PROSPECTS FOR A DARK MATTER ANNIHILATION SIGNAL TOWARD THE SAGITTARIUS DWARF GALAXY WITH GROUND-BASED CHERENKOV TELESCOPES

Dark matter (DM) plays a key role in the dynamics of a large class of astrophysical systems in the universe. Though halos of DM are predicted to exist around all galaxies, dwarf spheroidal galaxies in particular are ideal targets for DM annihilation searches because: (1) their stellar dynamics show that they are among the most DM-dominated objects in the universe; (2) due to the lack of recent star formation activity, their environment is relatively quiet in terms of background astrophysical gamma-ray emission; and (3) many of them lie at distances below 100 kpc from the Galactic center.

The search for secondary gamma rays from annihilations of DM particles is a powerful indirect detection technique because gamma rays do not suffer from propagation effects, the gamma-ray signal should be proportional to the square of the DM density, and characteristic features such as lines or steps may be present in the energy spectrum at these energies (Bergström 2000; Bringmann et al. 2008). Imaging atmospheric Cherenkov telescopes (IACTs), such as HESS (2003), MAGIC (2003), and VERITAS (2007), are particularly well suited to deep searches of targeted objects because of their large effective areas (∼10⁵ m² above 100 GeV). However, since IACTs are multipurpose astrophysical experiments and have a short duty cycle (∼1000 hr yr⁻¹), the observation time dedicated to these objects is typically limited to tens of hours per year.

Since the flux of the expected gamma-ray signal is inversely proportional to the square of distance, one would expect the best dwarf spheroidal target to be the nearest one. However, such dwarfs are also the closest to the Galactic center and experience the tidal effect of the Milky Way. Recently, it has been shown that one could take advantage of this effect to trace back the evolution history of the object (Peñarrubia et al. 2008b). During the orbital motion of a dwarf galaxy, multiple crossings of the dwarf galaxy through the Galactic disk of the Milky Way give rise to the formation of tidal streams, a careful study of which allows to one infer the gravitational potential of the dwarf galaxy.

In the case of the Sagittarius dwarf (SgrDw) galaxy, the tidal streams have been detected with multiple tracer populations (Yanny et al. 2000; Vivas et al. 2001; Watkins et al. 2009; Mateo 1998; Majewski et al. 1999, 2003; Martinez-Delgado et al. 2001; Newberg et al. 2002) and have been used to derive the DM halo potential. Furthermore, measurements of stars within SgrDw and the luminosity of its core and surrounding debris allow the estimate of the DM content prior to tidal disruption (Niederste-Ostholt et al. 2010; Peñarrubia et al. 2010). Other peculiar features of SgrDw include the presence of the M54 globular cluster coincident in position with its center of gravity (Ibata et al. 1994), and hints of the presence of a central intermediate-mass black hole (IMBH; Ibata et al. 2009). The latter point is supported by the observation of a deviation from a flat behavior in the surface brightness density profile toward the center of the object.

Constraints on a DM annihilation signal toward SgrDw, Canis Major, Sculptor, and Carina have been reported by HESS (Aharonian et al. 2008, 2009; Abramowski et al. 2011); toward Draco, Willman 1, and Segue 1 by MAGIC (Albert et al. 2008; Aliu et al. 2009; Aleksic et al. 2011); toward Draco, Ursa Minor, Boötes 1, and Willman 1 by VERITAS (Acciari et al. 2010); and toward Draco and Ursa Minor by Whipple (Wood et al. 2008). Because of its location in the southern hemisphere, HESS is better suited for observations of SgrDw with respect to other currently operating IACTs. Observations with the Fermi Large Area Telescope (Fermi-LAT, a space-based telescope sensitive to gamma rays between 20 MeV and 300 GeV), are also well suited due to its large duty cycle and wide field of view, though the energy range probed is lower than that of IACTs. The Fermi-LAT Collaboration put strong constraints on the GeV DM mass range of dwarf spheroidal galaxy satellites of the Milky Way (Abdo et al. 2010a; Ackermann et al. 2011). However, their study is restricted to high galactic latitude (|b| > 30°) objects to avoid systematic contamination from galactic diffuse gamma-ray emission, and therefore no constraints on the measured flux in the direction of SgrDw have yet been published using Fermi-LAT data.

