A simple recipe for estimating masses of elliptical galaxies and clusters of galaxies

Transcription

1 A simple eipe fo estimating masses of elliptial galaxies and lustes of galaxies Quik and obust mass estimates - fo elliptial galaxies fom optial data tested on simulated galaxies by Ose et al fo lustes of galaxies fom optial data tested on simulated halos by Dolag et al. 009 N. Lyskova 1, E. Chuazov 1, I. Zhuavleva 1, T. Naab 1, L. Ose 1, O. Gehad, X. Wu MNAS, 01 1 Max Plank Institute fo Astophysis Max Plank Institute fo Extateestial Physis

2 Looking fo a simple, fast in implementation and obust method fo estimating masses of elliptials and lustes of galaxies... Elliptial galaxies Main poblem: degeneay between the anisotopy of stella obits and the mass. Options iial theoem: 3σ isothemal potential, losed spheial, stationay system +: anisotopy does not matte : ode of magnitude estimate Cental veloity dispesion: +: available fo most galaxies : depends on the size of apetue, should wok if obits ae isotopi Can we do bette?..

3 Chuazov The et main al. 010 idea of estimate the method fom I, σ and thei slopes Bolzman distibution 0 e mφ kt Φ ln + 0 e onst m ln kt d ln m d ln m kt I 0 kt m kt σ estimate! pimaily depends on I, σ and thei deivatives slopes

4 Chuazov et al. 010 The method is based on the stationay non-steaming Jeans equations d d d d Φ + σ β σ onst + Φ ln 1 σ σ β θ Stella anisotopy paamete Exteme types of stella obits: Isotopi β 0 adial β 1 Ciula β - stella luminosity density, σ - adial omponent of the veloity dispesion tenso weighted by luminosity Assumption: Gavitational potential d I d I 1 β σ σ Obsevable quantities: sufae bightness I & LOS veloity dispesion σ

5 Algoithm fo estimating 1. Calulate α, γ, δ fom obseved I and σ pofiles: α d lni d ln ln σ, γd dln,δ d ln[i σ ] dln. Calulate fo the exteme types of stella obits Full analysis iso σ 1+α+γ сi σ 1+α+γ/α ad σ α+ γ +δ1 Simplified analysis iso σ 1+α сi σ 1+α/α ad σ α 1 3. Estimate at a adius sweet point sweet whee all thee uves inteset eah othe. sweet is not affeted muh by the anisotopy.

6 Example: Sufae bightness I LOS veloity dispesion σ Deviation of the estimated fom the tue one Logaithmi deivatives iso tue tue 1% Almost flat tue α d LnI d Ln

7 Analysis of massive and slowly otating galaxies at diffeent edshifts at sweet Fation of galaxies % Almost unbiased estimate Modest satte even at high edshifts Deviation iso tue tue Can be useful fo galaxy suveys!

8 1 ρ Ciula speed fom X-ay data Spheial symmety + hydostati equilibium of gas: dp dφ d d GM Subsample of most massive galaxies: M > M ʘ Gas pessue P nkt Cyan at eff Gas density ρ µ m p n Blak at eff n gas numbe density, m p poton mass, µ - mean atomi weight, T - tempeatue Gas motions X eff 3.0%! 4.0% Mass bias X eff

9 Clustes of galaxies Taes individual galaxies Numbe of galaxies pe unit aea LOS veloity dispesion Noisy pofiles simplified analysis! Zoom in: only isotopi + fom hydostatis I slope estimate

10 estimates of simulated halos Numbe of taes > 50 N 53 obets Numbe of taes > 100 N 33 obets

11 To onlude: Pat I. Elliptial galaxies. 1. Full analysis unbiased estimate of total M and modest satte MS 5-8% even fo highedshift galaxies. May be useful fo galaxy suveys.. X-ay + hydostati equilibium estimate of is biased low what an be taed to the pesene of gas motions. Pat II. Clustes. 1. Simplified analysis unbiased estimate of. May be useful fo alibation othe mass detemination methods hydostatis, weak lensing, et