Adam S. Trotter: Research Statement
Since 2006, I have worked at UNC-Chapel Hill with Prof. Dan Reichart and the Skynet Robotic
Telescope Network Lab. The primary research initiative of our lab is the study of gamma-ray burst
(GRB) afterglows. GRBs herald the deaths of massive stars and the births of black holes, and are
detected, in gamma-rays, at a rate of a few per week by satellite observatories. GRBs are first detected
and localized by spacecraft, currently NASA’s Swift and Fermi. As soon as a satellite receives a burst
trigger, ground-based telescopes race to point to its location and capture, in near-IR, optical and radio
wavelengths, the fading GRB afterglow, which, unlike the brief GRB itself, may persist for several days.
With bulk Lorentz factors of  ~ 100 and isotropic-equivalent luminosities of L ~ 1054 erg/sec, GRBs are
both probes of ultra-relativistic physics and “backlights” with which we can probe star-forming regions
and the early universe (e.g. Lamb & Reichart 2000, Ciardi & Loeb 2000, Bromm & Loeb 2002).
In §1, I describe the facilities and broad astronomical research capabilities of UNC’s PROMPT
observatory and the Skynet Robotic Telescope Network. In §2, I present the GRB Afterglow Modeling
Project (AMP), including a detailed description of the computational tools, foundational statistics and
extinction and absorption models that underlie my Ph.D. thesis work. Finally, in §3, I outline a plan for
recruiting and training undergraduates at High Point University to participate in ongoing AMP research.
1. Facilities: PROMPT and the Skynet Robotic Telescope Network
UNC-Chapel Hill has built PROMPT – six 16-inch diameter fully automated, or robotic, optical
telescopes at Cerro Tololo Inter-American Observatory (CTIO) in Chile – and Skynet – telescope control
and web-based, dynamic queue scheduling software capable of controlling many telescopes
simultaneously and most types of commercially available small telescope hardware. PROMPT and
Skynet were created in order to capture, simultaneously at multiple wavelengths, photometric images of
these GRB afterglows within tens of seconds of the initial satellite trigger. To date, GRB localizations
have reached PROMPT within 12 – 79 seconds (90% range) of detection. If observable at that time,
PROMPT has responded within 14 – 61 seconds (90% range) of notification, with our fastest response
being 12 seconds. To date, PROMPT has observed 41 GRBs on such rapid timescales, detecting 24
optical afterglows.
Our most significant discovery to date occurred on September 4th, 2005, when then-undergraduate student
Joshua Haislip and Dan Reichart discovered and identified the most distant explosion in the universe then
known, GRB 050904 at redshift z = 6.3, using both PROMPT and the 4.1-meter diameter SOAR
telescope (Cusumano et al. 2006, Haislip et al. 2006, Kawai et al. 2006). For the WMAP cosmology, this
redshift corresponds to 12.8 billion years ago, when the universe was only 6% of its current age. Over the
past two years, GRBs have also been discovered at z = 6.7 and 8.3, and so can potentially serve as probes
of the very early universe, prior to the epoch of reionization (Greiner et al. 2009, Salvaterra et al. 2009,
Tanvir et al. 2009).
When no GRBs are observable, which is approximately 85% of the time, PROMPT is used by
professional astronomers, students of all ages – graduate through elementary – and members of the
general public across North Carolina, the US, and the world for a wide array of research, research
training, and EPO efforts. PROMPT, often in campaigns with other optical and radio telescopes around
1
the world and also with space telescopes, is being used to study blazars, a wide variety of variable and
eclipsing binary stars and pulsating white dwarfs, and rotating and binary asteroids, as well as to carry out
supernova (SNe) and exo-planet searches (Fischer et al. 2006, Osterman Meyer et al. 2008, Descamps et
al. 2009, Reed et al. 2010, Barlow et al. 2010, Thompson et al. 2010, Cenko et al. 2010, Pravek et al.
2010, Layden et al. 2010, Pignata et al. 2010, Hełminiak et al. 2011). The largest of these efforts has
been the CHilean Automated Supernova sEarch (CHASE), which to date has resulted in the discovery of
98 SNe, including at least 35 Type Ia SNe, which are used to measure Hubble’s constant and to calibrate
cosmic acceleration. PROMPT is now the most successful discoverer of SNe in the southern hemisphere
(Pignata et al. 2009).
Over the past five years, GRB and non-GRB research has resulted in 18 journal articles (with another
approximately half dozen in preparation across the collaboration; Reichart et al. 2005, Moran & Reichart
2005, Dai et al. 2007, Updike et al. 2008, Nysewander et al. 2009, Cano et al. 2010, and references listed
above), two conference proceedings (Pignata et al. 2009, Trotter, Reichart & Foster 2009), approximately
200 observing reports (GCN, CBET, IAUC, MPB, ATel), two doctoral dissertations (Nysewander 2006,
Trotter 2011), at least four masters theses, and at least three undergraduate honors theses.
In partnership with other institutions, many of them in North Carolina, Skynet has enabled us to grow
PROMPT into a network of small, robotic optical telescopes. The Skynet Robotic Telescope Network
now spans three, and soon four, continents. To date, we have integrated eight non-PROMPT telescopes
(California, Colorado, Italy, four in North Carolina, and Virginia), and are currently scheduled to
integrate eight more non-PROMPT telescopes (Arizona, New Mexico, four in North Carolina, including a
32-inch diameter telescope, Virginia, and a 40-inch diameter telescope in Wisconsin) over the next 18
months. The rate at which Skynet is taking exposures is increasing by about 1,000 exposures per month.
We have recently secured funding to expand Skynet’s geographic and wavelength footprints to include:
(1) a new, 32-inch diameter robotic telescope at CTIO, with simultaneous near-infrared (NIR), wide-field
optical, and lucky optical imaging capabilities; (2) a new 24-inch diameter robotic polarimeter at CTIO,
funded by the Kingdom of Thailand; (3) four new, 16-inch diameter robotic telescopes at Siding Spring
Observatory in Australia, also with simultaneous NIR and optical imaging capabilities, enabling nearcontinuous, simultaneous multi-wavelength observing of southern hemisphere targets, as well as live
observing for EPO in North Carolina; and (4) a 20meter diameter radio telescope at the National Radio
Astronomy Observatory (NRAO) in Green Bank,
West Virginia, including the development of a radio
version of our telescope control and web-based,
dynamic queue scheduling software, which will be
installed with new, state-of-the-art X- and L-band
receivers and a fully modern back-end, including the
same highly flexible digital spectrometer hardware
used by the GBT (Figure 1).
Figure 1: The 20-meter diameter radio telescope at
NRAO-Green Bank.
2
PROMPT Collaboration institutions currently include (1) UNC-CH, (2) 12 regional undergraduate
institutions, including three minority-serving institutions (Appalachian State University, Elon University,
Fayetteville State University, Guilford College, Guilford Technical Community College, HampdenSydney College, NC A&T, UNC-Asheville, UNC-Charlotte, UNC-Greensboro, UNC-Pembroke, and
Western Carolina University), (3) UNC-CH’s Morehead Planetarium and Science Center (MPSC), and
(4) the US and Chilean astronomical communities. PROMPT Collaboration access began on February 1,
2006, only a year and a half after receiving funding, and to date these four groups have used 5,525, 4,569,
1,494, and 9,272 hours of observing time, respectively.
Site
Cerro Tololo Inter-American Observatory,
Chile
Morehead Observatory, NC
Dark Sky Observatory, NC 2
Dolomiti Astronomical Observatory, Italy
Hampden-Sydney College Observatory, VA
Pisgah Astronomical Research Institute, NC
Coyote Rim Ranch, CO
Hume Observatory, CA
Yerkes Observatory, WI
Siding Spring Observatory, Australia 2
Cline Observatory, NC
Selu Observatory, VA
Winer Observatory, AZ
McNair Observatory, NC
Smithies-White-Edgell Observatory, NM
National Radio Astronomy Observatory, WV
Telescope
16″
16″
16″
16″
16″
16″
24″
32″
24″
14″
16″
17″
32″
16″
16″
16″
14.5″
14″
40″
16″
16″
16″
16″
16″
14.5″
14.5″
14″
14”
20-m
Owner
University of North Carolina at Chapel
Hill
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill & Thailand
UNC-Chapel Hill & Astro Optik
UNC-Chapel Hill
Appalachian State University
ASU
ASU & Dean Glace
ASU
Carlo Magno Zeledria Hotel
Hampden-Sydney College
Pisgah Astronomical Research Institute
Jack Harvey
Sonoma State University
University of Chicago
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill
UNC-Chapel Hill
Guilford College
Radford University
University of Iowa
NC A&T State University
Oliver Smithies3 & Marshall Edgell
National Radio Astronomy
Observatory
Online
6/05
8/05
12/05
12/05
12/05
1
1
1
9/08
6/08
1
6/10
1
2/09
6/09
3/08
11/05
5/06
1
1
1
1
1
1
1
1
1
1
4
1
Will be integrated into Skynet over the next 18 months.
