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-\lyxformat 344
+#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\begin_document
\begin_header
\textclass aastex
\shortauthors{Collapsed Cores in Globular Clusters}
\end_preamble
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+\suppress_date false
+\justification true
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+\index Index
+\shortcut idx
+\color #008000
+\end_index
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\quotes_language english
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-\author ""
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\end_header
\begin_body
\begin_layout Author
S.
Djorgovski
-\begin_inset ERT
-status collapsed
+\begin_inset Flex altaffilmark
+status open
\begin_layout Plain Layout
-
-
-\backslash
-altaffilmark{1,2,3}
+1,2,3
\end_layout
\end_inset
and Ivan R.
King
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
\begin_layout Plain Layout
-
-
-\backslash
-altaffilmark{1}
+1
\end_layout
\end_inset
C.
D.
Biemesderfer
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
\begin_layout Plain Layout
-
-
-\backslash
-altaffilmark{4,5}
+4,5
\end_layout
\end_inset
R.
J.
Hanisch
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
\begin_layout Plain Layout
-
-
-\backslash
-altaffilmark{5}
+5
\end_layout
\end_inset
Space Telescope Science Institute, Baltimore, MD 21218
\end_layout
-\begin_layout Standard
-\begin_inset ERT
+\begin_layout Altaffilation
+\begin_inset Argument 1
status open
\begin_layout Plain Layout
+1
+\end_layout
+\end_inset
-\backslash
-altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American Observatory.
+Visiting Astronomer, Cerro Tololo Inter-American Observatory.
CTIO is operated by AURA, Inc.
-\backslash
- under contract to the National Science Foundation.}
-\end_layout
-
-\begin_layout Plain Layout
+\begin_inset space \space{}
+\end_inset
+under contract to the National Science Foundation.
\end_layout
-\begin_layout Plain Layout
-
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{2}{Society of Fellows, Harvard University.}
+\begin_layout Plain Layout
+2
\end_layout
-\begin_layout Plain Layout
+\end_inset
+Society of Fellows, Harvard University.
\end_layout
-\begin_layout Plain Layout
-
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{3}{present address: Center for Astrophysics, 60 Garden Street,
- Cambridge, MA 02138}
+\begin_layout Plain Layout
+3
\end_layout
-\begin_layout Plain Layout
+\end_inset
+present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
+ 02138
\end_layout
-\begin_layout Plain Layout
-
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{4}{Visiting Programmer, Space Telescope Science Institute}
-
+\begin_layout Plain Layout
+4
\end_layout
-\begin_layout Plain Layout
+\end_inset
+Visiting Programmer, Space Telescope Science Institute
\end_layout
-\begin_layout Plain Layout
-
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{5}{Patron, Alonso's Bar and Grill}
+\begin_layout Plain Layout
+5
\end_layout
\end_inset
-
+Patron, Alonso's Bar and Grill
\end_layout
\begin_layout Abstract
\end_inset
collisions can be expressed in terms of fermion strings of the form
-\begin_inset Formula \begin{equation}
-\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),\end{equation}
+\begin_inset Formula
+\begin{equation}
+\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
+\end{equation}
\end_inset
\end_inset
and the unit matrix 1 as
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
\gamma^{\mu} & = & \left(\begin{array}{cc}
0 & \sigma_{+}^{\mu}\\
-\sigma_{-}^{\mu} & 0\end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
+\sigma_{-}^{\mu} & 0
+\end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
-1 & 0\\
-0 & 1\end{array}\right),\\
-\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),\end{eqnarray*}
+0 & 1
+\end{array}\right),\\
+\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
+\end{eqnarray*}
\end_inset
giving
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\hat{a}=\left(\begin{array}{cc}
0 & (\hat{a})_{+}\\
-(\hat{a})_{-} & 0\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},\end{equation}
+(\hat{a})_{-} & 0
+\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
+\end{equation}
\end_inset
The spinors are expressed in terms of two-component Weyl spinors as
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
u=\left(\begin{array}{c}
(u)_{-}\\
-(u)_{+}\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.\end{equation}
+(u)_{+}
+\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
+\end{equation}
\end_inset
\end_layout
\begin_layout MathLetters
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
-v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)\end{eqnarray}
+v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
+\end{eqnarray}
\end_inset
\begin_layout Standard
Consider a task that computes profile parameters for a modified Lorentzian
of the form
-\begin_inset Formula \begin{equation}
-I=\frac{1}{1+d_{1}^{P(1+d_{2})}}\end{equation}
+\begin_inset Formula
+\begin{equation}
+I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
+\end{equation}
\end_inset
where
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{1}=\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}\]
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{2}=\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}\]
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
-x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\]
+\begin_inset Formula
+\[
+x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
+\]
\end_inset
-\begin_inset Formula \[
-y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta\]
+\begin_inset Formula
+\[
+y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\]
\end_inset
\begin_inset Formula $M_{\sun}$
\end_inset
-, but the assumption is that the alternate results should be less than 90
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-degr
-\backslash
-
-\end_layout
-
-\end_inset
-
-out of phase with previous values.
+, but the assumption is that the alternate results should be less than 90°
+ out of phase with previous values.
We have no observations of
\begin_inset ERT
status collapsed
\backslash
-anchor{ftp://www.aas.org/pubs/}{AAS ftp site}
+anchor{
+\end_layout
+
+\end_inset
+
+ftp://www.aas.org/pubs/
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{
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+
+\end_inset
+
+AAS ftp site
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
\end_layout
\end_inset
\begin_layout Standard
Consider once again a task that computes profile parameters for a modified
Lorentzian of the form
-\begin_inset Formula \begin{equation}
-I=\frac{1}{1+d_{1}^{P(1+d_{2})}}\end{equation}
+\begin_inset Formula
+\begin{equation}
+I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
+\end{equation}
\end_inset
\end_layout
\begin_layout MathLetters
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}\]
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}\end{equation}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\end{equation}
\end_inset
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
-y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta\end{eqnarray}
+y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\end{eqnarray}
\end_inset
\begin_layout Standard
For completeness, here is one last equation.
-\begin_inset Formula \begin{equation}
-e=mc^{2}\end{equation}
+\begin_inset Formula
+\begin{equation}
+e=mc^{2}
+\end{equation}
\end_inset
\end_layout
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projects / lyx.git / blobdiff