SOLAR CONSTRAINTS ON ASYMMETRIC DARK MATTER

During the last three decades, overwhelming evidence has been found for the existence of dark matter in the universe. This achievement is the result of a careful analysis of the available cosmological observational data, combined with a variety of well-structured theoretical physical models coming from quite different and complementary research fields in particle physics, cosmology, and astrophysics. Such studies have led the way to identification of the basic gravitational effects of dark matter, and their contribution to the formation of structure in the universe. In spite of this, the fundamental nature of the dark matter particles remains a mystery.

Current observational studies suggest that the matter present in the universe is composed predominantly of dark matter particles and baryons (Munshi et al. 2011). Recent measurements of the cosmic microwave background by the WMAP team (Larson et al. 2011) give precise measurements of the dark matter density and the baryonic density: Ω_DMh² = 0.1109  ±  0.0056 and Ω_Bh² = 0.02258^+0.00057_{− 0.00056}. These observational studies also measure the imbalance between baryons and antibaryons, i.e., the baryon asymmetry, which is found to be equal to (0.88 ± 0.021) × 10⁻¹⁰.

Among the most popular candidates for dark matter are a group of particles that occur naturally in supersymmetric extensions of the standard model of particle physics, usually called weakly interacting massive particles (WIMPs), the neutralino, the lightest supersymmetric stable particle, being the typical example. Significant constraints in the properties of WIMP candidates and similar particles have been made using stars (Bertone et al. 2005), such as the Sun (e.g., Lopes & Silk 2010a, 2010b; Taoso et al. 2010; Cumberbatch et al. 2010), Sun-like stars (Casanellas & Lopes 2011a, 2011b), and neutron stars (e.g., Kouvaris 2012; Kouvaris & Tinyakov 2010, 2011; Bertone & Fairbairn 2008). Although, WIMP candidates can be either Dirac or Majorana particles, usually, WIMPs are considered to be of the latter type, as such these particles do not have an asymmetry such as the baryon asymmetry. Recently, several authors (e.g., Gudnason et al. 2006; Foadi et al. 2009; Hooper et al. 2005) following previous work (e.g., Nussinov 1985; Kaplan 1992) have proposed a new type of matter, known as asymmetric dark matter, which has an asymmetry identical to baryons (Kaplan et al. 2009). Like WIMPs, such particles are non-relativistic massive particles that interact with baryons on the weak scale, thereby having a sizeable scattering cross section with baryons (Kaplan et al. 2009), but unlike WIMPs, such a type of dark matter is produced in the primordial universe by a mechanism similar to baryogenesis. This type of dark matter, much the same as baryons, is considered to have an asymmetry that we choose to represent by the parameter η. Hence, this dark matter is composed of an unequal amount of matter and antimatter (e.g., Farrar & Zaharijas 2006). Furthermore, these particles have a mass of the order of a few GeV (e.g., Kang et al. 2011; Cohen et al. 2010). We will refer to this type of dark matter as η-parameterized asymmetric dark matter (ηADM) or simply as η-asymmetric dark matter.

Several experiments committed to direct dark matter searches show evidence of positive particle detection, although these results are still very controversial and not universally accepted: the DAMA/LIBRA (Bellini et al. 2012; Bernabei et al. 2008) and CoGeNT (Aalseth et al. 2011) experiments find evidence of a particle candidate with a mass of the order of a few GeV (likely between 5 and 12 GeV), and a spin-independent scattering cross section of baryons of the order of 10⁻⁴⁰ cm². The CRESST (Brown et al. 2012) experiment also points to unexplained events consistent with direct detection of a light mass particle. Unfortunately, other direct detection experiments, such as CDMS (Ahmed et al. 2011) and XENON10/100 (Aprile et al. 2011; Angle et al. 2011) find no indication of the existence of such particles. Nevertheless, several theoretical explanations based on the existence of asymmetric dark matter have been suggested to explain and accommodate all these positive and negative detections (e.g., Chang et al. 2010; Farina et al. 2011; Hooper & Kelso 2011; Del Nobile et al. 2011).

