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Orphan of Destiny
Book 3 of the Youngest Templar series
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SPOILER ALERT: This book is the third book in a series and should be read after Keeper of the Grail and Trail of Fate.
Tristan and his companions—the fiery archer Robard Hode and the assassin maid Maryam—have escaped to England. But tragedy has occurred to Tristan's beloved abbey while they were on the Third Crusade, and Robard's home in Sherwood Forest suffers under the rule of the Sheriff of Nottingham. Many obstacles still prevent them from delivering the Holy Grail into safe hands. Tristan must defeat the evil Sir Hugh in one final battle. And he must learn the secret of his birth, a secret Richard the Lionheart and Eleanor of Aquitaine are willing to kill to protect!
The Youngest Templar Series:
More Books for Older Kids
Orphan of Destiny is the final book in the trilogy. I received a great deal of give and take from readers concerning the cliff hanger endings of the first two books. The percentage of complaints were pretty small compared to the number of supporters and about 90% of the people who complained immediately followed with "When is the next book out?"
I also got a kick out of a reader on Amazon.com who said the book was very well written except for the ending, which was 'totally a money making gimmick'. You know what, dude? Guilty. Writers want to make a living, sell books and keep readers coming back. Imagine!
So, now that all three books are here will you take the plunge? See what all the fuss is about? I hope so.
Download the Reading Guide.
A Reading Guide for Orphan of Destiny
This 4-page download is a great resource! An interview with Mike, some info about him and the book, a discussion guide, and a list of projects that span the curriculum, and a list of projects that span the curriculum in addition to Reading: Writing, Art, and History.
The Guide for The Youngest Templar: Orphan of Destiny was created by was created by Tracie Vaughn Zimmer, a reading specialist and children's author.
Keeper Of The Grail 2010-2011 MASL Readers Award Nominee Video
See what this young student from Missouri had to say about the very first book Keeper Of The Grail.
Michael P. Spradlin's critically acclaimed The Youngest Templar series arrives to a dramatic close with the action-packed Orphan of Destiny, where the intrigue and danger continue as Spradlin brings the Crusader era to life in Tristan's final, nail-biting adventure!
- John Dorian, International Business Times
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★ 2010-2011 MASL Readers Award Nominee
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SPOILER ALERT: This book is the third book in a series, and should be read after Keeper of the Grail and Trail of Fate. The following excerpt contains spoilers.
A well-traveled road led directly from the castle into Calais.
"Where to, squire?" Robard asked. His voice was strong and deep over the rushing wind and clatter of hooves. In the moonlight, Maryam clutched him tightly around the waist, her face buried in his shoulder. His relief at having her back and unhurt was evident in his tone and manner.
"Head for the docks. We need to acquire a ship or boat and cross the channel as quickly as we can," I answered.
"Acquire?" Maryam queried, a teasing tone in her voice.
"I do not welcome another sea voyage, but we cannot walk to England. My trick with the Captain's sword will not stay the castle door for long." I dug my heels into the horse's flank and pulled ahead of my friends. Angel ran before us, leading the way.
Robard and Maryam loved to make sport of my plans. It was their own fault, since they left all the thinking to me. Still, it was hard to blame them for being concerned. I had managed to get us into a number of dangerous situations. Yet, here we were, free again, at least temporarily.
Sir Hugh wasted little time. As the castle receded behind us, the sound of a loud horn cut through the darkness. We reined up and saw men atop the battlements waving torches back and forth. From the town below us, a bell sounded a few moments later and the shouts of men carried on the wind.
"What's happening?" Maryam asked.
"I don't know. Sir Hugh has sounded the alarm. The castle must have a way of alerting the village. If there are soldiers or Templars quartered there, we must be doubly careful!" We galloped away, and I feared our pursuers were close at hand. Had they managed to raise the gate?
Within minutes we reached the outskirts of Calais. There were few villagers about at this hour, and only the faintest trace of starlight guided our way.
"Which way?" Robard asked.
"Robard," I said, exasperated, "we need a boat. I believe boats are kept at or near the ocean."
"Don't get testy with me, squire," Robard muttered. I felt bad momentarily but I was trying to think. Something was telling me to avoid the village.
"Hold," I said, pulling the reins as my horse skidded to a stop. We had entered on a deserted street, lined by a few simple huts. A pathway between the structures led farther into the heart of the town.
"What's wrong?" Maryam asked.
"I did not count on Sir Hugh being able to sound a warning. No one here will know exactly what to look for, but they know the castle has raised an alarm. I'm wondering if—" My words were cut off by a whizzing sound, and I cried out as a crossbow bolt thunked into the pommel of my saddle. My horse jumped and bolted forward, and I nearly lost my grip.
"Go!" Robard yelled. He slapped reins and we darted forward, our horses churning up ground as the small huts flew by. Off to our right I could hear shouts of "after them!" and "this way!" I had no idea yet if our pursuers were mounted or on foot, but they were most definitely armed. I understood Robard's disdain of the crossbow. The distinctive twang of a bowstring and the flight of an arrow from a longbow made noise as it traveled through the air. At least it gave one a fighting chance to dodge or drop to the ground to avoid it. You never heard a crossbow bolt until it appeared, as if by magic, in the center of your chest.
"Stay low," Robard shouted, bending forward, hugging his mount's neck. I did the same and could swear I felt the air move as another bolt hummed by where my head had been moments before.
The hard ground turned to cobblestone as we entered Calais proper, and the clatter of hoofbeats thundered through the darkness. Soon, buildings lined both sides of the street and the noise of our escape echoed off the walls. Up ahead, I thought I saw movement and warned Robard to turn.
"LEFT, Robard! LEFT!" I shouted. He steered as I commanded down a side street.We were not getting closer to the docks by this route, and finding a boat seemed unlikely. Our abrupt turn gained us some distance on those following us, but it sounded as if several squads of men were moving through the town in an effort to surround us. I believed we were riding south, which would put us parallel to the coast, but I couldn't be sure. The streets were narrow and dark, and it was easy to get turned around.
We had nearly reached the southern edge of Calais, and through a break in the buildings I could see the ocean, and regained my bearings.
"Tristan?" Robard said.
"This way!" I gave rein and pulled ahead of him. Angel was barking madly in the dark, and the village dogs took up the chorus. We were making more noise than a regimento of Templars in full-scale battle. I turned my horse toward the ocean. Somewhere ahead, there must be a boat for us.
We darted and weaved through the streets and alleys. I could hear more horses and knew the longer we waited, the better the chances that Sir Hugh would arrive from the castle with even more men. I cursed my stupidity for heading straight to the village. We should have ridden north or south and found a boat along the coast somewhere. My eagerness to get away from him had clouded my judgment.
The moon peeked over the horizon to the northwest. It was late in the year, so it would stay low in the sky, but the extra light was a blessing and a curse.
"Hold," I said, and we pulled our horses to a stop.
"Why are we stopping?" Maryam asked.
"We need to get off these streets," I said. "With the moon rising we'll be seen, so we need to be quiet." I nudged my horse forward at a walk. "We need to head for the countryside. Find a place where we—"
"No," Robard said quietly.
"What?" I replied.
"I said no. We're getting a boat and getting out of this bloody country," he declared.
"Robard, that is not a good idea," I explained. "The alarm has been raised; they will be waiting at the docks—"
"Then I'll shoot them," he interrupted, shaking his bow at me.
"Robard, maybe Tristan is right—" Maryam said.
"Not tonight." Robard pointed over his shoulder toward the ocean. "England lies across that water. Home is so close I can almost smell it. I'll not wait another night. Not another minute. I will kill every King's Guard with my bare hands if I have to. But we sail tonight."
The moonlight played across Robard's face. It had turned to stone, and I could see it would be useless to argue.
My shoulders sagged as exhaustion hit me. I was so tired. My head still ached from being knocked unconscious when we had first been captured. I couldn't think. Angel growled from a few paces away, her nose working the air, and her head turned to look off toward the way we had come.
"Someone is coming," Maryam said.
"All right. Let's skirt the town; avoid the cobblestone streets where possible. We'll make less noise. We'll circle around to the docks. Perhaps they are not guarded yet," I said. But my words held little enthusiasm.
"Excellent," Robard said.
A few minutes of careful riding later, we rode back into the town, with the channel to our left. We stopped, momentarily, listening. It was strangely quiet. Perhaps we had temporarily eluded those chasing us. Could we have been lucky enough for them to lose our trail? Did they assume we had ridden away to the countryside?
"I don't hear anything. Do you?" Robard asked.
"Yes. I hear a voice. Telling me over and over that this is a very bad idea."
Robard snorted in reply. His mind was made up.
We walked the horses a few hundred yards farther into town, and up ahead I could see a single wooden wharf extending out into the harbor, with several small boats tied to it. Farther out, larger vessels bobbed gently at anchor. The waterfront was lined by a row of shops, inns and other buildings. They all were dark this time of night and their emptiness felt wrong. It was too quiet.
"Let's go the rest of the way on foot," I suggested. "We can tie the horses here, and if it's a trap, we may be able to recover them."
Robard did not disagree. We tied both of them to a nearby post and made our way toward freedom, keeping to the shadows as much as possible.
"Angel, lead," I said. As always, the little golden dog appeared to know exactly what I needed. She trotted about twenty paces ahead of us, cocking her head left and right, pausing occasionally and sniffing at the ground.
Robard held his bow at the ready, Maryam had drawn her daggers and my short sword rested comfortably in my hand. I could barely breathe as we crept forward, my eyes scanning every nook and cranny, any spot where a man with a crossbow might conceal himself.
I saw nothing.
We waited, keeping the dock in sight, hoping anyone hiding there might grow careless and reveal their presence.
"All clear," said Robard.
He stepped out of the shadows and crossed the street, the dock only a few paces away. Maryam followed closely, and then it was my turn.
As I ventured into the street, I felt something punch me in my right side. Worse than a punch—a punch would not hurt as much. I looked down at my right hip and was shocked to see a crossbow bolt protruding from it. The pain was instantaneous and immense.
"Beauseant!" I shouted, not knowing why I chose to utter the Templar battle cry. I tried to step forward, to warn Robard and Maryam, but my leg was not working correctly. Angel barked and I heard Maryam's ululating war cry and Robard's curse. His bow twanged and someone screamed. Then another cry and the sound of running feet. My vision swirled and I thought for a moment I was back in Acre, with Sir Thomas beside me.
"Sir Thomas commands…" I could not finish, for it hurt even to breathe. I saw Maryam's flashing daggers and heard a groan of anguish, and I believe someone died right in front of me.
Then I heard a familiar soft humming sound, coming from everywhere and nowhere all at once. I felt warm and strangely comforted by it. Nearby came the sounds of running feet and shouts of angry men. And as the ground rushed up to meet me, my last thought was, Please don't let me die in France.
End of Excerpt
Orphan of Destiny is available in the following formats:
ISBN: 13: 978-0399247651
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\section{Introduction}

