D O I: 10.1051/0004-6361/201220367
© E S O 2014
Astrophysics
3D global simulations of a cosmic-ray-driven dynamo in dwarf galaxies
H. Siejkowski1,2, K. Otmianowska-Mazur2, M. Soida2, D. J. Bomans3,4, and M. Hanasz5
1 AGH University of Science and Technology, ACC Cyfronet AGH, ul. Nawojki 11, PO Box 386, 30-950 Kraków 23, Poland e-mail: h .s ie jk o w s k i@ c y f r o n e t.p l
2 Astronomical Observatory of the Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland
3 Astronomical Institute of Ruhr-University Bochum, Univeristatsstr. 150/NA7, 44780 Bochum, Germany
4 Ruhr-University Bochum Research Department: Plasmas with Complex Interactions, Univeristatsstr. 150, 44780 Bochum, Germany 5 Centre for Astronomy, Nicolaus Copernicus University, Faculty of Physics, Astronomy and Informatics, Grudziadzka 5,
87100 Torun, Poland
Received 11 September 2012 / Accepted 29 November 2013
ABSTRACT
Context. Star-forming dwarf galaxies can be seen as the local proxies of the high-redshift building blocks of more massive galaxies according to the current paradigm of the hierarchical galaxy formation. They are low-mass objects, and therefore their rotation speed is very low. Several galaxies are observed to show quite strong magnetic fields. These cases of strong ordered magnetic fields seem to correlate with a high, but not extremely high, star formation rate.
Aims. We investigate whether these magnetic fields could be generated by the cosmic-ray-driven dynamo. The environment of a dwarf galaxy is unfavourable for the large-scale dynamo action because of the very slow rotation that is required to create the regular component of the magnetic field.
Methods. We built a 3D global model of a dwarf galaxy that consists of two gravitational components: the stars and the dark-matter halo described by the purely phenomenological profile proposed previously. We solved a system of magnetohydrodynamic equations that include an additional cosmic-ray component described by the fluid approximation.
Results. We found that the cosmic-ray-driven dynamo can amplify the magnetic field with an exponential growth rate. The e-folding time is correlated with the initial rotation speed. The final mean value of the azimuthal flux for our models is on the order of few uG and the system reaches its equipartition level. The results indicate that the cosmic-ray-driven dynamo is a process that can explain the magnetic fields in dwarf galaxies.
Key words. magnetohydrodynamics (MHD) - dynamo - galaxies: magnetic fields - galaxies: dwarf - methods: numerical
1. Introduction
S tar-form ing d w arf galaxies are sm aller, fainter, and less m a s
sive than their spiral counterparts, b u t they are the m o st n um er
ous population in the U niverse (B lanton e t al. 2002) . T he m a g n etic fields in dw arf galaxies m ay p lay a very im portant role.
F irst, the observations show that the m agnetic field is an im po rtan t source o f p ressure for the interstellar m edium (B oulares
& C ox 1990) . It is often assum ed that th e interstellar m edium (ISM ) in galaxies is in equipartition w ith the alm o st equally d is
tributed energy in m agnetic fields, cosm ic rays, and turbulence.
S econd, these objects are less m assive, hence the gravitational p o tential w ell is shallow er an d this facilitates the escape o f the gas from the galaxy in the form o f galactic w inds (M ac L ow &
F errara 1999) . This w ind can also drag th e m agnetic field out o f the disk into the intergalactic m edium (IG M ) since the m agnetic field is frozen into the outflow ing plasm a. P ossible m ag n etisa
tion o f the IG M via the m agnetised w in d has been studied by B ertone et al. (2006) and fo r d w arf galaxies by K ronberg et al.
