10.3. Mass-concentration relations

Possible keyword choices for gXXX_FLAG_CDELTAMDELTA variables

Warning

Be aware that different \(c_\Delta-M_\Delta\) parametrisations are only valid for restricted mass scales, which are given in the table below.

Also note that the distant-dependent descriptions kPIERI11_AQUARIUS, kPIERI11_VIALACTEA, kB01_VIR_RAD, and kMOLINE17_200 are at the moment only usable for Galactic subhalos in the -g module. Their usage for subhalos in the -h and -e modules is still under development.

Note

Various \(c_\Delta-M_\Delta\) parametrisations use the same fitting formula from Lavalle et al. (2008),

\[\ln (c_{\Delta} ) = \sum_{i=0}^{n} C_i \cdot \left[ \ln\left(\frac{M_{\Delta}}{M_\odot}\right) \right]^{i} + \ln\left(\frac{1}{1+z}\right)\,.\]

In these cases, we provide the \(C_i\) coefficients in the table below.

Keyword Description
kB01_VIR Bullock et al. (2001): extrapolation down to any mass range.

\(C_{i} = \{ - 4.34,\, 0.0384,\, -3.91\times 10^{-4},\, - 2.2\times 10^{-6},\, - 5.5\times 10^{-7}\}\)
kB01_VIR_RAD Kuhlen et al (2008): adaption of Bullock et al. (2001) with radial dependence.
kCORREA15_PLANCK_200 Correa et al. (2015): Only for extragalactic haloes and Planck cosmology.
kENS01_VIR Eke et al. (2001): extrapolation down any mass range.

\(C_{i} = \{3.14,\;-0.018,\; -4.1\times 10^{-4}\}\)
kNETO07_200 Neto et al. (2007): valid for \(M>10^8 M_\odot\).

\(c_{200} = 4.67\times\left(\frac{M_{200}}{10^{14}M_\odot}\right)^{-0.11}\times\;(1+z)^{-1}\;\;\) [their Eq. 5].
kDUFFY08F_VIR Duffy et al. (2008), \(\Delta=\Delta_{\rm vir}(z)\): valid for \(M>10^8 M_\odot\).

\(c_{\rm vir}=A \left( \frac{M_{\rm vir}}{2\times10^{12}M_{\odot}}\right)^B(1+z)^C\;\;\) [see their Table 1 for A, B, C].
kDUFFY08F_200 Duffy et al. (2008), \(\Delta=200\): valid for \(M>10^8 M_\odot\).
kDUFFY08F_MEAN Duffy et al. (2008), \(\Delta=200\times\Omega_{\rm mean}(z)\): valid for \(M>10^8 M_\odot\).
kETTORI10_200 Ettori et al. (2010): valid for \(M>10^8 M_\odot\)

\(c_{200} = 10^{0.62} \times \left(\frac{M_{200}}{10^{15}M_\odot}\right)^{-0.1}\times\;(1+z)^{-1}\;\;\) [see their Eq. 5].
kGIOCOLI12_VIR Giocoli et al. (2012): extrapolation down to any mass range.
kLUDLOW16_200 Ludlow et al. (2016): Only for extragalactic haloes and Planck cosmology.
kMOLINE17_200 Moliné et al. (2017), Eq. (6): improvement on Sánchez-Conde & Prada (2014) for Galactic subhalos accounting for spatial dependence of subhalos in field halos.
kPIERI11_VIALACTEA Pieri et al. (2011), Eq.(11): extrapolation down to any mass range, inspired by Via Lactea II simulation results (also has an explicit spatial dependence).
kPIERI11_AQUARIUS Pieri et al. (2011): extrapolation down to any mass range, inspired by Aquarius simulation results (also has an explicit spatial dependence).
kPRADA12_200 Prada et al. (2012), Eqs.(12-17,19-23): valid for \(M>10^8 M_\odot\).
kROCHA13_SIDM_VIR Only applicable to a Burkert-profile, resulting in core densities according to Eq. (20) of Rocha et al. (2013).
kSANCHEZ14_200 Sánchez-Conde & Prada (2014): extrapolation down to any mass range.

\(C_{i} = \{ 37.5153,\, -1.5093,\, 1.636\times 10^{-2},\, 3.66\times 10^{-4},\, -2.\times 10^{-5},\) \(\;5.32\times 10^{-7}\}\)


 

See also

Fig. 6.12 for a comparison of the various concentration-mass relations.