Ultra-fine dark matter structure in the Solar neighbourhood
aa r X i v : . [ a s t r o - ph . GA ] A ug Mon. Not. R. Astron. Soc. , 1–9 (2011) Printed 24 October 2018 (MN L A TEX style file v2.2)
Ultra-fine dark matter structure in the Solarneighbourhood
Daniele S. M. Fantin , ⋆ , Anne M. Green , Michael R. Merrifield School of Physics & Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD Centro de Investigaciones de Astronom´ıa, Apdo. Postal 264, M´erida 5101-A, Venezuela
24 October 2018
ABSTRACT
The direct detection of dark matter on Earth depends crucially on its density andits velocity distribution on a milliparsec scale. Conventional N-body simulations areunable to access this scale, making the development of other approaches necessary. Inthis paper, we apply the method developed in Fantin et al. (2008) to a cosmologically-based merger tree, transforming it into a useful instrument to reproduce and analysethe merger history of a Milky Way-like system. The aim of the model is to investigatethe implications of any ultrafine structure for the current and next generation ofdirectional dark matter detectors. We find that the velocity distribution of a MilkyWay-like Galaxy is almost smooth, due to the overlap of many streams of particlesgenerated by multiple mergers. Only the merger of a 10 M ⊙ analyse can generatesignificant features in the ultra-local velocity distribution, detectable at the resolutionattainable by current experiments. Key words: methods: numerical - Galaxy: evolution - Galaxy: halo - Galaxy: kine-matics and dynamics - Galaxy: solar neighbourhood - dark matter
In the last forty years, dark matter (hereafter DM) has beenone of the more challenging topics in astronomy. After thefirst pioneering studies (Zwicky 1933 and Smith 1936), con-vincing evidence for the existence of DM came from the ro-tation curves of spiral galaxies (Freeman 1970, Einasto 1974,Rubin & Ford 1970, Rubin et al. 1978, 1980, 1982, 1985). Itspresence has been also supported by recent indirected mea-surements of its density, obtained by surveys such as SDSS(Tegmark et al. 2006), or by satellites like WMAP (Komatsuet al. 2009, Larson et al. 2010). Despite all this evidence, thenature of DM is still unknown. The most widely acceptedidea is that it consists of non-relativistic, weakly interacting,non-baryonic particles (Cowsik & McClelland 1973; Szalay& Marx 1976), emitting no (or very little) electromagneticradiation.Numerical simulations provide a reliable method of cal-culating the DM distribution on large scales, making robustpredictions for its clustering. The resolution of the first sim-ulations (Peebles 1982, Frenk et al. 1985) was not sufficientto resolve the inner parts of the DM halos, but the gap hasstarted to be filled in the last decade, with N-body simu- ⋆ E-mail: [email protected] lations able to provide results for halos of the size of thelargest galaxy clusters (Springel et al. 2005, Boylan-Kolchinet al. 2009). More recently simulations such as Via LacteaII (Diemand et al. 2008), GHALO (Stadel et al. 2009) andAquarius (Springel et al. 2008) were able to reproduce theformation and the structure of a Milky Way-like DM halodown to a resolution of about 100 pc.Particle physics provides us with various well-motivateddark matter candidates, including weakly interacting mas-sive particles (hereafter WIMPs). They interact with or-dinary matter through elastic scattering on atomic nuclei(Goodman & Witten 1985), and many experiments are cur-rently underway aiming to detect this phenomenon, suchas CDMS II (Ahmed et al. 2010), Xenon100 (Aprile et al.2010) and Zeplin III (Akimov et al. 2010). The goal of theseexperiments is to measure the number of recoil events perunit energy and, in some case, its temporal or angular de-pendence. These quantities depend on the local DM densityand speed distribution of the incident particles in the detec-tor rest frame (Jungman et al. 1996, Lewin & Smith 1996).Therefore, the possible presence of a significant amount offine-grained structure in the DM distribution in the Solarneighbourhood, such as overdensities and streams, wouldhave important consequences for these direct detection ex-periments. © Fantin et al.