In this paper, the current constraints on a DM annihilation signal toward SgrDw are reassessed in light of more realistic DM halo models than those previously used (Evans et al. 2004; Aharonian et al. 2008). The sensitivity of the future generation of IACTs, i.e., the Cherenkov Telescope Array (CTA; Cherenkov Telescope Array 2010), is used to evaluate its potential for the detection of a DM annihilation signal. The CTA design-study sensitivity is used to investigate possible conventional gamma-ray emission, e.g., to the population of millisecond pulsars (MSPs) in the globular cluster M54 at the center of SgrDw, or from the jet of a hypothetical central IMBH. It is shown that such standard astrophysical signals may limit the sensitivity to DM annihilations with the CTA in case of long observation times, eventually requiring the modeling and subtraction of these astrophysical components.

The paper is structured as follows. Section 2 is dedicated to the description of current and future instruments as well as the calculation of the sensitivity to DM signals. In Section 3, the modeling of the DM halo of SgrDw is described together with the astrophysical contribution to the DM flux. In the absence of an astrophysical gamma-ray background, exclusion limits on the velocity-weighted annihilation cross-section of DM are derived in Section 4. Section 5 deals with the estimate of the gamma-ray emission from the MSP population and the IMBH candidate of M54. Section 6 is devoted to a summary.

2.1. Current and Future Instruments

2.2. Sensitivity Calculation and Background Estimates

The sensitivity for IACTs is calculated by comparing the number of events expected from an assumed gamma-ray emission scenario with the expected level of background events. In the case of DM searches, the assumed emission is from the annihilation of DM particles of mass m in the halo of the host galaxy, the differential gamma-ray flux of which is given by

$$\begin{equation} \frac{d\Phi (\Delta \Omega,E_{\gamma })}{dE_{\gamma }}=\frac{1}{8\pi }\,\underbrace{\frac{\langle \sigma v\rangle }{m^2}\,\frac{dN_{\gamma }}{dE_{\gamma }}}_{\rm Particle\,Physics}\,\times \,\underbrace{\bar{J}(\Delta \Omega)\Delta \Omega }_{\rm Astrophysics}, \end{equation} \tag{ 1 }$$

where 〈σv〉 is the velocity-weighted annihilation cross-section and dN_γ/dE_γ is the photon spectrum per annihilation. The astrophysical factor is defined as

$$\begin{equation} \bar{J}(\Delta \Omega) = \frac{1}{\Delta \Omega } \int _{\Delta \Omega } d\Omega \int _{\rm LOS} \rho ^2[r(s)] ds . \end{equation} \tag{ 2 }$$

When treating the self-annihilation of DM particles, this factor scales with the squared density of DM, ρ², over the whole observation cone. The integral is then taken along the line of sight (LOS) and inside the solid angle ΔΩ. The solid angle is chosen as the angular resolution for point-like searches. The number of expected signal events can be calculated by

$$\begin{equation} N_{\gamma } = T_{\rm obs} \int _{0}^{\infty } A_{\rm eff}(E_{\gamma })\, \frac{d\Phi _{\gamma }}{dE_{\gamma }} \, dE_{\gamma }, \end{equation} \tag{ 3 }$$

where T_obs is the observation time and A_eff(E_γ) is the effective area of the detector as a function of the gamma-ray energy. In the case where the background is not measured experimentally, it can still be estimated assuming that the background consists of misidentified hadron showers. The estimate of the expected number of background events in the signal region can be determined using the following expression (see Bergström et al. 1998):

$$\begin{equation} \frac{d^2 \Phi _{\rm had}}{d\Omega dE_{\gamma }} = 8.2 \times 10^{-8} \epsilon _{\rm had} \left(\!\frac{E_{\gamma }}{\rm 1 \,TeV} \!\right)^{-2.7} ({\rm TeV^{-1}\, cm^{-2} \,s^{-1} \,sr^{-1}}), \end{equation} \tag{ 4 }$$

where _had is the hadron detection efficiency. To take into account the performance of the future IACTs the hadron rejection is taken at the level of 90%, which corresponds to _had = 0.1. This parameterization gives remarkable agreement with CTA background simulations (Di Pierro et al. 2011).

