\input{preface} %\include{preface} \chapter{Bound HII regions and Young Massive Protoclusters} \label{ch:ympc} \section{Preface} During a visit from Eli Bressert, we discussed methods of identifying the precursors to young massive clusters. A central idea was that the primary unbinding energy comes from ionized gas, so that if a region could remain bound against the pressure provided by ionized gas, it would proceed to high star formation efficiency. This notion resulted in two papers: the theory paper \verb|\citep{Bressert2012}| and the observational paper \verb|\citep{Ginsburg2012a}|. The observational paper, which summarizes the population of proto-YMCs discovered in the BGPS, is reproduced here. Since this paper is a Letter, a great deal of the work that went in to this chapter is hidden in a few short phrases. In particular, the search for distances to the candidate source occupied an enormous amount of time and will be the limiting factor in future searches for candidate proto-clusters. Since its publication, parts of the proposed follow-up work were carried out by another group. At the end of this chapter, I incorporate their new data to enhance our results and re-measure the Cluster Formation Rate $1 < CFR < 3$ \permyr ($1-\sigma$) more accurately. \subsection{Abstract} We search the $\lambda=1.1$ mm Bolocam Galactic Plane Survey for clumps containing sufficient mass to form $\sim10^4~\msun$ star clusters. %by identifying %compact ($r\lesssim2.5$ pc) massive ($M_{\rm clump}>10^4$ \msun) dust clumps. \ncandidates\ candidate massive proto-clusters are identified in the first Galactic quadrant outside of the central kiloparsec. This sample is complete to clumps with mass M$_{\rm clump}>\mmin$ and radius $r\lesssim2.5$ pc. The overall Galactic massive cluster formation rate is $CFR({\rm M}_{\rm cluster}>10^4) \lesssim \CFR\ \permyr$, which is in agreement with the rates inferred from Galactic open clusters and M31 massive clusters. We find that all massive proto-clusters in the first quadrant are actively forming massive stars and place an upper limit of $\tau_{starless}10^4$ \msun) in the process of forming from a dense gas cloud. In \verb|\citet{Bressert2012}|, we examine the theoretical properties of MPCs: MPCs are assumed to form from massive, cold starless clumps analagous to pre-stellar cores \verb|\citep{Williams2000}|. In this paper, we refer to two classes of objects: starless MPCs, which have very low luminosity and do not contain OB stars, and MPCs, which are gas-rich but have already formed OB stars. The only currently known starless MPC is G0.253+0.016, which lies within the dense central molecular zone and is subject to greater environmental stresses than similar objects in the Galactic plane \verb|\citep{Longmore2012}|. Because massive clusters contain many massive stars, at some point during their evolution ionization pressure will prevail over protostellar outflows as the dominant feedback mechanism. Other sources of feedback are less than ionization pressure up until the first supernova explosion \verb|\citep{Bressert2012}|. These proto-clusters must have masses M$_{\rm clump}>{\rm M}_{*}/SFE$ \footnote{We define a star formation efficiency $SFE={\rm M}_{\rm *,final} / {\rm M}_{\rm gas,initial}$.}, or about $3\ee{4}$ \msun\ for an assumed SFE=30\% (an upper limit on the star formation efficiency), confined in a radius $r\lesssim2.5$ pc, in order to remain bound against ionization feedback. These properties motivate our search for proto-clusters in the Bolocam Galactic Plane Survey \citep[BGPS;][ \url{http://irsa.ipac.caltech.edu/data/BOLOCAM_GPS/}]{Aguirre2011}. The distinction between relatively short-lived `open clusters' and long-lived ($t\gtrsim1$ Gyr) bound clusters occurs at about $10^4$ \msun \verb|\citep{PortegiesZwart2010}|. Clusters with ${\rm M}_{\rm cluster} < 1\ee{4} \msun$~will be destroyed by interactions with giant molecular clouds over the course of a few hundred million years after they have dispersed their gas \verb|\citep{Kruijssen2011}|, while clusters with ${\rm M}_{\rm cluster}\gtrsim10^4 \msun$ may survive $\gtrsim 1$ Gyr. Closer to the Galactic center, within approximately a kiloparsec, all clusters will be destroyed on shorter timescales by strong tidal forces or interactions with molecular clouds. %Because the lower-mass clusters are destroyed on shorter %timescales, it is difficult to get a complete census of their population; %assessing their birth rate may be the best way to determine their overall %population. In the Galaxy, there are few known massive clusters. \verb|\citet{PortegiesZwart2010}| catalogs a few of them, of which NGC 3603, Trumpler 14, and Westerlund 1 and 2 are the likely descendants of the objects we investigate. These clusters have $r_{eff} \lesssim 1$ pc, $M\sim10^4$ \msun, and ages $t\lesssim4$ Myr. We present a census of their ancestral analogs. % Bound open clusters and massive clusters may predominantly form from clumps with % gravitational escape speeds greater than the sound-speed in photo-ionized gas. % \S\ 2 uses the BGPS to identify % candidate dense, massive clumps which may be progenitors to young massive % clusters. Any clump for which M$_{\rm clump} \times {\rm SFE}(30\%) > 10^4$ % \msun\ is considered to be a young massive proto-cluster (MPC). \ncandidates\ % candidates are sufficiently massive to produce clusters similar to NGC 3603. % \S\ 4 discusses these results and \S\ 5 provides concluding remarks. \section{Observations and Analysis} \label{sec:ympcobservations} \subsection{The Bolocam Galactic Plane Survey} \begin{figure*} \includegraphics[width=7in]{{figures_chboundhii/candidates_galacticplot_26.0kpc_10kmsun}.png} \caption{ \label{fig:galplot} Plot of the massive proto-cluster (MPC) candidates overlaid on the Galactic plane. %Only sources with $M>1000 \msun$ are included; above %this cut %The symbol size is proportional to the log of the source mass. The green circle represents the galactic center, and the yellow $\odot$ is the Sun. A 15 kpc radius disc centered on the Galactic Center indicates the approximate extent of Galactic star formation. The white region indicates the coverage of the Bolocam Galactic Plane survey and our source selection limits based on distance and longitude. The inner cutoff (light grey) is the nearby incompleteness limit set by the Bolocam spatial filtering; the catalog includes sources but is incomplete in this region. The red dashed circle traces the solar circle. Blue filled circles represent initial candidates that passed the mass-cutoff criterion $M(20K)>\mmin$; red stars are those with $M(20K) > 3\ee{4} \msun$. In the legend, $M_4$ means mass in units of $10^4 \msun$. %Empty squares represent flux-cut candidates that failed the mass cutoff %criterion. %The diamonds are sources from the \verb|\citet{Faundez2004}| SIMBA survey %of southern IRAS sources subject to the same cutoffs applied to the Bolocam %data: filled (green) sources have $M>\mmin$. The central yellow star is the %Galactic Center. The empty stars are massive clusters %\verb|\citep{PortegiesZwart2010}|. %\todome{Add legend for size-mass} % Done } \end{figure*} The BGPS is a 1.1 mm survey of the first quadrant of the Galactic plane in the range $-0.5 < b < 0.5$ with resolution $\sim33\arcsec$ sensitive to a maximum spatial scale of $\sim120\arcsec$ \verb|\citep{Aguirre2011,Ginsburg2012}|. The BGPS `Bolocat' v1.0 catalog includes sources identified by a watershed decomposition algorithm and flux measurements within apertures of radius 20\arcsec, 40\arcsec, and 60\arcsec\ \verb|\citep{Rosolowsky2010}|. We searched the BGPS for candidate MPCs in the 1st quadrant ($6 < \ell < 90$; 5991 sources). The inner 6 degrees of the Galaxy are excluded because physical conditions are significantly different from those in the rest of the galaxy \verb|\citep{YusefZadeh2009}| and the BGPS is confusion-limited in that region. \subsection{Source Selection \& Completeness} \label{sec:selection} We identify a flux-limited sample by setting our search criteria to include all sources with ${\rm M}_{\rm clump}>10^4$ \msun\ in a 20\arcsec\ radius out to 26 kpc, or a physical radius of 2.5 pc at that distance. The radius cutoff is motivated by completeness and physical considerations: the cutoff of 26 kpc includes the entire star forming disk in our targeted longitudes, and $r=2.5$ pc corresponds to the radius at which a $3\ee{4}$ \msun\ mass has an escape speed $v_{esc}=10$ \kms, i.e. ionized gas will be bound. The maximum radius and minimum mass imply a minimum mean density $\bar{n}=6\times10^3~\percc$, which implies a maximum free-fall time $t_{ff}<0.65$~Myr. %These limitations guide our analysis in Section \verb|\ref{sec:discussion}|. Using the Bolocat v1.0 catalog, we first set a flux limit on the sample by assuming the maximum distance of $d=26$ kpc and imposing a mass cutoff of ${\rm M}_{\rm clump}\geq10^4$ \msun\ inside a 20\arcsec\ (2.5 pc) radius aperture. Following equation 19 in \verb|\citet{Aguirre2011}|: \begin{equation} {\rm M}_{\rm gas}\approx 14.3 \left( e^{13.0/T_d}-1 \right) \left({S_\nu\over 1\; {\rm Jy}} \right) \left(\frac{D}{{\rm 1~kpc}}\right)^{2} \msun \end{equation} and assuming $T_{dust}=20$K, the implied flux cutoff is 1.13 Jy \footnote{As per \verb|\citet{Rosolowsky2010}|, \verb|\citet{Aguirre2011}|, and \verb|\citet{Ginsburg2012}|, a factor of 1.5 calibration correction and 1.46 aperture correction are required for the 20\arcsec\ radius aperture fluxes reported in the catalog. These factors have been applied to the data. }, above which \nsample\ `flux-cutoff' candidates were selected