Draft version October 31, 2018
Preprint typeset using LATEX style emulateapj v. 11/26/04
THREE DIFFERENT TYPES OF GALAXY ALIGNMENT WITHIN DARK MATTER HALOS
A. Faltenbacher
, Cheng Li
, Shude Mao
, Frank C. van den Bosch
, Xiaohu Yang
, Y.P. Jing
, Anna Pasquali
and H.J. Mo
Draft version October 31, 2018
ABSTRACT
Using a large galaxy group catalogue based on the Sloan Digital Sky Survey Data Release 4 we
measure three different types of intrinsic galaxy alignment within groups: halo alignment between the
orientation of the brightest group galaxies (BGG) and the distribution of its satellite galaxies, radial
alignment between the orientation of a satellite galaxy and the direction towards its BGG, and direct
alignment between the orientation of the BGG and that of its satellites. In agreement with previous
studies we find that satellite galaxies are preferentially located along the major axis. In addition, on
scales r < 0.7Rvir we find that red satellites are preferentially aligned radially with the direction to
the BGG. The orientations of blue satellites, however, are perfectly consistent with being isotropic.
Finally, on scales r < 0.1Rvir, we find a weak but significant indication for direct alignment between
satellites and BGGs. We briefly discuss the implications for weak lensing measurements.
Subject headings: galaxies: clusters: general — galaxies: kinematics and dynamics — surveys
1. INTRODUCTION
A precise assessment of galaxy alignments is im-
portant for two main reasons: it contains information
regarding the impact of environment on the formation
and evolution of galaxies, and it can be an important
source of contamination for weak lensing measurements.
In theory, the large scale-tidal field is expected to
induce large-scale correlations between galaxy spins and
galaxy shapes (e.g., Pen et al. 2000; Croft & Metzler
2000; Heavens et al. 2000; Catelan et al. 2001;
Crittenden et al. 2001; Porciani et al. 2002b; Jing
2002). In addition, the preferred accretion of new
material along filaments tends to cause alignment with
the large scale filamentary structure in which dark
matter halos and galaxies are embedded (e.g., Jing 2002;
Faltenbacher et al. 2005; Bailin & Steinmetz 2005). On
small scales, however, inside virialized dark matter
haloes, any primordial alignment is likely to have been
significantly weakened due to non-linear effects such
as violent relaxation and (impulsive) encounters (e.g.,
Porciani et al. 2002a). On the other hand, tidal forces
from the host halo may also induce new alignments,
similar to the tidal locking mechanism that affects
the Earth-Moon system (e.g., Ciotti & Dutta 1994;
Usami & Fujimoto 1997; Fleck & Kuhn 2003).
Observationally, the search for galaxy alignments has
a rich and often confusing history. To some extent this
owes to the fact that numerous different forms of align-
ment have been discussed in the literature: the align-
ment between neighbouring clusters (Binggeli 1982; West
1989; Plionis 1994), between brightest cluster galaxies
(BCGs) and their parent clusters (Carter & Metcalfe
1980; Binggeli 1982; Struble 1990), between the orienta-
1 Shanghai Astronomical Observatory, Nandan Road 80, Shang-
hai 200030, China
2 University of Manchester, Jodrell Bank Observatory, Maccles-
field, Cheshire SK11 9DL, UK
3 Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany
4 Department of Astronomy, University of Massachusetts,
Amherst MA 01003-9305
tion of satellite galaxies and the orientation of the cluster
(Dekel 1985; Plionis et al. 2003), and between the ori-
entation of satellite galaxies and the orientation of the
BCG (Struble 1990). Obviously, several of these align-
ments are correlated with each other, but independent
measurements are difficult to compare since they are of-
ten based on very different data sets.
With large galaxy redshift surveys, such as the
two-degree Field Galaxy Redshift Survey (2dFGRS,
Colless, M., et al. 2001) and the Sloan Digital Sky Sur-
vey (SDSS, York, D. G., et al. 2000), it has become pos-
sible to investigate alignments using large and homoge-
neous samples. This has resulted in robust detections of
various alignments: Brainerd (2005), Yang et al. (2006)
and Azzaro et al. (2007) all found that satellite galax-
ies are preferentially distributed along the major axes
of their host galaxies, Trujillo et al. (2006) found that
spiral galaxies located on the shells of large voids have
rotation axes that lie preferentially on the void surface,
and Pereira & Kuhn (2005) and Agustsson & Brainerd
(2006b) noticed that satellite galaxies tend to be prefer-
entially oriented towards the galaxy at the center of the
halo.
In this Letter we use a large galaxy group catalogue
constructed from the SDSS to study galaxy alignments
on small scales within dark matter haloes that span a
wide range in masses. The unique aspect of this study
is that we investigate three different types of alignment
using exactly the same data set consisting of over 60000
galaxies. In addition, by using a carefully selected galaxy
group catalogue, we can discriminate between central
galaxies and satellites, and study their mutual alignment.
The latter is particularly important for galaxy-galaxy
lensing, where it can be a significant source of contami-
nation. Finally, exploiting the large number of galaxies
in our sample, we also investigate how the alignment sig-
nal depends on the colors of the galaxies. Throughout we
adopt Ωm = 0.3 and ΩΛ = 0.7 and a Hubble parameter
h = H0/100 km s
−1Mpc−1.
2. DATA & METHODOLOGY
http://arxiv.org/abs/0704.0674v2
2 Galaxy alignment within dark matter halos
satellite
Fig. 1.— Illustration of the three angles θ, φ and ξ, which
are used to test for halo alignment, radial alignment and direct
alignment, respectively. The three angles are not independent: if
ordered by size α ≥ β ≥ γ then α = min[β + γ, 180◦ − β − γ].
We apply our analysis to the SDSS galaxy group cat-
alogue of Yang et al. (2007, in prep.). This cata-
logue is constructed using the halo-based group finder
of Yang et al. (2005) and applied to the New York Uni-
versity Value Added Galaxy Catalog (NYU-VAGC) 5
that is based on the SDSS Data Release Four (DR4;
Adelman-McCarthy et al. 2006). This group finder uses
the general properties of CDM halos (i.e. virial ra-
dius, velocity dispersion, etc.) to determine the mem-
berships of groups (cf. Weinmann et al. 2006). In this
study we only use those groups with redshifts in the
range 0.01 ≤ z ≤ 0.2 and with halo masses between
5 × 1012 h−1M⊙ and 5 × 10
14 h−1M⊙. In addition, we
only focus on group members with 0.1M
−5 logh ≤ −19.
