From 10efbdbe20a0a904bb8ab30a7e9144f130bb5e03 Mon Sep 17 00:00:00 2001 From: Alex Binks Date: Tue, 12 Apr 2022 14:04:13 -0400 Subject: [PATCH 1/6] New tutorial to calculate radial velocity from multiple measurements This tutorial is designed to assess the multiplicity status of a star and calculate a "final" radial velocity for stars when there are several (> 2) individual measurements. Principally the program: 1) reads in a table of RV measurements for any set of stars 2) makes a decision on whether the star is multiple or likely single 3) calculates a final RV from the individual measurements. --- tutorials/multiple_rvs/MultipleRVs.ipynb | 444 +++++++++++++++++++++++ 1 file changed, 444 insertions(+) create mode 100644 tutorials/multiple_rvs/MultipleRVs.ipynb diff --git a/tutorials/multiple_rvs/MultipleRVs.ipynb b/tutorials/multiple_rvs/MultipleRVs.ipynb new file mode 100644 index 00000000..65374085 --- /dev/null +++ b/tutorials/multiple_rvs/MultipleRVs.ipynb @@ -0,0 +1,444 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2d9a5e47", + "metadata": {}, + "source": [ + "# Dealing with multiple Radial Velocity measurements" + ] + }, + { + "cell_type": "markdown", + "id": "9ef2636c", + "metadata": {}, + "source": [ + "It is a common task in astronomy to calculate a final measured quantity (and error) when there are multiple individual measurements for a particular object. This is often the case when dealing with radial velocities (RVs) for stars, particularly in the era of large spectroscopic surveys such as RAVE, Gaia DR2 (soon to be DR3) and GALAH.\n", + "\n", + "We also know that approximately half of all stars belong in multiple systems, and depending on their orbital properties (e.g., physical separation, eccentricity, inclination), their multiplicity status is given away by the fact that the components vary in RV from as low as 1 to 100 km/s. Whilst obvious temporal changes in RV are a giveaway for identifying multiples, it should be noted there is always some (usually small) probability that multiple systems evade detection because they are observed at the same orbital phase!\n", + "\n", + "### With this in mind, the following program:\n", + "\n", + "- reads in a table of RV measurements for any set of stars\n", + "\n", + "- makes a decision on whether the star is multiple or likely single\n", + "- calculates a final RV from the individual measurements." + ] + }, + { + "cell_type": "markdown", + "id": "7a1639b6", + "metadata": {}, + "source": [ + "### Some points before we begin:\n", + "\n", + "1. The table consists of a star identifier (that must be exactly the same if multiple entries are present), a reference to the source catalogue, the RV, and the RV error.\n", + "\n", + "2. For the cases where no RV error is calculated (tut, tut), for lack of a better method, we have assumed this error to be twice the median error bar from the whole sample of RV measurements. It is the user's discretion whether or not to include data that are missing errors (but sometimes even these measurements have intrinsic value if, say, there are no other measurements).\n", + "\n", + "3. The confidence placed in the reliability of each RV measurement is equal regardless of provenance.\n", + "\n", + "4. In the rare case where two RV measurements for a source differ by an amount greater than the physical maximum for an equal mass binary system, $\\delta RV \\geq 437\\times\\frac{\\sqrt{M/M_{\\odot}}}{\\sqrt{a/R_{\\odot}}}$ km/s -- *Bowers & Deeming 1984, 1984astr.book.....B*) then we discard the largest outlier." + ] + }, + { + "cell_type": "markdown", + "id": "458886b8", + "metadata": {}, + "source": [ + "### Part 1: Reading in the catalogue and pre-cleaning" + ] + }, + { + "cell_type": "markdown", + "id": "32ac145f", + "metadata": {}, + "source": [ + "Import python modules" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "afe48f62", + "metadata": {}, + "outputs": [], + "source": [ + "from astropy.table import unique, Table\n", + "from astropy.io import ascii\n", + "from astropy.stats import sigma_clip\n", + "import numpy as np\n", + "import itertools" + ] + }, + { + "cell_type": "markdown", + "id": "1ad9f2af", + "metadata": {}, + "source": [ + "Read in the input file\n", + "The minimum requirement is;\n", + "- name\n", + "- RV\n", + "- eRV\n", + "- reference\n", + "\n", + "Currently the following line would read in a basic ascii (space-separated)\n", + "file, but \"ascii.read\" can take all kinds of formats, which are described\n", + "in: https://docs.astropy.org/en/stable/io/ascii/read.html\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "a9f2d11d", + "metadata": {}, + "outputs": [], + "source": [ + "f_in = ascii.read(\"AllRVs.dat\", format='basic', delimiter=' ', guess=False)" + ] + }, + { + "cell_type": "markdown", + "id": "42c598d8", + "metadata": {}, + "source": [ + "In case of missing errors, use 2x the median error from all observations. In our example missing errors are marked as \"-999\". Please modify this line to make sense of your own dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "c9d553c4", + "metadata": {}, + "outputs": [], + "source": [ + "f_in[\"eRV\"] = np.where(f_in[\"eRV\"] < -99, 2.0*np.median(f_in[\"eRV\"]), f_in[\"eRV\"])" + ] + }, + { + "cell_type": "markdown", + "id": "c7a31abe", + "metadata": {}, + "source": [ + "Get a list of unique names for each star" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "99aecd9a", + "metadata": {}, + "outputs": [], + "source": [ + "f_un = unique(f_in, keys='name')" + ] + }, + { + "cell_type": "markdown", + "id": "8c8ec938", + "metadata": {}, + "source": [ + "The maximum possible RV difference between two observations was given earlier (point 4). One may wish to include columns in their input table of estimated mass and radius. In our case we are dealing mainly with early K-type pre-main sequence stars: mass = $0.8M_{\\odot}$ and radius = $0.7R_{\\odot}$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "503b7eff", + "metadata": {}, + "outputs": [], + "source": [ + "mass, radius = 0.8, 0.7\n", + "d_max = 437.*np.sqrt(mass)/np.sqrt(radius)" + ] + }, + { + "cell_type": "markdown", + "id": "8b10711a", + "metadata": {}, + "source": [ + "Now we want to remove any entries in the catalogue that cause $\\delta RV \\geq 437\\times\\frac{\\sqrt{M/M_{\\odot}}}{\\sqrt{a/R_{\\odot}}}$ km/s. Note that we only remove the object that we believe is causing the (unphysically) large RV difference. To do so we loop over each unique star name, and if there are $\\geq 2$ measurements, construct an array of pairwise RV differences, for example:\n", + "- 3 measurements: A vs B, A vs C, B vs C\n", + "- 4 measurements: A vs B, A vs C, A vs D, B vs C, B vs D, C vs D\n", + "\n", + "The arrays are sorted from largest to smallest values in $\\Delta RV$. