30:T894,view = { const twopi = 2 * Math.PI; const scale = d3.scaleLinear().domain([-fov_radian/2, +fov_radian/2]).range([0, view_width]); const xy0 = scale(0); const context = DOM.context2d(view_width, view_width); context.fillStyle = '#000'; context.fillRect(0, 0, view_width, view_width); context.strokeStyle = '#fff'; const Sk = displayOptions.includes('curvature') ? model.Sk : r => r; // The attenuation is the relative surface brightness given the color, i.e. // it has a (1+z)^2 factor for the effects of expansion on angular size and // a (1+z) factor for time dilation. The final (1+z) factor due to redshift // is represented by color in this visualization, so omitted here. // Note that surface brightness is independent of curvature. const attenuation = displayOptions.includes('angle') ? (displayOptions.includes('time') ? z => 1/(1+z)**3 : z => 1/(1+z)**2) : (displayOptions.includes('time') ? z => 1/(1+z) : z => 1); // Assume source all have violet rest-frame color. In 'pseudo' mode, map // the full range of redshifts to the visible band. In 'true' mode, only // map the first factor of 2 (z < 1) to the visible band. const zmax = ztype == 'pseudo' ? params.zmax : 1; const color = displayOptions.includes('redshift') ? z => redshifted_color(z, zmax, attenuation(z)) : z => redshifted_color(0, zmax, attenuation(z)); const angsize = displayOptions.includes('angle') ? (d,z) => 1e-3 * src_radius / Sk(d) * (1+z) : (d,z) => 1e-3 * src_radius / d; const [xpoint,ypoint,zpoint] = structure == 'random' ? random_points : grid_points; const redshifts = structure == 'random' ? random_redshifts : grid_redshifts; for(let i=0; i < xpoint.length; i++) { const redshift = redshifts[i]; if(redshift >= zclip) continue; let [x,y,z] = [xpoint[i],ypoint[i],zpoint[i]]; const zc = Sk(z); if(Math.max(Math.abs(x), Math.abs(y)) > fov_radian * zc) continue; x = scale(x / zc); y = scale(y / zc); const r = scale(angsize(z,redshift)) - xy0; context.beginPath(); context.arc(x, y, r, 0, twopi); context.fillStyle = color(redshift); context.fill(); } return context.canvas; }31:[{"id":"b6fad58d1ab93cbfb7fee14a1ce9695a06a83f06e14cd869a43d0be90453be870dcc7f8f932e83570a78778bd35d9841d157a38152509b317007e3e25c97e7d0","href":"https://static.observableusercontent.com/files/b6fad58d1ab93cbfb7fee14a1ce9695a06a83f06e14cd869a43d0be90453be870dcc7f8f932e83570a78778bd35d9841d157a38152509b317007e3e25c97e7d0","name":"HUDF-1x1-arcmin.jpg","type":"image/jpeg","lastModified":1605487065666.711,"size":1935650}] 2e:{"title":"Cosmic window","cells":[{"id":0,"value":"md`# Cosmic window\n\nRender a universe filled with a uniform comoving density of identical glowing spheres to demonstrate the visual effects of expansion and curvature.\n\nTODO:\n - Add view along z showing curved fov and R0?\n - Faster rendering?\n\nNote that the effects of curvature on angular size are correctly included, but very hard to see because of the much larger position displacements and overall faintness (due to their large angular size) of distant objects.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":472,"value":"// from https://www.spacetelescope.org/images/heic0611b/\nhudf = html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":488,"value":"viewof ztype = radio({\n title: 'Observed color versus redshift',\n options:[ {label:'pseudo redshift', value:'pseudo'}, {label:'true redshift', value:'true'} ],\n value: 'pseudo'})","pinned":false,"hidden":false,"mode":"ojs"},{"id":524,"value":"zlegend = {\n const zmax = ztype == 'pseudo' ? params.zmax : 1;\n return legend({\n color: d3.scaleSequential([0,1], x => redshifted_color(x * params.zmax, zmax)),\n width: 0.6 * view_width,\n tickValues: linspace(0, 1, params.zmax + 1),\n tickFormat: x => Number(x * params.zmax).toFixed(0)\n })\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":440,"value":"viewof src_radius = slider({\n min:1, max:10, step:1, value:4,\n format: z=>html`Galaxy radius ${Number(z).toFixed(0)} kpc` // why is the span necessary??