Analytical solutions to the mass-anisotropy degeneracy with higher order Jeans analysis: a general method

Richardson, Thomas D.; Fairbairn, Malcolm

doi:10.1093/mnras/stt686

Cited by 47 publications

(43 citation statements)

References 51 publications

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“…2, where all slopes γ ∈ [0, 1] are allowed at the 95% level). The difficulty to constrain this slope is generally attributed to the degeneracy of the DM parameters with the anisotropy parameter βani(r), and methods relying on higher order of the Jeans analysis have been proposed to circumvent this issue (Richardson & Fairbairn 2013. See also the MAMPOSSt approach in Mamon et al (2013).…”

Section: Preliminary Discussionmentioning

confidence: 99%

“…The main source of uncertainty in this ideal case is the velocity anisotropy profile. Higher-order Jeans analyses will probably appear as very helpful tools for reducing these uncertainties (see e.g., Richardson & Fairbairn 2013. However, we have found that even in the context of a maximum knowledge analysis (i.e., with the light profile and velocity anisotropy perfectly known), the best that can be achieved is J ±95% CI /J median 1.5 at αint = αc, and 2.5 at 0.1 αc and 10 αc.…”

Section: Conclusion For the Different Sample Sizesmentioning

confidence: 99%

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Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - impact of physical parameters and triaxiality

Bonnivard

Combet

Maurin

et al. 2014

Monthly Notices of the Royal Astronomical Society

102

131

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Dwarf spheroidal (dSph) galaxies are among the most promising targets for the indirect detection of dark matter (DM) from annihilation and/or decay products. Empirical estimates of their DM content-and hence the magnitudes of expected signals-rely on inferences from stellar-kinematic data. However, various kinematic analyses can give different results and it is not obvious which are most reliable. Using extensive sets of mock data of various sizes (mimicking 'ultra-faint' and 'classical' dSphs) and an MCMC engine, here we investigate biases, uncertainties, and limitations of analyses based on parametric solutions to the spherical Jeans equation. For a variety of functional forms for the tracer and DM density profiles, as well as the orbital anisotropy profile, we examine reliability of estimates for the astrophysical J-and D-factors for annihilation and decay, respectively. For large (N 1000) stellar-kinematic samples typical of 'classical' dSphs, errors tend to be dominated by systematics, which can be reduced through the use of sufficiently general and flexible functional forms. For small (N 100) samples typical of 'ultrafaints', statistical uncertainties tend to dominate systematic errors and flexible models are less necessary. We define an optimal strategy that would mitigate sensitivity to priors and other aspects of analyses based on the spherical Jeans equation. We also find that the assumption of spherical symmetry can bias estimates of J (with the 95% credibility intervals not encompassing the true J-factor) when the object is mildly triaxial (axis ratios b/a = 0.8, c/a = 0.6). A concluding table summarises the typical error budget and biases for the different sample sizes considered.

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Section: Preliminary Discussionmentioning

confidence: 99%

Section: Conclusion For the Different Sample Sizesmentioning

confidence: 99%

Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - impact of physical parameters and triaxiality

Bonnivard

Combet

Maurin

et al. 2014

Monthly Notices of the Royal Astronomical Society

102

131

View full text Add to dashboard Cite

show abstract

“…In the literature, one can find other approaches to lift the mass/anisotropy degeneracy, for example, by fitting the LOS velocity kurtosis profiles together with the LOS velocity dispersion profiles (Łokas 2003;Łokas & Mamon 2003;Richardson & Fairbairn 2013).…”

Section: Dynamical Modelsmentioning

confidence: 99%

Investigation of dark matter and modified Newtonian dynamics in early-type galaxies through globular cluster systems