( 1999) and S cannapieco & B ruggen (2010) . L ocal sim ulations o f the cosm ic-ray dynam o p rocess in d w arf galaxies (Siejkow ski et al. 2010) show significant loss o f the m agnetic field from the dom ain and it depends on th e supernova ra te (SN R). Studies o f d w arf galaxy form ation b y D ubois & Teyssier (2010) also im plied IG M seeding via galactic w inds. A dditionally, there are
studies on galactic w inds driven by cosm ic rays by B ooth et al.
(2013) and H anasz e t al. (2013) .
S trong m agnetic fields w ere discovered in a b rig h t dw arf irregular galaxy N G C 4449 w ith a total field strength o f ab o u t 12 u G and a regular com ponent o f up to 8 u G (K lein e t al. 1996; C hyzy et al. 2000) . K epley et al. (2010) reported sim ilar m agnetic fields in N G C 1569. T he radio observations o f these tw o galaxies show som e large-scale m agnetic fields w ith a sign o f a spiral pattern, b u t no optical counterparts. T he ro ta
tion m easure m aps im ply th at th e m agnetic field is alm ost p ara l
lel to the disk plane. In o ther d w arf objects such as N G C 6822, IC 10 (C hyzy et al. 2003) an d the L arge M agellanic C loud (K lein e t al. 1989; G aensler e t al. 2005) the observed m agnetic fields are w eaker, reaching a value about 5 - 7 u G . It is w orth noting that these galaxies, especially N G C 1569 and N G C 4449, are under strong influence o f infalling gas from the surroundings, w hich have a significant im pact on the m agnetic-field structure.
O bservations o f the above m entioned objects b rought som e insight into th e dynam o process in d w arf galaxies, b u t all these objects are optically b right and show ed disturbed kinem atics.
T herefore the sam ple m ight be influenced b y strong selection ef
fects. C hyzy e t al. (2011) com pleted a sam ple o f dw arf and sm all irregular galaxies from th e L ocal G roup. T hey found th at the star form ation ra te (SFR) regulates the strength o f m agnetic fields, b ecause the SNR, w hich is p roportional to the SFR, contributes
Article published by EDP Sciences A136, page 1 of 6
to drive th e turbulence in the ISM . T hese results are very sim ilar to th e conclusions o f our previous theoretical study (Siejkow ski et al. 2010) o f the cosm ic-ray-driven dynam o in th e m edium o f irregular galaxies. C hyży et al. (2011) have also investigated a p ossible relation betw een the m axim um vrot an d the m agnetic- field strength. F o r slow ro tation (< 4 0 k m s -1) all galaxies have w eak fields, below 4 p G . W ith increasing m axim um rotation speed in the follow ing objects th e observed m agnetic fields are stronger. H owever, som e objects, such as N G C 4449, show very strong m agnetic fields, but their ro tation is rath er slow. T he re lation o f the m agnetic field versus the m axim um rotation speed is p robably d istorted by the fact th at objects w ith strong m a g n etic fields are undergoing heavy star form ation. T he contribu
tion to th e turbulent energy b y supernovae explosions can cause strong disturbances in th e velocity pattern, therefore estim ating the m axim um ro tation speed and assigning a clear rotation curve is difficult.
It is believed th at the m agnetic dynam o is responsible for the strength and structure o f m agnetic fields in galaxies (B eck 2009) . O ne o f the rec en t dynam o m odels is driven b y therm al energy output from supernovae explosions, described b y G ressel e t al.
(2 008a,b ) . T hese authors fo u n d that the e-folding tim e o f the am plification m echanism is ab o u t Te = 250 M y r and is d epen
den t on the rotation speed. A nother m odel suggested by Parker ( 1992) relies on the buoyancy instability o f in terstellar m edium filled w ith m agnetic fields and cosm ic rays (P arker 1965) . The cosm ic-ray-driven dynam o w as constructed for the first tim e w ithin the fram ew ork o f a local shearing box m odel b y H anasż et al. (2004) . A n extensive p aram eter study o f this local m odel w as p resented in H anasz e t al. (2009a) . T he e-folding tim e-scale o f the m agnetic-field am plification by the cosm ic-ray-driven d y nam o is generally com parable to th e galactic ro tation p erio d and can b e as short as 140 M y r (H anasz et al. 2006) . S iejkow ski et al.
