PoS(ICRC2019)513 http://pos.sissa.it/ ˙ ˙ zych 1, PL-30084 Kraków, zych 1, PL-30084 Kraków, ∗ [email protected] [email protected] Speaker. The large-scale magnetic fields arePatterns in of the paramount motion importance of forgalactic interstellar magnetic the medium fields, especially cosmic may in provide ray our . some astrophysics. in It constraints attempts seems on that to magnetic the fully fields structure cannot addressis be of the ignored ionized problem to of a the degreemagnetic sufficient rotation tension for of influences the its spiral magnetic motion, . modifying fieldof the to The predictions galactic freeze-in interstellar of rotation. the purely gas gas, gravitational models The somass-to-light ratio that inclusion and the of so resulting might magnetic help fields to reduce has the implications missing mass for problem. the predicted local ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 36th International Cosmic Ray Conference -ICRC2019- July 24th - August 1st, 2019 Madison, WI, U.S.A. Poland E-mail: Łukasz Bratek Institute of Physics, Cracow University ofPoland Technology, ul. Podchora¸ E-mail: Joanna Jałocha Institute of Physics, Cracow University of Technology, ul. Podchora¸ Galactic magnetic fields in the contextmatter. of Influence dark on the rotation curvesgalaxies. of spiral PoS(ICRC2019)513 ) as L / M Łukasz Bratek ]. The interstellar gas is 1 ], share the opinion that magnetic fields are 3 , 2 1 ]. However, the effects are subject to modelling 5 , 4 ]), would be sufficient to reduce the local-mass-to light ratio to 11 , 10 , 9 . This ratio, although low (1-2 in the interior), steeply increases, reaching a value 1 ] where we reported on the results concerning NGC 891. The input data con- A possible effect of the influence of magnetic fields on the dynamics of galaxies we described It should be noted that the studies on the influence of magnetic fields on rotation curves have The role of magnetic fields in astrophysics cannot be overestimated. To give a few examples, The turbulent and large-scale magnetic fields can influence the motion of at least partially ion- 6 in [ assumptions. 2. Magnetic fields in modelling rotation curves of spiral galaxies shown in Figure acceptable lower values. sisted of the rotation curve, surfaceframework brightness of profile global and disk the model, neutral wellgards approximating for distribution. a a flattened In while mass the the hypothetical distribution dark whenin halo, one conjunction we disre- obtained with a the surface mass brighntness density profile, distribution, which led us to a local mass-to-light ratio profile ( responsible for the flatteningarguments or that rise the of influence thetion, is outer leading unlikely parts or to of even an rotation may even curves, higher impede others halo the mass provide gravitationally supported [ sound rota- 8 in the outer parts.gravitationally Such dominating a the rapid luminous increase stuff is ineven usually the minute outer attributed changes to parts. within measurement a But errors non-baryonic inin in dark the the a matter disk external significant model halo parts reduction framework, of of rotationprofile curves, the may in surface result mass the density. outer This parts.increase in of turn At the reduces this rotation the stage local curve.eral we micro-gauss, mass-to-light supposed such It as that turned observed magnetic out infields field that NGC in was 891 the spiral (which responsible dynamical galaxies is for effect [ a the of value magnetic typical for fields large-scale of magnetic sev- been inconclusive so far. Some authors, e.g. [ ionized to a degree sufficient fornetic the tension can magnetic be field assumed to to freeze-inof hold the purely the gas gravitational gas, models. and so so Because that influence the thethe its gas resulting motion, magnetic density mag- modifying effect decreases the becomes with predictions the important galactocentrictained for distance, mainly larger based radii. on Rotation theavailable curves observations in of of the spiral gaseous outer galaxies clouds, regions are and ofcurves, ob- or these these even galaxies. measurements their are rise, As could the so,In be only the simply particular, observed the it flatness result might of of turn outer interactionof out, with disk non-baryonic interstellar that rotation dark magnetic taking matter fields. required magnetic by fields models into which account ignore would magnetic reduce fields. the amount the fields alter the trajectories of cosmicneutron rays, they are magneto-spheres, crucial for for the star physicsfields formation of accretion processes, cannot disks, as jets, be well ignored asspiral for also galaxies. stellar when winds. one Magnetic attempts to fully understand theized problem gaseous fraction. of The rotation mechanism of of the influence was described in [ Galactic magnetic fields and rotation curves 1. Introduction PoS(ICRC2019)513 Łukasz Bratek and shortly discussed in the 2 ] show that the magnetic field is 11 , 9 2 ] (the fields may be even stronger in the central regions). The present measure- 13 ] we investigated a possible influence of magnetic fields on the dynamics of galaxy NGC A change in the local mass-to-light ratio profile of spiral galaxy NGC 891 resulting from a small 12 ], the reducing effect will be noticeable for magnetic fields of 11 microgauss, which