The establishment of a reliable model for the Milky Waystill represents a significant source of uncertainty. One ofthe main reasons is that the scale relevant for direct de-tection experiments ( ∼ . − M ⊙ (Green et al. 2004). Unfortunately, suchmicro-halos are far smaller than the smallest subhalos re-solvable by simulations, which have mass ∼ M ⊙ and size ∼ f ( v ) at a single spatial point ofphase-space, identified as an ideal terrestrial detector (Stiff& Widrow 2003). This result was achieved using a reversetechnique that allowed them to reach a resolution that can-not be obtained by N-body simulations. They found that f ( v ) is characterised by the presence of a small number ofdiscrete streams of particles. Unfortunately, the reverse inte-gration is unstable, requiring the introduction of a softeninglength of 20 kpc into the adopted gravitational force law.This softening is large enough to affect the DM phase-spacedistribution imprinting on a terrestrial detector.Other theoretical investigations have argued that the ultra-local WIMP distribution consists of a much larger numberof streams, of the order of 10 − (Helmi et al. 2002; Vogels-berger et al. 2009). Overlapping DM streams in the innerpart of the halo lead to more complex configurations, whichmay ultimately be indistinguishable from a smooth distri-bution. Moreover, direct cosmological simulations show thatthe most massive local streams only contribute about 1 per-cent of the local DM density (Diemand et al. 2008, Vogels-berger et al. 2011). Schneider et al. (2010) found that atEarth’s location the DM ultra-fine distribution is composedof over 10 streams, which are generated by the tidal disrup-tion of DM “cold” microhalos (Schneider et al. 2010). Theyconclude that the material these streams are composed of isnot dense enough to be relevant for detection experiments.Recently Vogelsberger and White (2011; hereafter VW) haveargued that the picture on ultra-local scales is not too dif-ferent from that suggested by N-body simulations. Using anew technique for calculating the phase-space distributionfunction in the neighbourhood of a simulation particle (Vo-gelsberger et al. 2008), they estimate the presence of about ∼ unresolved streams at the Solar position. Their con-clusion is that the local velocity distribution is smooth (Vo-gelsberger & White 2011).In this paper, we present a new method of simulatingthe DM distribution of the Milky Way, building on the ap-proach developed by Fantin et al. (2008; hereafter Paper I).Applied to a merger tree describing the history of a MilkyWay-like galaxy, the model attributes to each progenitor ofthe halo a characteristic DM distribution, using the methoddeveloped in Paper I. The final result, obtained by summingthe contributions of all the progenitors, provides a model ofthe ultra-fine DM distribution in the Solar neighbourhoodat arbitrarily high spatial resolution, obtained without thecomputational overhead of a complete numerical integra-tion.The paper is organised as follows. In Section 2 wepresent the technique to calculate the ultra-fine DM dis- Figure 1.
The rotation curve of the isochrone potential, with thescale length taken to be equal to the Solar radius. Although notintended as a fully realistic model, it is a reasonable approxima-tion to the measured rotation curve of the Milky Way (Fig. 5 ofSofue et al. 2009). tribution of a merger tree. Section 3 contains our results,Section 4 draws some conclusions, and Section 5 provides asummary.
In Paper I we modelled the interaction between an unboundsystem of particles and a Milky Way-like galaxy. Althoughnot intended as a quantitative description of the Milky Way,this approach makes possible a detailed exploration of phase-space, and a thorough analysis of the expected signature ofa series of merger events in a terrestrial DM detector. Themethod has the great benefit of being analytically soluble,allowing the calculation of the dynamics of the merger re-markably simply. Furthermore, the gravitational force doesnot have to be artificially softened, providing a significantimprovement in accuracy. To describe the Milky Way grav-itational well we adopt the isochrone potential. Despite notbeing a realistic representation of a complex system suchas the Milky Way, for example causing an overestimationof the granularity of the system at the present time, thequalitative properties of the potential are similar to those ofour galaxy. Fig 1 presents the rotation curve calculated witha scale length equal to the solar radius. Both the value ofthe circular speed at the Solar radius and the overall shapeof the rotation curve are in reasonable agreement with theMilky Way rotation curve shown in Fig. 1 and 5 of Sofue etal. (2009)Concerning the merging halo, we model its initial DMphase-space distribution by assuming a bivariate Gaussian, f ( r , v ) ∝ e − [( r − r sat ) / σ )] e − [( v − v sat ) / σ ] , (1)where ( r sat , v sat ) is the initial location of the merging haloin phase-space, which allows us to simply parametrise its © , 1–9 ltra-fine dark matter structure in the Solar neighbourhood main properties, where σ s models its initial spatial extentand σ v its velocity dispersion.Galaxy formation models (Kauffmann et al. 1993; Coleet al. 1994) and N-body simulations (Springel et al. 2005,Boylan-Kolchin et al. 2009) both suggest that galaxiesformed though a continuous and regular hierarchical pro-cess. We therefore embed the model for a single merger intoa cosmological context by combining it with a merger tree.This approach allows us to describe a system in which lotsof DM satellites fall into the Galactic potential well. Fur-thermore, it produces a more realistic estimate of the finalvelocity distribution of the Galactic halo than the one pre-sented in Paper I because the merger tree describes a halo of10 M ⊙ , which has not undergone any recent major merger,as in the Milky Way. The tree has been kindly generated byAndrew Benson, using a semi-analytic method (Cole et al.2000, Parkinson et al. 2008) based on the assumption of thefollowing cosmological parameters: Ω = 0 .