Dark Sky Observatory and Siding Spring Observatory will have simultaneous multi-wavelength imaging capability
like Cerro Tololo Inter-American Observatory.
3
Nobel laureate
4
Will be refurbished over the next 12 months and integrated into Radio Skynet over the next 30 months.
2
Skynet has proven to be an attractive option for non-PROMPT telescope owners because (1) they no
longer need to staff their telescopes at night, or in the case of campus telescopes they no longer need to
keep their students awake night after night if they want to do observational astronomy curricula or
3
research/research training; and (2) Skynet allows telescope owners to queue observations on the other
telescopes on the network when they are not otherwise in use, giving them free access to different and
often better telescopes, instrumentation, parts of the sky, and site and weather conditions. Skynet has now
taken over 2.7 million exposures, currently at a rate of about 70,000 per month and this rate is increasing
by about 1,000 per month.
As a member of the original Skynet Robotic Telescope Network development team, and as continuing
leader of the GRB Afterglow Modeling Project (§2), I am personally guaranteed ongoing, high-priority
access to 2% of UNC’s share of observing time on the Skynet telescopes that UNC owns or shares: 8
exisiting and planned CTIO/PROMPT telescopes; the 4 new telescopes under construction at Siding
Spring, Australia; the 24-inch Morehead Observatory telescope; and the 20-meter radio telescope at
NRAO in Green Bank (see table on p. 3). For the 13 optical telescopes, assuming an average of 10.5
hours of dark time per night, an average of 275 clear nights per year among the sites, and UNC’s average
share of 90% the available time, this equates to approximately 675 hours per year of guaranteed optical
telescope time (which includes access to wide-field optical, NIR, polarimetry and lucky imaging
instruments). The 20-meter radio telescope at Green Bank can operate 24 hours a day, in almost any
weather conditions, and UNC will have a 30% share of this time; this gives approximately 50 hours per
year of guaranteed radio telescope time in the X and L bands. (Like all Skynet members, I will also have
access to all other Skynet telescopes at varying levels of priority, as they are available.) This guaranteed
telescope time will be available for: personal research, by me or my colleagues; undergraduate research
projects; and any number of EPO activities, including new introductory and advanced observational
laboratory exercises that may enhance the new undergraduate physics and astronomy curriculum at HPU.
2. The GRB Afterglow Modeling Project (AMP)
My PhD thesis serves as the foundational statistical and modeling basis for a major new research initiative
in the Skynet Lab: The Gamma-Ray Burst Afterglow Modeling Project (AMP). The goal of AMP is to
create a statistically self-consistent library of fitted model parameters that describe the time- and
frequency-dependent intrinsic emission and line-of-sight extinction and absorption of every GRB
afterglow ever observed, using all available radio, IR, optical, UV and X-ray data, including data
published by other research groups. AMP will result in an ever-growing catalog of GRB afterglow
physical and environmental parameters, and statistically valid uncertainties in these parameters, which
can itself be analyzed in population studies, with the hopes of identifying new classes of bursts, and a
more comprehensive picture of the range of circumburst environments and their evolution, both over the
duration of a given burst, due GRB modification of their local environments, and among multiple bursts
over cosmological time scales.
To obtain a fit to a GRB afterglow, we require: observational data; a statistic; a model describing GRB
emission and line-of-sight extinction and absorption; and tool that applies the statistic to find the best-fit
model to the data. For AMP, the data are photometric flux measurements made by Skynet telescopes
(§1), plus all available observations in the literature. The foundational statistics underlying AMP, and
construction of the extinction and absorption models, constitute the bulk of my Ph.D. thesis, and are
described in some detail in §2.B. Our model fitting tool is Galapagos, a highly flexible software package
we have developed that is based on genetic algorithms, which I describe in §2.A, below. We are
4
designing a user-friendly database and web-based interface for AMP to compile all these necessary
components, and all resulting model fits, for every GRB afterglow ever observed. This will soon enable
any new researcher, including undergraduates, to participate in AMP with a minimum of training, as I
will discuss in §3.
2.A. The Model Fitting Tool: Genetic Algorithms and Galapagos
The theoretical models we employ to describe GRB afterglow emission and line-of-sight absorption as a
function of time and frequency are described by dozens of parameters (see §2.B.2). While the
permissible values of some of these parameters are themselves constrained by prior observations, which
can significantly reduce the volume of parameter space that must be explored, we are still faced with a
daunting computational task that cannot be effectively tackled by traditional means. However, there
exists a powerful technique, the genetic algorithm (GA), that is well-suited for systematic and efficient
exploration of complex parameter spaces.
To this end, we have developed a highly flexible software package, called Galapagos, which is broadly
applicable to every conceivable model-fitting scenario, not only across astrophysics but across all of
science. GAs work by simulating the mechanism by which heredity and natural selection guide the
evolutionary process in creating organisms able to thrive under a given set of conditions. First, we
generate a series of “organisms” or model parameterizations by randomly selecting “genes” or values
from the range of all valid parameters for each dimension of the solution. Each of these organisms, the set
of which now form a “population”, are then assigned a “fitness” by evaluating the probability of the
corresponding hypothesis it (along with their model) represents. Speaking loosely, this objectively
measures how well the candidate solution matches the data. The organisms are then ranked according to
fitness, whence the selection phase occurs; the less “fit” solutions are discarded, while those with greater
fitness are combined to replenish the ranks. This “mating” is accomplished by selecting a pair of parents,
and then randomly choosing genes from among the pair to build an “offspring”. After these offspring are
evaluated for fitness, they are added to the population to replace the least-fit members. Iterating this
process of continually replacing less-fit solutions with those better suited to the data, the weaker
organisms wither away as a particular genotype of high fitness eventually comes to dominate the
population. At which point, we arrive at a solution of maximum likelihood and terminate the search.
The following sections describe some of the more technical details of our implementation of Galapagos.
§2.A.1 is a summary of the Bayesian statistic we employ for GRB fitting, including the concept of priors,
and its implementation in terms of the modular structure of Galapagos. §2.A.2 introduces the concepts of
data groups and parameter linking, a powerfully flexible, and useful, feature of Galapagos that can be
employed in a wide range of model fitting problems.
2.A.1. Bayesian Inference, Priors and the Modular Structure of Galapagos
One of the primary design goals for Galapagos was flexibility, which, in a system such as this, means
pervasive component modularity. We generally break the fitness function down into a “statistic” that
measures how well a hypothesis describes the data and a “model” that maps a range of independent inputs
to a hypothesis’s prediction. The statistic generally implements the probability function discussed above
and takes a model, a corresponding parameterization, and a set of evidence (i.e., prior information) as
5
arguments. This allows the optimization engine to be applied to a whole slew of problems, given the right
metrics for classifying candidate solutions. In terms of data regression, one such metric could be a simple
2 measure that sums the squares of the differences between the model prediction and the observation at
each available data point. Returning this summed 2 measure as a particular parameterization’s fitness
provides a way of objectively ranking these sets of parameters such that hypotheses matching the data
more closely have better fitness values. Therefore, given a data set and an appropriate model, simply
pointing Galapagos to this statistic will produce a 2 regression.
In modeling GRBs, however, we employ a significantly more involved full Bayesian treatment. Bayes’
theorem states that the posterior probability of a hypothesis H, given a set data D and prior information I,
is proportional to the product of the probability of the data given the hypothesis and prior information
(which we call the likelihood function, L) and the probability of the hypothesis given the prior
information (which can be expressed as the product of a series of independent “priors”):
p( H | DI )  L( D | HI ) pi ( H | I ) .
