A&A 488, 511-518 (2008)
DOI: 10.1051/0004-6361:20078057
M. López-Corredoira1 - E. Florido2 - J. Betancort-Rijo1,3 - I. Trujillo1,4 - C. Carretero1,5 - A. Guijarro2,6 - E. Battaner2 - S. Patiri1,7
1 - Instituto de Astrofísica de Canarias, C/.Vía Láctea, s/n,
38200 La Laguna (S/C de Tenerife), Spain
2 - Departamento de Física Teórica y del Cosmos,
Universidad de Granada, Spain
3 - Departamento de Astrofísica, Universidad de La Laguna, Tenerife,
Spain
4 - School of Physics and Astronomy, University of Nottingham,
University Park, Nottingham NG7 2RD, UK
5 - Estin & Co Strategy Consulting, 43 Av. de
Friedland, 75008 Paris, France
6 - Centro Astronómico Hispano Alemán, Almería, Spain
7 - Case Western Reserve University, Cleveland (Ohio), USA
Received 11 June 2007 / Accepted 6 June 2008
Abstract
Context. Hydrodynamical cosmological simulations predict flows of the intergalactic medium along the radial vector of the voids, approximately in the direction of the infall of matter at the early stages of the galaxy formation.
Aims. These flows might be detected by analysing the dependence of the warp amplitude on the inclination of the galaxies at the shells of the voids with respect to the radial vector of the voids. This analysis will be the topic of this paper.
Methods. We develop a statistical method of analysing the correlation of the amplitude of the warp and the inclination of the galaxy at the void surface. This is applied to a sample of 97 edge-on galaxies from the Sloan Digital Sky Survey. Our results are compared with the theoretical expectations, which are also derived in this paper.
Results. Our results allow us to reject the null hypothesis (i.e., the non-correlation of the warp amplitude and the inclination of the galaxy with respect to the void surface) at 94.4% C. L., which is not conclusive. The absence of the radial flows cannot be excluded at present, although we can put a constraint on the maximum average density of baryonic matter of the radial flows of
.
Key words: intergalactic medium - galaxies: statistics - galaxies: kinematic and dynamics - large-scale structure of Universe
Warps seem to be an almost universal structural feature in spiral galaxies. Indeed, most of the spiral galaxies for which we have relevant information on their structure (because they are edge on and nearby) present warps in their stellar and gas distributions. Sánchez-Saavedra et al. (1990, 2003) and Reshetnikov & Combes (1998) show that nearly half of the spiral galaxies of selected samples are warped, and many of the rest might also be warped since warps in galaxies with low inclination are difficult to detect. They are more clearly observed in the HI distribution (see e.g. van der Kruit 2007 and references therein). Warps are also detected at about z=1, even with a larger amplitude (Reshetnikov et al. 2002).
Despite the compelling observational evidence of warps in the spiral discs, there is not consensus on what could be the origin of this property of the galaxies. Nevertheless, it seems clear that warps should be produced by an interaction of the disc with an external element. In fact, Hunter & Toomre (1969) showed that in an isolated galaxy (without a dark matter halo), an initial warp would soon disappear and leave as its only trace a thickening of the edge of the disc.
The number of ideas suggested to explain the origin of the warp in discs is vast. One explanation for the warps is gravitational tidal effects due to satellite galaxies. At least in the Milky Way galaxy, this explanation does not work with Magellanic Clouds as satellite (Hunter & Toomre 1969), and it is controversial whether it works in combination with the amplification of the halo (as proposed by Weinberg 1998 and criticised by García-Ruiz et al. 2002). Also, the intergalactic magnetic field has been suggested as the cause of galactic warps (Battaner et al. 1990, 1991; Battaner & Jiménez-Vicente 1998).