(2010) investigated th e cosm ic-ray driven dynam o action in low- m ass objects, such as dw arf- and interm ediate-m ass irregular galaxies. This study led to the follow ing results: th e grow th rate o f th e m agnetic field is strongly dependent on the rotation speed, b u t fo r objects w ith vrot > 40 km s-1 th e saturation o f the dynam o is rea ch ed after the sam e perio d o f tim e. T he e-folding tim e is also d ependent on the SN R and the tim e o f q uiescent state (no supernovae activity). T he larger th e SNR , the faster the grow th rate, b u t excessive supernova activity can suppress the dynam o action. H anasz e t al. (2009b) dem onstrated cosm ic-ray-driven dynam o action v ia global disk spiral galaxies, and K ulpa-D ybeł et al. (2011) confirm ed the resu lt for barred galaxies. T hey found th at th e azim uthal m agnetic flux grows on a tim e-scale o f about 270 Myr.
2. Numerical model and setup
To sim ulate the dw arf galaxy m odel a num erical code called Go d u n o v-M H D was em ployed (K ow al e t al. 2009) . It solves the system o f ideal m agnetohydrodynam ic (M H D ) equations in a conservative form in 3D space. T he key elem ents and assu m p tions o f th e cosm ic-ray-driven dynam o global galactic m odel w ere adopted from H anasz e t al. (2009b) . B elow w e describe our choice o f sim ulation param eters. A n isotherm al equation o f state w as assum ed, th at is p = pci2, w here cs is the isotherm al speed o f sound set to 7 k m s-1 , w hich corresponds to a gas tem perature o f 6000 K. W e assum ed the m agnetic diffusivity n to be constant an d equal to 0.1 k p c2 G yr-1 = 3 x 1025 cm 2 s-1 . The investigation by H anasz e t al. (2009a) show ed th at this value is optim al for th e grow th o f the m agnetic field in th e buoyancy- driven dynam o.
T he cosm ic ray (CR) com ponent is d escribed by the diffusion-advection transport equation in term s o f fluid approx
im ation follow ing Schlickeiser & L erch e ( 1985) and H anasz &
L esch (2003) . W e related th e C R pressure to th e C R energy d en sity ec r v ia the adiabatic C R index, th at is pc r = (yc r - 1)ecr
an d yc r = 1 4 /9 adopted from R yu et al. (2003) . F ollow ing G iacalone & Jokipii ( 1999) , w e assum ed th at the diffusion o f cosm ic rays is anisotropic w ith resp ect to the direction o f the m agnetic field. T he typical values o f the diffusion coefficient fo u n d by m odelling C R d ata (see e.g. Strong et al. 2007) are (3 + 5) x 102 8 cm2 s-1. T he applied value o f the p erpendicular CR diffusion coefficient is K ± = 1 k p c2 G y r-1 = 3 x 102 6 cm2 s-1
an d th e p arallel one is Ky = 10 k p c2 M y r-1 = 3 x 1027 cm2 s-1. T he p arallel diffusion coefficient is 10% o f the realistic value b e cause th e tim e-step o f the ex plicit diffusion algorithm becom es prohibitively short w hen the diffusion coefficient is too high.
T he effect o f the reduced C R diffusion coefficients was inves
tigated b y H anasz et al. (2 009a), show ing th at th e m agnetic-field grow th only slightly depends on the Ky value, b u t the key fac
to r in the cosm ic-ray-driven dynam o is the anisotropy o f the diffusion.