These subcomponents of the posterior probability – the likelihood function and the priors – can be
computed in a modular fashion (Figure 2). The structure of the Bayesian inference statistic in Galapagos
allows the user to add and interchange priors at will. In fact, since priors operate on the full
parameterization of the model being evaluated, they are allowed to be arbitrarily complex, from
measuring the likelihood of a single parameter with a simple Gaussian distribution to implementing userdefined functions that operate on the whole candidate genome. In the same manner, the likelihood
function is also flexible; in fact, it can be a whole additional nested statistic. For example, we could use a
simple 2 statistic as the likelihood function to perform a regression as above, but bias the parameters
using independently determined information in the form of priors to arrive at a more complete solution.
Thus implemented, we are even free to extend this treatment using the statistics of Reichart (2001),
D’Agostini (2005), or Trotter, Reichart & Foster (2011).
Figure 2: AMP’s modular fitness function.
The other important component of the fitness function is
the model: a function, which, given a particular set of
parameters, maps a vector of independent variables to a
prediction. Data modeling is often an organic process of
synthesizing various sundry components whose
respective functional forms are both well understood and
determined by theory. Therefore, like the statistic, the
model can range in complexity from a simple function to a whole hierarchy of interdependent modules.
For instance, our typical GRB model is separated into emission and absorption models, each of which has
a number of sub-components which can be added, removed, and configured by the user at will, that
specify the flux density as a function of frequency and time, as well as a module that integrates the model
flux density over frequency, weighted by the filter response function appropriate for each given
photometric flux measurement.
6
2.A.2. Data Groups and Parameter Linking
Galapagos has been designed to easily handle the general problem of simultaneously fitting models to
multiple data subsets that may share in common certain descriptive model parameters. Consider the
following illustrative problem, which was the basis for a recent ERIRA student project (see teaching
statement): We wish to determine the mass of a planet by measuring the positions of N of its moons as a
function of time and modeling the orbital dynamics. For an edge-on projection, and assuming roughly
circular orbits, the observed offset of each moon from the planet is described by the function
x(t )  a sin( GM / a3 t   ) , where a is the semi-major axis of the orbit, G is the gravitational constant, M
is the mass of the central body, and  is a phase constant. Now, one approach is to model each trajectory
independently, and thus arrive at N distinct values for M, which can then be averaged to provide a
reasonably accurate estimation. The alternative is to recognize that the underlying phenomena producing
the data, while largely independent, actually share some characteristics, namely the parameter M. A more
complete treatment would be to include this information from the outset.
Galapagos allows us to do this by defining the notion of data groups, semi-independent subsets of the
overall data set. When we perform a regression using multiple data groups, Galapagos actually performs
multiple regressions simultaneously by expanding the genome of each organism to include N
“chromosomes” or semi-independent parameterizations for the model. In the example above, this means
the organisms we generate will have not 3 parameters (a, M, and ), but 3N parameters, one set for each
moon trajectory. During the fitness evaluation, the statistic iterates over the entire data set and compares
how well the overall parameterization predicts each moon’s position. The statistic decides which 3parameter set to use when calculating the model prediction based on which data group it is being
evaluated at that instant. At the end of the run, the overall solution is N different parameterizations (of 3
values each) that quantify the orbits of the N distinct moons in the context of the functional form
mentioned above.
As before, this produces N distinct values for the mass of the central object; however, we are able to
enforce a relationship between the data groups by “linking” the parameter M across the different
chromosomes. This amounts to setting the N different mass parameters in each organism to be identical
after its inception. What was a fit with 3N free parameters becomes one with 2N+1 free parameters, and
we gain the advantage that the optimization engine now determines which single value of M best
describes the data as a whole, all other factors being unrelated.
Data groups and linking become powerful concepts when combined with GAs. Even though adding
groups, in this manner, multiplies the dimensionality of the overall fit by N, linking parameters across
groups actually subtracts from the total number of free parameters and thus reduces the size of the
solution space. Besides this, GAs are extremely well suited to searches over a large number of
dimensions, as mentioned before, because they scale quite naturally in this respect. When modeling GRB
data, we apply data groups to capture changing temporal characteristics of burst events. For instance, we
define a handful of data groups corresponding to natural breaks in the behavior of the GRB light curve.
During the modeling step we hold a number of parameters constant across the entire interval of the GRB;
for instance, the redshift parameter, z, does not change measurably over the duration of the burst event.
We also allow other parameters to vary, like AV, which describes the dust-extinction characteristics in the
source frame of the burst (see §2.B.2). By modeling all temporal components simultaneously and sharing
7
or freeing key values, we ensure the integrity of the overall fit while securing the ability to measure small,
but telling changes in certain parameters. For example, trends in the value of AV over time indicate a
changing dust profile in the circumburst environment as time progresses, probably a result of jet
spreading illuminating different dust populations, both those affected and unaffected by high-energy
radiation from the GRB itself (e.g., Draine 2000, Fruchter, Krolik & Rhoads 2001).
Decomposing data into semi-independent subsets and modeling the relationships between the groups
becomes exceptionally important when integrating data from different sources. For instance, networks of
small robotic telescopes provide a wealth of useful photometric data, but non-uniformities in the data
acquisition, calibration, and reporting process can skew results if not properly handled. Even highly
controlled surveys can exhibit significant photometric zero-point uncertainties that propagate to all
measurements based on those standards. Assigning data from various sources to specific data groups, we
can account for and measure these uncertainties by allowing the optimization engine to perturb entire
subsets in a uniform way. Concretely, this is accomplished by supplementing the model’s
parameterization with additional entries defining data offset values. We then constrain these parameters
with zero-centered Gaussian priors with widths suggested by the data calibration uncertainty. The end
result is that the optimizing engine can shift the data group, as a unit, by some small but reasonable
amount if it benefits the overall fit, and can provide a measure of the systematic calibration error.
2.B. Ph.D. Thesis: Foundational Statistics, and Extinction and Absorption Models
The complete model for GRB afterglow emission and all sources of absorption and extinction along the
line of sight contains dozens of parameters. However, most of these parameters are not truly “free”, but
are constrained by prior probability distributions, either on the parameter values themselves, or on sets of
parameters that describe the correlation of one parameter with another. These priors greatly reduce the
volume of parameter space that must be explored to find a best-fit model for a given burst (§2.A.1).
These correlation parameter priors are obtained by using Galapagos to fit models to various twodimensional data sets. In my Ph.D. thesis, I present a new, very general, statistic for evaluating the fitness
of a model to two-dimensional data sets (§2.B.1), and apply that statistic to construct priors that constrain
certain parameters in a complete line-of-sight extinction and absorption model (§2.B.2). The new
statistic, and the resulting extinction and absorption models, will be published in the summer of 2011 as
the first two, foundational papers of the AMP series (Trotter, Reichart & Foster 2011) [TRF].
2.B.1. TRF: A New Statistic for Fitting Models to Data in Two Dimensions
The TRF statistic is a new approach to the very general problem of fitting models to data in two
dimensions, where there is intrinsic uncertainty in the measured quantities in both dimensions, as well as
additional scatter in the data that is greater than can be accounted for by the intrinsic uncertainties alone.
The TRF statistic is both invertible, unlike the statistic of D’Agostini (2005) [D05], and reduces to a onedimensional, 2-like statistic, unlike the statistic of Reichart (2001) [R01]. As a general solution to the
problem of fitting data in two dimensions, this work is broadly applicable, not only across astrophysics
but across all of science. In all that follows, I assume that the intrinsic measurement uncertainties and the
extrinsic scatter, or sample variance, are normally distributed and independent in both dimensions.
8
Figure 3: Left: Intrinsic error ellipse of a data point and extrinsic sample variance convolved with model curve.
The joint probability of the data point and the model is the integral over the x-y plane of the product of these two
distributions. Right: This joint probability is equivalent to a path integral through a convolved error ellipse, where
intrinsic errors and extrinsic sample variance are added in quadrature. The model curve is approximated by the red
line tangent to the convolved error ellipse. TRF projects the differential element of path integration onto the blue
line. Shaded areas indicate 1, 2, and 3 confidence regions.
