A&A 575, A93 (2015) AstronomyDOI: 10.1051/0004-6361/201323113 & × cESO 2015 Astrophysics
The effect of supernova rate on the magnetic field evolution in barred galaxies K.Kulpa-Dybeł1,N.Nowak1, K. Otmianowska-Mazur1, M. Hanasz2,H.Siejkowski3, and B. Kulesza-˙Zydzik1 1 Astronomical Observatory, Jagiellonian University, ul. Orla 171, 30-244 Krak, Poland e-mail: nala@oa.uj.edu.pl 2 Centre for Astronomy, Nicolaus Copernicus University, Faculty Physics, Astronomy and Informatics, Grudziadzka 5, 87100 Toru´ n, Poland 3 AGH University of Science and Technology, ACC Cyfronet AGH, ul. Nawojki 11, PO Box 386, 30-950 Krak 23, Poland Received 22 November 2013 / Accepted 5 November 2014 ABSTRACT Context. For the frst time, our magnetohydrodynamical numerical calculations provide results for a three-dimensional model of barred galaxies involving a cosmic-ray driven dynamo process that depends on star formation rates. Furthermore, we argue that the cosmic-ray driven dynamo can account for a number of magnetic features in barred galaxies, such as magnetic arms observed along the gaseous arms, magnetic arms in the inter-arm regions, polarized emission that is at the strongest in the central part of the galaxy, where the bar is situated, polarized emission that forms ridges coinciding with the dust lanes along the leading edges of the bar, as well as their very strong total radio intensity. Aims. Our numerical model probes what kind of physical processes could be responsible for the magnetic feld topology observed in barred galaxies (modes, etc.). We compare our modelled results directly with observations, constructing models of high-frequency (Faraday rotation-free) polarized radio emission maps out of the simulated magnetic feld and cosmic ray pattern in our modeled galaxy. We also take the effects of projection into account as well as the limited resolution. Methods. We applied global 3D numerical calculations of a cosmic-ray driven dynamo in barred galaxies with different physical input parameters such as the supernova (SN) rate. Results. Our simulation results lead to the modelled magnetic feld structure similar to the one observed on the radio maps of barred galaxies. Moreover, they cast new light on a number of properties in barred and spiral galaxies, such as fast exponential growth of the total magnetic energy to the present values. The quadrupole modes of magnetic feld are often identifed in barred galaxies, but the dipole modes (e.g., in NGC 4631) are found very seldom. In our simulations the quadrupole confguration dominates and the dipole confguration only appears once in the case of model S100, apparently as a consequence of the choice of the random number seed. Synthetic radio maps of our models display X-type structure similar to what is observed in real galaxies. Conclusions. We conclude that a cosmic-ray driven dynamo process in barred galaxies can amplify magnetic felds efficiently. The fastest rate of magnetic feld increase is 195 yr for a SN frequency of 1/50 yr−1.The obtained strength of magnetic feld corresponds to the observational values (a few μG in spiral arms). The polarization and rotation measure maps also agree with observations. We found the effect of shifting magnetic arms in 4 models (out of the sample of 5). Key words. dynamo – magnetohydrodynamics (MHD) – methods: numerical – galaxies: magnetic felds 1. Introduction Radio observations indicate that magnetic felds are important agents in the interstellar medium (ISM) within both spiral and barred galaxies (Beck 2012). The large-scale structure of mag-netic feld in such galaxies is generally represented by a super-position of modes with different azimuthal and vertical feld di-rections and symmetries. In the galactic disks, the axisymmetric spiral (ASS) mode is the strongest one (Ruzmaikin et al. 1988); however, the bi-symmetric spiral mode (BSS) or a mixture of both with a preponderance of either pattern is also observed (Beck et al. 1996; Krause 2004; Beck 2012). The vertical sym-metry can be even (quadrupole) or odd (bipolar). Rotation mea-sure observations show that the ASS magnetic feld is present in several galaxies, for example, in M31 (Sofue & Takano 1981), IC 342 (Sokoloff
et al. 1992), or the Large Magellanic Cloud (Gaensler et al. 2005). The BSS mode was unequivocally ob-served just in one galaxy, M81 (Sokoloff
