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[READ-ONLY] Mirror of https://github.com/emilyhunt/hr_selection_function. Selection function for the Hunt & Reffert 2024 open cluster catalogue.
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It takes three arguments: Gaia data density ($\\rho_\\mathrm{data}$ in the paper), number of stars, and median parallax error." ] }, { "cell_type": "code", "execution_count": 5, "id": "3fde06f8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x74bdb2d28bf0>" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pick some basic things\n", "n_stars = np.geomspace(5, 200)\n", "median_parallax_error = np.full(50, 0.1)\n", "threshold = np.full(50, 3)\n", "\n", "fig, ax = plt.subplots()\n", "for density in [100, 1000, 10000, 100000]:\n", " gaia_density = np.full(50, density)\n", " result = model(gaia_density, n_stars, median_parallax_error, threshold)\n", " ax.plot(n_stars, result, label=f\"Data density: {density:.0f}\")\n", "\n", "ax.set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Detection probability\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "4e2040d4", "metadata": {}, "source": [ "It also works if you specify coordinates instead, in cases where you don't know the data density." ] }, { "cell_type": "code", "execution_count": 6, "id": "03649c60", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[None, Text(0.5, 0, 'Number of stars'), Text(0, 0.5, 'Detection probability')]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_stars = np.geomspace(5, 200)\n", "median_parallax_error = np.full(50, 0.1)\n", "threshold = np.full(50, 3)\n", "\n", "coordinates = SkyCoord(\n", " l=np.full(50, 0)*u.deg,\n", " b=np.full(50, 0)*u.deg,\n", " pm_l_cosb=np.full(50, 0)*u.mas/u.yr,\n", " pm_b=np.full(50, 0)*u.mas/u.yr,\n", " distance=np.full(50, 2000)*u.pc,\n", " frame=\"galactic\"\n", ")\n", "\n", "\n", "fig, ax = plt.subplots()\n", "result = model(coordinates, n_stars, median_parallax_error, threshold)\n", "ax.plot(n_stars, result, label=f\"Data density: {density:.0f}\")\n", "\n", "ax.set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Detection probability\")" ] }, { "cell_type": "markdown", "id": "f155c1ec", "metadata": {}, "source": [ "We can also query different samples of the walkers, and query the model probabilistically! This is useful if you want to incorporate **systematic errors** in the model fit into your eventual work - every time you query the function, you could take a randomly sampled model." ] }, { "cell_type": "code", "execution_count": 7, "id": "abadd0de", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 2 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pick some basic things\n", "n_stars = np.geomspace(5, 100)\n", "median_parallax_error = np.full(50, 0.1)\n", "threshold = np.full(50, 3)\n", "gaia_density = np.full(50, 1000)\n", "\n", "fig, ax = plt.subplots(nrows=2, sharex=True)\n", "result_median = model(gaia_density, n_stars, median_parallax_error, threshold)\n", "for i in range(50):\n", " result = model(\n", " gaia_density, n_stars, median_parallax_error, threshold, mode=\"random_sample\"\n", " )\n", " ax[0].plot(n_stars, result, \"k-\", alpha=0.05, lw=0.5)\n", " ax[1].plot(n_stars, result - result_median, \"k-\", alpha=0.5, lw=0.5)\n", "\n", "ax[0].set(ylabel=\"Detection probability\")\n", "ax[1].set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Residual between models\")\n", "\n", "fig.subplots_adjust(hspace=0.)" ] }, { "cell_type": "markdown", "id": "62396b03", "metadata": {}, "source": [ "## The number of stars predictor\n", "\n", "If you don't know n_stars or median_parallax_error for your cluster, you can predict it with the `NStarsPredictor` in this library." ] }, { "cell_type": "code", "execution_count": 10, "id": "e7cd2fae", "metadata": {}, "outputs": [], "source": [ "# Initialize with lower models number to make it faster for demo. In principle, you\n", "# can use upto 250 models for higher accuracy (and slower speeds.)