diff --git a/main.cpp b/main.cpp index 31ef955..16e84b3 100644 --- a/main.cpp +++ b/main.cpp @@ -42,15 +42,23 @@ private: gsl_spline *spline; }; -void plummer(double M, double b, const double3& pos, double3& acc) +double3 plummer(const double M, const double b, const double3& pos) { - double r2 = (pos[0]*pos[0] + pos[1]*pos[1] + pos[2]*pos[2] + b*b); + double r2 = pos.squaredNorm() + b*b; double r = sqrt(r2); double r3_inv = 1/(r*r2); - acc = -G*M*pos*r3_inv; + return -G*M*pos*r3_inv; } -void miyamoto_nagai(double M, double a, double b, double phi, double theta, const double3& pos, double3& acc) +double3 nfw(const double rho_0, const double b, const double3& pos) +{ + double r2 = pos.squaredNorm(); + double r = sqrt(r2); + double tmp = -4*M_PI*G*rho_0*b*b*b*(log(1+r/b) - r/(b+r))/(r2*r); + return pos*tmp; +} + +double3 miyamoto_nagai(const double M, const double a, const double b, const double phi, const double theta, const double3& pos) { // Construct new z-axis from the angles double cos_theta = cos(theta); @@ -76,47 +84,44 @@ void miyamoto_nagai(double M, double a, double b, double phi, double theta, cons acc_in_rotated_frame[2] = - tmp * new_pos[2] * (z_tmp + a)/z_tmp; // Return to original frame - acc = rot.inverse() * acc_in_rotated_frame; + return rot.inverse() * acc_in_rotated_frame; } class Galaxy { public: Galaxy(std::string file_name) { - auto data = Loadtxt(file_name, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}).get_cols(); + auto data = Loadtxt(file_name, {1, 2, 3, 4, 5, 6, 7, 8}).get_cols(); auto& t_data = data[0]; std::transform(begin(t_data), end(t_data), begin(t_data), [t0=t_data[0]](const double& x){ return x-t0; }); - for (int i=0; i<10; i++) interp[i] = Interp(t_data, data[i+1]); + for (int i=0; i<7; i++) interp[i] = Interp(t_data, data[i+1]); } void func(const std::array &y, std::array &f, const double t) { f[0] = y[3]; // vx -> x' f[1] = y[4]; // vy -> y' f[2] = y[5]; // vz -> z' - double m_disk = interp[0](t); - double phi = interp[1](t); - double theta = interp[2](t); + double phi = interp[0](t); + double theta = interp[1](t); + double m_disk = interp[2](t); double a_disk = interp[3](t); double b_disk = interp[4](t); - double m_halo = interp[5](t); - double b_halo = interp[6](t); - double3 dalembert; - // for (int i=0; i<3; i++) dalembert[i] = interp[7+i](t); - dalembert = {0,0,0}; + double rho_0_nfw = interp[5](t); + double b_nfw = interp[6](t); - double3 acc_disk, acc_halo; - const double3 pos(y.data()); - miyamoto_nagai(m_disk, a_disk, b_disk, phi, theta, pos, acc_disk); - plummer(m_halo, b_halo, pos, acc_halo); - for (int i=0; i<3; i++) f[3+i] = acc_disk[i] + acc_halo[i] + dalembert[i]; + double3 pos(y.data()); + double3 acc_disk = miyamoto_nagai(m_disk, a_disk, b_disk, phi, theta, pos); + double3 acc_halo = nfw(rho_0_nfw, b_nfw, pos); + for (int i=0; i<3; i++) f[3+i] = acc_disk[i] + acc_halo[i]; } + private: Interp interp[10]; } galaxy("subhalo_411321_parameters_processed.dat"); extern "C" -int integrate(const double y0[], const double t_max, const double stride_size, double y[]) +void integrate(const double y0[], const double t_max, const double stride_size, double y[]) { using namespace boost::numeric::odeint; using Coordinates = std::array; @@ -127,7 +132,7 @@ int integrate(const double y0[], const double t_max, const double