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\chapter{Introduction}
\section{Preface}
This thesis describes
the research I have performed with a wide variety of collaborators, mostly
centered on the Bolocam Galactic Plane Survey team led by John Bally and Jason
Glenn. The BGPS data reduction process, at the core of this work, was done in
collaboration with James Aguirre and Erik Rosolowsky.
However, the work proceeded somewhat haphazardly: I came into the BGPS team as
a (perhaps foolish) student enthusiastic about data reduction. I never planned to take
over the BGPS data, but it happened a few years into my time at CU. This
thesis is therefore somewhat scattered: some of the observations reported here
were taken as `follow-up' to the BGPS before it was completed.
This document primarily consists of a number of published papers centered
around a common theme of radio and millimeter observations of the Galaxy, with
the common driving question being `How do stars form?' I have therefore added
thesis-specific introductions to each section to describe where they fit in to
the bigger picture of this document. I've also included sections describing
work that is not yet published but (hopefully) soon will be.
\section{Star Formation in the Galaxy}
It has been known for at least half a century that stars form from the
gravitational collapse of clouds of cool material. The gas that will
eventually form stars is typically observed as dark features obscuring
background stars. The brighter nebulae, which have been studied for far longer
\verb|\citep{Messier1764}|, contain hot and diffuse gas. These nebulae, while
spectacular, are not the construction materials of new stars. However,
they mark the locations where new stars have formed - nebulae are often
stellar nurseries.
To track down the cool star-forming material, it is necessary to observe at
longer wavelengths. Infrared observations can pierce through obscuring
material, as dust becomes more transparent at longer wavelengths. With near-
and mid-infrared observations, such as those enabled by HgCdTe detectors like
those in the NICFPS and TripleSpec instruments at Apache Point Observatory and
the InSb detectors used on the Spitzer Space Telescope, it is possible to
observe obscured young stars. These objects have just ignited fusion in their
cores and represent the youngest generation of new stars.
But this material has already formed stars. To see the truly cold material, that
which still has potential to form new stars, we need to examine gas that is not
heated at all by stars. Assuming we want to look for gas that can form a star
like our sun and that the density of the gas to form is $\sim10^4$ \hh particles
per cubic centimeter (an assumption left unjustified for now), the Jeans scale
requires a temperature $T\sim10$ K, which means we need to look at wavelengths
$\lambda \gtrsim 100 \um$ in order to observe this gas.
Gas at these densities turns out to be quite rare. While there are thousands
of stars within 100 pc of the sun, the closest known star-forming globules are
at distances greater than 100 pc. While this sparsity is explained in part by
our current position in the Galaxy (we're buzzing along its outskirts at 250
\kms), it reflects the reality that star formation in the present epoch is
dispersed and rare.
Even more rare are the massive stars that end their lives in supernovae. While there
are hundreds of stellar nurseries within a few hundred parsecs, the nearest
region of massive star formation is the Orion Molecular Cloud at a distance of
400 pc. Out to 1000 pc, though, there are still only a handful of massive star
forming regions, including Monoceros R2 and Cepheus A.
These massive stars in many ways are the most important to study in order to
understand the evolution of gas and dust in the universe and our own origins.
In their deaths, they produce the heavy elements required to form dust,
planets, and life. Throughout their lives and deaths, massive stars dump
energy into the interstellar medium and effectively control the motions and
future of the gas around them.
The bigger the star, the shorter it lives, so massive stars are nearly as rare
as their birth regions. They also tend to be found nearby or within these
birth regions. Since they can be found near large globs of dust, finding these
globs can help us discover new groups of massive stars.
This thesis summarizes surveys within our Galaxy to discover and examine
regions forming new massive stars and clusters. The largest body of work
described here is the Bolocam Galactic Plane Survey, the first dust continuum
survey of a significant fraction of the Galactic Plane.
With that broad overview in place, the next sections describe a few of the
specific problems addressed in this thesis in greater detail.