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "30713fcb", + "metadata": {}, + "outputs": [], + "source": [ + "for f in f_un:\n", + " g = f_in[f_in[\"name\"] == f[\"name\"]]\n", + "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", + " x = len(g)\n", + "# Remove stars that cause RV differences larger than d_max.\n", + "# Get pair-wise RV measurements and find their differences\n", + "# using \"itertools.combinations\"\n", + " if x >= 2:\n", + " p = list(itertools.combinations(g[\"RV\"], 2))\n", + " b = list((i,j) for ((i,_),(j,_)) in itertools.combinations(enumerate(g[\"RV\"]), 2))\n", + " c1, c0, darr = [g[\"eRV\"][c[1]] for c in b], [g[\"eRV\"][c[0]] for c in b], [abs(z[1]-z[0]) for z in p]\n", + "# for the new pairwise arrays, find the locations where the RV difference > d_max\n", + " arr_bad = np.array(b)[np.array(darr) > d_max]\n", + "# if there are any examples where the RV difference > d_max\n", + " # and at least 2 cases where this happens\n", + " if np.any(arr_bad) and len(arr_bad) >= 2:\n", + " ind_outliers = np.array(arr_bad).ravel()\n", + " # find the entry which is causing the big RV difference (occurs the most often)\n", + " g_r = g[np.bincount(ind_outliers).argmax()]\n", + " f_in_r = [(f_in[\"cat\"] == g_r[1]) & (f_in[\"name\"] == g_r[0])]\n", + " f_in_ind = np.where(f_in_r)[1]\n", + " # remove this entry...\n", + " f_in.remove_row(f_in_ind[0])\n", + "\n", + " # if only one occasion where RV difference is large (i.e., 2 measurements)\n", + " if np.any(arr_bad) and len(arr_bad) < 2:\n", + " ind_outliers = np.array(arr_bad).ravel()\n", + " g_r = g[ind_outliers]\n", + " # select the entry with the largest RV error as the outlier to remove\n", + " g_max = g[g_r[\"eRV\"] == max(g_r[\"eRV\"])]\n", + " f_in_r = [(f_in[\"cat\"] == g_max[\"cat\"]) & (f_in[\"name\"] == g_max[\"name\"])]\n", + " f_in_ind = np.where(f_in_r)[1]\n", + " f_in.remove_row(f_in_ind[0])" + ] + }, + { + "cell_type": "markdown", + "id": "73400815", + "metadata": {}, + "source": [ + "### Part 2: The decision process for multiple/single stars" + ] + }, + { + "cell_type": "markdown", + "id": "27ca8ff2", + "metadata": {}, + "source": [ + "The next job is to combine multiple RV measurements again (this time without any extreme RV outliers), and create an array of pairwise RV differences. Sort the array in descending values of RV difference. If the RV difference is larger than the following criteria:\n", + "\n", + "$\\Delta RV > \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$, where $\\zeta = 3.0$ (but can be altered).\n", + "\n", + "Then we flag the star as a likely binary. If this criteria is not matched, move to the next lowest RV difference and recalculate. If, at the end this still isn't matched, then flag the star as a probable single." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "bf55bad5", + "metadata": {}, + "outputs": [], + "source": [ + "Nsig = 3.0" + ] + }, + { + "cell_type": "markdown", + "id": "50e32131", + "metadata": {}, + "source": [ + "Create an empty array \"F_arr\", which will store the designated multiplicity status, where:\n", + "- F_arr = 5: multiple, at least one $\\Delta RV > \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$\n", + "- F_arr = 3: (probably) single, every $\\Delta RV \\leq \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$\n", + "- F_arr = 1: = only 1 RV measurement, we can't say anything about multiplicity status\n", + "- F_arr = 0: = no RV measurements available\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "2ccd5674", + "metadata": {}, + "outputs": [], + "source": [ + "f_un = unique(f_in, keys='name')\n", + "F_Arr = []\n", + "\n", + "for f in f_un:\n", + " g = f_in[f_in[\"name\"] == f[\"name\"]]\n", + "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", + " x = len(g)\n", + "\n", + " if x >= 2:\n", + " p = list(itertools.combinations(g[\"RV\"], 2))\n", + " b = list((i,j) for ((i,_),(j,_)) in itertools.combinations(enumerate(g[\"RV\"]), 2))\n", + " c1, c0, darr = [g[\"eRV\"][c[1]] for c in b], [g[\"eRV\"][c[0]] for c in b], [abs(z[1]-z[0]) for z in p]\n", + " z = np.argsort(darr)\n", + " RVd_arr = [[darr[z[i]], c1[z[i]], c0[z[i]]] for i in z]# if darr[i] < d_max]\n", + " \n", + "# fill out the RV flag arrays based on the RV differences (and errors)\n", + "# 5 = multiple, dRV > d_max\n", + "# 3 = single, dRV <= d_max\n", + "# 1 = only 1 RV\n", + "# 0 = no RVs\n", + " for j in range(len(RVd_arr)):\n", + " eRV_max = max(RVd_arr[j][2], RVd_arr[j][1])\n", + " if RVd_arr == None:\n", + " F_Arr.append(0)\n", + " break\n", + " if len(z) > 1:\n", + "# if at any point |RV| > N*max(eRV) then we have no choice\n", + "# but to flag it as a probable multiple.\n", + " if (RVd_arr[j][0] > Nsig*eRV_max):\n", + " F_Arr.append(5)\n", + " break\n", + "# |RV| <= N*max(eRV)\n", + "# could be single, check the next RV difference\n", + " if (RVd_arr[j][0] <= Nsig*eRV_max):\n", + " j=j+1\n", + "# if after all the iterations we get here and we still didn't see any\n", + "# evidence of binarity, flag it as a single star.\n", + " if j == len(z)-1:\n", + " F_Arr.append(3)\n", + " break\n", + " if len(z) == 1:\n", + " if (RVd_arr[j][0] > Nsig*eRV_max):\n", + " F_Arr.append(5)\n", + "# break\n", + " if (RVd_arr[j][0] <= Nsig*eRV_max):\n", + " F_Arr.append(3)\n", + "# break\n", + "\n", + " if x == 1:\n", + " if g[\"RV\"][0] > -900:\n", + " F_Arr.append(1)\n", + " else:\n", + " F_Arr.append(0)\n", + " if x == 0:\n", + " F_Arr.append(0)" + ] + }, + { + "cell_type": "markdown", + "id": "f3251216", + "metadata": {}, + "source": [ + "### Part 3: obtaining a final RV measurement\n", + "Regardless of the multiplicity status assigned in Part 2, we now calculate a final RV measurement, and flag \"how\" we measure RV using a measurement flag (Mflag).\n", + "\n", + "#### If the star is a probable single, there are two paths to calculating a final RV.\n", + "\n", + "1. If the standard deviation in the error bars is less than the standard deviation in the measurements, then take the inverse weighted mean, using the square of the error bars as weights. Mflag = 2.\n", + "2. Otherwise, adopt the final RV as the value corresponding to the lowest error bar. Mflag = 3.\n", + "\n", + "The associtated error in the weighted mean is found using equation (2) and (3) at this link: http://seismo.berkeley.edu/~kirchner/Toolkits/Toolkit_12.pdf\n", + "\n", + "#### If the star is likely to be a multiple, use path 1 described above.\n", + "Mflag = 4.\n", + "\n", + "The cases with only 1 or 0 RV measurements is trivial, Mflag = 1 and 0, respectively.\n", + "\n", + "Two error bars are provided:\n", + "- \"sRV\", the error in the weighted mean.\n", + "- \"eRV\", the average value of the individual error bars." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "d3367b77", + "metadata": {}, + "outputs": [], + "source": [ + "RV_f, eRV_f, sRV_f, RV_T = [], [], [], []\n", + "\n", + "for k, l in enumerate(f_un):\n", + " g = f_in[f_in[\"name\"] == l[\"name\"]]\n", + " sdRV = np.std(g[\"RV\"])\n", + " sdeRV = np.std(g[\"eRV\"])\n", + "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", + " x = len(g)\n", + " if x >= 2:\n", + "# if we don't class the star as a possible binary\n", + " w = np.array(1.0/(g[\"eRV\"]**2))\n", + " if F_Arr[k] != 5:\n", + "# if the std in the errors is less than the std in the mean RV\n", + "# take the weighted average and error\n", + "\n", + "# weighted error is found like this:\n", + "# http://seismo.berkeley.edu/~kirchner/Toolkits/Toolkit_12.pdf\n", + "\n", + " if sdeRV <= sdRV:\n", + " w_RV = np.average(g[\"RV\"], weights=w)\n", + " val = np.array(g[\"RV\"]**2)\n", + " var = ((np.sum(w*val)/np.sum(w))-w_RV**2) * (x/(x-1))\n", + " RV_f.append(w_RV)\n", + " sRV_f.append(np.sqrt(var/x))\n", + " eRV_f.append(np.average(g[\"eRV\"]))\n", + " RV_T.append(2)\n", + " else:\n", + " RV_f.append(g[\"RV\"][np.argsort(g[\"eRV\"][0])][0])\n", + " eRV_f.append(g[\"eRV\"][np.argsort(g[\"eRV\"][0])][0])\n", + " sRV_f.append(np.average(g[\"eRV\"]))\n", + " RV_T.append(3)\n", + " if F_Arr[k] == 5:\n", + " w_RV = np.average(g[\"RV\"], weights=w)\n", + " val = np.array(g[\"RV\"]**2)\n", + " var = ((np.sum(w*val)/np.sum(w))-w_RV**2) * (x/(x-1))\n", + " RV_f.append(np.average(g[\"RV\"], weights=w))\n", + " sRV_f.append(np.sqrt(var/x))\n", + " eRV_f.append(np.average(g[\"eRV\"]))\n", + " RV_T.append(4)\n", + " if x == 1:\n", + " RV_f.append(g[\"RV\"][0])\n", + " sRV_f.append(0.0)\n", + " eRV_f.append(g[\"eRV\"][0])\n", + " RV_T.append(1)" + ] + }, + { + "cell_type": "markdown", + "id": "a2581278", + "metadata": {}, + "source": [ + "Finally, print all these results to a table." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "a902d3c9", + "metadata": {}, + "outputs": [], + "source": [ + "f_out = [f_un[\"name\"], RV_f, sRV_f, eRV_f, RV_T]\n", + "\n", + "f_table = Table(data=f_out, masked=False, names=('Name','RVfin','sRV','eRV','RV_T'))\n", + "\n", + "f_table[\"Name\"].format = '%s'\n", + "f_table[\"RVfin\"].format = '%+9.2f'\n", + "f_table[\"sRV\"].format = '%9.2f'\n", + "f_table[\"eRV\"].format = '%9.2f'\n", + "f_table[\"RV_T\"].format = '%i'\n", + "\n", + "ascii.write(f_table, \"finalRVs.csv\", format='csv', overwrite=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 592be63ccea9fefc234f63fd57117a1491622c05 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Tue, 12 Apr 2022 18:16:51 +0000 Subject: [PATCH 2/6] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- tutorials/multiple_rvs/MultipleRVs.ipynb | 28 ++++++++++-------------- 1 file changed, 11 insertions(+), 17 deletions(-) diff --git a/tutorials/multiple_rvs/MultipleRVs.ipynb b/tutorials/multiple_rvs/MultipleRVs.ipynb index 65374085..dc65ca4d 100644 --- a/tutorials/multiple_rvs/MultipleRVs.ipynb +++ b/tutorials/multiple_rvs/MultipleRVs.ipynb @@ -59,7 +59,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "id": "afe48f62", "metadata": {}, "outputs": [], @@ -90,7 +90,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": null, "id": "a9f2d11d", "metadata": {}, "outputs": [], @@ -108,7 +108,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": null, "id": "c9d553c4", "metadata": {}, "outputs": [], @@ -126,7 +126,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": null, "id": "99aecd9a", "metadata": {}, "outputs": [], @@ -144,7 +144,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": null, "id": "503b7eff", "metadata": {}, "outputs": [], @@ -167,7 +167,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": null, "id": "30713fcb", "metadata": {}, "outputs": [], @@ -229,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": null, "id": "bf55bad5", "metadata": {}, "outputs": [], @@ -251,7 +251,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": null, "id": "2ccd5674", "metadata": {}, "outputs": [], @@ -340,7 +340,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": null, "id": "d3367b77", "metadata": {}, "outputs": [], @@ -401,7 +401,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": null, "id": "a902d3c9", "metadata": {}, "outputs": [], @@ -421,11 +421,6 @@ } ], "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, "language_info": { "codemirror_mode": { "name": "ipython", @@ -435,8 +430,7 @@ "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.7" + "pygments_lexer": "ipython3" } }, "nbformat": 4, From bb9cfb56efb0d822c1ff795826f095ac81cecf2b Mon Sep 17 00:00:00 2001 From: Alex Binks Date: Tue, 12 Apr 2022 14:26:00 -0400 Subject: [PATCH 3/6] Add the RV data file --- tutorials/multiple_rvs/AllRVs.dat | 656 ++++++++++++++++++++++++++++++ 1 file changed, 656 insertions(+) create mode 100644 tutorials/multiple_rvs/AllRVs.dat diff --git a/tutorials/multiple_rvs/AllRVs.dat b/tutorials/multiple_rvs/AllRVs.dat new file mode 100644 index 00000000..cbce0496 --- /dev/null +++ b/tutorials/multiple_rvs/AllRVs.dat @@ -0,0 +1,656 @@ +name cat d_as RV eRV +J000453.05-103220.0 LauraRV 0.0 7.7 13.4 +J001527.62-641455.2 I/345/gaia2 0.703 6.08 1.36 +J001527.62-641455.2 III/283/ravedr6 0.81 6.77 2.94 +J001527.62-641455.2 J/AJ/147/146/stars 0.94 6.7 0.3 +J001527.62-641455.2 LauraRV 0.0 6.3 0.9 +J001536.79-294601.2 III/283/ravedr6 1.423 0.05 4.7 +J001536.79-294601.2 J/A+A/649/A6/table1c 0.952 0.018 4.842 +J001536.79-294601.2 J/AJ/157/234/table2 1.48 0.61 1.31 +J001536.79-294601.2 Sept_14_Alex_RV 0.0 0.984 0.704 +J001536.79-294601.2 LauraRV 0.0 -28.8 4.9 +J001552.28-280749.4 I/345/gaia2 0.519 -0.44 0.65 +J001552.28-280749.4 III/283/ravedr6 0.578 6.99 2.03 +J001555.65-613752.2 J/AJ/147/146/stars 0.7 19.9 0.7 +J001709.96+185711.8 I/345/gaia2 0.243 33.13 0.73 +J001709.96+185711.8 LauraRV 0.0 32.7 1 +J001723.69-664512.4 echelle_dec13 0.0 11.42 0.81 +J001723.69-664512.4 I/345/gaia2 0.751 8.75 1.09 +J001723.69-664512.4 III/283/ravedr6 0.878 974.68 9.31 +J001723.69-664512.4 J/AJ/147/85/table4 0.975 11.4 0.8 +J001723.69-664512.4 J/AJ/154/129/catalog 0.9 10.7 0.2 +J001723.69-664512.4 J/ApJ/840/87/targets 0.84 -4.84 5.64 +J002101.27-134230.7 III/283/ravedr6 1.897 1.25 0.81 +J003057.97-655006.4 J/AJ/147/146/stars 0.94 13.6 0.9 +J003057.97-655006.4 Sept_14_Alex_RV 0.0 7.164 2.48 +J003234.86+072926.4 III/198/main 0.63 2.4 0.9 +J003234.86+072926.4 LauraRV 0.0 -4.6 0.7 +J003903.51+133016.0 LauraRV 0.0 -7 1.5 +J004210.98-425254.8 I/345/gaia2 0.783 6.63 0.75 +J004210.98-425254.8 J/AJ/147/146/stars 0.72 8.7 0.1 +J004210.98-425254.8 Sept_14_Alex_RV 0.0 6.919 0.543 +J004524.84-775207.5 III/283/ravedr6 2.193 4.04 2.7 +J004524.84-775207.5 III/283/xgaia2 2.028 6.14 1.04 +J004524.84-775207.5 LauraRV 0.0 3.6 2.1 +J004528.25-513734.4 I/345/gaia2 0.791 8.2 1.56 +J004528.25-513734.4 J/ApJ/840/87/targets 0.99 -0.72 4.89 +J004528.25-513734.4 LauraRV 0.0 -8 1.3 +J004528.25-513734.4 V/137D/XHIP 2.001 -1.6 10.0 +J004826.70-184720.7 J/A+A/649/A6/table1c 0.854 7.21 0.68 +J004826.70-184720.7 LauraRV 0.0 5.6 1.4 +J005633.96-225545.4 I/345/gaia2 0.499 16.34 7.15 +J010126.59+463832.6 I/345/gaia2 0.273 -86.5 14.94 +J010243.86-623534.8 III/283/ravedr6 0.807 11.25 6.3 +J010243.86-623534.8 J/AJ/147/146/stars 0.85 7.0 2.0 +J010251.05+185653.7 J/A+A/649/A6/table1c 0.815 19.749 2.937 +J010629.32-122518.4 