stride_size, d std::copy(y0, y0+6, begin(y_current)); std::copy(y0, y0+6, y); double t = 0; - const double h = 1./4096.; + const double h = std::min(1./4096., stride_size); for (int i=0; i" + "" ] }, "execution_count": 9, @@ -331,7 +334,8 @@ "V = array([Vx, Vy, Vz])\n", "legend(('$x$', '$y$', '$z$'))\n", "\n", - "plot(t, X_center_stars-V*(t-t[-1])[:,None])\n", + "X_adjusted = X_center_stars-V*(t-t[-1])[:,None]\n", + "plot(t, X_adjusted)\n", "legend(('x', 'y', 'z'))\n", "xlabel('$t$ [Gyr]')\n", "ylabel('$\\mathbf{r}_\\mathrm{corrected}$ [kpc]')" @@ -370,8 +374,8 @@ "k = 6 # Spline order\n", "midpoint = 0.5*(t[0]+t[-1])\n", "knots = r_[[t[0]]*(k+1), midpoint, midpoint, midpoint, [t[-1]]*(k+1)]\n", - "spline = scipy.interpolate.make_lsq_spline(t, X_center_stars-V*(t-t[-1])[:,None], knots, k)\n", - "plot(t, X_center_stars-V*(t-t[-1])[:,None])\n", + "spline = scipy.interpolate.make_lsq_spline(t, X_adjusted, knots, k)\n", + "plot(t, X_adjusted)\n", "plot(t, spline(t), c='k', alpha=0.4, ls='--')\n", "legend(('$x$', '$y$', '$z$', 'splines'))\n", "xlabel('$t$ [Gyr]')\n", @@ -419,30 +423,63 @@ "cell_type": "code", "execution_count": 13, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'acceleration [kpc/Gyr${}^2$]')" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ - "output_file_name = file_name[:-4] + '_processed.dat'\n", - "with open(output_file_name, 'w') as f:\n", - " for i in range(len(snapshot)):\n", - " output_string = '%d %.8E %.8E %15.8E %15.8E %.8E %.8E %.8E %.8E %15.8E %15.8E %15.8E\\n' % (\n", - " snapshot[i],\n", - " t[i],\n", - " M_disk[i],\n", - " phi_inertia_fixed[i], theta_inertia[i],\n", - " a_mn[i], b_mn[i],\n", - " M_halo[i],\n", - " b_halo[i],\n", - " -acc[i,0], -acc[i,1], -acc[i,2]\n", - " )\n", - " f.write(output_string)" + "# Try the numerical derivative instead of the B-splines\n", + "V_ = diff(X_center_stars, axis=0)/diff(t)[:,None]\n", + "t_ = 0.5*(t[1:] + t[:-1])\n", + "A_ = diff(V_, axis=0)/diff(t_)[:,None]\n", + "t_ = 0.5*(t_[1:] + t_[:-1])\n", + "plot(t_, A_)\n", + "legend(('$a_x$', '$a_y$', '$a_z$', 'splines'))\n", + "xlabel('$t$ [Gyr]')\n", + "ylabel('acceleration [kpc/Gyr${}^2$]')" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "output_file_name = file_name[:-4] + '_processed.dat'\n", + "#X_adjusted[:,0] = t*1000\n", + "#X_adjusted[:,1] = -t*500\n", + "#X_adjusted[:,2] = 0\n", + "with open(output_file_name, 'w') as f:\n", + " for i in range(len(snapshot)):\n", + " output_string = '%d %.8E %15.8E %15.8E %.8E %.8E %.8E %.8E %.8E\\n' % (\n", + " snapshot[i],\n", + " t[i],\n", + " phi_inertia_fixed[i], theta_inertia[i],\n", + " M_disk[i], a_mn[i], b_mn[i],\n", + " rho_0_nfw[i], b_nfw[i],\n", + " )\n", + " f.write(output_string)" + ] } ], "metadata": { diff --git a/subhalo_411321_parameters.dat b/subhalo_411321_parameters.dat new file mode 100644 index 0000000..10baab1 --- /dev/null +++ b/subhalo_411321_parameters.dat @@ -0,0 +1,75 @@ +25 2.14210194E+00 -3.18382346E+04 6.01965396E+03 -7.40300600E+04 1.33692061E+00 1.80178885E-01 1.07239431E+00 2.21308507E-01 1.19572159E+09 7.94136718E-01 1.05392287E+00 -3.18383203E+04 6.01986518E+03 -7.40299989E+04 2.02651928E+11 1.60254784E+01 1.82777387E+07 9.86242602E+00 4.09770782E-04 +26 2.23439941E+00 -3.15303561E+04 5.98829853E+03 -7.33346472E+04 5.83566346E-01 2.99007463E-01 1.10209300E+00 4.30789753E-01 