In the case of no gamma-ray signal, a limit on the number of gamma rays at the 95% confidence level (CL), $N^{\rm 95\% {\rm CL}}_{\gamma }$, can be calculated using the method of Rolke et al. (2005). In what follows two cases are considered. In the case of current IACTs, the $N^{\rm 95\% {\rm CL}}_{\gamma }$ calculation uses the numbers of gamma-ray and background events extracted from 11 hr HESS measurements (Aharonian et al. 2008). The projected $N^{\rm 95\% {\rm CL}}_{\gamma }$ for 50 hr observation time is obtained by extrapolating both the numbers of gamma-ray and background events from 11 hr to 50 hr. In the case of 95% CL sensitivity calculations, $N^{\rm 95\% {\rm CL}}_{\gamma }$ is calculated assuming the background-only hypothesis. For the HESS sensitivity the number of background events is taken from the extrapolation at 50 hr of observation. For the CTA sensitivity, the number of background events is calculated by integrating the background event flux given in Equation (4) after multiplication by the effective area of the detector and the observation time. $N^{\rm 95\% {\rm CL}}_{\gamma }$ is then calculated using five off regions.

Replacing Equation (1) in Equation (3), the DM sensitivity can be then expressed in terms of the remaining particle physics parameters, 〈σv〉, m, and dN/dE_γ. The 95% CL limit on the velocity-weighted annihilation cross-section is given by the following expression:

$$\begin{equation} \left\langle \sigma v \right\rangle _{\rm min}^{\rm 95\% {\rm CL}} = \frac{8\pi }{\bar{J}(\Delta \Omega)\Delta \Omega } \times \frac{m^{2} N_{\gamma }^{\rm 95\% {\rm CL}}}{T_{\rm obs} \int _{0}^{m}\!\! A_{\rm eff}(E_{\gamma }) \, \frac{dN_{\gamma }}{dE_{\gamma }}(E_\gamma) \, dE_{\gamma }} \,. \end{equation} \tag{ 5 }$$

SgrDw is the only satellite galaxy in the Milky Way that shows clear evidence of ongoing tidal mass stripping (Ibata et al. 2001) in the form of an associated tidal stream (Mateo et al. 1998; Majewski et al. 1999, 2003; Martinez-Delgado et al. 2001, 2004; Belokurov et al. 2006; Watkins et al. 2009). This galaxy is currently located at a close distance from the Milky Way center (≈17 kpc; Mateo et al. 1998). Indeed, it underwent its last perigalacticon passage only 17 Myr ago (Law & Majewski 2010; Peñarrubia et al. 2009), which is a relatively short time compared with its internal dynamical time t_dyn = R_c/σ₀ ≈ 47 Myr, where R_c is the galaxy core radius and σ₀ the central velocity dispersion (Mateo 1998).

The proximity of the SgrDw to the Milky Way plus the fact that this galaxy is shedding stars to tides complicates its dynamical modeling in a number of ways. On the one hand, the distribution of DM and stars has been clearly altered from its original configuration by tidal mass stripping. Given that the actual amount of stars and DM in the tidal tails is unknown (Niederste-Ostholt et al. 2010), the original mass, luminosity, and size of the SgrDw remain fairly uncertain quantities. On the other hand, the assumption of dynamical equilibrium may not be adequate, specially in the outskirts of the galaxy where the population of unbound stars may dominate in number over that of bound members (Peñarrubia et al. 2009).

