Orientador: Rogério Rosenfeld / Banca: Alberto Vasquez Saa / Banca: Bruto Max Pimentel Escobar / Resumo: Na última década várias observações indicam que o universo está expandindo aceleradamente. Essa expansão acelerada pode ser explicada em um universo composto de 70% de energia escura e 30% de matéria (25% de matéria escura e 5% de matéria bariônica). A energia escura proporciona a pressão negativa necessária para produzir a aceleração em grandes escalas. Nesse trabalho faz-se uma revisão do modelo de um campo escalar como fonte da energia escura, conhecido genericamente como modelo de quintessência. Estuda-se o modelo de quintessência acoplada à matéria escura / Abstract: In the previous decade many observations indicate that the universe is accelerating. This rapid expansion can be explained in an universe made up of 70% of dark energy and 30% of matter (25% of dark matter and 5% of baryonic matter). The dark energy provides negative pressure to produce acceleration. In this work it is studied the model of Quintessence, a model of scalar field, as source of the dark energy. It is studied the model of Coupled Quintessence with dark matter / Mestre

The modern era of particle physics is driven by experimental anomalies. Experimental efforts have become increasingly diverse and are producing enormous volumes of data. In such a highly data-driven scientific environment theoretical models are necessary to understand this data and to help inform the development of new experimental approaches. In this dissertation I present two significant contributions to this effort relevant to the energy, intensity, and cosmic frontiers of modern particle physics research. Part 1 of this dissertation discusses methods to understand modern dark matter direct detection results. In particular I present an analysis under the hypothesis of inelastic dark matter, which supposes that dark matter must scatter inelastically, i.e. that it must gain or loose mass during a collision with atomic nuclei. This hypothesis is attractive because it can alleviate otherwise contradictory results from a number of dark matter detection facilities. The main conclusion of this work is a presentation of the analytical tools, along with a mathematica package that can be used to run the analysis, and the discovery that there are regions of inelastic dark matter parameter space which are consistent with all current experimental results, and constraints. Part 2 of this dissertation discusses a phenomenon of modern interest called kinetic mixing which allows particles from the standard model to spontaneously transform into particles which experience a new, as of yet undiscovered, force. This phenomenon is relatively common and well motivated theoretically and has motivated significant experimental effort. In this work, I present an analysis of a general case of kinetic mixing, called nonabelian kinetic mixing. This work shows that, In general, kinetic mixing predicts the existence of a new particle and that, under certain conditions, this particle could be detected at modern particle colliders. Furthermore, the mass of this particle is related to the strength of kinetic mixing. This relationship suggests novel ways to constrain kinetic mixing parameter space, and if observed would provide a very striking indication that such a model is realized in nature.

Galactical and cosmological evidence show that a quarter of the energy budget of our universe is made of collisionless, non-relativistic, and non-baryonic dark matter. Its potential coupling to standard model particles, however, has not yet been understood. One of the leading candidates - Weakly Interacting Massive Particles (WIMP) - allows the production of a dark matter relic density as observed today and couples to standard model particles at or below the weak scale. LUX-ZEPLIN (LZ) is a future tonne-scale two-phase xenon TPC aiming to detect WIMP recoils with xenon nuclei. The experiment will begin WIMP search data-taking in 2020 at the Sanford Underground Research Facility (SURF) in Lead, South Dakota and has a projected sensitivity of 3 × 10^-48 cm² or better in probing a 40 GeV/c² WIMP. The main observables of particle interactions in LZ are the primary scintillation (S1) and secondary scintillation (S2). However, optimising and achieving a stable S2 signal in such a tonne-scale TPC is non-trivial. Effects from the structural design of the S2 production region (top-corner structure), TPC tilt, and the xenon circulation system requires precise monitoring of the liquid surface. Such monitoring is achieved by the capacitive liquid level sensors developed within this thesis. The sensors are strategically placed to ensure that nonuniformity of the S2 signal due to the effects can be understood and corrected. In this thesis, the development of a monitoring system designed to optimise the quality of the S2 signal, based on the capacitive level sensors is discussed. A design of the electronics scheme based on a differential measurement allows femtofarad precision measurement of sensor's capacitance at picofarad level, even in the presence of cable capacitance at nanofarad level. A systematic study of the response of such a sensor to LXe and the application of the precision level sensors to two-phase TPC was carried out. Findings of intrinsic influences from LXe artefacts and LXe dielectric constant variation with its saturated temperature are identified; the result on the application of the sensors contributes to the designs of LZ circulation and the top-corner region. The final LZ level sensors show an artefact-free liquid level measurement and a 12 μm precision in measuring liquid nitrogen level (projection for LXe: ∼ 9 μm) over a 20 mm measurement range.