\subsection{Gas Flow and Collapse}
Stars form as the end state of the collapse of gas cores. The classic analysis
used to determine when stars will form from a gas cloud is the Jeans analysis, which
determines under what conditions an overdensity in a uniform isothermal medium
becomes unstable to gravitational collapse. Jeans analysis defines a length scale
$$L_J = \left( \frac{\pi c_s^2}{G \rho_0} \right)^{1/2}$$
and a mass scale
$$M_J = \left(\frac{2 \pi k T}{G \mu}\right)^{3/2} \rho_0^{-1/2} = \left(\frac{\pi}{G \mu}\right)^{3/2} c_s^3 \rho_0^{-1/2}$$
which defines the typical mass at which a core should form. In this equation,
$c_s$ is the sound speed in the gas, $\rho_0$ is the density of the medium, $T$
is the gas temperature, $\mu$ is the mean mass per particle in proton masses, and $G$ is
the gravitational constant. More careful analyses including other factors,
e.g. external pressure on the core, yield similar values.
The Jeans instability growth time scale $\tau_{J}$ is within a factor of a few
of the free-fall collapse time $\tau_{ff}$,
$$\tau_J = \left(\frac{1}{4 \pi G \rho_0}\right)^{1/2}$$
$$\tau_{ff} = \left(\frac{3\pi}{32 G \rho_0}\right)^{1/2} = \pi\sqrt{\frac{3}{8}} \tau_J$$
implying a typical mass infall rate for an isothermal core of
$$\dot{M}_J = M_J/\tau_J = \frac{1}{2} \pi^2 \frac{c_s^3}{G}$$
$$\dot{M}_{ff} = \pi \sqrt{\frac{3}{32}} \frac{c_s^3}{G}$$
Under free-fall collapse at 10 K, then, a 1 $\msun$ star takes only $\sim10^4$
years to form, but a 100 \msun star takes $\sim1$ Myr.
Real stars do not form so quickly, but initial accretion rates may be as high
as $10^{-4} \msun \peryr$ in cores, and the accretion must be at least that
fast for massive stars to form in times shorter than the lifetimes of their
parent clouds.
Low-mass stars go through subsequent phases of collapse, from the initial
unstable core to a hydrostatic core in which collapse no longer proceeds
isothermally because the dust becomes optically thick to its own radiation.
Eventually a protostar forms, surrounded by a disk and a core. The core
continues to accrete onto the star through the disk until all the material is
either accreted or blown away in outflows. The disk both accretes on to the
star and forms planets.
This process is well-understood for low-mass stars in the broad strokes
outlined here, and each phase in this process has been observationally
confirmed. For massive stars, the picture is far less clear. It is still
actively debated whether active stars ever have a ``core'' analogous to
low-mass pre-stellar cores, since a 100 \msun gas cloud unstable to collapse
would also be unstable at smaller scales and would therefore be likely to fragment
into many lower-mass cores.
The two main competing theoretical extremes to get around this problem are
known as the ``turbulent core''
\verb|\citep{McKee2003a,Krumholz2005a,Krumholz2009a,Tan2006a,McKee2007a}| and
``competitive accretion''
\verb|\citep{Klessen2000a,Bonnell2002a,Bonnell2004a,Bonnell2006a,Bonnell2008a}|
models. In the former, an additional support mechanism, turbulence, prevents
fragmentation in massive cores, allowing a single core with
$M_{core}>M_J(thermal)$ to form into a single stellar system. By contrast, the
competitive accretion model, in its most extreme form, asserts that all stars
start their lives as $\sim M_J$ cores which exist within a collapsing cloud.
They are then able to accrete additional material from the cloud and grow from
their minimum mass to populate the initial mass function (see Section
\verb|\ref{sec:massfunctions}|).
Neither theory is presently able to account for feedback from the formed stars.
Massive stars drastically affect their environment when they turn on, which can
be long before they are done accreting. Massive stars probably go through
phases similar to low-mass stars, but they may look quite different. They are
likely to ignite fusion while still accreting within a dense core; feedback
will begin while most of the matter that will eventually reach the star is still
in the `core' phase.
If this happens, the massive star will begin to
illuminate a hypercompact \hii region, in which the extremely high surrounding
densities trap the ionizing radiation. Over time, the star's luminosity will
grow and the surrounding density decrease, either by accreting or being
ejected, and the \hii region will expand, going through an ultracompact (UC)
\hii phase, then a diffuse \hii region, then ending its observable phase as it
blends into the low-density warm interstellar medium.
Understanding these early phases is important for understanding what sets a star's
final mass. In a core accretion model, $\sim2/3$ of the gas in the original
`core' may accrete, and the other $\sim1/3$ blow out, but the mass of the star
should be very near the core mass. In the competitive accretion model, the core
mass may have little influence on the final star mass, as most of the stellar mass
will be Bondi-Hoyle accreted from the surrounding medium.
