Galactic evolution in Nonlocal Gravity

Mahmood Roshan

Ferdowsi University of Mashhadmroshan@um.ac.ir

February 14, 2019

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 0 / 17

Outline:

1 "Fast bars" as a unsolved challenge for ΛCDM model

2 Mashhoon’s nonlocal gravity in the weak filed limit

3 Numerical method: N-body simulations withGALAXY code

4 Evolution of numerical galactic disks in NLG

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 0 / 17

Bar pattern speed Ωp:

The pattern speed is the rotationalvelocity of the bar. The observa-tional parameter R is a yardstick tocompare the pattern speed of differ-ent galaxies. This parameter is de-fined as

R =DL

aB

where DL is the corotation radius,and aB is the bar semi-major axis.In this case the bar is fast ifR . 1.4,and is slow if R & 1.4. DL

Ωp

Ω

0 2 4 6 8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Radius

Frequency

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 1 / 17

Measurements of Ωp in the simulations (R > 1.4):

M. D. Weinberg (1985) predicted analitically that the darkmatter halo should slow down the bars. (Dynamical friction)Hernquist & Weinberg (1992) found substantial angular momentumtransfer from the stellar bar to the DM halo and the stellar bar.Debattista & Sellwood (1998) via N-body simulations confirmedthis prediction for nonrotating halos, DM halos must have lowcentral densities if bars are to remain as fast as those observed.Debattista & Sellwood (2000) via N-body simulations showed thatthe rotating halos moderate the dark matter drag, but can notstop the rapid decrease in pattern speed.Simulations with gas component also show the slowdown of thebars: Villa-Vargas et al (2010), Athanassoula (2013).Cosmological hydrodynamical simulations confirms the rapidpattern speed slowdown: EAGLE project, Algorry et al (2017).

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 2 / 17

Observation of Ωp (R < 1.4):

Figure 1: Red circles denote measurements for SB0 galaxies, blue diamondscorrespond to SB0/a galaxies, and green squares represent spiral barredgalaxies. From Corsini (2010), based on Tremaine-Weinberg (TW) method.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 3 / 17

Figure 2: Aguerri et al (2015). The red symbols represent the R values ofCALIFA sample. The green stars represent the mean values of R forSB0-SB0/a, SBa-SBab, and SBb-SBbc galaxies. Four different methods havebeen used to calculate the patter speed. Fast bar solution cannot be ruled outfor any galaxy at 95% level.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 4 / 17

Figure 3: Algorry et al (2017): EAGLE cosmological hydrodynamicalsimulations. Most strong bars in our simulation are ‘slow’ at z = 0, incontrast with observational estimates.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 5 / 17

Proposed solutions in the context of particle dark matterparadigm:

Improvement in Baryonic physics:Higher resolution in cosmological simulations may resolve thisdiscrepancy (Algorry et al 2017 )Highly triaxial halos lead to higher pattern speeds (Athanassoula2014 )Higher gas fraction leads to higher pattern speeds (Athanassoula2014 )

Improvement in dark matter physics:Different properties of the dark matter itself are required.Ultralight scalar Bosons: Hu et al (2000); Hui, Ostriker, Tremaineand E. Witten (2017).

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 6 / 17

Nonlocal theory of gravity (NLG):

We are interested in theories which lead toYukawa corrections to the gravitational forcein the weak field limit:

F (r) = −m1m2G

r2

(1 + α− α(1 + βr)e−µr

)In NLG: α = 10.94± 2.56 andµ = 2β = 0.059± 0.028 kpc−1.In MOG: α = 8.89± 0.34 andµ = β = 0.042± 0.004 kpc−1,In MOG, the existence of extra scalar and vector fields, inducesYukawa corrections. (No screening effect!)In NLG, the nonlocal aspect of gravity appears as an extra mattersource:∇2Φ = 4πG(ρ+ ρD) where ρD(x) =

∫q(x− y)ρ(y)d3y.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 7 / 17

N-body simulations with GALAXY code:

The GALAXY code is written and developed by Jerry Sellwood .We generalized and tested some parts of the code by addingmodified gravity effects.The equilibrium initial conditions are constructed for the followingmatter components: (there is no bulge in our simulations.)

Σ(R) =Md

2πR2d

e−R/Rd , ρ(r) =3Mh

4πb3

[1 +

(rb

)2]−5/2

The free parameters of NLG, are assumed to be time independent.The initial Toomre’s parameter is Q > 1, thus the disk is locallystable.The disk has a Gaussian density profile in the vertical direction.All the scale lengths in the density profiles are chosen to becompatible with the typical values for real galaxies.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 8 / 17

Initial rotation curves:

Figure 4: Roshan & Rahvar, ApJ, (2019); ENLG: Exponential disk in NLG;EM: Exponential disk in MOG; EPL: Exponential disk + Plummer halo instandard gravity. For a meaningful comparison all the models should startfrom the same initial conditions (velocities, density profiles, velocitydispersion, ...).

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 9 / 17

Bar magnitude A2: (Fourier decomposition)

Figure 5: In the top panel we have N = 3× 106 particles; In the bottom panelwe have 2× 107 particles. Growth rate in NLG > Growth rate in MOG anddark matter model. Final magnitude of bar in NLG < final magnitude indark matter model.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 10 / 17

Figure 6: Bar instability (spiral excitation), Buckling instability, final barMahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 11 / 17

Power spectrum:

Figure 7: Beating between different modes, appear as oscillations in A2.Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 12 / 17

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 13 / 17

Long-term evolution of the pattern speed:

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 14 / 17

R for the exponential disk in NLG:

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 15 / 17

R in dark matter model and MOG:

Figure 8: Roshan, ApJ (2018);

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 16 / 17

Conclusions:

Although both dark matter model and the NLG model start withthe same initial conditions, the long-term evolution is significantlydifferent.The bar instability happens more rapidly in NLG.NLG leads to weaker bars compared to the dark matter model.NLG leads to faster bars compared with the dark matter model.More realistic simulations including bulges and gas componentmay help to discriminate between particle dark matter andmodified gravity.The absence of the dynamical friction in modified gravity mayinfluence the merging rate of galaxies during the matter dominatedphase.

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 17 / 17

Thank You for yourattention!

Mahmood Roshan (FUM) Baryons in galaxies & beyond, IPM February 14, 2019 17 / 17