%defs.tex cfm 2/23/00

\def\newpage	{\vfill\eject}
\newcommand	{\bs}{\bigskip}
\newcommand	{\ms}{\medskip}
\newcommand	{\cen}{\centerline}
\newcommand	{\dis}{\displaystyle}
\newcommand	{\pagenumbers}{\headline={\hss\tenrm\folio\hss}}
\def\undertext#1{$\underline{\smash{\hbox{#1}}}$}
\newcommand	{\beq}{\begin{equation}}
\newcommand	{\eeq}{\end{equation}}
\newcommand	{\beqa}{\begin{eqnarray}}
\newcommand	{\eeqa}{\end{eqnarray}}
\newcommand	{\bml}{\begin{mathletters}}
\newcommand	{\eml}{\end{mathletters}}

% ABBREVIATIONS
\newcommand	{\etal}{{et al.}}
\newcommand	{\ie}{i.e.}
\newcommand	{\eg}{e.g.}

% SPECIAL SYMBOLS
\def\avg#1	{\langle #1\rangle}
\newcommand	{\simlt}{\lower.5ex\hbox{$\; \buildrel < \over \sim \;$}}
\newcommand	{\simgt}{\lower.5ex\hbox{$\; \buildrel > \over \sim \;$}}
\newcommand	{\solar}{\ifmmode _{\mathord\odot}\else $_{\mathord\odot}$\fi}
\newcommand	{\del}{\nabla}
\newcommand     {\calc}{\ifmmode {{\cal C}} \else ${{\cal C}}$\fi}
\newcommand     {\calf}{\ifmmode {{\cal F}} \else ${{\cal F}}$\fi}
\newcommand     {\calg}{\ifmmode {{\cal G}} \else ${{\cal G}}$\fi}
\newcommand     {\calh}{\ifmmode {{\cal H}} \else ${{\cal H}}$\fi}
\newcommand     {\call}{\ifmmode {{\cal L}} \else ${{\cal L}}$\fi}
\newcommand     {\calm}{\ifmmode {{\cal M}} \else ${{\cal M}}$\fi}
\newcommand     {\caln}{\ifmmode {{\cal N}} \else ${{\cal N}}$\fi}
\newcommand     {\calo}{\ifmmode {{\cal O}} \else ${{\cal O}}$\fi}
\newcommand     {\calp}{\ifmmode {{\cal P}} \else ${{\cal P}}$\fi}
\newcommand     {\calq}{\ifmmode {{\cal Q}} \else ${{\cal Q}}$\fi}
\newcommand     {\calr}{\ifmmode {{\cal R}} \else ${{\cal R}}$\fi}
\newcommand     {\cals}{\ifmmode {{\cal S}} \else ${{\cal S}}$\fi}
\newcommand     {\calt}{\ifmmode {{\cal T}} \else ${{\cal T}}$\fi}
\newcommand     {\calv}{\ifmmode {{\cal V}} \else ${{\cal V}}$\fi}
\newcommand     {\calw}{\ifmmode {{\cal W}} \else ${{\cal W}}$\fi}

% POWERS
\def\power#1	{\ifmmode \times10^{#1}\else $\times~10^{#1}$\fi}
\newcommand	{\none}{\ifmmode ^{-1}\else $^{-1}$\fi}
\newcommand	{\e}{\ifmmode ^{-1}\else $^{-1}$\fi}
\newcommand	{\two}{\ifmmode ^{2}\else $^{2}$\fi}
\newcommand	{\ntwo}{\ifmmode ^{-2}\else $^{-2}$\fi}
\newcommand	{\ee}{\ifmmode ^{-2}\else $^{-2}$\fi}
\newcommand	{\three}{\ifmmode ^{3}\else $^{3}$\fi}
\newcommand	{\nthree}{\ifmmode ^{-3}\else $^{-3}$\fi}
\newcommand	{\eee}{\ifmmode ^{-3}\else $^{-3}$\fi}
\newcommand	{\four}{\ifmmode ^{4}\else $^{4}$\fi}
\newcommand	{\nfour}{\ifmmode ^{-4}\else $^{-4}$\fi}
\newcommand	{\five}{\ifmmode ^{5}\else $^{5}$\fi}
\newcommand	{\nfive}{\ifmmode ^{-5}\else $^{-5}$\fi}