The empirical evidence for the ubiquity of both stellar mass black holes (black hole mass $M_{\bullet}$
of ~\abt~$1-15\,M_{\odot}$) and supermassive black holes (SMBHs, $M_{\bullet}$~$>10^{5}~M_{\odot}$)
is well established. While it is estimated that there are about $10^7-10^9$
stellar-mass black holes in every galaxy \citep[e.g.,][]{ShapiroTeukolsky83,BrownBethe94},
every galactic bulge appears to host a SMBH. Moreover, the kinematically determined mass
of these SMBHs is correlated with the mass of the bulge, and even more strongly with the
central stellar velocity dispersion $\sigma$, the $M_{\bullet}-\sigma$ relation \citep{FerrareseMerritt00,gebhardtetal2000c,KormendyGebhardt01,Tremaine02}. Active galactic
nuclei (AGN), which have long been believed to be driven by accretion around SMBHs and
whose SMBH masses have been estimated from reverberation-mapping, are also consistent
with the $M_{\bullet}-\sigma$ relationship \cite[e.g.,][and references therein]{Wandel02,Bentz09}.
The corollary is that the nuclear activity is a phase (or more) in the life of (at least)
every galaxy with a bulge.

The $M_{\bullet}-\sigma$ relation has been extended down to black hole masses of \abt~$10^5\,M_{\odot}$
\citep{Barth05,GreeneHo06} by searching for central BHs within very low-luminosity AGN. Their
dynamical studies are an unambiguous verdict on the presence of central BHs in dwarf
ellipticals and very late-type spirals (e.g., NGC4395 by \citet{GreeneHo07} and references
therein). Even lower mass black holes have been inferred from non-dynamical methods for other
low-luminosity AGN \cite[e.g.,][]{Dong07}. In spite of considerable
efforts, however, evidence for black holes of still lower mass, \viz the intermediate-mass black
holes (IMBHs, of masses $10^2-10^4M_{\odot}$), is relatively sparse. Attempts to discover IMBHs
in globular clusters via their X-ray emission have been on for a long time,
\cite[e.g.,][]{BahcallOstriker75}, and although the recently discovered ultra-luminous
X-ray sources (ULXs) have been attributed to IMBHs \cite[e.g.,][]{ColbertMushotsky99},
this suggestion has also been contested \cite[e.g.,][]{Berghea08}.

Extrapolating the $M_{\bullet}-\sigma$ correlation down the mass scale predicts that IMBHs
can be found in stellar systems that have velocity dispersions of $<30$~km/sec,
clearly pointing to the globular clusters. Observational evidence for such black holes
are only a handful, however ({\it cf.} references in Table~\ref{tab:sampleclusters}).
Furthermore, theoretical results on IMBHs in globular clusters remain ambiguous, at best.
Some theories predict the necessity of most (if not all) Galactic
globular clusters to host central black holes \citep[e.g.,][]{MillerHamilton02},
while some argue for the impossibility of globular clusters to form
and/or retain black holes in their cores \citep[e.g.,][]{Favata04,KawakatuUmemura05}.
The importance of investigating the possibility of globular clusters hosting IMBHs
cannot be overestimated. While a central IMBH would clearly impact the evolution
of the globular cluster itself, more generally, IMBHs are crucial to link the
formation processeses of stellar-mass BHs and SMBHs, and could have served as
seeds for the growth of SMBHs. Extending the local BH mass function to the extreme
low end can help in understanding whether there is a minimum galaxy mass or
velocity dispersion below which BHs are unable to form or grow \citep[e.g.,][]{Bromley04}.
Globular clusters and galactic bulges are both `hot' stellar systems, and, since all large bulge
systems seem to have a central black hole, to the extent that a massive, bound
globular cluster can be viewed as a ``mini-bulge", it may be that every dense
stellar system (small or large) hosts a central black hole \citep{Gebhardt02}.
BHs at the low end of the mass ladder can be used as a constraint on theoretical
models with different predictions on the $M_{\bullet}-\sigma$ behaviour. For example, the
prediction that $M_{\bullet}-\sigma$ relation shall substantially steepen below $\sigma=150$ km/sec
\citep{Granato04} is not supported by the low-mass AGN sample \citep{Barth05}.
The question of IMBHs also has bearing on debates in cosmology, since the cosmic
mass-density of IMBHs could exceed that of SMBHs ($\O\approx 10^{-5.7}$), and
may even account for all the baryonic dark matter in the universe, with
$\O\approx 10^{-1.7}$ \citep{vanderMarel03}.