Following the evidence that galaxies seem to be embedded in a massive dark matter halo, the interaction between the halo and the disc was explored. Ideas like `dynamical friction' between the disc and a spherical halo (Bertin & Mark 1980; Nelson & Tremaine 1995), a flattened halo misaligned with the disc (Toomre 1983; Dekel & Shlosman 1983; Sparke & Casertano 1988; Kuijken 1991), or resonant interactions with a triaxial halo (Binney 1981) were explored. All these ideas, however, were rejected when the dark matter halo was modelled correctly as a deformable mass of collisionless particles, rather than as a rigid body (Binney et al. 1998). Since a warp represents a misalignment of the disc's inner and outer angular momentum, Ostriker & Binney (1989) and Jiang & Binney (1999) proposed a model in which warps are generated through accretion of material into the halo with a misaligned spin that changes the major axis of the halo with respect to the disc and consequently produces a torque over the disc. There is a need for substantial accretion of low angular momentum material from the IGM into the galaxies (Fraternali et al. 2007), and the direction of the net angular-momentum vector of the material that is currently being accreted should be constantly changing (Quinn & Binney 1992).
Also based on infalling of material, but with a much weaker dependence on halo properties, some works (Mayor & Vigroux 1981; Revaz & Pfenninger 2001; López-Corredoira et al. 2002; Sánchez-Salcedo 2006) have proposed a mechanism for the formation of the warp in terms of the infall of a very low density intergalactic medium onto the disc without the dynamical intervention of an intermediate halo. Both S-type and U-type warps can be produced by this interaction (López-Corredoira et al. 2002; Saha & Jog 2006). Even if there are other mechanisms able to produce warps, at least we know that the infall of material onto the disc will always produce warps.
If the infall of material is relevant to the formation of the warp of the disc,
the orientation of the galaxies within the cosmological large-scale structure
where they are embedded should have an effect on the formation of these
features. There is growing evidence that disc galaxies are not oriented
randomly, but their angular momentum primarily point parallel to the filaments
(or sheets) where they are located. In the supergalactic plane, there is a hint
of an excess of galaxies whose angular momentum lie in this plane (Kashikawa &
Okamura 1992; Navarro et al. 2004). Beyond the local universe, Trujillo et al. (2006) show at the 99.7% level that spiral galaxies located on the shells of the largest cosmic voids (
Mpc) have rotation axes that lie primarily on the void surface. Paz et al. (2008) point out that the angular momentum of flattened spheroidals in SDSS galaxies tends to be perpendicular to the large-scale structure. These alignments are expected to be a consequence of the gain in angular momentum of the galaxies at the early stages of their formation, when both the baryonic component and the dark matter protohalo are suffering tidal torques from neighbouring fluctuations. Using N-body simulations, the
alignments of the angular momentum of the haloes with the large-scale
distribution have been also found (Porciani et al. 2002; Bailin & Steinmetz 2005; Brunino et al. 2007; Aragón-Calvo et al. 2007; Hahn et al. 2007; Paz et al. 2008).
The aim of this paper is to check whether the orientation of the spiral galaxies in the void surfaces is related to the presence of a warp or not. In contrast to filaments (which are strongly affected by redshift-space distortion), large cosmological voids are a feature easy to characterise from the observational point of view. In addition, another important advantage of the void scheme is that (because of the radial growing of the voids) the vector joining the centre of the void with the galaxy position is a good approximation of the direction of the maximum compression of the large-scale structure at that point. Consequently, the radial vector of the void at the galaxy position approximately represents the direction of the infall of matter at the early stages of the galaxy formation. At later epochs, however, most of the accretion of material in the galaxy is expected to be through the filaments (i.e. parallel to the void surface). According to López-Corredoira et al. (2002), the infall of material should produce a correlation between the orientation of the galaxy and the amplitude and direction of the S-component, or the U-component or both of them. We want to check this hypothesis here. The aim of this paper is producing a method for analysing the relationship of the warp amplitude in galaxies with the inclination of the galaxy with respect to the line ``centre of void''-galaxy (to check the early accretion of material). This method is then applied to the edge-on galaxies and void catalogue used by Trujillo et al. (2006) for available images from Sloan Digital Sky Survey (SDSS) survey. The work presented here is an attempt to observationally characterise the influence of the large-scale structure (and, consequently, the cosmic infall of material) on the formation of the warps. Some works have previously dealt with no random orientations of warps on large scales (Battaner et al. 1991) or in the Local Group (Zurita & Battaner 1997), but not at the void shells.