Made available in DSpace on 2018-07-27T18:26:17Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-08-28. Added 1 bitstream(s) on 2018-07-27T18:30:43Z : No. of bitstreams: 1 000876019.pdf: 830419 bytes, checksum: d04b4fc0f1ac3688428cce3a07901b9e (MD5) / A matéria escura é responsável por cerca de 85% de toda a matéria do universo. Sabe-se que ela possui um longo tempo de vida, que é neutra e interage com a matéria comum apenas gravitacionalmente. Muitos modelos foram aventados para descrever as possíveis partículas de matéria escura, muitos deles baseados em extensões do modelo padrão para partículas elementares. Em particular, há os modelos de partículas massivas interativas por força forte, os SIMPs, que estendem o modelo padrão com um setor escalar extra contendo todas as partículas de matéria escura, cuja estabilidade é garantida por uma simetria discreta, a qual respeitam. Essa simetria também estende as possível interações entre as partículas de matéria escura para além da usual auto-aniquilação de pares e do contexto do problema de Lee-Weinberg, descrito pelas partículas massivas interagentes por força fraca, os WIMPs. Neste trabalho postulamos a existência de um setor escalar com uma simetria discreta 'Z IND. 3'; consequente de uma quebra de simetria U(1)DM global. Esta simetria permite que processos de semi-aniquilação e aniquilação 3 SETA 2 também ocorram, além do usual processo de auto-aniquilação. Estudaremos esses três cenários, encontrando as soluções das equações de Boltzmann e comparando suas respectivas abundâncias com o resultado observacional, para podermos avaliar nosso modelo. Começaremos por revisar importantes conceitos da cosmologia padrão e por apresentar o modelo. Então revisaremos as soluções numéricas para as equações, e apresentaremos nossos próprios resultados para soluções semi-analíticas dos processos de semianiquilação e de aniquilação 3 'SETA' 2. Concluiremos por apresentar nossos próprios resultados para a solução da equação de Boltzmann para o processo 3 'SETA' 2 usando uma seção de choque que é dependente da temperatura, calculada com o pacote CalcHEP / Dark matter accounts for approximately 85% of all the matter in the universe. It is known to have a long lifetime, to be neutral and to interact with ordinary matter almost only gravitationally. There have been several models to suggest possible particles for the dark matter, many of them relying on extensions to the standard model of elementary particles. In particular, there are SIMP (strongly-interacting massive particles) models, which extend the standard model by an extra scalar sector containing the dark-matter particles, whose stability is provided by a discrete symmetry. This symmetry also extends the possible interactions between the dark-matter particles to beyond the usual pair annihilation and Lee-Weinberg scenario described by the WIMP (weakly-interacting massive particles) models. In our study, we postulate the existence of an extended dark sector with a 'Z IND. 3' discrete symmetry, which is the consequence of a global U(1)DM symmetry breaking. This symmetry allows the semi-annihilation and 3 'SETA' 2 annihilation processes to take place, besides the usual self-annihilation process. We will study each of these three scenarios, solving the respective Boltzmann equations and comparing the correspondent relic abundance to the observed one, in order to verify the liability of each of them. We will start by reviewing important aspects of standard cosmology and presenting our model. Then we will review the numerical solutions for the equations, and present our own results for semi-analytical solutions to the semi- and 3 'SETA' 2 annihilation processes. We will end by presenting our own results on solving the 3 'SETA' 2 Boltzmann equation for a temperature-dependent cross-section, calculated with the CalcHEP package