The few recent reports on the detection of central black holes
in some globular clusters seem to suggest that globular clusters do
follow the $M_{\bullet}-\sigma$ relation for SMBHs \citep{vanderMarel02,McLaughlin06,
Noyola08,Lanzoni07,Gebhardt02} and that these BHs represent the `true' IMBHs in
the mass range of $10^2-10^4\,M_{\odot}$. In this paper, we compile published discoveries
of central black holes in globular clusters and investigate the consistency of
the data with the $M_{\bullet}-\sigma$ and $M_{\bullet}-$luminosity relations. Using these
globular clusters as a constraint on the slope of the extended $M_{\bullet}-\sigma$
relation, we estimate the black hole masses for a sample of globular
clusters that are proposed to host IMBHs and discuss the implications.

\section{$M_{\bullet}-\sigma$ Correlation}
\label{sec:Msigma}

Although the $M_{\bullet}-\sigma$ relationship for galaxies is very well established, the
published estimates for the slope parameter $\b$ of the relationship span a
wide range (3.68 to 4.86), the reasons for this discrepancy discussed
by \cite{Tremaine02} and \cite{FerrareseFord05}. As a rough estimate from
this correlation, for a typical globular cluster with cenral dispersion
$\sigma_c$ of the order $10$ km/sec, the mass of the central black hole
would be $M_{\bullet} \sim 10^3\,M_{\odot}$. This roughly coincides with the estimate
from the Maggorian relation $M_{\bullet}$\abt~10$^{-3\pm 1}\,M$ \citep{Magorrian98},
and with the theoretical estimates of the formation of the central BH from the
initial $\sim 50 M_{\odot}$ seed by stellar/low-mass objects accretion
\citep{MillerHamilton02}, $M_{\bullet}$=10$^3\,M_{\odot}\times 10^{-(M_{\rm V}+10)/2.5}$.

\subsection{Constraints on the $M_{\bullet}-\sigma$ relation by globular clusters candidates}
\label{subsec:sigma_fits}

For investigation of the very low-end extrapolation of the $M_{\bullet}-\sigma$
relation, we take the globular clusters where the presence of the central
black hole was inferred from optical observations of either individual stars or by
using integrated light techniques. The data on the clusters are given in
Table~\ref{tab:sampleclusters}.

\begin{table*}
\begin{center}
\caption{Globular clusters with the reported central black holes}
\label{tab:sampleclusters}
\vskip 0.1in
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\rule[-3mm]{0mm}{8mm}
Cluster &Other    & $M_{\bullet}$ & $\sigma$     & $M_{\rm V}$ & Ref.\\
Name    &  Name   &  ($10^3\,M_{\odot}$)  & (km/sec) &    & \\
\hline
\rule[-3mm]{0mm}{8mm}NGC~104          & 47Tuc   &$1.0^{+0.5}_{-0.5}$  &$11.6\pm 0.8$&-9.42 &1\\
\rule[-3mm]{0mm}{8mm} NGC~5139$^{*}$   & $\o$ Cen&$40.0^{+7.5}_{-10.0}$&$23.0\pm 2.0$&-10.29&2\\
NGC6388$^{\dag}$                      &         &$5.7^{+5.7}_{-2.85}$ &$18.9\pm 3.6$&-9.42 &3\\
\rule[-3mm]{0mm}{8mm}NGC~7078$^{\ddag}$& M15     &$2.5^{+0.7}_{-0.8}$  &$14.1\pm 3.2$&-9.17 &4,5,6 \\
\rule[-3mm]{0mm}{8mm} G1 (M31)        & Mayal II&$18.0^{+5.0}_{-5.0}$ &$25.1\pm 1.7$&-10.94&7\\
\hline
\end{tabular}
\end{center}
\noindent
\vskip 5mm
{\it Key to columns:} (1)-(2) cluster identification number and name,
(3) BH mass $M_{\bullet}$ with error bars (where reported),
(4) central velocity dispersion, (5) V-band absolute magnitude, (6) references are the BH
measurement papers: (1) \citet{McLaughlin06}; (2) \citet{Noyola08};
(3) \citet{Lanzoni07}; (4) \citet{vanderMarel02}; (5) \citet{Gerssen02}; (6) \citet{Gerssen03};
(7) \citet{Gebhardt05}.\\
$^{*}$ this value has recently been reduced to the upper limit of $1.2\times 10^4\,M_{\odot}$
\citep{AndersonvanderMarel09}, see discussion in Sec.~\ref{subsec:regions}.\\
$^{\dag}$ a factor of two uncertainty has been assigned to this BH mass.\\
$^{\ddag}$  the reported masses for this cluster range from $1$ to
$9\times 10^3\,M_{\odot}$; the listed mass is the most probable value, see latest \citep{Kiselev08}.
\end{table*}

In Figure~\ref{fig:msigma} we plot the black hole masses and central velocity dispersions for
globular clusters (Table~\ref{tab:sampleclusters}), together with the sample of galaxies
with secure BH mass estimates available to date. The galaxy data consist mainly of a
sample of 49 galaxies \citep{Gultekin09} with directly dynamically-measured black hole
masses (called GRG sample hereafter). The galaxies included in their sample are only
elliptical or with classical bulges or psedobulges, and since a globular cluster can be
viewed as a `mini-bulge', we favour this sample. To the GRG sample we have added six
galaxies from \cite{Hu08}; the reason for their absence in GRG sample is unclear,
since their mass measurements are also dynamical, and the galaxies are either elliptical
or having pseudobluges. We have also added the latest estimates of the black hole mass
in NGC~4395 \citep{Peterson05} and Pox 52, the lowest-mass AGN to date \citep{Barth04}.
Though mass estimates for these two black holes are not from gas or stellar dynamics
(the reason why AGN, for example, were excluded from GRG sample), these measurements
were made by multiple methods and are considered to be quite reliable. The data for
these additional galaxies are given in Table~\ref{tab:addgalaxies} in Appendix~B.

