modefit_psi4_ylm

Modefit for psi4 for stable boson star with perturbation 0.01 Y_20+0.01 Y_22
The functions f1 -> f12 are the list of Quasinormal modes for l=2, stable boson stars..
This program uses uses the "Fit" function in mathematica that performs a linear least square fit.

${{68.9999999999998`, -1.06446`*^-8}, {69.1499999999998`, 3.2803`*^-9}, {69.2999999999998`, 1.81343`*^-8}, {69.4499999999998`, 3.26115`*^-8}, {69.5999999999998`, 4.54201`*^-8}, {69.7499999999998`, 5.54027`*^-8}, {69.8999999999998`, 6.16477`*^-8}, {70.0499999999998`, 6.35808`*^-8}, {70.1999999999998`, 6.10269`*^-8}, {70.3499999999998`, 5.42356`*^-8}, {70.4999999999998`, 4.38653`*^-8}, {70.6499999999998`, 3.09265`*^-8}, {70.7999999999998`, 1.66884`*^-8}, {70.9499999999998`, 2.5578`*^-9}, {71.0999999999998`, -1.006`*^-8}, {71.2499999999998`, -1.99028`*^-8}, {71.3999999999998`, -2.59814`*^-8}, {71.5499999999999`, -2.76849`*^-8}, {71.6999999999999`, -2.48482`*^-8}, {71.8499999999999`, -1.77746`*^-8}, {71.9999999999999`, -7.2101`*^-9}, {72.1499999999999`, 5.7304`*^-9}, {72.2999999999999`, 1.96768`*^-8}, {72.4499999999999`, 3.31468`*^-8}, {72.5999999999999`, 4.4704`*^-8}, {72.7499999999999`, 5.31136`*^-8}, {72.8999999999999`, 5.74787`*^-8}, {73.0499999999999`, 5.73422`*^-8}, {73.1999999999999`, 5.27419`*^-8}, {73.3499999999999`, 4.42111`*^-8}, {73.4999999999999`, 3.27242`*^-8}, {73.6499999999999`, 1.95912`*^-8}, {73.7999999999999`, 6.3121`*^-9}, {73.9499999999999`, -5.5928`*^-9}, {74.1`, -1.47583`*^-8}, {74.25`, -2.01339`*^-8}, {74.4`, -2.111`*^-8}, {74.55`, -1.7594`*^-8}, {74.7`, -1.00254`*^-8}, {74.85`, 6.716`*^-10}, {75.`, 1.31951`*^-8}, {75.15`, 2.60205`*^-8}, {75.3`, 3.75845`*^-8}, {75.45`, 4.64767`*^-8}, {75.6`, 5.16151`*^-8}, {75.75`, 5.23831`*^-8}, {75.9`, 4.87099`*^-8}, {76.05`, 4.1083`*^-8}, {76.2`, 3.04907`*^-8}, {76.35`, 1.82986`*^-8}, {76.5`, 6.0777`*^-9}, {76.65`, -4.5968`*^-9}, {76.8000000000001`, -1.23497`*^-8}, {76.9500000000001`, -1.61856`*^-8}, {77.1000000000001`, -1.56208`*^-8}, {77.2500000000001`, -1.075`*^-8}, {77.4000000000001`, -2.236`*^-9}, {77.5500000000001`, 8.7754`*^-9}, {77.7000000000001`, 2.08061`*^-8}, {77.8500000000001`, 3.22425`*^-8}, {78.0000000000001`, 4.15521`*^-8}, {78.1500000000001`, 4.7491`*^-8}, {78.3000000000001`, 4.92737`*^-8}, {78.4500000000001`, 4.66821`*^-8}, {78.6000000000001`, 4.00969`*^-8}, {78.7500000000001`, 3.0447`*^-8}, {78.9000000000001`, 1.90825`*^-8}, {79.0500000000001`, 7.5883`*^-9}, {79.2000000000001`, -2.4367`*^-9}, {79.3500000000002`, -9.6035`*^-9}, {79.5000000000002`, -1.29295`*^-8}, {79.6500000000002`, -1.19786`*^-8}, {79.8000000000002`, -6.924`*^-9}, {79.9500000000002`, 1.4742`*^-9}, {80.1000000000002`, 1.19773`*^-8}, {80.2500000000002`, 2.30448`*^-8}, {80.4000000000002`, 3.30568`*^-8}, {80.5500000000002`, 4.05496`*^-8}, {80.7000000000002`, 4.44298`*^-8}, {80.8500000000002`, 4.41366`*^-8}, {81.0000000000002`, 3.97262`*^-8}, {81.1500000000002`, 3.18667`*^-8}, {81.3000000000002`, 2.17415`*^-8}, {81.4500000000002`, 1.08754`*^-8}, {81.6000000000002`, 9.083`*^-10}, {81.7500000000002`, -6.6504`*^-9}, {81.9000000000002`, -1.06503`*^-8}, {82.0500000000003`, -1.04762`*^-8}, {82.2000000000003`, -6.1445`*^-9}, {82.3500000000003`, 1.6944`*^-9}, {82.5000000000003`, 1.18519`*^-8}, {82.6500000000003`, 2.2779`*^-8}, {82.8000000000003`, 3.28018`*^-8}, {82.9500000000003`, 4.03784`*^-8}, {83.1000000000003`, 4.43377`*^-8}, {83.2500000000003`, 4.40629`*^-8}, {83.4000000000003`, 3.95907`*^-8}, {83.5500000000003`, 3.16087`*^-8}, {83.7000000000003`, 2.13523`*^-8}, {83.8500000000003`, 1.04127`*^-8}, {84.0000000000003`, 4.891`*^-10}, {84.1500000000003`, -6.8795`*^-9}, {84.3000000000003`, -1.05588`*^-8}, {84.4500000000003`, -1.0001`*^-8}, {84.6000000000003`, -5.3343`*^-9}, {84.7500000000004`, 2.655`*^-9}, {84.9000000000004`, 1.26473`*^-8}, {85.0500000000004`, 2.30008`*^-8}, {85.2000000000004`, 3.20167`*^-8}, {85.3500000000004`, 3.82165`*^-8}, {85.5000000000004`, 4.05841`*^-8}, {85.6500000000004`, 3.87351`*^-8}, {85.8000000000004`, 3.29831`*^-8}, {85.9500000000004`, 2.42914`*^-8}}$

