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Hierarchical massive quadruple systems are ideal laboratories for examining the theories of star formation, dynamical evolution, and stellar evolution. The successive mergers of hierarchical quadruple systems might explain the mass gap between neutron stars and black holes. Looking for light curves of O-type binaries identified by LAMOST, we find a (2+2) quadruple system: TYC 3340-2437-1, located in the stellar bow-shock nebula (SBN). It has a probability of over 99. 99\% being a quadruple system derived from the surface density of the vicinity stars. Its inner orbital periods are 3. 390602 (89) days and 2. 4378 (16) days, respectively, and the total mass is about (11. 47 + 5. 79) + (5. 2 + 2. 02) = 24. 48 M_. The line-of-sight inclinations of the inner binaries, B₁ and B₂, are 55. 94 and 78. 2 degrees, respectively, indicating that they are not co-planar. Based on observations spanning 34 months and the significance of the astrometric excess noise (D>2) in Gaia DR3 data, we guess that its outer orbital period might be a few years. If it were true, the quadruple system might form through the disk fragmentation mechanism with outer eccentric greater than zero. This eccentricity could be the cause of both the arc-like feature of the SBN and the noncoplanarity of the inner orbit. The outer orbital period and outer eccentric could be determined with the release of future epoch astrometric data of Gaia.
Li et al. (Tue,) studied this question.