Consider a set of N points in the x-y plane with intrinsic uncertainties (“error bars”) in both dimensions
{xn, yn; xn, yn} and a model distribution, described by a curve defined by M parameters yc(x; m) and by
extrinsic sample variances x and y. The intrinsic two-dimensional probability distribution function of a
measured data point is:
pint ( x, y | xn , yn , xn , yn )  G( x, xn , xn )G( y, yn , yn ) ,
where G is the Gaussian function:
G ( x, xn , xn ) 
1
2  xn
 1  x  x 2 
n
 .
exp 
 2   xn  


The model probability distribution is given by the convolution of the model curve with a two-dimensional
Gaussian:
pmod ( x, y | m , x , y ) 
  ( y  yc ( x;m ))G( x, x, x )G( y, y, y )dxdy .
x , y 
Bayes’ theorem allows us to compute the probability of a given model distribution, given a set of
measurements and any prior constraints on the values of the model parameters. Assuming the prior
distributions of the parameters are flat, the best-fit model is found by maximizing the likelihood:
N
N
L ( m ,  x ,  y | x n , y n ,  xn ,  yn )    pint ( x, y | x n , y n ,  xn ,  yn )  p mod ( x, y |  m ,  x ,  y )dxdy   p n
n 1 x , y
n 1
.
For independent Gaussian intrinsic uncertainties and extrinsic sample distributions, the joint probability
pn is equivalent to a path integral through a convolved two-dimensional Gaussian probability distribution:
9
pn (m , x , y | xn , yn , xn , yn )   G( x, xn ,  xn ) G( yc ( x;m ), yn ,  yn ) ds ,
s
2
2
where  xn   x2   xn
and  yn   y2   yn
.
For a given data point, the path integral along the curve yc is approximated by finding the point at which
the curve is tangent to an error ellipse centered on (xn, yn) with axes proportional to (Σxn, Σyn) and
integrating the convolved probability along a line through that point with slope mt = tant. The surprising
fact is that the result of this 1D linear path integral depends upon which axis the differential path element
ds is projected onto (or, equivalently, whether you rotate the x-y coordinate system before performing the
integral). D05 chose ds = dx (no rotation). R01 chose ds  dx2  dy2  dx 1  mt2  1/ cost (rotation by
the angle t).
With TRF, the differential element ds is projected onto a line perpendicular to the segment connecting the
data point centroid and the tangent point of the curve to the convolved error ellipse; the angle between
this line and the tangent line is t, and its angle with respect to the x-axis is t. This is equivalent to
setting the differential path element to:
 2yn  mt2 2xn
cost
ds 
dx 
dx ,
cost
 4yn  mt2 4xn
or, equivalently, to rotating the coordinate system by an angle t before performing the integration. A
more intuitive interpretation of TRF is that it is mathematically equivalent to a modified 1D 2-like
statistic:
pnTRF 
 1   2 
exp   tn   ,
2 tn
 2  tn  


1
where tn is the radial distance between the data point centroid and the tangent point (the point at which
the model curve is closest to the data point, in terms of , and tn is the 1-sigma radius of the convolved
error ellipse along that axis.
Three criteria motivate this choice: (1) The statistic should be invertible, i.e., if xn  yn, xn  yn, and
x  y, the best-fit model parameters should describe the curve xc(y;m) = yc-1(x;m); (2) The statistic
should reduce to the traditional 1D 2-like statistic in y or x when xn = 0 or yn = 0, respectively; and (3)
When applied to a data set consisting of only two points, the statistic should produce a best-fit line that
intersects the centroids of both points’ error ellipses in as many cases as possible.
The following table summarizes the properties of the D05, R01, and TRF statistics:
D05
R01
TRF
Differential Element ds =
dx
Invertible?
No
1/cost dx
Yes
cosφt /cost dx
Yes
Reduces to 1D  ?
If xn = 0
No
Yes
Fits 2 Data Points?
If xn = 0
If xn =yn
If xn = 0, yn = 0, or
xn =yn
2
10
Linear fits to circularly symmetric Gaussian random clouds of points illustrate the bias inherent in the
D05 statistic. R01 and TRF fits are invertible (mxy=1/myx), while D05 is biased towards m = 0 whether
fitting to y vs. x or x vs. y: The probability distributions of = tan-1(m) for ensembles of fits to Gaussian
random clouds of N points are pR01() = pTRF() = constant, while pD05()  cosN. Linear fits to sets of
data points generated by adding Gaussian random noise to a linear model show that D05 consistently
underestimates the generating slope when there are error bars in two dimensions. The only case for which
D05 correctly recovers the generating parameters is when the intrinsic uncertainty and sample variance
are in the y-direction only, where D05 is equivalent to a 1D χ2-like statistic. The R01 statistic does not
reduce to a χ2-like statistic in the 1D case, and the best-fit slopes are biased in cases where the axial ratios
of the error ellipses are large (R01 is equivalent to TRF when xn =yn).
Figure 4: Left: Linear fits to circularly symmetric Gaussian random cloud of N=100 data points. Red lines show
fits with the non-invertible D05 statistic to y vs. x and x vs. y. Green line shows fit with the invertible TRF statistic.
Right: Probability distribution of fitted position angle ϑ to ensembles of such Gaussian random clouds. For D05,
fitted ϑ is biased towards 0 by a factor cosNϑ, while for TRF all position angles are equally likely.
2.B.2. AMP Extinction and Absorption Models
While the intrinsic emission of an afterglow can typically be described by one or more power-law curves
(sometimes smoothly broken) in time and frequency, accounting for the absorption due to gas and
extinction due to dust in the host galaxy, the Milky Way, and the intergalactic medium is rather more
complicated. The full extinction/absorption model contains no fewer than 50 parameters. Though most of
these parameters are constrained by priors, finding the best-fit afterglow model in this complicated
parameter space would be effectively impossible without a tool as flexible and efficient as Galapagos.
Furthermore, using Galapagos’s parameter-linking capabilities (§2.A.2), it is possible to explore changes
in the circumburst environment over time: Those parameters that describe source-frame extinction and
absorption can be allowed to vary independently for different subsets of the data, while others, such as the
burst redshift and the parameters that describe intergalactic absorption and extinction due to dust in the
Milky Way along the line of sight, can be linked across the entire data set.
11
Figure 5: The combined CCM/FM dust-extinction
model.
Extinction due to dust in the source frame of the
host galaxy and in the Milky Way is modeled
using the near-UV through infrared extinction
model of Cardelli, Clayton & Mathis (1989)
[CCM] and the UV extinction model of Fitzpatrick
& Massa (1988, 1990) [FM]. The extinction at a
given wavelength  can be expressed as:
A
1 E (  V )
1
AV
RV E ( B  V )
.
The parameter AV normalizes the extinction curve in the V band, and RV = AV /E(B-V) is a measure of the
extinction in the B band relative to that in the V band. Extinction due to dust in the Milky Way is
described by the CCM model, with an asymmetric Gaussian prior, log RVMW  0.423 00..082
010 , and a fixed
value of E(B-V)MW for the burst’s line of sight, obtained from all-sky IR dust-emission maps (Schlegel,
Finkbeiner & Davis 1998). Extinction in the host galaxy is described by a combination of the CCM and
FM models; the only free parameters are AV and the CCM model parameters c2 and c4. The other
parameters in the model, including RV, are constrained by priors obtained by fitting empirical functional
relationships, using Galapagos and the TRF statistic, to measured extinction parameters for 417 stars in
the Milky Way and 23 stars in the Large and Small Magellanic Clouds (Valencic, Clayton & Gordon
2004, Gordon et al. 2003).
For source-frame x = ( / 1 μm)-1 < 1.82, we use the CCM extinction model:
A
b( x )
,
 a ( x) 
AV
RV
where a(x) and b(x) are empirical functions fitted by CCM. For 3.3 < x < 10.96, we use the FM extinction
model:
c
E (  V )
x2
 c1  c2 x  32
E(B  V )
 ( x 2  x02 ) 


2
 x2
 c4 F ( x) ,
where F(x) is an empirical function fitted by FM that describes the shape of the far-UV excess. For 1.82 <
x < 3.3, we use a weighted average of the two models (Figure 5). In the AMP dust-extinction model: c2,
c4 and AV are free parameters; c1, UV bump height c3/2, and RV are constrained by priors on the
correlation model parameters (Figure 6); while  and x0 are constrained by Gaussian priors:
  0.895  0.141 and x0  4.584  0.019 .