A single supernova explosion w as m od elled by a 3D G aussian distribution o f cosm ic-ray energy inp u t and equals 10% o f th e canonical kin etic energy output o f the super
n ova explosion, th at is 1051 erg. In the initial p erio d in t e (100 M yr, 400 M yr), every one in ten explosions injects a ra n dom ly oriented dipole m agnetic field into the ISM in addition to th e C R energy input. T he injection o f the m agnetic field is only to seed the dynam o action through a ran d o m field a t the b egin
n ing o f the sim ulation. W e stopped th e injection b ecause (1) it allow ed us to study the efficiency o f the p ure cosm ic-ray-driven dynam o w hile the injected m agnetic field w as only the seed field an d (2) after several hundred M y r the seeding becom es insignif
ic an t w ith resp ect to th e existing field.
T he position o f each supernova explosion w as chosen ra n dom ly w ith resp ect to the local gas density, th at is p3 / 2. This follow s the sim ple self-gravitational p icture draw n by S chm idt ( 1959) and K ennicutt ( 1989), w here the large-scale star fo rm a
tion rate volum e density scales w ith p3 / 2. T he n um ber o f su
pernovae is given by th e supernova explosion frequency over th e d isk area. In ou r m odel its value w as set to fS N = 3 x 103 k p c -2 G y r-1 an d it w as constant during w hole sim ulation tim e. This value corresponds roughly to th e density o f the star form ation rate (2S F R ) equal to 10-3 M 0 y r-1 k p c -2 and is a ty p ically fo u n d in non-starbursting d w arf galaxies (see e.g. C hyzy e t a l. 2011) .
T he d w arf galaxy p otential w ell is given by tw o com ponents:
a dark-m atter (D M ) halo and a thin stellar disk. This type o f galaxy has n o bulge (G overnato e t al. 2010) , w hich is presen t in m ore m assive disk galaxies. In ou r m o d el the stars are d is
tributed in an infinitesim ally thin K uzm in disk follow ing p revi
ous num erical w orks on d w arf galaxies (M arcolini e t al. 2 0 0 3 , 2004) . F or th e D M halo w e used the purely phenom enological profile p roposed by B urkert ( 1995) . Its gravitational p otential is described by
0D M(r) = - n G p o Ą {n - 2(1 + x -1)a rc ta n x
+2(1 + x -1) ln ( 1 + x) - ( 1 - x -1) ln ( 1 + x2)} , (1)
w here G is the gravitational constant, p0 is the central density, r0
is the core radius, r is the distance to th e centre, and x = r / r0.
Table 2. Comparison o f the simulation results with observations.
Table 1. Parameters o f the models v40 and v70.
Param eter v40 v70 U nit
M ass o f stars 1.0 6.0
Oso
P0 21.5 15.0 106 M0 kpc-3
r
0 1.4 2.4 kpcPg 29.5 29.5 106 M0 kpc-3
Rc 1.2 3.6 kpc
,.max 40 70
km s-1
M odel nmax v , [km s 1]
ESFR [ M0 yr-1 kpc-2]
B [pG]
v40 40 10- 3 1.0
v70 70 10-3 8.0
O bject
IC 1613 37 3.7 x 10-
4
2.8 ± 0.7NGC 4449 40 1.7 x 10-
2
9.3 ± 2.0NGC 1569 42 1.5 x 10-
1
14.0 ± 3.0 IC 10 47 5.2 x 10-2
9.7 ± 2.0 NGC 6822 60 6.0 x 10-3
4.0 ± 1.0LMC 72 4.0 x 10-
3
4.3 ± 1.0T he gas distribution o f a d w arf galaxy w as set in hydrostatic equilibrium in its in itial state. T he gas density distribution in equatorial p lan e was assum ed in the follow ing form :
(2)
w here pg and RC are the central gas density and core rad iu s, re
spectively. To find the global gas distribution w e used the p o te n tial m eth o d described in W ang et al. (2010) . T he d etailed p ara m eters o f the gravitational potentials are show n in Table 1 and its values w ere m ostly taken from M arcolini et al. (2003) w ith only slight m odifications. F ro m th e gas distribution th e C R co m p o nent distribution w as found, assum ing that they are in pressure equilibrium . W e assum ed B = 0 a t t = 0.