in the Bolocat v1.0 catalog. Cutoffs of 4.3 Jy for the 40\arcsec\ and 10.2 Jy for the 60\arcsec\ Bolocat v1.0 apertures were used to select more nearby candidates inside the same physical radius, but no sources were selected based on these larger apertures. %By measuring flux within an aperture, we are measuring the mass within a given %radius, which means that the source may be substantially smaller than we %assume. The identified sources may therefore have higher escape velocities %than the minimum $\sim10~\kms$ required. % redundant? We applied a $M_{\rm clump} > 10^4$ \msun\ cutoff at %the maximum distance of 17.5 kpc; we are therefore complete to a progenitor %mass of $1\times10^4$ \msun. The BGPS is insensitive to scales larger than 120\arcsec\ \verb|\citep[][]{Ginsburg2012}|\footnote{\verb|\citet{Ginsburg2012}| presents v2.0 of the BGPS}. As a result, the survey is incomplete below a distance $$D_{min} = \mindist \left(\frac{r_{cluster}}{2.5 \textrm{pc}}\right) \textrm{kpc} $$ from the Sun. Within this radius, alternate methods must be sought to determine the total mass within $r_{cluster} < \rcluster$ pc. Although the sample is incomplete for $D < \mindist$ kpc, sources that have sufficient mass despite the 120\arcsec\ spatial filtering are included. %We are %able to identify some sources within this cutoff distance because they have %enough mass in a smaller radius, but we are not complete at %$D3\times10^4$ \msun, though % there were a handful with $M>10^4 \msun$. The masses were computed assuming a temperature $T_{dust}=20$K, opacity $\kappa_{271.1 GHz} = 0.0114~\mathrm{cm}^2 \mathrm{g}^{-1}$, and gas-to-dust ratio of 100 \verb|\citep{Aguirre2011}| \footnote{$T_{dust}=20$K is more appropriate for a typical pre-star-forming clump than an evolved HII-region hosting one \verb|\citep[e.g.]{Dunham2010}|. However, because we are interested in cold progenitors as well as actively forming clusters, the selection is based on $T_{dust}=20$K, which is more inclusive. }. The mass estimate drops by a factor of $2.38$ if the temperature assumed is doubled to $T_{dust}=40$K. \verb|\citet{Ginsburg2011}| notes that significant free-free contamination, as high as 80\%, is possible for some 1.1 mm sources, so the selected candidates may prove to be more moderate-mass and evolved proto-clusters. We used the NRAO VLA Archive Survey \verb|\citep[NVAS;][]{Crossley2008}| to estimate the free-free contamination for the sample. For most sources, the free-free contamination inferred from the VLA observations is small ($<20\%$), but for a subset the contamination was $\sim20-35\%$ assuming that the free-free emission is optically thin. Corrected masses using the measured free-free contamination and higher dust temperatures are listed in Table \verb|\ref{tab:candidates}|; these are reasonable lower limits on the total mass of these regions. All of the contamination estimates are technically lower limits both because of the assumption that the free-free emission is optically thin and because the VLA filters out large-scale flux. However, in most cases, the emission is likely to be dominated by optically thin emission \citep[evolved HII regions tend to be optically thin and bright, while compact HII regions are optically thick but relatively faint;][]{Keto2002} and for most sources VLA C or D-array observations were used, and at 3.6 and 6 cm the largest angular scale recovered is 180-300 \arcsec, greater than the largest angular scale in the BGPS. Applying a cutoff of M$_{\rm clump} > 10^4$ \msun\ left \ncandidates\ protocluster candidates out of the original \nsample. The more stringent cut M$_{\rm clump} > 10^4 / SFE \approx 3\ee{4}$ \msun\ leaves only \nMPC\ MPCs . % All of the \nsample\ % `flux-cutoff' candidates with $M>10^3$ \msun\ are shown in \figref{fig:galplot} % providing context of their location in the Galaxy. The final candidate list contains only sources with $M(20K)>10^4 \msun$ (the completeness limit; see Table \verb|\ref{tab:candidates}|). The table lists their physical properties, their literature distance, their mass (assuming $T_{dust}=20 \textrm{~and~} 40 K$ and a free-free subtracted lower-limit) , %\todome{Discuss varying dust opacity? Martin et al 2011} % Ignored. Unnecessary. and their inferred escape speed ($v_{esc} = \sqrt{2 G M(20K) / r}$) assuming a radius equal to the aperture size at that distance. The table also includes measurements of the IRAS luminosity in the 60 and 100 \um\ bands within the source aperture. %The literature search %revealed that all candidates are known massive-star-forming regions. \subsection{Source Separation} These \ncandidates\ candidates include some overlapping sources. There are two clumps in W51 separated by about 1.5 pc and 4.5 \kms\ along the line of sight that are each independently massive