12
Figure 6: 1, 2, and 3 fitted model distributions to correlations of dust-extinction parameters measured for 441
stars in the Milky Way and Large and Small Magellanic Clouds. Low values of the UV extinction parameter c 2 ~ 0
correspond to “gray dust”, typical of young star-forming regions (SFRs) with strong stellar winds, as in the Orion
Nebula; high values correspond to higher ratios of small grains to large grains, typical of older SFRs with
supernova shocks, as in the SMC. Left: c1 vs. c2. Middle: RV vs. c2. While RV ~ 3.1 is typical of stars in the Milky
Way and older SFRs, higher values, i.e. smaller E(B-V), are found in young SFRs with low c 2 values. Right: UV
bump height vs. c2. UV bumps are thought to be due to resonances in the lattice structure of graphitic dust grains,
and are typical of Milky Way dust-extinction spectra. Dust-extinction spectra in SFRs, with both high and low values
of c2, exhibit less prominent UV bumps.
To model Lyα absorption in the intergalactic medium, I used Galapagos and the TRF statistic to fit an
empirical model to transmission T vs. absorber redshift z based on observed flux deficits for 64 QSOs,
measured in binned regions of width z of their spectra blueward of Lyα in the source frame (Figure 7;
Songaila 2005, Fan et al. 2006). The empirical model has the form:
ln(  ln T )  ln exp b1  tan 1 z  z1   exp b2  tan  2 z  z 2  ,
1
with sample variance in ln(-lnT) given by  ln( ln T )   0 (1  z ) (z ) 2 . The redshifts z1 and z2 are chosen
to minimize correlations among fitted parameters. AMP models Lyα-forest absorption by fitting to
parameters b1, 1, b2, 2, 0, and , which are constrained by priors based on the empirical fit to QSO
transmission data; AMP also allows for an offset in each
photometric filter in ln(-lnT) with a zero-mean Gaussian prior
that scales as (1  z F ) z F
 12
, where z F and z F are the
effective weighted mean absorber redshift and bin width,
respectively, of the overlap of filter F with the Ly forest. The
host-galaxy redshift zGRB is typically held fixed, based on
spectral or other observations, but can be allowed to vary if we
wish to independently determine a photometric redshift.
Figure 7: IGM Lyα transmission vs. source-frame absorber redshift
measured for 64 QSOs. The solid line is the best-fit empirical model
curve, transformed into lnT space; shaded regions are the
transformed 1, 2, and 3 sample variance intervals for a typical bin
width z = 0.07. Note the onset of the Gunn-Peterson trough near
redshift z ~ 6.
13
The AMP model also includes a damped Lyα absorber profile at the source redshift, whose shape is
parameterized solely by the neutral-hydrogen column density NH, while assuming total absorption at
wavelengths shorter than the Lyman limit  < 912 Å in the source frame. The column density NH may be
fit as a free parameter, or with prior constraints from X-ray or preferably optical spectroscopic
observations, when available. I have also developed an empirical model of absorption due to rotovibrationally excited molecular hydrogen, based on fits to theoretical spectra (Draine 2000).
2.C. Summary
We now have all the components of AMP necessary to begin fitting models to observed GRB afterglows:
the observational data provided by Skynet telescopes (§1) and the literature; a statistic (§§2.A.1 and
2.B.1); a model (§2.B.2, plus a library of intrinsic GRB emission models not discussed here); and a model
fitting tool, Galapagos (§2.A). Figure 8 illustrates one of our first AMP model fitting efforts, the “slowrising” GRB 090313 (which I also present in my Ph.D. thesis). This burst was selected so as to exercise
as many components of the extinction and absorption models as possible. Its redshift of z=3.375 places
both the Lyα forest and the source-frame UV extinction model of Fitzpatrick & Massa (1988, 1990) in the
optical BVRI bandpasses in the observer’s frame. The underlying emission model is a smoothly-broken
power law in time (first brightening, then dimming), and a single power law in frequency. The plot in
Figure 8, which is an actual screen shot of Galapagos in action, shows the model flux as a function of
frequency and time (log scale; green) superimposed on the observed flux data (red). The onset of the Lyα
forest is clearly visible as a “shelf” in the foreground of the model surface plot. Though not visible on the
scale of this plot, the model also includes the so-called “UV-bump”, as well as a source-frame damped
Lyα absorber. Given the difficulty of monitoring a large list of ever-changing model parameters values,
rough, real-time plots such as this are very useful in guiding a fit in its initial stages, alerting the user to
cases where it may diverge into unphysical regimes or get stuck in local minima.
Figure 8: Mid-run screen capture of
Galapagos fitting Skynet/PROMPT
and Skynet/DAO (Italy) observations
of the slow-rising afterglow of GRB
090313 at z = 3.375, which exercises
both
AMP’s
extinction
and
absorption models (the Ly forest
can be seen in the foreground of the
image). AMP measures source-frame
AV = 0.55 – 0.59 mag and an SMClike c2 = 2.1 – 2.5 depending on the
emission model.
14
3. Research Plan: Opportunities for Undergraduate Participation
3.A. Undergraduate Recruitment
Figure 9 illustrates the “recruitment pyramid” that we have developed at UNC-CH to train and guide new
undergraduates into astronomical research and STEM careers. The base of the pyramid is our
astronomical facilities, including Skynet’s UNC-owned assets. Students begin with our introductory
astronomy course (ASTR101, which is analogous to HPU’s PHY 1000), and our Skynet-based
introductory astronomy laboratory (ASTR101L, which may be taken independently of the lecture courses,
and which is described in detail in my teaching statement). These courses are primarily aimed at nonscience majors seeking to fulfill their core curriculum science and laboratory requirements. A fraction of
these students will continue on to take the second semester lecture course (ASTR102, analogous to
HPU’s PHY 1050). The majority of students selected for the one-week summer ERIRA program are
recruited from this second group (though anyone may apply). ERIRA has proven to be an excellent tool
for selecting promising new research assistants.
Currently, all members of the Skynet Lab are
ERIRA alumni (either participants, educators or
both). Students selected to be undergraduate
research assistants typically become physics
majors, and with few exceptions, go on to
graduate school in astronomy, physics or related
STEM fields.
Figure 9: UNC-CH Astronomy Recruitment Pyramid
I envision a similar process for training and recruiting undergraduates into astronomy research at HPU. I
will recruit exceptional undergraduates from HPU’s introductory astronomy courses (and, at least
initially, from higher-level courses) for research positions, primarily to work on AMP (though I am
certainly open to mentoring research in other areas of astronomy, as opportunities arise). For example,
we could create an REU-like experience, where students are introduced to AMP and trained in use of its
tools at HPU during the academic year, and then get to work in the Skynet Lab at UNC-CH during the
summer. In fact, REU supplements on existing Skynet NSF grants is a promising potential source of
summer funding, until I establish my own grants at HPU.
Immersive summer research experiences are critical, providing an opportunity for students to participate
in research to a greater depth and with greater focus than is possible during the academic year, when
coursework competes for attention. As part of this summer experience, students could also participate in
the one-week ERIRA program at NRAO-Green Bank (see teaching statement); I can think of no way
better to “jump-start” a student into active research. The proximity of HPU to Chapel Hill will facilitate
ongoing participation in AMP, both during the summer and during the following academic years.
Participation in AMP, especially at these early stages of its development, would likely lead to any number
15
of excellent senior honors theses, and certainly would lead to undergraduate co-authorships on journal
articles and conference proceedings.
3.B. What Will They Actually Do?
While Dan Reichart will continue to supervise the overall progress and funding of AMP, I will remain in
charge of leading the actual GRB modeling efforts, and of publishing the results of our model fits.
Having established the details of the GRB extinction and absorption models, and the priors that constrain
that model’s various parameters, we are now in a position to begin fitting models, using Galapagos, to the
vast and ever-growing library of GRB afterglow observations that have been observed to date. UNC-CH
graduate student Justin Moore, as part of his PhD thesis work, has begun to construct a comprehensive
database, and a user-friendly, web-based interface, in which we will compile all available GRB afterglow
observations since 1997, and the results of our analysis of each.
