1 kev Plasma. Theoretical model of a collisionally ionized plasma kt=1 kev with solar abundances The lines are 'narrow' Notice dynamic range of 10 5

Transcription

1 1 kev Plasma Theoetical model of a collisionally ionized plasma kt=1 kev with sola abundances The lines ae 'naow' Notice dynamic ange of 10 5

2 Obsevational data fo a collisionally ionized plasma kt=1 kev with sola abundances Notice the vey lage blend of lines nea 1 kev- L shell lines of Fe Notice dynamic ange of 10 7

3 Ratio of model to a 'pue' H/He plasma This plot is designed to show the lines Collsionally Ionized Equilibium Plasma

4 Line emission Bemms (black) Recombin ation (ed) photon geen Stong Tempeatue Dependence of Specta

5 The equilibation timescales between potons and electons is t(p,e) ~ x 10 8 y at an 'aveage' location In collisional ionization equilibium population of ions is diectly elated to tempeatue Relevant Time Scales 3m1 π ( kt ) τ (1,) = 8π m n Z Z e ln Λ ln( b max 5 T τ ( e, e) K τ ( p, p) = m / m τ ( e, e) τ ( p, e) = ( m p / b p / m min e e ) / 4 3/ ln Λ ne cm 43τ ( e, e) ) τ ( e, e) 1800τ ( e, e) 1 y Ion faction fo Fe vs electon tempeatue

6 How Did I Know This?? Why do we think that the emission is themal bemmstahlung? X-ay specta ae consistent with model X-ay 'image' is also consistent Deived physical paametes 'make sense' Othe mechanisms 'do not wok' (e.g. spectal fom not consistent with black body, synchoton fom a powe law: pesence of x- ay spectal lines of identifiable enegy agues fo collisional pocess; atio of line stengths (e.g. He to H-like) is a measue of tempeatue which agees with the fit to the continuum)

7 Mean Fee Path fo Collisions/ Enegy λ 3 T 8 10 K 10 3 ne cm 3 1 kpc = 8 3 3/ π n ( kt At T>3x10 7 K the majo fom of enegy emission is themal bemmstahlung continuum ε~ 3x10-7 T 1/ n egs/cm 3 /sec- how long does it take a pacel of gas to lose its enegy? τ~nkt/ε 8.5x10 10 ys(n/10 3 ) 1 T 8 1/ At lowe tempeatues line emission is impotant λ p λ e e e 4 ) ln Λ

8 To fist ode if the gas wee coole it would fall to the cente of the potential well and heat up If it wee hotte it would be a wind and gas would leave cluste Idea is that gas shocks as it 'falls into' the cluste potential well fom the IGM Is it 'mege' shocks (e.g. collapsed objects meging) O in fall (e.g. ain) BOTH Why is Gas Hot

9 Physical Conditions in the Gas the elastic collision times fo ions and electons ) in the intacluste gas ae much shote than the time scales fo heating o cooling, and the gas can be teated as a fluid. The time equied fo a sound wave in the intacluste gas to coss a cluste is given by T s ~6.6x10 8 y (T gas /10 8 ) 1/ (D/Mpc) (emembe that fo an ideal gas v sound = (γp/ρ g ) (P is the pessue, ρ g is the gas density, γ=5/3 is the adiabatic index fo a monoatomic ideal gas )

10 Hydostatic Equilibium Kaise 19. Equation of hydostatic equil P=-ρ g φ() whee φ() is the gavitational potential of the cluste (which is set by the distibution of matte) P is the gas pessue ρ g is the gas density

11 Hydodynamics ρ + ( ρv) = 0 mass consevation (continuity) t Dv ρ + P + ρ φ = 0 momentum consevation (Eule) Dt Ds ρt = H L entopy (heating & cooling) Dt ρkt P = equation of state µ m p φ

12 density and potential ae elated by Poisson s equation φ = 4πρG and combining this with the equation of hydostaic equil. (1/ρ P)=- φ =-4πGρ o, fo a spheically symmetic system 1/ d/d ( /ρ dp/d)=-4πρgρ

13 Deiving the Mass fom X-ay Specta Fo spheical symmety this educes to (1/ρ g ) dp/d=-dφ()/d=gm()/ With a little algeba and the definition of pessue - the total cluste mass can be expessed as M()=kT g ()/µgm p ) (dlnt/dln+dlnρ g /dln) k is Boltzmans const, µ is the mean mass of a paticle and m H is the mass of a hydogen atom Evey thing is obsevable The tempeatue T g fom the spatially esolved spectum The density ρ g fom the knowledge that the emission is due to bemmstahlung And the scale size,, fom the convesion of angles to distance

14 The emission measue along the line of sight at adius, EM(), can be deduced fom the X-ay suface bightness, S(Θ): EM() =4 π (1 + z)4 S(Θ)/Λ(T, z) ; = da(z) Θ whee Λ(T, z)is the emissivity in the detecto band, taking into account the instument spectal esponse, da(z) is the angula distance at edshift z. The emission measue is linked to the gas density ρ g by: EM() = ρ g (R) Rd/ (R - ) The shape of the suface bightness pofile is thus govened by the fom of the gas distibution, wheeas its nomalization depends also on the cluste oveall gas content.

