B} studied a sample of 31 FRI galaxies with $S_{5~\rm GHz} > 55$~mJy (and in many cases $S_{5~\rm GHz} > 1$~Jy) and found that the median ratio of the core emission to the total emission was $\sim 0.06$.  This could be because spectral ageing effects, which are not included in the original simulation or our modification, are significant for these brighter sources. Spectral ageing would cause the spectrum of the extended emission to steepen with increasing frequency, so including it would require a higher core fraction to be included to fit the observed source counts and spectral index distribution. For example, if spectral ageing were to increase the average spectral index between 1.4 and 15~GHz of the extended emission to 0.85 (rather than the 0.75 currently assumed for all extended emission), then a core fraction of 0.04 would be required.
Other studies, however, have found core fractions for brighter sources which are significantly lower. For example, \citet{1988A&A...199...73G} found a core fraction which decreased exponentially with increasing total radio power; this underestimates the core fraction that we have found to be required at luminosities less than $ 10^{25} \rm W \, Hz^{-1}$, predicting a core fraction of 0.02 at $L_{1.4~\rm GHz} = 10^{24} \rm W \, Hz^{-1}$, but is consistent with our results at higher luminosities, predicting a core fraction of 0.002 at $L_{1.4~\rm GHz} = 10^{26} \rm W \, Hz^{-1}$. \citet{1990A&A...227..351D} find a similar exponential relationship.
The abrupt change in core fraction used in this model is clearly not realistic, but we found that more complicated functions were not warranted but the data.

It is unclear what might cause some radio galaxies to have a paucity of extended emission. The core emission from a source is a measure of the instantaneous power produced by the jet, while the total emission traces the total jet power integrated over time. These lower luminosity radio galaxies with relatively high core fractions could therefore be young sources, or could be intermittent sources with a short duty cycle (e.g.\ \citealt{1994cers.conf...17R,2009ApJ...698..840C}).
Alternatively, differences in the jet mechanism and/or environmental factors could be the cause.  \citet{2015A&A...576A..38B} suggest that FR0s have lower jet bulk speeds, $\Gamma$, than FRIs which cause their jets to be more subject to instabilities and entrainment, and therefore more likely to be prematurely disrupted. They speculate that a lower black hole spin may be the underlying cause of this lower jet speed, as a relationship between black hole spin and $\Gamma$ has been suggested by several authors \citep{2005ApJ...630L...5M,2012ApJ...759..114C}. \citet{2011MNRAS.417..184B}, however, find evidence that black hole spin is not as important as previously thought, and suggest that other factors, such as environmental density, the age of the radio sources and the black hole mass may play a more important role.

Indeed, there is evidence that the presence of a powerful core, indicating current AGN activity, is strongly dependent on the type of cluster in which a radio galaxy resides. \citet{2015MNRAS.453.1201H} studied a sample of 246 brightest cluster galaxies and found that a much higher proportion of `cool core' clusters hosted a radio galaxy with a powerful active core than `non-cool core' clusters; in their sample 60 per cent of `cool cores' compared to 12 per cent of `non-cool cores' have a distinguishable central engine, and 83 per cent of the `cool cores' have luminosities greater than $10^{23}~\rm W \, Hz^{-1}$ compared to just 5 per cent of non-cool cores. This suggests that the dominance of the core is strongly linked to the cluster state, so understanding the structures of faint radio galaxies is key to understanding how they relate to their environment.

Low-luminosity radio galaxies have not been studied in the way that the more luminous sources have, particularly at moderately high redshifts, and, as we have seen, models such as S$^3$ tend to assume they have less dominant cores than we have found necessary to reproduce the observed counts.
The lower luminosity sources therefore have less dominant jets relative to their cores than previously estimated from observations at lower frequencies.   This has implications for the way in which radio sources are able to influence their host galaxy and surrounding environment -- understanding this is therefore key to understanding AGN feedback and the interplay between star-formation and AGN.
High resolution radio observations of a sample of high-frequency selected sub-mJy radio galaxies which allow their structure to be resolved are required to investigate this further.

\section{Conclusions}\label{section:conclusions}

We have shown that by adding a flat-spectrum core component to the FRI sources in S$^3$, the derived 18~GHz source counts, which were previously a poor fit to the observed counts below $S_{18~\rm GHz} \sim 10$~mJy, are consistent with the 9C and 10C source counts. The observed spectral index distribution, which was a particularly poor fit to the original simulation, is also reproduced. We find that the observed counts are well fitted by assuming that the sources have cores with a spectral index $\alpha^{15.7}_{1.4} = 0.0$ and fraction of the total 1.4-GHz flux density which increases with decreasing 1.4-GHz luminosity from $5 \times 10^{-4}$ for $L_{1.4~\rm GHz} > 10^{25} \rm W \, Hz^{-1}$ to 0.31 for $L_{1.4~\rm GHz} < 10^{25} \rm W \, Hz^{-1}$.

These FRI sources with higher core fractions are therefore less dominated by extended emission, and may be equivalent to the compact FR0 sources found to dominate several recent surveys.

The physical interpretation of the paucity of extended emission in these radio galaxies is unclear; it could be due to a lower black hole spin, resulting in a lower jet speed, or differing jet lifetimes, or caused by environmental factors.

\section*{Acknowledgements}

We thank the referee for their comments on this manuscript. We thank Rob Fender for useful discussions. IHW and MJJ acknowledge the financial assistance of the South African SKA Project (SKA SA) towards this research (www.ska.ac.za). This research has made use of NASA's Astrophysics Data System. IHW thanks the South African Astronomical Observatory, where some of this work was carried out.

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