25, Λ = 0 . b = 0 . h = 0 .
73 and σ = 0 .
9. The information pro-vided by the merger tree are the virial mass M of the merg-ing subhalos and the scale factor a at which they fall into themain progenitor. The mass resolution of the tree is 10 M ⊙ .Knowing the epoch in the past at which each satellite fallsinto the Milky Way’s halo and the initial position of themerging satellite in phase-space at that time, ( r sat , v sat ), themodel evolves the system analytically backwards in time.This allows us to map out the full velocity distributionwithin the “ideal” detector, which is located at the Solarposition, at a distance r = (8 . , ,
0) kpc from the Galac-tic centre. We assume that each subhalo falls into the hostsystem on a radial orbit from a random position on a sphereof radius r sat = r vir , where r vir is the (redshift dependent)virial radius of the Milky Way halo. Experiments reveal thatthese assumptions are not critical. For example, replacingthe radial orbits with orbits that have a peri-to-apo-centreratio of 1:6, the median found in cosmological simulations(Ghigna et al. 1998, Diemand et al. 2008), results in veloc-ity distributions that are indistinguishable. Similarly, start-ing the disintegration of each subhalo at its first pericentrepassage rather than at the Milky Way’s virial radius on itsinitial infall does not substantively alter the final velocitydistribution. The quantity v sat is approximated by the ve-locity of a body falling from an infinite distance, v sat = r GMr vir . (2)Finally, we use the virial theorem M vir = r vir σ G , (3)and the definition of virial mass M vir = 43 π ∆ vir ρ crit r , (4)to relate the velocity dispersion, the spatial extent and thevirial mass. The virial overdensity ∆ vir is defined as the den-sity relative to the mean density within r vir times the criticaldensity ρ crit at that redshift (Bryan & Norman 1998), and ρ crit is the critical density. Assuming a value for the con-centration parameter c = r vir /σ s = 10 (Bullock et al. 2001;Benson 2005), Eqs. (3) - (4) give an estimate of the twocharacteristic scales of the merging subhalo. Figure 2.
Energy spectrum of a Milky Way-like halo for an evo-lution time of ≃ . M ⊙ does not include any recent major merger. One velocity-unit corresponds to 570 km s − . To summarise, the principal steps of this modelling processare: • Pick a merger tree that gives a realistic representationof a Milky Way-like system. • Calculate the initial conditions for each subhalo in themerger tree. • Evaluate the velocity distribution, observable withinthe detector for each subhalo, using the model developedin Paper I. • Evaluate the total velocity distribution by summing allthe constituent mergers.
The model we have developed above is not intended to pre-dict in quantitative detail the experimental signal that aterrestrial detector would observe. Nevertheless, it is inter-esting to define quantities related to the ones measured bydirectional detectors, with the aim of investigating qualita-tively the properties of the system. In Section 3.1 we firstdetermine the local DM energy spectrum of a Milky Way-like halo as a quantity that can be directly measured byexperiments. Secondly, we present the velocity distributionas a function of direction and speed, quantities that cangive important indications about the evolution history ofthe Galactic halo. In Section 3.2 we present the contribu-tion to the velocity distribution produced by the addition ofa new progenitor to the same Milky Way-like halo, in orderto determine if late-merging subhalos might be detectable.
The energy spectrum is an observable quantity, and the anal-ysis of its features can shed light on the evolution history ofa system. For example, the particles of a stream produced bythe recent merger of a subhalo normally group around par-ticular values of the energy, forming “overdensities”. Fig. 2presents the energy spectrum of the Galactic halo for an ©000
The energy spectrum is an observable quantity, and the anal-ysis of its features can shed light on the evolution history ofa system. For example, the particles of a stream produced bythe recent merger of a subhalo normally group around par-ticular values of the energy, forming “overdensities”. Fig. 2presents the energy spectrum of the Galactic halo for an ©000 , 1–9 Fantin et al.