These difficulties have not deterred a large body of theoretical work devoted to uncovering the actual content and distribution of DM in SgrDw. To date these efforts have focused on (1) analytical models of the dynamical properties of the remnant core and (2) N-body simulations that aim to reproduce the spatial and kinematical distribution of the tidal tails.

The simplest analytical models assume dynamical equilibrium and adopt a cosmologically motivated halo density profile to describe the kinematics of individual stars

$$\begin{equation} \rho _{\rm NFW}(r) = \frac{\rho _{\rm s}}{(r/r_{\rm s})(1+ r/r_{\rm s})^2}, \end{equation} \tag{ 6 }$$

where r_s is a scale radius and ρ_s is a characteristic density (Navarro et al. 1996, hereafter NFW). Note that this profile diverges at small radii as ρ∝r⁻¹, which is typically referred to as a DM "cusp." It was shown in Peñarrubia et al. (2008b) that the tightly bound DM cusp is more resilient to disruption than the more loosely bound stellar core profile, which can be accurately described with a King (1966) profile (Mateo 1998), and that tidal stripping does not change the inner profile of DM halos.

Assuming that the external tidal field does not influence the kinematics of stars that locate the central regions of the dwarf, and ignoring the effects of tidal stripping on the outer (r ≫ r_s) DM halo profile, one can use the Jeans equations to search the DM halo parameters that best fit the stellar central velocity dispersion for an observed King "core" radius of this object. The King–NFW degeneracy gives rise to a family of NFW halo models which can reproduce the stellar dynamics (Peñarrubia et al. 2008a). One way to break this degeneracy is using the relationship between the virial mass and concentration found in cosmological N-body simulations (see, for instance, Bullock et al. 2001). Using this procedure on the Sloan Digital Sky Survey (SDSS) data provides a value of r_s = 1.3 kpc. Considering the scatter on the relationship between virial mass and concentration, the 2σ error on r_s is found to be ∼0.2 kpc. This corresponds to the family of models with ρ_s spanning from 7.5 × 10⁻³ to 1.3 × 10⁻² M_☉ pc⁻³. In Table 1 we show the results of our fits together with the astrophysical factors $\bar{J}$ for different solid angles ΔΩ. Taking into account the error on the halo profile parameters the value of the astrophysical factor can vary by a factor of two. Interestingly, an independent analysis by Łokas et al. (2010) provides similar values for these parameters. In this case the astrophysical factors are found to be of a few higher than the ones presented here.

However, numerical N-body models that aim to describe the observed structural and kinematical distributions of stars in the tidal tails as well as the remnant core provide a more consistent approach to the dynamical analysis of SgrDw. Yet most of the existing N-body models of this galaxy assume for simplicity that DM and stars share the same spatial distribution (the so-called mass-follows-light models), an assumption that is not supported by detailed kinematic data of dwarf spheroidal galaxies (e.g., Walker et al. 2009). The only exception to date corresponds to recent N-body models constructed by Peñarrubia et al. (2010), who explore the possibility that SgrDw may have originally been a rotating galaxy. In these models the galaxy is composed of an exponential stellar disk embedded in an extended DM halo. The DM density profile is taken as a cored isothermal (ISO) profile

$$\begin{equation} \rho _{\rm ISO}(r)= \frac{m_{\rm h} \alpha }{2 \pi ^{3/2} r_{\rm cut}}\frac{\exp [-(r/r_{\rm cut})^2]}{\big(r_{\rm c}^2+r^2\big)}, \end{equation} \tag{ 7 }$$

where m_h is the halo mass, r_c is the core radius, and α ≃ 1.156 (Peñarrubia et al. 2010). The DM halo mass can be estimated using the initial luminosity and a given mass-to-light ratio. Using the results from Niederste-Ostholt et al. (2010) the initial luminosity is estimated to be ∼10⁸ L_☉. Assuming a typical mass-to-light ratio for dwarf galaxies of 25 (Mateo 1998), the DM halo mass is found to be m_h = 2.4 × 10⁹ M_☉. To account for the initial tidal disruption of the SgrDw halo by the Milky Way, a truncation of the halo profile is imposed at r_cut = 12 r_c. The evolution of SgrDw in the Milky Way potential is obtained via an N-body model of SgrDw using the particle-mesh gravity code SUPERBOX (Fellhauer et al. 2000). The evolution code allows us to recover the actual DM profile by using the constraint of the observed stellar distribution. The values of the parameters of the present ISO profile are given in Table 1.

