The Local Group Timing Argument •Real galaxies Milky Way (MW) Andromeda (M31) Indranil Banik ([email protected]) Supervisor: Hongsheng Zhao University of Saint Andrews MNRAS, 459 (2), 2237 – 2261 Governing Equations r In a homogeneous Universe: r a() t .. .. a GM()()r r GM r r r r MW MW M31 M 31 a 3 3 r rMW r r M 31 Can derive this from General Relativity (flat Universe assumed) Governing Equations r In a homogeneous Universe: r a() t .. .. a GM()()r r GM r r r r MW MW M31 M 31 a 3 3 r rMW r r M 31 Can derive this from General Relativity (flat Universe assumed) Model assumptions • All objects following Hubble flow at early time (no peculiar velocity) – spherical symmetry initially • Mass dominated by MW & M31 • MW – M31 orbit is radial (Sohn et. al., 2012) Local group axisymmetric • Test particles can’t start too close to MW or M31 – an equipotential is drawn which encloses the initial MW + M31 mass in a homogeneous Universe. Test particles starting within this equipotential are discarded. Close approaches • Particles that approach MW or M31 too closely are accreted and increase mass of accreting galaxy. • Force from MW and M31 is r -1 at short range (but r -2 at long range). This is to match their observed flat rotation curves. Model deficiencies • Interactions between LG dwarf galaxies not included. Would likely have caused a velocity dispersion of ~15 km/s (Kirby et. al., 2014) • Might be good to include M33 • Tides from distant galaxies might matter a little (though we included Cen A directly and regions too close to other massive galaxies were not included in the analysis) • Force from MW & M31 transitions from r -1 at short range to r -2 at long range, but exact recipe for transition somewhat arbitrary • Initial separation varied until final separation MW-M31 separation, Mpc 0.25 0.75 1.25 First step: MW–M31 trajectory = 0.783 Mpc (McConnachie, 2012) 0.5 0 1 0 2 Time since Big Bang, Gyr 4 6 8 10 12 14 •Real galaxies Milky Way (MW) Andromeda (M31) 2 1 0 -1 0.5 1 1.5 2 Gravity slows cosmic expansion vr H0 d Gravity slows cosmic expansion vr H0 d Gravity Input data • Data for LG galaxies from McConnachie (2012) • Targets selected same as in work of Peñarrubia et. al. (2014), but we excluded Andromeda 18. • Velocity field smooth near target galaxies, allowing well-defined velocity prediction. If this isn’t true, computer rejects target (rare). Satellite galaxies not included in analysis Analysis • 2D Newton-Raphson used to get test particle trajectory landing where an actual galaxy is • Velocity projected onto line of sight from MW to get galactocentric radial velocity (GRV) • Distance from MW increased by 1σ & analysis repeated to get uncertainty in GRV due to uncertainty in distance • Error due to GRV measurement added • σextra also added: extra variance. This is due to interactions between LG dwarf galaxies • Value reduced for M31 as it is hard to budge Observed GRV, km/s Best-fit model and observations -200 -100 100 200 300 -100 0 Model galactocentric radial velocity (GRV), km/s -50 0 50 100 150 200 250 Best-fit model and observations 300 s / 200 m k , V 100 R G σ d extra e 0 v r e s b -100 O -200 -100 -50 0 50 100 150 200 250 Model galactocentric radial velocity (GRV), km/s • How much extra dispersion do we need? Probability density 0.01 0.02 0.03 0.04 0.05 • 10 km/s less if M31 not treated specially 0 0 Results: extra variance 20 40 extra , km/s 60 80 100 Explaining σextra • Line of sight dispersion of 45 km/s implies dispersion of 80 km/s in 3D • LG dwarf galaxies rotate at << 50 km/s (more like 15 km/s, Kirby et. al., 2014) • Velocities more often above model than below Interactions between LG dwarf galaxies can’t easily account for the discrepancies • Looked carefully at tides and MW / M31 satellites ΛCDM does not match the observations Consider Modified Newtonian Dynamics (MOND) MW – M31 separation in ΛCDM c 1.25 p M , 1 n o i t a 0.75 r a p e 0.5 s 1 3 0.25 M - 0 W 0 2 4 6 8 10 12 14 M Time since Big Bang, Gyr • Past MW–M31 flyby not possible: gravity too weak • In any case, dynamical friction between dark matter halos would cause merger, not flyby Flyby inevitable under wide range of assumptions MW-M31 separation, Mpc 0.2 0.4 0.6 0.8 Modified Newtonian Dynamics 0 1 0 2 4 Time after Big Bang, Gyr 6 Astronomy & Astrophysics 557: L3 (2013) 8 10 M too high M just right M too low 12 14 Basic principle: gravitational slingshots • Heavy galaxy (e.g. MW) moves right at 5 km/s • Small object moving right at 1 km/s Relative speed = 4 km/s 5 km/s 1 km/s 4 km/s Basic principle: gravitational slingshots • Heavy galaxy (e.g. MW) moves right at 5 km/s • Small object moving right at 1 km/s Relative speed = 4 km/s • MW reverses relative velocity of object Object now moves at (5 + 4) km/s 5 km/s 4 km/s 1 km/s 4 km/s MOND • In this model, there was a close encounter between the MW & M31 in the past • This caused substantial dynamical heating of the Local Group Very high GRV’s occur as some LG galaxies flung out at high speed by fast-moving MW./.M31 (around time of their encounter) • Process also occurs in ΛCDM, but MW–M31 relative motion much slower as no close flyby Observed – predicted GRVs (ΛCDM) 0.8 GRV > 0 Never One GRV < 0 y galaxy t i 0.6 interacted with 15 km/s s MW / M31 n e Gaussian d y t i l 0.4 i b a b o r 0.2 P 0 0 20 40 60 80 100 120 140 |GRV|, km/s • Objects with ΔGRV < 0 roughly consistent Observed – predicted GRVs (ΛCDM) 0.8 GRV > 0 Never One GRV < 0 y galaxy t i 0.6 interacted with 15 km/s s MW / M31 n e Gaussian d Flung out y t i by MW l 0.4 i Flung out by M31 b a (~2× heavier b than MW) o r 0.2 P 0 0 20 40 60 80 100 120 140 |GRV|, km/s • Objects with ΔGRV < 0 roughly consistent • Not true for objects with ΔGRV > 0 Smooth velocity field Disturbed velocity field Distances from LG barycentre of observed ‘target’ galaxies Flung out by MW/M31 Timing Argument in MOND • Main difference: galaxies moving outwards very fast must all have been at ~same place at same time (i.e. close to Local Group barycentre at time of MW–M31 flyby) Galaxies furthest away now must have been flung out fastest (and still be going fastest) d = v Δt (elapsed time since flyby) v = d k 1 k t Distant objects going faster? • Not all objects flung out by MW or M31 Should see lots of objects with ΔGRV ≈ 0 BUT: some objects will follow ΔGRV d • Note: velocities plotted (ΔGRVs) are net of the best-fitting model (which at long range is ~a pure Hubble flow: a uniformly expanding Universe with v = H0d) DDO 99 s / KKH 98 DDO 190 100 DDO 125 m NGC 404 k UGC Leo P , Sextans B 8508 KKH 86 HIZSS V Tucana NGC 3109 NGC 55 UGC 9128 Sextans A NGC 300 IC 3104 R UGC 4879 KKR 3 KKR 25 GR 8 G 0 WLM UKS 2323-326 NGC 4163 Andromeda Aquarius ESO 294-G010 Sagittarius Antila IC 5152 IC 4662 Leo A -100 0 0.5 1 1.5 2 2.5 3 3.5 Distance from LG barycentre, Mpc •H0 = 67 km/s/Mpc (at d = 1 Mpc, v = H0d = 67 km/s in a uniformly expanding Universe) Universe age ≈ 1 Mpc ÷ 67 km/s = 13.8 Gyr DDO 99 s / KKH 98 DDO 190 100 DDO 125 m NGC 404 k UGC Leo P , Sextans B 8508 KKH 86 HIZSS V Tucana NGC 3109 NGC 55 UGC 9128 Sextans A NGC 300 IC 3104 R UGC 4879 KKR 3 KKR 25 GR 8 G 0 WLM UKS 2323-326 NGC 4163 Andromeda Aquarius ESO 294-G010 Sagittarius Antila IC 5152 IC 4662 Leo A -100 0 0.5 1 1.5 2 2.5 3 3.5 Distance from LG barycentre, Mpc •H0 = 67 km/s/Mpc (at d = 1 Mpc, v = H0d = 67 km/s in a uniformly expanding Universe) Universe age ≈ 1 Mpc ÷ 67 km/s = 13.8 Gyr DDO 99 s / KKH 98 DDO 190 100 DDO 125 m NGC 404 k UGC Leo P , Sextans B 8508 KKH 86 HIZSS V Tucana NGC 3109 NGC 55 UGC 9128 Sextans A NGC 300 IC 3104 R UGC 4879 KKR 3 KKR 25 GR 8 G 0 WLM UKS 2323-326 NGC 4163 Andromeda Aquarius ESO 294-G010 Sagittarius Antila IC 5152 IC 4662 Leo A -100 0 0.5 1 1.5 2 2.5 3 3.5 Distance from LG barycentre, Mpc •H0 = 67 km/s/Mpc (at d = 1 Mpc, v = H0d = 67 km/s in a uniformly expanding Universe) Universe age ≈ 1 Mpc ÷ 67 km/s = 13.8 Gyr • Observe excess of ~40 km/s/Mpc in Local Group Flyby time ≈ 1 Mpc ÷ (67 + 40) km/s = 8.7 Gyr ago Other flyby time estimates 1 c p M , 0.8 n o i t a r 0.6 a p High e s ΔGRV 0.4 1 objects 3 ASP ConferenceM too low M - 0.2 Series,M vol just 230, right W Thick Timing M disk age p 87M (2001) too high 0 argument 0 2 4 6 8 10 12 14 Time after Big Bang, Gyr (billions of years) • All three age estimates agree, within errors Flyby ~7–9 Gyr ago (5–7 Gyr after Big Bang) Conclusions • ΛCDM does not describe the dynamics of Local Group galaxies very well (1128 models tried) • Distant LG galaxies with high radial velocities were flung out at high speed at ~same time as thick disk of MW formed (~5 Gyr after Big Bang) • More detailed lecture: www.youtube.com/watch?v=U3HTzJohNAw Constraining The Extra Variance ()v 2 1 2 Probability e 2 • View as equation in σ • At first, raising σ lowers χ2 and raises the probability.