Figure 3.
Fractional departure, η , of the velocity-squared of theGalactic halo simulated in Figure 4 from a smooth distributionfor an evolution time t ≃ . − . evolution time of ≃ . η = N e − N rel N rel , (5)where N e is the number of particles in a range of velocitiesat t i and N rel is the number of objects in the same rangeonce the system is relaxed.In Figure 3 we present η for the same system as Fig. 2. Fromthe plot it is evident that the fractional departure is abso-lutely indiscernible from the distribution that the halo as-sumes when completely relaxed. The absence of any featureleads to the conclusion that the ultra-fine DM distributionin the Solar neighbourhood is composed of a huge number ofstreams. These overdense structures, clearly visible when weanalyse the interaction of a single satellite, overlap, generat-ing a smooth DM distribution and consequently a featurelessfractional departure.In principle, more information might be preserved if welook at the full velocity distribution as a function of angle, asrecorded by some DM detectors. Fig. 4 is a representation ofthe velocity distribution f ( r , v ) of the Milky Way-like halosimulated above in the (cos θ, v ) space, where θ is definedas the angle at which DM particles enter the detector, mea-sured relative to the direction of Solar motion in the MilkyWay. The plot is grey-scaled, and the shade of each pixelcovers a range of six orders of magnitude in f ( r , v ). Thisrange is large enough to show the most significant contribu-tions to the velocity distribution of the system. Assuming v max = 570 km s − , a value slightly larger than the escapespeed from the Milky Way ( v esc = 544 km s − , Smith et al.2007), and v min = 0 km s − , the velocity resolution of eachcell along the x -axis is ≃ . − . The angular resolution varies between ≃ ◦ (for small angles) and ≃ ◦ (for largeangles). To investigate the presence of overdensities in theangle distribution we apply a boxcar smoothing technique.This removes all the small differences in the velocity-spacedistribution, mainly due to pixelation artifacts. Fig. 4 showsthat in a system resembling our galaxy no clear featuresare present, except for a central overdensity. The overdensi-ties are relative to the surrounding pixels. The fact that theoverdensities are not easily distinguishable means that a fullquantitative analysis is not justified, but there is clearly in-formation in these structures. The particles composing thisregion have velocities in the range 285 km s − . v . − , which in the plot correspond to 0 . . v . .
7, andangles 60 ◦ . θ . ◦ ( − . . cos θ . . ≃ ◦ and ≃ . − .An investigation on the origin of these two levels of over-densities can be carried out by analysing the contributionsto the final velocity distribution of progenitors with similarmass. Using the same smoothing technique applied above,in Figure 5 we group together the satellites with mass ofthe same order of magnitude. The three groups we adoptare: 10 − M ⊙ (Fig. 5a), 10 − M ⊙ (Fig. 5b) and10 − M ⊙ (Fig. 5c). The three figures show that thecontributions from these groups of subhalos are heteroge-neous. The number of direct progenitors in the range of mass10 − M ⊙ is large ( ∼ ) and their total contribution tothe final velocity-space distribution is not negligible. Mostof the particles have 75 ◦ . θ . ◦ ( − . . cos θ . . − M ⊙ and 10 − M ⊙ are very similar. A significant difference can be seen: the ve-locity distribution produced by 10 M ⊙ subhalos does notshow any particular feature, while that from 10 M ⊙ satel-lites has a central overdensity. This suggests that the mostpronounced overdensity of Fig. 4 is mostly produced bysatellite with masses in the range 10 − M ⊙ . This motivates the study of the contribution from singlemergers. The method we adopt to investigate this issue con-sists of adding a DM satellite to the Galactic halo and ofanalysing its contribution to the final velocity-space dis-tribution. The properties of the additional progenitor thatwe vary are the mass and the time at which it falls intothe Galaxy. For the mass, we consider four different cases:10 M ⊙ , 10 M ⊙ , 10 M ⊙ and 10 M ⊙ . The main reasonthat motivates the limit of 10 M ⊙ is the absence of major © , 1–9 ltra-fine dark matter structure in the Solar neighbourhood Figure 4.