To define a warp amplitude, we first rotate the galaxy to have
the mean plane of the galaxy coincident with the constant declination
axis in the local plane of the sky (perpendicular to the line of sight).
The position angle is calculated with an iterative method that fits the
central part of galaxies (size of galaxy/2) to a straight line. This
method uses the position angle from Trujillo et al. (2006) as starting point. The position angle was determined in this way to an
accuracy of about 0.5 degrees. This error was adopted like that of the rms
using the mean least square method in the rotation procedure. We then
have a right and a left part of the galaxy, each having its own warp.
The right part is the one with a lower right ascension.
To quantitatively estimate the warp amplitude we define the
warp parameter W, on the left(l) or right(r) side of the galaxy, as
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Figure 1: Graphical representation of the warp measurement. |
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Figure 2:
Left: graphical representation of a perfect S-warp (![]() ![]() |
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Expression (1) is adimensional,
therefore the value of W only depends on
the shape of the edge-on galaxy but not on the intrinsic size or on the
distance of a galaxy (neglecting the change of
the factor (1+z)4 (i.e. cosmological dimming)
in the surface brightness of the galaxies
throughout our sample since most of them are at a similar ).
For numerical purposes and working in pixels, we use the discrete expression
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(2) |
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(3) |
In a S-shape warped galaxy,
and
have the same sign. In a
U-shaped galaxy,
and
have different signs.
We define the variables S and U as
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(4) |
A serious difficulty arising in any observational study of warps is that companions, spiral arms, and other effects may mimic warps. The errors introduced by a misidentification are difficult to evaluate. However, the images do not suggest that the warps are confused with spiral arms. On the other hand, the companions which are far away from the plane of the main galaxy are not confused with the warp, and if they were very close to the galactic outskirts, the galaxy would be removed from our list.
For each galaxy, given its position angle and the position with respect
to the centre of the void (see Trujillo et al. 2006 for details),
we calculated the inclination of the rotation
axis with respect to the line ``centre of void''-galaxy. The sense of
the rotation axis makes the ``right'' warp positive,
that is, toward increasing declination. And the inclination i is defined
positive (between 0 and )
if the line ``centre of void''-galaxy
is to the right (decreasing position angle) of the rotation axis or
negative (between 0 and
)
otherwise.
Figure 2 illustrates this.
The error in this inclination stems from the error on
the distance to the galaxies in Trujillo et al. (2006) sample.
Due to the intrinsic motion of the galaxies away from the Hubble flow,
this error is estimated to be around
4 h-1 Mpc, and the error in the distance to the centre of the void,
around 2 h-1 Mpc. Taking into account that the average distance
of the galaxies to the centre is 12 h-1 Mpc,
this leads to an average error of
14
.
Since these
errors are statistical and not systematic, they will not affect
the average signal that we find in the data, but will only
decrease the signal-to-noise ratio.
The predictions of the model with accretion of intergalactic
medium (IGM) onto the disc for an average Milky Way-like galaxy
is given in López-Corredoira et al. (2002, Fig. 11). A
fit of the curves in that figure gives the theoretical values
and
:
S-component:
![]() |
(6) |
where
in these expressions is the
direction of the IGM wind with respect to the rotation axis of the galaxy,
and v the relative velocity of the wind. Together,
U0 and S0 represent the maximum
amplitude of the
and
that we calculate
in the following sections.
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Figure 3:
Dependence of
![]() ![]() ![]() |
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Assuming there is a wind flowing radially outwards in the void with velocity
km s-1 (details will be given in
Betancort-Rijo & Trujillo 2008), we must add
the dispersion of velocities of the galaxies:
km s-1,
km s-1(Betancort-Rijo & Trujillo 2008) in
the radial velocity v1 (the projection of the velocity into the
radial direction of the void) and the perpendicular component v2 with
respect to the radial direction of the void with angular azimuth
.
To obtain these numbers, Betancort-Rijo & Trujillo used the
linear theory of growing fluctuations in the large-scale structure.