In order for Bondi-Hoyle (BH) accretion to be effective, though, the surrounding `clump'
medium must have a very high density. The BH accretion rate is strongly dependent on the
mass of the accreting star and the sound speed of the gas:
$$\dot{M}_{BH} = \frac{4 \pi \rho G^2 M^2}{c_s^3} $$
For a low-mass star in a low-density medium and a high-mass star in a high-density medium,
the values are
$$\dot{M}_{BH} = 1.6\times10^{-7} \left(\frac{M}{M_\odot}\right)^2 \left(\frac{n}{10^4 \mathrm{cm}^{-3}}\right) \left(\frac{c_s}{1 \mathrm{km s}^{-1}}\right)^{-3} \msun \peryr$$
$$\dot{M}_{BH} = 1.6\times10^{-4} \left(\frac{M}{10 M_\odot}\right)^2 \left(\frac{n}{10^5 \mathrm{cm}^{-3}}\right) \left(\frac{c_s}{1 \mathrm{km s}^{-1}}\right)^{-3} \msun \peryr$$
The timescale for a 10\msun star to double its mass in a $n\sim10^5\percc$
medium is $\sim50$ kyr, but drops to only $5$ kyr for density
$n\sim10^6\percc$.
It is therefore crucial that we measure the density of the bulk of the gas
around massive stars - the mass and density of the surrounding medium are
essential parameters for determining whether competitive accretion is a viable
model for growing massive stars.
Throughout the thesis, I examine the local gas density on parsec scales via
line ratios and simpler column-density based estimates. I also examine tracers
of infall and outflow to determine accretion properties of forming stars.
\subsection{Turbulence}
Turbulence is one of the defining features of the interstellar medium.
Turbulence is thought to govern many properties of the ISM, rendering it
scale-free and defining the distribution of velocities, densities,
temperatures, and magnetic fields in the gas between stars.
Turbulence forms in fluids when the inertial force greatly exceeds the
viscosity. It creates instabilities in the fluid that start on large scales
and ``cascade'' energy to smaller scales. Once a small enough size-scale is
reached, the viscosity exceeds the interial force and the energy heats the
fluid on local scales.
Turbulence is most easily modeled by a Kolmogorov spectrum, in which $\Delta v
\propto \ell^{1/3}$, i.e. the typical velocity dispersion is greatest at the
largest size scales. Kolmogorov turbulence strictly only describes
incompressible fluids without magnetic fields, while the ISM is compressible
and threaded by magnetic fields. Nonetheless, Kolmogorov turbulence is nearly
consistent with some observed properties of the ISM. The Larson size-linewidth
relation ($\sigma_{\kms}\approx1.1 L_{pc}^{0.38}$), in particular, is similar
to that predicted by Kolmogorov turbulence.
Turbulence is often quoted as a source of \emph{pressure} based on the
Kolmogorov description. At size scales much smaller than the driving scale of
the turbulence (the ``box size'' in a simulation), turbulence becomes isotropic
and can add support against gravitational collapse.
However, turbulence decays rapidly. The turbulent decay timescale
$\tau_{decay}\propto \ell / v$, where $\ell$ is the turbulent length scale and $v$ is
the velocity scale. It therefore increases with size scale as
$\tau_{decay}\propto \ell^{2/3}$. Turbulence decays most quickly on the smallest
sizescales.
We are therefore left with two conditions: Turbulence must be driven at large
scales for turbulence to provide support against gravity\footnote{Once stars form
in a cloud and stellar feedback becomes significant, turbulence can be driven at all
scales, but the turbulent support needed to slow or prevent the initial
collapse of starless cores cannot be driven by local stars.}, and it must be
constantly driven to resupply the turbulence that is transferred to heat on the
smallest scales.
Once stars form, however, large-scale driving of turbulence may not be the
dominant shaping mechanism for the gas. Outflows from low-mass stars, soft UV
from B stars, and ionizing UV and strong winds from OB stars can drive gas
motions, disrupting gas or replenishing turbulent energy. Once stars have
formed in a cloud, local feedback rather than the turbulent cascade is likely
to govern the future evolution of the cloud.
Because the ISM is compressible, interacting flows within the turbulent medium
will result in density enhancements and voids. Many simulation studies have
determined that the resulting density distribution, and correspondingly the
column-density distribution, should be log-normal. Observational
studies agree that in regions not yet significantly affected by gravity, the
column-density distribution is log-normal. In regions where stars are actively
forming, i.e. regions in which gas self-gravity has affected a significant fraction
of the gas, a high-density power-law tail forms.
