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antenna_lib.cpp

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    • Bruce Allen's avatar
      74d0770f
      In this code the relevant phases are the · 74d0770f
      Bruce Allen authored
      DIFFERENCES between those at the different detectors.  So to
      make for a less confusing visual display in the GUI, I have
      offset the output phase as a function of psi, in a way that
      tries to reduce confusion about the meaining of the orbital
      coalescence phase.
      74d0770f
      History
      In this code the relevant phases are the
      Bruce Allen authored
      DIFFERENCES between those at the different detectors.  So to
      make for a less confusing visual display in the GUI, I have
      offset the output phase as a function of psi, in a way that
      tries to reduce confusion about the meaining of the orbital
      coalescence phase.
    antenna_lib.cpp 11.72 KiB
    // Copyright Bruce Allen 2017
    // Compile with gcc -o antenna antenna.c -lm
    
    // REMAINING THINGS TO CHECK:
    // (a) sign conventions for h, which arm is positive
    // (b) direction and origin conventions for the polarization axis
    // (c) double check the hand calculations
    
    #include <math.h>
    #include <stdio.h>
    #include <stdlib.h>
    #include <string.h>
    #include "antenna_lib.h"
    
    // Global variables for passing information. Ugly style but doesn't
    // matter for this!
    struct InputStruct inputdata;
    
    // For converting degrees to radians
    const double deg_to_rad = M_PI/180.0;
    
    // For computing arrival time delays, need mean radius of the earth in
    // milliseconds. Get this by dividing radius in km by speed of light in
    // km/s.
    const double radius_earth = 6371.0*1000.0/299792.458;
    
    // Event time
    // GPS 1187008882
    // UTC:	Thu 2017 Aug 17	12:41:04
    // Julian Day 2457983.02852
    // Modified Julian Day 57982.52852
    
    // The convention in this code is that Lattitude is measured north of
    // the equator.  So Lattitude -10 means 10 degrees SOUTH of the
    // equator.  Longitude is measured East of Greenwich.  So longitude
    // -90 means 90 degrees West of Greenwich (somewhere in the USA).
    
    // Galaxy NGC 4993 (from Wikipedia):
    //    Right ascension: 13h 09m 47.2s
    //    Declination: −23° 23′ 4″
    // We will need to convert this to location over the Earth at the
    // event time.  It will turn out to be:
    //    Lattitude −23.3844 degrees (south of equator)
    //    Longitude 41.092981 degrees (east of Greenwich)
    
    
    // From Chapter 11 of "Astronomical Algorithms" by Jean Meeus, published 1991
    void print_galaxy_coordinates() {
       
       // Here is the Julian day of the event, including a fractional part
       double JD = 2457983.02852;
       
       // This is the Julian day (note previous integer part!)
       double JD0 = 2457982.5;
       
       // Compute Julian century t
       double day = JD0-2451545.0;
       double t = day/36525.0;
       
       // The following is equation 11.4 of the previous reference
       double degrees = 280.46061837 + 360.98564736629*(JD-2451545.0)+t*t*0.000387933 - t*t*t/38710000.0;
       degrees = fmod(degrees,360.0);
    
       printf("Greenwich Mean Sidereal time is %f degrees\n", degrees);
       
       // Now the longitude of our source (with sign conventions above) is given by L = RA - MST, where
       // MST (in degrees) is given above and RA is the RA of our source
       // Here a positive number means "East of Greenwich"
       double longitude = (13*3600.0+9*60+47.2)/240 - degrees;
       printf("Longitude of source is %f degrees\n", longitude);
    }
    
    //  Note these are in the order lattitude,longitude.  See routine
    // "print_galaxy_coordinates" to convert location on sky to Earth
    // location at event time.  These are set/used in the function
    // populate_source() below.
    
    struct Source {
       // lattitude north of equator, radians
       // longitude east from Greenwich, radians
       double location[2];
       
       // Unit vector from Earth to source
       double vec[3];
    
       // Unit vectors defining plane perpendicular to the source
       // direction.  U points east, V points north
       double u[3];
       double v[3];
    };
    
    struct Source source;
    
    struct Detector {
       // null terminated char string
       char name[8];
       
       // lattitude north of equator, radians
       // longitude east from Greenwich, radians
       double location[2];
       
       // orientation of Y arm CCW from North, radians
       double orientation;
    
       // Unit vector from center of Earth to detector
       double vec[3];
    
       // Unit vectors pointing along the north and east directions at the
       // detector site
       double north[3];
       double east[3];
    
       // Unit vectors along the two arms
       double lx[3];
       double ly[3]; 
    };
    
    // LLO, LHO, Virgo, in that order
    struct Detector detectors[3];
    