enough to be classified as MPCs, but are only discussed as a single entity because they are likely to merge if their three-dimensional separation is similar to their projected distance. The candidates in W49 are more widely separated, about 4.4 pc and 7 \kms\ along the line of sight, but could still merge. Additionally, 9 of the \ncandidates\ are within 8.7 kpc, so the mass estimates are lower limits. These are promising candidates for follow-up, but cannot be considered complete for population studies. If our radius restriction is dropped to 1.5 pc, the minimum complete distance drops to 5.2 kpc and the three lowest-mass sources in Table \verb|\ref{tab:candidates}| no longer qualify, but otherwise the source list remains unchanged. Our analysis is therefore robust to the selection criteria used. %(except the W51 pair, which meets %the selection criteria despite its proximity). % Not really interesting? % \subsection{Line Widths} % To back up the claim that these proto-clusters cannot be unbound by ionization % pressure, we examine the line widths in dense gas tracers. Using a tracer that % measures the internal motions of the gas in the gravitational potential, we % expect the approximately gaussian line-width to represent the quasi-equilibrium % state of the gas (i.e., if the line width is changing, it is doing so slowly % relative to the star formation process). Because the line widths are much % larger than the sound speed in the neutral gas, the observed clouds must be % gravitationally bound, otherwise they would expand and their linewidths would % drop to the sound speed on a dynamical timescale. % %\todojohn{This is in keeping with results on GMCs, i.e. that they are in equilibrium. % %Is there a better way to state it? Are there other results / theoretical arguments that % %should be cited?} % % Heterodyne observations of HCO$^+$ 3-2 and N$_2$H$^+$ 3-2 data from % \verb|\citet{Schlingman2011}| are presented in Table \verb|\ref{tab:candidates}|. With % critical densities $\gtrsim 2\ee{6}$ \percc, these both trace dense gas and therefore % are limited to the proto-cluster region. However, HCO$^+$ has frequently been % observed in self-absorption, so the N$_2$H$^+$ widths are more reliable. % We report the FWHM of single-component fits. In order to mitigate the effects % of self-absorption on the line fitting, we report HCO$^+$ line widths fitted by % ignoring the central self-absorbed pixels; the channel selection was done by % eye. % All of the candidates selected as proto-massive-cluster candidates have % $v_{internal} \approx v_{esc} > v_{ionized}$, confirming their candidacy. %In Table 1 we provide a grading scheme to quantify the quality of the %candidates. Candidates associated with a grade of {\bf A} will form a $\gtrsim %10^4$ \msun\ cluster, even if $T_{dust}=40$K and SFE = 30\%, where it's mass is %reduced from the estimates shown in Table 1 by a factor of 2.38. The two latter %grades, {\bf B} and {\bf C}, follow the same assumptions and the candidates %masses will fall down to $\sim 10^4$ \msun\ and $<10^4$ \msun, respectively. % \subsection{Nearby Candidates} % \label{sec:nearcand} % Because the BGPS is insensitive to large angular scales, we must resort to % other methods for determining protocluster masses in nearby star-forming % regions. % The strongest candidates within 5.8 kpc are M17, NGC 7538, W3, S255, W43, W33, G34.15, and others? While these % regions are all known to be forming massive stars and have total gas reservoirs % with $M>10^5$\msun, their large spatial extents mean that they are all more likely % to form OB associations than bound clusters. However, some are likely to be MPs... %In the 3-6 kpc range, W43, W33 %For example, in the W3 region, no clumps have velocity dispersions %$\sigma_{FWHM} > 6$ \kms, implying that none can keep ionized gas bound %\verb|\citep{Bieging2011}|. % We searched the BGPS for candidate MPCs in the 1st quadrant ($6^o < \ell < % 90^o$). Using the Bolocat catalog we marked sources with flux densities in a % 20\arcsec\ aperture that yield a mass $M_{\rm clump}\geq 3\times 10^{4}$ \msun\ % at a distance of 17.5 kpc or less ($20\arcsec\ = 1.7 $ pc at 17.5 kpc) % assuming $T_{dust}=20$K. We applied a $M_{\rm clump} \times {\rm SFE}(30\%) > % 10^4$ \msun\ cutoff at the maximum distance of 17.5 kpc; we are therefore % complete to a progenitor mass of $3\times10^4$\msun. These criteria led to a % flux-density cutoff of 3.2 Jy, above which 16 candidates were detected in the % Bolocat catalog. Distances to these candidates were determined via a % literature search. The final candidate list is given in Table 1 along with % their physical properties of measured line widths from N$_2$H+, their % literature distance, their mass (assuming $T_{dust}=20 K$), and their % inferred escape speed ($v_{esc} = \sqrt{2 G M / r}$) assuming a radius equal % to the aperture size at that distance. The literature search also revealed % that all of our candidates are known star-forming regions, so our list % contains no contaminants. % % With distance determinations to these candidates, we were able to compute % masses assuming a temperature $T_{dust}=20$K, opacity \verb|\citep{Aguirre2010}|, % and gas-to-dust ratio of 100 \footnote{$T_{dust}=20$K is more appropriate for % a typical pre-star-forming clump than an evolved HII-region hosting one % \verb|\citep[e.g.][]{Dunham2009}|. However, because we are interested in cold % progenitors as well as actively forming clusters, we estimate the masses of % the cluster progenitor candidates using $T_{dust}=20$K or $T_{dust}=40$K to % reflect whether the environment is cold and quiescent or actively forming % stars. } % The mass estimate drops by a factor $2.38$ if the temperature assumed is % doubled to $T_{dust}=40$K. Additionally, for more nearby sources, larger % apertures (corresponding to the same physical radius) were used to include % more source flux. Applying a cutoff of M$_{\rm clump} \times {\rm SFE}(30\%) % > 10^4$ \msun\ left 2 MPCs out of the 16. All of the 16 flux-cutoff % candidates are shown in Figure \verb|\ref{fig:galplot}| providing context on where % they are in the Galaxy. % % In Table 1 we provide a grading scheme to quantify the quality of the candidates. Candidates associated with a grade of {\bf A} will form a $\gtrsim 10^4$ \msun\ cluster, even if $T_{dust}=40$K and SFE = 30\%, where it's mass is reduced from the estimates shown in Table 1 by a factor of 2.38. The two latter grades, {\bf B} and {\bf C}, follow the same assumptions and the candidates masses will fall down to $\sim 10^3$ \msun\ and $<10^3$ \msun, respectively. %\subsection{IRAS luminosities} %We can and should derive IRAS luminosities for the candidates (this is trivial) %and compare them to the IRAS luminosity function in the GP. We can then %extrapolate the observations to the southern hemisphere and be TRULY complete. \section{Results} % \subsection{Proto-Cluster Mass Function} % \choppingblock % In order to measure a mass function, we need better detection statistics than % are provided by our \nMPC\ MPCs. We note that our observations are complete to % $M>5000\msun$ in the range $5.8 < D < 12.4$ kpc \todome{Is the 5000 \msun\ % cutoff used anywhere else? I don't think so}. In this range, there are % \ncomplete\ candidates, which follow a mass function $\alpha=\plaw\pm\plawerr$ % \footnote{Computed using the \verb|\citet{Clauset2009}| MLE as implemented at % \url{http://code.google.com/p/agpy/wiki/PowerLaw}}. If these candidates represent proto-clusters, they should % follow a Schechter function with a cutoff near $10^4$ \msun\ % \verb|\citep{PortegiesZwart2010}|. However, the distribution is more consistent with % a power law $\alpha=2$ than a Schechter function with a cutoff $M<5\times{10^5} % \msun$. Above this cutoff, the Schecter function and power-law are % indistinguishable for our sample. \todome{Discuss implications? Not if % chopped} % unnecessary comment % The mass function of \emph{all} of our candidates independent of % mass and distance is consistent with a power-law with $\alpha=1.8\pm0.1$ and % completeness cutoff 800 \msun, but we don't believe this is a fair description % of the observations because of the varying sensitivity with distance. \subsection{Cluster formation rate} \label{sec:cfr} The massive clumps in Table \verb|\ref{tab:candidates}| can be used to constrain the Galactic formation rate of massive clusters (MCs) above \mmin\ if we assume that the number of observed proto-clusters is a representative sample. The region surveyed covers a fraction of the surface area of the Galaxy $f_{observed}=A_{survey} / A_{Galaxy} \approx \obsfrac\%$ assuming the star forming disk has a radius of 15 kpc\footnote{The observed fraction of the galaxy changes to 21\% if we only include the area within the solar circle as discussed in \S \verb|\ref{sec:discussion}|.}. %The fraction observed is also %about 28\% if we assume the star-forming disk %truncates at 13.5 instead of 15 kpc \verb|\citep{Kennicutt2012}|.}. The cumulative cluster formation rate above a cluster mass ${\rm M}_{cl}$ is given by $$CFR(>{\rm M}_{cl}) = \frac{N_{MPC}}{\tau_{SF} f_{observed}}$$ where $ \tau_{SF} \approx 2$\ Myr is the assumed cluster formation timescale \footnote{$\tau_{SF}$, the time from the start of star formation until gas expulsion, is a poorly understood quantity, but is reasonably constrained to be $\gtrsim1$~Myr from the age spread in the Orion Nebula cluster \verb|\citep{Hillenbrand1997}| and $\lesssim10$~Myr because the most massive stars will go supernova by that time.