The Virgo spectrum is polluted by many lines and in this entry I attempted to identify the lines generated by the high order modes of the mirrors.

In the first attached figure is reported the frequency evolution over several run weeks of the drum modes of the end mirrors (black symbols, right vertical axis). As well known from many monts the NE mirror mode is spoiled for some unknown reason (cloudy curve). The red symbols represents the corresponding "butterfly" modes (211 in the Cypres zoology) at 3884 Hz. The overlap is very good if the adopted scaling factor is 0.6Hz/K for the drum mode and 0.28Hz/K for the butterfly mode (as foreseen by the FEM). The 211 mode of the NE seems not spoiled as the corresponding drum mode.

Other modes are expected below 10kHz:  311 at abot 7560Hz, 201 at about 8030 and 101 at about 9010 Hz. It should be noted that the error in these numbers is of about 100Hz because they strongly depends on the thickness of the mirror (and the input and end mirrors differ by about 1mm  (30Hz of difference in the 211 mode, about 40Hz on the drum mode)) and in the constrains (suspension wires, spacers,...).

In the second figure the 201 modes of the input mirrors (at 8036Hz) have been identified thanks to the corresponding frequency evolution.

In the third figure the probable 211 mode of the NE mirror has been found at 7561Hz, although a small discrepancy is evident in the first part of the plot.

The 101 around 9010Hz is undetected, but this could be suppresses by the aliasing filters.

The problem is that other lines appear above 9kHz and they are strangely related to the thermal modes. In the fourth figure the butterfly 211 modes of the end mirrors (at about 3884 Hz) are overlapped to a pair of modes found at 9628Hz. The correspondence is good, but the trick is that the right vertical axis (the red one) has been reversed, as indicated by the arrows. The only way to explain it is that that lines are the alias image of other mirror modes above 10kHz. In effect we expect the 111 mode at about 10154Hz and the 001 mode at about 10380Hz. The lines at 9628Hz are hence the candidates to be the alias of the 001 mode at 10380Hz.

But another line (NE-001-bis) is candidate to the same role; in the fifth figure a line at 9632Hz overlaps (with the same inversion trick) with the evolution of the NE drum mode for many weeks (and then something occurs). 

Another aliased line (NE-111-bis), at 9831Hz, follows exactly the evolution of the aliased line at 9632 Hz (NE-001-bis) as shown in the 6th figure and it is a candidate to be the alias image of the expected 10154Hz 111 mode of the NE mirror.

The forest of alias of the mirror thermal lines is not concluded: in the 7th and 8th picture show other aliased mirror lines at 9871Hz and 9888-9889Hz that merit to be candidates to the same 111 modes of the end mirrors (in effect we coud expect that the high order modes are splitted in doublets or multiplets because of the broken symmetry of the mirrors due to the lateral flats) .

The first conclusion of this long entry is that our high frequency range is spoiled by many aliasing effects.

The second conclusion is that this analysis has been performed using the line database tool: https://slvtf.virgo.infn.it/vtf/wwwDev/lmTest/stable/index.php developed by the Kiel Howe (SURF student) with the Irene and Gabriele support and it is very useful ... we need it online as soon as possible.