Gravitational Redshiftin Clusters of Galaxies

Marton TrencseniEotvos University, Budapest

Gravitational Redshift

• Photon escapes from gravitational well• Gains potential energy• Speed cannot decrease =)

• The photon redshiftsto conserve energy

Gravitational redshift in galaxies

• Possible to measure within galaxies

• See Coggins’ 2003 PhD thesis (Merrifield):

Gravitational Redshifts and the Mass Distribution of Galaxies and Clusters

• Not what I’m doing…

Gravitational redshift in clusters

• Others have tried before

• No conclusive results

• Pre-SDSS datasets were too small

Gravitational redshift in clusters

• With SDSS data,

• You can’t get a signal from 1 cluster

• Instead, you re-scale and add several hundred/thousand clusters

• And measure the average gravitational redshift

• Dark Matter (DM)

• If the cluster is sittingin a blob of DM, thegravitational redshiftsignal might constrainthe DM mass

Why?

Verify cosmology

Catalogs

• NYU catalog:

• Andreas Berlind (NYU) created an SDSS galaxy cluster catalog based on spectro galaxies

• in 2006,

• based on DR3 data

Catalogs

• ELTE catalog:

• Own based on DR6 spectro galaxies

• DR6 has roughly twice as many galaxies

• Smaller errors bars, etc.

Clustering

• Friend-of-Friend (FOF) algorithm• 2 parameters: tangential and radial separation• If two galaxies’ separation are within the

above two limits, they’re friends• Make it associative to get the clusters

Clustering

• The trick is to get the two parameters right

• Too small: only finds cluster cores, clusters break up

• Too big: field contamination

Clustering

• Berlind (NYU): used cosmological simulations with a-priori cluster membership data and played with the two parameters to get statistics that matched the simulation

• Careful: predictions that contradict the simulations’ model are meaningless

Samples

• Three volume limited samples

• Absolute r-magnitude limits:

• Mr18: M < -18• Mr19: M < -19• Mr20: M < -20 (brightest)

Samples

brighter

Clustering Parameters

Clustering results

• NYU:(DR3)

• ELTE:(DR6)

Cluster richness

• NYU

Cluster richness

• ELTE

Cluster centers

• We now have clusters

• Gravitational redshift signal expected at the “center” of the cluster

• Center = ?

cD ellipticals & BCG

• cD = central diffuse, ellipticals• These are usually the brightest galaxies in

their cluster, hence they’re also called:• BCG = Brightest Cluster Galaxy

• Usually much (up to 10 times) brighter than the other galaxies in the cluster

cD ellipticals

• Abell S740

BCG subsample

• First cut / selection:

• Brightest galaxy should be no more than r_max away from the mean ra/dec center of the cluster

BCG subsample

• NYU:(DR3)

• ELTE:(DR6)

Gravitational redshift signal

• NYU: (DR3)

• ELTE: (DR6)

Bright, stationary BCG subsample

• Better cut / selection:

• The BCG should be really bright!• R magnitude difference between brightest (cD) and

third brightest should be at least 1.0 magnitude• The BCG should be stationary!• The peculiar velocity of the brightest should be less

than 200km/s (small) as compared to the average

Bright, stationary BCG subsample

• NYU (DR3):

• ELTE (DR6):

Gravitational redshift signal

• NYU (DR3):

• ELTE (DR6):

Supporting evidence?

• Hypothesis:If there is a gravitational redshift signal, it should depend on various physical parameters like cluster size, brightness, velocity dispersion

• E.g. bigger, brighter cluster more massive stronger signal

Supporting evidence?

• Just showing the NYU (DR3) case:

abs.R.magn. velocity disp. radius

Dark matter model

• Blob of DM around cluster• Additional blobs of

DM around galaxies

Dark matter content

Assumptions

• First, naïve model:

• Flat DM distribution:density is constant w.r.t. radius

Cluster DM blob

• Cluster blob is very large (Mpc), so the potiential well is not very deep

• For it to result in the measured signal, the DM content of the clusters would have to be huge:

• ~ 1700kg of DM for 1kg of visible mass

• Inconsistent with current cosmological models

Galaxy DM blob

• Here the mass is more concentrated• ~ 10kg of DM for 1kg of visible mass• (Caution: visible mass of BCG galaxy)• Consistent with current cosmological models

• This does not mean that there is no cluster blob, you just can’t measure its gravitational redshift signal…

Flat distribution?

• How naïve is the flat DM assumption?

• Second, trendy DM model:

• Navarro-Frenk-White (NFW) density:

NFW potential

• Flat vs. NFW potential: no “big” difference

Mass estimated

• Flat case:• Total DM mass ~ 0.65 * z * c^2 * R

• NFW case:• Total DM mass ~ 0.38 * z * c^2 * R

• ~ 5.5kg of DM for 1kg of visible mass• (Caution: visible mass of BCG galaxy)

• Consistent with current cosmological models

Navarro-Frenk-White DM estimate

• If what we’re measuring is theBCG’s DM blob…

• Then given that other galaxies are also sitting in DM blobs, and also have some gravitational redshift

• Then really what we measured is the excess gravitational redshift of the BCG…

Self-consistency

Self-consistency

• …Due to the excess DM fluctuation around it

Self-consistency

• … so in reality the gravitational redshift signal may be larger then we measured

Self-consistency

• Handwaving:

• This fits in nicely with the fact that no signal was measured for Mr18 and Mr19 subsamples,

• Which are fainter• Less cD clusters

What have we learned?

• Gravitational redshift can be measured for clusters with massive galaxy, bright at center

• Gravitational redshift signal due to blob of DM around cD

• ~ 6-10kg of DM for 1kg of visible mass

• Consistent with current cosmological models