et al. 1992). Many other observations indicate that the BSS mode can occur in the ASS mode, e.g., in M33 or NGC 2276 (Hummel & Beck 1995) or NGC 4631 (Hummel et al. 1991). According to the magnetohydrodynamical (MHD) dynamo theory, the galactic magnetic felds should have the even symmetry rather than the odd one, and the global magnetic felds of spherical objects (including stars and planets) are mostly dipolar, while those of fattened ob-jects (spiral galaxies) are quadrupolar (Beck et al. 1996; Krause 2004). Although a distinct ASS or BSS mode was detected in several galaxies, most of magnetic feld structures seem to be a superposition of the different dynamo modes (Beck 2012). This could be due to the many processes occurring in disks of galaxies, which may be correlated with the MHD dynamo process, for example, “cosmic-ray” driven one (see below for explanation). The main theoretical model of the dynamo process is the mean-feld dynamo theory (Ruzmaikin et al. 1988), which can explain magnetic felds in various environments, terrestrial, so-lar, or stellar. The theory describes the generation of regular large-scale magnetic feld in galaxies as an effect of the com-bined action of differential rotation Ω and helical turbulent Article published by EDP Sciences A93, page 1 of 10 motions of interstellar gas (the so-called α-effect). However, the classic kinematic dynamo gives a rather long timescale of mag-netic feld amplifcation for galaxies, about 109 yr, which is too long to account for strong magnetic felds in high-redshift galaxies beyond z = 1(Berezinski et al. 1990). A faster amplifcation is possible when the cosmic-ray (CR) driven dynamo (Parker 1992; Hanasz & Lesch 2003; Hanasz et al. 2006, 2009a,b; Kulpa-Dybeł et al. 2011) is applied, involving three principal effects: frst, the CR energy is continuously supplied by super-novae (SNe) remnants to the galactic disk, which became tur-bulent through buoyancy of magnetic feld due to CRs; second, the fast turbulent magnetic reconnection (Lazarian & Vishniac 1999; Kowal et al. 2009, 2012; Hanasz et al. 2004) allows small-scale loops of magnetic feld to merge into large-scale coherent structures in the limit of vanishing resistivity; and third, the differential rotation leads to generating a toroidal magnetic feld component from the poloidal one. However, every dynamo requires a seed feld. The origin of frst magnetic felds in the Universe is still one of the most challenging problems in modern astrophysics (e.g., Kulesza ˙ Zydzik et al. 2010). Two different views of the generation of seed felds are presently considered: one, the seed felds can be essentially of cosmological (primordial) origin, and second, the seed felds are generated in astrophysical processes at work in the ISM. A variety of cosmological processes occurring in the early Universe were proposed (magnetic felds could be generated in various phase transitions, such as the electroweak tran-sition (Quashnock et al. 1989), and the quark-hadron phase transition (Quashnock et al. 1989), or during the infation era (Turner & Widrow 1988)). These processes lead to creating very tiny magnetic felds of about 10−20−10−25 G(Widrow 2002; Subramanian 2010). Another possibility is generation of seed felds in astrophysical processes, such as the Biermann battery (Syrovatskii 1970; Xu et al. 2008). In this scenario, even if magnetic felds are initially absent in a star, a weak feld is produced via the Biermann mechanism owing to the different inertia of electrons and ions. The newly created tiny magnetic felds are then amplifed by a stellar dynamo. Next, a star can explode as an SN, releasing magnetized material that spreads into the ISM. Rees (1987) suggested that Crab-type SNe remnants have felds of the order of 10−4 G. He also estimated that at an early stage in galactic evolution there could have been as much as 106 randomly oriented SNe remnants similar to the Crab Nebula, giving rise to quite substantial seed felds of the order of 10−9 G. The re-cent simulations by Hanasz et al. (2009b)and Kulpa-Dybeł et al. (2011) have shown that small-scale magnetic felds of stellar ori-gin can be amplifed exponentially by the CR driven dynamo up to the observed values, which means that SNe explosions can produce a sufficiently strong seed feld for the CR dynamo action. Dubois & Teyssier (2010) did 3D MHD calculations of an isolated dwarf galaxy that had been formed self-consistently in-side a cooling halo. Their simulations took the infuence of supernova explosions onto ISM and the galactic magnetic feld into account. They found a linear growth of the total magnetic energy caused by differential rotation, as well as a strong magnetic wind into the halo contributing to the intergalactic magnetic feld (see also Siejkowski et al. 2010, 2011). The recent radio observations of magnetic felds in dwarf irregulars (Chy˙zy et al. 2011) do not indicate that such galaxies could effectively provide magnetic feld to the intergalactic medium, but dwarf galaxies with high starburst can provide such a feld to the intergalactic medium. The paper showing 2D numerical MHD simulations of a barred galaxy was published by Kim&Stone (2012), who considered the effect of gaseous fow to the galactic central black hole and fnd that the gas streams down much faster after including the magnetic feld in the calculations. They also confrm our process of shifting magnetic arms into the inter-arm region. Another model of fast galactic dynamo, the so-called supernova-driven dynamo, has been proposed by Gressel et