T he d w arf g alaxy m odel w as sim ulated in 3D C artesian d o m ain o f size 14 x 14 x 7 k p c in x, y, z coordinates, resp e c
tively. T he cell size w as 50 p c in each direction. U p p er and low er boundary conditions w ere set to outflow, and w e enforced the gas to follow the p rescribed ro tation curve in th e horizontal dom ain boundaries.
3. Results and discussion
T he m odels p resented in Table 1 correspond to the different m a x im um rotation speeds. W e set up m odels w ith = 4 0 k m s -1 and 70 k m s-1 . T he m odel v40 corresponds to objects like N G C 1569 o r IC 10, w hile the v70 m o d el m im ics the L arge M agellanic C loud o r N G C 6822 (e.g. C hyży e t al. 2011) . The rotation curves o f these m odels are show n in Fig. 1.
T he evolution o f th e total m agnetic energy and th e m agnetic flux are show n in Fig. 2 . In both m odels the m agnetic-field en ergy and the m agnetic flux are grow ing exponentially in tim e.
T he initial peak, visible up to t = 400 M yr, is cau sed by the m agnetic field injected into the system v ia the m agnetised su
pernovae. L ater th e m agnetic field injection w as stopped, and the m agnetic grow th was only caused by the operation o f the dynam o.
A fter the initial injection o f the m agnetic field the system experiences a p eriod o f stabilization an d the m agnetic-field en ergy decreases by ab o u t h a lf an o rder o f m agnitude. A fter this, at about t = 1 Gyr, the m agnetic field starts to be am plified. In the evolution o f the m agnetic flux w e see a co nstant grow th, w ithout
N otes. The last colum n shows the value of mean magnetic field in the disk (B) for the models; for real objects the total magnetic field (Btot) is given. All the observational values are taken from Chyży et al. (2011).
any stabilization periods. This is b ecause the injected m agnetic field is random and is ordered b y the global rotation. This also suggests that during the stabilization perio d the random ly o ri
en ted m agnetic field is expelled and/or d issipated by m agnetic diffusivity b eyond the sim ulation dom ain, w hile the ordered a z im uthal m agnetic flux is retained.
W hen the d ynam o begins to operate effectively, the m agnetic field and its azim uthal part are exponentially am plified in tim e.
T he grow th rate o f th e azim uthal m agnetic flux, m easured by th e e-folding tim e, is different for each o f th e m odels and equals 1 0 2 3 M y r for v40 and 458 M y r for v70. F or m odel v70 the equipartition level is rea ch ed at about t = 5 Gyr. A round that tim e som e peaks appear in the evolution o f the m agnetic-field energy, b u t w hen the equipartition level is reached - they b e com e dam ped. In m odel v40 the equipartition level is reached at t = 10 Gyr, but th e transition is sm oother than in the previous case. In both cases the saturation o f the grow th o f B^ occurs at th e sam e tim e as for the m agnetic energy.
T he final m ean value o f the m agnetic field for m odel v40 is B (t = 10 G yr) = 1.0 p G and for m odel v70 it is B (t = 5 G yr) = 8.0 p G . T he results are com pared w ith the m agnetic field found in observations o f d w arf galaxies in Table 2 . T he m o d el v70 can b e com pared w ith N G C 6822 an d th e L arge M agellanic Cloud, w hich rotate as fast as 6 0 - 7 0 k m s-1 , an d w hose 2 S F R is o f the o rder o f 10-3 M 0 y r-1 k p c -2 . In both cases the observed m a g n etic field is abo u t 4 p G . T he m odel v40 w ith resp ect to its ro ta
tional velocity can b e com pared w ith galaxies such as IC 1613, IC 10, N G C 4449, and N G C 1569. T he observed m agnetic field in the first o bject is abo u t 2.8 p G , w hich agrees w ell w ith our sim ulations. In other objects the m agnetic field is m uch higher, starting from 9 p G up to even 14 p G . However, these objects have a m uch h igher SFR. In o ur m odelling the applied supernova frequency is equivalent to 2S F R = 10-3 M 0 y r-1 k p c -2 , w hile in these galaxies the observed values are given in Table 2 . The 2 S F R value is com parable only for IC 1613, b u t in other cases th e observed values are m uch higher. This leads to the conclu
sion th at th e enhanced SFR can increase the m agnetic field in the g alaxy disk, but to state it m ore clearly, m o re n um erical investi
gations need to b e m ade.