LauraRV 0.0 2.7 1.5 +J010711.99-193536.4 III/283/ravedr6 0.823 9.58 3.9 +J010711.99-193536.4 J/AJ/147/146/stars 0.88 9.3 0.5 +J010711.99-193536.4 J/AJ/154/129/catalog 0.8 11.5 1.4 +J010711.99-193536.4 LauraRV 0.0 7.1 1.1 +J011846.91+125831.4 I/345/gaia2 0.183 -5.59 3.8 +J012118.22-543425.1 III/283/ravedr6 0.924 26.43 1.48 +J012118.22-543425.1 J/AJ/147/146/stars 0.98 24.0 0.3 +J012118.22-543425.1 LauraRV 0.0 25.8 1.3 +J012245.24-631845.0 J/AJ/147/146/stars 0.95 7.8 1.4 +J012245.24-631845.0 LauraRV 0.0 18.3 5.3 +J012332.89-411311.4 J/AJ/147/146/stars 1.09 5.7 1.4 +J012532.11-664602.6 J/AJ/147/146/stars 0.93 7.1 5.1 +J013110.69-760947.7 III/283/ravedr6 0.558 29.0 5.97 +J013110.69-760947.7 Sept_14_Alex_RV 0.0 28.282 0.618 +J014156.94-123821.6 I/345/gaia2 0.427 13.36 1.12 +J015057.01-584403.4 III/283/ravedr6 0.949 11.43 6.45 +J015057.01-584403.4 J/AJ/147/146/stars 1.03 11.1 0.5 +J015057.01-584403.4 LauraRV 0.0 9.3 1.5 +J015257.41+083326.3 J/other/RAA/15.1182/dr1mcat 1.007 -4.206 23.6 +J015350.81-145950.6 III/283/ravedr6 0.668 1.26 4.4 +J015350.81-145950.6 J/AJ/154/69/table4 0.59 10.5 0.4 +J015350.81-145950.6 J/MNRAS/475/1960/tablea6 0.59 10.34 11.8 +J015455.24-295746.0 LauraRV 0.0 37.7 2 +J020012.84-084052.4 J/AJ/147/146/stars 1.33 4.5 0.4 +J020012.84-084052.4 J/MNRAS/475/1960/tablea6 1.05 4.58 27.3 +J020012.84-084052.4 LauraRV 0.0 5.5 1.4 +J020805.55-474633.7 echelle_dec13 0.0 4.82 0.74 +J020805.55-474633.7 I/345/gaia2 0.482 2.77 0.77 +J021258.28-585118.3 I/345/gaia2 0.68 10.22 2.09 +J021258.28-585118.3 III/283/ravedr6 0.623 -5.73 13.39 +J021258.28-585118.3 J/AJ/147/146/stars 0.7 9.1 0.8 +J021258.28-585118.3 J/ApJ/840/87/targets 0.7 4.45 5.0 +J021258.28-585118.3 Sept_14_Alex_RV 0.0 8.382 1.906 +J021330.24-465450.3 III/283/ravedr6 0.205 1.17 4.64 +J021330.24-465450.3 J/AJ/157/234/table2 0.36 10.33 1.02 +J021330.24-465450.3 J/ApJ/840/87/targets 0.34 9.36 6.0 +J022240.88+305515.4 J/A+A/649/A6/table1c 0.727 42.359 4.81 +J022424.69-703321.2 J/AJ/147/146/stars 0.79 11.8 0.3 +J022424.69-703321.2 Sept_14_Alex_RV 0.0 12.485 1.225 +J023005.14+284500.0 I/345/gaia2 0.812 -26.16 1.07 +J023139.36+445638.1 J/ApJ/758/56/mdwarfs 1.21 -4.7 3.8 +J024552.65+052923.8 I/345/gaia2 0.571 6.77 1.55 +J024746.49-580427.4 I/345/gaia2 0.635 11.17 1.1 +J024746.49-580427.4 III/283/ravedr6 0.772 5.43 2.83 +J024746.49-580427.4 J/AJ/147/146/stars 0.81 13.1 0.5 +J024746.49-580427.4 LauraRV 0.0 12.2 1 +J024852.67-340424.9 III/283/ravedr6 0.753 10.53 12.96 +J024852.67-340424.9 J/AJ/147/146/stars 0.93 23.3 0.5 +J024852.67-340424.9 J/AJ/154/129/catalog 0.8 14.6 0.3 +J024852.67-340424.9 J/AJ/154/69/table4 0.84 14.8 0.5 +J024852.67-340424.9 J/ApJ/840/87/targets 0.88 14.47 5.54 +J024852.67-340424.9 LauraRV 0.0 12.5 2 +J025154.17+222728.9 J/A+A/612/A49/tableb1 1.46 -18.849 -999 +J025154.17+222728.9 J/A+A/656/A162/table1 1.42 9.14 0.08 +J025154.17+222728.9 J/MNRAS/475/1960/tablea6 1.46 9.09 29.2 +J025154.17+222728.9 LauraRV 0.0 11.4 2.6 +J025913.40+203452.6 I/345/gaia2 0.575 -25.08 19.66 +J030002.98+550652.4 I/345/gaia2 0.409 -6.88 1.73 +J030002.98+550652.4 LauraRV 0.0 17.9 4.2 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0.0 6.1 1.2 +J234926.23+185912.4 I/345/gaia2 0.449 6.28 0.38 From 12213a2a5f629ce6980084bb479ca9e7035f856c Mon Sep 17 00:00:00 2001 From: Alex Binks Date: Wed, 13 Apr 2022 20:55:22 -0400 Subject: [PATCH 4/6] Here are some modifications to the ipython notebook from yesterday on measuring radial velocities. The major modifications are that we now use numpy matrices rather than itertools which is easier to read and runs faster than the previous method. --- tutorials/multiple_rvs/AllRVs.dat | 7 + tutorials/multiple_rvs/MultipleRVs.ipynb | 740 ++++++++++++++++------- 2 files changed, 523 insertions(+), 224 deletions(-) diff --git a/tutorials/multiple_rvs/AllRVs.dat b/tutorials/multiple_rvs/AllRVs.dat index cbce0496..d8a6f22a 100644 --- a/tutorials/multiple_rvs/AllRVs.dat +++ b/tutorials/multiple_rvs/AllRVs.dat @@ -1,4 +1,11 @@ name cat d_as RV eRV +J000000.00-000000.0 Dummy1 0.0 10.0 0.5 +J000000.00-000000.0 Dummy1 0.0 10.2 0.4 +J000000.00-000000.0 Dummy1 0.0 10.3 0.5 +J000000.00-000000.0 Dummy1 0.0 10.1 0.3 +J000000.00-000000.0 Dummy1 0.0 10.5 0.5 +J000000.00-000000.0 Dummy1 0.0 1000.0 0.5 + J000453.05-103220.0 LauraRV 0.0 7.7 13.4 J001527.62-641455.2 I/345/gaia2 0.703 6.08 1.36 J001527.62-641455.2 III/283/ravedr6 0.81 6.77 2.94 diff --git a/tutorials/multiple_rvs/MultipleRVs.ipynb b/tutorials/multiple_rvs/MultipleRVs.ipynb index dc65ca4d..ee4853c7 100644 --- a/tutorials/multiple_rvs/MultipleRVs.ipynb +++ b/tutorials/multiple_rvs/MultipleRVs.ipynb @@ -8,37 +8,67 @@ "# Dealing with multiple Radial Velocity measurements" ] }, + { + "cell_type": "markdown", + "id": "80ab7d13", + "metadata": {}, + "source": [ + "# Authors\n", + "Alex Binks, Moritz Guenther" + ] + }, + { + "cell_type": "markdown", + "id": "a10bd8da", + "metadata": {}, + "source": [ + "# Learning goals\n", + "- Input/Output: Read an ascii file of tabulated data and output a results file using [astropy.io.ascii](https://docs.astropy.org/en/stable/io/ascii/index.html).\n", + "- Coding: Produce reusable codes with functions. Apply matrix operations using numpy.\n", + "- Science: Learn how to detect stars as components of multiple stellar systems through radial velocity (RV) variations and measure error-weighted RVs.\n", + "- Visualisation: Plot histograms using matplotlib." + ] + }, + { + "cell_type": "markdown", + "id": "846d3413", + "metadata": {}, + "source": [ + "# Keywords\n", + "radial velocity, multiple stars, astropy.io, numpy, matrix operations, error propagation" + ] + }, { "cell_type": "markdown", "id": "9ef2636c", "metadata": {}, "source": [ - "It is a common task in astronomy to calculate a final measured quantity (and error) when there are multiple individual measurements for a particular object. This is often the case when dealing with radial velocities (RVs) for stars, particularly in the era of large spectroscopic surveys such as RAVE, Gaia DR2 (soon to be DR3) and GALAH.\n", + "# Summary\n", + "It is a common task in astronomy to calculate a final measured quantity (and error) when there are multiple individual measurements for a particular object. If the measurement errors are similar in magnitude, one might choose an error weighted average. In other cases where there are large and small error bar it may be better to simply use the quantity corresponding to the lowest error.\n", + "\n", + "This is often the case when dealing with radial velocities (RVs) for stars, which (as the name suggests) measures the velocity in the line-of-sight of the observer (positive value are receeding from the observer). In the era of large spectroscopic surveys such as RAVE, Gaia DR2 (soon to be DR3) and GALAH, correct RV measurements are crucial to properly interpret data for millions of stars. When combined with positions, proper motions (the angular displacement on the sky per year) and distance measurements, a full 6D spatio-kinematic map of the star can be produced. Three examples of how RV measurements can be utilised are:\n", + "\n", + "1. Determine membership status for candidate members of comoving clusters and groups.