Throughout this paper all magnitudes are k+e corrected
to z = 0.1 following Blanton et al. (2003). Using the
method of Li et al. (2006) we split our galaxies in three
color bins. In short, we divide the full NYU-VAGC sam-
ple in 282 subsamples according to the r-band luminosity,
and fit the 0.1(g−r) color distribution for each subsample
with a double-Gaussian. Galaxies in between the centers
of the two Gaussians are classified as ‘green’, while those
with higher and lower values for the 0.1(g − r) color are
classified as ‘red’ and ‘blue’, respectively. The final sam-
ple, on which our analysis is based, consists of 18576
groups with a total of 60724 galaxies, of which 29780 are
red, 20604 are green, and 10340 are blue.
In what follows, we use these groups to examine (i)
halo alignment between the orientation of the brightest
group galaxies (BGG) and the distribution of its satel-
lite galaxies, (ii) radial alignment between the orientation
of a satellite galaxy and the direction towards its BGG,
and (iii) direct alignment between the orientation of the
BGG and that of its satellites. In particular, we define
the angles θ, φ and ξ as illustrated in Fig. 1, and in-
vestigate whether their distributions are consistent with
isotropy, or whether they indicate a preferred alignment.
Following Brainerd (2005) and Yang et al. (2006), the
orientation of each galaxy is defined by the major axis
position angle (PA) of its 25-magn arcsec−2 isophote in
the r-band.
For each satellite galaxy we compute its projected dis-
tance, r, to the BGG, normalized by the virial radius,
Rvir, of its group (as derived from the group mass). For
each of 5 radial bins, equally spaced in r/Rvir, we then
compute 〈θ〉, 〈φ〉 and 〈ξ〉, where 〈.〉 indicates the average
over all BGG-satellite pairs in a given radial bin. Next
we construct 100 random samples in which the positions
5 http://wassup.physics.nyu.edu/vagc/
Fig. 2.— Mean angle, θ, between the PA of the BGG and the line
connecting the BGG with a satellite galaxy, as function of r/Rvir.
Different line styles indicate (sub)samples determined according to
the satellites’ color. The shaded areas mark the parameter space
between the 16th and 84th percentiles of the distributions obtained
from the 100 random samples. A signal outside this shaded region
means that it is inconsistent with no alignment (i.e., with isotropy)
at more than 68 percent confidence.
of the galaxies are kept fixed, but their PAs are random-
ized. For each of these random samples we compute 〈θ〉,
〈φ〉 and 〈ξ〉 as function of r/Rvir, which we use to com-
pute the significance of any detected alignment signal.
3. RESULTS
3.1. Halo alignment
Fig. 2 shows the results thus obtained for the angle θ
between the orientation of the BGG and the line con-
necting the BGG with the satellite galaxy. Clearly, for
all four samples shown (all, red, green and blue, where
the color refers to that of the satellite galaxy, not that of
the BGG) we obtain 〈θ〉 < 45◦ at all 5 radial bins and at
high significance6. This indicates that satellite galaxies
are preferentially distributed along the major axis of the
BGG, in good agreement with the findings of Brainerd
(2005), Yang et al. (2006) and Azzaro et al. (2007), but
opposite to the old Holmberg (1969) effect. Note that
there is a clear indication that the distribution of red
satellites is more strongly aligned with the orientation
of the BGG than that of blue satellites, again in good
agreement with previous studies (cf. Yang et al. 2006;
Azzaro et al. 2007)
3.2. Radial alignment
Hawley & Peebles (1975) were the first to report a
possible detection of radial alignment in the Coma
cluster, which has subsequently been confirmed by
Thompson (1976) and Djorgovski (1983). However,
in a more systematic study based on the 2dFGRS,
Bernstein & Norberg (2002) were unable to detect any
significant radial alignment of satellite galaxies around
isolated host galaxies. On the other hand, using a very
similar selection of hosts and satellites, but applied to
the SDSS, Agustsson & Brainerd (2006b) found signifi-
cant evidence for radial alignment on scales. 70 h−1kpc.
In addition, Pereira & Kuhn (2005) found a statistically
robust tendency toward radial alignment in a large sam-
ple of 85 X-ray selected clusters.
Fig. 3 shows the results obtained from our group cat-
alogue. It shows, as function of r/Rvir, the mean angle
6 More than 99 percent, except for the 0.3Rvir bin for the blue
and the 0.9Rvir bin for the green satellites.
Faltenbacher et al. 3
Fig. 3.— Same as Fig. 2, but for the angle φ (see Fig. 1).
φ between the PA of the satellite and the line connect-
ing the satellite with its BGG. As in Fig. 2 results are
shown for all four different samples, together with the
16th and 84th percentiles obtained from the random sam-
ples. There is a clear and very significant indication that
the major axes of red satellites point towards the BGG
(i.e., 〈φ〉 < 45◦), at least for projected radii r . 0.7Rvir.
The signal for the green satellites is significantly weaker,
but still reveals a preference for radial alignment on small
scales: in fact, for the 3 radial bins with r ≤ 0.5Rvir the
null-hypothesis of no radial alignment can be rejected at
more than 95 percent confidence level. In contrast, for
the blue galaxies the data is perfectly consistent with
no radial alignment. Since the 2dFGRS is more biased
towards blue galaxies than the SDSS, this may at least
partially explain why Bernstein & Norberg (2002) were
unable to detect significant radial alignment.
3.3. Direct alignment
The search for direct alignment has mainly been
restricted to galaxy clusters (e.g., Plionis et al. 2003;
Strazzullo et al. 2005; Torlina et al. 2007), mostly result-
ing in no or very weak indications for alignment be-
tween the orientations of BCG and satellite galaxies.
Agustsson & Brainerd (2006b) extended the search for
direct alignment to a samples of 4289 host-satellites pairs
selected from the SDSS DR4, finding a weak but signif-
icant signal on scales . 35 h−1kpc. On larger scales,
however, no significant alignment was found, in agree-
ment with Mandelbaum et al. (2006).