% UNITS
% length
\newcommand	{\cm}{\ifmmode {\rm cm}\else cm\fi}
\newcommand	{\m}{\ifmmode {\rm m}\else m\fi}
\newcommand	{\km}{\ifmmode {\rm km}\else km\fi}
\newcommand	{\pc}{\ifmmode {\rm pc}\else pc\fi}
\newcommand	{\kpc}{\ifmmode {\rm kpc}\else kpc\fi}
\newcommand	{\Mpc}{\ifmmode {\rm Mpc}\else Mpc\fi}
\newcommand	{\ly}{\ifmmode {\rm ly}\else ly\fi}
% time
\newcommand	{\s}{\ifmmode {\rm s}\else s\fi}
\newcommand	{\Hz}{\ifmmode {\rm Hz}\else Hz\fi}
\newcommand	{\yr}{\ifmmode {\rm yr}\else y\fi}
% other
\newcommand	{\K}{\ifmmode {\rm K}\else K\fi}
\newcommand	{\ster}{\ifmmode {\rm ster}\else ster\fi}
\newcommand	{\erg}{\ifmmode {\rm erg}\else erg\fi}
\newcommand	{\dyn}{\ifmmode {\rm dyn}\else dyn\fi}
\newcommand     {\mug}{\ifmmode {\mu \rm{G}} \else {$\mu$G}\fi}
\newcommand	{\Msun}{\ifmmode {M}_{\mathord\odot}\else 
			$M_{\mathord\odot}$\fi}
\newcommand	{\msun}{\ifmmode {M}_{\mathord\odot}\else 
			$M_{\mathord\odot}$\fi}


\newcommand	{\Rsun}{\ifmmode {R_\odot}\else R$_\odot$ \fi}
\newcommand	{\AU}{\ifmmode {{\rm AU}}\else AU \fi} 
\newcommand	{\kms}{\ifmmode{\rm km\;s^{-1}}\else km~s\e \fi}
\newcommand	{\kps}{\ifmmode{\rm km\;s^{-1}}\else km~s\e \fi}


\newcommand{\kB}{k_{B}}
\newcommand{\mH}{m_{\rm H}}
\newcommand{\nH}{n_{\rm H}}
\newcommand{\nHfour}{n_{\rm H4}}
\newcommand{\NH}{N_{H}}
\newcommand{\Av}{A_{V}}
\newcommand{\Avs}{A_{Vs}}
\newcommand{\AvCR}{A_{V{\rm CR}}}
\newcommand{\muH}{\mu_{\rm H}}
\newcommand{\tff}{t_{\rm ff}}
\newcommand{\deltagr}{\delta_{\rm gr}}

\newcommand{\rhobg}{\rho_{\rm cl}}
\newcommand{\rhoa}{\rho_{a}}
\newcommand{\rhocl}{\rho_{\rm cl}}
\newcommand{\rhow}{\rho_{w}}
\newcommand{\Sigmacl}{\Sigma_{\rm cl}}
\newcommand{\SigmaCR}{\Sigma_{\rm CR}}
\newcommand{\SigmaP}{\Sigma_p}
\newcommand{\sigmath}{\sigma_{\rm th}}
\newcommand{\sigmant}{\sigma_{\rm NT}}
\newcommand{\twind}{t_{w}}
\newcommand{\vwind}{v_{w}}
\newcommand{\vw}{v_{w}}
\newcommand{\tw}{t_{w}}
\newcommand{\fw}{f_{w}}

\newcommand{\Lw}{L_{w}}
\newcommand{\vesc}{v_{\rm esc}}
\newcommand{\lrho}{{l_\rho}}
\newcommand{\krho}{{k_\rho}}
\newcommand{\lr}{{l_r}}
\newcommand{\mbarstar}{\overline{m}_\star}
\newcommand{\mdotstar}{\dot{m}_\star}
\newcommand{\mdotwind}{\dot{m}_w}
\newcommand{\mdotw}{\dot{m}_w}
\newcommand{\mw}{m_{w}}
\newcommand{\pw}{p_{w}}
\newcommand{\pdotw}{\dot{p}_{w}}
\newcommand{\ptilde}{\tilde{p}_{w}}