According to the current cosmological paradigm, ``Lambda Cold Dark Matter'' (LambdaCDM), only ~20% of the gravitating matter in the universe is made up of ordinary (i.e. baryonic) matter, while the rest consists of invisible dark matter (DM) particles, which existence can be inferred from their gravitational influence on baryonic matter and light. Despite the large success of the LambdaCDM model in explaining the large scale structure of the Universe and the conditions of the early Universe, there has been debate on whether this model can fully explain the observations of low mass (dwarf) galaxies. The Local Group (LG), which hosts most of the known dwarf galaxies, is a unique laboratory to test the predictions of the LambdaCDM model on small scales. I analyze the kinematics of LG members, including the Milky~Way-Andromeda (MW-M31) pair and dwarf galaxies, in order to constrain the mass of the LG. I construct samples of LG analogs from large cosmological N-body simulations, according to the following kinematics constraints: (a) the separation and relative velocity of the MW-M31 pair; (b) the receding velocity of dwarf galaxies in the outskirts of the LG. I find that these constraints yield a median total mass of 2*10^{12} solar masses for the MW and M31, but with a large uncertainty. Based on the mass and the kinematics constraints, I select twelve LG candidates for the APOSTLE simulations project. The APOSTLE project consists of high-resolution cosmological hydrodynamical simulations of the LG candidates, using the EAGLE galaxy formation model. I show that dwarf satellites of MW and M31 analogs in APOSTLE are in good agreement with observations, in terms of number, luminosity and kinematics. There have been tensions between the observed masses of LG dwarf spheroidals and the predictions of N-body simulations within the LambdaCDM framework; simulations tend to over-predict the mass of dwarfs. This problem is known as the ``too-big-to-fail'' problem. I find that the enclosed mass within the half-light radii of Galactic classical dwarf spheroidals, is in excellent agreement with the simulated satellites in APOSTLE, and that there is no too-big-to-fail problem in APOSTLE simulations. A few factors contribute in solving the problem: (a) the mass of haloes in hydrodynamical simulations are lower compared to their N-body counterparts; (b) stellar mass-halo mass relation in APOSTLE is different than the ones used to argue for the too-big-to-fail problem; (c) number of massive satellites correlates with the virial mass of the host, i.e. MW analogs with virial masses above ~ 3*10^{12} solar masses would have faced too-big-to-fail problems; (d) uncertainties in observations were underestimated in previous works. Stellar mass-halo mass relation in APOSTLE predicts that all isolated dwarf galaxies should live in haloes with maximum circular velocity (V_max) above 20 km/s. Satellite galaxies, however, can inhabit lower mass haloes due to tidal stripping which removes mass from the inner regions of satellites as they orbit their hosts. I examine all satellites of the MW and M31, and find that many of them live in haloes less massive than V_max=20 km/s. I additionally show that the low mass population is following a different trend in stellar mass-size relation compared to the rest of the satellites or field dwarfs. I use stellar mass-halo mass relation of APOSTLE field galaxies, along with tidal stripping trajectories derived in Penarrubia et al., in order to predict the properties of the progenitors of the LG satellites. According to this prediction, some satellites have lost a significant amount of dark matter as well as stellar mass. Cra~II, And~XIX, XXI, and XXV have lost 99 per-cent of their stellar mass in the past. I show that the mass discrepancy-acceleration relation of dwarf galaxies in the LG is at odds with MOdified Newtonian Dynamics (MOND) predictions, whereas tidal stripping can explain the observations very well. I compare observed velocity dispersion of LG satellites with the predicted values by MOND. The observations and MOND predictions are inconsistent, in particular in the regime of ultra faint dwarf galaxies. / Graduate

No description available.