To date, I have mentored one graduate and three undergraduate students at UNC-CH in conducting model
fits to GRBs using Galapagos, though the learning curve was rather steep in AMP’s preliminary phases,
and computational resources were sometimes limited. By the summer of 2012, I expect the AMP
database and interface to be sufficiently developed to easily allow undergraduate students to participate
with a minimum of training, and to be able to explore in detail models of several bursts over, say, the
course of a summer project (including time to present and publish their results).
Given the large number of archival bursts that we intend to analyze for AMP, and the continual addition
of new bursts as they occur (most of which will have increasingly broad and accurate observational
coverage), there will be no shortage of potential research projects suitable for undergraduates in the
foreseeable future. Thanks to the modular construction of Galapagos, new users will not be required to
understand every detail of the statistics and priors that underlie the extinction and absorption models in
order to make meaningful contributions. They may choose from a variety of available emission models,
or construct new ones (which provides an opportunity to gain a basic familiarity with C++), and
concentrate on actually performing fits, interpreting the results, and publishing them.
The tasks involved in fitting models to a given burst, or set of bursts, are ideally suited for introducing
undergraduates to scientific research. First, it is necessary to perform a thorough review of all published
literature for a given burst, to compile a table of observed fluxes as a function of frequency and time, and
to enter these data into the master AMP database. These published data will typically come from a wide
range of instruments, including space-based X-ray and UV observations, IR and optical observations from
multiple telescopes using a range of photometric filters, and, when available, radio observations from
instruments like the NRAO Very Large Array. In compiling these data, students will gain a familiarity
with researching the astronomical literature and with the technical language (including flux measurement
conventions) employed to describe observational results over a wide range of astronomical
instrumentation.
Once the data are compiled, the next task is preliminary data visualization, in the form of plots of flux
versus time and frequency; this requires gaining familiarity with the SuperMongo plotting package. The
plots will help inform the choice of emission models, data grouping, and extinction and absorption
parameter variation over the duration of the burst. I will train and guide students in interpreting these
16
preliminary plots, identifying interesting and unusual trends in the data, and selecting a set of potential
models to test.
The next step is to use Galapagos to actually determine the relative fitness of the various candidate
models. This is a computationally intensive process, and it used to take hours or even days to arrive at a
best-fit on a single-processor machine. Fortunately, Galapagos has been recently re-designed to take full
advantage of parallel processors, and even processors distributed over a network; and it has been shown
that, in its current form, the Galapagos’ time to best-fit convergence increases linearly with processor
number. We have recently obtained and successfully tested Galapagos on a 48-core machine, and will
soon have access to a ~800-core machine shared by UNC’s Department of Physics and Astronomy. We
are also actively developing the capability to distribute the computational burden of Galapagos among
multiple machines in a network, in the same spirit as SETI@Home. With these resources, and with
further computational resources I will work to acquire for HPU, a GRB model fit will take not hours or
days, but minutes, and it will be possible to fully explore all physically interesting models for a given
burst in a matter of weeks. Based on their relative fitness and fitted parameter values, we can then rule
out those models that are statistically or physically implausible, and arrive at one (or, at most, a small
handful) of models to explore in more detail.
The final task is to perform detailed parameter estimation analysis for the plausible models, including
obtaining estimates of the probability distributions (i.e., uncertainties) on each physically interesting
parameter. These parameter estimates, along with plots of the best-fit models, will then be entered into
the AMP database for the burst, to be employed in later GRB population studies. Tables and plots of the
fits will be generated in formats suitable for formal presentations and publication in astronomical
journals.
3.C. Going Forward
Developing a library of GRB afterglow models is an ongoing, evolving project. As we proceed through
the catalog, we fully expect to encounter bursts that cannot be adequately described by the models
currently in our library. Development of new models and exploration of new extinction and absorption
scenarios, as well as the eventual GRB population studies, will be a data-driven process, informed by the
model fitting results obtained by undergraduates and other participants in AMP. Part of the excitement
of AMP is that we really don’t yet know what we will find; GRB research is a relatively new field in
astronomy, and there is much to be discovered. I believe AMP to be an ideal, and fertile, vehicle for
introducing a new generation to astrophysical research.
Finally, there are a number of interesting unresolved problems that I plan to continue exploring, together
with Dan Reichart. The extinction and absorption priors will always be subject to revision and
elaboration as new data warrant. As we begin to systematically construct the AMP catalog of GRB model
parameters, there will be untold opportunities for meta-analysis of these data, to explore and discover
underlying trends in GRBs themselves, and to reconstruct the evolution of star-forming regions in the
early universe. Galapagos is more than a tool for GRB modeling; it is generally applicable to almost any
data-driven modeling project that can be imagined. There are a number of unresolved issues related to
the TRF statistic and its implementation that I wish to investigate, including dealing with non-normal
probability distributions, the treatment of correlated measurement uncertainties in a data set, and
extension to data sets in greater than two dimensions.
17
References
B. N. Barlow, B. H. Dunlap, J. C. Clemens, A. E. Lynas-Gray, K. M. Ivarsen, A. P. LaCluyzé, D. E.
Reichart, J. B. Haislip, and M. C. Nysewander. Photometry and spectroscopy of the new sdBV CS 1246.
MNRAS, 403:324–334, March 2010.
V. Bromm and A. Loeb. The Expected Redshift Distribution of Gamma-Ray Bursts. ApJ, 575:111–116,
August 2002.
Z. Cano, D. Bersier, C. Guidorzi, R. Margutti, K. M Svensson, S. Kobayashi, A. Melandri, K. Wiersema,
A. Pozanenko, A. J. van der Horst, G. G. Pooley, A. Fernandez-Soto, A. J. Castro-Tirado, A. de Ugarte
Postigo, M. Im, A. P. Kamble, D. Sahu, J. Alonso-Lorite, G. Anupama, J. L. Bibby, M. J. Burgdorf, N.
Clay, P. A. Curran, T. A. Fatkhullin, A. S. Fruchter, P. Garnavich, A. Gomboc, J. Gorosabel, J. F.
Graham, U. Gurugubelli, J. Haislip, K. Huang, A. Huxor, M. Ibrahimov, Y. Jeon, Y. Jeon, K. Ivarsen, D.
Kasen, E. Klunko, C. Kouveliotou, A. LaCluyzé, A. J. Levan, V. Loznikov, P. A. Mazzali, A. S.
Moskvitin, C. Mottram, C. G. Mundell, P. E. Nugent, M. Nysewander, P. T. O’Brien, W. -. Park, V.
Peris, E. Pian, D. Reichart, J. E. Rhoads, E. Rol, V. Rumyantsev, V. Scowcroft, D. Shakhovskoy, E.
Small, R. J. Smith, V. V. Sokolov, R. L. C. Starling, I. Steele, R. G. Strom, N. R. Tanvir, Y. Tsapras, Y.
Urata, O. Vaduvescu, A. Volnova, A. Volvach, R. A. M. J. Wijers, S. E. Woosley, and D. R. Young. A
tale of two GRB-SNe at a common redshift of z = 0.54. ArXiv e-prints, December 2010.
J. A. Cardelli, G. C. Clayton, and J. S. Mathis. The relationship between infrared, optical, and ultraviolet
extinction. ApJ, 345:245–256, October 1989 [CCM].
S. B. Cenko, D. A. Frail, F. A. Harrison, J. B. Haislip, D. E. Reichart, N. R. Butler, B. E. Cobb, A.
Cucchiara, E. Berger, J. S. Bloom, P. Chandra, D. B. Fox, D. A. Perley, J. X. Prochaska, A. V.
Filippenko, K. Glazebrook, K. M. Ivarsen, M. M. Kasliwal, S. R. Kulkarni, A. P. LaCluyzé, S. Lopez, A.
N. Morgan, M. Pettini, and V. R. Rana. Afterglow Observations of Fermi-LAT Gamma-Ray Bursts and
the Emerging Class of Hyper-Energetic Events. ArXiv e-prints, April 2010.
B. Ciardi and A. Loeb. Expected Number and Flux Distribution of Gamma-Ray Burst Afterglows with
High Redshifts. ApJ, 540:687–696, September 2000.
