Systematic study of gravitational waves from galaxy mergers

A systematic study of gravitational waves from galaxy mergers, through $N$-body simulations, was performed. In particular, we investigated the relative importance of galaxy components (disk, bulge and halo) and effects of initial relative velocity, relative angular momentum and mass ratio of the galaxies. We found that the features of light curve of gravitational waves, such as peak width and luminosity, are reliably simulated with particle numbers larger than $\sim {10}^4$. Dominant contribution to gravitational wave emission came from the halo component, while peak luminosity amounted to ${10}^{31}\mathrm{erg}/\sec$ for the collision of two halos with mass $3.8\times {10}^{12}{h}^{-1}{M}_{\odot }$. We also found that the initial relative velocity in the direction of the initial separation did not significantly affect gravitational wave emission, while the initial relative angular momentum broadened the peak width and suppressed the luminosity. Mass dependence of the peak luminosity was also investigated, and we obtained evidence that the luminosity is proportional to the cubic mass when the scaling relation is satisfied. This behavior was considered by a simple analysis.

Figure 1

Rotation curve, $V_{\mathrm{c}}(r)=\sqrt{GM(r)/r}$, for $\mathrm{\text{halo}}+\mathrm{\text{disk}}+\mathrm{\text{bulge}}$ (solid line), halo (dashed line), disk (dotted line), and bulge (dash-dotted line) for a range from galactic center to $r_{\mathrm{t}}$. Top: Model-0. Middle: Model-A. Bottom: Model-D.

Figure 2

Time evolution of luminosity of gravitational waves for Model-0.

Figure 3

Top: comparison of gravitational wave luminosities calculated with three different approaches for Model-0. See text for detail. Bottom: ratios of luminosity, $\mathrm{F}1/\mathrm{F}3$ and $\mathrm{F}2/\mathrm{F}3$.

Figure 4

Dependence on particle number ($5.4\times {10}^5$: solid line, $5.4\times {10}^4$: dashed line, $5.4\times {10}^3$: dotted line). Other parameters are the same as the Model-0.

Figure 5

Time evolution of luminosity of gravitational waves for Model-0 with contribution from halo (dashed line), disk (dotted line), bulge (dash-dotted line) only. Total luminosity is also shown (solid line).

Figure 6

Time evolution of luminosity of gravitational waves for Model-0 (solid line), Model-A (dashed line), and Model-D (dotted line).

Figure 7

Top: the density profile of Model-0 (solid), Model-A (dashed), and Model-D (dotted). Bottom: the mass of Model-0 (solid), Model-A (dashed), and Model-D (dotted) within the radius.

Figure 8

Top: density profile of the fiducial halo with $1.3\times {10}^{14}{h}^{-1}{M}_{\odot }$ (solid line) which is well fitted by the NFW profile with $r_{\mathrm{s}}\sim 170h^{-1}\mathrm{kpc}$ (dashed line). For reference, the density profile of the galaxy (Model-0) used in Sec. 3a is also shown (dotted line). The density and the radius are normalized with the average density ${\rho }_{\mathrm{avg}}$, and the virial radius $r_{\mathrm{vir}}$ of each galaxy. However, the virial radius of the galaxy used in Sec. 3a is replaced by the tidal radius. Middle: the mass of the fiducial galaxy (solid line) and one used in Sec. 3a (dotted line) within the radius. As in the top figure the radius is normalized, and the axis of ordinate is normalized by the total mass of each model. Bottom: rotation curves of the fiducial galaxy (solid line) and one used in Sec. 3a (dotted line).

Figure 9

Comparison of luminosity evolution varying the initial relative velocity in the direction of initial separation (Models A-1, A-2 and A-3).

Figure 10

Amplitude of the plus mode in the $z$ direction at $10h^{-1}\mathrm{Mpc}$ from the galaxies for Models A-1, A-2 and A-3.

Figure 11

Amplitude of the plus (top) and cross (bottom) modes in the $x$, $y$ and $z$ directions at $10h^{-1}\mathrm{Mpc}$ from the galaxies for Model A-2.

Figure 12

Luminosity evolution varying the initial relative velocity in the direction orthogonal to the direction of the initial separation (Models B-1, B-2 and B-3).

Figure 13

Fourier spectrum of the luminosity for Models B-1, B-2, B-3.

Figure 14

Amplitude of the plus (top) and cross (bottom) modes in the $x$, $y$ and $z$ directions at $10h^{-1}\mathrm{Mpc}$ from the galaxies for Model B-2.

Figure 15

Peak luminosity as a function of mass fixing mass ratio to $1:1$.

Figure 16

Luminosity evolution varying the mass ratio (Models B-1, C-1 and C-2).