PoS(ICRC2015)023 http://pos.sissa.it/ ∗ [email protected] [email protected] Speaker. Mapping the dark matter distributionnear future across as our a Galaxy new representscomes generation online. a of Here central space-borne we challenge and present for ground-based abaryonic content synopsis astronomical the and of surveys the the kinematics swiftly present of status thedark Milky of matter Way the component. and field, outlining The the reviewing discussion methods briefly then used proceeds the on to with our infer some own of the work. the latest In developments particular, based wethe present rotation a new curve compilation of of the kinematicsetting measurements Galaxy the tracing and contribution of an stellar exhaustive bulge, stellar array discdiscrepancy of and between gas observation-based these to baryonic the two models total components gravitational potential. isthe dark The then matter quantified distribution and to on derive modified the Newtonianof dynamics. future latest We directions constraints shall to end on improve with our an mapping overview of the dark matter distribution in the . ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

The 34th International Cosmic Ray Conference, 30 July- 6 August, 2015 The Hague, The Netherlands Fabio Iocco ICTP South American Institute for FundamentalInstituto Research, de and Física Teórica - UniversidadeRua Estadual Dr. Paulista Bento (UNESP), Teobaldo Ferraz 271, 01140-070E-mail: São Paulo, SP Brazil Miguel Pato The Oskar Klein Centre for CosmoparticleDepartment Physics, of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden E-mail: Mapping dark matter in the Milky Way, a synopsis PoS(ICRC2015)023 , ] and 5kpc . stellar 8 11 ; ,

− Miguel Pato 5 10 M , as inferred . 7 stellar bulge

10 M = 6 0 R 10 × 4 . , separated into the different ] in the 1920s, shortly before 2 2 of molecular, atomic and ionised

]. The gravitational influence of the M 9 is instead devoted to the determination 14 3 , 10 ] and Oort [ with an outlook on the future prospects in 1 × 13 5 2 01pc [ . , comprising about 5 gas 3kpc with its barred shape and total mass of order 10 ] and references therein), where the Sun lies in between the Perseus − ] measured the Doppler shift of emission and absorption lines in the , before finalising in Sec. 15 4 4 ; and

M ]. 10 12 10 ] in Sec. 9 × ]. The local standard of rest (LSR) moves around the Galactic centre at the so-called , ) 8 5 18 , , 7 ] postulated the existence of large amounts of dark matter to explain the dynamics of the − 3 , 2 17 6 ( ]) confirmed the fast rotation of Andromeda and indicated an almost flat rotation curve. , 5 The Milky Way is a complex, gravitationally-bound system of stars, gas and dark matter. In Here we give a synopsis of the ongoing efforts in determining the dark matter distribution It is almost one hundred years since the presence of an invisible component of matter across the 16 , often split in thin and thick populations with a fast decaying radial profile and total mass , 13 and Sagittarius arms, in a local armlet, at a distance to the Galactic centre the field. These proceedingswhich are we intended refer as the interested a reader synopsisthe to only, recent the review not list [ as of references, a in comprehensive particular review, to for the books [ supermassive dominates theinterested central in, pc, namely above but 1kpc becomesFor negligible off our in the purposes the Galactic here, centre, regionsdominating there we so the are we are innermost three 2 shall neglect main it baryonic in components the of following. the Galaxy: 2. Tour of the Galaxy the very centre of the Galaxy sits a with a mass 4 Zwicky [ baryonic components and the total massof distribution. Sec. the dark matterwell content, as including their strengths a and description pitfalls.works of We then [ the summarise the so-called latest local developments based and on global our recent methods as from the orbits of tens of S-stars in the inner 0 [ across the Milky Way. We start with a brief tour of the Galaxy in Sec. Coma cluster of galaxies. The historyin of dark 1939, matter when in individual Babcock galaxiesgas started [ soon of afterwards, our closest spiral(e.g. galaxy, [ Andromeda. ThroughoutThis the same following behaviour decades, was several thenand studies 1980s, observed lending in support numerous to the otheritself, dark spiral is matter much paradigm. galaxies more Curiously, throughout the complicated. the case Whileconvenient of 1970s many lines our external Galaxy, of galaxies a sight happen spiral with tois lie particularly not towards convenient much particularly inclination we can angles, do:and in our velocities. the inside Milky position Therefore, Way makes there enterprise it determining still extremely today. the hard Current to rotation and measure forthcoming curve accuratestaggering astronomical of improvements distances surveys, in however, our hold the the field Galaxy promise over of remains the coming a years. challenging cosmos has first been suggested. Thecomponent earliest date remarks back on to the the dynamical seminal contribution of works an of invisible Kapteyn [ Mapping dark matter in the Milky Way, a synopsis 1. Preamble disc around hydrogen (and heavier elements). Thefour stellar main disc arms and (see the Ref. gas [ have a marked spiral structure with PoS(ICRC2015)023 (2.1) ] ] ] ] ] ] ] ] ] ] ] ] ] ] 26 26 27 28 29 30 31 32 33 34 35 36 37 38 Miguel Pato . Similarly, the spatial ◦ , likely extending hundreds and 45 . ], with the Sun leading the LSR ◦ ]) summarises the different bary- 7 18 dm ]. The three baryonic components , φ 18 + 23 , , 23 gas 22 , while kinematic data trace the total grav- , φ , dark matter halo + gas 25 21 φ , , , 24 20 3 disc ] vary between 10 , φ disc 31 19 + φ ] for a full description of each model. , (adapted from Ref. [ , 7 km/s [ , 1 30 ) 6 , 9 bulge bulge 29 φ − φ , 7 = 250km/s [ , 28 , − 26 tot , HI, HII optical | microwave | radio [ , HI, HII optical | microwave | radio [ φ 27 2 2 − , 210 5 , 26 = 11 0 . The dark matter contribution follows from the comparison of these two v − tot ]; please refer to Refs. [ φ 10 2 H 345 gaussian plus nucleus6 truncated power law7 power law plus long infrared1 bar truncated power law2 double infrared ellipsoid optical | infrared3 thin plus thick4 thin optical plus | thick infrared5 thin plus thick plus1 halo thin infrared plus thick plus halo single [ maximal optical disc [ optical H optical optical [ [ optical [ [ [ [ [ [ 12 exponential E2 gaussian G2 optical optical [ [ 7 The morphology of the bulge has been extensively mapped with the help of optical model specification data Ref. = (