One theory of star formation holds that the initial mass function of stars is
determined entirely by turbulence \verb|\citep{Padoan2002,Padoan2007,Krumholz2005c}|. In this
description, the highest overdensities in the turbulent medium become
gravitationally unstable and separate from the turbulent flow as they collapse
into proto-stellar cores. This idea has been a hot topic in the past few
years, but it may be an overly simplistic view.
Turbulence is appealing to theorists as it is a difficult problem to address
directly with observations, but it may have great predictive power. If turbulence
is the dominant governing process of the ISM, then it is possible to derive a
reasonably robust star-formation theory based on the excursion set theory
successfully applied to cosmological structure formation
\verb|\citep{Hopkins2012b,Hennebelle2011a,Hopkins2012d}|.
However, in reality, turbulence is just one of many processes governing the ISM
and star formation. Stellar feedback, in the form of radiation, winds,
supernovae, and outflows imposes a preferred driving scale on any individual
region, and in many cases these processes will happen faster than turbulent
processes. The notion of \emph{initial conditions} for star formation,
while theoretically appealing, may prove too strong an oversimplification
when searching for a complete theory of star formation.
Throughout this thesis, I consider and measure the drivers, effects and
properties of turbulence on a few different scales.
In the W5 and IRAS 05358 regions (Chapter \verb|\ref{ch:w5}| and
\verb|\citet{Ginsburg2009}|), I examined outflows as potential drivers of turbulence.
In IRAS 05358, I concluded that the outflows could provide the observed
turbulence in the $\sim$pc-scale `clump', but that the central core had energy
dissipation much faster than turbulence could be resupplied. In W5, I rule out
protostellar outflows as a significant driver of turbulence.
In Chapter \verb|\ref{ch:h2co}|, I examine the density probability distribution
function (PDF) in giant molecular clouds (GMCs). Because \formaldehyde is
uniquely capable of measuring local volume density, I was able to place
interesting constraints on the density PDFs in non-star-forming GMCs, namely
that they are unlikely to be the simple log-normal distributions expected from
isothermal incompressible turbulence.
\subsection{Mass Functions}
\label{sec:massfunctions}
Perhaps the most fundamental goal of star formation studies is to determine the
Initial Mass Function (IMF) of stars and what, if anything, causes it to vary.
It is also one of the most challenging statistically and observationally.
The IMF defines the probability distribution function of stellar masses at
birth, and therefore differs greatly from the present-day stellar mass function
that is very strongly affected by stellar death at the highest masses. In
order to determine the mass function for the most massive stars, it is
necessary to look at their birth places. These birth places are dusty, dense,
and rare.
It remains somewhat unclear whether the IMF is a universal function or is sampled
independently for individual clusters. If it is universal, there is a possibility of
forming massive stars anywhere stars form. If cluster-dependent, then a massive star
must form with a surrounding cluster.
Some groups now claim that the initial mass function is decided in the gas
phase by the formation of cores. The Core Mass Function (CMF) measures the
probability distribution function of core masses, where cores are generally
identified observationally as column-density peaks in millimeter/submillimeter
emission maps. The CMF has a similar functional form to the IMF, but its mean
is higher by a factor $\sim3$ in local star forming regions, leading to the claim
that star formation proceeds from CMF $\rightarrow$ IMF with 30\% efficiency.
This idea has recently been explored theoretically by \verb|\citet{Chabrier2010a}| and
\verb|\citet{Hopkins2012b}| and observationally by the Herschel Gould's Belt team
\verb|\citep{Arzoumanian2011a,Andre2010a}|.
Gas clouds follow a mass function that extends up to the largest
possible coherent scales, giant molecular clouds with scales $\sim50-100$ pc
that are limited by the scale-height of the ISM in Galactic disks.
Between `cores' and GMCs, intermediate scale blobs are often called `clumps'.
The mass function of these clumps has yet to be determined.
The mass function of GMCs was determine from CO emission towards the Galactic
plane and in nearby galaxies (e.g., M33) where they can be resolved. The CMF
was measured in nearby ($D<500$ pc) clouds where 30\arcsec\ beams easily resolve $\sim0.1$
pc cores. However, clumps are only found in large numbers in the Galactic
plane, where distances are uncertain. They cannot be resolved in other
galaxies (or at least, could not prior to ALMA).