In this paper, we investigate the origin of such light ηADM particles, and discuss how this type of matter influences the evolution of stars. We look for their impact on the present structure of the Sun. The Sun, by means of two groups of observables, helioseismology and solar neutrino fluxes, provides one of the most powerful tests of stellar evolution (Turck-Chieze & Couvidat 2011) and of alternative theories of modern physics and cosmology (Casanellas et al. 2012; Turck-Chieze et al. 2012; Lopes et al. 2002). Although both groups of observables are equally relevant for such types of studies, we have chosen preferentially to study the impact on solar neutrino fluxes, as neutrinos are the most sensitive probe of changes in the structure of the solar core. In particular, we will compare the neutrino fluxes of a "Sun" evolving in a halo of asymmetric dark matter with the current measurements of solar neutrino fluxes, namely, the ⁸B and ⁷Be neutrino fluxes. Moreover, we will complete the study with a succinct helioseismology diagnostic.

In the reminder of this paper, we consider that the dark matter asymmetry is identical to the baryon asymmetry, and likewise leads to an unbalanced amount of particles and antiparticles. This η-asymmetry occurs well before the epoch of thermal decoupling of the dark matter. We do not discuss here any of the possible mechanisms for the generation of such asymmetry, but rather treat this quantity as a free parameter. This asymmetric dark matter framework is used to study the impact of such matter in the evolution of the Sun for a wide range of particle masses, annihilation cross sections, and dark matter asymmetries.

In Section 2, we present the basic properties of ηADM and explain how the relic dark matter density of the present-day universe is computed. In Sections 3–5, we discuss the changes caused in the Sun by the presence of ηADM in its core, as well as the impact on the flux of solar neutrinos and helioseismology. In the last section, we summarize our results and draw some conclusions.

In the early stages of the universe, the cosmic fluid rapidly reached thermal equilibrium, as a consequence of standard and dark matter particles having a very high rate of interactions. In this work, we allow dark matter to be constituted by a mixture of particles and antiparticles, χ and $\bar{\chi }$ with a mass m_χ, and g_χ being the number of internal degrees of freedom (Drees et al. 2006). The universe is considered to have a temperature T and an effective number of relativistic degrees of freedom g_⋆ (Iminniyaz et al. 2011). Unlike symmetric dark matter, χ and $\bar{\chi }$ particles are not necessarily identical. Following the usual convention, the asymmetric nature of the dark matter is defined by the parameter η, which is equal to the difference of particle and antiparticle populations. Without loss of generality, we conventionally define η ⩾ 0, i.e., particles are more abundant than antiparticles. Here η stays constant throughout the evolution of the universe. The asymmetry η is similar to the asymmetry for baryons η_B, both of which originate in the early phases of the universe. If not stated otherwise, in the numerical examples, the population of χ and $\bar{\chi }$ particles is constituted by elementary particles with mass m_χ ∼ 10 GeV, g_⋆ = 90, and g_χ = 2. This is equivalent to a particle population formed by Dirac fermions (Dent et al. 2010; Drees et al. 2006).

As the universe expands, the interactions between all particles become sparse, the temperature of the plasma drops, the universe gets cooler, up to the moment that the $\chi \bar{\chi }$ annihilation rate drops below the Hubble expansion rate, leading to dark matter becoming decoupled from the rest of the cosmic fluid. The dark matter density, Ω_DM, has frozen out and has been constant ever since. The relic densities of χ and $\bar{\chi }$ particles are determined by solving the coupled system of Boltzmann equations that follows the time evolution of the number density of particles and antiparticles in the expanding universe (Iminniyaz et al. 2011).

The present-day dark matter density, Ω_DM, depends on the relic densities of particles and antiparticles, Ω_χ and $\Omega _{\bar{\chi }}$, which in turn depend on the mass of the particle, m_χ, the $\chi \bar{\chi }$ annihilation cross section, σ, and the dark matter asymmetry η.

Primarily, the value of Ω_DM relies on the properties of the $\chi \bar{\chi }$ annihilation cross section. In most cases, the thermal averaging of the $\chi \bar{\chi }$ annihilation cross section times the relative velocity of colliding particles v can be expanded as $\langle \sigma v\rangle = a +b v^2 + {\cal O} (v^4)$. If the annihilation initial state is unsuppressed, the first term of the previous equation dominates (a ≠ 0). This process is known as the s-wave annihilation channel. Alternatively, if the initial state is suppressed, a = 0 and b ≠ 0, this is the p-wave annihilation channel. This expansion is valid for all known examples of s-wave channel, p-wave channel, or both channels, up to an accuracy of a few percent. The expression 〈σv〉 can be simplified further, if the reacting particles are non-relativistic, $\langle \sigma v\rangle = a +6 b x^{-1} + {\cal O} (x^{-2})$ where x defines the ratio of m_χ over the temperature of the universe T (Iminniyaz et al. 2011).