The smoothed velocity distribution of a Milky Way-like DM halo of mass 10 M ⊙ as a function of cos θ and v . The angledistribution is smoothed over a (5 ×
5) box. The detector is located at a position r = (8 . , ,
0) kpc. We use an array of dimensions n v , n θ = (150 × ≃ . − . The angular resolution on the y-axis varies between 10 ◦ ′ (for small angles) and ≃ ◦ (for large angles). The greyscale, with the shade of each pixel determined by the corresponding array of thedistribution function f ( r , v ), covers six orders of magnitude. Black corresponds to the upper limit and light grey to the lower one. Theblack circle highlights the region where overdensities, relative to the surrounding pixels, are present. mergers in the recent history of the Milky Way, based ontheoretical considerations which show that the accretion ofa 1 : 10 satellite galaxy could destroy the disk of the MilkyWay (Purcell et al. 2009). To get a complete overview of theevolution of the mergers we select four times, looking backinto the past, at which the progenitor fell into the host halo: • t ≃ .
75 Gyr ago ( z = 0 . z = 0. • t ≃ . z = 0 . • t ≃ . z = 1 . • t ≃
13 Gyr ago ( z = 8 . z = 0 of one of the extra progenitors andthe Milky Way-like halo only.The effect of the addition of an extra progenitor of mass be-tween 10 M ⊙ and 10 M ⊙ to the merger tree of the Galactichalo is always negligible. The contribution is not negligi-ble anymore when the mass of the new merging subhalo is Mass M ⊙ / Infall Time (Gyr ago) 1.75 2.0 7.5 1310 × × × × × × × × X × X X X X X X
Table 1.
Table showing the presence (or absence) of differencesbetween the velocity distribution of a system composed of theMilky Way-like halo plus the contribution of a single subhalo andthe Milky Way-like halo only. Different masses are considered forthe new progenitor, as well as different infall times. The symbol X is used if there are differences in these two values of f ( r , v ) (ina range of six orders of magnitude). On the other hand, if thevalues of the two f ( r , v ) are identical, the symbol × is used. equal to 10 M ⊙ . If plotted separately, without the presenceof the “background” distribution produced by the Galactichalo, the contribution is present and clearly visible. Unfor-tunately, once we merge in the same plot these two contribu-tions, the one of the extra progenitor is not visible anymorebecause it is concealed by the smooth “background” distri- © , 1–9 Fantin et al.
Fig. 5a: 10 M ⊙ M < M ⊙ Fig. 5b: 10 M ⊙ M < M ⊙ Fig. 5c: 10 M ⊙ M < M ⊙ Figure 5.
Series of plots presenting the contribution to the Milky Way-like halo angle distribution, simulated in Fig. 4, from the satelliteswith mass in the range 10 M ⊙ M < M ⊙ (Fig. 5a), 10 M ⊙ M < M ⊙ (Fig. 5b), and 10 M ⊙ M < M ⊙ (Fig. 5c).The greyscale and the dimensions of each pixel are the same as used Fig. 4. bution produced by the Galactic halo.The only case in which the merger of an extra progenitorgenerates clear features in the angle distribution of the MilkyWay is when the mass of the subhalo is equal to 10 M ⊙ .This configuration is shown in the four snapshots of Fig. 6.Fig. 6a represents the fall of the subhalo into the Galaxy ap-proximately 1.75 Gyr ago. Two vertical, narrow stripes areclearly visible. They both have an angular width of approx-imately 15 ◦ − ◦ : the first does not have sharp contours,while the second is centred in the range 79 ◦ . θ . ◦ ( − . . cos θ . . t the two vertical stripes have almost completely dis-appeared (Fig. 6b). This behaviour is expected because themain body of the satellite is still coherent and it is not lo-cated anywhere near the Solar neighbourhood.At t the satellite has performed several orbits aroundthe Galactic centre (Fig. 6c). At each orbit the phase mixingacts on the satellite, increasing the number of streams andthe amount of debris into which the subhalo is disrupted.The streams overlap and the velocity distribution of the sub-halo becomes smooth and uniform. Nevertheless, there is a © , 1–9 ltra-fine dark matter structure in the Solar neighbourhood Fig. 6a: t ≃ .
75 Gyr Fig. 6c: t ≃ . t ≃ . t ≃
13 Gyr
Figure 6.
Series of snapshots presenting the angle-velocity plot at z = 0 of a system composed of the Milky Way-like halo and a subhaloof mass 10 M ⊙ . The four plots describe configurations in which the progenitor falls into the host halo on a radial orbit at differenttimes. In Fig. 6a it fell ≃ .