\n", + "2. Traceback the orbits of stars through the Galaxy\n", + "3. reveal the large-scale kinematic structure of the Milky Way.\n", "\n", - "We also know that approximately half of all stars belong in multiple systems, and depending on their orbital properties (e.g., physical separation, eccentricity, inclination), their multiplicity status is given away by the fact that the components vary in RV from as low as 1 to 100 km/s. Whilst obvious temporal changes in RV are a giveaway for identifying multiples, it should be noted there is always some (usually small) probability that multiple systems evade detection because they are observed at the same orbital phase!\n", + "We also know that approximately half of all stars belong in multiple systems, and depending on their orbital properties (e.g., physical separation, eccentricity, inclination), their multiplicity status is given away by the fact that the components vary in RV, typically between 1-100 km/s. Whilst obvious temporal changes in RV are a giveaway for identifying multiples, it should be noted there is always some (usually small) probability that multiple systems evade detection because they are observed at the same orbital phase!\n", "\n", "### With this in mind, the following program:\n", "\n", "- reads in a table of RV measurements for any set of stars\n", - "\n", "- makes a decision on whether the star is multiple or likely single\n", - "- calculates a final RV from the individual measurements." - ] - }, - { - "cell_type": "markdown", - "id": "7a1639b6", - "metadata": {}, - "source": [ + "- calculates a final RV from the individual measurements.\n", + "\n", "### Some points before we begin:\n", "\n", - "1. The table consists of a star identifier (that must be exactly the same if multiple entries are present), a reference to the source catalogue, the RV, and the RV error.\n", + "1. Table rows consist of a star identifier (that must be exactly the same if multiple entries are present), a reference to the source catalogue, the RV, and the RV error.\n", "\n", "2. For the cases where no RV error is calculated (tut, tut), for lack of a better method, we have assumed this error to be twice the median error bar from the whole sample of RV measurements. It is the user's discretion whether or not to include data that are missing errors (but sometimes even these measurements have intrinsic value if, say, there are no other measurements).\n", "\n", "3. The confidence placed in the reliability of each RV measurement is equal regardless of provenance.\n", "\n", - "4. In the rare case where two RV measurements for a source differ by an amount greater than the physical maximum for an equal mass binary system, $\\delta RV \\geq 437\\times\\frac{\\sqrt{M/M_{\\odot}}}{\\sqrt{a/R_{\\odot}}}$ km/s -- *Bowers & Deeming 1984, 1984astr.book.....B*) then we discard the largest outlier." + "4. The physical maximum RV difference for an equal mass binary system is $\\Delta RV_{\\rm max} \\geq 437\\times\\frac{\\sqrt{M/M_{\\odot}}}{\\sqrt{a/R_{\\odot}}}$ km/s -- [Bowers & Deeming 1984](https://adswww.harvard.edu/abs/1984astr.book.....B). We discard these RV outiers from analysis when considering the multiplicity status and measuring the final RV." ] }, { @@ -59,16 +89,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 282, "id": "afe48f62", "metadata": {}, "outputs": [], "source": [ "from astropy.table import unique, Table\n", "from astropy.io import ascii\n", - "from astropy.stats import sigma_clip\n", "import numpy as np\n", - "import itertools" + "\n", + "from matplotlib import pylab as plt\n", + "\n", + "np.set_printoptions(precision=3, suppress=True)\n", + "\n", + "%matplotlib inline" ] }, { @@ -90,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 283, "id": "a9f2d11d", "metadata": {}, "outputs": [], @@ -98,40 +132,232 @@ "f_in = ascii.read(\"AllRVs.dat\", format='basic', delimiter=' ', guess=False)" ] }, + { + "cell_type": "code", + "execution_count": 284, + "id": "dcccb174", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "\n", + " name cat d_as RV eRV \n", + " str19 str27 float64 float64 float64\n", + "------------------- -------------------- ------- ------- -------\n", + "J000000.00-000000.0 Dummy1 0.0 10.0 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.2 0.4\n", + "J000000.00-000000.0 Dummy1 0.0 10.3 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.1 0.3\n", + "J000000.00-000000.0 Dummy1 0.0 10.5 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 1000.0 0.5\n", + " ... ... ... ... ...\n", + "J234326.88-344658.5 III/283/ravedr6 1.017 8.47 3.12\n", + "J234326.88-344658.5 J/A+A/649/A6/table1c 0.91 8.529 3.114\n", + "J234333.91-192802.8 LauraRV 0.0 -13.4 4.1\n", + "J234347.83-125252.1 I/345/gaia2 0.474 3.61 2.41\n", + "J234857.35+100929.3 I/345/gaia2 0.433 -5.98 0.88\n", + "J234924.87+185926.7 LauraRV 0.0 6.1 1.2\n", + "J234926.23+185912.4 I/345/gaia2 0.449 6.28 0.38" + ] + }, + "execution_count": 284, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f_in" + ] + }, { "cell_type": "markdown", - "id": "42c598d8", + "id": "76db5bcf", "metadata": {}, "source": [ - "In case of missing errors, use 2x the median error from all observations. In our example missing errors are marked as \"-999\". Please modify this line to make sense of your own dataset." + "Locate the indices for measurements without RV errors. " ] }, { "cell_type": "code", - "execution_count": null, - "id": "c9d553c4", + "execution_count": 285, + "id": "d96354ff", "metadata": {}, "outputs": [], "source": [ - "f_in[\"eRV\"] = np.where(f_in[\"eRV\"] < -99, 2.0*np.median(f_in[\"eRV\"]), f_in[\"eRV\"])" + "ind = f_in['eRV'] < -99" + ] + }, + { + "cell_type": "code", + "execution_count": 286, + "id": "f2541ec4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 286, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind.sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 287, + "id": "f941dc1e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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J231246.53-504924.8LauraRV0.0-22.6-999.0