    // input is a lattitude/longitude set in radians
    // output is unit vectors
    void make_unit_vectors(double *out, double *in) {
       double lat = in[0];
       double lon = in[1];
       out[0] = cos(lon)*cos(lat);
       out[1] = sin(lon)*cos(lat);
       out[2] = sin(lat);
    }
    
    void make_u_v_vectors(struct Source *src) {
       // lattitude and longitude
       double lat = src->location[0];
       double lon = src->location[1];
    
       // construct unit vectors perpendicular to line of sight
       // u points east
       src->u[0] = -sin(lon);
       src->u[1] = cos(lon);
       src->u[2] = 0.0;
    
       // v points north, so u,v are a right-handed pair like x,y
       src->v[0] = -sin(lat)*cos(lon);
       src->v[1] = -sin(lat)*sin(lon);
       src->v[2] = cos(lat);
    }
    
    // input is a lattitude/longitude set in radians
    // output is unit vectors in the north and east directions
    void make_north_east_vectors(struct Detector *det) {
    
       double lat = det->location[0];
       double lon = det->location[1];
       
       det->north[0] = -sin(lat)*cos(lon);
       det->north[1] = -sin(lat)*sin(lon);
       det->north[2] = cos(lat);
       det->east[0] = -sin(lon);
       det->east[1] = cos(lon);
       det->east[2] = 0.0;
    
       double cpsi = cos(det->orientation);
       double spsi = sin(det->orientation);
       int i;
       for (i=0; i<3; i++) {
          det->lx[i] =  cpsi*det->east[i] + spsi*det->north[i]; 
          det->ly[i] = -spsi*det->east[i] + cpsi*det->north[i];
       }
    }
    
    // sets up the different vectors needed to define the source
    void populate_source() {
       
       source.location[0] = -1.0*deg_to_rad*(23.0 + 23.0/60.0 + 4.0/3600.0);
       source.location[1] = deg_to_rad*41.092981;
       
    #if 0
       // for testing purposes, put source directly over a detector
       source.location[0] = 46.45*deg_to_rad;
       source.location[1] = -119.41*deg_to_rad;
    #endif
    
       
       make_unit_vectors(source.vec,source.location);
       make_u_v_vectors(&source);
    }
    
    // initially take detector locations and orientations from
    // https://arxiv.org/pdf/gr-qc/9607075.pdf
    // Be sure to check this later!!
    
    void populate_detectors(){
       
       // LLO
       // Sanity checked using Google Earth!
       strcpy(detectors[0].name, " LLO ");
       detectors[0].location[0] = 30.56*deg_to_rad;
       detectors[0].location[1] = -90.77*deg_to_rad;
       detectors[0].orientation = (198.0+inputdata.orientation[0])*deg_to_rad;
    
       // LHO
       // Sanity checked using Google Earth!
       strcpy(detectors[1].name, " LHO ");
       detectors[1].location[0] = 46.45*deg_to_rad;
       detectors[1].location[1] = -119.41*deg_to_rad;
       detectors[1].orientation = (126.8+inputdata.orientation[1])*deg_to_rad;
       
       // VIRGO
       // Sanity checked using Google Earth!
       strcpy(detectors[2].name, "VIRGO");
       detectors[2].location[0] = 43.63*deg_to_rad;
       detectors[2].location[1] = 10.5*deg_to_rad;
       detectors[2].orientation = (71.5+inputdata.orientation[2])*deg_to_rad;
    
       int i;
    
       // Coordinate system has x/y plane through the equator, north pole
       // along positive z axis, and Greenwich passing through x axis (ie
       // y=0).
       for (i=0;i<3;i++) {
          make_unit_vectors(detectors[i].vec, detectors[i].location);
          make_north_east_vectors(detectors+i);
       }
    }
    
    void print_detector(int det) {
       printf("name: %s\n"
    	  "lattitude (north): %f\n"
    	  "longitude (east): %f\n"
    	  "orientation: (CCW from North): %f\n"
    	  "earth center to detector %f %f %f\n"
    	  "vector along X arm %f %f %f\n"
    	  "vector along Y arm %f %f %f\n\n",
    	  detectors[det].name,
    	  detectors[det].location[0],
    	  detectors[det].location[1],
    	  detectors[det].orientation,
    	  detectors[det].vec[0], detectors[det].vec[1], detectors[det].vec[2],
    	  detectors[det].lx[0], detectors[det].lx[1], detectors[det].lx[2],
    	  detectors[det].ly[0], detectors[det].ly[1], detectors[det].ly[2]
    	  );
    }
    
    void print_source() {
       printf("source at:\n"
    	  "lattitude: %f\n"
    	  "longitude: %f\n"
    	  "earth center to source: %f %f %f\n"
    	  "U vector: %f %f %f\n"
    	  "V vector: %f %f %f\n\n",
    	  source.location[0],
    	  source.location[1],
    	  source.vec[0], source.vec[1],source.vec[2],
    	  source.u[0],source.u[1],source.u[2],
    	  source.v[0],source.v[1],source.v[2]
    	  );
    }
    