[Graphics:HTMLFiles/modefit_psi4_ylm_2022_6.gif]

$mycoeffs = Coefficient[myfit, {f1[x], f2[x], f3[x], f4[x], f5[x], f6[x], f7[x], f8[x], f9[x], f10[x], f11[x], f12[x]}] mycoeffs = mycoeffs^2$

${3.801551151908542`*^-9, 0.00023694658829355973`, -0.0007272615082030438`, -0.012720420310289752`, -0.04702775126386045`, -0.12060908563555617`, -0.17465628042484854`, -0.1928845382921741`, -0.15590857029003632`, -0.08157952202572559`, -0.02859817234983507`, -0.0033806202417118168`}$

${1.4451791160577163`*^-17, 5.61436857039577`*^-8, 5.289093013137659`*^-7, 0.00016180909287043203`, 0.0022116093889355277`, 0.014546551537844921`, 0.03050481629184333`, 0.03720444511218518`, 0.024307482289883196`, 0.006655218413945846`, 0.0008178554617508711`, 0.000011428593218671662`}$

$Export["/Users/ruxandra/boson_analysis/run128_ylm_2022_stable_031129/psi4_stable_y2022_53.dat", Table[{x, myfit}, {x, 69, 86, 0.01}]]$

$3.772146879328537`*^-6 Set :: patset : Warning: myfit_prob in assignment myfit_prob = ---------------------- + << 23 >> \ << 2 >> + << 21 >> represents a named pattern; use symbol::tag to represent a message name. x$

[Graphics:HTMLFiles/modefit_psi4_ylm_2022_23.gif]

[Graphics:HTMLFiles/modefit_psi4_ylm_2022_25.gif]

Converted by Mathematica (December 1, 2003)