Fig. 4 displays our results for the direct alignment,
based on the angle ξ between the orientations of a
satellite galaxy and that of its BGG. With the ex-
ception of the central bin (r/Rvir = 0.1) the null-
hypothesis of a random distribution cannot be rejected
at more than 1σ confidence level. Our study, based
on over 40000 BGG-satellite pairs, therefore agrees with
Agustsson & Brainerd (2006b) that there is a weak indi-
cation for direct alignment, but only on relatively small
scales: for the average group mass in our sample, M =
3.6×1013 h−1M⊙, a radius of r = 0.1Rvir corresponds to
70 h−1kpc. However, at least for the red satellites there
is a systematic trend towards angles < 45◦ which may
be caused by the group tidal field (cf. Lee et al. 2005).
3.4. Dependence on selection criteria
The sample used above is based on galaxies with
−5 log h ≤ −19. Typically, including fainter galax-
ies improves the number statistics but not necessarily
the signal-to-noise since the PAs of fainter galaxies carry
Fig. 4.— Same as Fig. 2, but for the angle ξ (see Fig. 1).
larger errors. To test the sensitivity of our results, we
repeated the above analysis using magnitude limits of
−17, −18, and −20. This resulted in alignment signals
that were only marginally different. We have also tested
the sentitivity of our results to the range of group masses
considered. Changing the lower limit to 1012 h−1M⊙ or
1013 h−1M⊙, or imposing no upper mass limit, all yields
very similar alignment signals. These tests assure that
our selection criteria lead to representative results.
4. DISCUSSION
The origin of the halo alignment described in § 3.1
has been studied by Agustsson & Brainerd (2006a) and
Kang et al. (2007) using semi-analytical models of galaxy
formation combined with large N -body simulations.
Since dark matter haloes are in general flattened, and
satellite galaxies are a reasonably fair tracer of the dark
matter mass distribution, 〈θ〉 will be smaller than 45◦ as
long as the BGG is aligned with its dark matter halo.
In particular, Kang et al. (2007) were able to accurately
reproduce the data of Yang et al. (2006) under the as-
sumption that the minor axis of the BGG is perfectly
aligned with the spin axis of its dark matter halo.
Kang et al. (2007) also showed that the color depen-
dence of the halo alignment has a natural explanation in
the framework of hierarchical structure formation: red
satellites are typically associated with subhaloes that
were more massive at their time of accretion. Since the
orientation of a halo is correlated with the direction along
which it accreted most of its matter (e.g., Wang et al.
2005; Libeskind et al. 2005), red satellites are a more ac-
curate tracer of the halo orientation than blue satellites.
The origin of the radial alignment is less clear. One
possibility is that it reflects a left-over from large-scale
alignments introduced by the large scale tidal field and
the preferred accretion of matter along filaments. Such
alignment, however, is unlikely to survive for more than
a few orbits within the halo of the BGG, so that the
observed alignment must be mainly due to the satellite
galaxies that were accreted most recently. Since these
satellites typically reside at relatively large halo-centric
radii, this picture predicts a stronger radial alignment at
larger radii, clearly opposite to what we find.
A more likely explanation, therefore, is that radial
alignment has been created locally by the group tidal
field. As shown by Ciotti & Dutta (1994), the timescale
on which a prolate galaxy can adjust its orientation to
the tidal field of a cluster is much shorter than the Hub-
ble time, but longer than its intrinsic dynamical time.
Consequently, prolate galaxies have a tendency to orient
4 Galaxy alignment within dark matter halos
themselves towards the cluster center. The fact that the
observed signal increases towards the group center sup-
ports this interpretation. In particular, satellites that
were accreted early not only are more likely to be red,
they also are more likely to reside at small group-centric
radii and to have relatively low group-centric velocities
(e.g., Mathews et al. 2004). This will enhance their ten-
dency to align themselves along the gradient in the clus-
ter’s gravitational potential, and they may well be the
major contributors to the pronounced signal on small
scales. In the case of disk galaxies, the conservation of
intrinsic angular momentum prevents the disk from re-
adjusting to the tidal field, which may explain why blue
satellites show no sign of radial alignment. Finally, the
tidal field of the parent halo also results in tidal strip-
ping, and the tidal debris may influence the inferred ori-
entation of the satellite galaxy (cf. Johnston et al. 2001;
Fardal et al. 2006). Detailed studies are required to in-
vestigate the interplay between intrinsic satellite orien-
tations and the groups tidal field.
In order to understand the direct alignment results,
first realize that the angles θ, φ and ξ are not indepen-
dent (see Fig. 1). However, the equation given in the cap-
tion is only applicable for single cases not for the mean
angles. Our results indicate that satellite galaxies are
more likely to be aligned ‘radially’ with the direction to-
wards the BGG, than ‘directly’ with the orientation of
the BGG. Since there is no clear theoretical prediction
for direct alignment, at least not one that can survive
for several orbital periods in a dark matter halo, while
radial alignment can be understood as originating from
the halo’s tidal field, we consider the relative weakness
of direct alignment to be consistent with expectations.
In recent years galaxy-galaxy (GG) lensing has
emerged as a primary tool for constraining the masses of
dark matter halos around galaxies (e.g., Brainerd 2004).
If satellite galaxies are falsely identified as sources lensed
by the BGG, which is likely to happen in the absence of
redshift information, the radial alignment detected here
will dilute the tangential GG lensing signal induced by
the dark matter halo associated with the BGG, thus re-
sulting in an underestimate of the halo mass. In agree-
ment with Agustsson & Brainerd (2006b), our findings
therefore emphasize the importance of an accurate rejec-
tion of satellite galaxies to achieve precision constraints
on dark matter halo masses from GG lensing measure-
ments. Similarly, the weak but significant detection of
direct alignment may contaminate the cosmic shear mea-
surements. Since we only detected a weak signal on small
scales, one can easily avoid this contamination by sim-
ply removing or down-weighting close pairs of galaxies in
projection (King & Schneider 2002; Heymans & Heavens
2003).