al. (2008). They assumed that the thermal energy is injected into the galactic disk during a SN explosion, neglecting the CR com-ponent. This contrasts to the CR driven dynamo model, where the CR energy is introduced to the galactic disk during a SN ex-plosion, while the thermal energy is not taken into account. In the supernova-driven dynamo, the authors also applied the cool-ing and heating functions to refect the multi-phase nature of the ISM. Numerical simulations in the shearing-box approximation have shown that the supernova driven-dynamo causes an exponential amplifcation of magnetic feld and can explain a number of observational features of magnetic felds in galaxies. Booth et al. (2013) made a numerical model of CR driven gas motions for two galaxies, the Milky Way and the Small Magellanic Cloud, including only gas and CR with no magnetic feld, so their model involved just the isotropic diffusion of CR gas in the disk of modelled galaxies. The model yielded a rea-sonable velocity of winds of CR and gas in both the galaxies. The aim of the paper is to address the question of what physical processes could be responsible for magnetic feld confg-urations observed in barred galaxies. To answer the question we apply global 3D numerical simulations of a CR driven dynamo with different values of SN rate, while the other param-eters are fxed. We constructed polarized radio-emission maps and compare our results with observations. The description of our model is provided in Sect. 2, the re-sults in Sect. 3, the discussion in Sect. 4, and the conclusions in Sect. 5. 2. Model 2.1. Basic equations The computations of evolution of a barred galaxy are done by solving the isothermal non-ideal MHD equations of the form ∂ρ + ∇·(ρυ) = 0, (1) ∂t  ∂υ 1 B2 B ·∇B + (υ ·∇)υ = −∇ p + pcr ++ −∇Φ, (2) ∂t ρ 8π 4πρ ∂B = ∇×(υ ×B −η∇×B), ∂t (3) ∇·B = 0, (4) where υ is the large-scale velocity of gas, ρ is the gas density distribution, p is the gas pressure, pcr is the CR pressure, Φ is the gravitational potential, B is the magnetic induction, e is the thermal energy density and η is the turbulent magnetic diffusivity. An isothermal equation of state was assumed, that is p = ρcs2, where cs is the isothermal speed of sound. We investigated the problem of propagation of CR transport (Schlickeiser & Lerche 1985) in the ISM by solving the following diffusion-advection equation: ∂ecr + ∇(ecrυ) = ∇( Kˆ∇ecr) −pcr(∇·υ) + CRsource, (5) ∂t where ecr is the CR energy density, pcr = (γcr − 1)ecr is the CR pressure, K ˆthe diffusion tensor, υ the gas velocity A93, page 2 of 10 K. Kulpa-Dybeł et al.: The effect of supernova rate on the magnetic feld evolution in barred galaxies Table 1. Parameters adopted for the barred galaxy model. Parameter Meaning Value Units Md disk mass 4.0 × 1010 M ad length scale of the disk 0.6 kpc Mb bulge mass 1.5 × 1010 M ab length scale of the bulge 5.0 kpc Mh halo mass 1.2 × 1011 M ah length scale of the halo 15.0 kpc Mbar bar mass 1.5 × 1010 M abar length scale of bar major axis 6.0 kpc bbar length scale of bar minor axis 3.0 kpc cbar length scale of bar vertical axis 2.5 kpc Ωbar bar angular velocity 30.0 km s−1 kpc CR corotation radius 6.0 kpc IILR Inner Inner Lindblad Resonance 0.4 kpc OILR Outer Inner Lindblad Resonance 3.0 kpc OLR Outer Lindblad Resonance 8.5 kpc RBG galaxy radius 13.5 kpc and CRsource the source term for the CR energy. Moreover, we assume that 10% of 1051 erg of the SNe kinetic energy from their outburst is transformed into the CR energy and leave out the ther-mal energy, we also applying the value of adiabatic index for the CR gas as γcr = 14/9 and adding the CRs pressure to the to-tal pressure in the ISM gas motion equation as ∇pcr (Berezinski et al. 1990). It is also assumed that the CR gas diffuses anisotropically (Ryu et al. 2003). The CR diffusion tensor K is defned as Kij = K⊥δij + (K − K⊥)ninj, (6) where K⊥ and K are the parallel and perpendicular (with respect to the local magnetic feld direction) CR diffusion coefficients and ni = Bi/B are components of unit vectors tangent to the magnetic feld lines. 2.2. Galactic disk model We made similar kinematical and dynamical assumptions to those in Kulpa-Dybeł et al. (2011). The CR-driven dynamo mod-els of a barred galaxy were solved numerically in a 3D computational box with the size of Lx = Ly = 30 kpc and Lz = 7 kpc. The domain resolution is 300 × 300 × 75 grid zones in the x, y, and zdirections, respectively. We introduced the following units: time was given in Gyr, the mass, length, velocity, and magnetic feld are measured in 106 M , kpc, km s−1,and μG, respectively. The initial state of the modelled galactic disk was that of hydrostatic equilibrium. In our simulations, we assumed that the barred galaxy contains four components of gravitational po-tentials: a large and massive dark matter halo, a central bulge, a rotating stellar disk, and a bar. The halo and bulge components were represented by two Plummer