Oct 25, 2017

• Evolution in groups and clusters • Dynamical friction and the formation of cDs • Ram pressure sweeping • Harassment • Tidal interactions

• Presentation part of HW #6

• HW#7 will be posted shortly and is due next Wed. Part of it relates to

your final project; the first two parts require short answers based on class notes, the textbook and PE#16 and should be easy!

HW #6

• The final project is meant to be a significant piece of work.

• Be sure to follow instructions in the homework about what to include.

X-ray from hot ICM in clusters • Clusters of galaxies are the most common bright

extragalactic X-ray sources; clusters have very high LX ~ 1043-45 erg s-1 but the range of LX is very high. Emission is by thermal bremsstrahlung (breaking) radiation also known as free-free emission due to the hot gas. We deduce that the emission is bremsstrahlung from its spectrum:

4πε(ν) = 6.8 x 10-38

where ne(r=0) ~ 10-3 cm-3, T~ 108 K

• For a thermal plasma with solar abundance , the total bremsstrahlung emission depends on the temperature T of the hot gas and the density ne as:

ne exp (-hν/kT) √T

Deceleration of free electron leads to

emission of photon

“breaking radiation”

X-ray emission in clusters

Hot gas in clusters • The X-ray surface brightness is usual described by a “beta” β-model

“Beta model”

See: Schneider 6.4.2

• X-ray distribution centered on cluster center, as determined by the galaxy distribution, or on active galaxy in the cluster.

• Favored model: isothermal, hydrostatic • Both gas and galaxies are assumed to

be: 1. Isothermal 2. Bound to cluster 3. In equilibrium

⇒ Galaxies assumed to have an isotropic velocity dispersion, but the gas & galaxies are NOT assumed to have the same velocity dispersion

µ mp σr2

kTgas where µ = mean molecular weight in amu

mp = mass of proton σr = 1-D velocity dispersion Tgas = gas temperature in K

β ≡

Then ρgas ∝ ρgalβ

X-ray observations of hot ICM in clusters Assume a galaxy distribution has a “King” analytic form (truncated

isothermal sphere=> finite mass) Space density: n(r) = no [ 1 + (r/rc)2 ] -3/2

Surface density: Σ(b) = Σo [ 1 + (b/rc)2 ] -1

Σo = 2 no rc where rc is the core radius Then the X-ray surface brightness IX goes as

IX(b) ∝ [ 1 + (b/rc)2 ] -3β + ½

• Typical fits to X-ray SB yield <β> ~ 0.65 => gas more extensively distributed than galaxies rc ~ (0.1 to 1.2 Mpc) => wide range

from Mulchaey (2000)

LX ∝ σ4.4 LX ∝TX3

TX ∝ σ2 Close relations between X-ray L and T and velocity dispersion of cluster

T(keV) = 1.602 x 10-9 erg 1.38 x 10-16 erg K-1

= 1.16 x 107 K

Global correlations in clusters • The central galaxy density is higher for higher Lx. • The fraction of spirals is lower for higher Lx. • The temperature T is proportional to Lx and typically 108K • The gas metallicity is lower for higher T and typically 1/3 of solar • The ratio of gas-mass to galaxy-mass increases with T up to 4 or

more • The dominant component in all

clusters is dark matter, as measured by the dynamics of the galaxies, the hydrostatic equilibrium of the X-ray gas and from gravitational lensing.

• Typical ratios are: galaxies: X-ray gas: dark matter = 1:4:25

Interactions in clusters • Gravitational interaction:

galaxy - cluster • Gravitational interaction:

galaxy - galaxy • Ram pressure: galaxy

ISM – intracluster medium (ICM)

(Kenney et al. 1995)

(Böhringer et al. 1994)

(Kenney et al. 2004)

VLA Survey of Virgo in Atomic Gas: VIVA

www.astro.yale.edu/viva/

cD N4881 in Coma

cD = “cluster diffuse” Much brighter than next brightest galaxy

Surf

ace

brig

htne

ss

Log radius

excess

• In the cores of regular rich clusters (or at a density enhancement) – Local conditions are important