75 Gyr ago. Fig. 6b corresponds to a infall time of ≃ . t ≃ . ≃
13 Gyr ago. The greyscale and the dimensions of each pixel of the four snapshots are the same as Fig.4, and the angle distribution is smoothed over a (5 ×
5) box. narrow, vertical stripe at velocity ≃
430 km s − ( v ≃ . ◦ . θ . ◦ ( − . . cos θ . . M ⊙ satellite is not complete.Finally, Fig. 6d presents the configuration in which themerger of the subhalo happened 13 Gyr ago. The stripesthat are present in other plots are now completely washedout. The absence of stripes confirms the presence of an al-most homogeneous distribution. Nevertheless, the remnant of the central part of the satellite is not completely disruptedand it still shows up as an overdensity. This overdensity islocated in the speed range 400 km s − . v .
430 km s − (0 . − . v . .
75 km s − ), with an angular width ofabout ≃ ◦ ( − . . cos θ . . © , 1–9 Fantin et al.
The conclusion inferred from the analysis of the energy spec-trum of a system resembling the Milky Way is that the ultra-fine DM distribution in the Solar neighbourhood is com-posed of a large number of streams. The streams overlapand produce a smooth distribution. Our result is in agree-ment with the conclusion of VW, which has been reachedusing an approach complementary to this analysis. VW’stechnique must be used in tandem with a N-body simula-tion. This implies the need of a large computational timeand it requires a softening length of 3 . f ( r , v ) in the(cos θ, v ) space, the results suggest the presence of two levelsof overdensities. They are the marks left by recent mergeractivity and we have verified that they have been mostly pro-duced by satellites with mass in the range 10 − M ⊙ . Theprobability of detecting such overdensities is however low.This is mainly caused by both the lack of strong features,and the limited angular resolution of the current generationof instruments. Nowadays this resolution is ≃ ◦ (Dujmic etal. 2008, Ahlen et al. 2010), one order of magnitude largerthan that required for the detection of these overdensities( ≃ ◦ ).The analysis of the contribution from single mergersto the ultra-fine DM distribution of a Milky Way-like haloshows the presence of features when the mass of the addi-tional satellite is equal or larger than 10 M ⊙ . The featuresgenerated by the merger of a satellite of mass M ⊙ are concealed by the smooth “background” distribution pro-duced by the Galactic halo, that dominates the (cos θ, v )space. Once this “background” is subtracted, it is possible tosee the imprint left by the additional satellite. Nevertheless,its angular width is too small ( ≃ ◦ ) to be detectable withthe present-day technology. Moreover, the angular width ofthe features generated by the merger of a 10 M ⊙ progeni-tor is 15 ◦ − ◦ , which is accessible to ongoing experiments.This raises the possibility to detect these peculiar features.This possibility depends on the probability of finding theremnant of a 10 M ⊙ subhalo in the Solar neighbourhoodand that this subhalo merged into the Galactic halo in therecent past ( . M h , is provided mostly by the accretion of subhalos of mass ∼ (0 . − . M h . Furthermore, it has been estimated thatthe probability of a Milky Way-like system of having experi-enced a merger with a subhalo of 10 M ⊙ in the last 8 Gyris ∼
80% (Stewart et al. 2008).
In this paper we have refined the method developed in Fantinet al. (2008), applying it to the formation of the Milky Wayin a cosmological context. The refinement consists of com-bining a merger tree, which describes the hierarchical growthof a Milky Way-like halo, with the model previously devel-oped, which simulates the interaction between an unboundsystem of particles and a larger parent halo. This allows usto produce a more complete and realistic treatment of themerger history of the Galactic halo, mapping out the sub-mpc-scale structure of the halo. Using such a simulation wecan obtain new insights into the likely signature of a halomerger event in a small terrestrial DM detector.We find that the velocity distribution does not contain anyclear feature. This is caused by the overlapping of a hugenumber of streams, which generates a uniform and smoothvelocity distribution. This result is in agreement with recentworks, such as Vogelsberger & White (2011) and Schneideret al. (2010). Detectable signatures in the ultra-fine velocitydistribution in the Solar neighbourhood are present only inthe case of the recent merger into the Galactic halo of a sub-halo of 10 M ⊙ . In this particular configuration the angularwidth of these features is larger than 10 ◦ , a resolution acces-sible to ongoing experiments. Finally, in the scenarios thatwe have analysed, the presence of some overdensities hasbeen identified. The current generation of detectors doesnot have the angular resolution required to observe thesefeatures, but a future generation of detectors with resolu-tion of ∼ ◦ would resolve them, allowing the recent historyof the Milky Way to be revealed. We thank Andrew Benson for providing the merger treesused to develop the project, and Frazer Pearce for usefuldiscussions.
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