\newcommand{\muesc}{{\mu_{\rm esc}}}
\newcommand{\thesc}{{\theta_{\rm esc}}}
\newcommand{\mwmstar}{m_w/m_\star}
\newcommand{\mstar}{m_\star}
\newcommand{\Mstar}{{M_\star}}
\newcommand{\Nstarff}{{{\mathcal N}_{\star\rm ff}}}
\newcommand{\Nstardiss}{{{\mathcal N}_{\star\rm diss}}}
\newcommand{\mstarmax}{m_{\rm \star,\,max}}
\newcommand{\mstarmin}{m_{\rm \star,\,min}}
\newcommand{\tAD}{t_{\rm AD}}
\newcommand{\tdo}{t_{\rm d0}}
\newcommand{\tinterstar}{t_{\star\star}}
%\newcommand{\mag}{{\rm mag}}
\newcommand{\ma}{M_{a}}
\newcommand{\Ah}{A_{h}}
\newcommand{\rh}{R_{h}}
\newcommand{\rhnought}{R_{h0}}
\newcommand{\zh}{z_{h}}
\newcommand{\zht}{\tilde{z}_{h}}
\newcommand{\zho}{z_{h0}}
\newcommand{\zhot}{\tilde{z}_{h0}}
\newcommand{\rhot}{\tilde{r}_{h0}}
\newcommand{\varpt}{\tilde{\varpi}}
\newcommand{\thetaeq}{\theta_{\rm eq}}
\newcommand{\etain}{{\eta_{\rm in}}}
\newcommand{\etah}{{\eta_{h}}}
\newcommand{\Ein}{{E_{\rm in}}}
\newcommand{\Einj}{{E_{\rm inj}}}
\newcommand{\Einjmom}{{E_{\rm inj,\,mom}}}
\newcommand{\Einjmag}{{E_{\rm inj,\,mag}}}
\newcommand{\Pin}{{P_{\rm in}}}