G. Cusumano, V. Mangano, G. Chincarini, A. Panaitescu, D. N. Burrows, V. L. Parola, T. Sakamoto, S.
Campana, T. Mineo, G. Tagliaferri, L. Angelini, S. D. Barthelemy, A. P. Beardmore, P. T. Boyd, L. R.
Cominsky, C. Gronwall, E. E. Fenimore, N. Gehrels, P. Giommi, M. Goad, K. Hurley, J. A. Kennea, K.
O. Mason, F. Marshall, P. Mészáros, J. A. Nousek, J. P. Osborne, D. M. Palmer, P. W. A. Roming, A.
Wells, N. E. White, and B. Zhang. Gamma-ray bursts: Huge explosion in the early Universe. Nature,
440:164, March 2006.
G. D’Agostini. Fits, and especially linear fits, with errors on both axes, extra variance of the data points
and other complications. ArXiv e-prints, November 2005 [D05].
P. Descamps, F. Marchis, J. Durech, J. Emery, A. W. Harris, M. Kaasalainen, J. Berthier, J.-P. TengChuen-Yu, A. Peyrot, L. Hutton, J. Greene, J. Pollock, M. Assafin, R. Vieira-Martins, J. I. B. Camargo, F.
Braga-Ribas, F. Vachier, D. E. Reichart, K. M. Ivarsen, J. A. Crain, M. C. Nysewander, A. P. LaCluyzé,
J. B. Haislip, R. Behrend, F. Colas, J. Lecacheux, L. Bernasconi, R. Roy, P. Baudouin, L. Brunetto, S.
Sposetti, and F. Manzini. New insights on the binary Asteroid 121 Hermione. Icarus, 203:88–101,
September 2009.
18
B. T. Draine. Gamma-Ray Bursts in Molecular Clouds: H2 Absorption and Fluorescence. ApJ, 532:273–
280, March 2000.
X. Fan, M. A. Strauss, R. H. Becker, R. L. White, J. E. Gunn, G. R. Knapp, G. T. Richards, D. P.
Schneider, J. Brinkmann, and M. Fukugita. Constraining the Evolution of the Ionizing Background and
the Epoch of Reionization with z~6 Quasars. II. A Sample of 19 Quasars. AJ, 132:117–136, July 2006.
D. A. Fischer, G. Laughlin, G. W. Marcy, R. P. Butler, S. S. Vogt, J. A. Johnson, G. W. Henry, C.
McCarthy, M. Ammons, S. Robinson, J. Strader, J. A. Valenti, P. R., McCullough, D. Charbonneau, J.
Haislip, H. A. Knutson, D. E. Reichart, P. McGee, B. Monard, J. T. Wright, S. Ida, B. Sato, and D.
Minniti. The N2K Consortium. III. Short-Period Planets Orbiting HD 149143 and HD 109749. ApJ,
637:1094–1101, February 2006.
E. L. Fitzpatrick and D. Massa. An analysis of the shapes of ultraviolet extinction curves. II - The far-UV
extinction. ApJ, 328:734–746, May 1988 [FM].
E. L. Fitzpatrick and D. Massa. An analysis of the shapes of ultraviolet extinction curves. III - an atlas of
ultraviolet extinction curves. ApJS, 72:163–189, January 1990 [FM].
A. Fruchter, J. H. Krolik, and J. E. Rhoads. X-Ray Destruction of Dust along the Line of Sight to γ-Ray
Bursts. ApJ, 563:597–610, December 2001.
K. D. Gordon, G. C. Clayton, K. A. Misselt, A. U. Landolt, and M. J.Wolff. A Quantitative Comparison
of the Small Magellanic Cloud, Large Magellanic Cloud, and Milky Way Ultraviolet to Near-Infrared
Extinction Curves. ApJ, 594:279–293, September 2003.
J. Greiner, T. Krühler, J. P. U. Fynbo, A. Rossi, R. Schwarz, S. Klose, S. Savaglio, N. R., Tanvir, S.
McBreen, T. Totani, B. B. Zhang, X. F. Wu, D. Watson, S. D. Barthelmy, A. P. Beardmore, P. Ferrero, N.
Gehrels, D. A. Kann, N. Kawai, A. K. Yoldaş, P. Mészáros, B. Milvang-Jensen, S. R. Oates, D. Pierini, P.
Schady, K. Toma, P. M., Vreeswijk, A. Yoldaş, B. Zhang, P. Afonso, K. Aoki, D. N. Burrows, C.
Clemens, R. Filgas,, Z. Haiman, D. H. Hartmann, G. Hasinger, J. Hjorth, E. Jehin, A. J. Levan, E. W.,
Liang, D. Malesani, T.-S. Pyo, S. Schulze, G. Szokoly, K. Terada, and K. Wiersema. GRB 080913 at
Redshift 6.7. ApJ, 693:1610–1620, March 2009.
J. B. Haislip, M. C. Nysewander, D. E. Reichart, A. Levan, N. Tanvir, S. B. Cenko, D. B. Fox, P. A.
Price, A. J. Castro-Tirado, J. Gorosabel, C. R. Evans, E. Figueredo, C. L. MacLeod, J. R. Kirschbrown,
M. Jelinek, S. Guziy, A. D. U. Postigo, E. S. Cypriano, A. Lacluyze, J. Graham, R. Priddey, R. Chapman,
N. Kawai, G. Kosugi, K. Aoki, T. Yamada, T. Totani, K. Ohta, M. Iye, T. Hattori, W. Aoki, H. Furusawa,
K. Hurley, K. S. Kawabata, N. Kobayashi, Y. Komiyama, Y. Mizumoto, K. Nomoto, J. Noumaru, R.
Ogasawara, R. Sato, K. Sekiguchi, Y. Shirasaki, M. Suzuki, T. Takata, T. Tamagawa, H. Terada, J.
Watanabe, Y. Yatsu, and A. Yoshida. An optical spectrum of the afterglow of a γ-ray burst at a redshift of
z = 6.295. Nature, 440:184–186, March 2006.
K. G Hełminiak, M. Konacki, K. Złoczewski, M. Ratajczak, D. E. Reichart, K. M. Ivarsen, J. B. Haislip,
J. A. Crain, A. C. Foster, M. C. Nysewander, A. P. LaCluyzé, A. P. Orbital and physical parameters of
eclipsing binaries from the All-Sky Automated Survey catalogue. III. Two new low-mass systems with
rapidly evolving spots. A&A, 527: A14, March 2011
D. Q. Lamb and D. E. Reichart. Gamma-Ray Bursts as a Probe of the Very High Redshift Universe. ApJ,
536:1–18, June 2000.
19
A. C. Layden, A. J. Broderick, B. L. Pohl, D. E. Reichart, K. M. Ivarsen, J. B. Haislip, M. C.
Nysewander, A. P. Lacluyze, and T. M. Corwin. Searching for Long-Period Variables in Globular
Clusters: A Demonstration on NGC 1851 Using PROMPT. PASP, 122:1000–1007, September 2010.
M. C. Nysewander. Exploring optically dark and dim gamma-ray bursts: Instrumentation observation
and analysis. PhD thesis, The University of North Carolina at Chapel Hill, June 2006.
M. Nysewander, D. E. Reichart, J. A. Crain, A. Foster, J. Haislip, K. Ivarsen, A. Lacluyze, and A. Trotter.
Prompt Observations of the Early-Time Optical Afterglow of GRB 060607A. ApJ, 693:1417–1423,
March 2009.
A. Osterman Meyer, H. R. Miller, K. Marshall, W. T. Ryle, H. Aller, M. Aller, J. P. McFarland, J. T.
Pollock, D. E. Reichart, J. A. Crain, K. M. Ivarsen, A. P. LaCluyzé, and M. C. Nysewander. Results of
the First Simultaneous X-ray, Optical, and Radio Campaign on the Blazar PKS 1622-297. AJ, 136:1398–
1405, September 2008.
G. Pignata, J. Maza, R. Antezana, R. Cartier, G. Folatelli, F. Forster, L. Gonzalez, P. Gonzalez, M.
Hamuy, D. Iturra, P. Lopez, S. Silva, B. Conuel, A. Crain, D. Foster, K. Ivarsen, A. Lacluyze, M.