is the The main message of this observation is that one can significantly reduce the mass-to-light ra- It is known that the rotation curve indicated by the cepheids and carbon in the outer In [ The galaxy NGC 891 shows also some anomaly in the behaviour of the vertical gradient of 12 ]. The new measurements confirmed that the rotation curve of NGC 253 decreases at large dis- 14 tio profile in the outer regionseffect by is including easier magnetic to fields in achieve in thesmall disk the changes model disk in model. model the due This rotation reducing to curve. high sensitivity of the predicted mass density to 3. Magnetic field estimates from galactic rotation. The galaxy. disk of the Galaxy is markedly lower than the rotation curve of rarefied ionised gas clouds in the figure caption. value observed in this galaxy. The results are illustrated in Figure ments of ionised gas clouds cover[ more distant regions than previous rotation curve measurements tances from the centre. ThisMoreover, indicates considering that that the the amount rotation of curve darkcannot measurements exclude matter an concern may additional the be reduction ionized lower of than gasmagnetic the expected. fraction, expected fields, one mass-to-light the profile more due that toin the interaction with [ fields are exceptionally strong in NGC 253. As we have shown the azimuthal component of gasin velocity. This the gradient, S-W being quadrant. highdisk in the In and N-E this above quadrant, it. galaxy, vanishes non-symmetric, the At being large-scale the intense magnetic and same field stronglymagnetic time, is field ordered the measured might in be measurements both the the [ inside reason S-W of the quadrant. the observed The asymmetry in asymmetry the253. in velocity The the gradient. galaxy is characterized by exceptionallythe strong outer magnetic regions fields [ from 7 to 18 microgauss in Figure 1: modification of its outer rotationthat curve. after accounting The for original the local presence mass-to-light of ratio magnetic profile field [dotted [solid blue red line] line] (only and N-E quadrant considered). Galactic magnetic fields and rotation curves PoS(ICRC2019)513 ) R ( can ) σ R ( . from the σ ) Φ Z R Łukasz Bratek RB ∂ ( together with the ∂ R 3 B reduce to 1 ) πρ 4 Z , = from the axis of cylindrical Φ ,  R R G ( | Φ R ∂ RV ∂ R is a width-scale parameter. The V h , Φ 3 R , where B ∂ ) ∂ ) h Φ / Z B ( ) 1 2 R ( ( 1 2 πρ σ 4 cosh − h 4 2 Φ R B ) = ]. 1 Z πρ , 4 12 R ] we determined the maximum likelihood stellar and gaseous smooth outer ( − ρ 16 2 Φ is the volume density of gas corresponding to a column mass density v R ρ δ ]. In [ = 15 R R V ∂ . In this situation the equations in cylindrical cordinates ∂ Rotation curves (left panel) and resulting mass-to-light ratio profiles (right panel) in disk model of Φ R B V In the vicinity we model the magnetic field by finding a solution of the sta- and ]. The solid line (labelled 1) – a rotation curve that fits in the rotation data within error bars (with some R 14 symmetry. Here, according to equation We assume that all quantities depend solely on the radial distance same region [ tionary Navier-Stokes equation for an inviscidthe and vertical pressureless medium. component In of this magnetic region field we to assume be vanishing to first order in the distance galaxy NGC 253. The full[ circles with error bars in the left panel represent the rotation measurements from rotation curves using a greaterand smoothing number algorithm of is velocity described therein). tracersposition-velocity data (the The used curves conditional to are obtain distribution shown these functions in curves.more figure visible, and turned The out difference to betweendifference be the is increasing two what with curves became one the galacto-centric should distance. expectthe in This distance at increase magnetic large of field, radii the because while the theenhancing gravitational density the force of weakens dynamical mass with effect the drops of distance off magnetic (thereby with tension relatively on ionised gas). Figure 2: excess of mass density over themodification observed of gas rotation density). curve (1) The fordisk dotted which line model the (labelled a resulting 2) mass-to-light small – ratioThe an change profile dashed example in becomes of line decreasing the a (labelled (in small rotation 3)some can denotes hypothetical largely dynamical a contribution influence rotation of curvethe the the lowered magnetic estimation magnetic at field of strength tension larger column values radii tosignificantly observed mass in the reduced in density). motion such and this of a decreases galaxy. gas, way withdensity The to remains consistently higher corresponding consistent with account galactocentric with mass-to-light the for ratio distances, amount profile of whileon visible is our at gas results at the published large same radii. in [ time The figures the were reconstructed mass based Galactic magnetic fields and rotation curves galactic plane, while we keepB the radial and the azimuthal components of that field, respectively, PoS(ICRC2019)513 , G 2 | π Φ V < | is small ε ε | , 1 ± Łukasz Bratek = η , ε set various directions , the above equations ε ρ cos η ) ], the magnetic field ansatz and R is insensitive to the direction ( 16 G | B 2 Φ Φ that can be solved numerically. v ]. To solve the above