Added asymptotic form of the spherical deprojection of the exponential disk as an option to EmpCylSL

Author: Martin D. Weinberg

expui/BiorthBasis.cc

@@ -1610,6 +1610,8 @@ namespace BasisClasses
       EmpCylSL::mtype = EmpCylSL::Exponential;
       if (mtype.compare("exponential")==0)
 	EmpCylSL::mtype = EmpCylSL::Exponential;
+      else if (mtype.compare("expdeproj")==0)
+	EmpCylSL::mtype = EmpCylSL::ExpDeproj;
       else if (mtype.compare("gaussian")==0)
 	EmpCylSL::mtype = EmpCylSL::Gaussian;
       else if (mtype.compare("plummer")==0)
@@ -1620,7 +1622,7 @@ namespace BasisClasses
       } else {
 	if (myid==0) std::cout << "No EmpCylSL EmpModel named <"
 			       << mtype << ">, valid types are: "
-			       << "Exponential, Gaussian, Plummer, Power "
+			       << "Exponential, ExpDeproj, Gaussian, Plummer, Power "
 			       << "(not case sensitive)" << std::endl;
 	throw std::runtime_error("Cylindrical:initialize: EmpCylSL bad parameter");
       }

exputil/EmpCylSL.cc

@@ -69,10 +69,11 @@ double   EmpCylSL::PPOW            = 4.0;
 bool     EmpCylSL::NewCoefs        = true;
 
 
-EmpCylSL::EmpModel EmpCylSL::mtype = Exponential;
+EmpCylSL::EmpModel EmpCylSL::mtype = ExpDeproj;
 
 std::map<EmpCylSL::EmpModel, std::string> EmpCylSL::EmpModelLabs =
   { {Exponential, "Exponential"},
+    {ExpDeproj,   "ExpDeproj"  },
     {Gaussian,    "Gaussian"   },
     {Plummer,     "Plummer"    },
     {Power,       "Power"      },
@@ -552,6 +553,9 @@ double EmpCylSL::massR(double R)
   case Exponential:
     ans = 1.0 - (1.0 + R)*exp(-R); 
     break;
+  case ExpDeproj:
+    ans = erf(sqrt(R)) - 2.0/3.0*sqrt(R/M_PI)*exp(-R)*(3.0 + 2.0*R);
+    break;
   case Gaussian:
     arg = 0.5*R*R;
     ans = 1.0 - exp(-arg);
@@ -589,6 +593,9 @@ double EmpCylSL::densR(double R)
   case Exponential:
     ans = exp(-R)/(4.0*M_PI*R);
     break;
+  case ExpDeproj:
+    ans = exp(-R)/(3.0*M_PI*sqrt(R*M_PI));
+    break;
   case Gaussian:
     arg = 0.5*R*R;
     ans = exp(-arg)/(4.0*M_PI*R);

include/EmpCylSL.H

@@ -364,6 +364,7 @@ public:
   //! Type of density model to use
   enum EmpModel {
     Exponential,
+    ExpDeproj,
     Gaussian, 
     Plummer,
     Power,