spheres, the disk of stars was represented by an isochrone gravitational potential, and the bar was given as a prolate spheroid (see Table 1). We started our calculations without a bar potential, introducing it from the time t = 0.1Gyr to t = 0.4 Gyr, until it reached the mass Mbar assumed for the respective model. To keep the total mass of our model galaxy constant, we reduced the mass of the bulge, keeping Mbar(t) + Mb(t) = const. throughout the simulation. It was further assumed that the angular velocity of the bar’ rotation Ωbar = 30 kms−1 kpc−1, which determines the values of RILR = 0.4 kpc, RCR = 6 kpc, and ROLR = 8.5 kpc. (see Kulpa-Dybeł et al. 2011), as well as the speed of sound as cs = 5.12 kms−1 and gas density at the galactic disk centre ρ0 is equal to 1.0Hcm−3. At each time step, we added a small amount of mass in the galactic plane to compensate for the gas escaped through the outer domain boundaries. We also applied (e.g., Strong et al. 2007), the following values of the cos 3 × 1028 2 −1 mic ray diffusion: K = cms= 100 kpc2 Gyr−1 and 2 −1 K⊥ = 3 × 1026 cms= 1 kpc2 Gyr−1, and set the diffusion 2 −1 coefficient η as 3 × 1024 cms= 0.1 kpc2 Gyr−1 s, assuming that initially the CR pressure is equal to the gas pressure, pcr β = (7) pgas and that β is constant and equal to 1. Furthermore, we applied the outfow boundary conditions in the x, y,and zdirections. We performed fve different simulations of the barred galaxy and analysed its evolution for a set of different SN frequencies of fSN. As the SNe probability distribution and its rate, we use the (Schmid 1959) law in the form ΣSFR ∝ Σn (8) gas where ΣSFR is the surface density of the star formation, Σgas is the surface density of gas, and n = 1(Kennicutt 1998). The probability distribution of SN explosion in xy plane is computed according to the Schmidt-Kennicutt law. The probability distribution in z coordinate is described by the Gaussian distribution with the width of 40 corresponding to 1.14 kpc. Each SN rem-nant is represented by aspherically symmetric Gaussian profle with the radius rSN = 50 pc. In all models we assume that 10% of 1051 erg of the SN kinetic energy output is converted into the CR energy, while the thermal energy from SNe explosions was neglected. In some of the models weak and randomly oriented magnetic vector potentials were also injected during SNe explosions. Following Jackson (1999)(see also Hanasz et al. 2009b), the magnetic vector potential A of dipolar magnetic feld pro-duced by an individual SN explosion can be expressed as rsin θ A(r,φ,θ) = A0 3/2 eφ, (9) 2 rSN + r2 + 2rrSN sin θ where rSN is the radius of the SN remnant; r, θ,and φare spherical coordinates; and A0 is the amplitude. Parameter rSN denotes the half-width of the Gaussian profle describing the distribution A93, page 3 of 10 of injected CR energy. To obtain a model that is fully reproducible, a random distribution of SNe explosions is initialized using the same “seed”1. Following Ferrière (1998) the observed SN frequency for the Galaxy is 1/445 yr−1 for Type I and 1/52 yr−1 for Type II SNe. Taking both types of SNe into account, one explosion occurs every 47 years. In our simulations, we denoted the frequency of SN explosion fSN as equal to 25 when there is one SN in every 25 years. All parameters of our model are summarized in Table 1. 3. Results 3.1. General evolution for the reference model RM (S200) To show the essential dynamical and magnetic features of the simulated barred galaxy, we present below a short description of the time evolution of the reference model RM (S200, fSN = 1/200 yr−1), which was published in Kulpa et al. (2011). We chose this model because, in our opinion, it is the representative example that we are going to refer to (see Table 1). 3.1.1. Polarization maps In Fig. 1, we present the magnetic feld evolution in time as seen in the polarized synchrotron emission for the reference model RM using the following time steps: t = 0.5, 1.5, 2.5, 3.75, 4.75, 6.0 Gyr. The polarization maps show the distribution of polarization angle and polarized inten-sity superimposed onto the gas column density during 6.0 Gyr of galactic evolution. All face-on and edge-on polarization maps have been smoothed down to the resolution of 40 pc. At frst, the magnetic feld maxima correspond to the gas density enhancements, where SN explosions are located, which can be easily seen at t = 0.5Gyr (Fig. 1). At this time, there is a magnetic feld in the gaseous arms, as well as in the central part of the galaxy. Figure 1 shows that prominent spiral arms appear in early stages of the simulation. A plausible explanation of the magnetic arms growing towards in inter-arm regions is a local dynamo action. However at polarization maps (Fig. 1) magnetic arms start to de-tach from the gaseous spirals and drift into the inter-arm region. For instance, at the time steps t = 2.5 Gyr or 4.75 Gyr (Fig. 1), the magnetic spiral is located in the