" + ], + "text/plain": [ + "\n", + " name cat d_as RV eRV \n", + " str19 str27 float64 float64 float64\n", + "------------------- ----------------------- ------- ------- -------\n", + "J025154.17+222728.9 J/A+A/612/A49/tableb1 1.46 -18.849 -999.0\n", + "J050827.31-210144.3 J/A+A/612/A49/tableb1 0.21 33.752 -999.0\n", + "J062047.17-361948.2 J/MNRAS/447/1267/table1 0.11 16.5 -999.0\n", + "J075830.92+153013.4 III/198/main 2.0 18.0 -999.0\n", + "J112105.43-384516.6 J/MNRAS/494/2429/table1 0.74 10.85 -999.0\n", + "J114728.37+664402.7 J/A+A/612/A49/tableb1 1.16 -9.543 -999.0\n", + "J173353.07+165511.7 J/A+A/612/A49/tableb1 1.74 -22.484 -999.0\n", + "J210708.43-113506.0 J/MNRAS/494/2429/table1 1.05 -9.515 -999.0\n", + "J224500.20-331527.2 J/AJ/154/69/table4 2.03 2.0 -999.0\n", + "J231246.53-504924.8 LauraRV 0.0 -22.6 -999.0" + ] + }, + "execution_count": 287, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f_in[ind]" ] }, { "cell_type": "markdown", - "id": "c7a31abe", + "id": "42c598d8", "metadata": {}, "source": [ - "Get a list of unique names for each star" + "In case of missing errors, use 2x the median error from all observations. In our example missing errors are marked as \"-999\". Please modify this line to make sense of your own dataset." ] }, { "cell_type": "code", - "execution_count": null, - "id": "99aecd9a", + "execution_count": 288, + "id": "cce51c93", "metadata": {}, "outputs": [], "source": [ - "f_un = unique(f_in, keys='name')" + "f_in[\"eRV\"][f_in[\"eRV\"] < -99] = 2.0 * np.median(f_in[\"eRV\"][~ind])" + ] + }, + { + "cell_type": "code", + "execution_count": 289, + "id": "9f04f2cb", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "\n", + " name cat d_as RV eRV \n", + " str19 str27 float64 float64 float64\n", + "------------------- -------------------- ------- ------- -------\n", + "J000000.00-000000.0 Dummy1 0.0 10.0 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.2 0.4\n", + "J000000.00-000000.0 Dummy1 0.0 10.3 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.1 0.3\n", + "J000000.00-000000.0 Dummy1 0.0 10.5 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 1000.0 0.5\n", + " ... ... ... ... ...\n", + "J234326.88-344658.5 III/283/ravedr6 1.017 8.47 3.12\n", + "J234326.88-344658.5 J/A+A/649/A6/table1c 0.91 8.529 3.114\n", + "J234333.91-192802.8 LauraRV 0.0 -13.4 4.1\n", + "J234347.83-125252.1 I/345/gaia2 0.474 3.61 2.41\n", + "J234857.35+100929.3 I/345/gaia2 0.433 -5.98 0.88\n", + "J234924.87+185926.7 LauraRV 0.0 6.1 1.2\n", + "J234926.23+185912.4 I/345/gaia2 0.449 6.28 0.38" + ] + }, + "execution_count": 289, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f_in" ] }, { @@ -139,12 +365,12 @@ "id": "8c8ec938", "metadata": {}, "source": [ - "The maximum possible RV difference between two observations was given earlier (point 4). One may wish to include columns in their input table of estimated mass and radius. In our case we are dealing mainly with early K-type pre-main sequence stars: mass = $0.8M_{\\odot}$ and radius = $0.7R_{\\odot}$.\n" + "The maximum possible RV difference between two observations, $\\Delta RV_{\\rm max}$ was given earlier (point 4). One may wish to include columns in their input table of estimated mass and radius. In our case we are dealing mainly with early K-type pre-main sequence stars: mass = $0.8M_{\\odot}$ and radius = $0.7R_{\\odot}$.\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 290, "id": "503b7eff", "metadata": {}, "outputs": [], @@ -158,269 +384,334 @@ "id": "8b10711a", "metadata": {}, "source": [ - "Now we want to remove any entries in the catalogue that cause $\\delta RV \\geq 437\\times\\frac{\\sqrt{M/M_{\\odot}}}{\\sqrt{a/R_{\\odot}}}$ km/s. Note that we only remove the object that we believe is causing the (unphysically) large RV difference. To do so we loop over each unique star name, and if there are $\\geq 2$ measurements, construct an array of pairwise RV differences, for example:\n", - "- 3 measurements: A vs B, A vs C, B vs C\n", - "- 4 measurements: A vs B, A vs C, A vs D, B vs C, B vs D, C vs D\n", + "Now we want to measure the differences in RV between each measurement to test for multiplicity. The condition is set as follows:\n", "\n", - "The arrays are sorted from largest to smallest values in $\\Delta RV$. " + "$\\Delta RV > \\zeta\\times (\\sigma_{RV_{1}} + \\sigma_{RV_{2}})$, where $\\zeta = 3.0$ (but this can be altered).\n", + "\n", + "In practice, this is done with a function called \"test_mult\".\n", + "\n", + "First we create a square matrix of RV measurements where the n observations are repeated over n rows. A matrix of RV differences, $c$, is calculated by subtracting this matrix by its transpose.\n", + "\n", + "Next we remove any measurements that cause $\\Delta RV > \\Delta RV_{\\rm max}$ by locating their position in the numpy array (np.where) and deleting them (np.delete). Then the matrix $c$ is recalculated (without the outliers).\n", + "\n", + "The combined errors ($\\sigma_{RV_{1}} + \\sigma_{RV_{2}}$) are found in a similar way, where the n errors are repeated over n rows. The corresponding error matrix, $e_c$, is found by calculating the sum of the corresponding error matrix and its transpose.\n", + "\n", + "Since the matrix has repeating values (and zeroes along the diagonal), we extract the subset of matrix elements that have $c > 0$. If any of these elements satisfy $\\frac{c}{e_c} > \\zeta$, the star is flagged as a probable multiple, otherwise it is likely single." ] }, { "cell_type": "code", - "execution_count": null, - "id": "30713fcb", + "execution_count": 362, + "id": "5c7af073", "metadata": {}, "outputs": [], "source": [ - "for f in f_un:\n", - " g = f_in[f_in[\"name\"] == f[\"name\"]]\n", - "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", - " x = len(g)\n", - "# Remove stars that cause RV differences larger than d_max.\n", - "# Get pair-wise RV measurements and find their differences\n", - "# using \"itertools.combinations\"\n", - " if x >= 2:\n", - " p = list(itertools.combinations(g[\"RV\"], 2))\n", - " b = list((i,j) for ((i,_),(j,_)) in itertools.combinations(enumerate(g[\"RV\"]), 2))\n", - " c1, c0, darr = [g[\"eRV\"][c[1]] for c in b], [g[\"eRV\"][c[0]] for c in b], [abs(z[1]-z[0]) for z in p]\n", - "# for the new pairwise arrays, find the locations where the RV difference > d_max\n", - " arr_bad = np.array(b)[np.array(darr) > d_max]\n", - "# if there are any examples where the RV difference > d_max\n", - " # and at least 2 cases where this happens\n", - " if np.any(arr_bad) and len(arr_bad) >= 2:\n", - " ind_outliers = np.array(arr_bad).ravel()\n", - " # find the entry which is causing the big RV difference (occurs the most often)\n", - " g_r = g[np.bincount(ind_outliers).argmax()]\n", - " f_in_r = [(f_in[\"cat\"] == g_r[1]) & (f_in[\"name\"] == g_r[0])]\n", - " f_in_ind = np.where(f_in_r)[1]\n", - " # remove this entry...