Pattern Speed of Lopsidedness in Galactic Disks

Mem. S.A.It. Suppl. Vol. 18, 119 Memorie della c SAIt 2011 Supplementi Pattern speed of lopsidedness in galactic disks C. J. Jog Department of Physics, Indian Institute of Science, Bangalore, India e-mail: [email protected] Abstract. The disks of spiral galaxies commonly show a lopsided mass distribution, with a typical fractional amplitude of 10% for the Fourier component m = 1. This is seen in both stars and gas, and the amplitude is higher by a factor of two for galaxies in a group. The study of lopsidedness is a new topic, in contrast to the extensively studied bars and two- armed spirals (m = 2). Here, first a brief overview of the observations of disk lopsidedness is given, followed by a summary of the various mechanisms that have been proposed to explain its physical origin. These include tidal interactions, gas accretion, and a global instability. The pattern speed of lopsidedness in a real galaxy has not been measured so far, the various issues involved will be discussed. Theoretical studies have shown that the m = 1 slow modes are long-lived, while the modes with a moderate pattern speed as triggered in interactions, last for only about a Gyr. Thus a measurement of the pattern speed of lopsided distribution will help identify the mechanism for its origin. Key words. galaxies: kinematics and dynamics – galaxies: groups – galaxies: ISM – galaxies: spiral – galaxies: structure 1. Introduction files compiled for a large sample of galaxies, Richter & Sancisi (1994) concluded that nearly It is known that the light and hence the mass half the galaxies show lopsidedness. distribution in disks of spiral galaxies is not strictly axisymmetric, as for example in M101 The near-IR observations show that lopsid- or in NGC 1637, where the isophotes are elon- edness is common in stars as well. The stel- gated in one half of the galaxy. This phe- lar disks in 30% of galaxies studied are signif- nomenon was first highlighted in the paper by icantly lopsided, with an amplitude A1 > 0:1. Baldwin et al. (1980) for the atomic hydro- This is measured as the Fourier amplitude of gen gas in the outer regions in the two halves the m = 1 component normalized to the av- of some galaxies, and they called these ‘lop- erage value (Rix & Zaritsky 1995). The lopsided’ galaxies. A galaxy is said to be lopsidedness is stronger at larger radii. This was sided if it displays a non-axisymmetric mass confirmed for a larger sample of 149 galaxies distribution of type m = 1 where m is the (Fig. 1) from the Ohio State University (OSU) azimuthal wavenumber, or a cosφ distribution database by Bournaud et al. (2005). Thus, lop- where φ is the azimuthal angle in the plane sidedness is a typical feature, hence it is impor- of the disk. From the HI global velocity pro- tant to study its dynamics. In a first such study, a similar Fourier anal- Send offprint requests to: Chanda J. Jog ysis for the interstellar atomic hydrogen gas 120 Jog: Lopsidedness in galactic disks Fig. 1. The histogram showing the number of galaxies vs. the lopsided amplitude, measured in 149 galaxies at the inclination of < 70◦ from the OSU Fig. 2. The lopsided amplitude and phase of the HI sample (Bournaud et al. 2005). The typical normal- surface density distribution vs. radius (in units of the disk scalelength) for the galaxy UGC 068 in the ized lopsided amplitude hA1i measured over the radial range between 1:5−2:5 disk scalelengths is 0.1. Eridanus group, taken from Angiras et al. (2006). Thus most spiral galaxies show significant lopsided- The amplitude increases with radius (top panel), and ness. the phase is nearly constant indicating that m = 1 is a global mode (bottom panel). (HI) has been done by analyzing the two- 2. Origin of disk lopsidedness dimensional surface density plots for 18 galaxies in the Eridanus group (Angiras et al. 2006). A non-axisymmetric feature will tend to get wound up in a few dynamical timescales or Using HI as the tracer allows the asymmetry to 8 be measured up to several times the disk scale- in a few ×10 yr, due to the differential rota- lengths, see Fig. 2. This is more than twice tion in the galactic disk. This is the well-known the radial distance covered for the stars, since winding dilemma. However, a high fraction the sky background in the near-IR limits the of galaxies is observed to be lopsided. To Fourier analysis to ∼ 2:5 disk scalelengths. get around the limited lifetime implied by the Note that, during the Fourier decomposition, winding problem, a number of models have the same centre has to be used for all the an- been proposed. nular radial bins (Rix & Zaritsky 1995; Jog & Combes 2009). 