}. % $v_{esc}$ is the escape speed from radius $R$ and $f_A \sim 0.1$ is the % projected area filling-factor of dense star-forming gas in the clump. Dense % cores may survive for $f_A$ crossing-times before colliding. %The cumulative %cluster formation rate is given by %$$ %CFR (>M_{cl}) = %{{f_A N_{MPC}(>M) [SFE ]V_{esc} } % \over % { 2 R f_{observed} }} %$$ %where $f_A = 0.1$, $V_{esc} $= 10 %\kms , $R = \rcluster$ pc, and $\tau_{SF} = 2$ Myr. With the measured $N_{MPC}({\rm M}_{\rm cluster}>10^4\msun) = \nMPC $\ proto-clusters, we infer a Galactic formation rate $$CFR \lesssim \CFR \left(\frac{\tau_{SF}}{2 ~\textrm{Myr}}\right)^{-1} \textrm{~Myr}^{-1}$$ This cluster formation rate is statistically weak, with Poisson error of about 3.5 \permyr\ and can be improved with more complete surveys \verb|\citep[e.g., Hi-Gal,][]{Molinari2010}|. This formation rate is an upper limit because all of the estimated masses are upper limits as discussed in Section \verb|\ref{sec:selection}|. \subsection{Comparison to Clusters in Andromeda} %Comparison to Andromeda or direct measurements should provide a prediction of %the number of clusters in the largest (two?) mass bins. Do our observations %agree with such a prediction? % %If YES, the implication is that cluster formation proceeds rapidly and %forms massive, dense, proto-cluster "cores" before actually forming the %cluster. %If NO, cluster formation is SLOW and accretion onto the cluster after the %initial formation may continue and increase cluster mass by factors $>2$ (less %than that, it doesn't really matter). In this case, predicting the cluster %formation rate from protoclusters requires completeness down to smaller mass - %i.e., we need to be able to observe the cluster `seeds' in addition to the dense %pre-clusters. We use cluster observations in M31 from \verb|\citet{Vansevicius2009}| to infer the massive cluster formation rate in M31. They observe 2 clusters with ${\rm M}_{\rm cluster}>10^4\msun$ and ages $<10$ Myr in 15\% of the M31 star-forming disk. The implied cluster formation rate in Andromeda is $\dot{N_{cl}} = N_{cl}/0.15 / (10 ~\mathrm{Myr}) \approx 1.3$ \permyr. Given M31's total star formation rate $\sim 5\times$ lower than the Galactic rate \citep[Andromeda $\mdot=0.4$, Milky Way $\mdot=2$ \msun \permyr;][]{Barmby2006,Chomiuk2011}, the predicted Galactic cluster formation rate is $\dot{N_{cl}}(MW) = 5~ \dot{N_{cl}}(M31) = 6.5$ \permyr \citep[assuming the CFR scales linearly with the SFR; ][]{Bastian2008}. %Given our assumed star formation timescale $\tau_{SF}$, the expected %present-day number of clusters $N_{cl}(MW) = (6.5 \textrm{~MC~}\permyr) (\tau_{SF}) = 13$ %clusters in the Galaxy. Using the mass cutoff of $3\times10^4$ \msun, we %detect \nMPC\ MPCs, implying there are \nMPCtot\ MPCs in the galaxy. The scaled-up Andromeda cluster formation rate matches the observed Galactic cluster formation rate. The samples are small, but as a sanity check, the agreement is comforting. % \choppingblock % The agreement between the M31-based % prediction and our observations is (un?) remarkable, considering that Poisson % statistics alone imply a $>50\%$ uncertainty in each of the cluster counts % produced above. % We present a CFR function dependent on the local surface density of gas in a % galaxy $\Sigma_{\rm gas}$ (normalized by $\Sigma_0 = Value$), the survival time % of the cluster $\tau$, and the initial mass of the cluster, $M_{init}$. We assume % that it has a functional form % $$ CFR = A \biggr[ {{\tau} \over {t_{10}}} \biggr] ^{\alpha} \biggr[ {{M_{init}} \over {M_3}} \biggr] ^{\beta} \biggr[ {{\Sigma_{\rm gas}} \over {\Sigma_0}} \biggr] ^{\gamma} $$ % in units of number of clusters forming per $10^6$ years (= 1 Myr) per square kpc. % Here $t_{10}$ is in units fo 10 Myr, and $M_3$ is in units of $10^3$ \msun . From % a fit to Galactic and extra-galactic cluster catalogs approximate values are $A = 2$ % to $5$ clusters per square kpc per Myr, $\alpha = -1.0$, $\beta = -1.5$, and % $\gamma = 1.5$. This implies a one square kpc region around the Sun contains % about 20 to 50 short-lived ($ 10^4\msun$) clusters. Assuming a power-law distribution with $\beta=2$ and % %that the Piskunov sample measures a CFR for clusters in the range $100 < M_C < % %1000 \msun$, we derive a CFR of $2-5\times10^{-4} \permyr \perkpc$. Assuming % %these live $\sim 20$ Myr, corresponding to the longest lifetime in Portegies % %Zwart et al's MC list, the expected number of massive clusters is % %$\sim0.3-0.8$ within the solar circle. % % This number is FAR too low, considering that simply counting MCs gets you at least 7 XXXX % % % \verb|\citet{Piskunov2008}| claim a cluster formation rate % of 0.4 \perkpc \permyr\ integrated over all local ($d<850$ pc) clusters. Integrated over the Galactic % plane, this implies $CFR = 281 \permyr$. However, the clusters observed in this % local sample all have large radii ($r>10$ pc) or small masses ($M<10^3 \msun$), % and therefore it is difficult to place constraints on the massive CFR from this data. % % Given our observed cluster counts, there was only a 5\% probability % of finding an $M>3\times10^4$ \msun\ proto-cluster and 17\% probability of an $M>10^4\msun$ % proto-cluster within the 850 pc completeness zone of \verb|\citet{Piskunov2008}|. Multiplying % by the ratio of a MC / MP lifetime (about an order of magnitude) suggests that % we were likely to find 1-2 objects with $M>10^4$ \msun\ in the Piskunov sample. % None were found. \todome{What are the chances of finding 0 in the local sample given % the ``measured'' rate?} % % \verb|\citet{Piskunov2008}| also observe a steepening of the cluster mass function % with age, from $\alpha\sim1$ to $\alpha\sim2$. Our observed proto-cluster mass % function is steep, with $\alpha\sim2$. This contradiction suggests % either a selection effect in the \verb|\citet{Piskunov2008}| sample avoiding low-mass % young clusters, that our sample \emph{under}estimates the cluster masses particularly % on the high-mass end, or that low-mass proto-clusters live longer than % high-mass proto-clusters. The latter explanation would result in an excess of % observable low-mass protoclusters compared to the cluster % mass function (i.e., observable protoclusters should have $\alpha>2$). It is also expected in theory since, for fixed radius, % $t_{ff} \propto M^{-1/2}$. \subsection{Star Formation Activity} In the sample of potential proto-clusters, all have formed massive stars based on a literature search and IRAS measurements. A few of the low mass sources, G012.209-00.104, G012.627-00.016, G019.474+00.171, and G031.414+00.307 have relatively low IRAS luminosities ($L_{IRAS} = L_{100}+L_{60} < 10^5 \lsun$) and little free-free emission. However, \emph{all} are detected in the radio as H~II regions (some ultracompact) and have luminosities indicating early-B type powering stars. %The lowest IRAS 100 \um\ luminosity in our sample is %$L_{100}(G19.47)\approx6\times10^3 \lsun$; the rest have $L_{100} > %2\times10^5 \lsun$. All of the massive candidates therefore require O-type %powering stars. Non-detection of `starless' proto-cluster clumps implies an upper limit on the starless lifetime. For an assumed $\tau_{sf} \sim 2$~Myr, the $1\sigma$ upper limit on the starless proto-MC clump is $\tau_{starless} < (\sqrt{N_{cl}}/N_{cl}) \tau_{sf} = \tsuplim~\mathrm{Myr}$ assuming Poisson statistics and using all 18 sources. This limit is consistent with massive star formation on the clump free-fall timescale ($\tau_{ff}\leq0.65$ Myr). It implies that massive stars form rapidly when these large masses are condensed into cluster-scale regions and hints that massive stars are among the first to form in massive clusters. %, also the crossing time for $c_s=10 \kms$ and $r=1.7$ pc). %It may indicate that massive stars form simu %before all of the proto-cluster mass %has been collected into a compact region, i.e. that collapse from molecular %cloud to proto-cluster clump proceeds after massive stars have ignited within %the proto-cluster, although the small number statistics allow for other %explanations. \section{Discussion} \label{sec:discussion} Assuming a lower limit 30\% SFE and T$_{dust} = 20 {\rm K}$, \nMPC\ candidates in Table \verb|\ref{tab:candidates}| will become massive clusters like NGC 3603: G010.472+00.026, W51, and W49 (G043.169+00.01). Even if T$_{dust} = 40 {\rm K}$, W49 is still likely to form a $\sim10^4$ \msun\ MC, although G10.47 would be too small. W51, which is within the spatial-filtering incompleteness zone, passes the cutoff and is likely to form a pair of massive clusters. However, if the dust in W51 is warm and the free-free contamination is considered, the total mass in each of the W51 clumps is below the 3\ee{4} \msun\ cutoff. % \todocara{Do massive clusters in the galactic center affect this discussion? % Eli's comment: No, different physics in the GC mean we should not be % concerned.