ACKNOWLEDGMENTS
This work is supported by NSFC (10533030,
0742961001, 0742951001) and the Knowledge Innova-
tion Program of the Chinese Academy of Sciences, grant
KJCX2-YW-T05. AF and CL are supported by the
Joint Program in Astrophysical Cosmology of the Max
Planck Institute for Astrophysics and the Shanghai As-
trophysical Observatory. YPJ is partially supported by
Shanghai Key Projects in Basic research (04JC14079 and
05XD14019).
REFERENCES
Adelman-McCarthy, J. K., et al. 2006, ApJS, 162, 38
Agustsson, I. & Brainerd, T. G. 2006a, ApJ, 650, 550
—. 2006b, ApJ, 644, L25
Azzaro, M., Patiri, S. G., Prada, F., & Zentner, A. R. 2007,
MNRAS, 376, L43
Bailin, J. & Steinmetz, M. 2005, ApJ, 627, 647
Bernstein, G. M. & Norberg, P. 2002, AJ, 124, 733
Binggeli, B. 1982, A&A, 107, 338
Blanton, M. R., et al. 2003, ApJ, 592, 819
Brainerd, T. G. 2004, in AIP Conf. Proc. 743: The New Cosmology:
Conference on Strings and Cosmology, ed. R. E. Allen, D. V.
Nanopoulos, & C. N. Pope, 129–156
Brainerd, T. G. 2005, ApJ, 628, L101
Carter, D. & Metcalfe, N. 1980, MNRAS, 191, 325
Catelan, P., Kamionkowski, M., & Blandford, R. D. 2001, MNRAS,
320, L7
Ciotti, L. & Dutta, S. N. 1994, MNRAS, 270, 390
Colless, M., et al. 2001, MNRAS, 328, 1039
Crittenden, R. G., Natarajan, P., Pen, U.-L., & Theuns, T. 2001,
ApJ, 559, 552
Croft, R. A. C. & Metzler, C. A. 2000, ApJ, 545, 561
Dekel, A. 1985, ApJ, 298, 461
Djorgovski, S. 1983, ApJ, 274, L7
Faltenbacher, A., Allgood, B., Gottlöber, S., Yepes, G., & Hoffman,
Y. 2005, MNRAS, 362, 1099
Fardal, M. A., Babul, A., Geehan, J. J., & Guhathakurta, P. 2006,
MNRAS, 366, 1012
Fleck, J.-J. & Kuhn, J. R. 2003, ApJ, 592, 147
Hawley, D. L. & Peebles, P. J. E. 1975, AJ, 80, 477
Heavens, A., Refregier, A., & Heymans, C. 2000, MNRAS, 319, 649
Heymans, C. & Heavens, A. 2003, MNRAS, 339, 711
Holmberg, E. 1969, Arkiv for Astronomi, 5, 305
Jing, Y. P. 2002, MNRAS, 335, L89
Johnston, K. V., Sackett, P. D., & Bullock, J. S. 2001, ApJ, 557,
Kang, X., van den Bosch, F. C., Yang, X., Mao, S., Mo, H. J., Li,
C., & Jing, Y. P. 2007, MNRAS, in press (astro-ph/0701130)
King, L. & Schneider, P. 2002, A&A, 396, 411
Lee, J., Kang, X., & Jing, Y. P. 2005, ApJ, 629, L5
Li, C., Kauffmann, G., Jing, Y. P., White, S. D. M., Börner, G., &
Cheng, F. Z. 2006, MNRAS, 368, 21
Libeskind, N. I., Frenk, C. S., Cole, S., Helly, J. C., Jenkins, A.,
Navarro, J. F., & Power, C. 2005, MNRAS, 363, 146
Mandelbaum, R., Hirata, C. M., Ishak, M., Seljak, U., &
Brinkmann, J. 2006, MNRAS, 367, 611
Mathews, W. G., Chomiuk, L., Brighenti, F., & Buote, D. A. 2004,
ApJ, 616, 745
Pen, U.-L., Lee, J., & Seljak, U. 2000, ApJ, 543, L107
Pereira, M. J. & Kuhn, J. R. 2005, ApJ, 627, L21
Plionis, M. 1994, ApJS, 95, 401
Plionis, M., Benoist, C., Maurogordato, S., Ferrari, C., & Basilakos,
S. 2003, ApJ, 594, 144
Porciani, C., Dekel, A., & Hoffman, Y. 2002a, MNRAS, 332, 325
—. 2002b, MNRAS, 332, 339
Strazzullo, V., Paolillo, M., Longo, G., Puddu, E., Djorgovski,
S. G., De Carvalho, R. R., & Gal, R. R. 2005, MNRAS, 359,
Struble, M. F. 1990, AJ, 99, 743
Thompson, L. A. 1976, ApJ, 209, 22
Torlina, L., De Propris, R., & West, M. J. 2007, ArXiv Astrophysics
e-prints
Trujillo, I., Carretero, C., & Patiri, S. G. 2006, ApJ, 640, L111
Usami, M. & Fujimoto, M. 1997, ApJ, 487, 489
Wang, H. Y., Jing, Y. P., Mao, S., & Kang, X. 2005, MNRAS, 364,
Weinmann, S. M., van den Bosch, F. C., Yang, X., & Mo, H. J.
2006, MNRAS, 366, 2
West, M. J. 1989, ApJ, 344, 535
Yang, X., Mo, H. J., van den Bosch, F. C., & Jing, Y. P. 2005,
MNRAS, 356, 1293
http://arxiv.org/abs/astro-ph/0701130
Faltenbacher et al. 5
Yang, X., van den Bosch, F. C., Mo, H. J., Mao, S., Kang, X.,
Weinmann, S. M., Guo, Y., & Jing, Y. P. 2006, MNRAS, 369,
York, D. G., et al. 2000, AJ, 120, 1579

  Using a large galaxy group catalogue based on the Sloan Digital Sky Survey
Data Release 4 we measure three different types of intrinsic galaxy alignment
within groups: halo alignment between the orientation of the brightest group
galaxies (BGG) and the distribution of its satellite galaxies, radial alignment
between the orientation of a satellite galaxy and the direction towards its
BGG, and direct alignment between the orientation of the BGG and that of its
satellites. In agreement with previous studies we find that satellite galaxies
are preferentially located along the major axis. In addition, on scales r < 0.7
Rvir we find that red satellites are preferentially aligned radially with the
direction to the BGG. The orientations of blue satellites, however, are
perfectly consistent with being isotropic. Finally, on scales r < 0.1 \Rvir, we
find a weak but significant indication for direct alignment between satellites
and BGGs. We briefly discuss the implications for weak lensing measurements.

