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\title{Modeling AGN Feedback}
\author{Otho Ulrich}
\maketitle

\begin{abstract}
    Active Galactic Nuclei (AGN) are believed to be intricately involved with the evolution of their host galaxies through a process called AGN feedback.
    The mechanisms by which this occurs are not well-understood.
    It has been known for some time that the population of high-luminosity AGN, associated with large supermassive black holes, peaked during the early universe, and are extinct in the modern universe.
    AGN activity in the universe peaked around the same time as galactic star formation, and while this correlation is not completely understood, astronomers consider it a strong possibility that AGN play an important role in the regulation of star formation rates.
    Refining modeling methods will be more useful as observational resolution is increased by future telescope missions.
    AGN feedback may be responsible for quenching cold stellar winds, thus reducing star formation rates, and is needed to reproduce the observed intergalactic medium.
    Chaotic cold accretion is a likely mechanism by which AGN feedback occurs, allowing the AGN to ``cycle'' through a process of heating and cooling that reaches equilibrium with the host galaxy, until available cold gasses are consumed.
    Modeling AGN feedback presents significant challenges, but has improved upon observational predictions derived from the \LCDM\ cosmology-based Millenium Simulation.
    Only a few subclasses of AGN have been studied regarding their feedback mechanisms, and with only the most rudimentary first-principle approaches, but the necessity of including AGN feedback to correctly predict colors and luminosities of galaxy mergers and quasars seems increasingly likely.
    


\end{abstract}


%─────────────
\section{Introduction}
    \label{sec:intro}
    Quasars are the most luminous objects in the cosmos ($10^{12}-10^{15}$ \Lo.
    In 1964, Zel’dovich and Novikov described for the first time the luminosity of a quasar emerging from the accretion of matter by a supermassive black hole (SMBH). 
    \cite{koristafeedback}
    We now know that SMBHs on the order of $10^6$ - $10^9$ \Mo\ are common at the center of galaxies, and when their accretion process results in strong luminosities across the electromagnetic spectrum, we call these Active Galactic Nuclei (AGN).
    \cite{2017arXiv170306889H}
    \cite{maoz2007astrophysics}
    Gas is readily available in the central region, shed by stars during their evolution, and from tidal disruptions caused by the SMBH.
    The Eddington luminosity $L_E$ describes the luminosity necessary to induce radiation-driven outward matter flows, and for pure ionized hydrogen, 
    \begin{equation}
        \centering
        L_E=\frac{4\pi cGMm_p}{\sigma_T}\approx1.3\times10^{38}\textrm{ergs s}^{-1}\frac{M}{M_\odot}.
    \end{equation}
    Quasars are AGN radiating near or above their Eddington luminosities, making this an important measure of their brightness, and at $>10^{45}\textrm{ergs s}^{-1}$ they can outshine their entire host galaxy!
    For a $10^9$ \Mo black hole to maintain its Eddington luminosity, it must accrete $40$~\Mo per year.
    Central black holes in present-day galaxies apparently accrete at medium-to-low rates compared to rates needed to produce $L_E$, and observational studies show that quasars were much more common in the past, with their activity having peaked about 10 Gyr ago.
    \cite{maoz2007astrophysics}

    \begin{figure}
        \centering
        \includegraphics[width=.72\textwidth]{CenA_xray-opt-radio.jpg}
        \caption{Centaurus A (NGC 5128), a nearby radio galaxy whose active galactic nucleus ejects a relativistic jet with discernible emission in X-ray and radio wavelengths.
        This galaxy has a supermassive black hole equivalent to 55 million \Mo.
        A galaxy collision is suspected to be the cause of increased star formation and nuclear activity. \cite{2006ApJ...645.1092Q}}
        \label{fig:CenA}
    \end{figure}