} % IGNORED unless the referee says otherwise The BGPS covers about \obsfrac\% of the Galactic star-forming disk in the range 1 kpc $< R_{gal}<15$ kpc. We can extrapolate our \nMPC\ detections to predict that there are $\leq$\nMPCtot\ ($\pm \nMPCtoterr$) proto-clusters in the Galaxy outside of the Galactic center. The agreement between the SFR-based prediction from M31 and our observations implies that we have selected genuine massive proto-clusters (MPCs). These most massive sources have escape speeds greater than the sound speed in ionized gas, indicating that they can continue to accrete gas even after the formation of massive stars. Assuming they are embedded in larger-scale gas reservoirs, we are measuring lower bounds on the `final' clump plus cluster mass. % Additionally, in the 15\% of the galaxy within the 5.8 kpc % radius in which the survey is incomplete due to spatial filtering, we predict % that there should be $2\pm1$ MPCs. % it's actually 41%, we probably predict more like a few.... %\subsection{Lifetimes} %In order to estimate the formation rate from our candidate source counts, we %need to include a %\begin{figure} %\includegraphics[width=8.5cm]{figures/mass_vs_omega.pdf} %\label{fig:m_vs_o} %\caption{The mass of the young massive proto-clusters (MPCs) versus their respective $\Omega$ value ($V_{esc} / C_{s}$). We present MPC candidates that have $\Omega > 1$ and clump masses greater than $10^3$ \msun. The candidates are graded based on their potential to forming a high mass stellar cluster regarding their assumed temperature and star formation efficiency (SFE). For the grading scheme we assume that $T_{dust}=40$K and a SFE of 30\%, essentially a worst case scenario for cluster forming conditions as the mass of the gas clumps is reduced by 42\%. The candidates are ranked on how much stellar mass they will have after gas dissipation. The red triangles represent grade {\bf A} candidates where their stellar mass will be greater than $10^4$ \msun\. Green squares represent grade {\bf B} candidates where their stellar mass will be greater than $10^3$ \msun. The blue diamonds are grade {\bf C} candidates that will have less the $10^3$ \msun\ in stellar mass.} %\end{figure} %this paragraph is somewhat in contradiction to Piskunov2008 % Open clusters generally have masses $<10^4$~\msun\ with a lifetime of $<1$~Gyr % and their disruption can start early in life from their local environment % \verb|\citep{PortegiesZwart2010}|. MCs ($>10^4$~\msun) on the other hand are less % sensitive to the surrounding environment than open clusters and typically % remain bound for 1 $2.5$ pc) accretion, substantial reservoirs of gas should surround these most massive regions and be flowing into them. Signatures of this accretion process should be visible: MPCs should contain molecular filamentary structures feeding into their centers \verb|\citep[e.g.][]{Correnti2012,Hennemann2012,Liu2012}|. Alternatively, lower mass clumps may merge to form massive clusters \verb|\citep{Fujii2012}|, in which case clusters of clumps - which should be detectable in extant galactic plane surveys - are the likely precursors to massive clusters. Finally, massive clusters may form from the global collapse of structures on scales larger than we have probed, which could also produce clusters of clumps. \section{Conclusions} \label{sec:ympcconclusions} Using the BGPS, we have performed the first flux-limited census of massive proto-cluster candidates. We found \ncandidates\ candidates that will be part of the next generation of open clusters and \nMPC\ that could form massive clusters similar to NGC 3603 (${\rm M}_{\rm cluster} > 10^4$ \msun). We have measured a Galactic massive cluster formation rate $CFR({\rm M}_{\rm cluster}>10^4) \lesssim \CFR\ \permyr$\ assuming that clusters are equally likely to form everywhere within the range 1 kpc $ < R_{gal} < $ 15 kpc. %however, we think formation limited to 1 2$ Myr) star formation timescale. Observations are needed to distinguish competing models for MC formation: Birth from isolated massive proto-cluster clumps, either compact and rapid or diffuse and slow, or from smaller clumps that never have a mass as large as the final cluster mass. This sample of the \ncandidates\ most massive proto-cluster clumps in the first quadrant (where they can be observed by both the VLA and ALMA) presents an ideal starting point for these observations. % \section{Acknowledgements} % We thank the referee for thorough and very helpful comments that strengthened % this Letter. This work was supported by NSF grant AST 1009847. %\bibliography{boundhii} \input{tables_chboundhii/boundhiitable} \section{Follow-up work} In order to get a complete census of massive proto-clusters in the Galactic plane, it is necessary to examine the southern plane as well. \verb|\citet{Urquhart2013a}| began this examination using ATLASGAL data and identified 6 new candidates in the southern sky. In principle, the detectin of more sources in the South indicates either some incompleteness in the BGPS or a genuinely higher cluster formation rate in the southern sky (which, with such small numbers, is easily consistent with uniform sampling from a disk distribution). However, we note that two of the candidates in \verb|\citet{Urquhart2013a}| are assigned the wrong kinematic distance - they are placed at the far distance when strong evidence exists putting them instead at the near. \subimport{/Users/adam/work/boundhii/distance_massiveclumps/}{solo} \input{solobib} \end{document}