Draft version October 31, 2018
Preprint typeset using LATEX style emulateapj v. 11/26/04
THREE DIFFERENT TYPES OF GALAXY ALIGNMENT WITHIN DARK MATTER HALOS
A. Faltenbacher
, Cheng Li
, Shude Mao
, Frank C. van den Bosch
, Xiaohu Yang
, Y.P. Jing
, Anna Pasquali
and H.J. Mo
Draft version October 31, 2018
ABSTRACT
Using a large galaxy group catalogue based on the Sloan Digital Sky Survey Data Release 4 we
measure three different types of intrinsic galaxy alignment within groups: halo alignment between the
orientation of the brightest group galaxies (BGG) and the distribution of its satellite galaxies, radial
alignment between the orientation of a satellite galaxy and the direction towards its BGG, and direct
alignment between the orientation of the BGG and that of its satellites. In agreement with previous
studies we find that satellite galaxies are preferentially located along the major axis. In addition, on
scales r < 0.7Rvir we find that red satellites are preferentially aligned radially with the direction to
the BGG. The orientations of blue satellites, however, are perfectly consistent with being isotropic.
Finally, on scales r < 0.1Rvir, we find a weak but significant indication for direct alignment between
satellites and BGGs. We briefly discuss the implications for weak lensing measurements.
Subject headings: galaxies: clusters: general — galaxies: kinematics and dynamics — surveys
1. INTRODUCTION
A precise assessment of galaxy alignments is im-
portant for two main reasons: it contains information
regarding the impact of environment on the formation
and evolution of galaxies, and it can be an important
source of contamination for weak lensing measurements.
In theory, the large scale-tidal field is expected to
induce large-scale correlations between galaxy spins and
galaxy shapes (e.g., Pen et al. 2000; Croft & Metzler
2000; Heavens et al. 2000; Catelan et al. 2001;
Crittenden et al. 2001; Porciani et al. 2002b; Jing
2002). In addition, the preferred accretion of new
material along filaments tends to cause alignment with
the large scale filamentary structure in which dark
matter halos and galaxies are embedded (e.g., Jing 2002;
Faltenbacher et al. 2005; Bailin & Steinmetz 2005). On
small scales, however, inside virialized dark matter
haloes, any primordial alignment is likely to have been
significantly weakened due to non-linear effects such
as violent relaxation and (impulsive) encounters (e.g.,
Porciani et al. 2002a). On the other hand, tidal forces
from the host halo may also induce new alignments,
similar to the tidal locking mechanism that affects
the Earth-Moon system (e.g., Ciotti & Dutta 1994;
Usami & Fujimoto 1997; Fleck & Kuhn 2003).
Observationally, the search for galaxy alignments has
a rich and often confusing history. To some extent this
owes to the fact that numerous different forms of align-
ment have been discussed in the literature: the align-
ment between neighbouring clusters (Binggeli 1982; West
1989; Plionis 1994), between brightest cluster galaxies
(BCGs) and their parent clusters (Carter & Metcalfe
1980; Binggeli 1982; Struble 1990), between the orienta-
1 Shanghai Astronomical Observatory, Nandan Road 80, Shang-
hai 200030, China
2 University of Manchester, Jodrell Bank Observatory, Maccles-
field, Cheshire SK11 9DL, UK
3 Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany
4 Department of Astronomy, University of Massachusetts,
Amherst MA 01003-9305
tion of satellite galaxies and the orientation of the cluster
(Dekel 1985; Plionis et al. 2003), and between the ori-
entation of satellite galaxies and the orientation of the
BCG (Struble 1990). Obviously, several of these align-
ments are correlated with each other, but independent
measurements are difficult to compare since they are of-
ten based on very different data sets.
With large galaxy redshift surveys, such as the
two-degree Field Galaxy Redshift Survey (2dFGRS,
Colless, M., et al. 2001) and the Sloan Digital Sky Sur-
vey (SDSS, York, D. G., et al. 2000), it has become pos-
sible to investigate alignments using large and homoge-
neous samples. This has resulted in robust detections of
various alignments: Brainerd (2005), Yang et al. (2006)
and Azzaro et al. (2007) all found that satellite galax-
ies are preferentially distributed along the major axes
of their host galaxies, Trujillo et al. (2006) found that
spiral galaxies located on the shells of large voids have
rotation axes that lie preferentially on the void surface,
and Pereira & Kuhn (2005) and Agustsson & Brainerd
(2006b) noticed that satellite galaxies tend to be prefer-
entially oriented towards the galaxy at the center of the
halo.
In this Letter we use a large galaxy group catalogue
constructed from the SDSS to study galaxy alignments
on small scales within dark matter haloes that span a
wide range in masses. The unique aspect of this study
is that we investigate three different types of alignment
using exactly the same data set consisting of over 60000
galaxies. In addition, by using a carefully selected galaxy
group catalogue, we can discriminate between central
galaxies and satellites, and study their mutual alignment.
The latter is particularly important for galaxy-galaxy
lensing, where it can be a significant source of contami-
nation. Finally, exploiting the large number of galaxies
in our sample, we also investigate how the alignment sig-
nal depends on the colors of the galaxies. Throughout we
adopt Ωm = 0.3 and ΩΛ = 0.7 and a Hubble parameter
h = H0/100 km s
−1Mpc−1.
2. DATA & METHODOLOGY
http://arxiv.org/abs/0704.0674v2
2 Galaxy alignment within dark matter halos
satellite
Fig. 1.— Illustration of the three angles θ, φ and ξ, which
are used to test for halo alignment, radial alignment and direct
alignment, respectively. The three angles are not independent: if
ordered by size α ≥ β ≥ γ then α = min[β + γ, 180◦ − β − γ].