The topic of this thesis is the study of the vertical structure of the disk galaxies and their dark matter halos through theoretical modeling and numerical calculations. The basic theoretical model of the galactic disk used involves gravitationally-coupled stars and gas under the force-field of a dark matter halo; the disk is rotationally-supported in the plane and pressure-supported perpendicular to the plane of the galaxy. The first part of the thesis involves evaluating the vertical structure of stars and gas in normal as well as dwarf spiral galaxies. The second part of the thesis deals with probing the dark matter halo density profiles of disk galaxies using both the observed rotation curve and the H i scale height data. Following is the layout of the thesis. Chapter 1 gives a general introduction to the topic of vertical structure of spiral galaxies and their dark matter halos, followed by a broad overview of the theoretical development of the topic and ends with highlighting the motivation and challenges met in this thesis. Chapters 2 & 3 deal with the vertical structure of stars and gas in galaxies, Chapters 4-6 focus on obtaining the dark matter halo density profiles of disk galaxies from the observed rotation curve and the H i scale height data whereas Chapter 7 is devoted to the summary of results and future research plans. Vertical structure of stars and gas in galaxies The vertical thickness of the stars and the gas, namely atomic hydrogen (H i) and molecular hydrogen (H2) in a spiral galaxy, is crucial in regulating the disk dynamics close to the mid-plane, especially in the inner galaxy. However, measuring it observationally is not in general practicable due to the limitations of astronomical observations, and often impossible as in the case of face-on galaxies. Therefore, it is imperative to develop a theoretical model of the galaxy which can predict the thickness of the disk components by using as input parameters the physical quantities, which are more observationally-amenable compared to the disk thickness. The vertical thickness of the disk components is determined by a trade-off between the upward kinetic pressure and the net downward gravitational pull of the galaxy. The fraction of the disk mass due to the stars is an order of magnitude higher than that of the gas in ordinary spiral galaxies, and therefore the gas contribution to the disk gravity is ignored in general. We have developed a multi-component model of gravitationally-coupled stars, HI and H2 subjected to the force-field of an external dark matter halo, and conclusively demonstrated the importance of the inclusion of gas gravity in explaining the steep vertical stellar distribution observed in galaxies. These apart, this model does not implicitly assume a flat rotation curve for the galaxy and therefore is applicable in general to obtain the thickness of stars and gas in dwarfs (with linearly rising rotation curves) as well as in ordinary spirals. In Chapter 2, we investigate the origin of the steep vertical stellar distribution in the Galactic disk. One of the direct fall outs of our above model of the galaxy, which incor¬porates the self-gravity of the gas unlike the earlier theoretical models, lies in explaining the long-standing puzzle of the steep vertical stellar density distribution of the disk galax¬ies near the mid-plane. Over the past two decades, observations revealed that the vertical density distribution of stars in galaxies near the mid-plane is substantially steeper than the sech2 function that is expected for a self-gravitating system of stars under isothermal ap¬proximation. However, the physical origin for this has not been explained so far. We have clearly demonstrated that the inclusion of the self-gravity of the gas in the dynamical model of the Galaxy solves the problem even under the purview of isothermal approximation for the disk components. Being a low dispersion component, the gas resides closer to the mid¬plane compared to the stars, and forms a thin, compact layer near the mid-plane, thereby strongly governing the local disk dynamics. This novel idea, highlighting the significance of gas gravity has produced substantial impact on the field and triggered research activities by other groups in related areas of disk dynamics. The strong effect of the gas gravity on the vertical density profile of the stellar disk indicates that it should also bear its imprint on the Milky way thick disk, as the epoch of its formation 109 years ago is marked by a value of gas fraction, almost an order of magnitude higher than its present day value. Interest-ingly, the findings of the upcoming Gaia mission can be harnessed to verify this theoretical prediction. It may also hold the clue as to the reason behind the absence of thick disk in superthin galaxies. In Chapter 3, we use the same model to theoretically determine the H i vertical scale heights in the dwarf galaxies: DDO 154, Ho II, IC 2574 & NGC 2366 for which most of the necessary input parameters are available from observations. We stress the fact that the observational determination of the gas thickness in these dwarf irregulars is not viable. Nevertheless, it is important to estimate it theoretically as it plays a crucial role in calculating the star-formation activities and other related phenomena. However, two vital aspects have to be taken care of while modeling these dwarf galaxies. Firstly, the mass fraction in gas in these galaxies is comparable to that of the stars, and hence the gas gravity cannot be ignored on any account unlike in the case of large spirals. Secondly, dwarf galaxies have a rising rotation curve over most of the disk unlike the flat rotation curves of ordinary spirals. Both these factors have been