) W , Details of the baryonic models used to set the stellar bulge, stellar disc and gas in our Galaxy. Table V , gas disc bulge Photometric data play a crucial role in tracing and discerning the different baryonic compo- U ( by described above are supposed to be embedded in a onic models used for the morphology of each component. Stellar bulge and infrared surveys (such as COBE/DIRBE,structure, OGLE known and as 2MASS), the revealing an bar,bar elongated with with triaxial near respect end to at thereported positive in Galactic Galactic the longitudes. centre literature line The [ of inclination sight of has the not been precisely measured and angles adapted from Ref. [ local circular velocity of kpc but whose properties arepotential not of well our Galaxy constrained receives at contributionsseparately: present. from To the sum baryons up, (bulge, the disc, total gas) gravitational and dark matter The key challenge is thenthe to individual constrain baryonic the components different terms in this equation. Photometric data trace Table 1: Mapping dark matter in the Milky Way, a synopsis itational potential nents. In the following weinto morphology go and through normalisation. the Tab. specifics of each component and divide the discussion inputs. 2.1 Baryonic components (photometry) PoS(ICRC2015)023 , , ] 2 ]. 2 57 47 38 , ] and , ]. The 56 ]. 10 37 , 6 36 55 Miguel Pato , 54 , 53 ]. This procedure is ] or the kinematics of 41 , 51 40 , 39 ] and masers in star forming regions 70 25kpc) and a thick population (of scale , . 0 69 ∼ , 68 , 4 line and dispersion measures of pulsars for ionised 67 in the inner Galaxy and HI in the outer Galaxy. The , α 2 discrepancy between different 21cm line surveys in 2 66 , ∼ 65 ], stars [ In a galaxy like our own, star encounters are relatively rare and stars 64 These include mainly young objects or regions that track the Galactic ]. ]. The distribution at larger scales has been compiled in Refs. [ , ] or dynamically with a Jeans analysis of the kinematics of specific tracer ]. Here we shall focus instead on rotation curve tracers and star population 50 48 63 46 and from a factor , 52 , 2 62 45 ]. A new, up-to-date compilation of tracers has been presented in Ref. [ , Optical photometric surveys, most prominently SDSS, have been instrumental in 74 53 ] describe the morphology of the disc with a double exponential profile [ , , ] for H 35 73 61 75kpc). There are also works implementing a single effective component [ 49 , . , ]. , ). Regarding the normalisation of the bulge, one possibility is to use the measurement of , 0 1 34 ]. 72 44 60 37 , ∼ , , The gas in our Galaxy is mainly composed of molecular, atomic and ionised hydrogen (H , 36 33 There are numerous kinematic observables used to track down the total mass distribution 71 43 59 , , , , 18 32 42 main normalisation uncertainties of the gas componentfactor arise [ from the poorly constrained CO-to-H Overall, the gas content is dominated by H the inner 15kpc for HI [ 58 Star population tracers feel on average the smoothgiven gravitational set potential of of stars the as whole a system. collisionless gas We and can apply therefore the treat collisionless a Boltzmann equation. The first across the Galaxy. Some include timing arguments in the [ gas. The observations show a very patchy morphology in the very inner 10pc of the Galaxy [ 2.2 Total gravitational potential (kinematics) tracers. Rotation curve tracers rotation. While in externalGalaxy galaxies we the can only also tracerToday, despite available resolve to the stars us challenges and is posedprecisely star-forming by the measured regions our gas, from position and in about inside the use 1 the case to those Galaxy, of 30 as the our kpc rotation kinematic off curve tracers. the can Galactic be centre using gas [ two components, a thin populationheight (of scale height Gas HI and HII, respectively).molecular Each gas; component 21cm is line probed for atomic with gas; different H observations:and CO a lines disc-like structure for otherwise, includingdisc features such in as the a inner central 2kpc molecular zone [ and a holed Milky Way