{ "cells": [ { "cell_type": "markdown", "id": "79324ae2", "metadata": {}, "source": [ "# Inferring the progenitor of a recoiling SMBH: JWST RBH-1\n", "\n", "**RBH-1** is a candidate recoiling supermassive black hole identified in\n", "HST/JWST imaging by Islam, Venumadhav & Wadekar (2026,\n", "[arXiv:2601.18986](https://arxiv.org/abs/2601.18986)), with an inferred\n", "recoil velocity of\n", "\n", "$$v_{\\rm kick} = 954^{+110}_{-126}\\ {\\rm km\\,s^{-1}}.$$\n", "\n", "Such a large recoil can only come from a fairly specific progenitor —\n", "high, misaligned spins and near-comparable masses. We **infer the\n", "progenitor** mass ratio and spin magnitudes from the measured kick with\n", "`gwGenealogy.core.KickToProgenitor`, which inverts the IW2025\n", "precessing-kick flow.\n", "\n", "The flow is a *conditional* density $p(v_{\\rm kick}\\,|\\,q, a_1, a_2)$\n", "(spin angles marginalised internally). `KickToProgenitor` uses it as a\n", "likelihood and applies Bayes,\n", "\n", "$$p(q,a_1,a_2\\,|\\,d) \\propto \\Big[\\int p(d\\,|\\,v)\\,p(v\\,|\\,q,a_1,a_2)\\,dv\\Big]\\,\\pi(q,a_1,a_2),$$\n", "\n", "marginalising the (asymmetric) measurement uncertainty $p(d\\,|\\,v)$ and\n", "importance-sampling over the prior $\\pi$." ] }, { "cell_type": "code", "execution_count": 1, "id": "c3128376", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:30.956100Z", "iopub.status.busy": "2026-06-13T10:28:30.955895Z", "iopub.status.idle": "2026-06-13T10:28:32.507672Z", "shell.execute_reply": "2026-06-13T10:28:32.507227Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings('ignore', 'Wswiglal-redir-stdio')\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from gwGenealogy.core import KickToProgenitor\n", "from gwGenealogy.utils import set_rcparams\n", "\n", "set_rcparams()" ] }, { "cell_type": "markdown", "id": "d4f00681", "metadata": {}, "source": [ "## Set up and run the inversion\n", "\n", "The $954^{+110}_{-126}$ km/s error bar is asymmetric, so we pass\n", "`sigma_lo=126` and `sigma_hi=110` — `KickToProgenitor` models the\n", "measurement as a split normal and marginalises over the true kick. Priors:\n", "$q\\sim\\mathcal{U}[1,20]$, $a_1, a_2\\sim\\mathcal{U}[0,1]$ (the defaults)." ] }, { "cell_type": "code", "execution_count": 2, "id": "4d41e548", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:32.509201Z", "iopub.status.busy": "2026-06-13T10:28:32.509076Z", "iopub.status.idle": "2026-06-13T10:28:37.565641Z", "shell.execute_reply": "2026-06-13T10:28:37.565255Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "KickToProgenitor(n_kicks=1, Gaussian errors, n_prior=300000, n_posterior=40000)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " kick 1/1: v=954 km/s ESS=40805/300000 -> q=3.01, a1=0.79, a2=0.52\n", "\n", "RBH-1 progenitor (median, 90% CI):\n", " q = 3.01 [1.17, 6.88]\n", " a1 = 0.79 [0.41, 0.98]\n", " a2 = 0.52 [0.05, 0.93]\n" ] } ], "source": [ "k2p = KickToProgenitor(\n", " v_kicks=954.0, sigma_lo=126.0, sigma_hi=110.0,\n", " q_min=1.0, q_max=20.0, # spins default to U[0, 1]\n", " n_prior=300_000, n_posterior=40_000, seed=0)\n", "print(k2p)\n", "\n", "results = k2p.infer(verbose=True)\n", "\n", "summary = k2p.summary(ci=90)\n", "print('\\nRBH-1 progenitor (median, 90% CI):')\n", "for p in ('q', 'a1', 'a2'):\n", " print(f' {p:>3s} = {summary[p + \"_median\"][0]:5.2f} '\n", " f'[{summary[p + \"_low\"][0]:.2f}, {summary[p + \"_high\"][0]:.2f}]')" ] }, { "cell_type": "markdown", "id": "76ce618c", "metadata": {}, "source": [ "## Progenitor posterior" ] }, { "cell_type": "code", "execution_count": 3, "id": "99590776", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:37.566968Z", "iopub.status.busy": "2026-06-13T10:28:37.566890Z", "iopub.status.idle": "2026-06-13T10:28:37.826678Z", "shell.execute_reply": "2026-06-13T10:28:37.826279Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = k2p.plot_posteriors(index=0)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d757bab4", "metadata": {}, "source": [ "The large recoil drives the **primary spin high** ($a_1 \\approx 0.8$,\n", "disfavouring $a_1 \\lesssim 0.4$) and favours **comparable masses**\n", "($q$ peaks near 2–3). The secondary spin $a_2$ is only weakly constrained.