\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":393,"value":"viewof zclip = slider({\n min:0.1, max:params.zmax, step:0.1, value:1,\n format: z=>html`Galaxy redshift limit ${tex`z < ${Number(z).toFixed(1)}`}`\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":336,"value":"viewof displayOptions = checkbox({\n title: 'Included effects:',\n options:[\n {value:'redshift', label:'redshift'},\n {value:'time', label:'time dilation'},\n {value:'angle', label:'angular size'},\n {value:'curvature', label:'curvature'},\n ],\n value:[]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":267,"value":"viewof Om0 = slider({\n min:params.Om0[0], max:params.Om0[1], step:0.1, value:0.3,\n format: x=>tex`\\Omega_{m,0} = ${Number(x).toFixed(2)}`\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":270,"value":"viewof Ode0 = slider({\n min:params.Ode0[0], max:params.Ode0[1], step:0.1, value:0.7,\n format: x=>tex`\\Omega_{\\Lambda,0} = ${Number(x).toFixed(2)}`\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":628,"value":"setbenchmark = {\n // See https://observablehq.com/@mbostock/views-are-mutable-values\n const form = html`\n`;\n form.benchmark.onclick = () => {\n viewof Om0.input.value = 0.3; viewof Om0.dispatchEvent(new CustomEvent('input'));\n viewof Ode0.input.value = 0.7; viewof Ode0.dispatchEvent(new CustomEvent('input'));\n }\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":599,"value":"viewof structure = radio({\n title: 'Type of large-scale structure',\n options:[ {label:'random', value:'random'}, {label:'grid', value:'grid'} ],\n value: 'random'})","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":221,"value":"md`### Visualization`","pinned":false,"hidden":false,"mode":"ojs"},{"id":475,"value":"view_width = Math.floor(width / 2) - 8","pinned":false,"hidden":false,"mode":"ojs"},{"id":341,"value":"redshifted_color = {\n // Map [0,1] to a spectral hue (but varying luminosity) with 0=violet, 1=red.\n const cmap = d3.scaleSequential([1,0], d3.interpolateSpectral);\n // Color to return when redshifted outside the visible band.\n const notvisible = d3.color('black');\n return function(z, zmax, attenuation=1) {\n if(z < 0 || z > zmax) return notvisible;\n const base = d3.lab(cmap(z / zmax));\n // Set a fixed reference luminosity then apply attenuation.\n base.l = attenuation * 90;\n return base;\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":603,"value":"grid_redshifts = interp(grid_points[2], init.d, init.z, {clipped:true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":25,"value":"grid_points = {\n const [dxy, dz] = [size, dcmax - mindist];\n let r = 4000; // target ratio of xy : z densities.\n const nxy = Math.round((r * dxy / dz * nsrc) ** (1/3));\n const nz = Math.round(nsrc / nxy ** 2);\n const xymax = (nxy - 1) / nxy * size / 2;\n const xy = linspace(-xymax, xymax, nxy);\n const rshift = 0.1 * Math.PI;\n const x = xy.map(x => x - (rshift/2) * size / nxy);\n const y = xy.map(y => y + rshift * size / nxy);\n const z = linspace(mindist, dcmax, nz);\n return prepare(meshgrid([x, x, z]).flat(2));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":416,"value":"random_redshifts = interp(random_points[2], init.d, init.z, {clipped:true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":46,"value":"random_points = {\n const r = size / 2;\n const x = RNG.uniform(-r,r).array(nsrc, {dtype:Float32Array});\n const y = RNG.uniform(-r,r).array(nsrc, {dtype:Float32Array});\n const z = RNG.uniform(mindist, dcmax).array(nsrc, {dtype:Float32Array});\n return prepare(gather(interleave(x, y, z), 