We assume that there is an underlying relation of the form
\begin{equation}
y=\a +\b x\,,
\label{eq:basic}
\end{equation}
where $y=\log(M_{\bullet}/M_{\odot})$, $x=\log(\sigma_e/\sigma_0)$; $\sigma_0$ is some reference
value usually chosen to be 200 km/sec (it was noticed by \cite{Tremaine02}
that this choice reduces the uncertainties in the intercept $\a$), and $\sigma_e$
is the effective velocity dispersion, defined in \citet{Gultekin09} as the spatially
averaged, rms, line-of-sight stellar velocity within the effective radius $r_e$. It was
noticed by \citet{MerritFerrarese01} that  $\sigma_e$ might be expected to reflect the
depth of the stellar potential well more accurately than the central velocity dispersion,
$\sigma_c$. However, when this was not available, we have used $\sigma_c$ as, on average, there
is remarkably little difference between $\sigma_e$ and $\sigma_c$ \citep{MerritFerrarese01,Gultekin09}.
Many of the galaxies in the sample have assymetric quoted errors, but
for simplicity we assume here that the measurement errors are symmetric in both
parameters with root-mean-square (rms) values $\epsilon_{xi}$ and $\epsilon_{yi}$ for galaxy
(or cluster) $i$. In our sample we used the published bounds to the 1$\sigma$ range in
BH mass, and upper and lower limits to the dispersion\footnote{\footnotesize
Errors in $x$ and $y$ are assumed to be $(\log{\sigma_{\rm upper}}-
\log{\sigma_{\rm low}})/2$ and $(\log{M_{\bullet,\rm high}}-
\log{M_{\bullet,\rm low}})/2$, respectively. The measurement errors
in mass are added together with the intrinsic scatter, $\epsilon_0=0.4$,
in quadrature, using the best estimate of $\epsilon_0$ from GRG
sample.}. The goal is to estimate the
best-fit values of $\a$ and $\b$ and their associated uncertainties for the
total sample of galaxies and five globular clusters (using the symmetric
least-squares method).

\begin{figure*}[ht!]
\begin{center}
\epsfig{figure=SafonovaShastri_fig1.ps,width=0.5\textwidth,angle=-90}
\epsfig{figure=SafonovaShastri_fig2.ps,width=0.5\textwidth,angle=-90}
\caption{\small Mass of the central black hole $M_{\bullet}$ (in solar masses)
vs. velocity dispersion $\sigma\,(=\sigma_e/200)$ km/sec for galaxies and globular
clusters. Dotted line is the linear
regression fit for only galaxies and solid line is the fit including the globular
clusters. Dashed line is the 2-sigma error on the regression. Solid curved line is
the quadratic fit for GRG sample (see in the text). Single star is the most
recent estimate of the $\omega$~Cen black hole mass \citep{AndersonvanderMarel09}.
{\it Right}: Clearly seen the division of the plot into three distinct regions,
upper part is occupied by SMBHs, middle by MBHs with inclusion of N205 and IC342
upper limits, bottom by IMBHs. Filled triangles are the sample of low-mass
AGNs of \cite{GreeneHo06}. See discussion in Sec.~\ref{subsec:regions}.}
\label{fig:msigma}
\end{center}
\end{figure*}

Figure~\ref{fig:msigma} shows the correlation between $M_{\bullet}$ and the velocity
dispersion of the host. The best-fit linear relation for the sample with only
galaxies (designated ``Subsample") is
\begin{equation}
\log\left(\frac{M_{\bullet}}{M_{\odot}}\right)= ( 8.17\pm 0.06) + (4.16\pm 0.3)
\log\left(\frac{\sigma_e}{\sigma_0}\right)\,,
\label{eq:fit1}
\end{equation}
and the slope of the relation changes only slightly with inclusion of the
five globular clusters (``Full sample")
\begin{equation}
\log\left(\frac{M_{\bullet}}{M_{\odot}}\right)= (8.19 \pm 0.06) + (4.20\pm 0.2)
\log\left(\frac{\sigma_e}{\sigma_0}\right)\,.
\label{eq:fit2}
\end{equation}

These data are summarised and compared with the best results from \citet{Gultekin09}
in Table~\ref{tab:msigma_stats}.

\begin{table*}
\begin{center}
\caption{}
\label{tab:msigma_stats}
\vskip 0.1in
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Sample & $\a$  & $\b$  & $\chi^2$   &  $\chi^2/$dof  \\
\hline
Subsample & $8.17\pm 0.06$  & $4.16\pm 0.3$  & 50.9 & 0.85 \\
Full sample &$8.19\pm 0.06$ & $4.20\pm 0.2$ & 50.9 & 0.78 \\
GRG (TO2ind)$^{\dag}$ & $8.19\pm 0.06$ & $4.06\pm 0.37$ & ... &... \\
GRG best$^{\ddag}$    & $8.12\pm 0.08$  & $4.24\pm 0.41$ & ... & ...\\
\hline
\end{tabular}
\end{center}
\vskip 5mm
\noindent
$^{\dag}$ Method of \cite{Tremaine02} applied to a GRG sample without the
upper limits \citep{Gultekin09}. The intrinsic scatter is added in quadrature
to the measurements errors in the expression for $\chi^2$. \\
$^{\ddag}$ The best fit in \citet{Gultekin09}.
\end{table*}

The fact that globular clusters fit the $M_{\bullet}-\sigma$  relation is remarkable, and
rather puzzling, considering that the formation mechanisms for the central black
holes are believed to be different: the SMBHs in galaxies are hypothesized
to have formed through gas collapse and subsequent gas accretion,
while the central black holes in globular clusters are believed to have formed
through either collapse of a stellar cluster \citep[e.g.,][]{PortegiesZwartMcMillan02}
or through stellar (or low-mass remnants) accretion onto an
existing relatively massive black hole \citep{MillerHamilton02}.
However, both theories agree that
there may have been an initial seed, an IMBH of order $\sim 10^3 M_{\odot}$
for the case of galaxies, and a $\sim 50\,M_{\odot}$ black hole for the
case of globular clusters. The fact that all proposed BHs in globular
clusters fit the $M_{\bullet}-\sigma$ correlation suggests that there must be some
previously unrecognized connection between the formation and evolution
of globular clusters, galaxies and their central black holes.

\subsection{SMBHs to IMBHs through massive black holes}
\label{subsec:regions}

Apart from the remarkably consistent extrapolation of the $M_{\bullet}-\sigma$ relation down
to the very low end, the right panel in Figure~\ref{fig:msigma}
displays three distinct regions. The top right corner is populated by a well-known and
well-established sample of a SMBHs, which has a relatively sharply defined
low edge. It was proposed long ago that there might be a physically
determined lower limit [$>10^6M_{\odot}$] to the mass of a SMBH \citep{Haehnelt98},
and recently \citet{WehnerHarris06} argued that formation of a black hole is
strongly favoured above this limit. It was the need to determine the low
end of the SMBH mass function that started the active IMBH search. Elucidating
the demographics of low-mass BHs can provide the critical
input to test the theoretical models of quasar formation \citep{Haehnelt98}.
In particular, the low-mass cut-off in the BH mass function today
provides a constraint on the mass function of seed BHs. Models of
different seed masses predict different BH occupation fractions at the low
end of the mass ladder, ranging from some galaxies hosting tiny
($<10^4$~$M_{\bullet}$) BHs to virtually no central black holes below 60 km/sec (see discussion in
Sect.~4.2).

