Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/ftp/meetings/galaxy-morphology/henriksen.ps Äàòà èçìåíåíèÿ: Wed Sep 7 18:19:49 1994 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 17:05:10 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coma

Tidal Triggering of Star Formation and the Butcher­Oemler
Effect
Mark J. Henriksen (University of Alabama and UCLA)
Gene Byrd (University of Alabama)
We have calculated the expected level of star formation which would be induced in a disk
galaxy falling into the potential well of a cluster of galaxies due to: drag force from the
ICM, the radial tidal force from the cluster potential, and the lateral tidal force from the
cluster potential. We evaluated these forces for three different cluster mass distributions:
(1) a 250 kpc core radius King distribution, the canonical virialized cluster model, (2) the
distribution from an isothermal X­ray gas, (3) the distribution from an adiabatic X­ray gas
distribution, which is more centrally peaked than the King model, and (4) that inferred from
gravitational lensing, which is the most centrally peaked. The latter two peaked potentials
show a progressively more significant lateral compression of the galaxy disk from the tidal
field within 250 kpc of the cluster center due to the increase in cluster mass compared to the
King function.
For the centrally peaked potentials, inside of approximately 250 kpc, tidal forces from the
cluster potential on galaxies will be important and will trigger collisions of neutral Hydrogen
clouds which will increase the level of expected star formation in a disk galaxy. Galaxies are
very likely to pass within a radius of approximately 250 kpc as a cluster undergoes collapse
and tidal triggering should show an increase in the blue fraction at this approximate radius
relative to nearby clusters. The lens data (which indicates a centrally concentrated mass
profile) comes primarily from clusters at the epoch (redshift) at which the Butcher Oemler
effect is observed. Therefore, the lensing potential may be a more realistic potential for
the central region of a cluster at this epoch. Compared to nearby clusters with virialized
gas distributions, a cluster undergoing initial gravitational collapse is likely to have a lower
gas density. Studies of cluster evolution in the X­ray indicate that there may be some
increase in the luminosity of clusters between the epoch of the Butcher Oemler effect and
the present. Therefore, during collpase, the importance of ram­pressure will be reduced
for an infalling galaxy compared to a galaxy in a virialized cluster. For these reasons, tidal
triggering is more generally applicable to star formation in a cluster undergoing gravitational
1

Henriksen & Byrd Tidal Triggering of Star Formation and the Butcher­Oemler Effect
collapse than ram­pressure. If ram­pressure were the primary triggering mechanism, then
correlations of star formation with the X­ray luminosity should be apparent at some level in
all of the clusters showing the Butcher Oemler effect (BOE). However, no clear correlation
is seen in the available data. We interpret this as due to the enhanced importance of tidal
triggering and the decreased importance of ram­ pressure in these clusters.
Presented at Quantifying Galaxy Morphology at High Redshift, a workshop held at
the Space Telescope Science Institute, Baltimore MD, April 27--29 1994
1 Cluster Mass Models
Cluster mass profiles in the central region are calculated: two from the X­ray gas density
and temperature distributions (isothermal and adiabatic), one from gravitational lensing
constraints, and the standard King model.
TABLE 1: Normalized Cluster Mass Distribution from 4 Distributions
Radius (kpc) King Model X­ray X­ray Lensing
mass unit is 10 13 M fi
50 0.07 0.12 0.32 2.1
100 0.5 0.83 2.2 3.9
150 1.1 2.4 5.6 10.5
200 3.3 4.7 9.8 13.6
250 5.6 7.5 13.7 16.2
280 7.8 10.4 15.8 17.4
350 12.3 19.5 19.6 20.0
500 24. 24. 24. 24.
The mass distributions in Table 1 should encompass the range found in clusters and are
normalized so that the mass inside of 500 kpc is the same for each distribution.
2 Lateral Tidal Force
Table 2 contains the ratio of the lateral acceleration to the internal centripetal acceleration
of the galaxy for the 4 cluster mass distributions.

Henriksen & Byrd Tidal Triggering of Star Formation and the Butcher­Oemler Effect
TABLE 2: Lateral Acceleration from 4 Mass Distributions
10 \Gamma9 cm sec \Gamma2
Radius (kpc) King Model X­ray (fl = 1) X­ray (fl = 5/3) Lensing
50 0.45 0.77 2.1 13.4
100 0.4 0.66 1.9 3.1
150 0.26 0.57 1.6 2.5
200 0.33 0.47 1.4 1.4
250 0.29 0.38 0.71 0.83
280 0.28 0.38 0.58 0.63
350 0.23 0.36 0.37 0.37
500 0.15 0.15 0.15 0.15
The centrally peaked lensing distribution results in a larger lateral acceleration for a galaxy
passing within 250 kpc of the cluster center than does the other two potentials. For the King
model potential which uses the Coma parameters, the lateral compression is negligible at all
radii.
3 Radial Forces
3.1 Drag Force
Simulations (Thomas and Couchman 1991) show that the central density of the intracluster
medium is approximately 10 times lower 5 Gyr ago (for a cluster formation time of 10 Gyr)
relative to the virialized gas density found in a rich cluster such as Coma. If ram pressure is
not sufficient to remove the nebular components, the galaxy shoud be treated as a hard shell.
The motion of the intracluster medium is then supersonic, laminar flow around the galaxy
since the galaxy velocity should be nearly the free fall velocity (¸2000 km s \Gamma1 ). The drag
force, the pressure acting on the surface area of a spherical galaxy surface, is shown in Table 3.
The drag force will act to accelerate clouds inward and collisions between clouds will induce
shocking. The drag force is relatively weak in the central region, but will dominate radially
outside of approximately 250 kpc. Over a period of time the drag force may accelerate clouds
to supersonic velocities capable of collisionally shocking the most massive clouds to become
unstable to gravitational collapse.