They computed the r.m.s. of the corresponding components of
the velocity of mass particles on the surface of a void of 10 h-1 Mpc
with respect to its centre of mass. These numbers agree
within a few per cent with the numbers found in numerical simulations.
Hence, the average warps are given by
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(10) |
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(11) |
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(12) |
From López-Corredoira et al. (2002, Figs. 10, 11, Eq. (39)), we can
derive roughly that the maximum height y of the m=1 component of
warp of a Milky Way-like
galaxy and baryonic mean density of the
intergalactic medium
(roughly
the average density of the IGM
flows radially ejected from the void to produce the observed effect):
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(17) |
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(18) |
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Figure 4:
Warp curves and contour maps of three selected galaxies ( up);
and 5-filters combined SDSS images of them ( down), 50
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Similarly, from López-Corredoira et al. (2002, Figs. 10, 11, Eq. (45)), we
derive roughly that the maximum height y of the m=0 component of the
warp of a Milky Way-like
galaxy with IGM baryonic mean density
is
![]() |
(21) |
![]() |
(22) |
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Figure 5: Dependence of S and U on the inclination i in the observational data (stars). The squares with error bars represent the average in bins of i of 30 degrees. |
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We used the data of the SDSS-DR3 (3rd. data release)
that have already been used in
Trujillo et al. (2006). These data are their edge-on
(inclination larger than 78)
galaxies, which are within the shells
Mpc surrounding the largest voids, where
Mpc is its radius.
The lower the inclination of the galaxy, the
greater the thickness of the projected disc and, consequently, the greater
the error in the determination of the centroid of y(x). In the worst
case (78
), the thickness of the projected disc is comparable
to its intrinsic thickness (Dalcanton & Bernstein 2002),
so the error in the warp amplitude
is not significantly increased with respect to a 90
inclination galaxy.
The voids were located
using maximal spheres empty of galaxies with magnitude over
(H0=100 h km s-1 Mpc),
and they were found by means of the HB void finder
(Patiri et al. 2006). From the SDSS available public data,
we used the filter ``r'' images. In total we have 114 galaxies.
For seventeen galaxies there were difficulties measuring the warp amplitude (for instance, due to the proximity of a star in the field or interaction with other galaxies), so there remain N=97 galaxies with which we carried out the statistics (Table 1). In Fig. 4, we show three examples.
Some images of warped galaxies could be the subject of alternative interpretations. For instance, considering the isophote maps, warp curve, and image in the central panel of Fig. 4, a feature is found at x=-12, y=5, either a companion galaxy or an inteloper, which could produce/modify the warp curve. However, we find that the warp at this galactocentric radius is real, as directly deduced from a detailed study of the isophote maps.
If we plot their values of S and U vs. i, we get the
results of Fig. 5.
There are slight trends in S(i) [
]
and in U(i)
[
].
The errors in the correlations are calculated as
and
;
where
,
and
are the rms of the values of S, U, and i.
The scattering of Fig. 5 may be for several reasons. For example,
To check whether the null hypothesis is compatible with the observed
U-components distribution,
we computed the probability, P(i*), based on the binomial distribution
of finding no more than n0- galaxies with U<0 and
,
and no more than n1+ galaxies with U>0 and
,
assuming that there is no correlation between iand U (i.e., the null-hypothesis). With this assumption,
the probability that U>0 is 1/2 for
any value of i, and using the binomial distribution for
n1+, n0-, we find
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(25) |
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(27) |
Table 1: Amplitude of the warp (with the corresponding error), in units of 10-3, and inclination with respect to the radial direction of the void of the used SDSS galaxies in this paper.
With this value of
,
the probability that our data are
compatible with the null hypothesis is
P=0.056; that is, the null hypothesis is excluded
within 94.4% C.L. If we took
,
we would get
P=0.0043 (rejection of non-correlation within 99.57% C.L.), but
this value of i* is not justified, a priori; therefore, the statistical
significance must be less than this. For a higher value of i*,
we also get rejection of the null hypothesis.
For
we get rejection within 95.7% C.L.
If we do the same calculation for the S vs. i data, we find
that the probability of null hypothesis cannot be rejected
(
).