Samurovic

2014

A&A

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Context. The departures from Newtonian dynamics based on the mass-follows-light approach discovered in the outer parts of some early-type galaxies imply the existence of dark matter and/or necessary modifications to the Newtonian approach. We study dynamical models of a sample of ten early-type galaxies in both Newtonian and MOND approaches. Aims. The measurements of the radial velocities of the globular clusters in ten massive early-type galaxies are used to test the predictions of dynamical models with and without dark matter assuming Newtonian and MOND approaches out to several effective radii. Methods. The globular clusters taken from the SLUGGS database are used as tracers of the gravitational potential of the galaxies in a sample. We solve the Jeans equation for both the Newtonian (mass-follows-light and dark matter models) and the MOND approaches by assuming spherical symmetry and compare the resulting mass-to-light ratios with stellar population synthesis models. For both approaches, we apply various assumptions on velocity anisotropy. Results. We find that the Newtonian mass-follows-light models without a significant amount of dark matter can provide successful fits for only one galaxy (NGC 2768), and for the remaining nine early-type galaxies, various amounts of dark matter are required in the outer parts beyond 2−3R e . With MOND models, we find that four early-type galaxies could be fit without dark matter and that the remaining six galaxies require an additional dark component to successfully fit the line-of-sight observed velocity dispersions; the galaxy NGC 4486 (M 87) is the only galaxy for which dark matter is required in the inner regions, and MOND cannot fit the data without additional dark matter. In the inner region, the galaxy NGC 4365 requires higher mass-to-light ratios than the stellar values from population synthesis, but a reasonable mass-to-light ratio can be reached for MOND assuming slightly tangential orbits. The ten galaxies can be split into two classes: those with concentrations at (NGC 1407) or above the ΛCDM concentration-mass relation, given their measured virial masses, and those below this relation. The former generally require dark matter in both Newtonian and MOND approaches, while the latter do not require appreciable amounts of dark matter.

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“…Since using higher order moments might reduce the degeneracy between the velocity anisotropy and the mass profile (e.g. Merrifield & Kent 1990;Richardson & Fairbairn 2013) we choose to use four velocity moments. We do not use higher moments since these are observationally harder to constrain.…”

Section: Fitting Orbital Weightsmentioning

confidence: 99%

Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy

Hagen

Helmi

Breddels

2019

A&A

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Aims. The goal of this work is to test the ability of Schwarzschild's orbit superposition method in measuring the mass content, scale radius and shape of a flattened dwarf spheroidal galaxy. Until now, most dynamical model efforts have assumed that dwarf spheroidal galaxies and their host halos are spherical. Methods. We use an Evans model (1993) to construct an isothermal mock galaxy whose properties somewhat resemble those of the Sculptor dwarf spheroidal galaxy. This mock galaxy contains flattened luminous and dark matter components, resulting in a logarithmic profile for the global potential. We have tested how well our Schwarzschild method could constrain the characteristic parameters of the system for different sample sizes, and also if the functional form of the potential was unknown. Results. When assuming the true functional form of the potential, the Schwarzschild modelling technique is able to provide an accurate and precise measurement of the characteristic mass parameter of the system and reproduces well the light distribution and the stellar kinematics of our mock galaxy. When assuming a different functional form for the potential, such as a flattened NFW profile, we also constrain the mass and scale radius to their expected values. However in both cases, we find that the flattening parameter remains largely unconstrained. This is likely because the information content of the velocity dispersion on the geometric shape of the potential is too small, since σ is constant across our mock dSph. Conclusions. Our results using Schwarzschild's method indicate that the mass enclosed can be derived reliably, even if the flattening parameter is unknown, and already for samples containing 2000 line-of-sight radial velocities, such as those currently available. Further applications of the method to more general distribution functions of flattened systems are needed to establish how well the flattening of dSph dark halos can be determined.

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Analytical solutions to the mass-anisotropy degeneracy with higher order Jeans analysis: a general method

Cited by 47 publications

References 51 publications

Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - impact of physical parameters and triaxiality

Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - impact of physical parameters and triaxiality

Investigation of dark matter and modified Newtonian dynamics in early-type galaxies through globular cluster systems

Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy

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