\n", "The $q$ posterior sits well below the prior's upper edge, so the\n", "$q \\le 20$ bound is immaterial and we stay within the flow's calibrated\n", "range ($q \\lesssim 14$)." ] }, { "cell_type": "markdown", "id": "56439540", "metadata": {}, "source": [ "## Posterior-predictive check\n", "\n", "`posterior_predictive` draws one kick from each posterior progenitor.\n", "Because the flow **marginalises over spin orientation**, a single\n", "$(q, a_1, a_2)$ maps to a *broad* kick distribution — the same progenitor\n", "can recoil at very different speeds depending on the (unobserved) spin\n", "geometry. So the predictive distribution is wide and not sharply peaked at\n", "954 km/s: the inference constrains masses and spin magnitudes, not the\n", "spin angles that set the exact recoil." ] }, { "cell_type": "code", "execution_count": 4, "id": "5fb2b39c", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:37.828176Z", "iopub.status.busy": "2026-06-13T10:28:37.828088Z", "iopub.status.idle": "2026-06-13T10:28:37.973225Z", "shell.execute_reply": "2026-06-13T10:28:37.972759Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "posterior-predictive kick: median=554 90% CI=[72, 1375] km/s\n" ] } ], "source": [ "vk_pp = k2p.posterior_predictive(index=0, n=20000, seed=1)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 4.5))\n", "ax.hist(vk_pp, bins=80, density=True, alpha=0.6, label='posterior-predictive')\n", "ax.axvline(954, color='C3', ls='--', lw=2, label=r'observed $954$ km/s')\n", "ax.axvspan(954 - 126, 954 + 110, color='C3', alpha=0.15)\n", "ax.set_xlabel(r'$v_{\\rm kick}$ [km/s]'); ax.set_ylabel('Density')\n", "ax.set_title('Posterior-predictive kicks vs the RBH-1 measurement')\n", "ax.legend(frameon=False)\n", "plt.tight_layout(); plt.show()\n", "\n", "print(f'posterior-predictive kick: median={np.median(vk_pp):.0f} '\n", " f'90% CI=[{np.percentile(vk_pp, 5):.0f}, {np.percentile(vk_pp, 95):.0f}] km/s')" ] }, { "cell_type": "markdown", "id": "335690a2", "metadata": {}, "source": [ "## Many kicks at once\n", "\n", "`KickToProgenitor` accepts an **array** of kicks and returns a posterior\n", "for each (here treated as exact, `sigma=None`). The inferred primary spin\n", "rises monotonically with the recoil — the expected trend." ] }, { "cell_type": "code", "execution_count": 5, "id": "39933068", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:37.974497Z", "iopub.status.busy": "2026-06-13T10:28:37.974402Z", "iopub.status.idle": "2026-06-13T10:28:38.373400Z", "shell.execute_reply": "2026-06-13T10:28:38.372961Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v_arr = np.array([100, 300, 500, 700, 900])\n", "multi = KickToProgenitor(v_arr, q_min=1, q_max=20,\n", " n_prior=200_000, n_posterior=20_000, seed=0)\n", "multi.infer()\n", "ms = multi.summary(ci=68)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 4.5))\n", "ax.errorbar(v_arr, ms['a1_median'],\n", " yerr=[ms['a1_median'] - ms['a1_low'], ms['a1_high'] - ms['a1_median']],\n", " fmt='C0-o', capsize=4, label=r'inferred $a_1$ (median, 68%)')\n", "ax.set_xlabel(r'observed $v_{\\rm kick}$ [km/s]')\n", "ax.set_ylabel(r'inferred primary spin $a_1$')\n", "ax.set_title('Recovered spin vs kick (array of kicks, exact)')\n", "ax.legend(frameon=False)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "e7494d27", "metadata": {}, "source": [ "## Caveats\n", "\n", "- **Posterior, not a unique progenitor.** The recoil is a many-to-one\n", " function of $(q, a_1, a_2)$ and the spin angles, so the widths above are\n", " real physical degeneracy.\n", "- **Spin tilts are unrecoverable.** The flow's context is only\n", " $(q, a_1, a_2)$; the tilt/azimuth dependence is marginalised inside it.\n", " We constrain spin *magnitudes* and mass ratio, never the orientations.\n", "- **Prior-dependent.** `KickToProgenitor` takes a range + distribution or\n", " an explicit prior array per parameter; an astrophysically motivated\n", " SMBH-merger prior would sharpen or shift the result. Watch the `ess` —\n", " kicks in the model's far tail thin the prior pool and need a larger\n", " `n_prior`.\n", "- **Single-event inference.** Each kick is treated independently; a\n", " population of recoiling SMBHs would call for hierarchical inference." ] } ], "metadata": { "kernelspec": { "display_name": "gwgen_env", "language": "python", "name": "gwgen_env" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.15" } }, "nbformat": 4, "nbformat_minor": 5 }