Henriksen & Byrd Tidal Triggering of Star Formation and the Butcher­Oemler Effect
3.2 Radial Tidal Force
This acts to resist the drag force and in the central region is dominant so that the drag force
is effective only outside of the core. The lateral tidal force is a strong triggering mechanism
of star formation through cloud collisions and acts on the entire disk because of the disk's
rotation, in only 1/4 of a rotation period. It is one lateral component relative to the galaxy
center and is the same on both sides of the galaxy.
TABLE 3: Acceleration from 3 Forces: Lensing Potential
Radius (kpc) Tidal Radial Tidal Lateral Drag
10 \Gamma8 cm s \Gamma2
50 20. 5. 0.29
100 2.4 1.2 0.25
150 1.2 0.9 0.21
200 0.4 0.5 0.19
250 0.1 0.31 0.15
350 ­0.07 0.14 0.10
The potential for the cluster may be given by a King model (or isothermal gas) in the outer
region of the cluster and a central region described by the lensing mass distribution or the
adiabatic gas mass distribution. In this case, the radial tidal component will trigger star
formation at approximately 825 kpc (Byrd and Valtonen 1990).
4 Likelihood of Star Formation
In our paper, we show that the scenario where star formation results from cloud collisions
induced by tidal compression, is plausible. The collision induces an isothermal shock front
which traverses the stationary cloud, raising the density above a critical value corresponding
to that required for self­gravitation and collapse. Table 4 contains the downstream post­
shock critical mass. Comparison to the typical neutral hydrogen cloud (280 M fi ) shows that
the postshock clouds should be unstable to gravitational collapse when the galaxy is within
200 ­ 250 kpc of the cluster center.
TABLE 4: Post­shock Critical Mass for Neutral Hydrogen Cloud

Henriksen & Byrd Tidal Triggering of Star Formation and the Butcher­Oemler Effect
Radius (kpc) a(10 \Gamma8 cm s \Gamma2 ) V(km s \Gamma1 ) Mach Number m c
0. ­ 2080. 2080. 5.
50. 30.0 201. 201. 55.
100. 1.2 128. 128. 86.
150. 0.92 70. 70. 157.
200. 0.50 38. 38. 290.
250. 0.31 18. 18. 611.
350. 0.14 0.
5 Discussion, Predictions, and Comparison to Obser­
vations
Simple predictions follow as a disk galaxy falls into the cluster. Tidal triggering predicts that
star formation should appear at some characteristic radius, 800 kpc where radial tidal forces
from a King, or isothermal potential becomes important. If the central distribution of cluster
mass is given by the gravitational lensing constraints, as is well established for clusters in
this redshift range, then lateral tidal forces will be comparable to the radial tidal forces in
the center of the cluster and star formation should increase toward the center, hastening the
exhaustion of the gas supply in the disk. This is suggested in the data shown in figure 5 (in
Butcher and Oemler 1985). The BOE is an overabundance of blue galaxies in clusters in the
redshift range 0.2 ­ 0.5 relative to nearby clusters. In this figure, the data show the BOE at
high statistical significance in the cluster center and out to a radius of approximately 1 Mpc.
The effect is not statistically significant beyond this distance. Qualitatively, this matches
the predictions of tidal stripping if the potential at large radii is given by a King model
and at smaller radii by a peaked potential. It is worth noting that the effect reported for
Coma (Caldwell et al. 1994) is well outside of this region, suggesting a different triggering
mechanism for the star formation episode. The addition of star formation due to lateral
compression should appear as an annulus of star formation in the disk in only 1/4 of a
rotation period. It is important to study these clusters in the X­ray to measure the gas
parameters directly, since strong cluster evolution between the BOE epoch and the present
would mean that late infalling galaxies (such as in Coma) see a different gas distribution than
would those at an early epoch, when most of the galaxies fall in. X­ray studies imply that
there are fewer bright clusters at intermediate redshift (Gioia 1990), suggesting a decrease
in the amount of the intracluster gas which has been shocked up to a high density and

Henriksen & Byrd Tidal Triggering of Star Formation and the Butcher­Oemler Effect
temperature visible in X­rays is found (e.g., ''luminosity evolution''). The hypothesis of
star formation triggered by ram­pressure sweeping of the disk on first infall, will only be
applicable to the galaxies which fall in late and see a dense ICM. It is important to extend
the investigation of the BOE through optical studies of clusters to include clusters with
lower X­ray luminosities in the z = 0.2 ­ 0.5 redshift range. This would clearly separate gas
dependent triggering from tidal triggering. We suggest that the processes discussed here,
primarily the lateral tidal force from a peaked cluster mass distribution and the drag force
of the ICM, may have a more general application to the problem of galaxy evolution in the
redshift range of z = 0.2 ­ 0.5.