We apply our analysis to the SDSS galaxy group cat-
alogue of Yang et al. (2007, in prep.). This cata-
logue is constructed using the halo-based group finder
of Yang et al. (2005) and applied to the New York Uni-
versity Value Added Galaxy Catalog (NYU-VAGC) 5
that is based on the SDSS Data Release Four (DR4;
Adelman-McCarthy et al. 2006). This group finder uses
the general properties of CDM halos (i.e. virial ra-
dius, velocity dispersion, etc.) to determine the mem-
berships of groups (cf. Weinmann et al. 2006). In this
study we only use those groups with redshifts in the
range 0.01 ≤ z ≤ 0.2 and with halo masses between
5 × 1012 h−1M⊙ and 5 × 10
14 h−1M⊙. In addition, we
only focus on group members with 0.1M
−5 logh ≤ −19.
Throughout this paper all magnitudes are k+e corrected
to z = 0.1 following Blanton et al. (2003). Using the
method of Li et al. (2006) we split our galaxies in three
color bins. In short, we divide the full NYU-VAGC sam-
ple in 282 subsamples according to the r-band luminosity,
and fit the 0.1(g−r) color distribution for each subsample
with a double-Gaussian. Galaxies in between the centers
of the two Gaussians are classified as ‘green’, while those
with higher and lower values for the 0.1(g − r) color are
classified as ‘red’ and ‘blue’, respectively. The final sam-
ple, on which our analysis is based, consists of 18576
groups with a total of 60724 galaxies, of which 29780 are
red, 20604 are green, and 10340 are blue.
In what follows, we use these groups to examine (i)
halo alignment between the orientation of the brightest
group galaxies (BGG) and the distribution of its satel-
lite galaxies, (ii) radial alignment between the orientation
of a satellite galaxy and the direction towards its BGG,
and (iii) direct alignment between the orientation of the
BGG and that of its satellites. In particular, we define
the angles θ, φ and ξ as illustrated in Fig. 1, and in-
vestigate whether their distributions are consistent with
isotropy, or whether they indicate a preferred alignment.
Following Brainerd (2005) and Yang et al. (2006), the
orientation of each galaxy is defined by the major axis
position angle (PA) of its 25-magn arcsec−2 isophote in
the r-band.
For each satellite galaxy we compute its projected dis-
tance, r, to the BGG, normalized by the virial radius,
Rvir, of its group (as derived from the group mass). For
each of 5 radial bins, equally spaced in r/Rvir, we then
compute 〈θ〉, 〈φ〉 and 〈ξ〉, where 〈.〉 indicates the average
over all BGG-satellite pairs in a given radial bin. Next
we construct 100 random samples in which the positions
5 http://wassup.physics.nyu.edu/vagc/
Fig. 2.— Mean angle, θ, between the PA of the BGG and the line
connecting the BGG with a satellite galaxy, as function of r/Rvir.
Different line styles indicate (sub)samples determined according to
the satellites’ color. The shaded areas mark the parameter space
between the 16th and 84th percentiles of the distributions obtained
from the 100 random samples. A signal outside this shaded region
means that it is inconsistent with no alignment (i.e., with isotropy)
at more than 68 percent confidence.
of the galaxies are kept fixed, but their PAs are random-
ized. For each of these random samples we compute 〈θ〉,
〈φ〉 and 〈ξ〉 as function of r/Rvir, which we use to com-
pute the significance of any detected alignment signal.
3. RESULTS
3.1. Halo alignment
Fig. 2 shows the results thus obtained for the angle θ
between the orientation of the BGG and the line con-
necting the BGG with the satellite galaxy. Clearly, for
all four samples shown (all, red, green and blue, where
the color refers to that of the satellite galaxy, not that of
the BGG) we obtain 〈θ〉 < 45◦ at all 5 radial bins and at
high significance6. This indicates that satellite galaxies
are preferentially distributed along the major axis of the
BGG, in good agreement with the findings of Brainerd
(2005), Yang et al. (2006) and Azzaro et al. (2007), but
opposite to the old Holmberg (1969) effect. Note that
there is a clear indication that the distribution of red
satellites is more strongly aligned with the orientation
of the BGG than that of blue satellites, again in good
agreement with previous studies (cf. Yang et al. 2006;
Azzaro et al. 2007)
3.2. Radial alignment
Hawley & Peebles (1975) were the first to report a
possible detection of radial alignment in the Coma
cluster, which has subsequently been confirmed by
Thompson (1976) and Djorgovski (1983). However,
in a more systematic study based on the 2dFGRS,
Bernstein & Norberg (2002) were unable to detect any
significant radial alignment of satellite galaxies around
isolated host galaxies. On the other hand, using a very
similar selection of hosts and satellites, but applied to
the SDSS, Agustsson & Brainerd (2006b) found signifi-
cant evidence for radial alignment on scales. 70 h−1kpc.
In addition, Pereira & Kuhn (2005) found a statistically
robust tendency toward radial alignment in a large sam-
ple of 85 X-ray selected clusters.
Fig. 3 shows the results obtained from our group cat-
alogue. It shows, as function of r/Rvir, the mean angle
6 More than 99 percent, except for the 0.3Rvir bin for the blue
and the 0.9Rvir bin for the green satellites.
Faltenbacher et al. 3
Fig. 3.— Same as Fig. 2, but for the angle φ (see Fig. 1).
φ between the PA of the satellite and the line connect-
ing the satellite with its BGG. As in Fig. 2 results are
shown for all four different samples, together with the
16th and 84th percentiles obtained from the random sam-
ples. There is a clear and very significant indication that
the major axes of red satellites point towards the BGG
(i.e., 〈φ〉 < 45◦), at least for projected radii r . 0.7Rvir.
The signal for the green satellites is significantly weaker,
but still reveals a preference for radial alignment on small
scales: in fact, for the 3 radial bins with r ≤ 0.5Rvir the
null-hypothesis of no radial alignment can be rejected at
more than 95 percent confidence level. In contrast, for
the blue galaxies the data is perfectly consistent with
no radial alignment. Since the 2dFGRS is more biased
towards blue galaxies than the SDSS, this may at least
partially explain why Bernstein & Norberg (2002) were
unable to detect significant radial alignment.