Dynamical studies present an unambiguous verdict on the existence of central black
holes in dwarf stellar systems, and these BHs can be properly named massive
black holes --- MBHs --- as opposed to their higher-mass counterparts,
with a range in masses of $\sim 10^4-10^6M_{\odot}$ and velocity dispersions
of $\sim 25-65$ km/sec. This region is flanked from the top by a few massive/supermassive
galaxies such as, for example, M32, Milky Way and Circinus with the lowest mass in
SMBH region of $1.7\times 10^6M_{\odot}$. It is populated by  well-established dwarfs,
such as NGC~4395 and POX52 (see Table~\ref{tab:addgalaxies}). The upper limits
for black holes in the galaxies IC342 and NGC~205 ($1.5\times 10^4 M_{\odot}$ from
\citet{Boeker99} and $2.2\times 10^4M_{\odot}$ from \citet{Valluri05}, respectively)
lie in this region as well. However, current dynamical techniques do not have
the spatial resolution needed to resolve the gravitational sphere
of influence of a low-mass ($\sim 10^5M_{\odot}$) BH outside of the Local Group, while even
local studies can only place upper limits (e.g. NGC~205), or reject the existence of
a BH altogether (M33). Therefore, the search is forced to
use AGN activity as a signature for the BH. The recently discovered SDSS DR4 sample of
dwarf Seyfert 1 nuclei galaxies, referred to herein as the sample of \cite{GreeneHo06},
may represent an upper envelope of the population of MBHs --- black holes in low-mass
galaxies. This sample has a median mass of $\laM_{\bullet}\rangle=1.3\times 10^6M_{\odot}$
\citep{GreeneHo06} with the lowest BH mass of $8\times 10^4M_{\odot}$, and the
host galaxies do belong to the low-mass (low-luminosity) population.
The broad-line AGN SDSS DR4 sample with mass range of $5\times 10^4-10^6M_{\odot}$
\citep{Dong07} brings the present census of these AGN MBHs up to 400.
However, since the majority of this MBH population are AGNs, being quite
compatible with the low-end extension of active SMBHs in their properties,
the question still remains as to whether normal dwarfs also have central BHs.
Furthermore, globular clusters G1 and $\o$~Cen, that lie at the lower end of the MBH
region, are now believed to be not genuine globular clusters, but
the cores of the accreted galaxies stripped by tidal forces
\citep[][and refs therein]{MackeyvandenBergh05}. As such, the central
black holes of G1 and $\o$~Cen are still {\it galactic} black holes,
and their masses of $\sim \mbox{few} \times 10^4\,M_{\odot}$ thus represent
the lowest limit for the massive {\it galactic} black holes. Incidentally,
the ratio of $M_{\bullet}$ to the total mass of $\o$~Cen is
much higher than the ``canonical" value of $\sim 0.3\%$, but if $\o$ Cen is the core
of an accreted dwarf, most of its mass would have been stripped during the tidal
evolution and, once corrected for that, a mass of $4\times 10^7\,M_{\odot}$ obtained
by modeling \citep{Noyola08}, puts the observed black hole near the $0.3\%$ value,
which suggests that when this galaxy was accreted, it already
possessed a central black hole. It should be noted that recently \citet{AndersonvanderMarel09}
reported new, reduced, values for both BH mass and velocity dispersion leave the
$\omega$ Cen black hole on the same $M_{\bullet}-\sigma$ relation, and in the same MBH region.

The other, ``genuine", globular clusters, such as M15, 47 Tuc and NGC~6388, represent
a third region of the `genuine' IMBH domain, narrowing the mass range of IMBHs to
$\sim 10^2-10^4M_{\odot}$.

Thus, the earlier existing gap in the BH `mass ladder' seems to be rapidly
filling up; with BHs smoothly populating the whole range from $1 M_{\odot}$ up to nearly
$10^{10}M_{\odot}$, with a clear distinction of mass ranges
between different stellar systems; stellar-mass black holes are loners
or in binary systems, IMBHs live in small stellar systems like GCs,
and massive black holes (MBH+SMBH) in the cores of galaxies. This
brings back the question of dynamical detection of BHs in low-mass non-active
stellar systems, with globular clusters being the best potential candidates.
Most of the Galactic globular clusters are close by, and while optical observations
are still difficult due to the extreme crowding in the centres, it may be
possible to discover BHs from radio and X-ray observations
and, in the future, from microlensing \citep{SafonovaStalin06}
and gravitational waves's observations.

\subsection{Black hole mass estimates in a sample of globular clusters}
\label{subsec:mass_estimates}

It was found that the $M_{\bullet}-\sigma$ relation is a powerful tool as it allows the
prediction of BH masses (which are difficult to measure directly) from
readily available galaxy parameters \citep{Lauer07}; for example, from a
single, low-resolution observation of a galaxy's velocity dispersion, its central BH mass
can be estimated with an accuracy of $\sim 30\%$ or better \citep{FerrareseMerritt00}.
Notably, BH masses measured by reverberation-mapping
and BH virial mass estimates for some local AGNs are broadly consistent
\citep{gebhardtetal2000c,GreeneHo06}. Based on the remarkable consistency of
the BH masses discovered in globular clusters described in the previous section,
we applied the $M_{\bullet}-\sigma$ relation to estimate the
masses of possible central black holes in some Galactic globular clusters.
Although the precise nature of this correlation is not yet understood, there may
be no limit to the range of velocity dispersions over which the $M_{\bullet}-\sigma$ relation can
apply \citep{BegelmanNath05}. We have applied the results of the Sec.~\ref{subsec:sigma_fits}
(Eq.~\ref{eq:fit2}) to estimate the masses of black holes for a sample of globular
clusters and presented the results in Table~\ref{tab:GCmasses}. The list of candidate
globular clusters grows continuously as different methods of detections are being
suggested. Our sample of Galactic GCs that may host a central black hole
(Table~\ref{tab:GCmasses}) was compiled on the basis of these different proposals.

Since high-centrally concentrated globular clusters and especially
core-collapsed clusters have long been proposed as harbouring central
black holes, we have included in our sample all Galactic core-collapsed
(or post-core-collapsed) clusters \citep{Trager95}. However,
this view has been challenged recently by \cite{Baumgardt05} who has argued
that, on the contrary, no core-collapsed clusters can harbour central black
holes, as they would quickly puff up the core by enhancing the rate of close
encounters, tending to prevent the core collapse and leaving an imprint of a
shallow cusp; in other words, the clusters with flat large cores and King
profiles outside would rather host a central black hole. This view was further
reinforced by \cite{Miocchi07}, who in addition suggested looking for
the extreme horizontal-branch (EHB) stars as a possible fingerprint of
the presence of an IMBH. However, \citet{Hurley07} issued a cautionary
note on using large core radius as an indicator of an IMBH presence, since
other factors, such as the presence of a stellar BH-BH binary in the
core, can flatten the measured luminosity profile and enlarge the core radius,
and that it is still too early to abandon the IMBH indicators used earlier,
such as the steepening of a M/L ratio in GC cores \citep{Gebhardt05}. In our
candidate sample (Table~\ref{tab:GCmasses}) we have included
candidates from \cite{Baumgardt05} and \cite{Miocchi07}.

It should be noted that in Table~\ref{tab:sampleclusters} of reported
BH cases both variants are included, G1 and $\o$ Cen having large cores and
M15 a collapsed core. NGC~6388 is the cluster for which both \cite{Miocchi07}
and \cite{Baumgardt05} agree on the existence of the central black hole.

Recently \citet{DrukierBailyn03} have suggested that high-velocity
stars in GCs cores can be used to reveal the central BHs and have
drawn a list of most probable clusters based on existing observations.
Based on radio emission as a possible test of the existence of IMBHs
in GCs, \citet{Maccarone04} suggested that the radio, rather than the
X-ray, observations can be a more successful test for a central
IMBH and have calculated expected radio flux densities for a few possible candidates.
One more technique to search for the massive BH-BH binary system in the core
of GCs is the use of exotic ejected binary systems, for which the cluster NGC~6752
is a very good candidate, having a binary pulsar system at 3.3
half-mass radii from the core and a high central mass-to-light ratio
\citep{Colpi03}. In Table~\ref{tab:GCmasses}, the last but one
column lists the reason for the selection of a cluster. Black hole masses
from these different predictions are listed in the last column of the Table.