inter-arm region, while at t = 6.0Gyr (Fig. 1), it is less visible, because it merges with the inner edge of the adjacent arm. 3.2. Dependence on the SN frequency In Fig. 2 we present magnetic feld structures of the following models (from left to right): S25, S50, and S100, and in Fig. 3 for the S200 and S500 models. In the top panel we present the dis-tribution of toroidal magnetic feld in vertical (top) and horizon-tal (bottom) slices and the face-on (bottom) and edge-on (top) polarization maps of the presented models, in the bottom panels. In four experiments, S25, S50, S200, and S500, the magnetic feld in vicinity of the disk and the halo of the barred galaxy was of even (quadrupole-like) symmetry. An odd (dipole-type) con-fguration of magnetic feld with respect to the galactic plane ap-peared in all the models at an early stage of evolution. However, A seed is the argument that initializes a pseudo-random number generator, which then produces a succession of the random numbers used in the SNe explosion algorithm. only in the S100 model ( fSN = 1/100 yr−1) was such a confg-uration observed during the entire simulation time. The variable polarity of magnetic feld apparent in the horizontal slice show-ing model S100 is caused by the corrugated surface dividing the regions of positive and negative azimuthal magnetic felds. Forming magnetic arms could be observed in the case of S200 and S500 (see Fig. 3, left and right panels), as well as S50 and S100 (see Fig. 2, middle and right panels). The polariza
tion vectors in the edge-on maps revealed the so-called X-shaped structure in all the experiments (see Figs. 2 and 3). In the S25 model, with the highest SN activity ( fSN = 1/25 yr−1), the initial random toroidal magnetic feld component evolved towards well-ordered structures only in the bar region. At the time t = 4.5Gyr (Fig. 2, the left top panel), the large-scale magnetic feld was of even (quadrupole like) parity with respect to the disk mid-plane. Model S25 has weaker feld strength, which is presumably due to the high star formation rate applied in this model. The high SN rate increases the efficiency of the dynamo, but only up to a certain maximum value. Above this value the losses caused by galactic winds are greater than the rate of generation in the dynamo process. In fact, the am-plifcation of magnetic feld only occurs in the bar region. The lack of magnetic arms is also apparent in the polarization maps (Fig. 2 bottom right). Characteristic for this model is strong con-centration of gas in the galactic centre. Therefore star formation, CR energy density, and magnetic feld strongly contrast with the remaining parts of the disk. In Fig. 4 we show the face-on (bottom panel) and edge-on maps (top panel) of Faraday rotation measures RM for all the ex-periments S25, S50 , S100 , S200, and S500, at the time 4 Gyr. The Faraday rotation measure RM is proportional to the product of the thermal electron density ne and the line-of-sight com-ponent B|| of a regular magnetic feld, integrated over the path  length L:RM = 0.81 neB||dL. Negative RM (face-on maps) in bar can be observed in two models S25 (about –680 rad m−2) and S200 (about –440 rad m−2). In the S200 model, we can also see a positive RM about 30 rad m−2 in spiral arms. A negative RM means that the line-of-sight component of magnetic feld points away from us. In the models S50 (about 860 rad m−2), S100 (about 160 rad m−2), and S500 (about 35 rad m−2), we fnd a positive RM in the bar and a negative RM in the spiral arms. However, a different sequence of random numbers used second time in model S100 leads to quadrupole magnetic feld confgurations (see Fig. 4; Model S100 NEW). This showed that observed magnetic confgurations in our simulations depend on the pseudo random number sequence of SN coordinates and the orientation of magnetic dipoles. In Fig. 5, the evolutions of the total fux (bottom panel) of azimuthal magnetic feld component and of the total magnetic feld energy (top panel) for all the models are shown. The time evolution of magnetic energy and magnetic fux are shown in Fig. 5. Magnetic energy is summed over the whole computa
tional volume. Magnetic fux is calculated through to the vertical plane extending from the disk axis to the vertical edge of the domain. Both are normalized with respect to the values achieved at the end of the simulations. It is apparent that a very similar exponential growth takes place for all of them. The fastest amplifcation of total magnetic feld is observed for the model with an intermediate supernova rate, S50. For the S25 model, we got a bit longer amplifcation time. In both cases, the magnetic feld reaches its saturation state approximately at the time t ∼ 3.1−3.3 Gyr. The equipartition in the S100 and S200 models is achieved approximately 1 Gyr later than in the A93, page 4 of 10 K. Kulpa-Dybeł et al.: The effect of supernova rate on the magnetic feld evolution in barred galaxies Fig.
