\section{Science Overview}

\subsection*{Background}


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% \textbf{Some history:}
% 
% \begin{itemize}
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% \item In 1943, Carl Seyfert discovered bright spots in the nuclei of some spiral galaxies. The spots were associated with broad emission lines. 
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% \item In the 1950s, Quasars were first detected.
% \pause
% \item During the 1960s,
% \begin{itemize}
%  \item Salpeter, Zel'dovich, and Lynden-Bell suggested that AGN are powered by accretion onto supermassive black holes (SMBH).
%  \item Lynden-Bell suggested a connection between distant quasars and AGN in nearby galaxies.
% \end{itemize}
% 
% \pause
% \item During the 1970s,  Faber and Jackson identified a relation between central $\sigma_*$ and spheroid luminosity.
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% \item Through the 1970s - 1980s, the connection between AGN, quasars, and SMBH accretion became better-accepted.
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% \end{itemize}
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\begin{frame}\frametitle{The $M_{BH}-\sigma_*$ relation}
\begin{itemize}
  \item Through the 1990s and early 2000s,
  \begin{itemize}
    \item It became evident that essentially \textit{all} galaxies and at least \textit{some} GCs contain nuclear SMBHs.
    \item The radio source Sag $A^*$ near the center of the MW was found to be associated with a $\sim10^6M_\odot$ SMBH.\pause
    \item Ferrarese \& Merritt and Gebhardt et al. discovered a (relatively) tight relationship between $M_{BH}$ and central $\sigma_*$  for the spheroidal component of local galaxies.

\[ \log\left(M_{BH}/M_\odot\right) = \alpha +  \beta\log\left(\sigma_*/\sigma_0 \right)\]
  \end{itemize}
\end{itemize}
\pause
A careful review by Tremaine et al. 2002, based on observations of 31 local galaxies, found
\[ \alpha= 8.13\pm0.06,\qquad\beta=4.02\pm0.32,\qquad \mbox{where } \sigma_0=200\mbox{ km/s} \]

\end{frame}
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\subsection*{The \msig Relation}

\begin{frame}
Summary plot from Tremaine et al. 2002
\begin{columns}[t]   
 \begin{column}{5.5cm}

\vspace{0.4cm}

\begin{list}{$\circ,\bullet$}%{\leftmargin=0cm}
  \item  masses determined from stellar kinematics.
\end{list}
\begin{list}{$\scriptstyle\triangle$}
 \item   masses determined from gas kinematics.
\end{list}
\begin{list}{$*$}
 \item  masses determined from maser kinematics.
\end{list}
\begin{list}{$\bullet$}
 \item  masses from  Gebhardt et al.
\end{list}
 
\begin{list}{- -}
 \item 1 $\sigma$ limit on best fit.
\end{list}

 \end{column}
\begin{column}{5.5cm}

\begin{center}
 \includegraphics[width=5.5cm]{./images/tremaine-et-al-summary.png}
 % tremaine-et-al-summary.png:
\end{center}

\end{column}
\end{columns}


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\begin{frame}\frametitle{Implications of the $M_{BH}-\sigma_*$ relation}

What causes $M_{BH}$ and $\sigma_*$ to be related? 

\vspace{0.25cm}

Some possibilities:

\begin{itemize}
 \item The SMBH and bulge form in the same potential well. They share an environment and history.
 \item The SMBH and bulge interact through feedback in such a way as to produce the relation.
 \item A combination of these.
\end{itemize}

\vspace{0.15cm}\pause

Analytic and numerical models successfully reproduce the relation using \textbf{different} assumptions.

\vspace{0.15cm}

Models disagree as to the evolution of the relation with cosmological time.


\end{frame}

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\begin{frame}\frametitle{Implications and Evolution of $M_{BH}-\sigma_*$}

Depending on the assumed initial conditions and the feedback mechanism used, there are three broad possibilities:

\vspace{0.25cm}

For a fixed value of $\sigma_*$,

\begin{enumerate}
 \item $M_{BH}$ increases with redshift; black holes develop more rapidly than spheroids at early times.\pause
 \item $M_{BH}$ decreases with redshift; spheroids initially grow more rapidly than black holes.\pause
 \item $M_{BH}$ is independent of redshift; the mechanisms which set the relation act very quickly. \pause
\end{enumerate}

\textbf{Note:} Analyzing \textit{deviations} from the local relation does not strongly constrain theoretical models\ldots
  

\end{frame}

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\begin{frame}\frametitle{Implications and Evolution of $M_{BH}-\sigma_*$}

Recall: \[ \log\left(M_{BH}/M_\odot\right) = \alpha +  \beta\log\left(\sigma_*/\sigma_0 \right)\]


\vspace{0.2cm}

The normalization, $\alpha$ and the slope, $\beta$ could independently vary with look-back time.  

\vspace{0.3cm}\pause

$\therefore \;$ Properly testing the evolution of $M_{BH}-\sigma_*$ requires the analysis of samples of galaxies in several narrow redshift bins. Otherwise, there could be degeneracies.  

\vspace{0.3cm}

Depending on the evolution of $\alpha$ and $\beta$, certain hypotheses could be discarded. For instance, models employing thermal AGN feedback predict that $\alpha$ evolves with time, while $\beta$ is independent of time.