In the case of symmetric dark matter particles ($\bar{\chi }=\chi$), the relic abundance Ω_χ is mainly determined by the annihilation rate 〈σv〉. Furthermore, Ω_χ is equal to the dark matter value Ω_DM. Alternatively, in the case of asymmetric dark matter ($\bar{\chi }\ne \chi$), χ and $\bar{\chi }$ particle contributions have to be added such that $\Omega _{{\rm DM}}= \Omega _{\chi }+\Omega _{\bar{\chi }}$, as there are more particles than antiparticles (or the reverse). The antiparticles are annihilated away more efficiently, with large numbers of particles left behind without a partner to annihilate them. Consequently, the relic dark matter abundance is determined not only by the 〈σv〉 as in the symmetric dark matter case, but also by the asymmetry parameter η.

With the objective of computing the evolution of the Sun in different cosmological scenarios, we start by determining the relic densities of particles and antiparticles, Ω_χ and $\Omega _{\bar{\chi }}$ for specific ηADM models. The computation is done by following closely the numerical procedure of Iminniyaz et al. (2011). Figure 1 shows the dark matter density Ω_DM for light asymmetric particles with m_χ ∼ 10 GeV computed for several values of η and 〈σv〉. Two types of $\chi \bar{\chi }$ annihilation rates are considered, a pure s-wave and a pure p-wave annihilation channels. Annihilation channels with non-vanishing a and b terms are qualitatively similar to the previous ones.

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In general, such results show that there are two limiting asymmetric dark matter scenarios, one for very high and other for very low values of η: (1) for the high values of η, the dark matter is "strongly" asymmetric as the relic density is dominated by particles over antiparticles, $\Omega _{\bar{\chi }}\ll \Omega _{\chi } \approx \Omega _{{\rm DM}}$; this scenario is identical to the baryogenesis process related to ordinary baryons; (2) for the low values of η, the dark matter is "weakly" asymmetric or symmetric (η ≈ 0), $\Omega _{\bar{\chi }}\approx \Omega _{\chi } \approx \Omega _{{\rm DM}}$; the final relic abundances of particles and antiparticles are comparable. This generally corresponds to the standard thermal WIMP scenario.

If we consider the present measurements of Ω_DM (Hütsi et al. 2011), we find that the number of asymmetric dark matter scenarios that are compatible with observations is relatively reduced, i.e., only η − 〈σv〉 dark matter models with a relic density 0.1053 ⩽ Ω_DMh² ⩽ 0.1165. Nevertheless, for reasons of convenience,⁶ in this work we choose the observational interval to be such that 0.10 ⩽ Ω_DMh² ⩽ 0.12 (region between blue lines in Figure 1).

If we restrict our analysis to the asymmetric models of particles with a mass of 10 GeV compatible with dark matter density observations, it is possible to determine a critical value of 〈σv〉_c for which there is a change of dark matter regime (see Figure 1). The critical value 〈σv〉_c is approximately 1.6 × 10⁻²⁴ cm³ s⁻¹ and 1.2 × 10⁻²³ cm³ s⁻¹ for s-wave and p-wave annihilation channels. There is also a maximum value of asymmetry η_c, above which the asymmetric dark matter models have a Ω_DM larger than the current observational value. η_c is equal to 3.6 × 10⁻¹¹ for the s-wave annihilation channel and 2 × 10⁻¹¹ for the p-wave annihilation channel. If a model has 〈σv〉 < 〈σv〉_c, Ω_DM becomes uniquely dependent on η (independent of 〈σv〉). This corresponds to cosmological models for which the $\chi \bar{\chi }$ annihilation rate is so efficient that the relic abundance depends only on the initial η asymmetry. Conversely, if a model has 〈σv〉 > 〈σv〉_c, the dark matter density becomes purely determined by the value of 〈σv〉 (independent of η). It follows that the dark matter density content is determined by the low value of the annihilation rate.

It is worth noticing that the dependence of Ω_DM with the particle mass is quite small for asymmetric dark matter models of light particles (m_χ ⩽ 20 GeV). In cosmological dark matter models for particles with a mass between 5 GeV and 20 GeV, 〈σv〉_c for both channels is identical to the case of a particle with a mass of 10 GeV. For the same range of masses, η_c varies between 8–2 × 10⁻¹¹ for a s-wave (a ≠ 0) channel and 7–2 × 10⁻¹¹ for p-wave channel (b ≠ 0).