We also checked the null hypothesis with
the Spearman rank correlation coefficient. This test
gives higher probabilities of a null correlation:
P=0.154 for U(i) and P=0.739 for S(i).
If we assume that Eq. (14) with some positive U0 applies,
the mean value of U for ,
,
is given
by Eq. (26):
We assume that the distribution
of the probabilities of a value of U, P(U), is Gaussian, centred
at
with r.m.s.
.
For galaxies with
,
the probability that U<0 is
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(29) |
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(30) |
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(31) |
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(32) |
With our data and
,
the values are:
,
,
.
Using our model, we can use these numbers to put a constraint
on the IGM density.
From Eqs. (28) and (24), we find
that
kg/m3
(95% C.L.). This allows us to put an upper limit on the IGM density
but not a minimum.
The same calculation with S-component gives a tighter constrain:
,
,
;
kg/m3 (95% C.L.).
The correlation of S with a cosine function
(approximately the expected shape theoretically) is
.
The correlation of U with
(also approximated to be a cosine function) is
.
We can get a better constraint for the maximum density from
these correlations: with the S-component measurement
and the expressions (15) and (20),
we find that
kg/m
(95% C.L.
);
with the U-component measurement and the expressions (16) and (24),
we find that
kg/m
(95% C.L.).
Therefore, summarising the contents of this section,
we reject the null hypothesis (i.e., the inclination of galaxies
and the amplitude of the warp are not related to each other) at
94.4% C.L. Using our model, we can estimate the average density of
the radial flow from the void to be
0-4
.
Cosmological hydrodynamical simulations predict flows of IGM along the radial
vector of the void. This radial direction is approximately the same as the
infall of matter in the early stages of the galaxy formation at the shells of
the void. One way to search for the effect of this IGM flow
in these shells is to measure the
dependence of the warp amplitude on their galaxies as a function of
their inclination with respect to the radial vector of the void. In
this paper, we have developed a method to measure that effect, and
we made a first attempt to find this effect.
The signal found in the U-component of the warp (the null hypothesis is
rejected at 94.4% C.L.) gives some hint
that such an effect might exist. This result is not
conclusive (5.6% is not a very negligible probability)
and the absence of the radial flows cannot be excluded at present.
If the IGM radial flows in the radial direction of the voids exist,
their baryonic matter density should be
kg/m
.
This density would increase inversely
proportional to the square of the mean flow velocity if its value differs from
200 km/s. There is also the possibility that the accretion of material have
different initial velocities than the radial direction of the void.
There may be other mechanisms of warp formation different to the accretion onto the disc, but they would produce noise in the correlation if they have nothing to do with the IGM accretion. If the correlation of S-component amplitude and inclination were observed, although it would be an argument in favour of López-Corredoira et al. (2002) theory, it would not be totally conclusive because there might be alternative explanations for the correlation. The mechanism of accretion into the halo (Ostriker & Binney 1989; Jiang & Binney 1999) rather than onto the disc might possibly explain the correlation. There might be a relationship between warps and filaments associated to the void produced by primordial magnetic fields, or the frozen magnetic fields were aligned with the filaments (Florido & Battaner 1997), if the magnetic fields are also responsible for the warp formation (Battaner et al. 1990, 1991; Battaner & Jiménez-Vicente 1998). However, these theories do not explain the U-component (the asymmetry of the S-warps), which are clearly observed in many galaxies (e.g., Reshetnikov & Combes 1998; Sánchez-Saavedra et al. 2003). The trend in the correlation of the U-component with the inclination of the galaxy obtained in this paper, if confirmed with higher statistical significance, could be taken as confirmation that the mechanism of IGM accretion onto the disc produces warps. The application of the method presented in this paper to galaxy samples with more objects and/or better measurements of the warp amplitude is expected to give more accurate results.
Acknowledgements
Thanks are given to the anonymous referee for helpful comments, and to Joly Adams (language editor of A&A) for proof-reading this paper. Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. MLC was supported by the Ramón y Cajal Programme of the Spanish Science Ministery. We thank the Spanish Science Ministery for support under grant AYA2007-67625-CO2-01.