3.3. Direct alignment
The search for direct alignment has mainly been
restricted to galaxy clusters (e.g., Plionis et al. 2003;
Strazzullo et al. 2005; Torlina et al. 2007), mostly result-
ing in no or very weak indications for alignment be-
tween the orientations of BCG and satellite galaxies.
Agustsson & Brainerd (2006b) extended the search for
direct alignment to a samples of 4289 host-satellites pairs
selected from the SDSS DR4, finding a weak but signif-
icant signal on scales . 35 h−1kpc. On larger scales,
however, no significant alignment was found, in agree-
ment with Mandelbaum et al. (2006).
Fig. 4 displays our results for the direct alignment,
based on the angle ξ between the orientations of a
satellite galaxy and that of its BGG. With the ex-
ception of the central bin (r/Rvir = 0.1) the null-
hypothesis of a random distribution cannot be rejected
at more than 1σ confidence level. Our study, based
on over 40000 BGG-satellite pairs, therefore agrees with
Agustsson & Brainerd (2006b) that there is a weak indi-
cation for direct alignment, but only on relatively small
scales: for the average group mass in our sample, M =
3.6×1013 h−1M⊙, a radius of r = 0.1Rvir corresponds to
70 h−1kpc. However, at least for the red satellites there
is a systematic trend towards angles < 45◦ which may
be caused by the group tidal field (cf. Lee et al. 2005).
3.4. Dependence on selection criteria
The sample used above is based on galaxies with
−5 log h ≤ −19. Typically, including fainter galax-
ies improves the number statistics but not necessarily
the signal-to-noise since the PAs of fainter galaxies carry
Fig. 4.— Same as Fig. 2, but for the angle ξ (see Fig. 1).
larger errors. To test the sensitivity of our results, we
repeated the above analysis using magnitude limits of
−17, −18, and −20. This resulted in alignment signals
that were only marginally different. We have also tested
the sentitivity of our results to the range of group masses
considered. Changing the lower limit to 1012 h−1M⊙ or
1013 h−1M⊙, or imposing no upper mass limit, all yields
very similar alignment signals. These tests assure that
our selection criteria lead to representative results.
4. DISCUSSION
The origin of the halo alignment described in § 3.1
has been studied by Agustsson & Brainerd (2006a) and
Kang et al. (2007) using semi-analytical models of galaxy
formation combined with large N -body simulations.
Since dark matter haloes are in general flattened, and
satellite galaxies are a reasonably fair tracer of the dark
matter mass distribution, 〈θ〉 will be smaller than 45◦ as
long as the BGG is aligned with its dark matter halo.
In particular, Kang et al. (2007) were able to accurately
reproduce the data of Yang et al. (2006) under the as-
sumption that the minor axis of the BGG is perfectly
aligned with the spin axis of its dark matter halo.
Kang et al. (2007) also showed that the color depen-
dence of the halo alignment has a natural explanation in
the framework of hierarchical structure formation: red
satellites are typically associated with subhaloes that
were more massive at their time of accretion. Since the
orientation of a halo is correlated with the direction along
which it accreted most of its matter (e.g., Wang et al.
2005; Libeskind et al. 2005), red satellites are a more ac-
curate tracer of the halo orientation than blue satellites.
The origin of the radial alignment is less clear. One
possibility is that it reflects a left-over from large-scale
alignments introduced by the large scale tidal field and
the preferred accretion of matter along filaments. Such
alignment, however, is unlikely to survive for more than
a few orbits within the halo of the BGG, so that the
observed alignment must be mainly due to the satellite
galaxies that were accreted most recently. Since these
satellites typically reside at relatively large halo-centric
radii, this picture predicts a stronger radial alignment at
larger radii, clearly opposite to what we find.
A more likely explanation, therefore, is that radial
alignment has been created locally by the group tidal
field. As shown by Ciotti & Dutta (1994), the timescale
on which a prolate galaxy can adjust its orientation to
the tidal field of a cluster is much shorter than the Hub-
ble time, but longer than its intrinsic dynamical time.
Consequently, prolate galaxies have a tendency to orient
4 Galaxy alignment within dark matter halos
themselves towards the cluster center. The fact that the
observed signal increases towards the group center sup-
ports this interpretation. In particular, satellites that
were accreted early not only are more likely to be red,
they also are more likely to reside at small group-centric
radii and to have relatively low group-centric velocities
(e.g., Mathews et al. 2004). This will enhance their ten-
dency to align themselves along the gradient in the clus-
ter’s gravitational potential, and they may well be the
major contributors to the pronounced signal on small
scales. In the case of disk galaxies, the conservation of
intrinsic angular momentum prevents the disk from re-
adjusting to the tidal field, which may explain why blue
satellites show no sign of radial alignment. Finally, the
tidal field of the parent halo also results in tidal strip-
ping, and the tidal debris may influence the inferred ori-
entation of the satellite galaxy (cf. Johnston et al. 2001;
Fardal et al. 2006). Detailed studies are required to in-
vestigate the interplay between intrinsic satellite orien-
tations and the groups tidal field.
In order to understand the direct alignment results,
first realize that the angles θ, φ and ξ are not indepen-
dent (see Fig. 1). However, the equation given in the cap-
tion is only applicable for single cases not for the mean
angles. Our results indicate that satellite galaxies are
more likely to be aligned ‘radially’ with the direction to-
wards the BGG, than ‘directly’ with the orientation of
the BGG. Since there is no clear theoretical prediction
for direct alignment, at least not one that can survive
for several orbital periods in a dark matter halo, while
radial alignment can be understood as originating from
the halo’s tidal field, we consider the relative weakness
of direct alignment to be consistent with expectations.
In recent years galaxy-galaxy (GG) lensing has
emerged as a primary tool for constraining the masses of
dark matter halos around galaxies (e.g., Brainerd 2004).
If satellite galaxies are falsely identified as sources lensed
by the BGG, which is likely to happen in the absence of
redshift information, the radial alignment detected here
will dilute the tangential GG lensing signal induced by
the dark matter halo associated with the BGG, thus re-
sulting in an underestimate of the halo mass. In agree-
ment with Agustsson & Brainerd (2006b), our findings
therefore emphasize the importance of an accurate rejec-
tion of satellite galaxies to achieve precision constraints
on dark matter halo masses from GG lensing measure-
ments. Similarly, the weak but significant detection of
direct alignment may contaminate the cosmic shear mea-
surements. Since we only detected a weak signal on small
scales, one can easily avoid this contamination by sim-
ply removing or down-weighting close pairs of galaxies in
projection (King & Schneider 2002; Heymans & Heavens
2003).