The accumulation of particles (χ) and antiparticles ($\bar{\chi }$) inside the star depends on the star's gravitational field and the interaction of the dark matter particles with baryons. In our description of the impact of the ηADM on stellar evolution, we closely follow earlier discussions of the impact of "classical" asymmetric dark matter⁷ with the evolution of the Sun and other stars (Scott et al. 2009; Cumberbatch et al. 2010; Taoso et al. 2010; Casanellas & Lopes 2009; Lopes et al. 2011).

In the following we discuss the capture and accumulation of ηADM by the Sun. Although, such particles interact with baryons in a similar way as WIMPs, the fact that we have two distinct populations of particles leads to a quite different impact on the evolution of the star. Like WIMPs, the amount of ηADM captured by the star depends explicitly on the mass of the dark matter particle m_χ, the cross section for scattering with baryons, namely, the spin-dependent scattering cross section σ_SD, and the spin-independent scattering cross section σ_SI (Lopes et al. 2011). However, unlike WIMPs, ηADM depends also on the two channels (p-wave and s-wave) for annihilation 〈σv〉 and the η-asymmetry parameter. The total number of particles N_χ and antiparticles $N_{\bar{\chi }}$ that accumulates inside the Sun at a certain epoch is computed by solving the system of coupled equations:

$$\begin{eqnarray} &&\frac{dN_{i}}{dt}=C_{i}-C_{a} N_{\chi }N_{\bar{\chi }}, \end{eqnarray} \tag{ 1 }$$

with i being χ or $\bar{\chi }$. The constant C_i gives the rate of capture of particles (antiparticles) from the dark matter halo and C_a gives the annihilation rate of particles and antiparticles in the Sun. This approach is entirely different from other studies of accumulation of dark matter inside stars, in part because previous work only studied the capture of the population N_χ of dark matter particles. In such cases, the system of coupled equations (1) is substituted by one single equation. In the following, we will consider dark matter particles with a mass larger than 5 GeV, for which the evaporation of particles is negligible (Gould 1990). Furthermore, we neglect the rate of capture of dark matter particles by scattering off other dark matter particles that have already been captured within the Sun (Zentner 2009).

The capture rate for particles and antiparticles by the Sun's gravitational field and their scatterings off baryons is computed numerically from the integral expression of Gould (1987), implemented as indicated in Gondolo et al. (2004). The description of how this capture process is implemented in our code is discussed in Lopes et al. (2011). The scattering of particles and antiparticles on baryon nuclei is identical. It follows that, similarly to the symmetric dark matter case, σ_SD is only relevant for hydrogen nuclei and σ_SI is important for the scattering of dark matter particles on heavy nuclei. If the value of σ_SI is larger or equal to σ_SD, the capture of dark matter particles is dominated by the collisions with heavy nuclei, rather than by collisions with hydrogen (Lopes et al. 2011).

If not stated otherwise, we assume that the density of dark matter in the halo is 0.38 GeV cm⁻³(Catena & Ullio 2010), the amount of particles and antiparticles in the halo is in the same proportion as in the local universe, the stellar velocity of the Sun is 220 km s⁻¹, and the Maxwellian velocity dispersion of dark matter particles is 270 km s⁻¹ (e.g., Bertone et al. 2005). Recent measurements of local dark matter density yet to be published propose values of 0.3 GeV cm⁻³ (Bovy & Tremaine 2012) and 0.85 GeV cm⁻³ (Garbari et al. 2012). The annihilation rate C_a is computed from

$$\begin{eqnarray} &&C_{a}=N_{\chi }^{-1}N_{\bar{\chi }}^{-1}\;\int \langle \sigma v\rangle (r)\; n_{\chi }(r) n_{\bar{\chi }} (r)\;4\pi ^2 r^2 \;dr, \end{eqnarray} \tag{ 2 }$$

where 〈σv〉(r) is the $\chi \bar{\chi }$ annihilation rate as defined in the previous section, and n_χ(r) and $n_{\bar{\chi }}(r)$ are the number density of particles and antiparticles.

In this paper, in contrast to previous work, we assume that the dark matter particles and antiparticles present inside the Sun annihilate by the same physical process as the one that occurs in the early universe, therefore, i.e., $\langle \sigma v\rangle = a +6 b x^{-1} + {\cal O} (x^{-2})$ where x is now the ratio of mass of the dark matter particle over the local temperature of the Sun's plasma. It follows that inside the Sun the s-wave (a ≠ 0) annihilation channel is identical to the one present in the early universe, but the p-wave (b ≠ 0) annihilation channel is quite different, as the temperature inside the Sun is larger than the temperature in the early universe.