1.
Face-on and edge-on polarization maps at λ = 6.2 cm for selected times steps for the reference model RM (S200). Polarized intensity (contours) and polarization angles (dashes) are superimposed onto the column density plots. A93, page 5 of 10 Fig.
2.
Top panels: distribution of toroidal magnetic feld in vertical and horizontal slices through the disk centre for three models: S25 (left panel), S50 (middle panel), and S100 (right panel). Red represents regions with positive toroidal magnetic feld, blue with negative, while unmagnetized regions are white. To enhance weaker magnetic feld structures in the outer galactic disk (e.g., magnetic arms), the colour scale in the magnetic feld maps is saturated. Bottom panels: face-on and edge-on polarization maps for selected time steps for three models: S25 (left panel), S50 (middle panel), and S100 (right panel). Polarized intensity (contours) and polarization angles (dashes) are superimposed onto the column density plots. S25 and S50 models. For the S500 model, with the lowest SN rate, the magnetic feld energy attains its saturation value at time t ∼ 5.5 Gyr. The ultimate saturation levels of magnetic fux are lower than in the case of total magnetic energy. The e-folding times of magnetic fux growth deduced from the righthand panel of Fig. 5 are respectively 230 Myr for model S25, 194 Myr for model S50 (the fastest amplifcation), 326 Myr for model S100, 300 Myr for model S200, and 360 Myr for model S500 (see Table 2). It can be noticed that by varying the frequency of SNe explosions, one does not get any signifcantly different re-sults, so we found that after 1 Gyr, the supplied dipole magnetic feld from the supernova remnants was negligible in compari-son with the feld generated by the dynamo. This fact could ac-count for the narrow interval of the observed values of magnetic feld intensity in morphologically different galaxies. In fact, in all the simulations, two phases of increasing magnetic fux can be distinguished. The frst one starts at the beginning of calculations and lasts until time t ∼ 2.0 Gyr (bottom panel in Fig. 5). During that period, the magnetic fux reverses its sign, and its absolute value varies randomly around the exponential curve. These variations are associated with transformation of magnetic feld structures, that is in all the models during this time, the initial random toroidal magnetic feld component evolves, forming large-scale magnetic structures with odd symmetry. On the other hand, after time t ∼ 2.0 Gyr the total azimuthal fux stops to reverse. Then the toroidal magnetic feld becomes almost regular and reversals, if any, are very weak (see top right and middle panels in Fig. 2). The only exception is the S100 model, for which variations in magnetic fux, as well as reversals of toroidal magnetic feld component, are visible throughout the entire sim-ulation time. These results show that the magnetic feld ampli-fcation in barred galaxies is relatively insensitive to the value of SN rate, which means that the CR-driven dynamo process is efficient for a wide range of SN activity. In Table 2, the maximum magnetic feld strengths in the mag-netic arms (taken at the coordinate points belonging to the mag-netic arm regions) for all the models are presented. The high-est values of magnetic feld were reached for the models with weak SN activity. The maximum magnetic feld in magnetic arms (9.5 μG) was obtained in the S200 model. Similar values were observed for the models S100 (5.9 μG) and S500 (8.6 μG). For the models with strong SN activity, the maximum feld in magnetic arms was weaker, about 2.1 μG in model S50 or almost none (4.7 × 10−2 μG) in the case of model S25. A93, page 6 of 10 K. Kulpa-Dybeł et al.: The effect of supernova rate on the magnetic feld evolution in barred galaxies For model S25, with the strongest magnetic feld within the bar, the lowest value of mean magnetic feld became averaged over all coordinate points belonging to the bar region was ob-tained Bmean = 3.7 μG(seeTable 2). This is quite possible for a very low magnetic feld (of the order of 10−2 μG) in the outer part of the disk, located outside the corotation radius. On the other hand, for the S200 model, the mean magnetic feld had the highest value Bmean = 10.2 μG. In the S200 model the value of the magnetic feld in the spiral structure area averaged in all coordinate points belonging to the spiral arms (Barms )was ϕ about 9.5 μG. For models S50, S100, and S500, the values of mean magnetic feld were very similar ∼7 μG. The averaged mass outfow rate grew with increasing SN frequency (Table 2). The mass outfow through the upper and lower boundaries was calculated at each time step of calculations, and then the mass fux fz = ρvz was integrated over the surface area at the upper and lower domain boundaries for all the steps. Actually, in the S25 model with the highest SN rate, the overall rate of the mass outfow was 4.7 M /yr−1, while for the S500 model with the lowest SN activity, the overall rate of mass outfows was just 0.6 M yr−1. 3.2.1. Pitch angles To compare pitch angles of magnetic and gaseous arms, the results are shown in the coordinate system of azimuthal angle and ln(r)(r being the galactocentric distance). In this case, the logarithmic spiral is represented by a straight line inclined by a relevant pitch angle. In Fig. 6, the gas density (integrated along Fig.