satellites [ [ Stellar disc(s) stars [ the microlensing optical depth towards the central Galactic region [ pinpointing the structure of the[ stellar disc. Based on these data, several works in the literature Mapping dark matter in the Milky Way, a synopsis distribution has been fitted with(cf. several Tab. variants of exponential, gaussian and power law profiles particularly convenient in deriving model-independent constraintsdepend since on the the optical individual depth masses does of[ the not lenses but only on their mass density along the line of sight normalisation of the disc, inwith particular star censuses the [ local total stellar surface density, can be pinned down PoS(ICRC2015)023 ] for 12 Miguel Pato ] and above and 79 , 36 ]. 90 , which use data from dif- ], across the disc [ global methods 78 , 77 , , which use observations from one specific patch ], in which the mixed radial-vertical term in the 76 5 , 10 75 , ]. ]. The main advantage of this technique is to provide a 85 84 12 , , 83 89 , local methods , 82 88 , , 81 , 87 , kinematic data fix the total gravitational potential whereas photomet- , 2 80 86 Local methods couple the Jeans and Poisson equations, thereby relating the total mass density Global methods are based instead on the mass modelling of the Milky Way as a whole. Typi- As highlighted in Sec. Jeans equation is neglected and, assumingten a in flat terms rotation of curve, a theThis double total simple derivative mass scheme of density has the can been be velocitytions extended writ- dispersion often over of used the the years as stars to aneighbourhood in include test is the various to bed. vertical account corrections for direction. with A the simula- local criticalknown. dynamical This, step contribution together of in with baryons, constraining other which complexities is thecluding of not dark the precisely a method, matter induces very density substantial precise uncertainties in pre- Several measurement the works solar of in the the local literatureand dark data, implement matter see local density, e.g. methods Refs. at withtruly [ least different local with approaches, measurement current of assumptions the data. a dark global matter mass density model in forconstructing the the a solar whole clean neighbourhood Galaxy. sample without of assuming and The tracers the most and significant important of uncertainties pitfalls treating pertaining includesolar kinematically the neighbourhood. the inhomogeneous contribution For difficulty populations, a of of critical baryons discussion (most of notably, these gas) pitfalls, see in Ref. the [ in the solar neighbourhood with theconfiguration kinematics of is a the given nearby so-called population Oort of limit stars. The [ simplest cally, mass models for the baryonic componentsthe (in dark particular, matter stellar halo bulge and are stellar assigneddata disc) with and across a for the number Galaxy. of The free data parametersgas available that to are are the rather then measurement broad, fitted of ranging the to from Oort kinematic terminal constants and velocities the of kinematics the of stellar objects at large distances below the Galactic plane [ ferent regions to infer the darkof matter content local elsewhere. and An global excellent methods examplean is of extensive the the review. performance measurement Here of we the givemeasuring local a the dark brief local matter overview dark of density, matter see the density, Ref. strengths and [ and their complementarity. pitfalls of3.1 each method Local in methods 3.2 Global methods ric data set the individual baryonicto components; infer the the comparison between dark the mattersigned two distribution to can across perform then the this be comparison: used Milky Way. There are two classes of methods de- 3. Dark matter content of the sky to derive the dark matter content therein, and Mapping dark matter in the Milky Way, a synopsis momentum of the Boltzmann equation gives the Jeanspotential equations, to which the relate density the distribution total and gravitational Star velocity dispersions populations of are a given thus population invaluabletotal of kinematic gravitational selected potential stars. tracers in and the outer have halo in [ fact been used to pinpoint the PoS(ICRC2015)023 ] ). 