15 Density Pofile a simple model(the β model) fits the suface bightness well S()=S(0)(1//a) ) -3β+1/ cts/cm /sec/solid angle Is analytically invetible (invese Abel tansfom) to the density pofile ρ()=ρ(0)(1//a) ) -3β/ The convesion function fom S(0) to ρ(0) depends on the detecto The quantity 'a' is a scale facto- sometimes called the coe adius The Abel tansfom,, is an integal tansfom used in the analysis of spheically symmetic o axially symmetic functions. The Abel tansfom of a function f() is given by: f()=1/p df/dy dy/ (y - ) In image analysis tthe evese Abel tansfom is used to calculate the emission function given a pojection (i.e. a scan o a photogaph) of that emission function. In geneal the integal is not analytic which makes the

16 A geometical intepetation of the Abel tansfom in two dimensions. An obseve (I) looks along a line paallel to the x-axis a distance y above the oigin. What the obseve sees is the pojection (i.e. the integal) of the ciculaly symmetic function f() along the line of sight. The function f() is epesented in gay in this figue. The obseve is assumed to be located infinitely fa fom the oigin so that the limits of integation ae ± Abel Tansfom

17 Discussion in Saazin sec 5

18 Suface Bightness Pofiles It has become customay to use a 'β' model (Cavaliee and Fesco- Fumiano)' clustes have <β>~/3 1/ 3 / ) ( but teat as fitting paamete 1 ) ( = β β σ µ β ρ ρ c X gal p c I kt m

19 'Two' Types of Suface Bightness Pofiles 'Coed'- the pofile is flat in the cente Cental Excess Range of coe adii and β

20 The obseved x-ay emissivity is a pojection of the density pofile X-ay Emissivity A lage set of clustes ove a wide ange in edshift

21 Cluste Potentials (cont.) ρ dm,0 ρdm( ) = 3/ 1 + ρ c / 00 kpc c s

22 Compaison of Lensing to X-ay Masses is the ovedensity of the pat of the cluste compaed to the citical density

23 Cluste Potentials + + = + = s s s s s vi s vi s s s dm M c ) ln(1 4 ) ( 400 kpc Mpc, 5 fo clustes, / 1 ) ( 3 πρ ρ ρ ρ

24 Top Questions on Clustes of Galaxies that Can be Answeed by High Enegy Astophysics Ae clustes fai samples of the Univese? Can we deive accuate and unbiassed masses fom simple obsevables such as luminosity and tempeatue? What is the oigin of the metals in the ICM and when wee they injected? What is the oigin of the entopy of the ICM?

25 ρ Λ ρ µ ) ( )] ( [ ) ( 1 ) ( ) ( ) ( n T b db b I d d b d b I e b ν ν ν ν ν π ε ε = Λ = =

26 X-ay Mass Estimates use the equation of hydostatic equilibium Putting numbes in gives

27 Mass Pofiles fom Use of Hydostatic Equilibium Physical units Scaled units

28 Checking that X-ay Popeties Tace Mass Compaison of cluste mass fom lensing and x-ay hydostatic equilibium fo A390 and RXJ1340 (Allen et al 001) At the elative level of accuacy fo smooth elaxed systems the x-ay and lensing mass estimatos agee Suface mass density fo 4 Rosat selected clustes fom Sloan lensing analysis

29 'New' Physics The Cooling time ~τ~nkt/e ~8.5x10 10 ys(n/10-3 ) -1 T 8 1/ Fo bemmstahlung but fo line emission dominated plasmas it scales as 1 T 8-1/ ; That is as the gas gets coole it cools faste Λ=cooling function T cool =5/nkT/n Λ ~t Hubble T8Λ -1-3 n - -1 In cental egions whee the density (n) is lage can cool in t<10 9 ys 5/ (the enthalpy) is used instead of 3/ to take into the compession of as it cools (and emains in pessue equilibium)

30 Cooling Coes t cool = ne T cm 10 K 1/ Gy Notice that the cental suface bightness of cool coe clustes (left panel) is much highe than non-cooling coe clustes

31 Cooling Time fo a Sample of Clustes

32 Obseved Tempeatue Pofiles If the gas is in equilbium with the potential (of the NFW fom) it should be hotte in the cente But in many clustes it is coole Left panel (fom Buns et al 010) shows the theoetical tempeatue pofile if a NFW potential (in gey) compaed to an set of actual cluste tempeatue pofiles