\newcommand{\vh}{v_{h}}
\newcommand{\vhrp}{v_{h, rp}}
\newcommand{\vho}{v_{h0}}
% \newcommand{\req}{R_{\rm eq}}
% \newcommand{\teq}{t_{\rm eq}}
% \newcommand{\zeq}{z_{\rm eq}}
% \newcommand{\Aeq}{A_{\rm eq}}
 \newcommand{\req}{R_{f}}
 \newcommand{\teq}{t_{f}}
 \newcommand{\zeq}{z_{f}}
 \newcommand{\Aeq}{A_{f}}
\newcommand{\rout}{r_{\rm of}}
\newcommand{\vout}{v_{\rm of}}
\newcommand{\mout}{m_{\rm of}}
\newcommand{\pout}{p_{\rm of}}
\newcommand{\Vout}{V_{\rm of}}
\newcommand{\Vmax}{V_{m}}
\newcommand{\mmax}{m_{m}}
\newcommand{\mesc}{m_{\rm esc}}
\newcommand{\Mej}{M_{\rm ej}}
\newcommand{\KEmax}{{ K_{m}} }
\newcommand{\ceff}{c_{\rm eff}}
\newcommand{\vrms}{v_{\rm rms}}
\newcommand{\vrmsstar}{v_{\rm rms\star}}
\newcommand{\vrmsmax}{v_{\rm rms,\,max}}
\newcommand{\vrmseq}{v_{\rm rms,\,eq}}
\newcommand{\vrmsa}{v_{\rm rms,\,cl}}
\newcommand{\vrmso}{v_{\rm rms0}}
\newcommand{\vA}{v_{A}}
\newcommand{\KEwind}{{ K_{\rm wind}} }
\newcommand{\KEshell}{{ K_{\rm shell}} }
\newcommand{\KEout}{{ K_{\rm of}} }
\newcommand{\etaout}{{\eta_{d}}}
\newcommand{\Qout}{Q_{\rm of}}
\newcommand{\Qwind}{Q_{\rm wind}}
\newcommand{\tmax}{t_{m}}
\newcommand{\rmax}{r_{m}}
\newcommand{\taumax}{\tau_{m}}
\newcommand{\tgstarloc}{t_{{\rm AD}}}
\newcommand{\tgstar}{t_{g\star}}
\newcommand{\tgstarAD}{t_{g\star{\rm AD}}}
\newcommand{\tgstardyn}{t_{g\star{\rm dyn}}}
\newcommand{\chiad}{\chi_{\rm AD}}
\newcommand{\chiAD}{\chi_{\rm AD}}
\newcommand{\MCR}{M_{\rm CR}}
\newcommand{\Mcr}{M_{\rm cr}}
\newcommand{\Mphi}{M_\Phi}
\newcommand{\MPhi}{M_\Phi}
\newcommand{\Mamb}{M_{\rm amb}}
\newcommand{\Ps}{P_0}
\newcommand{\MJ}{M_{\rm J}}
\newcommand{\Mcl}{M_{\rm cl}}
\newcommand{\Mclo}{M_{\rm cl\,0}}
\newcommand{\Mcldot}{\dot{M}_{\rm cl}}
\newcommand{\Mdotcl}{\dot{M}_{\rm cl}}
\newcommand{\Mdotstar}{\dot{M}_{\star}}
\newcommand{\Mstardot}{\dot{M}_{\star}}
\newcommand{\Mclddot}{\ddot{M}_{\rm cl}}
\newcommand{\Mddotcl}{\ddot{M}_{\rm cl}}
\newcommand{\Rcl}{R_{\rm cl}}
\newcommand{\Rclo}{R_{\rm cl0}}
\newcommand{\Rcleq}{R_{\rm eq}}
\newcommand{\Rdotcl}{{\dot{R}}_{\rm cl}}
\newcommand{\Rcldot}{{\dot{R}}_{\rm cl}}
\newcommand{\Rddotcl}{{\ddot{R}}_{\rm cl}}
\newcommand{\Rclddot}{{\ddot{R}}_{\rm cl}}
\newcommand{\Mconf}{M_{\rm conf}}
\newcommand{\Rconf}{R_{\rm conf}}
\newcommand{\nconf}{n_{\rm conf}}
\newcommand{\Bphi}{B_{\phi}}
\newcommand{\etad}{{\eta_{d}}}
\newcommand{\etaw}{{\eta_{w}}}
\newcommand{\rBE}{r_{\rm BE}}
\newcommand{\MBE}{M_{\rm BE}}
\newcommand{\NBE}{N_{\rm BE}}
\newcommand{\pch}{p_{40}}
\newcommand{\twch}{t_{w,5}}
\newcommand{\tch}{t_{5}}
\newcommand{\mstarch}{m_{\star,0.5}}
\newcommand{\mdotch}{\dot{m}_{-5\star}}
\newcommand{\mdotwch}{\dot{m}_{w,-6}}
\newcommand{\mwmstarch}{3m_w/m_\star}
\newcommand{\vwch}{v_{w,200}}
\newcommand{\ceffch}{c_{\rm eff,2}}
\newcommand{\Omegach}{\Omega_{10^\circ}}
\newcommand{\thetach}{\theta_{10^\circ}}
\newcommand{\thetaeffch}{\theta_{\rm eff\,10^\circ}}
\newcommand{\nbarch}{n_{\rm H4}}
\newcommand{\nHch}{n_{\rm H3}}
\newcommand{\fwch}{f_{w,\,0.2}}
\newcommand{\mbarch}{\overline{m}_{\star,0.5}}
\newcommand{\mstarmbar}{(m_\star/\overline{m}_\star)}
\newcommand{\Machw}{{{\rm Ma}_{f}(t_w)}}
\newcommand{\MA}{{\rm Ma}_{A}}
\newcommand{\MAw}{{\rm Ma}_{A,w}}
\newcommand{\MAch}{{\rm Ma}_{A7}}
\newcommand{\mch}{{m_{\star \rm crit}}}
\newcommand{\Chiten}{{\chi_{10}}}
\newcommand{\cncrit}{ {(c_{\rm eff,2}^4 n_{\rm H4})_{\rm crit}} }
\newcommand{\cn}{ {(c_{\rm eff,2}^4 n_{\rm H4})} }
\newcommand{\ncrit}{ n_{\rm H,\,crit}}

\newcommand{\epsout}{\epsilon_{\rm of}}
\newcommand{\epsdotin}{\dot{\epsilon}_{\rm in}}
\newcommand{\mbarw}{\overline{m}_w}
\newcommand{\epsamb}{\epsilon_{\rm amb}}
\newcommand{\phiw}{{\phi_w} }
\newcommand{\phiwbar}{{\overline{\phi}_w} }
\newcommand{\SFE}{{\rm SFE}}
\newcommand{\SFEtot}{{\rm SFE_{\rm tot}}}


%\newcommand{\Rin}{R_{\rm 0,in}}
%\newcommand{\Rout}{R_{\rm 0,out}}
\def\rhoo{\rho_{01}}
\def\Rin{\varpi_{0,{\rm in}}}
\def\Rout{\varpi_{0,{\rm out}}}






