MAMPOSSt arguments

• Data

rr(ndata):projected radius vector (R) in kpc [size ndata] avz(ndata):absolute line-of-sight velocity vector (| v_LOS |) in km/s (assuming mean near 0) [size ndata] evz(ndata):error on line-of-sight velocity in km/s [size ndata] comp(ndata):observed component of tracer (1_all for single component, else 1_str1, 2_str2 …) mu(ndata):distance modulus (\(<=\) 0 for none) emu(ndata):error on distance modulus (-1 for none) ndata:number of data points

• Data parameters (vectors of ncomp length)

rrmindata(ncomp):  minimum projected radius (already computed from data to save time) rrmaxdata(ncomp):  maximum projected radius (already computed from data to save time) rrminallow(ncomp):  minimum allowed projected radius (\(<\) 0 for innermost data point) rrmaxallow(ncomp):  maximum allowed projected radius (\(<=\) 0 for outermost data point) avzmaxdata(ncomp):  maximum absolute LOS velocity (already computed from data to save time) avzmaxallow(ncomp):  maximum allowed absolute LOS velocity (\(<=\) 0 for largest data point) mu0:distance modulus of full system if known (ignored if no mu provided in data file or if all mu \(<\) 0)

• Tracer structure (vectors of ncomp length)

tracermodel(ncomp):  model of visible tracer; available models are:
Hernquist: \(\rho \propto r^{-1}(r+a)^{-3}\) (Hernquist 1990 model, \(r_{-2}/a=1/2\))
mHubble: \(\rho \propto (r^2+a^2)^{-3/2}\) (modified Hubble or non-truncated analytical King 1962 model, \(r_{-2}/a=\sqrt{2}\))
isothermal: \(\rho \propto (r^2+a^2)^{-1}\) (pseudo-isothermal)
Jaffe: \(\rho \propto r^{-2}(r+a)^{-2}\) (Jaffe 1983)
NFW: \(\rho \propto r^{-1}(r+a)^{-2}\) (Navarro, Frenk & White 1996 model, \(r_{-2}/a=1\))
Plummer: \(\rho \propto (r^2+a^2)^{-5/2}\) (Plummer 1911 model, \(r_{-2}/a=\sqrt{2/3}\))
gPlummer: \(\rho \propto r^\gamma (r^2+a^2)^{-5/2-\gamma/2}\) (generalized Plummer with free inner slope \(\gamma\), \(r_{-2}/a=\sqrt{(2+\gamma)/3}\))
PrugnielSimien: \(\displaystyle \rho \propto x^{-p(n)}\,\exp \left[-b(n)\,\left({r\over R_{\rm eff}}\right)^{1/n}\right]\) (Prugniel & Simien 1997 approximation to deprojected Sersic, where \(b(n)\) is from analytical approximation of Ciotti & Bertin 1999, while \(p(n)\) is given by Lima Neto, Gerbal & Marquez 1999) ltracerradius(ncomp):  \(\log_{10}\) scale radius of visible tracer (kpc) meanltracerradius(ncomp):  mean (best) externally derived log(tracer radius), \(<\) 0 for internally derived sigltracerradius(ncomp):  error in externally derived log(tracer radius), \(<\) 0 for internally derived tracerpar2(ncomp):  additional tracer parameter ltracermass(ncomp):  \(\log_{10}\) tracer mass in M_solar at rfid ltracermasstot:\(\log_{10}\) total tracer mass in M_solar at rfid fractracer(ncomp):  fraction of total tracer mass in tracer rfidtracer(ncomp):  fiducial radius for tracer mass or 0 for infinity, or \(<\) 0 for 10^ltracerradius (kpc)

• Tracer velocity anisotropy (vectors of ncomp length)

anismodel(ncomp):  

velocity anisotropy model(s) model1 etc. of visible

tracer(s); available models are:

iso: \(\beta = 0\) (isotropic)
cst: \(\beta\) = constant
ML: \(\displaystyle \beta = {1\over 2} {r\over r+r_\beta}\) (Mamon & Łokas 2005b)
OM: \(\displaystyle \beta = {r^2\over r^2+r_\beta^2}\) (Osipkov 1979; Merritt 1985)
gOM: \(\displaystyle \beta = \beta_0 + (\beta_\infty-\beta_0)\,{r^2\ r^2+r_\beta^2}\) (generalized Osipkov-Merritt)
Tiret: \(\displaystyle \beta = \beta_0 + (\beta_\infty-\beta_0)\,{r\over r+r_\beta}\) (Tiret et al. 2007)

anisflag:

0 \(\displaystyle \to \log_{10} \left({\sigma_r\over \sigma_\theta}\right)\qquad\) 1 \(\to \beta\qquad\) 2 \(\displaystyle \to \beta_{\rm sym} = {\sigma_r^2-\sigma_\theta^2 \over \sigma_r^2+\sigma_\theta^2}\)

lanis0(ncomp):

central velocity anisotropy (see anisflag)

lanisinf(ncomp):  

outer velocity anisotropy (see anisflag)

lanisradius(ncomp):  