Theories beyond the Standard Model (SM) of particle physics propose several particle DM candidates. For instance, some supersymmetric extensions of the SM predict a neutralino as the lightest stable supersymmetric particle, which is a good candidate for DM (Jungman et al. 1996; Bergström 2000). The parameterization of the neutralino self-annihilation gamma-ray spectrum dN_γ/dE_γ is taken from Bergström et al. (1998) for a typical neutralino annihilating into W and Z pairs. Figure 1 shows the upper limits of current IACTs on 〈σv〉 as a function of the DM mass m for ΔΩ = 2 × 10⁻⁵ sr. Using the HESS upper limits published in Aharonian et al. (2008), the new upper limits are calculated for the NFW and ISO DM halo profiles of Section 3 and $11 \,\mathrm{{\rm hr}}$ of observation time; the projected upper limits for $50 \,\mathrm{{\rm hr}}$ of observation time are also plotted. The limits are at the level of 5 × 10⁻²³ cm³ s⁻¹ around 1 TeV for $50 \,\mathrm{{\rm hr}}$. The sensitivity of HESS for 50 hr observation time is also displayed. The sensitivity limits for CTA on 〈σv〉 as a function of the DM mass m are presented in Figure 2 for 50 hr and 200 hr observation times. The limits are calculated with ΔΩ = 2 × 10⁻⁶ sr for the NFW DM halo profile and ΔΩ = 10⁻³ sr for the ISO DM halo profile. The sensitivity limits at 95% CL reach the level of 10⁻²⁵ cm³ s⁻¹ for DM masses of about 1 TeV in the case of the ISO DM halo profile.

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Two additional contributions to the overall gamma-ray flux that can modify the limits are considered: namely, the Sommerfeld effect and internal bremsstrahlung (IB) from the DM annihilation. The Sommerfeld effect is a non-relativistic effect that arises when two DM particles interact in an attractive potential. When the relative velocity between the DM particles is sufficiently low, the Sommerfeld effect can substantially boost the annihilation cross-section (Lattanzi & Silk 2009), since it is particularly effective in the very low velocity regime. The actual velocity-weighted annihilation cross-section of the neutralino can then be enhanced by a factor S defined as

$$\begin{equation} \left\langle \sigma v \right\rangle = S\langle \sigma v \rangle _0, \end{equation} \tag{ 8 }$$

where the value of S depends on the mass and relative velocity of the DM particle. Assuming that the DM particles only annihilate to a W boson, the attractive potential created by the Z gauge boson through the weak force before annihilation would give rise to an enhancement. Assuming that the DM velocity dispersion inside the halo is the same as for the stars, the value of the DM velocity dispersion is fixed at 11 km s⁻¹ for SgrDw (Mateo 1998). The value of the enhancement is numerically calculated as done in Lattanzi & Silk (2009) and then used to improve the upper limits on the velocity-weighted annihilation cross-section, 〈σv〉/S as a function of the DM particle mass. Additionally, every time a DM particle annihilates into charged particles, the electromagnetic radiative correction to the main annihilation channel can give a more or less significant enhancement to the expected gamma-ray flux in the observed environment due to IB (Bergström 1989; Bringmann et al. 2008). Restraining the Minimal Supersymmetric Standard Model parameter space to the stau co-annihilation region of the minimal supergravity models, for instance, the wino annihilation spectrum would receive a considerable contribution from IB (Bringmann et al. 2008). Figure 3 shows the 95% CL upper limits on 〈σv〉/S as a function of the DM mass m for current IACTs. The projected upper limit is shown for the NFW profile, $50\,\mathrm{{\rm hr}}$ observation time, and ΔΩ = 2 × 10⁻⁵ sr. The effect of the IB is only significant below ∼1  TeV. Some specific wino masses can be excluded due to the resonant enhancement in the Sommerfeld effect. Outside resonances, the projected upper limits are improved by more than one order of magnitude for DM masses above 1 TeV. The sensitivity at 95% CL for CTA on 〈σv〉/S as a function of the DM mass m is presented in Figure 4. The limits are calculated for the ISO DM halo profile, with $200\,\mathrm{{\rm hr}}$ observation time and ΔΩ = 10⁻³ sr. The values of 〈σv〉 corresponding to cosmological thermally produced DM, 〈σv〉 ∼3 × 10⁻²⁶ cm³ s⁻¹, can be tested for specific wino masses in the resonance regions of the Sommerfeld effect. Outside the resonances the sensitivity on 〈σv〉/S is improved by more than one order of magnitude for TeV DM masses, reaching the level of 10⁻²⁶ cm³ s⁻¹.

