Bar

• 描述棒星系的三个参数，长度，强度，和pattern speed [1]

strength

The bar strength is a parameter that measures the non-axisymmetric forces produced by the bar potential in the disc of galaxies (see, e.g., Laurikainen & Salo, 2002).

• measure the torques of the bar (e.g., Combes & Sanders , 1981; Quillen et al. , 1994; Buta & Block , 2001; Laurikainen et al. , 2007; Salo et al. , 2010)
• bar ellipticity Martinet & Friedli (1997); Aguerri (1999); Whyte et al. (2002); Marinova & Jogee (2007); Aguerri et al. (2009)
• Fourier decomposition of the galaxy light Ohta et al. (1990); Marquez et al. (1996); Aguerri et al. (2000); Athanassoula & Misiriotis (2002); Laurikainen et al. (2005).

pattern speed

defined as the rotational frequency of the bar.

• Bar cannot extend beyond the corotation resonance (CR) radius of the galaxy.
• CR is the region of the galaxy where the angular speed of the stars of the disc in circular motions equals the bar pattern speed.
• This limit is imposed by the stability of the main family of orbits forming the bar (the so-called x1 family; Contopoulos 1980) which are only stable within R(CR). Orbits in the outer region of the disc (R > RCR) cannot support a bar structure.
• hypothesis： that fast bars are formed by global instabilities in isolated galaxies, while slow bars are triggered by tidal interactions in dense environments arXiv:2511.02054