halox.cm: Mass-concentration relations

halox.cm: Mass-concentration relations#

halox provides utility functions to calculate concentration as a function of mass using several relations in the literature. For examples, see Mass-concentration relations.

duffy08()

Duffy et al. (2008) c-M relation using \(M_{200c}\).

klypin11()

Klypin et al. (2011) c-M relation using \(M_{\rm vir}\) at \(z = 0\).

prada12(cosmo)

Prada et al. (2012) c-M relation using \(M_{200c}\).

child18all(cosmo)

Child et al. (2018) c-M relation for all halos using \(M_{200c}\).

child18relaxed(cosmo)

Child et al. (2018) c-M relation for relaxed halos using \(M_{200c}\).
class halox.cm.duffy08[source]#

Duffy et al. (2008) c-M relation using \(M_{200c}\).

https://ui.adsabs.harvard.edu/abs/2008MNRAS.390L..64D/abstract

Parameters:

  • M (ArrayLike) – Halo mass \(M_{200c}\) [Msun].

  • z (ArrayLike) – Redshift.

Returns:

c – Concentration \(c_{200c}\).

Return type:

Array

Notes

  • Warning: input masses must be in Msun, not Msun/h

  • The functional form is

    \[c(M, z) = A \left(\frac{M}{M_0}\right)^B (1 + z)^C\]

    with \(M_0 = 2 \times 10^{12}\, M_\odot\).

  • Calibrated on WMAP5.

  • Valid for \(10^{11} \le M \le 10^{15}\, M_\odot\), \(0 \le z \le 2\).

class halox.cm.klypin11[source]#

Klypin et al. (2011) c-M relation using \(M_{\rm vir}\) at \(z = 0\).

http://adsabs.harvard.edu/abs/2011ApJ…740..102K

Parameters:

M (ArrayLike) – Halo mass \(M_{\rm vir}\) [h-1 Msun].

Returns:

c – Concentration \(c_{\rm vir}\).

Return type:

Array

Notes

  • Only implements the \(z = 0\) case from the original paper, which also provides redshift evolution.

  • Calibrated on WMAP7.

  • Valid for \(3 \times 10^{10}\) to \(5 \times 10^{14}\, h^{-1} M_\odot\), \(z = 0\) only.

class halox.cm.prada12(cosmo)[source]#

Prada et al. (2012) c-M relation using \(M_{200c}\).

http://adsabs.harvard.edu/abs/2012MNRAS.423.3018P

Parameters:

  • cosmo (jc.Cosmology) – Cosmology used to compute \(\sigma(M, z)\).

  • M (ArrayLike) – Halo mass \(M_{200c}\) [h-1 Msun].

  • z (ArrayLike) – Redshift.

Returns:

c – Concentration \(c_{200c}\).

Return type:

Array

Notes

  • Predicts concentration as a function of peak height via \(\sigma(M, z)\), capturing an upturn in concentration at high masses.

  • Cosmology-dependent through \(\sigma(M, z)\).

  • Valid for any cosmology, \(M > 0\), \(z \ge 0\).

class halox.cm.child18all(cosmo)[source]#

Child et al. (2018) c-M relation for all halos using \(M_{200c}\).

https://ui.adsabs.harvard.edu/abs/2018ApJ…859…55C/abstract

Parameters:

  • cosmo (jc.Cosmology) – Cosmology for \(\sigma(R)\) and the growth factor.

  • M (ArrayLike) – Halo mass \(M_{200c}\) [h-1 Msun].

  • z (ArrayLike) – Redshift.

Returns:

c – Concentration \(c_{200c}\).

Return type:

Array

Notes

  • Defines a characteristic mass \(M_*\) through

    \[\sigma(M_*, z) = \frac{\delta_{\rm sc}}{D(z)}\]

    Concentration depends on the ratio \(M / M_*\).

  • Calibrated on WMAP7.

  • Valid for \(M > 2.1 \times 10^{11}\, h^{-1} M_\odot\), \(0 < z < 4\).

class halox.cm.child18relaxed(cosmo)[source]#

Child et al. (2018) c-M relation for relaxed halos using \(M_{200c}\).

https://ui.adsabs.harvard.edu/abs/2018ApJ…859…55C/abstract

Parameters:

  • cosmo (jc.Cosmology) – Cosmology for \(\sigma(R)\) and the growth factor.

  • M (ArrayLike) – Halo mass \(M_{200c}\) [h-1 Msun].

  • z (ArrayLike) – Redshift.

Returns:

c – Concentration \(c_{200c}\).

Return type:

Array

Notes

  • Same functional form as child18all but calibrated for relaxed halo populations.

  • Calibrated on WMAP7.

  • Valid for \(M > 2.1 \times 10^{11}\, h^{-1} M_\odot\), \(0 < z < 4\).