\(\log_{10}\) anisotropy radius (kpc) (irrelevant for ‘isotropic’)

ncomp:

number of components

• Dark Matter

darkmodel:model of dark matter; available models are:
Burkert: \(\rho \propto (r+a)^{-1}(r^2+a^2)^{-1}\) (Burkert 1995 model, \(r_{-2}/a=(1-\sqrt{26/27})^{1/3}+(1+\sqrt{26/27})^{1/3})\)
Einasto: \(\rho \propto \exp[-b(n)\, r^{1/n}]\) (Einasto 1965 model, \(r_{-2}/a = (2n)^n\))
Hernquist: \(\rho \propto r^{-1}(r+a)^{-3}\) (Hernquist 1990 model, \(r_{-2}/a=1/2\))
gHernquist: \(\rho \propto r^\gamma (r+a)^{-4-\gamma}\) (generalized Hernquist model with free inner slope \(\gamma\), \(r_{-2}/a=1+\gamma/2\))
mHubble: \(\rho \propto (r^2+a^2)^{-3/2}\) (modified Hubble or non-truncated analytical King 1962 model, \(r_{-2}/a=\sqrt{2}\))
isothermal: \(\rho \propto (r^2+a^2)^{-1}\) (pseudo-isothermal)
Jaffe: \(\rho \propto r^{-2}(r+a)^{-2}\) (Jaffe 1983)
Kazantzidis: \(\rho \propto r^\gamma \exp(-r/a)\) (Kazantzidis et al. 2004 model, \(r_{-2}/a=2+\gamma\))
NFW: \(\rho \propto r^{-1}(r+a)^{-2}\) (Navarro, Frenk & White 1996 model, \(r_{-2}/a=1\))
cNFW: \(\rho \propto (r+a)^{-3}\) (cored NFW model, \(r_{-2}/a=2\))
gNFW: \(\rho \propto r^\gamma (r+a)^{-3-\gamma}\) (generalized NFW model with free inner slope, \(r_{-2}/a=2+\gamma\))
Plummer: \(\rho \propto (r^2+a^2)^{-5/2}\) (Plummer 1911 model, \(r_{-2}/a=\sqrt{2/3}\))
gPlummer: \(\rho \propto r^\gamma (r^2+a^2)^{-5/2-\gamma/2}\) (generalized Plummer with free inner slope \(\gamma\), \(r_{-2}/a=\sqrt{(2+\gamma)/3}\))
norm:normalization of dark matter (mass or radius, see darknormflag) darknormflag:flag for dark matter or total normalization norm:
-1: \(\log_{10} r_{\rm vir}\) (kpc)
0: \(\log_{10} M_{\rm vir}\) (\(\rm M_\odot\))
\(>\) 0: \(\log_{10} M(r_{\rm fid}^{\rm dark}\) = darknormflag) in \(\rm M_\odot\) darkscale:\(\log_{10}\) scale of dark matter (scale radius [generally \(r_{-2}\)] or concentration \(r_{\rm vir}/r_{\rm scale}\)) darkscaleflag:flag for darkscale -> 1: scale radius, 2: concentration (\(r_{\rm vir}/r_{\rm scale}\)) darktotflag:1: dark 2: total (norm then concerns total normalization) darkpar2:additional dark matter parameter

• Central Black Hole

lbhmass:\(\log_{10}\) black hole mass (\(\rm M_\odot\))

• 3D velocity model

v3dmodel:model of 3D velocities (Gauss for now)

• Cosmology

Delta:mean overdensity at virial radius relative to critical density of Universe h:dimensionless Hubble constant \(H_0\) / (100 km/s/Mpc) Omegam:density parameter at \(z=0\) z:redshift of object

• Other parameters

rmax:maximum LOS integration radius (kpc) MfLflag:[Mass-follows-Light] 1 -> force a_dark=a_tracer, tracermodel=darkmodel TLMflag:[Tied-Light-Mass] 1 -> force a_tracer=a_dark, tracermodel=darkmodel TALflag:[Tied-Anisotropy-radius-Light] 1 -> force a_anis=a_tracer a0lclM:normalization of log(concentration) vs log(halo-mass) relation a1lclM:slope of log(concentration) vs log(halo-mass) relation splitpflag:1 -> determine a_tracer separately to gain time (less accurate) if ltracerradius \(>=\) 9, solve for tracerradius and exit wt:weights [array of size ndata] distflag:for data with distance modulus (mu): 0: ignore mu, 1: Gaussian(mu) weight, 2: Gaussian(mu) * density weight lBilop:\(\log_{10} B\) for interlopers (virial units) ilopflag:0 -> halo only, 1 -> standard to infinity (with interlopers), 2 -> halo + interlopers jointly debug:0: no debug output, 1: lnL, 2: verbose, 3: more, 4: verbose