• Offset (too bright) from the luminosity function of normal galaxies • Extensive (~1Mpc) stellar envelopes of low surface brightness • Many have multiple nuclei.

cD galaxy in Abell 3827

cD galaxies

How do cD’s form? • Galactic Cannibalism (Ostriker & Hausman, 1977)

• Dynamical friction brings massive galaxies to the center of clusters • Merger of these massive galaxies in the cluster cores • Giant galaxy then swallows other galaxies going through the core

Centaurus A

Dynamical friction • Suppose an object of mass M is

moving within a sea of other objects of mass m, with m < M.

• As M moves forward, the other objects are pulled towards it, with the closest ones feeling the strongest force.

• This produces a region of enhanced density along the path of M, including a wake trailing it.

• Dynamical friction = net gravitational force on M due to others that opposes its motion.

• Kinetic energy is transferred from M to surroundings, thus reducing its speed.

Virgo: Nearest rich cluster to Local Group • At center of Local Supercluster

• Not very “rich” compared to most “Abell clusters” but nearest to Local Group

• Distance ~ 16.7 Mpc

• Ellipticals form relaxed core; spirals still in-falling

See: ACS Virgo cluster survey

Next Generation Virgo Survey (underway)

M87

Markarian’s chain

M87 = Virgo A

e.g. Million+ 2010 MNRAS 407, 2046

Evidence for ram pressure stripping in Virgo • Cluster has a healthy intracluster medium (ICM) seen in X-rays • Spirals in cluster are “atomic hydrogen poor” versus spirals

outside the cluster => HI deficiency” • Atomic hydrogen disks in

galaxies that are atomic hydrogen “poor” are smaller than disks in normal gas galaxies.

• In fact, Virgo is a “young cluster” with galaxies still falling into it.

• The elliptical galaxies fell in long ago; the spirals are still infalling.

NGC 4522

Contours: 6cm cont Greyscale: HI (Kenney et al. 2004)

Contours: 6 cm pol (Vollmer et al. 2004) Greyscale: B band

nearly edge-on disk about 1 Mpc from center

Ram pressure sweeping • Spirals in Virgo are HI deficient. • Hydrodynamical simulations show

effectiveness of ram pressure stripping • Stripping occurs if

ρICMV2 > 2πG ΣgasΣstars

Vollmer et al. 2001

• Ram pressure exerted by stationary gas on moving galaxy

• V is velocity of galaxy with respect to cluster

•Gravitational “restoring” force of stars and gas in galaxy

•Σ is surface density

Ram Pressure Stripping

http://www.aip.de/~rpiontek/ram.html

• The animation is fixed on the galaxy.

• The “wind” comes from the left.

• Similar effect if intracluster gas is fixed and galaxy is moving toward the left.

• The stars move like bullets through the wind, but the gas is “swept” in the direction opposite the wind.

Ram Pressure Stripping • Ram Pressure Stripping can remove the gas supply of galaxies that

pass through clusters – Interaction between ISM and ICM – Could explain metal content of the ICM – Episodes of starburst?

Simulation by B. Vollmer

Animation by Bengt Vollmer: astro.u-strasbg.fr/

~bvollmer/obspmweb/run_all.gif

• The arrow which appears represents the “turn-on” of ram pressure as the galaxy moves in the opposite direction (towards the cluster center, in the lower left)

Ram pressure stripping animation

http://www.hubblesite.org/newscenter/archive/releases/2014/14/video/b

Harassment • Supporting evidence:

–Intra cluster diffuse light (ICL) • Intergalactic stars, ~10-40% of the

cluster stellar population (Feldmeier et al., 2003)

–Tidal debris • e.g. Plumes and arc-like structures • The amount of tidal debris and ICL

depends on local density, which supports the merger scenario (Combes, 2004)

–Rings of star formation that are more common than two-armed spirals (Oemler et al., 1997) • Due to bars triggered during tidal

interactions?