    \subsection{Cosmology}
        \label{subsec:cosmo}
        Cosmology will not be covered in this work, but it is important to define a few terms.
        Many models of galaxy formation begin with the \LCDM\ cosmological structure predicted by the Millenium Run or other spatial structure simulation.
        \LCDM\ cosmology is the ``standard model'' of cosmology that includes the cosmological constant $\Lambda$ that defines the rate of expansion of the universe and cold dark matter (CDM), which is gravitationally significant but otherwise non-interacting and non-colliding.
        The Millenium Run and its following iterations are N-body simulations that predict the evolution of the spatial distribution of matter in the universe.
        It is considered a (successful) test of the \LCDM\ cosmology because it strongly coincides with the observed structure of the cosmos, and data from the iterations of the run are stored such that models can be built on top of them to predict observational quantities as needed.
        The density of a region is characterized by its halo mass, a measure of the mass distribution of dark matter halos, and therefore of the overall matter density in a region.
        \cite {2005Natur.435..629S}

    \subsection*{A note of Caution}
        \label{subsec:caution}
        AGN are energetically capable of regulating star formation through a number of suggested processes, but it is uncertain what caused the observed attenuation of star formation and what role AGN played in it.
        The timescales of feeding and feedback mechanisms are also uncertain.
        Great care must be taken when interpretting new data, as the AGN and stellar formation relationship may have phases, or may not exist at all. 
        \cite{2017arXiv170306889H}        

%─────────────
\section{AGN May Regulate Galaxy Evolution}
    \label{sec:galevol}
    For some time, astronomers have been aware that AGN and host galaxy evolution are correlated.
    The strong coupling of black hole mass with velocity dispersion in the surrounding galactic bulge was one of the first hints at this relationship, going back to 1998.
    \cite{koristafeedback} 
    \cite{2016AN....337..410T}
    In most massive galaxies, galaxy formation models require the injection of momentum by an AGN into the surrounding gasses in order to reproduce the low rate of cooling observed in galaxy clusters and the inefficiency of star formation in massive galaxy haloes.
    It is widely believed that the electromagnetic radiation from AGN regulates the rate of star formation in the host galaxy.
    Stellar feedback processes, such as supernovae, are also present but do not fully account for observations.
    Figure~\ref{fig:stellarhalo} demonstrates the necessity of including AGN feedback to predict stellar mass-halo mass ratios.
    \cite{2017arXiv170306889H}
    Furthermore, the high-mass end of the galaxy stellar mass function is over-predicted by modern simulations, indicating a phenomenon to regulate stellar formation is necessary, and AGN feedback is a strong candidate to fill this role.
    \cite{2016AN....337..410T}

    \begin{figure}
    \centering
        \includegraphics[width=.7\textwidth]{halomassstellarmass.pdf}
        \includegraphics[width=.6\textwidth]{starformbyz.pdf}
        \includegraphics[width=.38\textwidth]{quasarsbyz.pdf}
        \caption{Above: AGN feedback is necessary to predict stellar mass-halo mass ratios. Stellar formation feedback helps reproduce the proper ratios at low halo masses, but does not sufficiently account for the regulation of stellar formation at high halo masses. \cite{2017arXiv170306889H}
        Below Left: Star formation rate as a function of redshift z, i.e., age of universe. Bottom Right: Quasar density as a function of the same. Star formation and quasar density both peak about 11 Gyrs ago. \cite{koristafeedback}}
        \label{fig:stellarhalo}
    \end{figure}

    The mechanisms used by AGN feedback are under debate, and the discovery process is still disparate.
    X-ray astronomy has detected signatures from powerful disk winds in quasars, which are believed responsible for feedback effects during high-luminosity modes of the AGN.
    These winds have been observed close to the accretion disk, but are likely to have strong effects over galactic-scale distances.
    A connection has also been observed between one of these powerful accretion disk winds and a molecular outflow with infrared emission in a nearby galaxy, IRAS F11119+3257.
    This object is likely the result of a merger between two galaxies; mergers are an expected common mode of igniting Eddington luminous quasars, and are dicussed in Section~\ref{sec:mergers}.
    It is expected that improved resolution from future X-ray observatories, specifically ASTRO-H and Athena, will give a better picture of these outflows.
    \cite{2016AN....337..410T}

    Observations reveal regularities in galactic structure not predicted by the physics in current models. Initial conditions and the growth of CDM structure correctly predict the absorption by intergalactic medium density fluctuations, suggesting that the missing physics may lie with the baryons.
    \cite{2006ApJS..163....1H}
    As noted earlier, black hole mass of the central SMBH and velocity dispersion in the bulge of a galaxy are strongly correlated.
    Bulges are understood to result from galactic mergers of 2 or more massive galaxies, and these mergers have become a primary galactic evolutionary process used in the attempt to model AGN feedback.