To understand star formation on a galactic scale, it is necessary to understand
the transition from large-scale giant molecular clouds and proto-stellar cores.
Clouds follow a shallow mass function, with the largest clouds containing most
of the gas. Cores and stars are both drawn from steep mass functions in which
most of the mass is near some peak in the distribution. Presumably there must be
some intermediate state of the gas that is drawn from an intermediate
distribution, shallower than `cores' but steeper than `clouds'.
The BGPS (Chapter \verb|\ref{ch:v2}|) presents the first real opportunity to explore
the mass function of clumps on scales intermediate between cores and giant
clouds. While I do not explicitly examine core or clump mass functions in this
thesis, their measurement is an important motivation for the large-area surveys
we have performed.
\subsubsection{Star Clusters}
Star clusters are also drawn from a mass function comparable to stars, but
their distribution is better measured than for stars. Clusters are
easily visible - and resolvable - in other galaxies, and massive clusters are
less likely to be embedded than massive stars, since a bound cluster will outlive its few most
massive stars. In normal galaxies, cluster
populations are consistent with a Schechter distribution: a power-law
$\alpha\sim2$ with an exponential cutoff at large masses.
$$N(M)dM = C \left(\frac{M}{M_*}\right)^{-2} e^{-(M/M_*)} dM$$
Since clusters are not drawn from the same parent distribution as GMCs (which
have $\alpha\sim1$, so $N(M) dM \sim C M^{-1} dM$), it is plausible that their
precursors are, instead, the intermediate-scale `clumps' observed in the
millimeter continuum. However, the clump mass function has yet to be measured,
so even this first step of determining plausibility is incomplete.
Clusters are an important observational tool in astrophysics. For stellar
studies, they have been used to select populations of co-eval stars. In
extragalactic studies, they are frequently the smallest observable individual
units. However, many recent works have pointed out that clusters may be
short-lived, transient phenomena
\verb|\citep{Kruijssen2011a,Whitehead2013a,Gieles2011a,Whitmore2009a}|. Any study of
their populations must take in to account their dissolution. The most massive
clusters, however, are both the most easily observed and the longest lived, and
therefore provide some of the most useful tools for understanding stars.
As with massive stars, massive clusters are rare. Only a handful of young
massive clusters (YMCs) are known within our Galaxy, the most prominent being NGC
3603, the Arches cluster, and Westerlund 1 \verb|\citep{PortegiesZwart2010}|. These
are the only locations in the galaxy known to be forming multiple stars near
the (possible) upper stellar mass limit. Despite their importance,
the population of such clusters
is effectively unconstrained. The incomplete knowledge of clusters is due to
extinction and confusion within the Galactic plane at wavelengths where
the stars are directly observable.
In Chapter \verb|\ref{ch:ympc}|, I search the BGPS for candidate proto-massive star
clusters. Because the Galactic disk is optically thin at 1.1 mm, a complete
census of proto-clusters is possible. I use the detected candidates to infer
features about the population of Galactic YMCs, including their formation
timescales and rates.
%\subsection{Galactic Plane Surveys}
%The idea to observe the plane of the Galaxy is not new.
%\subsection{Statistics and Data Processing}
%This is a data-rich thesis, and as such has some emphasis on data statistics.
% \section{Observational Tools: Molecular Line Spectroscopy}
\section{Outline}
This thesis includes 6 chapters.
Chapter \verb|\ref{ch:w5}| describes observations of the W5 star-forming region to identify outflows;
this chapter is somewhat tangential to the rest.
Chapter \verb|\ref{ch:v2}| describes the BGPS data reduction process and data pipeline.
Chapter \verb|\ref{ch:ympc}| is a Letter identifying massive proto-clusters in the BGPS.
Chapter \verb|\ref{ch:h2co}| is the pilot study of \formaldehyde towards previously-known UCHII regions.
It includes the methodology and analysis of turbulent properties of Galactic GMCs.
Chapter \verb|\ref{ch:h2colarge}| expands upon Chapter \verb|\ref{ch:h2co}|, detailing the expansion of the \formaldehyde survey
to BGPS-selected sources.
Chapter \verb|\ref{ch:software}| summarizes software development for this thesis and beyond.
Chapter \verb|\ref{ch:conclusion}| concludes.
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