12 2.2 ]). Miguel Pato 100 , 99 shows the key results 1 ], to which the reader is 9 , 8 , ]. The major advantage of this 7 , 98 6 , ]). However, closer to the centre, 97 , 76 96 , 44 , 95 , 6 94 . The discrepancy between the rotation curve and , 1 93 , 92 , 91 ]) or to the shape of the dark matter halo (see e.g. Refs. [ 7 ) and a comprehensive compilation of rotation curve tracers (cf. Sec. 2.1 ], we have addressed the very observational evidence for part of the total gravita- 6 In Ref. [ Generically, the upshot is that local methods are usually less precise but more robust than That dark matter dominates the overall mass budget in the Milky Way has been inferred from the envelope representing the baryonic uncertainty appearsstatistical already analysis by needs eye; to nonetheless, be a performed thorough to properly assess the level of discrepancy. The outcome namely inside the solar circle,total gravitational where potential, dark baryons matter give constraints anrequired are today weaker increasingly for and important particle often dark lack contribution matter the tosimulations searches level of the and with accuracy for the interpreting highest the resolution. resultssecond of the In galaxy formation distribution this of context, dark wecircle), matter have making in addressed use the of first an innermost the extensive regions array presencecomponents of of (cf. and observation-based the descriptions Sec. of Galaxy the (i.e. different inside baryonic Here the we solar give a brief accountreferred of for a our detailed recent discussion. work based on Refs. [ 4.1 Evidence for dark matter of our analysis. Inbracketing the of left the panel, baryonic the contribution (greythe rotation band). convolution curve of Notice (red the that data 70 the alternative points)five baryonic baryonic is band discs models compared corresponds and that to directly can two be to gas generated the configurations with in the Tab. seven bulges, tional potential being generated bywas a to compare non-visible the component. rotation curve of Thecomponents the rationale in Galaxy behind with order the our to contribution approach duecentric quantify to radius the the observed and discrepancy baryonic to between assess the the two impact as of a all function relevant uncertainties. of the Fig. Galacto- global methods are, andin both the bring Milky complementary Way. input Thismethods regarding is probe the rather the evident dark solar in neighbourhood matteraround the itself the distribution Galactic case and centre, of global the comparison the methods between localtest probe both on determinations dark a can the matter be usually shape used of density: spherical as the a shell dark since diagnostic matter local halo, in particular whether this is oblate or prolate (see Ref. [ kinematic tracers in the outskirts of the Galaxy (e.g. Ref. [ technique is perhaps the wealthall of available structure data, of which our are Galaxy. invaluablematter The in density is reconstructing fundamental that the drawback they over- of are particularlymodelling global prone (see measurements to e.g. of systematics Ref. associated, the [ for local instance, dark to baryonic for a discussion).remains Given inconclusive. the sizeable uncertainties at present, the outcome4. of such Latest comparison developments Mapping dark matter in the Milky Way, a synopsis from the Galactic centre. Thisdark extensive matter fitting density procedure to fixes a several rather quantitiesmethods good such is rather precision, as rich, often the see around local e.g. 10% Refs. or [ better. The literature of global PoS(ICRC2015)023 20 ] and 7 Miguel Pato baseline Galactocentric radius (kpc) ]. Please refer and the inner 7 and references reproduces the , 0 10 6 ρ 2 ]). It is important 3.2 6 8kpc, a local circular = 0 R 5 uncertainties) in grey. The right panel σ ]. Plots taken from Refs. [ . It is clear that our ignorance about the 3 25 in terms of the cumulative goodness of fit as 4.1 1