equations, V = ) δ , 18 R S Φ | ( B Φ B V and ε sin ) . The divergence can be disregarded only when ε . However, the purpose of the model is to approximately R 1 ( 4 − sin . As we explained in [ B R Φ · )) = B R The residual rotation ( R 1 B RB and a small perturbation parameter ( ]). R is the difference of squares of circular velocities of gas η ∂ 20 S 1 | − 2 Φ R V − after [ . G 4 | sec. The position-velocity points for star and gas tracers in the northern (N) π 12 2 / Φ V ≈ = ε can be entirely attributed to the interaction of the partially ionised gas with is close to a function const 2 Φ 2 Φ 220km ) . v v r S | ( δ = δ B Φ o V V is some positive function ( ) Maximum likelihood stellar and gaseous rotation curves we obtained for the Milky Way galaxy R ( 5kpc and B . ] based on then available position-velocity data for stars and gas, assuming IAU Galactic constants 8 The divergence of magnetic field is Suppose that 1 ]. The quantity 16 = o 19 of the total magnetic field and to the sign of can be reduced to aThe single result is non-linear shown ordinary in equation figure for we assume that in the disc plane vicinity may be regarded as consistingmimics turbulent both field. of a Theeven large-scale magnitudes exceeding purely the of azimuthal magnitudes turbulent field of fields large-scale and in fields. a the Given correction Galaxy that may be comparable or enough or/and when be reliably approximated by the column[ mass density of neutral hydrogen which we adopted from and southern (S) side(open are squares), shown carbon stars for N cepheids (solidbars squares), N are gaseous (solid clouds not S circles), shown (stars) for cepheids andstellar clarity). gaseous S rotation clouds curve. (open The N The (pluses) circles), blue dashed (error solid carbonbelow lines the line stars show Galactic is the S plane corresponding the are rotation gaseous taken curves into rotation when account. curve, only the objects grey above or solid line is the R and that of stars where of the field; we assume determine the leading structure of the horizontal magnetic field, therefore we may allow for a small violation of the Figure 3: in [ the large-scale magnetic field ofof the the Galaxy. dominant Then, part weagreement of may with the predict the turbulent a required dynamo possible field. theory form and and observations The strength [ dominant field is likely to be axi-symmetric in Galactic magnetic fields and rotation curves PoS(ICRC2019)513 Łukasz Bratek the corresponding 0 for various width-scale = Z Right panel: . Magnetic fields as an alternative explanation (1992) 652 360 5 Nature , volume density of the gas in the Milky Way Galaxy at : 2kpc (solid line), 4kpc (dashed line) and 6kpc (dotted line). Left panel: h for the rotation curves of spiral galaxies Magnetic fields influence the motion of gas in spiral galaxies, modifying their rotation curves. In the disk model framework, applicable to flattened mass distributions, there is a high sensi- The results we have presented show that magnetic fields cannot be neglected in modelling [1] E. Battaner, J. L. Garrido, M. Membrado and E. Florido, divergence freedom by the partial field, assuming that it is cancelled by corrections to the total field. For the magnetic effect to occur,for the more gas must rarefied be gas, atplane. especially least in partially ionised, the and galaxy the outskirts effect enhances or at higher altitudestivity of above the the modelled galactic mass-to-light ratioof profile in the the rotation outer curve galactic regions (evenas to within we small the perturbations have seen rotation on curvesignificantly the measurement reduce example uncertainties). the of mass-to-light galaxy In ratio NGCobservation this and that 253, region, even the the invert difference its inclusion between tendency offor the of magnetic outermost gaseous growth. fields radii and allowed In (as stellar to view it rotation ofmissing seems curves the mass may to be problem be increasing the and casegalaxies. the for estimations our of Galaxy) this the may amount have of implications non-baryonic for dark the galactic matter rotation in curves. spiral We arethe not Galaxy sure are if characterized the byeffects real a we magnetic postulated. similar fields At dependence least, in on the NGCconsistent overall the with field 891, galactocentric magnitudes measurements. NGC distance we 253 have to obtained or cause are in of the the right order, References parameter magnitude of the large-scale magnetic fieldgaseous that rotation accounts curve for of the the observed Milky difference between Way Galaxy. the stellar and 4. Conclusions Figure 4: Galactic magnetic fields and rotation curves PoS(ICRC2019)513 , , , , , . Astronomy , (2012) 393 ]. ]. Łukasz Bratek ]. Astrophysical 427 (2012) L23 , Astrophysical (1991) 10. , (2016) 5 ]. 755 Astronomical Journal , 246 Dark Matter, Magnetic 68 1302.7253 1111.6417 [ [ 1009.1177 ]. [ The Interstellar Disk-Halo (1995) 691. , p. 287, Jan, 1991. , in 302 The large-scale radio continuum (2011) 71 (2013) 2172 (2012) 2155 Magnetic Flux Density from the Relative 1105.3867 [ 411 433 421 astro-ph/0503657 [ IAU Symposium Polarized radio emission at 2.8cm from a The Radio Halo of the Starburst Galaxy NGC 253 The role of large-scale magnetic fields in galaxy A possible influence of magnetic fields on the ]. 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