\section{$M_{\bullet}$ -- Luminosity correlation}

The black hole mass in galaxies correlates linearly with the absolute
luminosity of the bulge of the host galaxy \citep{KormendyRichstone95,Magorrian98}.
We use here the extinction-corrected,  bulge (or total for ellipticals), V-band
luminosities calculated from absolute magnitudes, using
\begin{equation}
\log{(L_V/L_{\sun,V})}=0.4 (4.83-M_V)\,,
\end{equation}
where $M_V$ for the GRG sample is taken from \citet{Gultekin09}, for additional galaxies
from \cite{Lauer07} (see Table~\ref{tab:addgalaxies}), and for globular clusters from
the Harris catalog \citep{Harris96}. By the same fitting method as in Sec.~\ref{subsec:sigma_fits},
with the exception of using measurement errors only on mass
\cite[routine `fit' from][]{Press92}, the linear regression for our sample gives
\begin{equation}
\log\left(\frac{M_{\bullet}}{M_{\odot}}\right)=(8.89\pm 0.08) + (1.03\pm 0.04) \log\left(\frac{L_V}{10^{11} L_{\sun,V}}\right)\,.
\label{eq:M_luminosity}
\end{equation}
Comparison with other fits is given in the Table~\ref{tab:M_luminosity}.

\begin{table*}
\begin{center}
\caption{}
\label{tab:M_luminosity}
\vskip 0.1in
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Sample & $\a$  & $\b$  & $\chi^2$   &  $\chi^2/$dof  \\
\hline
Full sample &$8.89\pm 0.08$ & $1.03\pm 0.04$ & 68.7 & 1.6 \\
Subsample & $9.05\pm 0.10$  & $1.33\pm 0.11$  & 62.5 & 1.52 \\
GRG best$^{\ddag}$    & $8.95\pm 0.11$  & $1.11\pm 0.18$ & ... & ...\\
Tremaine sample$^{\dag}$ & $8.41\pm 0.11$ & $1.40\pm 0.17$ & ... &... \\
\hline
\end{tabular}
\end{center}
\vskip 5mm
\noindent
$^{\dag}$ Symmetric least-squares fit applied to the \cite{Tremaine02} sample
by \cite{Lauer07}. \\
$^{\ddag}$ The best fit in \citet{Gultekin09}.
\end{table*}

\begin{figure}[h!]
\centerline{
\epsfig{figure=SafonovaShastri_fig3.ps,width=0.5\textwidth,angle=-90}}
\caption{\small Mass of the central black hole $M_{\bullet}$ (in solar masses)
vs. V-band luminosity of the bulge (or cluster) for galaxies and globular
clusters. The original full sample is represented by the filled squares. The
clusters from Table~6 are represented by crosses. Solid line is the linear
regression fit for our full sample. Dashed lines are 3-sigma errors on the
regression fit. Clusters with masses inferred from Eq.~\ref{eq:fit2} (crosses)
fall on and around the best-fit line.}
\label{fig:m_luminosity}
\end{figure}

Since five reported globular clusters fit this correlation quite well (within the scatter),
we may expect that the sample of candidate globular clusters will follow the same. We
have plotted the calculated black hole masses for globular clusters from
the Table~\ref{tab:GCmasses}, denoted by crosses, against their V-band luminosities in
Fig.~\ref{fig:m_luminosity}. It should be noted from Table~\ref{tab:GCmasses}
that black hole masses depend strongly on velocity dispersion, with
$\sigma_c \lesssim 7$ km/sec giving a mass too low to be considered seriously.
It is most likely that only the black holes of masses $\gtrsim 100 \,M_{\odot}$
would remain at the centres, with the lighter ones ejected from the cluster due
to gravitational interactions \citep[e.g.,][]{MillerHamilton02}.
Thus, for the Fig.~\ref{fig:m_luminosity} we retained only the black holes
with masses $> 100\,M_{\odot}$. The solid line gives the best fit for our full sample
and the dashed lines give the 3-$\sigma$ confidence limits on the fit.

It seems intriguing that the $M_{\bullet}$--luminosity relation is preserved even for the
putative GC black holes. The larger scatter than for $M_{\bullet}-\sigma$ relation is also
observed, just like for the more massive counterparts. Since the $M_{\bullet}$ -- luminosity relation
is considered to be the reflection of $M_{\bullet}$ -- bulge mass relation, and GCs follow
different fundamental-plane relations than galaxies with classical bulges
\citep[e.g.,][and the numerous references cited therein]{WehnerHarris06}, it seems
strange that they shall continue on the same relation. At least for the
low-mass local AGN sample, \citet{Greene08} suggested that this relation will look
different, with a bias towards more massive host galaxies for a given BH mass. This relation
is also suspected to deviate in the regime of the most luminous elliptical galaxies,
with black hole masses of more than $10^9\,M_{\odot}$ \citep{Lauer07}. It was proposed
that, at that end, the bulge luminosity is a better predictor for a black hole mass
than velocity dispersion, whereas at the low-mass end (globular clusters),
the BH growth really depends on a (relatively) local stellar velocity dispersion,
as would be expected in a model where the BH accretion is fed by the capture of
individual stars \citep{MiraldaEscude05} and, moreover, the GC mass is susceptible
to the tidal erosion. When we applied the weighted least-squares fit
(neglecting measurement errors in both variables for simplicity, using
routine `fit' from \citet{Press92}) to the sample of only globular clusters
(five clusters from Table~\ref{tab:sampleclusters} plus candidate clusters from
Table~\ref{tab:addgalaxies}), the slope indeed increased, but not dramatically,
only to $1.355\pm 0.25$, approaching the slope for the sample of only galaxies.
Similar analysis was done by Miocchi (2007) for the sample of
globular clusters, where black hole masses were estimated by
constraining the parametric model of a globular cluster with IMBH from
observed central surface density profile and concentration parameter.
In their sample the black hole mass appears to be poorly correlated with
the V-band luminosity of a cluster, however it shall be noted that
black hole masses obtained by that method have huge uncertainties and
the sample used to obtain the correlation is quite small. Their
$M_{\bullet}-\sigma$ relation also has a very shallow slope of 1.2. When using
the $M_{\bullet}-\sigma$ relation for the globular cluster
sample, though, it should be borne in mind that the reported velocity
dispersion measurements for most of our candidate clusters may not be
representative of the (higher) actual values in the inner (unresolved)
regions of the clusters. Observations of globular clusters with higher
spatial resolution may provide better constraint on this low-end mass-ladder extension.
The latest example of under-estimation of the central velocity dispersion is the report
by \cite{Ibata09}, in which the globular cluster M54 (NGC~6715) is found to
host a $\sim 10^4\,M_{\odot}$ black hole; the previous central velocity dispersion
from, for example, \cite{PryorMeylan93} was $\sigma=14.2$ km/sec,
but \cite{Ibata09} report a value of  $\sigma=20.2$ km/sec.

\section{Discussion}

\subsection{Central BHs and evolution of globular clusters}

The fact that globular clusters fit the extrapolation of the $M_{\bullet}-\sigma$ and
$M_{\bullet}-$luminosity correlations for massive black holes raises the possibility that
there may be some previously unrecognized connection between the formation and
evolution of galaxies, globular clusters and their central black holes.