considered in developing our model of the dwarf galaxies. We find that three out of the four galaxies studied show a flaring of their H i disks with increasing radius, by a factor of a few within several disk scale lengths. The fourth galaxy (Ho II) has a thick H1 disk throughout. A comparison of the size distribution of H1 holes in the four sample galaxies reveals that of the 20 type 3 holes, all have radii that are in agreement with them being still fully contained within the gas layer. Probing the dark matter halo profiles of disk galaxies The next part of the thesis involves the dynamical study of the shapes and density profiles of galactic dark matter halos using observational constraints on our theoretical model of a spiral galaxy. The density distribution of the dark matter halo is generally modeled using the observed rotation curve of the spiral galaxies. The rotational velocity at any radius is determined by the radial component of the net gravitational force of the galaxy, which, however, is weakly dependent on the shape of the dark matter halo. Therefore, one cannot trace the dark matter halo shape by the observed rotation curve alone. The vertical thickness of the stars and gas, on the other hand, is strongly dependent on the flattening of the dark matter halo, and therefore the observed gas thickness can be used as a diagnostic to probe the halo shape. In this thesis, we have used the double constraints of the rotation curve and the H i thickness data to obtain the best-fit values of the core density, core radius and the vertical-to-planar axis ratio (or flattening) of the dark matter halos of our largest nearby galaxy Andromeda (or M31), a low-surface brightness (LSB) superthin galaxy UGC 7321 and to study the dark matter halo shape of our Galaxy. In Chapter 4, we study the dark matter halo of M31 or Andromeda, the largest nearby galaxy to the Milky Way. We find that M31 has a highly flattened isothermal dark matter halo with the vertical-to-horizontal axis ratio equal to 0.4, which interestingly lies at the most oblate end of the halo shapes found in cosmological simulations. This indicates that either M31 is a unusual galaxy, or the simulations need to include additional physics, such as the effect of the baryons, that can affect the shape of the halo. This is quite a remarkable result as it challenges the popular practice of assuming a spherical dark matter halo in the dynamical modeling of the galaxy In Chapter 5, we have applied this technique to the superthin galaxy UGC 7321. Su¬perthins are somewhat the “extreme” objects in the local Universe because of their high gas fraction and absence of a thick disk component. It is interesting to analyze their so-called extreme characteristics in the light of the physical mechanisms which determined them to understand better the properties of ordinary spirals. We find that UGC 7321 has a spher¬ical isothermal halo, with a core radius almost equal to the disk scale length. This reveals that the dark matter dominates the dynamics of this galaxy at all radii, including the inner parts of the galaxy. This is unlike the case for the large spiral galaxies, where the core radius is typically about 3-4 disk scale lengths. Interestingly, the best-fit halo core density and the core radius are consistent, with deviations of a few percent, with the dark matter fundamental plane correlations, which depict the systematic properties of the dark matter halo in late-type and dwarf spheroidal galaxies. This apart, a high value of the gas velocity dispersion is required to get a better fit to the H i scale height data, although the superthin nature of the stellar disk implies a dynamically cold dynamic galactic disk. However, it explains the low star-formation rates in these galaxies since the Toomre Q criterion (Q < 1) for instability is less likely to be satisfied, and hence the disk is liable to be more stable to star formation. In Chapter 6, we investigate the shape of the dark matter halo in the outer Galaxy. We find that the halo is prolate, with the vertical-to-planar axis ratio monotonically increasing to 2.0 at 24 kpc, or 8 radial disk scale lengths. The resulting prolate-shaped halo can explain several long-standing puzzles in galactic dynamics, for example, it permits long-lived warps thus explaining their ubiquitous nature. It also imposes novel constraints on the galaxy formation models. Finally, in Chapter 7, the thesis is concluded with a summary of the main results and a brief discussion of the scope for future work.

Orientador: Rogério Rosendeld / Co-orientador: Nicolás Bernal / Banca: Ricardo D'Elia Matheus / Banca: Renata Zukanovich Funchal / Resumo: A matéria escura é responsável por cerca de 85% de toda a matéria do universo. Sabe-se que ela possui um longo tempo de vida, que é neutra e interage com a matéria comum apenas gravitacionalmente. Muitos modelos foram aventados para descrever as possíveis partículas de matéria escura, muitos deles baseados em extensões do modelo padrão para partículas elementares. Em particular, há os modelos de partículas massivas interativas por força forte, os SIMPs, que estendem o modelo padrão com um setor escalar extra contendo todas as partículas de matéria escura, cuja estabilidade é garantida por uma simetria discreta, a qual respeitam. Essa simetria também estende as possível interações entre as partículas de matéria escura para além da usual auto-aniquilação de pares e do contexto do problema de Lee-Weinberg, descrito pelas partículas massivas interagentes por força fraca, os WIMPs. Neste trabalho postulamos a existência de um setor escalar com uma simetria discreta 'Z IND. 3'; consequente de uma quebra de simetria U(1)DM global. Esta simetria permite que processos de