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Dwarf galaxies are generally believed to contain very little background emission from conventional astrophysical sources at VHE energies, and are therefore easy targets for DM searches. This assumption is based on their low gas content and stellar formation rate. However, some gamma-ray-emitting sources may still exist within them: in particular from pulsars and black hole accretion and/or jet emission processes. Both the Sagittarius and Carina dwarf galaxies host globular clusters (the M54 globular cluster is located at the center of SgrDw), and globular clusters are known to host MSPs. The collective emission of high-energy gamma rays by MSPs in globular clusters has been detected by Fermi-LAT (Abdo et al. 2010b), and emission in the VHE energy range has been predicted by several models for these objects, but has not yet been observed. The possible emission of VHE radiation by MSPs from the M54 globular cluster is examined in Section 5.1. Additionally, it has been suggested by some authors (see Lanzoni et al. 2007; Noyola et al. 2008 and references therein) that globular clusters may host black holes with masses of around 10²–10⁴ solar masses (called IMBHs). Indeed, Ibata et al. (2009) suggest SgrDw may also be a possible host for a 10⁴ M_☉ IMBH. Their claim is based on the study of the density profile around the central point and the observed rise in the velocity dispersion of stars. The high-energy emission from the IMBH candidate in the center of M54 is discussed in Section 5.2

5.1. Millisecond Pulsars in M54

The M54 globular cluster at the center of SgrDw likely harbors a large population of pulsars, especially MSPs. The number of MSPs in globular clusters has been shown by the Fermi-LAT Collaboration (Abdo et al. 2010b) to be correlated with the collision rate Γ defined by

$$\begin{equation} \Gamma = \rho ^{3/2}r_{\rm c}^{2} \,. \end{equation} \tag{ 9 }$$

In this equation, ρ is the central luminosity and r_c is the core radius. Taking a central surface brightness of μ_V ≃ (14.12–14.9) mag arcsec⁻² from Table 4 of Bellazzini et al. (2008) and a core radius r_c = 0.9 pc , the collision rate is found to be

$$\begin{equation} \Gamma _{\rm M54} \simeq (0.8\hbox{--}2.6)\times \Gamma _{\rm M62}\,, \end{equation} \tag{ 10 }$$

where Γ_M62 = 6.5 × 10⁶ L^3/2_☉ pc^−2.5 is the reference collision rate of the M62 globular cluster. The predicted number N_MSP of MSPs in M54 is estimated from the collision rate (Abdo et al. 2010b) by the relation

$$\begin{equation} N_{\rm MSP} = 18+50\times \left(\frac{\Gamma _{\rm M54}}{\Gamma _{\rm M62}}\right). \end{equation} \tag{ 11 }$$

The collision rate from Equation (10) gives the estimated number of MSPs in M54: N_MSP = 60–140. Note, however, that no MSP has been discovered to date in M54.