Just as the correlation between the BH mass and bulge properties of the galaxies
sheds light on their formation and evolution histories, the existence of BH in
globular clusters may help in understanding the evolution of globular clusters,
and how significantly, for instance, might the evolutionary effects influence the
survival of a cluster with a central IMBH.

Fig.~\ref{fig:2} shows $R_{\rm h}$, the radius that contains half of
the cluster stars in projection, plotted against $M_V$, the integrated luminosity,
for 146 Galactic globular clusters, highlighting the separate sets of GCs by
different symbols. The candidate set of \cite{Baumgardt05} is denoted by green
asterisks, the CC and post-CC candidates by red asterisks and the remaining
Galactic clusters are marked by blue triangles. Most theories agree that
present-day IMBHs most probably reside in massive, dense and concentrated
globular clusters, for example, the ones that
occupy the region near and under the straight line in Fig.~\ref{fig:2}, rather than
in loose and dissolving clusters, i.e., clusters from the so-called
`graveyard' \citep{MackeyvandenBergh05} --- the rightmost region in Fig.~\ref{fig:2}.
There is a
sharp edge to the main distribution of the clusters \citep[the Shapley line,][]{vandenBergh08b},
and only three Galactic clusters ($\o Cen$, M54 and NGC~2419),
and an M31 cluster G1 (marked by a black asterisk), lie above the upper envelope.
All of these globular clusters, including the rather
diffuse NGC~2419 (the uppermost left blue triangle), are believed to be the stripped cores of
now-defunct dwarf spheroidals accreted by our Galaxy. Though the recent work
by \cite{vandenBergh08a} indicates that this plot may be not the best way to
distinguish between globular clusters and dwarf spheroidals, (for example,
NGC~2419 may still be a genuine globular cluster, see refs in \citet{vandenBergh08a}),
it confirms $\o Cen$, M54 and G1(M31) to be ex-dwarfs on the basis of their
ellipticity. Several clusters, {\it viz.,} 47~Tuc, M15, NGC~6388 and NGC~6441, which is one of
the four brightest Galactic globular clusters, lie very close to this line.
The clustering of our candidates in a central area of the plot, in the region where
the clusters that are both `tight and bright' lie, may indicate
that dense and high-luminosity clusters are better candidates for central black
hole searches than diffuse and low-luminosity ones.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=90mm]{SafonovaShastri_fig4.eps}
\caption{$R_{h}$ vs $M_V$ for 146 Galactic globular clusters (data from
\citet{MackeyvandenBergh05}). The
Baumgardt's set is marked by red asterisks; the CC set by green
asterisks; the remaining clusters by blue triangles. The M31
globular cluster G1 is marked by a black asterisk, the measurement
for its $R_{\rm h}$ is taken from \cite{Barmby02}.
Above the slanted line the red asterisk marks $\o$ Cen, the green
asterisk M54.}
\label{fig:2}
\end{center}
\end{figure}

While some have argued on theoretical grounds that a central IMBH in the core
may increase the stability
of the cluster and thus its efficiency to withstand the tidal disruption for a longer
time during its passages through the Galaxy \citep[e.g.,][]{Hansen03}, the contrary
view also exists, that a central IMBH speeds up the dissolution of a star cluster, especially
if a cluster is surrounded by a tidal field \citep{Baumgardt04}. The observational
consequences of the latter view are that there may exist a population of `rogue'
IMBHs in the Galaxy (as MACHOS, for example), and that if such a cluster spirals
into the Galactic centre, the result would be an IMBH with a group of stars still
tidally bound to it (for example, it can explain the existence of a stellar complex
IRS~13E within 1~pc of the Galactic centre as the remains of a GC with an IMBH
\citep{Hansen03}). However, isolated IMBHs as MACHOs would have been detected by
microlensing surveys, which, incidentally, have ruled out the existence of MACHOs
in the mass range of $10^{-8}-100\,M_{\odot}$, and recently, at the 95\% confidence
level, MACHOs with masses $M > 43 \,M_{\odot}$ were excluded at the standard local halo density
\citep{Yoo04}, thus closing the MACHO mass window of $30-10^3\,M_{\odot}$. The second
suggestion that the Galactic central complex IRS~13E consists of an IMBH with few
stars still bound to it has also been ruled out \citep{Muzic08}.

Additional circumstantial evidence comes from the observations that clusters with high
central concentration index ($c=\log{r_{tidal}/r_{core}}$) appear to have retained
their low-mass stars, when compared to low-concentration clusters that show serious depletion.
A cluster loses low-mass stars due to evaporation, and mass segregation plays an important
role in this process by pushing the low-mass stars to the periphery of the cluster. However, it
is expected that IMBH in the globular cluster centre would quench mass segregation
\citep{Gill08}. The degree of mass segregation present was already applied to rule out
the presence of an IMBH in a low-concentration, small Galactic globular cluster
NGC~2298 \citep{Pasquato09}, which is also heavily depleted in low-mass stars
\citep{DeMarchi07}. Incidentally, NGC~2298 has a large core, which reinforces the
conclusions of \citet{Hurley07} that a large core is not
necessarily an indication of the presence of an IMBH in a globular cluster.

Thus, if the formation of a central black hole is a normal stage in the life of a
globular cluster, current observations favour that its presence would aid the survival of the
globular cluster in the field of the Galaxy.

\subsection{Model predictions; deviations from the log-linear relation}

Though the GRG sample statistically favours a log-linear relation, \cite{Barth05}
noticed that it is possible that the low-mass AGN sample does flatten the $M_{\bullet}-\sigma$
curve somewhat. They warn that while it is still too early for any
definitive conclusion,  it may be that AGNs follow a different $M_{\bullet}-\sigma$ relation altogether.
However, the sample of \citet{GreeneHo06} completely rules out the steepening of the slope
\citep{Barth05}. We have applied log-square and log-cubic fits to our
full sample in addition to the log-linear fit, and have calculated the AIC and BIC
factors for these fits (using \citet{RProject}).\footnote{\footnotesize
The idea behind the  Akaike Information Criterion \citep[AIC,][]{Akaike74} and
Bayesian Information Criterion \citep[BIC,][]{Schwarz78} is that we expect the
model with more parameters (e.g, log-quadratic) to achieve a higher maximized
log-likelihood that the model with fewer parameters (log-linear model). However,
it may be that the additional increase in the log-likelihood statistic, achieved
with more parameters, is not worth adding the additional parameters.
The smaller AIC values for the log-linear fit indicate that linear fit is better,
that is worth the additional parameters. However, since AIC is known to tend to overfit
sometimes, i.e., it may favour models with more parameters than they
should have, we have also calculated the BIC criteria, which imposes a larger penalty
for increase in the number of parameters than AIC.}
Table~\ref{tab:fits} shows the values for these parameters. It can be can seen from
the Table that log-linear relation provides a better fit to the $M_{\bullet}-\sigma$ relation
for the full sample. It should also be noted that the possible (low-significance)
log-quadratic fit to GRG sample, reported in \citet{Gultekin09} and shown by a
curved line in the left panel of Fig.~\ref{fig:msigma},
is ruled out once low-mass AGN and globular clusters are taken into account.