In Fig. 3 the slices through the dom ain o f m odel v70 are show n for selected tim e-steps. T he evolution o f B^ show s the initially random ly oriented m agnetic field, injected through the m ag n etised supernova explosions, is efficiently regularised. In th e xy p lan e at t = 0.15 G yr random ly p o sitioned spots appear
A136, page 3 of 6 p(R , z = 0) = p ---
2
,[1 + (R /Rc)
2
]2
Fig. 2. Left panel: magnetic-field energy evolution for models from Table 1. R ight panel: total azimuthal magnetic flux evolution. The plotted value is the absolute value of because it changes its sign at the beginning of the simulation and therefore it is difficult to show it in a log-plot.
Fig. 3. Evolution o f the m agnetic held. Upper pa n els’, evolution of the B,p com ponent (expressed in pG ) in edge-on and face-on view of the m odel v70 for selected time-steps: 0.15. 0.75. and 5.00 Gyr. Low er p a n els: energy density of the cosm ic rays and the norm alised vectors o f the magnetic held at the corresponding time-steps.
o f a p ositive (blue) and negative (red) azim uthal m agnetic field.
In the xz cu t a sim ilar pattern is revealed but only very close to the disk m idplane, th at is there are n o such structures in the halo.
T he differential rotation shears th e radially aligned structures and form s a spiral pattern o f an oppositely d irected azim uthal m agnetic field, w hich are clearly visible at t = 0.75 Gyr. In the disk a t th e end o f the sim ulation there is only negatively oriented m agnetic azim uthal flux. T he m agnitude o f B$ is th e strongest in the central p art o f the disk, and it slow ly decreases w ith the radius. T he negatively o riented flux is m ostly located in th e m id
plane o f the galaxy, b u t it extends also to som e vertical height in the form o f a disk corona.
T he in itial state o f th e cosm ic-ray energy follow s th e density distribution. A s th e system evolves and the supernovae explode, additional energy fluctuations appear (Fig. 3 , b ottom panels) . W eak and w ide stream s o f cosm ic-ray energy form in the vertical direction; they start from the disk m idplane and span up to the top an d b ottom dom ain boundaries (see Fig. 3 at t = 0.75 G yr).
T hese are the channels th at transfer the cosm ic-ray energy out o f the dom ain.
T he resu lt o f each sim ulation are the 3D cubes o f m a g n etic field and the C R energy density. U sing the C R co m p o n en t as the proxy for the distribution o f th e relativistic elec
trons, one can create a synthetic m aps o f total pow er and polarised synchrotron radiation (for details see O tm ianow ska- M azur et al. 20 0 9 , Sect. 3). F igure 4 show s the polarisation m ap fo r m o d el v70 a t t = 5 Gyr. T he m ap show s the synthetic d istri
bution o f the polarised intensity at T6.2 cm and th e polarisation angles, b oth superim posed o nto the colum n gas density. T he p o larised intensity in the d isk region has a very strong gradient at the edge o f the disk. T he m agnetic-field structure is d o m i
nated b y the azim uthal com ponent and the vertical slices through the com putational dom ain show th at the vertical m agnetic-field com ponent is relatively w eak. T he synthetic polarisation m ap o f the sim ulated galaxy shows th at the m agnetic field has a very strong toroidal com ponent and is alm o st p erfectly p arallel to the disk plane. S im ilar results have been found in observation o f N G C 1569 b y K epley et al. (2010) . This clearly hints at a lo n g term enhanced S FR in N G C 1569 as the origin o f the m agnetic field, w ith th e cu rrent bu rst only m odulating th e field topology.