\n", - " f_in.remove_row(f_in_ind[0])\n", - "\n", - " # if only one occasion where RV difference is large (i.e., 2 measurements)\n", - " if np.any(arr_bad) and len(arr_bad) < 2:\n", - " ind_outliers = np.array(arr_bad).ravel()\n", - " g_r = g[ind_outliers]\n", - " # select the entry with the largest RV error as the outlier to remove\n", - " g_max = g[g_r[\"eRV\"] == max(g_r[\"eRV\"])]\n", - " f_in_r = [(f_in[\"cat\"] == g_max[\"cat\"]) & (f_in[\"name\"] == g_max[\"name\"])]\n", - " f_in_ind = np.where(f_in_r)[1]\n", - " f_in.remove_row(f_in_ind[0])" + "def test_mult(trv, erv):\n", + " c = trv[:, None] - trv[None, :]\n", + " ee = c > d_max\n", + " x = np.array(np.where(ee))[0]\n", + " if len(x) > 0:\n", + " trv = np.delete(trv, x[0], 0)\n", + " erv = np.delete(erv, x[0], 0)\n", + " c = trv[:, None] - trv[None, :]\n", + " ec = np.abs(erv[:, None] + erv[None, :])\n", + " ratio = c / ec\n", + " ind = (c > 0)\n", + " return (ratio[ind] > 3).sum(), len(ind)" ] }, { "cell_type": "markdown", - "id": "73400815", + "id": "9a2ba8e0", "metadata": {}, "source": [ - "### Part 2: The decision process for multiple/single stars" + "Group together RV measurements by using the group_by function in astropy tables." + ] + }, + { + "cell_type": "code", + "execution_count": 369, + "id": "45f2d2a1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "\n", + " name cat d_as RV eRV \n", + " str19 str27 float64 float64 float64\n", + "------------------- -------------------- ------- ------- -------\n", + "J000000.00-000000.0 Dummy1 0.0 10.0 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.2 0.4\n", + "J000000.00-000000.0 Dummy1 0.0 10.3 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 10.1 0.3\n", + "J000000.00-000000.0 Dummy1 0.0 10.5 0.5\n", + "J000000.00-000000.0 Dummy1 0.0 1000.0 0.5\n", + " ... ... ... ... ...\n", + "J234326.88-344658.5 III/283/ravedr6 1.017 8.47 3.12\n", + "J234326.88-344658.5 J/A+A/649/A6/table1c 0.91 8.529 3.114\n", + "J234333.91-192802.8 LauraRV 0.0 -13.4 4.1\n", + "J234347.83-125252.1 I/345/gaia2 0.474 3.61 2.41\n", + "J234857.35+100929.3 I/345/gaia2 0.433 -5.98 0.88\n", + "J234924.87+185926.7 LauraRV 0.0 6.1 1.2\n", + "J234926.23+185912.4 I/345/gaia2 0.449 6.28 0.38" + ] + }, + "execution_count": 369, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "obs_by_name = f_in.group_by('name')\n", + "obs_by_name" ] }, { "cell_type": "markdown", - "id": "27ca8ff2", + "id": "2db6a978", "metadata": {}, "source": [ - "The next job is to combine multiple RV measurements again (this time without any extreme RV outliers), and create an array of pairwise RV differences. Sort the array in descending values of RV difference. If the RV difference is larger than the following criteria:\n", - "\n", - "$\\Delta RV > \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$, where $\\zeta = 3.0$ (but can be altered).\n", - "\n", - "Then we flag the star as a likely binary. If this criteria is not matched, move to the next lowest RV difference and recalculate. If, at the end this still isn't matched, then flag the star as a probable single." + "Create a results table for each unique star entry and print the multiplicity status returned from the test_mult function. Here \"n_comp\", \"n_mult\" and \"ismult\" refer to the number of observations used, the number of times a binary was flagged when comparing each measurement and the multiplicity status." ] }, { "cell_type": "code", - "execution_count": null, - "id": "bf55bad5", + "execution_count": 374, + "id": "4cfeb2b3", "metadata": {}, "outputs": [], "source": [ - "Nsig = 3.0" + "results = obs_by_name.groups.keys\n", + "x = [test_mult(t['RV'], t['eRV']) for t in obs_by_name.groups]\n", + "results['n_comp'] = [o[1] for o in x]\n", + "results['n_mult'] = [o[0] for o in x]\n", + "results['ismult'] = ['yes' if n > 0 else 'no' for n in results['n_mult']]" + ] + }, + { + "cell_type": "code", + "execution_count": 375, + "id": "dfb4ae07", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "\n", + " name n_comp n_mult mult? ismult\n", + " str19 int64 int64 str3 str3 \n", + "------------------- ------ ------ ----- ------\n", + "J000000.00-000000.0 5 0 no no\n", + "J000453.05-103220.0 1 0 no no\n", + "J001527.62-641455.2 4 0 no no\n", + "J001536.79-294601.2 5 3 yes yes\n", + "J001552.28-280749.4 2 0 no no\n", + "J001555.65-613752.2 1 0 no no\n", + " ... ... ... ... ...\n", + "J234243.45-622457.1 1 0 no no\n", + "J234326.88-344658.5 2 0 no no\n", + "J234333.91-192802.8 1 0 no no\n", + "J234347.83-125252.1 1 0 no no\n", + "J234857.35+100929.3 1 0 no no\n", + "J234924.87+185926.7 1 0 no no\n", + "J234926.23+185912.4 1 0 no no" + ] + }, + "execution_count": 375, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" ] }, { "cell_type": "markdown", - "id": "50e32131", + "id": "913cfcec", "metadata": {}, "source": [ - "Create an empty array \"F_arr\", which will store the designated multiplicity status, where:\n", - "- F_arr = 5: multiple, at least one $\\Delta RV > \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$\n", - "- F_arr = 3: (probably) single, every $\\Delta RV \\leq \\zeta\\times max(\\sigma_{RV_{1}}, \\sigma_{RV_{2}})$\n", - "- F_arr = 1: = only 1 RV measurement, we can't say anything about multiplicity status\n", - "- F_arr = 0: = no RV measurements available\n" + "Next, define a function named \"selectrv\" to calculate the final RV and error.\n", + "\n", + "Firstly, remove any stars that cause $\\Delta RV > \\Delta RV_{\\rm max}$, then measure the final RV (and error) in the following way:\n", + "\n", + "1. If the standard deviation in the error bars is less than the standard deviation in the measurements, then take the inverse weighted mean, using the square of the error bars as weights.\n", + "2. Otherwise, adopt the final RV as the value corresponding to the lowest error bar.\n" ] }, { "cell_type": "code", - "execution_count": null, - "id": "2ccd5674", + "execution_count": 377, + "id": "dc2d2426", "metadata": {}, "outputs": [], "source": [ - "f_un = unique(f_in, keys='name')\n", - "F_Arr = []\n", - "\n", - "for f in f_un:\n", - " g = f_in[f_in[\"name\"] == f[\"name\"]]\n", - "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", - " x = len(g)\n", - "\n", - " if x >= 2:\n", - " p = list(itertools.combinations(g[\"RV\"], 2))\n", - " b = list((i,j) for ((i,_),(j,_)) in itertools.combinations(enumerate(g[\"RV\"]), 2))\n", - " c1, c0, darr = [g[\"eRV\"][c[1]] for c in b], [g[\"eRV\"][c[0]] for c in b], [abs(z[1]-z[0]) for z in p]\n", - " z = np.argsort(darr)\n", - " RVd_arr = [[darr[z[i]], c1[z[i]], c0[z[i]]] for i in z]# if darr[i] < d_max]\n", - " \n", - "# fill out the RV flag arrays based on the RV differences (and errors)\n", - "# 5 = multiple, dRV > d_max\n", - "# 3 = single, dRV <= d_max\n", - "# 1 = only 1 RV\n", - "# 0 = no RVs\n", - " for j in range(len(RVd_arr)):\n", - " eRV_max = max(RVd_arr[j][2], RVd_arr[j][1])\n", - " if RVd_arr == None:\n", - " F_Arr.append(0)\n", - " break\n", - " if len(z) > 1:\n", - "# if at any point |RV| > N*max(eRV) then we have no choice\n", - "# but to flag it as a probable multiple.\n", - " if (RVd_arr[j][0] > Nsig*eRV_max):\n", - " F_Arr.append(5)\n", - " break\n", - "# |RV| <= N*max(eRV)\n", - "# could be single, check the next RV difference\n", - " if (RVd_arr[j][0] <= Nsig*eRV_max):\n", - " j=j+1\n", - "# if after all the iterations we get here and we still didn't see any\n", - "# evidence of binarity, flag it as a single star.