2.1. Kinematic model Since these galaxies belong to a group, this serendipitously allows a study of the effect of Starting with aligned orbits, Baldwin et al. group environment on lopsidedness. The aver- (1980) calculated the winding up time while age lopsided amplitude A1 for the group galax- taking account of the epicyclic motion of the ies is higher ∼ 0:2, see the histogram in Fig. 3. particles. This decreases the effective radial The fraction of galaxies showing lopsidedness range over which the differential rotation is ef- is higher in groups. For example, all the group fective, hence it increases the lifetime to be galaxies have A1 > 0:1, which is the mean about 5 times longer than for the usual mate- value for the field case. The frequent interac- rial arms, or ∼ 1 Gyr. This is still much smaller tions in galaxies in groups could explain the than the Hubble time so they concluded that higher fraction of galaxies showing lopsided- the lopsidedness seen could not be of primor- ness. dial origin. Jog: Lopsidedness in galactic disks 121 where Vc is the rotation velocity in the region of flat rotation, and lop denotes the small perturbation parameter in the potential which is taken to be constant with radius. The perturbation potential is taken to be non-rotating for simplicity. The equations of motion are solved using the first order epicyclic theory. The perturbed closed loop orbits are given by: R = R0(1 − 2lop cos φ) (3) VR = 2Vc lop sin φ (4) Vφ = Vc(1 + lop cos φ) (5) Thus an orbit is elongated along φ = 180◦ or the minimum of the perturbation potential, and it is shortened along the opposite direction ◦ Fig. 3. The histogram showing the number of galax- (along φ = 0 ). ies vs. the lopsided amplitude, A1, measured in The observations measure isophotes rather the 1.5-2.5 disk scalelength range for the Eridanus than orbits, hence the isophotal shapes are ob- group galaxies, from Angiras et al. (2006). The tained for an exponential galactic disk in a lop- group galaxies are more lopsided, compare with sided potential. The resulting isophotes have Fig. 1. an egg-shaped oval appearance. This agrees with the observed isophotal shapes in M101. On solving the equations of perturbed motion 2.2. Dynamical models (Eqs. 3–5), the equation of continuity, and the The various mechanisms that have been pro- effective surface density together, one gets: posed to explain the physical origin of the disk A1 lopsidedness are discussed next. lop = (6) ( 2R ) − 1 Rexp 2.2.1. Disk response to lopsided From this, the typical value of the perturbation potential parameter is obtained to be potential lop ∼ 0:05 for the average observed lopsided am- The basic features of the orbits, isophotes and plitude. This denotes the global distortion of kinematics in a lopsided galaxy can be un- the halo potential. Thus, the disk lopsidedness derstood by treating the disk response to an can be used as a diagnostic to study the lopsid- imposed lopsided perturbation potential (Jog edness of the halo potential. 1997; Schoenmakers et al. 1997). The origin The disk response to a distorted halo that of lopsided halo potential was assumed to be of gives spatial lopsidedness also results in kine- tidal origin. The results from Jog (1997, 2000) matic lopsidedness in the disk. The resulting are summarized below: rotation curve is asymmetric (Eq. 5). The rota- The unperturbed axisymmetric potential, tional velocity is maximum along φ = 0◦ and 0, and the first-order perturbation potential, minimum along the opposite direction. The lop, are taken to be respectively: typical difference in the two halves of a galaxy is 2lopVc or ∼ 10% of the rotation velocity, ∼ 2 25 km s−1 (Jog 2002). Thus observers should 0 = Vc ln R (1) give the full two-dimensional data for the azimuthal velocity, rather than an azimuthally av- 2 lop = Vc lop cos φ (2) eraged value. The observed asymmetry in the 122 Jog: Lopsidedness in galactic disks rotation curve then can be used as a tracer to mass ratio 2:1 is shown in Fig. 4. A strong determine the magnitude of the lopsided poten- lopsidedness is triggered during the interac- tial. tion, but it lasts for only ∼ 2 Gyr. Thus this mechanism cannot explain the high A1 seen in many isolated galaxies. The latter may be ex- plained due to an interaction with or accretion of a satellite with a much smaller mass, but this can also cause a vertical puffing up of the disk. This idea has to be explored systematically. In a recent paper, Mapelli et al. (2008) show that a fly-by encounter with a neighbouring galaxy UGC 1807 is the preferred mechanism for the origin of lopsidedness seen in NGC 891.

Load more