\begin{table}[h!]
\begin{center}
\caption{}
\label{tab:fits}
\vskip 0.1in
\begin{tabular}{|l|c|c|}
\hline
Full sample & AIC& BIC  \\
\hline
Log-linear$^{*}$       & 83.857 & 90.37 \\
Log-quadratic$^{\dag}$ & 85.518 & 94.22 \\
Log-cubic$^{\ddag}$    & 85.747 & 96.62 \\
\hline
\multicolumn{3}{l}{ } \\
\multicolumn{3}{l}{$^{*}$ $y=\a +\b x$, see Eq.~\ref{eq:basic},}\\
\multicolumn{3}{l}{$^{\dag}$ $y=\a +\b_1 x +\b_2 x^2$,}\\
\multicolumn{3}{l}{$^{\ddag}$ $y=\a +\b_1 x +\b_2 x^2 +\b_3 x^3$.} \\
\end{tabular}
\vskip 0.06in
\end{center}
\end{table}

The remarkable consistency of the $M_{\bullet}-\sigma$ correlation can be used as
a constraint on cosmological models making specific predictions for the low-mass
end of the $M_{\bullet}-\sigma$ relation. The low-mass cut-off in the BH mass function today
provides a constraint on the mass function of seed black holes for the SMBH.
If BH seeds are formed from the remnants of Population III stars and have masses
of $\sim 100\,M_{\odot}$, the so-called `light-seed model',
the merger tree calculations predict high BH occupation
fractions in low-mass galaxies \citep{Volonteri08},
though with such a steep slope of $M_{\bullet}-\sigma$ relation that
some galaxies hosting very tiny ($<10^4\,M_{\odot}$) black holes. The steepening of
the $M_{\bullet}-\sigma$ slope after $\sigma \sim 150$~km/sec is also predicted in the
hierarchical black hole growth scenario by \citet{Granato04}, where
supernova feedback becomes more efficient at slowing the AGN fueling rate.

Another prediction, proposed by \citet{Wyithe06},
was that this relation should flatten in the range between
70 to 380 km/sec, in other words, a log-quadratic relation providing a better fit
to the sample of SMBH masses and velocity dispersions. One of their predictions
was that in bulges with $\sigma \sim 10$ km/sec the minimum mass of the
black hole shall be $\sim 10^5 M_{\odot}$. The same flattening (at $20-50$ km/sec)
is predicted in the 'heavy-seed' model \citep{Volonteri08}. The different
`seed' cases show markedly different behaviour for the predicted BH occupation
fraction and $M_{\bullet}-\sigma$ relation at low masses, thus making globular clusters an
ideal laboratory to differentiate between the models.

\section{Conclusions}

We extend the $M_{\bullet}-\sigma$ relationship for galaxies to lower black hole masses
using black holes discovered in globular clusters.
The reported masses of black holes in the centres of globular clusters
M15, 47~Tuc, $\omega$~Cen, NGC~6388 and G1 are consistent with the linear extrapolation
of the $M_{\bullet}-\sigma$ relationship for galaxies to the low-mass end.
Using this extrapolated relationship, we have estimated the masses of putative
black holes in a sample of globular clusters, and find that these clusters
are consistent with the $M_{\bullet}-$luminosity relationship as well.

In the extended $M_{\bullet}-\sigma$ plot, points corresponding to different types of
stellar systems occupy distinct regions, suggesting that black hole masses of
\abt~few~$\times~10^{4}~M_{\odot}$ represent the {\it lowest} limit for the central
black holes  of galaxies.  Masses of the central black holes that are below this limit
correspond to the globular cluster domain (keeping in mind that G1 and
$\omega$~Cen are believed to be tidally stripped dwarf galaxies and not
genuine globular clusters).

The consistency of black hole masses in globular clusters with the
extrapolated $M_{\bullet}-\sigma$ and $M_{\bullet}-$luminosity relationships reinforces
the idea that globular clusters harbour IMBHs in their centres.
The central black holes of globular clusters place even stronger constraints
than low-luminosity AGNs on theoretical models of supermassive black hole growth
and evolution. If black holes in globular clusters do exist, they will rule out
models that predict either steepening or flattening of the $M_{\bullet}-\sigma$ relation
the low-mass region.

redpajama_set_name: RedPajamaArXiv


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In this edition you can read how Mexico City's New International Airport, known as the 'Airport of the Future,' is a great example of such digital representations made from integrated technologies. The Consortium IUYET, involved in the construction of the airport and a connecting railroad, used a wide array of laser scanning, GNSS and digital measurement tools to produce 3D models resulting in a safer and smarter facility.
ZOM, a leading residential developer in the U.S., discovered how construction documentation from Multivista is a simple and highly efficient process with online accessiblity. For its latest development, a luxury apartment complex in Miami, ZOM was able to digitalise operations and share the valuable progression data to the entire ecosystem of capital partners, architects, contractors, inspectors and other stakeholders involved in the project.
Our HxGN SmartNet, the GNSS correction services built on the world's largest reference station network, is bringing the construction industry closer to achieving its full digitalisation potential. Recognising efficiency and productivity gains, contractors are able to operate in complete Digital Realities connected to their stakeholders.
With the inspiration and desire to pursue what is possible in the future, you are now empowered to reach that next level of Digital Realities.
Advancing industries. Progressing technologies. Evolving business. This is what we're dedicated to, and we look forward to having you along with us for this journey. Enjoy your read.
Alessandro Nuzzo, Product Line Manager for Mobile Mapping at Leica Geosystems, explains new technology.
Two combines the comfort and confidence of visual images with the accuracy of a point cloud at vehicle speed together into a GIS-enabled interface with semi-automatic extraction tools.


for the end of the year completion.
Chancel rotted roof structure repairs are completed.
Wood plate is cut, marked for attachments, and lifted to the roof for installation.
Perlins and girders are replaced with new members.
Bell tower belfry roof is cleaned and assed for damages. Debris is removed.
Bell tower copper cross is stripped before gilding is applied.
Exterior stone scaling, tooling, and pointing continue.
BCA makes punch list inspections of the work that has been completed.
Precast stones arrive on site; are cut and installed.
glazing on the stained glass windows.
Sealant on the protective glazing is positive for asbestos and abatement begins.
Installation of the t-bars that hold the protective glazing begins.
Templates are made so that the new protective glazing can be produced to fit adequately.


much has changed from the iPhone 6s and 6s Plus. But that's definitely not the case. There's a Home button you can customize, a handy Portrait mode on the dual-camera iPhone 7 Plus and more. And Apple's updates to iOS 10 have added even more features to the phone.
Here's a look at how to make the most of some of the best features you'll find in the iPhone 7 and iPhone 7 Plus, along with a refresher on some other iPhone tips, such as adding widgets to your lock screen and using the phone's 3D Touch features. Already playing around with the iOS 11 public beta? Check our our iOS 11 tips as well.
One of the first things you'll notice with the iPhone 7 — well, maybe right after that missing headphone jack — is the fact that the Home button doesn't move at all. Instead, it's a trackpad-like cutout that responds to when you press on it. The Home button uses haptic feedback to simulate the feel of a button.
You can adjust the Home button to three different levels of feedback to find the one that feels most natural to your finger. Simply go to Settings General Home Button to find the right level of feedback.
No moving parts on your Home button means the method for forcing an iPhone restart changes with the iPhone 7 and 7 Plus. Instead of holding down the Home button and power button simultaneously as you did with previous iPhones, now you press and hold the power and volume buttons at the same time. It takes some getting used to, especially if you're iPhone user with a long muscle memory, but it's a pretty simple tip to master once you know where to press.