3));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":298,"value":"function prepare(points) {\n return transpose(points\n .filter(a => Math.max(Math.abs(a[0]), Math.abs(a[1])) <= 0.5 * fov_radian * maxcurve.Sk(a[2]))\n .sort((a,b) => b[2] - a[2]));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":49,"value":"RNG = new RandomState('cosmic window')","pinned":false,"hidden":false,"mode":"ojs"},{"id":293,"value":"// Number of sources in a rectangular volume with comoving dimensions size x size x (dcmax - clipdist)\nnsrc = Math.round(density * (dcmax - mindist) * size * size)","pinned":true,"hidden":false,"mode":"ojs"},{"id":289,"value":"// Objects closer than this distance in Mpc are clipped.\nmindist = 150","pinned":true,"hidden":false,"mode":"ojs"},{"id":225,"value":"md`### Cosmology`","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"// Comoving number density of sources in # / Mpc^3\n// Value of 0.24 from Fig 4 of https://arxiv.org/abs/1607.03909\ndensity = 0.24","pinned":true,"hidden":false,"mode":"ojs"},{"id":35,"value":"init = {\n const zgrid = linspace(0, params.zmax, 64);\n const dgrid=model.gridz(zgrid, 'comoving_distance');\n return {z:zgrid, d:dgrid};\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":399,"value":"maxdist = model.comoving_distance(0, zclip)","pinned":true,"hidden":false,"mode":"ojs"},{"id":277,"value":"model = new FluidsModel(0, Om0, Ode0, params.H0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":230,"value":"// Transverse size in Mpc that fills the FOV at dcmax in a model with max negative curvature.\nsize = maxcurve.Sk(dcmax) * fov_radian","pinned":false,"hidden":false,"mode":"ojs"},{"id":357,"value":"new FluidsModel(0, 0.2, 0.9, 70).comoving_distance(0, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":355,"value":"new FluidsModel(0, 0.2, 0, 70).comoving_distance(0, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":353,"value":"new FluidsModel(0, 0.2, 0.8, 70).comoving_distance(0, 9)","pinned":true,"hidden":false,"mode":"ojs"},{"id":351,"value":"new FluidsModel(0, 0.3, 0.7, 70).comoving_distance(0, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":317,"value":"// Build a model with the max allowed negative curvature\nmaxcurve = new FluidsModel(0, params.Om0[0], params.Ode0[0], params.H0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":260,"value":"fov_radian = (fov_arcmin / 60) * Math.PI / 180","pinned":false,"hidden":false,"mode":"ojs"},{"id":257,"value":"// this value matches the HUDF image so shouldn't be changed.\nfov_arcmin = 1","pinned":false,"hidden":false,"mode":"ojs"},{"id":236,"value":"// Maximum comoving distance in Mpc along the line of sight for z <= zmax.\ndcmax = new FluidsModel(0, params.Om0[0], params.Ode0[1], params.H0).comoving_distance(0, params.zmax)","pinned":false,"hidden":false,"mode":"ojs"},{"id":228,"value":"params = ({Om0:[0.2,1], Ode0:[0,0.8], H0:70, zmax:9})","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":521,"value":"import {legend} from '@d3/color-legend'","pinned":false,"hidden":false,"mode":"ojs"},{"id":89,"value":"d3 = require('d3-scale@3', 'd3-color@2', 'd3-scale-chromatic@2')","pinned":false,"hidden":false,"mode":"ojs"},{"id":32,"value":"import {radio,checkbox,slider} from '@jashkenas/inputs'","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"import {FluidsModel} from '@dkirkby/cosmocalc'","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"import {RandomState} from '@dkirkby/random'","pinned":false,"hidden":false,"mode":"ojs"},{"id":55,"value":"import {gather, interleave, transpose} from '@dkirkby/array-utilities'","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"import {linspace, interp, meshgrid} from '@dkirkby/jumpy'","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}