The collective VHE gamma-ray emission of MSPs from globular clusters has been predicted by several authors, notably Bednarek & Sitarek (BS; Bednarek & Sitarek 2007), Venter, De Jager, & Clapson (VJC; Venter et al. 2009), and Cheng et al. (CCDHK; Cheng et al. 2010). Using the effective area of CTA described in Section 2.1, one expects to observe, respectively, 1285 and 181 gamma rays per hour toward the 47 Tucanae globular cluster with the BS and CCDHK models. In the latter model, the relic gamma rays are assumed to be the target population. The prediction of the VJC model is somewhat smaller; only 71 gamma rays per hour are predicted assuming an interstellar magnetic field of 10 μG. The VJC model also predicts a synchrotron radiation emission. The emission in the keV range is predicted to be at the level of 10⁻¹⁶ TeV cm⁻² s⁻¹ for a magnetic field of 10 μG. This is easily accommodated by the measured diffuse X-ray emission in M54 which is ∼2 × 10⁻¹⁴ TeV cm⁻² s⁻¹ (Bogdán & Gilfanov 2010).

As suggested by Venter & de Jager (2008), a rough estimate of the collective VHE emission of M54 can be obtained from their predicted emission of 47 Tucanae by scaling by the factor

$$\begin{equation} x = \left(\frac{N_{\rm MSP}}{100}\right){\left(\frac{d_{\rm 47Tuc}}{d_{\rm M54}}\right)}^2{\left(\frac{\langle u_{\rm M54}\rangle }{\langle u_{\rm 47Tuc}\rangle }\right)}. \end{equation} \tag{ 12 }$$

In this equation, d_47Tuc and d_M54 are the distances to 47 Tucanae and M54, and 〈u_M54〉 and 〈u_47Tuc〉 the average luminosity per cubic parsec of the globular cluster. Taking the distances, luminosity, and half-mass radii of M54 and 47 Tucanae from Harris (1996, 2010 edition), one finds a correction factor x ≃ 1.6 × 10⁻², assuming that M54 contains 100 MSPs. The expected number of gamma rays per hour is thus 19.9 and 5.6 in the BS and CCDHK models. For the latter model, x was multiplied by an additional factor of two to take into account the different number of MSPs in 47 Tucanae and M54. For the VJC model, the number of expected gamma rays per hour is about 1.1.

Whether this signal is observable or not depends crucially on its spatial extension. The half-mass radius of M54 has an angular size of less than 1' so the signal would appear almost point-like in the BS and VJC models. The CCDHK model predicts an extended signal. The electrons and positrons responsible for the inverse Compton scattering on the cosmic microwave background radiation have a typical diffusion length of 100 pc, which corresponds to ≃ 12 ' at the distance of M54. The signal integration regions are taken as 3' for the BS and VJC models and 12' for the CCDHK model. With a hadron rejection factor of 10% as in Section 2.2, the amount of background per hour is ∼10 inside a 3' radius centered on M54. The significance of the collective MSP signal thus depends on the observation time T_obs (in hours) as, respectively, $4.5\ \sqrt{T_{\rm obs}},$ $0.31\ \sqrt{T_{\rm obs}}$, and $0.25 \ \sqrt{T_{\rm obs}}$ in the BS, CCDHK, and VJC models. The BS model would give a signal at the 4.5σ level after just a one-hour observation. The other models would give a much smaller signal, with a typical significance of 4σ after 200 hr of observation.

In summary, the MSPs of M54 could give a significant VHE gamma-ray signal in CTA with observation times of typically 200 hr. For a cosmological thermally produced DM particle, 〈σv〉 = 3 ×10⁻²⁶ cm³ s⁻¹, the corresponding signal would have a significance of 0.1σ after 200 hr of observation and without any boost factor. The collective MSP signal would be a few orders of magnitude stronger than the DM annihilation signal.