T he long enhanced SFR in N G C 1569 is consistent w ith th e re sults from H ST -based colour m agnitude analyses (V allenari &
B om ans 1996) .
4. Conclusions
W e have show n for the first tim e a global m o d el o f the cosm ic- ray-driven dynam o for a d w arf galaxy. T he m o d el consists o f (1) exploding supernovae th at supply the C R energy input and are distributed depending on the local gas d ensity; (2) seed
ing th e dynam o b y random ly oriented dipoles injected w ith the first bursts o f supernovae; (3) the B urkert D M profile, and (4) the ISM resistivity. W e studied the evolution o f the m a g n etic field for tw o galaxies characterised b y different rotation speeds: 40 k m s-1 an d 70 km s-1 . W e found that
- the cosm ic-ray-driven dynam o operating in a dw arf galaxy can am plify regular m agnetic fields exponentially in tim e, up to th e saturation level that corresponds to the equipartition m agnetic-field strength in real galaxies;
- the e-folding tim e-scales show that fast-rotating objects g en erate m agnetic fields faster than the slow ones, w hich is co nsistent w ith the aw -d y n am o paradigm (B randenburg &
S ubram anian 2005);
F ig.4. Polarization m ap at T6.2 cm for the m odel v70 at t = 5 Gyr.
The top panel shows the edge-on and the bottom panel the face-on view o f the galaxy. The contours of the polarisation intensity and the dashes o f the polarisation angles are superimposed onto the colum n gas den
sity (£ g) plot, w here mH is the hydrogen mass. The m aps have been sm oothed down to the resolution 40".
- the calculated tim e-scales for th e m agnetic-field energy evo
lution are com patible w ith those rep o rted by H anasz et al.
(2009b) and K ulpa-D ybeł et al. (2011) for m ore m assive galaxies th at show an e-folding tim e o f the m agnetic-field grow th rate o f abo u t 300 M yr; in ou r results, the tim e-scales are abo u t 450 M yr for v70 m odel and 1000 M y r fo r v40, im plying that the m agnetic field in dw arfs is m o re the resu lt o f a long-term slightly enhanced star form ation than due to one recen t strong burst;
- the 8 juG m agnetic fields generated in the m odel v70 are in the ran g e o f observed values p resented in C hyży e t al.
(2011). T he m agnetic field g enerated in m odel v40 reaches the saturation p h ase after abo u t 10 G yr and th e final values are also sim ilar to those o f real galaxies. O ne should keep in m in d th at the SFR history o r interaction w ith the environ
m en t in real galaxies differs from the m odelled ones, th ere
fore the m agnetic-field values do n o t m atch exactly.
T he results o f ou r m odelling indicate that the cosm ic-ray-driven dynam o can explain the observed m agnetic fields in d w arf galax
ies. In future w o rk w e plan to determ ine the influence o f other param eters an d p erfo rm m ore sim ulations to find an d reproduce th e observed relations.
Acknowledgements. This work was supported by the by the Polish National Science Centre through grants N N203 583440, N N203 511038, and NCN UMO-2011/03/B/ST9/01859. Calculations were made possible thanks to the PL- Grid Infrastructure, website: w w w .p lg rid .p l. This research was supported by the partnership program between the Jagellionian University Kraków and the Ruhr-University Bochum. D.J.B. is supported by the DFG special research unit FOR 1254 “Magnetisation of Interstellar and Intergalactic Media: The Prospects of Low-Frequency Radio Observations”. We thank J. Gallagher for discussions.
A136, page 5 of 6
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