\section{Modeling AGN Feedback in Galactic Mergers}
    \label{sec:mergers}
    Elliptical bulges are a characteristic feature of galaxies having undergone a merger.
    The \LCDM\ cosmology predicts ubiquitous mergers, so bulge formation occurs easily in these simulations.
    Semi-analytic methods (SAMs) are a set of analytic models that are applied on top of the dark matter halos predicted by a simulation, such as the Millenium Run.
    SAMs lump all bulges under the label ``spheroid'', then allow a disk to form around the spheroid from subsequent accretion of gas; all mergers above a given mass ratio result in spheroids.
    The galaxy morphology is defined by the spheroid to disk mass ratio.
    This approach reproduces the relationship between morphological type and color, color-magnitude relation, and observed populations of galaxy morphologies.
    SAMs also reproduces the number density of spheroids for high-luminosity galaxies, but over-predicts the number density among low-luminosity galaxies, and does not distinguish pseudobulges at all.
    There are several possibilities for this error: it may be introduced when computing the halo merger rates to stellar galaxy mergers; pseudobulges might be covering up already-existing bulges; mergers can result in pseudobulges; or classical bulge formation may be less efficient than currently thought.
    \cite{2016ASSL..418..317B}

    Historical simulations have produced galaxies with mass overly-concentrated at the center and with over-large stellar spheroids. This is a result of ``overcooling''.
    \cite{2016ASSL..418..317B}
    \cite{2016AN....337..410T}
    \cite{2016A&ARv..24...10T}
    Baryons cool rapidly, resulting in dense concentrations of stars and gas.
    The galaxies undergo multiple mergers, and each time the baryons transfer orbital angular momentum to the dark matter of the accreting halo.
    The dense baryons arrive at the center of the halo with almost no angular momentum, resulting in the classic sign of the ``angular momentum catastrophe''.
    Stellar feedback is a promising avenue to solve the cooling problem but takes places on a scale much too small to be resolved in cosmological simulations, so only global trends can be modelled.
    Current observational resolution presents the same issue.
    Stellar feedback is also not sufficient to reproduce small bulges in Milky Way-like massive disk galaxies, so this model either needs to be improved or AGN feedback is needed.
    \cite{2016ASSL..418..317B}

    AGN feedback may be responsible for quenching these cooling winds. Figure~\ref{fig:cycle} shows one hypothesized cycle over which AGN feedback occurs, and the flow of fuelling gasses that feed the AGN and stellar populations. This is known as th

    \begin{figure}
        \centering
        \includegraphics[width=.4\textwidth]{gasreservoir.pdf}
        \includegraphics[width=.55\textwidth]{feedbackcycle.pdf}
        \caption{
            Left:
            Schematic illustrating the fuel supply relationship between galaxy and black hole growth.
            Gas in the reservoir is replenished during a galaxy merger, from interstellar material, or recycled internal galactic material.
            AGN fuel must lose sufficient angular momentum to fall deep into the gravitational well.
            Both processes reduce the availability of fuel by ionizing, heating, shocking, and expelling material, but they can have both positive and negative impacts on fuel availability for the other process.
            \cite{2017arXiv170306889H}
            Right:
            Schematic of the ``cosmic cycle'' that plays out between galaxy formation and evolution regulated by black hole growth in galaxy mergers.
            Galaxies in the modern universe typically contain dead quasars.
            Mergers and other sources of inward gas flows trigger black hole growth through accretion, leading to strong luminosities, which lead to AGN feedback and the possible continuation of the cycle at each iteration.
            \cite{2006ApJS..163....1H}
        }
        \label{fig:cycle}
    \end{figure}

        \cite{2016A&ARv..24...10T}


    \subsection{Dwarf Galaxy Mergers}
        \cite{2016ASSL..418..317B}





    


\section{Color}
    \label{sec:color}



%─────────────
\section{Quasar Feedback Simulations}
\label{sec:feedbacksims}




    One of the 
    It is strongly believed by cosmologists that 




%─────────────
\section{Conclusion}
    \label{sec:conclusion}

    \cite{2005Natur.435..629S}

    \cite{springelfeedback}

\printbibliography

\end{document}