semi-aniquilação e aniquilação 3 "SETA" 2 também ocorram, além do usual processo de auto-aniquilação. Estudaremos esses três cenários, encontrando as soluções das equações de Boltzmann e comparando suas respectivas abundâncias com o resultado observacional, para podermos avaliar nosso modelo. Começaremos por revisar importantes conceitos da cosmologia padrão e por apresentar o modelo. Então revisaremos as soluções numéricas para as equações, e apresentaremos nossos próprios resultados para soluções semi-analíticas dos processos de semianiquilação e de aniquilação 3 'SETA' 2. Concluiremos por apresentar nossos próprios resultados para a solução da equação de Boltzmann para o processo 3 'SETA' 2 usando uma seção de choque que é dependente da temperatura, calculada com o pacote CalcHEP / Abstract: Dark matter accounts for approximately 85% of all the matter in the universe. It is known to have a long lifetime, to be neutral and to interact with ordinary matter almost only gravitationally. There have been several models to suggest possible particles for the dark matter, many of them relying on extensions to the standard model of elementary particles. In particular, there are SIMP (strongly-interacting massive particles) models, which extend the standard model by an extra scalar sector containing the dark-matter particles, whose stability is provided by a discrete symmetry. This symmetry also extends the possible interactions between the dark-matter particles to beyond the usual pair annihilation and Lee-Weinberg scenario described by the WIMP (weakly-interacting massive particles) models. In our study, we postulate the existence of an extended dark sector with a 'Z IND. 3' discrete symmetry, which is the consequence of a global U(1)DM symmetry breaking. This symmetry allows the semi-annihilation and 3 'SETA' 2 annihilation processes to take place, besides the usual self-annihilation process. We will study each of these three scenarios, solving the respective Boltzmann equations and comparing the correspondent relic abundance to the observed one, in order to verify the liability of each of them. We will start by reviewing important aspects of standard cosmology and presenting our model. Then we will review the numerical solutions for the equations, and present our own results for semi-analytical solutions to the semi- and 3 'SETA' 2 annihilation processes. We will end by presenting our own results on solving the 3 'SETA' 2 Boltzmann equation for a temperature-dependent cross-section, calculated with the CalcHEP package / Mestre

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, February 6, 2015. / We explore indirect detections of Dark Matter, focusing on deep radio observations of six dwarf spheroidal galaxies (dSph), Carina, Fornax, BootesII, Hercules, Segue2, Sculptor. We discuss the WIMP Dark Matter particle annihilation process and describe brie y the particles produced in this process. We consider the emissions, which can result from electrons and positrons produced. We describe why dSph are the best observational targets for indirect Dark Matter detection at radio frequencies. We describe the theoretical framework for predicting Dark Matter synchrotron emissions and make some predictions for the six dSph of interest to us. We discuss ATCA observations of these dSph and explore the background source subtraction process in detail. We obtain an upper limit on the WIMP mass and compare our results to various other experiments. We discuss prospects for this work towards attaining an indirect Dark Matter detection.

I carried out systematic studies on the assembly history of dark matter halos, using numerical simulations and semi-analytical methods. First, I look into dark halo mass assembly history. I confirmed that the halo mass assembly is divided into a fast accretion phase and a slow accretion phase. These two phases are found to be separated by the epoch when the dark halo potential reaches its maximum. The fast accretion phase is dominated by mergers, especially major mergers; the slow accretion phase is dominated by slow mass accretion. Each halo experiences about 3±2 major mergers since its main progenitor had a mass equal to 1 percent of halo mass. However, the average redshift at which these major mergers occur is strongly mass dependent. Secondly, I investigate the formation times and the assembly bias of dark halos. I use eight different definitions of halo formation times to characterize the different aspects of the halo assembly history. I find that these formation times have different dependence on halo mass. While some formation times characterize well the hierarchical nature of halo formation, the trend is reversed for other definitions of the formation time. In addition, the formation-time dependence of halo bias is quite strong for some definitions of formation time but weak or absent for others. Thirdly, I study sub-halo mass function in the halo assembly history, with the generally known unevolved sub-halo mass functions (USMFs). I find that for subhalos that merge into the main progenitor of a present-day halo, their USMF can be well described by a universal functional form; the same conclusion can also be reached for the USMF of all sub-halos that have merged during the entire halo merging history. In these two cases, the USMFs do not seem to depend on the redshift of the host halo either. However, due to the mass loss caused by dynamical effects, only small part of the accreted halos survived and became sub-structures in the present-day dark halos. In the cluster-sized halos, 30% survived sub-halos are sub-subhalos. The sub-halo mass function at given accretion time (redshift) is also investigated to find the origin of the statistics mentioned above.