ACKNOWLEDGMENTS
This work is supported by NSFC (10533030,
0742961001, 0742951001) and the Knowledge Innova-
tion Program of the Chinese Academy of Sciences, grant
KJCX2-YW-T05. AF and CL are supported by the
Joint Program in Astrophysical Cosmology of the Max
Planck Institute for Astrophysics and the Shanghai As-
trophysical Observatory. YPJ is partially supported by
Shanghai Key Projects in Basic research (04JC14079 and
05XD14019).
REFERENCES
Adelman-McCarthy, J. K., et al. 2006, ApJS, 162, 38
Agustsson, I. & Brainerd, T. G. 2006a, ApJ, 650, 550
—. 2006b, ApJ, 644, L25
Azzaro, M., Patiri, S. G., Prada, F., & Zentner, A. R. 2007,
MNRAS, 376, L43
Bailin, J. & Steinmetz, M. 2005, ApJ, 627, 647
Bernstein, G. M. & Norberg, P. 2002, AJ, 124, 733
Binggeli, B. 1982, A&A, 107, 338
Blanton, M. R., et al. 2003, ApJ, 592, 819
Brainerd, T. G. 2004, in AIP Conf. Proc. 743: The New Cosmology:
Conference on Strings and Cosmology, ed. R. E. Allen, D. V.
Nanopoulos, & C. N. Pope, 129–156
Brainerd, T. G. 2005, ApJ, 628, L101
Carter, D. & Metcalfe, N. 1980, MNRAS, 191, 325
Catelan, P., Kamionkowski, M., & Blandford, R. D. 2001, MNRAS,
320, L7
Ciotti, L. & Dutta, S. N. 1994, MNRAS, 270, 390
Colless, M., et al. 2001, MNRAS, 328, 1039
Crittenden, R. G., Natarajan, P., Pen, U.-L., & Theuns, T. 2001,
ApJ, 559, 552
Croft, R. A. C. & Metzler, C. A. 2000, ApJ, 545, 561
Dekel, A. 1985, ApJ, 298, 461
Djorgovski, S. 1983, ApJ, 274, L7
Faltenbacher, A., Allgood, B., Gottlöber, S., Yepes, G., & Hoffman,
Y. 2005, MNRAS, 362, 1099
Fardal, M. A., Babul, A., Geehan, J. J., & Guhathakurta, P. 2006,
MNRAS, 366, 1012
Fleck, J.-J. & Kuhn, J. R. 2003, ApJ, 592, 147
Hawley, D. L. & Peebles, P. J. E. 1975, AJ, 80, 477
Heavens, A., Refregier, A., & Heymans, C. 2000, MNRAS, 319, 649
Heymans, C. & Heavens, A. 2003, MNRAS, 339, 711
Holmberg, E. 1969, Arkiv for Astronomi, 5, 305
Jing, Y. P. 2002, MNRAS, 335, L89
Johnston, K. V., Sackett, P. D., & Bullock, J. S. 2001, ApJ, 557,
Kang, X., van den Bosch, F. C., Yang, X., Mao, S., Mo, H. J., Li,
C., & Jing, Y. P. 2007, MNRAS, in press (astro-ph/0701130)
King, L. & Schneider, P. 2002, A&A, 396, 411
Lee, J., Kang, X., & Jing, Y. P. 2005, ApJ, 629, L5
Li, C., Kauffmann, G., Jing, Y. P., White, S. D. M., Börner, G., &
Cheng, F. Z. 2006, MNRAS, 368, 21
Libeskind, N. I., Frenk, C. S., Cole, S., Helly, J. C., Jenkins, A.,
Navarro, J. F., & Power, C. 2005, MNRAS, 363, 146
Mandelbaum, R., Hirata, C. M., Ishak, M., Seljak, U., &
Brinkmann, J. 2006, MNRAS, 367, 611
Mathews, W. G., Chomiuk, L., Brighenti, F., & Buote, D. A. 2004,
ApJ, 616, 745
Pen, U.-L., Lee, J., & Seljak, U. 2000, ApJ, 543, L107
Pereira, M. J. & Kuhn, J. R. 2005, ApJ, 627, L21
Plionis, M. 1994, ApJS, 95, 401
Plionis, M., Benoist, C., Maurogordato, S., Ferrari, C., & Basilakos,
S. 2003, ApJ, 594, 144
Porciani, C., Dekel, A., & Hoffman, Y. 2002a, MNRAS, 332, 325
—. 2002b, MNRAS, 332, 339
Strazzullo, V., Paolillo, M., Longo, G., Puddu, E., Djorgovski,
S. G., De Carvalho, R. R., & Gal, R. R. 2005, MNRAS, 359,
Struble, M. F. 1990, AJ, 99, 743
Thompson, L. A. 1976, ApJ, 209, 22
Torlina, L., De Propris, R., & West, M. J. 2007, ArXiv Astrophysics
e-prints
Trujillo, I., Carretero, C., & Patiri, S. G. 2006, ApJ, 640, L111
Usami, M. & Fujimoto, M. 1997, ApJ, 487, 489
Wang, H. Y., Jing, Y. P., Mao, S., & Kang, X. 2005, MNRAS, 364,
Weinmann, S. M., van den Bosch, F. C., Yang, X., & Mo, H. J.
2006, MNRAS, 366, 2
West, M. J. 1989, ApJ, 344, 535
Yang, X., Mo, H. J., van den Bosch, F. C., & Jing, Y. P. 2005,
MNRAS, 356, 1293
http://arxiv.org/abs/astro-ph/0701130
Faltenbacher et al. 5
Yang, X., van den Bosch, F. C., Mo, H. J., Mao, S., Kang, X.,
Weinmann, S. M., Guo, Y., & Jing, Y. P. 2006, MNRAS, 369,
York, D. G., et al. 2000, AJ, 120, 1579