As the star evolves, after some time, t is larger than $\tau _{A}=\sqrt{C_{a}C_{\chi }}$, the rate of accumulation of particles inside the Sun $\dot{N}_{\chi }$ is proportional to the difference between the capture rate of the particles and antiparticles, i.e., $\dot{N}_{\chi } = D_{\chi }$ with $D_{\chi }=C_{\chi }- C_{\bar{\chi }}$. It follows that the total number of particles and antiparticles is given by $N_{\chi }\approx N_{\bar{\chi }}+ D_{\chi }\; t$ and $N_{\bar{\chi }}\approx C_{\bar{\chi }}/(C_{a} D_{\chi } \; t)$ (Griest & Seckel 1987). The value of τ_A depends of the values of dark matter parameters. For a typical dark matter halo of density 0.38 GeV cm⁻³ constituted by particles with a mass of 10 GeV and annihilation rate 10⁻²⁴ cm³ s⁻¹, τ_A of the order of 1 million year. Particles and antiparticles, once captured by the Sun during its evolution, end up in thermal equilibrium with baryons. The particle (and antiparticle) population follows a Maxwellian velocity distribution. The number density of particles (antiparticles), $n_{i}(r)\approx N_{i}e^{-m_\chi \phi (r) /T_{c} }$ where T_c is the central temperature of the star and ϕ(r) is the gravitational potential (Casanellas & Lopes 2009; Giraud-Heraud et al. 1990).

The code used to compute the evolution of asymmetric dark matter is a modified version of the stellar evolution code CESAM (Morel 1997). The basic reference model without dark matter is calibrated to produce a solar standard model (Turck-Chieze & Lopes 1993) identical to others in the literature (Guzik & Mussack 2010; Serenelli et al. 2009; Bahcall et al. 2005b; Turck-Chieze et al. 2010). The microscopic physics (updated equation of state, opacities, nuclear reactions rates, and an accurate treatment of microscopic diffusion of heavy elements) are in full agreement with the standard picture. The solar mixture of Asplund et al. (2005) is used in the computation of models. The modified evolution models are calibrated to the present solar radius, luminosity, mass, and age (e.g., Turck-Chieze & Couvidat 2011). The models are required to have a fixed value of the photospheric ratio (Z/X)_☉, where X and Z are the mass fraction of hydrogen and the mass fraction of elements heavier than helium. The value of (Z/X)_☉ is determined according to the solar mixture (Asplund et al. 2005).

The star evolves from the beginning of the pre-main sequence until its present age. Each solar model has more than 2000 layers, and it takes more than 80 time steps to arrive to the present age. For each set of dark matter parameters, a solar-like calibrated model is obtained by automatically adjusting the helium abundance and the convection mixing-length parameter until the total luminosity and the solar radius are within 10⁻⁵ of the present solar values. Typically a calibrated solar model is obtained after a sequence of 10 intermediate solar models, although the models with a large concentration of dark matter need more than 20 intermediate models. The increase of the number of iterations is related with the rapid variation of the structure in the center of the Sun. The values of the calibrating parameters, mixing-length parameter, and the initial content of helium changes slightly relative to the standard solar model, depending upon the accumulation of dark matter in the core of the star. The maximum variation obtained for these parameters due to the accumulation of dark matter in the center of the Sun is an increase of the mixing-length parameter of 5% and the initial content of helium is decreased by 0.5%.

The ηADM particles impact the evolution of the Sun, by a physical process identical to WIMPs. Likewise they provide an effective mechanism for the transport of energy, for which the efficiency depends locally on the average mean free path of the dark matter particles between successive collisions with baryons. Two distinct regimes of the transport of energy are usually considered: local and non-local transport corresponding to small and large average mean free paths, respectfully. Both energy transport mechanisms are implemented in our code (Lopes et al. 2011). This physical process leads to the reduction of the temperature gradient (Lopes et al. 2002; Lopes & Silk 2010b). In the more extreme case, the high frequency of collisions between baryons and dark matter particles forms an isothermal core (Lopes & Silk 2002).

This new type of asymmetric dark matter can have a much larger effect on the evolution of the Sun than the usual symmetric dark matter (Lopes & Silk 2010b) because the star can accumulate a much larger amount of particles (and antiparticles) in its core than in the latter case. This is due to the fact that asymmetric dark matter depends, among other parameters, on two major parameters that determine the concentration of dark matter inside the star: dark matter asymmetry, which determines the unbalanced amount of particles and antiparticles; and the annihilation cross section, which establishes the annihilation efficiency of particles and antiparticles. This is consistent with the results shown in Figure 1.