\end{frame}

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\begin{frame}\frametitle{Observed \mbh\ Evolution}

Woo, et al. (2006,2008) have measured $M_{BH}$ and $\sigma_*$ for galaxies at $z\approx0.36$ and $z\approx0.57$ with fairly low-luminosity AGN.


\begin{columns}[t]   
 \begin{column}{5.5cm}

\begin{center}
 \includegraphics[width=5.5cm]{./images/Mbh-sigmaz.png}
 % Mbh-sigmaz.png: 822x753 pixel, 72dpi, 29.00x26.56 cm, bb=0 0 822 753
\end{center}

\end{column}
\begin{column}{5cm}

\begin{itemize}
 \item Sample sizes were too small to determine $\alpha$ or $\beta$.
 \item For fixed \sig, \mbh\ is larger. 
 \item A similar result was found by Shields et al., 2006.
 \item Is this just because these are AGN hosts?
\end{itemize}

\end{column}
\end{columns}

%Shields et al 2006 found similar results, although they used CO emission line width as a proxy for \sig.
\end{frame}

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\begin{frame}

\begin{itemize}
 \item Bennert et al. (2010) performed a detailed analysis of nearby AGN host galaxies (with AGN dim enough to measure \sig).
 \item Within the uncertainty, the local AGN relation agrees with local inactive galaxy relation, but has somewhat more scatter. 
\end{itemize}
\begin{center}
 \includegraphics[width=10cm]{./images/local-AGN.png}
 % local-AGN.png: 1415x710 pixel, 72dpi, 49.91x25.04 cm, bb=0 0 1415 710
\end{center}


\end{frame}

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\subsection{Research Motivation}

\begin{frame}\frametitle{Increasing z and Sample Sizes}

\begin{itemize}
 \item The work of Woo et al. only employed low-luminosity AGN.
 \item Expanding the variety of objects and the redshift range would be beneficial.\pause
 \item Hiner and Canalizo have begun studying \msig\ for a different class of objects: dust-reddened quasars.
\begin{itemize}
 \item The AGN appears to be significantly obscured by dust.
 \item The stellar population seems to exhibit little or no dust-extinction.
 \item Both \sig\ and \mbh\ can be measured as far as $z \approx 1$
 \item At least some of these objects appear to be remnants of recent mergers\ldots 
\end{itemize}
\end{itemize}

\end{frame}

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\begin{frame}\frametitle{Uncertainties}


\begin{itemize}
 \item Observations of galaxies at $z>0$ are needed in order to constrain galaxy formation and evolution models.
 \item Measuring $M_{BH}$ for distant galaxies can only be done if there is an associated AGN.
 \item There is strong evidence that AGN are triggered by galaxy mergers.
 \item Galaxy mergers also trigger enhanced star formation episodes (starbursts).  
 \item Star formation adds dust to the ISM.
 \item It is unclear how merger evolution and dust attenuation effect the measurement of $\sigma_*$\ldots 
\end{itemize}

\end{frame}

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\begin{frame}\frametitle{Uncertainties}


Previous $M_{BH}-\sigma_*$ simulation studies have done little to explain the evolution of $\sigma_*$ during a merger:

\begin{itemize}
 \item Simulators typically wait until galaxies have reached a steady state and \textit{then} measure $\sigma_*$ (300 Myr - 2 Gyr after final coalescence)\pause
 \item Simulators typically report the mean $\sigma_*$ from $\sim 100$ projections of the merged system. \pause
 \item To my knowledge, only one paper (Johansson et al., 2009) has documented the variation of the mean value of $\sigma_*$ in high-resolution merger simulations. 
 \begin{itemize}
  \item The time resolution of measurements was low (200 Myr).
  \item The anisotropy of the dispersion was not analyzed in depth.
  \item The analysis placed more emphasis on the evolution of $M_{BH}$.
 \end{itemize}

\end{itemize}


\end{frame}

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\begin{frame}\frametitle{Some Uncertainties}

\begin{itemize}
 \item Simulators (T.J. Cox and K. Dasyra) have noted that $\sigma_*$ can fluctuate significantly before reaching a steady value. 
\begin{itemize}
 \item but they haven't published a detailed account!
\end{itemize}
 \item Because of the variations, galaxy modelers consider $\sigma_*$ to be well-defined only for quiescent systems (just as temperature is only well-defined for systems in equilibrium) 
\end{itemize}\pause

Meanwhile, 

\begin{itemize}

\item Observers make measurements of $\sigma_*$ for systems which have not relaxed to a steady state.
 \begin{itemize}
  \item Thus far, there is no 100\% reliable observational method of identifying the dynamical state. 
 \end{itemize}
   
\end{itemize}

\end{frame}


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\begin{frame}\frametitle{Some Uncertainties}

Furthermore, 

\begin{itemize}

\item When measuring \sig\ in simulations, the velocities of the star particles within the half-\textit{mass} radius are used. 
\item Observers make flux-weighted measurements of \sig\ using the light from the half-\textit{light} radius.
\item Dust extinction, and AGN contamination could cause the simulators' measurement of \sig\ to differ from the observers' measurement. 
\end{itemize}

\end{frame}

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\begin{frame}\frametitle{Some Uncertainties}

The impact of time-variation, anisotropy, and dust-extinction on measurements of \sig\ has not yet been explored in depth.  
\vspace{0.2cm}

\textbf{My questions:}\pause

\begin{itemize}
 \item How significant are these effects?\pause
 \item Do these effects lead to random or systematic discrepancies in the measured vs. actual \sig?\pause
 \item Are these effects responsible for some of the scatter observed in the \msig\ relation?\pause
 \item Could understanding these effects allow observers to better interpret measurements of \sig?
\end{itemize}

\end{frame}


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