\n", - " if j == len(z)-1:\n", - " F_Arr.append(3)\n", - " break\n", - " if len(z) == 1:\n", - " if (RVd_arr[j][0] > Nsig*eRV_max):\n", - " F_Arr.append(5)\n", - "# break\n", - " if (RVd_arr[j][0] <= Nsig*eRV_max):\n", - " F_Arr.append(3)\n", - "# break\n", - "\n", - " if x == 1:\n", - " if g[\"RV\"][0] > -900:\n", - " F_Arr.append(1)\n", - " else:\n", - " F_Arr.append(0)\n", - " if x == 0:\n", - " F_Arr.append(0)" + "def selectrv(trv, erv):\n", + " c = trv[:, None] - trv[None, :]\n", + " ee = c > d_max\n", + " x = np.array(np.where(ee))[0]\n", + " if len(x) > 0:\n", + " trv = np.delete(trv, x[0], 0)\n", + " erv = np.delete(erv, x[0], 0)\n", + " if (trv.std() > erv.std()):\n", + " return np.average(trv, weights=erv**-2), np.sqrt(1./np.sum(erv**-2))\n", + " else:\n", + " return trv[np.argmin(erv)], erv[np.argmin(erv)]" ] }, { "cell_type": "markdown", - "id": "f3251216", + "id": "ed341809", "metadata": {}, "source": [ - "### Part 3: obtaining a final RV measurement\n", - "Regardless of the multiplicity status assigned in Part 2, we now calculate a final RV measurement, and flag \"how\" we measure RV using a measurement flag (Mflag).\n", - "\n", - "#### If the star is a probable single, there are two paths to calculating a final RV.\n", - "\n", - "1. If the standard deviation in the error bars is less than the standard deviation in the measurements, then take the inverse weighted mean, using the square of the error bars as weights. Mflag = 2.\n", - "2. Otherwise, adopt the final RV as the value corresponding to the lowest error bar. Mflag = 3.\n", - "\n", - "The associtated error in the weighted mean is found using equation (2) and (3) at this link: http://seismo.berkeley.edu/~kirchner/Toolkits/Toolkit_12.pdf\n", - "\n", - "#### If the star is likely to be a multiple, use path 1 described above.\n", - "Mflag = 4.\n", - "\n", - "The cases with only 1 or 0 RV measurements is trivial, Mflag = 1 and 0, respectively.\n", - "\n", - "Two error bars are provided:\n", - "- \"sRV\", the error in the weighted mean.\n", - "- \"eRV\", the average value of the individual error bars." + "Call the \"selectrv\" function for each set of RV observations and print to the results table." ] }, { "cell_type": "code", - "execution_count": null, - "id": "d3367b77", + "execution_count": 378, + "id": "ccb120a3", "metadata": {}, "outputs": [], "source": [ - "RV_f, eRV_f, sRV_f, RV_T = [], [], [], []\n", - "\n", - "for k, l in enumerate(f_un):\n", - " g = f_in[f_in[\"name\"] == l[\"name\"]]\n", - " sdRV = np.std(g[\"RV\"])\n", - " sdeRV = np.std(g[\"eRV\"])\n", - "#if there are 2 or more measurements we want to test how consistent the RVs are.\n", - " x = len(g)\n", - " if x >= 2:\n", - "# if we don't class the star as a possible binary\n", - " w = np.array(1.0/(g[\"eRV\"]**2))\n", - " if F_Arr[k] != 5:\n", - "# if the std in the errors is less than the std in the mean RV\n", - "# take the weighted average and error\n", - "\n", - "# weighted error is found like this:\n", - "# http://seismo.berkeley.edu/~kirchner/Toolkits/Toolkit_12.pdf\n", - "\n", - " if sdeRV <= sdRV:\n", - " w_RV = np.average(g[\"RV\"], weights=w)\n", - " val = np.array(g[\"RV\"]**2)\n", - " var = ((np.sum(w*val)/np.sum(w))-w_RV**2) * (x/(x-1))\n", - " RV_f.append(w_RV)\n", - " sRV_f.append(np.sqrt(var/x))\n", - " eRV_f.append(np.average(g[\"eRV\"]))\n", - " RV_T.append(2)\n", - " else:\n", - " RV_f.append(g[\"RV\"][np.argsort(g[\"eRV\"][0])][0])\n", - " eRV_f.append(g[\"eRV\"][np.argsort(g[\"eRV\"][0])][0])\n", - " sRV_f.append(np.average(g[\"eRV\"]))\n", - " RV_T.append(3)\n", - " if F_Arr[k] == 5:\n", - " w_RV = np.average(g[\"RV\"], weights=w)\n", - " val = np.array(g[\"RV\"]**2)\n", - " var = ((np.sum(w*val)/np.sum(w))-w_RV**2) * (x/(x-1))\n", - " RV_f.append(np.average(g[\"RV\"], weights=w))\n", - " sRV_f.append(np.sqrt(var/x))\n", - " eRV_f.append(np.average(g[\"eRV\"]))\n", - " RV_T.append(4)\n", - " if x == 1:\n", - " RV_f.append(g[\"RV\"][0])\n", - " sRV_f.append(0.0)\n", - " eRV_f.append(g[\"eRV\"][0])\n", - " RV_T.append(1)" + "out = [selectrv(t['RV'], t['eRV']) for t in obs_by_name.groups]\n", + "results['RV'] = [o[0] for o in out]\n", + "results['eRV'] = [o[1] for o in out]" ] }, { "cell_type": "markdown", - "id": "a2581278", + "id": "5cdf836d", "metadata": {}, "source": [ - "Finally, print all these results to a table." + "Format the results table so there are a sensible number of significant figures for the RV and eRV columns." ] }, { "cell_type": "code", - "execution_count": null, - "id": "a902d3c9", + "execution_count": 379, + "id": "2e633f9b", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
Table length=9\n", + "
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namen_compn_multmult?ismultRVeRV
str19int64int64str3str3float64float64
J000000.00-000000.050nono10.190.18
J000453.05-103220.010nono7.7013.40
J001527.62-641455.240nono6.700.30
J001536.79-294601.253yesyes0.420.61
J001552.28-280749.420nono0.250.62
J001555.65-613752.210nono19.900.70
J001709.96+185711.820nono32.980.59
J001723.69-664512.450nono10.700.19
J002101.27-134230.710nono1.250.81
" + ], + "text/plain": [ + "\n", + " name n_comp n_mult mult? ismult RV eRV \n", + " str19 int64 int64 str3 str3 float64 float64\n", + "------------------- ------ ------ ----- ------ ------- -------\n", + "J000000.00-000000.0 5 0 no no 10.19 0.18\n", + "J000453.05-103220.0 1 0 no no 7.70 13.40\n", + "J001527.62-641455.2 4 0 no no 6.70 0.30\n", + "J001536.79-294601.2 5 3 yes yes 0.42 0.61\n", + "J001552.28-280749.4 2 0 no no 0.25 0.62\n", + "J001555.65-613752.2 1 0 no no 19.90 0.70\n", + "J001709.96+185711.8 2 0 no no 32.98 0.59\n", + "J001723.69-664512.4 5 0 no no 10.70 0.19\n", + "J002101.27-134230.7 1 0 no no 1.25 0.81" + ] + }, + "execution_count": 379, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "f_out = [f_un[\"name\"], RV_f, sRV_f, eRV_f, RV_T]\n", - "\n", - "f_table = Table(data=f_out, masked=False, names=('Name','RVfin','sRV','eRV','RV_T'))\n", - "\n", - "f_table[\"Name\"].format = '%s'\n", - "f_table[\"RVfin\"].format = '%+9.2f'\n", - "f_table[\"sRV\"].format = '%9.2f'\n", - "f_table[\"eRV\"].format = '%9.2f'\n", - "f_table[\"RV_T\"].format = '%i'\n", - "\n", - "ascii.write(f_table, \"finalRVs.csv\", format='csv', overwrite=True)" + "results['RV'].format = '{:.2f}'\n", + "results['eRV'].format = '{:.2f}'\n", + "results[0:9]" + ] + }, + { + "cell_type": "code", + "execution_count": 391, + "id": "7897e589", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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u7YP0vTMLzNHbSA8Df8j/X1X6bHovqx6it6EunXCtHwJ+eVXbzwH303uH+R7gZwbVOeGa/hz4CnBvt5PsHbf/JlzXQ/TO+R3vbiufDtrS/lqjzmvpffrjYeDmTd73f5zey+V7+/rp2nG26YTrurTbPl/uttXNXfuLgKPAyW64azPr6tbzA8DjwAv62rakv+j9EzkF/C+9DLtpnD4ad7/3UnpJatR2P4UiSVqHAS5JjTLAJalRBrgkNcoAl6RGGeCS1CgDXJIa9X8DDpwpwcJqWAAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plt.hist(results['RV'], bins=np.arange(-1000,1000,5))\n", "plt.show()" @@ -707,11 +405,6 @@ } ], "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, "language_info": { "codemirror_mode": { "name": "ipython", @@ -721,8 +414,7 @@ "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.7" + "pygments_lexer": "ipython3" } }, "nbformat": 4,