Figure 2 shows the variation for the ⁸B and ⁷Be neutrino fluxes relative to the solar standard models. The large reduction in ⁸B and ⁷Be neutrino fluxes is a direct consequence of the reduction of the temperature inside the solar core.

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This diminution of temperature is also visible in the sound speed profile near the center of the Sun. Figure 3 shows the profile of sound speed computed for a few ηADM scenarios. It also shows the observed sound speed profile obtain from the helioseismology data of the BISON and GONG observational networks (Basu et al. 2009). This sound speed is consistent with a previous sound speed inversion computed from high-accuracy data obtained by the GOLF and MDI instruments of the Solar and Heliospheric Observatory mission (Turck-Chieze et al. 1997). In the solar core, the impact of η-parameterized dark matter on the sound speed is much larger than can be accommodated by the current solar standard model (Turck-Chieze & Couvidat 2011). Moreover, although the sound speed is not inverted in the very central region of the Sun (Basu et al. 2009), the reduction in the Sun's speed profile caused by the presence of dark matter is much larger than previously determined tentative sound speed inversions of the Sun's core (Turck-Chieze & Couvidat 2011). As shown in Figure 3, these dark matter models produce a decrease in the square of the sound speed of the order of 3%–5%, well above 1% of the uncertainty of the current solar model. This reduction in temperature is accompanied by significant changes in the Sun's core structure, which leads to visible effects on other type of seismic diagnostics, such as the small acoustic mode separation(Lopes & Turck-Chieze 1994; Turck-Chieze & Lopes 1993). Cumberbatch et al. (2010) have found that dark matter particles that accumulate inside the Sun's core and produces a temperature variation of this order of magnitude, also have a small acoustic mode separation quite different from helioseismology data.

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The relationship between the solar neutrino fluxes and the sound speed with the temperature is easily established, if we note that the ⁸B and ⁷Be neutrino fluxes depend on the central temperature T_c as T²⁴_c and T¹⁰_c (Bahcall & Ulmer 1996; Bahcall 2002), and the square of sound speed can be expressed as C²_s ≈ T_c/μ_c, where μ_c is the molecular weight in the center (Turck-Chieze & Lopes 1993). This different sensitivity to temperature explains why the diagnostics provided by Φ(⁸B), Φ(⁷Be), and C²_s are quite distinct. We have also computed the solar neutrino fluxes of other pp-nuclear reactions and the results follow a similar behavior. Other seismic diagnostic are possible, such as comparing the observed acoustic oscillations to the theoretical acoustic oscillations, or their respective small separations. Nevertheless, the sensitivity of seismic quantities to changes in the Sun's core structure is always less visible than in solar neutrino fluxes.

The current standard solar model (Turck-Chieze & Lopes 1993; Turck-Chieze et al. 2010; Serenelli et al. 2011) is in agreement with the Φ(⁸B) and Φ(⁷Be) neutrino fluxes measured by the Sudbury Neutrino Observatory and Borexino detector (Aharmim et al. 2010; Bellini et al. 2010, 2011, 2012; Arpesella et al. 2008). The current ⁸B neutrino flux observational determination in the case of no-neutrino oscillations (or electron neutrinos; including the theoretical uncertainty of neutrino flux solar neutrinos in the solar standard model) is Φ(⁸B) = 5.05^+0.19_{− 0.20} × 10⁶ cm⁻² s⁻¹ for the SNO experiment (Aharmim et al. 2010) and Φ(⁸B) = 5.88 ± 0.65 × 10⁶ cm⁻² s⁻¹ for the Borexino experiment (Bellini et al. 2010). The Borexino experiment measures ⁷Be solar neutrino flux Φ(⁷Be) = 4.87 ± 0.24 × 10⁹ cm⁻² s⁻¹, under the assumption of the Mikheyev–Smirnov–Wolfenstein/large mixing angle scenario of solar neutrino oscillations (Bellini et al. 2011; Arpesella et al. 2008).