5.2. Intermediate-mass Black Hole

Significant radio and X-ray emissions are expected if the hypothesis of a central IMBH is valid. Unfortunately, only upper limits to the radio emission could be established from Very Large Array and MOST observations. Nevertheless, these limits can be used to constrain the candidate black hole mass. Regarding X-ray emission, Ramsay & Wu (2006a, 2006b) have analyzed the data taken with the Chandra satellite. They found seven bright sources within the half-mass radius of M54. Their source number 2 lies within 1'' of the density center of M54. Taking into account the Chandra astrometric accuracy of 06 and the systematics of 03 in the absolute position of the Chandra ACS camera, this source could be associated with the stellar cusp identified in Ibata et al. (2009). Source number 2 has an irregular shape and a luminosity of L_X = 0.72 × 10³³ erg s⁻¹ (Ramsay & Wu 2006a, 2006b).

The Ibata et al. (2009) estimate of the black hole mass is consistent with the (massive-black-hole host–galaxy) correlation of Ferrarese et al. (2006) only if the host system is M54 (M_IMBH/M_M54 ∼ 5%). For a similar mass ratio with SgrDw as the host system, a 1000 times more massive black hole would be necessary, suggesting this may be a system composed of a dwarf galaxy hosting a prominent stellar nucleus, which itself host a central IMBH. We estimate the largest contribution of the IMBH to a possible VHE gamma-ray signal, and assume that the IMBH is active and has a jet inclined toward the LOS with an angle θ. The contribution of the black hole to the VHE gamma-ray emission is estimated using the model developed by Reynoso et al. (2011) on the emission of relativistic jets associated with active galactic nuclei. The parameters of the model for the central black hole and jet are described in Reynoso et al. (2011). The calculation also uses the constraints from the upper limits in the radio band and the measured X-ray emission from source number 2. The modeled gamma-ray emission is shown in Figure 5. The parameters used in the model are given in Table 2. The emission depends only weakly on the black hole mass, but strongly on the assumed Lorentz factor Γ_b and inclination θ.

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Table 2. Model Parameters for the IMBH Candidate in M54

Parameter	Value
Mbh: black hole mass	5 × 103 M☉
Rg: gravitational radius	7.38 × 108 cm
L(kin)j: jet kinetic power at z0	6.28 × 1039 erg s−1
qj: ratio 2L(kin)j/LEdd	0.05
Γb(z0): bulk Lorentz factor of the jet at z0	4
θ: viewing angle	45°
ξj: jet's half-opening angle	5°
qrel: jet's content of relativistic particles	0.05
a: hadron-to-lepton power ratio	1
z0: jet's launching point	50 Rg
s: spectral index injection	2.1
η: acceleration efficiency	1. × 10−2
NH: column dust density	1021 cm−2

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The peak on the X-ray band comes from the synchrotron of electrons while a strong contribution from the synchrotron self-Compton scattering can be seen at GeV energies. At higher energies, in particular in the CTA energy range, the emission from pp interactions is dominant. However, for reasonable parameters, it is in the 10⁻¹⁸–10⁻¹⁷ erg cm⁻² s⁻¹ flux range—too faint to be detected by CTA.

Older publications (e.g., Evans et al. 2004; Aharonian et al. 2008) on DM search toward SgrDw used DM mass profiles which lead to somewhat optimistic constraints on particle DM self-annihilation cross-sections. These models were used because no accurate modeling of SgrDw existed at that time. Several realistic models are now published that loosen the existing constraints by more than one order of magnitude. The future CTA will be sensitive to 〈σv〉 values around a few 10⁻²⁵ cm³ s⁻¹. Some models could be excluded after 200 hr of observation if boost factors are taken into account.

However, the VHE emission of several astrophysical objects could give an observable signal for long enough observation times. The collective VHE emission of the MSPs of the M54 globular cluster, which is predicted by several models, could be much stronger than a DM signal. It could be observed in just a few tens of hours with CTA. The candidate IMBH located at the center is not expected to give an observable signal. Under favorable circumstances (active black hole and jet aligned toward the LOS), it might nevertheless be detectable in observations of SgrDw.