1

-1

-2 ] for earlier constraints) focussed on the gener-

/dof

χ 10 2 10 10 7 44 25 R [kpc] rotation curve data baryonic bracketing 20 ] (see also Ref. [ exclusion. The black line in both panels corresponds to a representative 7 σ 15 ]. 8 10

First, we performed a simple fit to the kinematic data, in which the dark matter

0 = 8 kpc 8 = R 230km/s and the peculiar solar motion of Ref. [ = Evidence for dark matter. The left panel shows the compilation of rotation curve tracers in red 0 ] for further details. 5 for all 70 baryonic models mentioned in Sec. v 6 γ

Given the evidence that the total gravitational potential of the Milky Way cannot be accounted cut = 2.5 kpc 2.5 = R 1 2

10 10 [km/s/kpc] ω actual baryonic morphology is preventing a more precise determination of the dark matter profile, for by visible matter only, wethe set missing out mass. to Two infer different the approaches distribution were of adopted dark for matter this that purpose: best accounts profile for fitting [ displays the cumulative goodness of fit asthe a function red of line Galactocentric radius corresponds for tobaryonic each model. single a baryonic This 5 model; figure assumes avelocity distance of the Sun to the Galactic centre to stress at this point thatand the the dark method matter described hypothesis so hasgravitational far not potentials been simply without introduced quantifies any at the theoretical all discrepancy prejudice. in between this the analysis, total and baryonic 4.2 Dark matter distribution Profile fitting distribution is described by aThis sort spherical of profile global method with has a been extensively parameteric, studied pre-assigned in the functional literature, form. cf.alised Sec. Navarro-Frenk-White (NFW) and Einasto profiles. The left panel of Fig. of such analysis is presented in the right panel of Fig. profile reconstruction [ therein. Our analysis in Ref. [ results for the generalised NFWslope profile in terms of the local dark matter density Figure 1: and the convolution of all baryonic models (together with their 1 a function of the Galactocentric radius forto each fit of the the observed 70 rotation baryonic curve models. –them All at actually baryonic more fall models than fail short five sigma of – matchingof already the approximately inside total the 5kpc. gravitational solar potential circle. already These Mostuncertainties at of results (including Galactocentric have radii fundamental been Galactic shown parameters,tainties, to peculiar data be solar selection robust and motion, against systematics, baryonic an cf. uncer- exhaustive supplementary set information of in Ref. [ Mapping dark matter in the Milky Way, a synopsis to Ref. [ PoS(ICRC2015)023 25 ]. R [kpc] 8 , 7 density determination baryonic bracketing Navarro-Frenk-White Einasto isothermal 20 Miguel Pato 8kpc, a local = 0 R ], we have adopted 15 8 confidence regions for a gen- σ ]. Plots taken from Refs. [ 10

25

0 = 8 kpc 8 = R . The dark matter density profile 2

5

cut = 2.5 kpc 2.5 = R

1

6 5 4 3 2 0 -1

dm -2 -3 -4

] [GeV/cm ρ 3 8 ] 1 3 since in that case we used an unbinned analysis to 20kpc) and each single baryonic model. The confidence = =20 kpc [GeV/cm s 0 s ρ 4.1 r 0.8 gen. NFW, r

σ

excluded >5 0.6 The previous technique is sound but relies on the assumption of a given ] for further details. 8 , 230km/s and the peculiar solar motion of Ref. [ σ 0.4 2 7 = 0 v 0.2 Inferring the dark matter distribution. The left panel shows the 2 goodness-of-fit region is also shown. The right panel displays a non-parametric reconstruction of the 0 1 0 2