The Φ(⁸B) neutrino measurements made by Borexino and SNO experiments suggest that the Sun's core is slightly hotter than expected, since the Φ(⁸B) measured value is higher than the value predicted by the current solar standard model. This discrepancy is validated by the Borexino measurement of Φ(⁷Be) which is sensitive to a region slightly off the Sun's center. The first measurement of the pep neutrinos was done recently by the Borexino experiment, Φ(pep) = 1.6 ± 0.3 × 10⁸ cm⁻² s⁻¹ (Bellini et al. 2011). The experimental value also suggests that the Sun is hotter than the solar standard model predicts. This diagnostic is quite reliable once we realize that Φ(pep) is strongly dependent on the luminosity of the star. All these independent solar neutrino experiment results suggest that the solar standard model is cooler than the actual Sun.

The internal structure of the Sun is well known by means of solar neutrinos and helioseismology data. Therefore, the theoretical uncertainty of the standard solar model is consistently taken into account by comparing the predictions of these two probes with observations. Several authors have shown that an important source of uncertainty on the calculation of the solar neutrino fluxes (electronic flavor) comes from the unclear measurements of heavy element abundances in the Sun's surface (Bahcall et al. 2005a, 2005b; Asplund et al. 2009). One other source of uncertainty is related to the determination of several pp-reaction rates and electron screening (Mussack & Dappen 2011; Serenelli et al. 2011; Weiss et al. 2001). Similarly, other standard and nonstandard physical processes that contribute for the evolution of the star can also be an important source of uncertainty. Among others we can refer to the following indirect processes: convective overshoot, low-z accretion, mass loss, solar rotation, and meridional circulation (Guzik & Mussack 2010; Turck-Chieze et al. 2010; Turck-Chieze & Couvidat 2011). These suggestions have been made mostly to resolve the discrepancy between the theoretical sound speed as obtained with the new solar abundances (Asplund et al. 2005, 2009) and the sound speed obtained from the acoustic oscillations. As previously mentioned such physical processes have a much smaller effect on solar neutrino fluxes than the accumulation of dark matter in the Sun's core.

In the study of the impact of dark matter in the Sun, we will choose to consider an interval of theoretical uncertainty that takes into account such processes. Therefore, considering both the theoretical and experimental uncertainties, we choose to rule out models that predict a ⁸B neutrino flux that deviates more than 30% from our solar standard model. Similarly, a ⁷Be neutrino flux of solar models which deviates more than 15% from our solar standard model can also be ruled out. This is consistent with the fact that Φ(⁸B) is two times more sensitive to the central temperature than Φ(⁷Be). The choice of this threshold is in agreement with other authors (e.g., Taoso et al. 2010). Furthermore, such intervals of uncertainties on ⁸B and ⁷Be also include the solar structure variations (e.g., temperature) in the Sun's interior, and in particular in the Sun's core that can be attributed to some of the physical processes previously mentioned.

Figure 2 shows the neutrino flux variations in more than 30 evolution models of the Sun computed for different values of η and 〈σv〉. This result is identical for both (s-wave and p-wave) annihilation channels. In the η versus 〈σv〉 plane, the iso-contours corresponding to Φ_ν(⁸B) and Φ_ν(⁷Be) show neutrino flux variations relatively to the solar standard model. We choose to present the case of dark matter particles that have m_χ = 10 GeV, spin-dependent scattering cross section σ_SD = 10⁻⁴⁰ cm², and spin-independent scattering cross section σ_SI = 10⁻³⁶ cm². The neutrino flux variation shown follows the decrease of the local halo density of particles ρ_χ, which follows the relic density Ω_χ specific to each set of values (η, 〈σv〉). The observed difference in sensitivity between Φ_ν(⁸B) and Φ_ν(⁷Be) neutrino fluxes is caused by the fact that ⁸B neutrinos are produced in a more central region than ⁷Be neutrinos.

If we adopt the 30% and 15% fixed thresholds for the ⁸B and ⁷Be neutrino fluxes, we conclude that we can rule out ηADM particles with a mass of 10 GeV, which have an η ⩾ 10⁻¹² and an annihilation rate (both annihilation channels) larger than 10⁻²³ cm³ s⁻¹. An analysis of other solar neutrino fluxes such as pp neutrinos reenforces the conclusions reached in this study.

In this paper, we proposed a new strategy to study the impact of dark matter in the evolution of Sun and stars. We started by computing the basic cosmological primitive model that is responsible by the formation of the dark matter asymmetric particles, assuming that dark matter like baryons has an asymmetry, analogous to the baryon asymmetry. As a consequence the population of dark matter particles and antiparticles in the current universe is fixed by the measured dark matter density Ω_DMh². The amount of particles and antiparticles depends on the dark matter asymmetry parameter η, as well as on the dark matter annihilation (p- and s-wave) channels. Considering that the Sun is formed in a dark matter halo that has the same amount of particles and antiparticles, we computed the evolution of the Sun in such conditions.