    // This dots the mass quadrupole with the antenna functions
    void get_UV_combinations(int det, double *alpha, double *beta, double *rdotn) {
      
       double a=0,b=0,dot=0;
       int i, j;
       
       double *su=source.u;
       double *sv=source.v;
       double *n=source.vec;
       
       double *dx=detectors[det].lx;
       double *dy=detectors[det].ly;
       double *r=detectors[det].vec;
       
       for (i=0; i<3; i++)
          for (j=0; j<3; j++)
    	 a += (su[i]*su[j] - sv[i]*sv[j]) * (dx[i]*dx[j] - dy[i]*dy[j]);
       
       for (i=0; i<3; i++)
          for (j=0; j<3; j++)
    	 b += (su[i]*sv[j] + sv[i]*su[j]) * (dx[i]*dx[j] - dy[i]*dy[j]);
    
       // The quantity dot is positive if the vector from the earth center
       // to a detector has the SAME direction as the vector from the
       // earth center to the source.  This means that the signal arrives
       // EARLIER at that detector.  Hence the signal waveform seen at the
       // detector is of the form h(t) = wave(t + R*dot) where R is the
       // (positive) earth radius in units of time and wave(t) is the
       // emitted source waveform.
       
       for (i=0; i<3; i++)
          dot += n[i]*r[i];
       
       *alpha = a;
       *beta = b;
       *rdotn = dot;
    }
    
    
    // library function that can be called either from the GUI code or
    // from a stand-alone terminal program.  This function does not modify
    // the input struct, but does populate/modify the output strut!
    void get_antenna(struct OutputStruct *out, struct InputStruct *in) {
       int i;
       // set up the source and detectors
       inputdata=*in;
       populate_source();
       populate_detectors();
    
       double iota = inputdata.iota;
       double psi = inputdata.psi;
    #ifdef DEBUG
       fprintf(stderror, "Iota = %f degrees\nPsi = %f degrees\n", iota, psi);
    #endif
       iota *= deg_to_rad;
       psi *= deg_to_rad;
    
       // get angles needed to calculate antenna response. The minus sign
       // in the definition of cos(iota) is because my calculational notes
       // assume that iota=0 corresponds to orbital motion CCW in the
       // (right-handed) UV coordinate system.  That corresponds to having
       // the orbital angular momentum pointing radially AWAY from earth.
       // But the standard convention is that iota=0 is face-on, meaning
       // orbital angular momentum pointing TO the earth.  So I change the
       // sign of cos(iota) below to correct for this.
       
       double ci = -cos(iota);
       double c2p = cos(2*psi);
       double s2p = sin(2*psi);
    
       // Now find waveforms.  At each site, waveform is w^2 [X sin(2wt) + Y cos(2wt) ]
       // loop over detectors
       for (i=0; i<3; i++) {
          double alpha, beta, X, Y, dt;
    
          // Ugly, should pass as argument to populate_detectors()
          strcpy(out->name[i], detectors[i].name);
          
          // get antenna pattern overlap with source plane
          get_UV_combinations(i, &alpha, &beta, &dt);
    
          // form combinations as functions of inclination and polarization angles
          X =         2.0*ci*(alpha*s2p - beta*c2p);
          Y = -(ci*ci + 1.0)*(alpha*c2p + beta*s2p);
          // compute time delay in milliseconds
          dt *= radius_earth;
          
          // printf("For detector %s the waveform is w^2 [ %.3f sin(2w(t%+.1f ms))%+.3f cos(2w(t%+.1f ms)) ]\n", detectors[i].name, X, dt, Y, dt);
    
          // compute alternative form of output
          // X sin(phi) + Y cos(phi) = sqrt(X^2+Y^2) sin(phi + ang) where ang=atan2(Y,X)
          
          double amp = sqrt(X*X + Y*Y);
          double ang = 180.0*atan2(Y, X)/M_PI;
          
          // pass outputs In this code the relevant phases are the
          // DIFFERENCES between those at the different detectors.  So to
          // make for a less confusing visual display in the GUI, I have
          // offset the output phase as a function of psi, in a way that
          // tries to reduce confusion about the meaining of the orbital
          // coalescence phase.
          out->amp[i]= amp;
          out->phase[i] = ang-2*psi*ci/deg_to_rad;
          out->dt[i] = dt;
    
          fprintf(stderr, "ang = %f psi = %f  ci =% f\n", ang, psi/deg_to_rad, ci);
          
    #ifdef DEBUG
          // degree character in UTF-8 character set (most likely terminal type!)
          int deg1=0xC2, deg2=0xB0;
          fprintf(stderr, "For detector %s the waveform is %.3f w^2 sin(2w[t%+.1f ms]%+.1f%c%c)\n", detectors[i].name, amp, dt, ang, deg1, deg2);
    #endif
       }
       return;
    }