From 01ae4611f51dcf8e63b5f9a1091ddba8b61477c2 Mon Sep 17 00:00:00 2001 From: Aaron LI Date: Sat, 22 Jul 2017 10:15:13 +0800 Subject: clusters/helper.py: Add "velocity_impact()" and "time_crossing()" Signed-off-by: Aaron LI --- fg21sim/extragalactic/clusters/helper.py | 74 ++++++++++++++++++++++++++++++-- 1 file changed, 71 insertions(+), 3 deletions(-) (limited to 'fg21sim/extragalactic') 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 -- cgit v1.2.2