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authorAaron LI <aly@aaronly.me>2017-07-22 10:15:13 +0800
committerAaron LI <aly@aaronly.me>2017-07-22 10:15:13 +0800
commit01ae4611f51dcf8e63b5f9a1091ddba8b61477c2 (patch)
tree67d1476215591981a76ba79da93f831b41dc7bab /fg21sim/extragalactic
parent4f31ff421a937b1ad5a188b39ceb8fb82c938ad0 (diff)
downloadfg21sim-01ae4611f51dcf8e63b5f9a1091ddba8b61477c2.tar.bz2
clusters/helper.py: Add "velocity_impact()" and "time_crossing()"
Signed-off-by: Aaron LI <aly@aaronly.me>
Diffstat (limited to 'fg21sim/extragalactic')
-rw-r--r--fg21sim/extragalactic/clusters/helper.py74
1 files changed, 71 insertions, 3 deletions
diff --git a/fg21sim/extragalactic/clusters/helper.py b/fg21sim/extragalactic/clusters/helper.py
index 5b84c93..f07f1c0 100644
--- a/fg21sim/extragalactic/clusters/helper.py
+++ b/fg21sim/extragalactic/clusters/helper.py
@@ -6,12 +6,17 @@ Helper functions
References
----------
-.. [cassano2007]
- Cassano et al. 2007, MNRAS, 378, 1565;
- http://adsabs.harvard.edu/abs/2007MNRAS.378.1565C
.. [arnaud2005]
Arnaud, Pointecouteau & Pratt 2005, A&A, 441, 893;
http://adsabs.harvard.edu/abs/2005A%26A...441..893
+
+.. [cassano2005]
+ Cassano & Brunetti 2005, MNRAS, 357, 1313
+ http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
+
+.. [cassano2007]
+ Cassano et al. 2007, MNRAS, 378, 1565;
+ http://adsabs.harvard.edu/abs/2007MNRAS.378.1565C
"""
@@ -156,3 +161,66 @@ def density_energy_thermal(mass, z=0.0):
kT = mass_to_kT(mass, z) * AUC.keV2erg # [erg]
e_th = (3.0/2) * kT * n_th
return e_th
+
+
+def velocity_impact(M_main, M_sub, z=0.0):
+ """
+ Estimate the relative impact velocity between the two merging
+ clusters when they are at a distance of the virial radius.
+
+ Parameters
+ ----------
+ M_main, M_sub : float
+ Total (virial) masses of the main and sub clusters
+ Unit: [Msun]
+ z : float, optional
+ Redshift
+
+ Returns
+ -------
+ vi : float
+ Relative impact velocity
+ Unit: [km/s]
+
+ References
+ ----------
+ Ref.[cassano2005],Eq.(9)
+ """
+ eta_v = 4 * (1 + M_main/M_sub) ** (1/3)
+ R_vir = radius_virial(M_main, z) * AUC.kpc2cm # [cm]
+ vi = np.sqrt(2*AC.G * (1-1/eta_v) *
+ (M_main+M_sub)*AUC.Msun2g / R_vir) # [cm/s]
+ vi /= AUC.km2cm # [km/s]
+ return vi
+
+
+def time_crossing(M_main, M_sub, z=0.0):
+ """
+ Estimate the crossing time of the sub cluster during a merger.
+
+ NOTE: The crossing time is estimated to be τ ~ R_vir / v_impact.
+
+ Parameters
+ ----------
+ M_main, M_sub : float
+ Total (virial) masses of the main and sub clusters
+ Unit: [Msun]
+ z : float, optional
+ Redshift
+
+ Returns
+ -------
+ time : float
+ Crossing time
+ Unit: [Gyr]
+
+ References
+ ----------
+ Ref.[cassano2005],Sec.(4.1)
+ """
+ R_vir = radius_virial(M_main, z) # [kpc]
+ vi = velocity_impact(M_main, M_sub, z) # [km/s]
+ # Unit conversion coefficient: [s kpc/km] => [Gyr]
+ uconv = AUC.kpc2km * AUC.s2Gyr
+ time = uconv * R_vir / vi # [Gyr]
+ return time