0.8 0.6 0.4 0.2 1.8 1.6 1.4 1.2 σ inner slope slope inner γ a method to performSpecifically, such we profile have reconstruction used assuming theand magnitude a the and spherical baryonic slope dark contributionMilky of matter to Way. the distribution. reconstruct The residuals the results betweenobtained dark are the with matter shown rotation this in method density curve is the in notdifferent right the very profiles panel precise with inner of and current 25kpc in Fig. data. factdark of it matter Notice is the component that not possible this described to is in discriminate entirely Sec. between consistent with the evidence for a especially its slope towards thematter inner density part is of (slightly) degenerate the with Galaxy.(heavily) the In degenerate morphology of with particular, the the we stellar morphology find disc of thatcise and the the the reconstruction stellar inner local of bulge. slope dark disc Therefore, is in andon the bulge the future would dark a be matter more extremely distribution pre- in valuable the in Milky achieving Way. better constraints Profile reconstruction parametric profile: the fitted parameters willaccurate. be useful Therefore, only it if is the important original to assumptionprofile reconstruct is – directly sufficiently with current from or the upcoming data data, – without the dark any matter parametric assumption. In Ref. [ eralised NFW profile (with fixed scale radius Please refer to Refs. [ infer the presence ofthe an profile additional reconstruction component stem but fromnecessary not the to its loss estimate magnitude. of the information slope Themethod introduced of large constitutes by the a uncertainties residuals. the first in binning Despite step procedure curve this in data the drawback, without effort the unnecessary to profile adhoc extract reconstruction assumptions,as the and the dark its quality matter relevance of at profile a the directly precision available from kinematic level rotation will data grow improves throughout the decade. Figure 2: region corresponding to a representative5 baryonic model is markeddark in matter black; profile, for obtained without thisreconstruction for assuming baryonic a any model, representative functional the baryonic form. model,all while baryonic The the models. grey red band error This encompasses bars the figure correspond reconstruction assumes to for a the distance of the Sun to the Galactic centre Mapping dark matter in the Milky Way, a synopsis circular velocity PoS(ICRC2015)023 , ApJ (1933) Miguel Pato 6 ] in the context of as a fitting parame- 9 0 ] (2018–2023) in the a significantly above those 105 0 a ]). This friction is less promi- Helvetica Physica Acta 101 , 9 (Apr., 1927) 275. ], launched in December 2013 by ESA and already in 3 102 ] covering both hemispheres, and the ground-based optical surveys 103 M. P. acknowledges the support from Wenner-Gren Stiftelserna in Stock- First Attempt at a Theory of the Arrangement and Motion of the Sidereal System Die Rotverschiebung von extragalaktischen Nebeln Observational evidence confirming Lindblad’s hypothesis of a rotation of the galactic ] (2017–2022) in the northern hemisphere and 4MOST [ , Bull. Astron. Inst. Netherlands 104 (May, 1922) 302. system 55 110–127. In this synopsis, we have summarised the considerable progress achieved by the community Acknowledgements. The setup described in the previous sections can also be used to test and constrain modifica- [2] J. H. Oort, [3] F. Zwicky, [1] J. C. Kapteyn, its 5-year science data taking period2 since (SDSS-IV, 2014–2020) July 2014, [ the ground-based infrared survey APOGEE- WEAVE [ in constraining the darkmajor matter conclusion density is that in – the– whereas Galaxy extensive the photometric ignorance over and about the kinematic the datauncertainties decades actual are in and morphology indeed determining in available of the recent the Galacticthe visible years. fundamental Galactic component parameters centre and A (i.e. and current the the observational in local distance pinpointing circular of the velocity) the still dark Sun aredetermination matter to of the component the dominating dark across sources matter the of densitytwo profile uncertainty Milky sources will Way. of depend crucially uncertainty. In on On ourcoming the ability that into near to respect, place: shrink future, a these a new the generation detailed Gaia of satellite astronomical [ surveys is steadily holm and F. I. from the Simons Foundation and FAPESP process 2014/22985-1. References nent in the case ofMOND, the they simple confirm interpolating the function. existing tension Whilethe between galactic some these MOND scale. results variants do and not observational data certainly at rule out 5. Future directions sourthern hemisphere. These instruments will deliverthe a Galaxy, comprehensive, especially exquisite in census the of solar stars neighbourhood.this in The batch main of challenge data for to the start next a decade new is precision to era use in mapping dark matter across the Milky Way. tions of gravity in the Milky Way. We have explored this direction in Ref. [ Mapping dark matter in the Milky Way, a synopsis 4.3 Modified Newtonian Dynamics Modified Newtonian Dynamics (MOND). Using(the two so-called of “standard” the and most “simple”rotation popular functions), curve interpolating data we functions for have each tested baryonicter. the model, In MOND taking the case the paradigm the critical with standard acceleration interpolatingMOND the function, can our explain findings the show that rotation for curveindicated most of baryonic by the models studies Milky Way of for external values spiral of galaxies (see e.g. Ref. [ PoS(ICRC2015)023 , , 704 215 ArXiv , ApJ , Miguel Pato ]. (Feb., 2010) Monitoring , ApJS (1939) 41–51. ]. Nature Physics , (June, 2014) 19 402 ]. 41 (Feb., 2009) 692 , MNRAS , ApJ arXiv:1006.0064 . Princeton University Press, 2008. ]. arXiv:1202.6128 arXiv:1401.5377 ]. Lick Observatory Bulletin , ]. ]. . Princeton University Press, 1998. (Feb., 2012) [ (July, 2009) 137–148. (Feb., 2011) 45–. 10 ]. 63 700 The massive black hole and nuclear star Journal of Physics G Nuclear Physics arXiv:1504.0632 , (Oct., 2010) 3121–3195, [ ]. 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