QNM ringing after the head-on collision of two unequal mass black holes . The continuous line corresponds to the full nonlinear numerical calculation while the dotted line is a fit to the fundamental and first overtone QNM.
The spectrum of QNM for a Schwarzschild black-hole, for = 2 (diamonds) and = 3 (crosses) . The 9th mode for = 2 and the 41st for = 3 are “special”, i.e. the real part of the frequency is zero ().
A graph which shows all the -modes: curvature, trapped and interface both for axial and polar perturbations for a very compact uniform density star with . The black hole spectrum is also drawn for comparison. As the star becomes less compact the number of trapped modes decreases and for a typical neutron star () they disappear. The of the curvature modes increases with decreasing compactness, and for a typical neutron star the first curvature mode nearly coincides with the fundamental black hole mode. The behavior of the interface modes changes slightly with the compactness. The similarity of the axial and polar spectra is apparent.
The response of a Schwarzschild black hole as a Gaussian wave packet impinges upon it. The QNM signal dominates the signal after while at later times (after ) the signal is dominated by a power-law fall-off with time.
Time evolution of axial perturbations of a neutron star, here only axial -modes are excited. It is apparent in panel D that the late time behavior is dominated by a time tail. In the left panels (A and C) the star is ultra compact () and one can see not only the curvature modes but also the trapped modes which damp out much slower. The stellar model for the panels (B and D) is a typical neutron star () and we can see only the first curvature mode being excited.
Excitation of polar modes due to an initial deformation of the star. The initial burst which is dominated mainly by the first -mode is followed by a sinusoidal waveform dominated by the and the first -mode. In the upper panel the actual waveform is shown, while in the lower panel is its power spectrum. The wide peak in the power spectrum corresponds to the -mode, while the sharp peaks correspond to the various fluid modes.
The left graph shows the numerically obtained -mode frequencies plotted as functions of the mean stellar density. In the second graph the functional is plotted as a function of the compactness of the star ( and are in km, and in kHz). The letters A, B, C, … correspond to different equations of state for which one can refer to .
© Max Planck Society and the author(s)