\n", "nstars_model = NStarsPredictor(models=10)" ] }, { "cell_type": "code", "execution_count": 11, "id": "6bc25f8d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Querying model 10 of 10\n" ] }, { "data": { "text/plain": [ "[Text(0.5, 0, 'Mass [MSun]'), Text(0, 0.5, 'Number of stars')]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pick values to query\n", "mass = np.linspace(50, 5000)\n", "extinction = np.full(50, 1)\n", "log_age = np.full(50, 7.5)\n", "metallicity = np.full(50, 0.0)\n", "differential_extinction = np.full(50, 0.2)\n", "\n", "coordinates = SkyCoord(\n", " l=np.full(50, 0)*u.deg,\n", " b=np.full(50, 0)*u.deg,\n", " pm_l_cosb=np.full(50, 0)*u.mas/u.yr,\n", " pm_b=np.full(50, 0)*u.mas/u.yr,\n", " distance=np.full(50, 2000)*u.pc,\n", " frame=\"galactic\"\n", ")\n", "\n", "n_stars_predicted, median_parallax_error_predicted = nstars_model(\n", " coordinates, \n", " mass=mass, \n", " extinction=extinction, \n", " log_age=log_age, \n", " metallicity=metallicity, \n", " differential_extinction=differential_extinction\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "\n", "ax.scatter(mass, n_stars_predicted)\n", "ax.set(xlabel=\"Mass [MSun]\", ylabel=\"Number of stars\")" ] }, { "cell_type": "markdown", "id": "c3cc4790", "metadata": {}, "source": [ "The bouncing around is because it's an _ensemble_ model, and it (sort of) randomly samples the number of stars that a given mass might have.\n", "\n", "We can use up to 250 models (the full ensemble) to get the most accurate prediction. **This will take longer to load and run, however.**\n", "\n", "We can also ask for full predictions from each model and use them to estimate uncertainties!" ] }, { "cell_type": "code", "execution_count": 13, "id": "f635d681", "metadata": {}, "outputs": [], "source": [ "nstars_model = NStarsPredictor(models=250)" ] }, { "cell_type": "code", "execution_count": 14, "id": "4b7ac723", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Querying model 250 of 250\n" ] }, { "data": { "text/plain": [ "[Text(0.5, 0, 'Mass [MSun]'), Text(0, 0.5, 'Number of stars')]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pick values to query\n", "mass = np.linspace(50, 5000)\n", "extinction = np.full(50, 1)\n", "log_age = np.full(50, 7.5)\n", "metallicity = np.full(50, 0.0)\n", "differential_extinction = np.full(50, 0.2)\n", "\n", "coordinates = SkyCoord(\n", " l=np.full(50, 0) * u.deg,\n", " b=np.full(50, 0) * u.deg,\n", " pm_l_cosb=np.full(50, 0) * u.mas / u.yr,\n", " pm_b=np.full(50, 0) * u.mas / u.yr,\n", " distance=np.full(50, 2000) * u.pc,\n", " frame=\"galactic\",\n", ")\n", "\n", "n_stars_predicted, median_parallax_error_predicted = nstars_model(\n", " coordinates,\n", " mass=mass,\n", " extinction=extinction,\n", " log_age=log_age,\n", " metallicity=metallicity,\n", " differential_extinction=differential_extinction,\n", " mode=\"full\",\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "\n", "median = np.median(n_stars_predicted, axis=1)\n", "errors = (\n", " median - np.percentile(n_stars_predicted, 16, axis=1),\n", " np.percentile(n_stars_predicted, 84, axis=1) - median,\n", " )\n", "ax.errorbar(\n", " mass,\n", " median,\n", " yerr=errors,\n", " fmt=\".\",\n", " capsize=2\n", ")\n", "ax.set(xlabel=\"Mass [MSun]\", ylabel=\"Number of stars\")" ] }, { "cell_type": "markdown", "id": "f8367419", "metadata": {}, "source": [ "There is still some scatter here (which is to be expected based on sampling & the fact that XGBoost isn't perfect), but this is still an accurate way to go from cluster parameters to number of stars." ] } ], "metadata": { "kernelspec": { "display_name": "hr-selection-function", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5}