3.
Top panels: distribution of toroidal magnetic feld in vertical and horizontal slices through the disk centre for models: S200 (left panel)and S500 (right panel). Red rep-resents regions with positive toroidal magnetic feld, blue with negative, while unmagnetized regions are white. To en-hance weaker magnetic feld structures in the outer galactic disk (e.g., magnetic arms), the colour scale in the magnetic feld maps is saturated. Bottom panels: face-on and edge-on po-larization maps for the selected time steps for two models: S200 and S500. Polarized intensity (contours) and polarization an-gles (dashes) are superimposed onto the column density plots. the line of sight) with overlaid contours of polarized intensity and B-vectors for four time steps (t = 0.75, 1.50, 2.25, 5.5Gyr) are shown. At the beginning at 0.75 Gyr, we can see that polar-ized structures form along the inner edges of spiral arms ob-served in actual galaxies that typically correspond to dust lanes. Later on, we observe an obvious drift of magnetic feld arms into the inter-arm region (between r = 6.9 kpc and r = 9.5 kpc). Initially we fnd that (t = 0.75 Gyr, Fig. 6) magnetic and gaseous arms possess similar pitch angles of ∼−13◦. However, at later times magnetic structures move to the inter-arm region and signifcantly decrease their pitch angles. Moreover, the estimated mean pitch angle (averaged over azimuthal angle and radius in the galaxy’s plane) changes only slightly during the evolution of the galaxy, ranging between −7◦ and −8◦ of the slope arms. 4. Discussion We present a series of simulations of CR-driven dynamo in barred galaxies for a wide range of SN rates. In most of our mod-els, the regular magnetic feld is axisymmetric (ASS topology, quadrupole topology). A distinct ASS mode is also observed in the actual galaxies, M31 (Sofue & Takano 1981) and IC 342 (Krause et al. 1989). The ASS symmetry in the presented numer-ical models is not surprising, since the axisymmetric mode can be excited most readily by a mean-feld dynamo process (Krause 2003). This shows that observed magnetic confgurations in our simulations depend on the pseudo-random number sequence de-termining SN coordinates and orientation of magnetic dipoles. A93, page 7 of 10 MODEL S200 MODEL S500 MODEL S100 NEW Fig.
4.
Faraday rotation maps for selected times steps for fve models: S25 (top left panel), S50 (top middle panel), S100 (top right panel), S200 (bottom left panel), S500 (bottom middle panel), and S100 NEW (bottom right panel) at the time 4.5 Gyr. The red area denotes the positive RM and blue area denotes the negative RM. In the S25, S50, S200, and S500 models, the toroidal mag-netic feld component has the same direction above and be-low the galactic disk. This confguration corresponds to the even (quadrupole-type) symmetry of magnetic felds in galaxies. This picture is supported by theoretical studies (e.g., Ruzmaikin et al. 1988), by observational evidence (e.g., Beck 2009; Heesen et al. 2009), as well as by a number of numerical investigations (e.g., Brandenburg et al. 1993). The quadrupole-like sym-metry was also obtained by Hanasz et al. (2009b), who studied CR driven dynamos in the case of axisymmetric galactic gravitational potential. The results presented in this work confrm that a CR-driven dynamo can produce odd dipolar symmetries of magnetic felds in barred galaxies. In the case of S100 model, the toroidal mag-netic feld component has a different direction above and below the disk plane, which indicates an odd (dipole-type) confguration of magnetic feld with respect to the galactic plane. The odd symmetry of the magnetic feld is not the preferred confguration in the disk geometry (Moss et al. 2010), while it has been found in some galaxies (e.g., in NGC 4631, Krause 2003). Magnetic arms between the gaseous spiral and the bar have been observed in most of the barred galaxy simulations. The drift of magnetic arms is caused by the same mechanism as proposed by Otmianowska-Mazur et al. (2002), Kulesza-˙ Zydzik et al. (2009), Kulpa-Dybeł et al. (2010, 2011), and Kim & Stone (2012). It could be explained as follows initially the gravitational potential of the bar rotates faster than the gas outside the coro-tation radius, generating spiral arms. The magnetic feld present in the galactic disk is advected with the gas velocity. In particu-lar, the magnetic feld produced by disturbances within the arms drifts with the gas velocity and, after some time runs into the next arm (see Kulesza-Zydzik et al. 2010, and references therein). Only in one model, S25, can no magnetic arms be discerned either in the gaseous arms or in the inter-arm area (right top and bottom panels in Fig. 2). The lack of magnetic arms can be traced back to the very high star formation rate ( fSN = 1/25 yr−1)applied in this model. If SNe explosions generate a random mag-netic feld in a continuous and violent manner, the outfow of the random feld component into the z direction advects the mag-netic feld in the outer part of the galaxy, so it cannot be trans-formed into a regular feld. In that case the polarized magnetic feld only appears in the bar region. The results obtained for the S25 model resemble the radio polarization structure observed in barred galaxies, for example in NGC 986 (Beck et al. 2002). In A93, page 8 of 10 K. Kulpa-Dybeł et al.: The effect of supernova rate on the magnetic feld evolution in barred galaxies Fig.
5.
Evolution of total magnetic energy EB (top panel) and of mean azimuthal fux Bφ (bottom panel) for different values of SN frequency fSN. Both quantities are normalized with respect to the saturation value. Table 2. Overview of the obtained parameters for the barred galaxy models. max Barms Model fSN τ Mlost ϕ Bmean [yr−1] [Myr] [M yr−1] [ μG] [ μG] S25 1/25230 4.74.7 × 10−23.7 S50 1/50194 3.22.16.4 S100 1/100 326 1.75.97.1 S200 1/200 300 1.19.5 10.2 S500 1/500 360 0.68.67.9 Notes. The columns show: the model name, the SN frequency fSN, e-folding time τ, the rate of the mass outfow Mlost, the maximum mag-netic feld in the galactic arms max Barms ϕ , and the mean od the total magnetic feld (regula and turbulent) Bmean (saturation state). this barred galaxy, the polarized emission was only found in the inner bar. The mass outfow rate by galactic winds in the barred galaxy simulations ranged from 0.6 to 4.7 M yr−1. The overall rate of mass outfow grew with increasing SN activity in the galactic disk. The galactic-scale outfows (galactic winds) from galactic disks are common phenomena that can be ob-served both in the nearby galaxies (Tlmann et al. 2006)and in the high-redshift Universe (Tapken et al. 2007). From ob-servations, one of the main sources of galactic winds are SNe explosions (e.g., Matsubayashi et al. 2009). According to the review of galactic winds by Bland-Hawthorn et al. (2007), the mass outfow rate in other observed spiral galaxies ranges be-tween 0.1 and 10 M yr−1. The authors fnd that the outfow rate increased with increasing star formation rate. The results presented in this paper support this statement and ft the observed values perfectly. In the barred galaxy simulations, there is apparent dependence of the magnetic feld growth rate on the SN rate (Beck 2012). The overall e-folding times presented in this work are comparable to the values obtained in other numerical experiments of CR driven dynamo. Hanasz et al. (2006, 2009a) performed shearing-box simulations of a CR driven dynamo and fnd that the e-folding timescale in normal spiral galaxies is about 150−250 Myr. Very similar results are presented by Gresseletal. (2008) who made galactic dynamo simulations in the box model, taking the turbulent ISM driven by multiple clustered SNe explosions into account. In the absence of CRs, only a 15-fold growth of the magnetic energy and a few times increase in azimuthal fux was observed (Kulesza-˙ Zydzik et al. 2009, Fig. 2) 5. Conclusions The following conclusions can be drawn from our investigations: 1. The polarized radio emission found in the face-on synthetic polarization maps indicates that the CR driven dynamo can be responsible for various magnetic structures discerned in actual observations of barred galaxies, such as the polar-ized emission that is at its strongest in the central part of the galaxy where the bar is present, and the polarized emission from the ridges marks the dust lanes along the leading edges of the bar. A93, page 9 of 10 2. In the case of simulated barred galaxies, a drift of magnetic arms can be observed during the entire simulation time in most of the experiments. 3. The synthetic edge-on radio maps of polarized emission show that the CR driven dynamo can reproduce the vertical magnetic feld structures observed in edge-on galaxies (so-called X-type). 4. In barred galaxies, the large-scale magnetic feld grows ex-ponentially on a timescale comparable to what is obtained for normal spirals. The fastest amplifcation of magnetic felds was obtained for the S50 model with a SN frequency of 1/50 yr−1 and with the corresponding e-folding time of 194 Myr. 5. For simulated barred galaxies, there is no signifcant de-pendence on the SN rate. We found that after about 1 Gyr from the beginning of evolution of the modelled galaxies, the total magnetic energy did not depend on how much of magnetic feld energy from the supernovae remnants we had introduced. 6. According to theoretical studies, the quadrupole-like sym-metry of magnetic feld is preferred in numerical studies of the galactic dynamo. The even symmetry of magnetic feld with respect to the mid-plane was found in most of barred galaxy simulations. Just one model involved the odd symmetry of magnetic feld. Our simulations of barred galaxies showed that the CR driven dynamo is able to efficiently amplify magnetic energy, as well as magnetic fux. 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