Nysewander, and D. Reichart. The CHilean Automatic Supernova sEarch (CHASE). In G. Giobbi, A.
Tornambe, G. Raimondo, M. Limongi, L. A. Antonelli, N. Menci, and E. Brocato, editors, American
Institute of Physics Conference Series, volume 1111 of American Institute of Physics Conference Series,
pages 551–554, May 2009.
G. Pignata, M. Stritzinger, A. Soderberg, P. Mazzali, M. M. Phillips, N. Morrell, J. P. Anderson, L. Boldt,
A. Campillay, C. Contreras, G. Folatelli, F. F¨orster, S. González, M. Hamuy, W. Krzeminski, J. Maza,
M. Roth, F. S. E. M. Levesque, A. Rest, J. A. Crain, A. C. Foster, J. B. Haislip, K. M. Ivarsen, A. P.
LaCluyzé, M. C. Nysewander, and D. E. Reichart. SN 2009bb: a Peculiar Broad-Lined Type Ic
Supernova. ArXiv e-prints, November 2010.
P. Pravec, D. Vokrouhlický, D. Polishook, D. J. Scheeres, A. W. Harris, A. Galád, O. Vaduvescu, F.
Pozo, A. Barr, P. Longa, F. Vachier, F. Colas, D. P. Pray, J. Pollock, D. Reichart, K. Ivarsen, J. Haislip,
A. Lacluyze, P. Kušnirák, T. Henych, F. Marchis, B. Macomber, S. A. Jacobson, Y. N. Krugly, A. V.
Sergeev, and A. Leroy. Formation of asteroid pairs by rotational fission. Nature, 466:1085–1088, August
2010.
P. A. Reed, G. E. McCluskey, Jr., Y. Kondo, J. Sahade, E. F. Guinan, A. Giménez, D. B. Caton, D. E.
Reichart, K. M. Ivarsen, and M. C. Nysewander. Ultraviolet study of the active interacting binary star R
Arae using archival IUE data. MNRAS, 401: 913–923, January 2010.
D. E. Reichart. Dust Extinction Curves and Lyα Forest Flux Deficits for Use in Modeling Gamma-Ray
Burst Afterglows and All Other Extragalactic Point Sources. ApJ, 553: 235–253, May 2001 [R01].
J. Rhoads, A. S. Fruchter, D. Q. Lamb, C. Kouveliotou, R. A. M. J. Wijers, M. B. Bayliss, B. P. Schmidt,
A. M.. Soderberg, S. R. Kulkarni, F. A. Harrison, D. S. Moon, A. Gal-Yam, M. M. Kasliwal, R. Hudec,
S. Vitek, P. Kubanek, J. A. Crain, A. C. Foster, J. C. Clemens, J. W. Bartelme, R. Canterna, D. H.
Hartmann, A. A. Henden, S. Klose, H.-S. Park, G. G. Williams, E. Rol, P. O’Brien, D. Bersier, F. Prada,
S. Pizarro, D. Maturana, P. Ugarte, A. Alvarez, A. J. M. Fernandez, M. J. Jarvis, M. Moles, E. Alfaro, K.
M. Ivarsen, N. D. Kumar, C. E. Mack, C. M. Zdarowicz, N. Gehrels, S. Barthelmy, and D. N. Burrows. A
photometric redshift of z = 6.39 ± 0.12 for GRB 050904. Nature, 440:181–183, March 2006.
R. Salvaterra, M. Della Valle, S. Campana, G. Chincarini, S. Covino, P. D’Avanzo, A. Fernández-Soto,
C. Guidorzi, F. Mannucci, R. Margutti, C. C. Thöne, L. A. Antonelli, S. D. Barthelmy, M. de Pasquale,
V. D’Elia, F. Fiore, D. Fugazza, L. K. Hunt, E. Maiorano, S. Marinoni, F. E. Marshall, E. Molinari, J.
20
Nousek, E. Pian, J. L. Racusin, L. Stella, L. Amati, G. Andreuzzi, G. Cusumano, E. E. Fenimore, P.
Ferrero, P. Giommi, D. Guetta, S. T. Holland, K. Hurley, G. L. Israel, J. Mao, C. B. Markwardt, N.
Masetti, C. Pagani, E. Palazzi, D. M. Palmer, S. Piranomonte, G. Tagliaferri, and V. Testa. GRB090423
at a redshift of z~8.1. Nature, 461:1258–1260, October 2009.
A. Songaila. The Properties of Intergalactic C IV and Si IV Absorption. I. Optimal Analysis of an
Extremely High Signal-to-Noise Quasar Sample. AJ, 130:1996–2005, November 2005.
D. J. Schlegel, D. P. Finkbeiner, and M. Davis. Maps of Dust Infrared Emission for Use in Estimation of
Reddening and Cosmic Microwave Background Radiation Foregrounds. ApJ, 500:525+, June 1998.
N. R. Tanvir, D. B. Fox, A. J. Levan, E. Berger, K. Wiersema, J. P. U. Fynbo, A. Cucchiara, T. Krühler,
N. Gehrels, J. S. Bloom, J. Greiner, P. A. Evans, E. Rol, F. Olivares, J. Hjorth, P. Jakobsson, J. Farihi, R.
Willingale, R. L. C. Starling, S. B. Cenko, D. Perley, J. R. Maund, J. Duke, R. A. M. J. Wijers, A. J.
Adamson, A. Allan, M. N. Bremer, D. N. Burrows, A. J. Castro-Tirado, B. Cavanagh, A. de Ugarte
Postigo, M. A. Dopita, T. A. Fatkhullin, A. S. Fruchter, R. J. Foley, J. Gorosabel, J. Kennea, T. Kerr, S.
Klose, H. A. Krimm, V. N. Komarova, S. R. Kulkarni, A. S. Moskvitin, C. G. Mundell, T. Naylor, K.
Page, B. E. Penprase, M. Perri, P. Podsiadlowski, K. Roth, R. E. Rutledge, T. Sakamoto, P. Schady, B. P.
Schmidt, A. M. Soderberg, J. Sollerman, A. W. Stephens, G. Stratta, T. N. Ukwatta, D. Watson, E.
Westra, T. Wold, and C. Wolf. A γ-ray burst at a redshift of z~8.2. Nature, 461:1254–1257, October
2009.
S. E. Thompson, M. H. Montgomery, T. von Hippel, A. Nitta, J. Dalessio, J. Provencal, W. Strickland, J.
A. Holtzman, A. Mukadam, D. Sullivan, T. Nagel, D. Koziel-Wierzbowska, T. Kundera, S. Zola, M.
Winiarski, M. Drozdz, E. Kuligowska, W. Ogloza, Z. Bognár, G. Handler, A. Kanaan, T. Ribeira, R.
Rosen, D. Reichart, J. Haislip, B. N., Barlow, B. H. Dunlap, K. Ivarsen, A. LaCluyze, and F. Mullally.
Pulsational Mapping of Calcium Across the Surface of a White Dwarf. ApJ, 714:296–308, May 2010.
A. S. Trotter, D. E. Reichart, and A. C. Foster. The GRB Afterglow Modeling Project (AMP): Statistics
and Lyα Forest Absorption Model. In C. Meegan, C. Kouveliotou, and N. Gehrels, editors, American
Institute of Physics Conference Series, volume 1133 of American Institute of Physics Conference Series,
pages 254–256, May 2009.
A. S. Trotter. The Gamma-Ray Burst Afterglow Modeling Project: Foundational Statistics and Extinction
and Absorption Models. PhD thesis, The University of North Carolina at Chapel Hill, August 2011 (in
preparation).
A. S. Trotter, D. E. Reichart and A. C. Foster. The Gamma-Ray Burst Afterglow Modeling Project
(AMP): I. Foundational Statistics, 2011 (in preparation) [TRF].
A. S. Trotter, D. E. Reichart and A. C. Foster. The Gamma-Ray Burst Afterglow Modeling Project
(AMP): II. Extinction and Absorption Models, 2011 (in preparation).
L. A. Valencic, G. C. Clayton, and K. D. Gordon. Ultraviolet Extinction Properties in the Milky Way.
ApJ, 616:912–924, December 2004.
21