Calcaneo-Roldan et al. (2000)

See: http://www.cita.utoronto.ca/~dubinski/rutgers/galaxies Evolution of galaxies in Virgo

• Cluster tides can be effective in stripping stars from galaxies and building up an intracluster stellar population

• See: http://astroweb.case.edu/craig/diffuse_light/diffuse_light.html

Formation of a cluster like Virgo

Ben Moore’s web site

Simulation by Ben Moore

Gravitational encounters

Schematic from Chris Mihos

“N-body” simulations: binary stars 1. Adopt the masses

of the 2 objects (so here N=2)

2. Adopt characteristics of the orbits (eccentricity, inclination, orientation)

3. Apply the laws of gravity to predict the relative positions of the two objects after every time step.

“N-body” simulations: Sun-Earth-Moon 1. Adopt the masses

of the 3 bodies (so here N=3)

2. Adopt characteristics of the orbits (eccentricity, inclination, orientation)

3. Apply the laws of gravity to predict the relative positions of the N objects after every time step.

• Each of the 3 bodies exerts a gravitational force on the other two

• Each of the 3 bodies feels the gravitational force from the other two

• They are all in motion!

Toomre & Toomre 1972

• The galaxy’s mass is concentrated at a point • The outer disk particles are arranged in 5 rings • They do not interact with each other (no self-gravity) • All passages involve two galaxies that have a close, slow moving

parabolic approach • Each time unit is 100 million years

Although much more sophisticated codes exist today, T&T72 demonstrated the overall damage done by tides.

Toomre2 results

• Galaxy encounters are not accidental; most pairs are bound already • Direct encounters cause more damage than retrograde ones • Tails (nice) are easier to make than bridges (messy) • Viewing geometry is critically important

Encounter geometry

Barnes, 1988, ApJ 331, 699

• Mass ratio ~1 • Disks shown in their original position. • Each disk inclined 60o with respect to orbital plane

Retrograde passages Toomre & Toomre found that retrograde passage (ones in the opposite direction to a galaxy’s spin) have little tidal effect.

From now, we will only discuss direct passages, which are far more disruptive

Flat retrograde (i=180º) parabolic passage of a companion of equal mass.

TT72 • Direct passages are more effective • More damage from equal mass companion

Tails • Unlike bridges, tails involve some particles escaping towards infinity

• To form major tails, the galaxies should be similar in mass.

• Like bridges, tail making is less effective at higher inclination planes. Again, the difference between 0° and 30 ° is small.

• However, in higher inclinations, the tail is raised from the orbit plane. This allows the tails to be crossed, as in NGC 4038/9 = “The Antennae”

N-body simulations

1. Adopt a model for each galaxy as a system of N “mass particles”. - N is less than the number of stars/gas clouds in the galaxy but

still can be big (millions). - The bigger N the better the simulation

2. Adopt a model for the rotation (spin) and orientation of the disk(s). 3. Adopt a model for the orbital motion of the two galaxies. 4. Compute the gravitational force on each mass particle due to every

other particle; 5. Figure out how the particle will move in response to that force and

move the particle there. 6. Then recompute the gravitational force (4) and the new position(5) 7. Keep repeating, to track what happens!

• Orientation and direction of disk spin

• Orientation and direction of orbit

M81/M82 encounter

M81/M82 encounter

https://www.astro.umass.edu/~myun/movie.gif

How likely are encounters? • Slow encounters are unlikely in dense clusters.

• Simulated passages are unlikely to be hyperbolic.

• Tails and bridges are the least observed in dense clusters.

• Close encounters unlikely in loose groups.

• Most tidal effects must have been created by galaxies that are gravitationally bound.

• Disruption damage

• Tidal force F ∝ rp-3 where rp is the separation at perigalacticon

• Duration T ∝ rp/v where v is the relative velocity

• In the impulse approximation (I = FT) , the “damage” is ~ 1/(rp2 v)

⇒ slow close encounters do the most “damage”

* Impulse approx: assume one of the forces exerted on a particle acts on for short time but is greater than any other force