Using the solar standard model as a reference model for the internal structure of the Sun, we have studied the impact of asymmetric dark matter on the production of solar neutrino fluxes. Following a procedure identical to the analysis proposed in Lopes & Silk (2010a, 2010b), we describe the impact of asymmetric dark matter on the Sun's core.

Several evolution models of the Sun were computed for a range of light dark matter particles. Particles with masses smaller than 5 GeV are not considered since evaporation becomes important in this mass range and a large number of dark matter particles escape the gravitational field of the star, significantly reducing the impact on the Sun's core (Gould 1990). Similarly, particles with a mass above 20 GeV produce a very small dark matter core and their effect in the Sun's structure is almost negligible (Lopes et al. 2011). Accordingly, dark matter particles with masses between 5 and 20 GeV produce a temperature decrease in the Sun's core that visibly affects the neutrino fluxes, although these depend on the values of specific parameters, such as the dark matter asymmetry and annihilation cross section. The impact of more massive dark particles in the evolution of a star like the Sun should be significantly smaller than in the case discussed in this work. The reason is the fact that the concentration of dark matter in the center of the star is usually characterized by a dark matter core radius (Casanellas & Lopes 2009), which is inversely proportional to the square root of the mass of the dark matter particle. The choice of other parameters of the scattering cross section will not change fundamentally such results.

We note incidentally that high annihilation rates for light dark matter particles are ruled out if accompanied by lepton production from observations of cosmic microwave background temperature fluctuations and of searches for gamma rays from nearby dwarfs. But these limits are irrelevant once asymmetric dark matter is important, and most importantly for us, assume specific annihilation channels. Our solar constraints come from accumulation of dark matter particles by the Sun, and complement other annihilation limits. The annihilations are of course important for fixing the relic abundance. However a key point of our paper is that we consider asymmetric dark matter for which the dependence on specific annihilation channels is very weak. Furthermore, the relic abundance is fixed by specifying the annihilation rate via freezeout physics.

Indeed, freezeout may be far more complicated than given by the simple connection that specifies the "thermal" freezeout cross section in terms of the observed relic abundance. Many models violate this condition. Our models test independently of freezeout the very important parameter space of annihilation rate today (in the low-energy universe) whereas relic abundances probe the annihilation rate in a model-dependent way at freezeout (at high energies). Moreover, the Sun probes asymmetric dark matter at the present solar radius, and complements the use of dwarfs in the halo and of cosmic microwave background in the early universe for testing Majorana-type dark matter.

In this work we have computed the ⁸B and ⁷Be neutrino flux variations for several ηADM particles, corresponding to different values of η and 〈σv〉. The values of η and 〈σv〉 were chosen in such a way that Ω_DM for each of the asymmetric dark matter scenarios considered is consistent with current observational measurements (cf. Figure 1). We have presented the results of light dark matter particles (typically 10 GeV), with the same characteristics as the candidates "observed" by DAMA/LIBRA and CoGeNT experiments. We find that such type of particles produces large variations on the flux of solar neutrinos. The ⁸B neutrino flux variation takes values between 35% and 65% for s-wave and p-wave annihilation channels, clearly above the uncertainty in the current solar models estimated to be of the order of 15% (Turck-Chieze & Couvidat 2011). This conclusion holds even for our more conservative threshold of 30% on ⁸B neutrino flux or a threshold of 15% on ⁷Be neutrino flux, as discussed in the previous section. Likewise, dark matter particles with m_χ = 15 GeV show ⁸B neutrino flux variations of the order of 16% up to 40%, which can be rejected if we consider the 15% threshold of uncertainty in the physics of the solar standard model. Therefore, it is reasonable to consider that light dark matter particles that have a scattering cross section of the order of a picobarn, as suggested by several theoretical models to explain the DAMA/LIBRA and CoGeNT experiments, produce neutrino fluxes that are in disagreement with the current neutrino flux observations. On this basis, assuming that stellar evolution is affected by dark matter as discussed here, it is reasonable to assume that such types of particles cannot exist in the current universe. Forthcoming solar neutrino flux experiments could restrain even further the parameters of the ηADM candidates proposed by the recent dark matter models.

This work was supported by grants from "Fundação para a Ciência e Tecnologia" and "Fundação Calouste Gulbenkian" and the NSF (grant OIA-1124453). We thank the referee for the useful comments and insightful suggestions that improved the quality of the paper.