1.31591092E+09 8.87113243E-01 1.02186940E+00 -3.15302146E+04 5.98856330E+03 -7.33346356E+04 2.10080414E+11 1.74192560E+01 4.40717228E+07 6.38641218E+00 1.97067096E-03 +27 2.38015340E+00 -3.10568480E+04 5.93850263E+03 -7.22527806E+04 7.57338142E-01 4.80623433E-01 1.05102590E+00 5.48323466E-01 1.55279964E+09 1.06245157E+00 9.89341552E-01 -3.10568871E+04 5.93837584E+03 -7.22525489E+04 2.15059634E+11 1.81431141E+01 2.93958529E+07 7.58405813E+00 5.81386959E-04 +28 2.53513003E+00 -3.05630665E+04 5.88423782E+03 -7.11224141E+04 8.38855341E-01 7.86295263E-01 9.47215546E-01 8.73080865E-01 1.79262431E+09 1.09986631E+00 1.15079511E+00 -3.05630626E+04 5.88406384E+03 -7.11223326E+04 2.33645824E+11 1.86967967E+01 4.15070463E+07 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2.17315992E-01 7.11831830E+10 2.10547864E+00 1.07998801E+00 5.57066861E+06 2.46772174E+01 +96 1.33225960E+01 -3.43217978E+00 1.52838792E-01 7.11764210E+10 2.07113010E+00 1.08823314E+00 5.05013580E+06 2.57770503E+01 +97 1.34575420E+01 -3.50205955E+00 1.09951602E-01 7.11599913E+10 2.09759609E+00 1.10617158E+00 4.36278412E+06 2.74481787E+01 +98 1.36611277E+01 -3.47216240E+00 4.90369794E-02 7.11249167E+10 2.14901344E+00 1.10485424E+00 5.10044065E+06 2.59174317E+01 +99 1.37976159E+01 -2.86799337E+00 2.86479549E-04 7.11003816E+10 2.07334177E+00 1.12603089E+00 4.11239026E+06 2.84813683E+01 diff --git a/three_components.py b/three_components.py index 3ce994f..fdfb415 100644 --- a/three_components.py +++ b/three_components.py @@ -15,8 +15,8 @@ file_name = 'data/subhalo_411321.hdf5' # centers_file_name = 'data/centers_411321.hdf5' ### Snapshot parameters ### -snapshot = 99 -a = 1.0 # Should read this value from somewhere! +snapshot = 25 +a = 0.2494928434225328 # Should read this value from somewhere! # Read the centre from separate file # DISABLED: we calculate on our own. @@ -32,6 +32,48 @@ particle_types['dm'] = '1' particle_types['stars'] = '4' particle_types['bhs'] = '5' +# Read DM +particle_type = 'dm' +with h5py.File(file_name, 'r') as f: + m = f[str(snapshot)][particle_types[particle_type]]['Masses'][...] + X = f[str(snapshot)][particle_types[particle_type]]['Coordinates'][...] * a / h0 + V = f[str(snapshot)][particle_types[particle_type]]['Velocities'][...] * sqrt(a) +M_tot = sum(m) + +# Calculate density centre and shift appropriately +X_center_new, V_center_new = def_dc(m, X, V) +X -= X_center_new +V -= V_center_new + +r = linalg.norm(X, axis=1) + +i = r.argsort() +rr = r[i] +m_cumulative = cumsum(m[i])/sum(m) + +nfw_cumulative_mass = lambda rho_0, b, r: 4*pi*rho_0*b**3*(log(1+r/b) - r/(b+r)) +cost = lambda args: sum((nfw_cumulative_mass(*args, rr) - m_cumulative)**2) +res = scipy.optimize.minimize(cost, [0.001, 30.], method='Nelder-Mead') +print(res) +rho_0_nfw, b_nfw = res.x + + +plot(rr, m_cumulative*sum(m)) +plot(rr, nfw_cumulative_mass(*res.x, rr)*sum(m)) + +figure() +counts, bin_edges = histogram(r, logspace(-2, 2, 65)) +volumes = 4*pi/3*(bin_edges[1:]**3 - bin_edges[:-1]**3) +means = lambda arr: 0.5*(arr[:-1]+arr[1:]) +bins = means(bin_edges) +density = counts*m[0]/volumes +loglog(bins, density) +nfw_density = lambda rho_0, b, r: rho_0/((r/b) * (1 + r/b)**2) +loglog(bins, nfw_density(*res.x, bins)*sum(m)) + +show() +raise SystemExit + # Read stars particle_type = 'stars' with h5py.File(file_name, 'r') as f: