ArticlePDF Available

Abstract

Recent observations of the rotation curve of M31 show a rise of the outer part that can not be understood in terms of standard dark matter models or perturbations of the galactic disc by M31's satellites. Here, we propose an explanation of this dynamical feature based on the influence of the magnetic field within the thin disc. We have considered standard mass models for the luminous mass distribution, a NFW model to describe the dark halo, and we have added up the contribution to the rotation curve of a magnetic field in the disc, which is described by an axisymmetric pattern. Our conclusion is that a significant improvement of the fit in the outer part is obtained when magnetic effects are considered. The best-fit solution requires an amplitude of ~4 microG with a weak radial dependence between 10 and 38 kpc.
arXiv:1010.0270v1 [astro-ph.CO] 1 Oct 2010
Magnetic fields and the outer rotation curve of M31
B. Ruiz-Granados and J.A. Rubi˜no-Mart´ın
Instituto de Astrof´ısica de Canarias (IAC), E-38200, La Laguna, Tenerife (Spain)
and
Departamento de Astrof´ısica, Universidad de La Laguna, E-38205, La Laguna, Tenerife (Spain)
E. Florido and E. Battaner
Departamento F´ısica Torica y del Cosmos. Universidad de Granada, Granada(Spain)
and
Instituto de F´ısica Torica y Computacional Carlos I, Granada(Spain)
ABSTRACT
Recent observations of the rotation curve of M31 show a rise of the outer part that can not
be understood in terms of standard dark matter models or perturbations of the galactic disc
by M31’s satellites. Here, we propose an explanation of this dynamical feature based on the
influence of the magnetic field within the thin disc. We have considered standard mass models
for the luminous mass distribution, a NFW model to describe the dark halo, and we have added
up the contribution to the rotation curve of a magnetic field in the disc, which is described by
an axisymmetric pattern. Our conclusion is that a significant improvement of the fit in the outer
part is obtained when magnetic effects are considered. The best-fit solution requires an amplitude
of 4µG with a weak radial dependence between 10 and 38 kpc.
Subject headings: galaxies: individual (M31) , galaxies: magnetic fields
1. Introduction
Recent high sensitivity measurements of the ro-
tation curve of M31 (Chemin et al. 2009; Corbelli et al.
2010, hereafter C09 and C10 respectively) suggest
that it highly rises at the outermost part of the
disc of M31 (r&25 30 kpc) (see Figure 1).
This behaviour cannot be considered an exception.
Similar outer rising rotation curves can be found in
other galaxies. Noordermeer et al. (2007) stated
that “in some cases, such as UGC 2953, UGC 3993
or UGC 11670 there are indications that the rota-
tion curves start to rise again at the outer edges
of the HI discs”, suggesting follow-up observa-
tions of higher sensitivity to investigate this fact
in more detail. Other examples could be found
in some rotation curves provided by Spano et al.
(2008), in particular the curves of UGC 6537
(SAB(r)c), UGC 7699 (SBcd/LSB), UGC 11707
(Sadm/LSB) or UGC 11914 (SA(r)ab) measured
by means of Fabry-Perot spectroscopy. Other
potential examples could be NGC 1832 and NGC
2841 (Kassin et al. 2006), even with a larger error,
and ESO 576-G51 and ESO 583-G7 (Seigar et al.
2005), even if the outer rising is small. Potential
nearby candidates could be NGC 3198, DDO 154
or NGC 7331 (de Blok et al. 2008). Therefore,
outer rising rotation curves are not uncommon
in spirals, being the case of M31 the most repre-
sentative. This puzzling dynamic feature requires
a theoretical explanation. A detailed study by
C09 showed that the NFW, Einasto or pseudo-
isothermal dark matter halos fail to reproduce the
exact shape of the rotation curve of M31 in the
outer region and found no differences between the
various halo shapes. Moreover, they found new HI
structures as an external arm and thin HI spurs
in the outskirts of the disc. These spurs have
been also observed by Braun et al. (2009). Thus,
a primarily explanation of this gas perturbations
1
could be the interactions with the M31’s satellites
as NGC 205 (Geehan et al. 2006; Corbelli et al.
2010). The main problem of matching the prop-
erties of the giant stellar stream observed in the
south of M31 (Ibata et al. 2001) is that the orbital
of the companion that produce the stream is not
constrained satisfactorily (Fardal et al. 2006) or
high velocities for the radial orbits are found (see
e.g. Howley et al. 2008). Although the northeast-
ern (NE) and southwestern (SW) parts of M31
show different kinematical properties, both sug-
gest a rise in the outer part of the rotation curve
(see Figure 5 and 6 in C09 and C10, respectively).
In this work, we show that magnetic dynamic
effects constitute a clear and simple basis to
interpret this feature. Some particular mod-
els of magnetically driven rotation curves have
been presented (Nelson 1988; Battaner et al. 1992;
Battaner & Florido 1995, 2000, 2007; Kutschera & Jalocha
2004; Tsiklauri 2008). Although those models
were originally developed to explain flat rotation
curves without dark matter, our purpose here is
more conventional and we will consider the con-
tribution of both a NFW dark matter halo and a
magnetic field added to match the velocity in the
outermost region.
Magnetic fields are known to slowly decrease
with radius (see e.g. Beck et al. 1996; Han et al.
1998; Beck 2001, 2004, 2005), and therefore they
become increasingly important at the rim. For
large radii, an asymptotic 1/r-profile for the field
strength provides an asymptotic vanishing mag-
netic force. This 1/r-profile has been found to
match the polarized synchrotron emission of the
Milky Way (Ruiz-Granados et al. 2010) and NGC
6946 (Beck 2007), and will be considered in this
work.
2. Mass models and the magnetic field of
M31
In this section, we briefly present the luminous
and dark mass models used to describe the ob-
servational rotation curve of M31. As we are in-
terested in the outer region (i.e. distances higher
than 10 kpc), we follow C10 and we neglect the
bulge contribution. We will also adopt from C09
and C10 the parameters describing stellar disc and
gaseous distribution, respectively. Therefore, we
will only leave as free parameters those describing
two physical components: the dark matter halo
and the magnetic field.
2.1. Disc model
The stellar disc is assumed to be exponen-
tial (Freeman 1970), being the surface mass den-
sity
Σ = Σ0exp r
Rd,(1)
where Σ0is the central density of stars and Rd,
the radial scale factor.
The contribution to the circular velocity of the
stellar disc is (see Binney & Tremaine 1987)
vd(r) = 4πGΣ0Rdy2[I0(y)K0(y)I1(y)K1(y)],
(2)
where y=r/2Rdand I0, K0, I1, K1are the modi-
fied Bessel’s functions for first and second order.
The gaseous disc mainly contains HI, molecular
gas and helium. The estimated gaseous distribu-
tion of M31 represents approximately a 9% (for
C09) and 10% (for C10) of the total mass of the
stellar disc (see Table 1).
For the spatial distribution of the gas, we again
assume the same exponential law given by Equa-
tion (1).
2.2. Halo model
The dark matter halo is described here by a
NFW profile (Navarro et al. 1996)
ρh(r) = δcρc
r
Rhh1 + r
Rhi2,(3)
where δcis a characteristic density contrast,
ρc= 3H2
0/8πG is the critical density and Rh
is the radial scale factor. The contribution to
the circular velocity due to this profile is given
by (Navarro et al. 1997)
vh(x) = V200s1
x
ln(1 + cx)cx
1+cx
ln(1 + c)c
1+c
,(4)
where V200 is the velocity at the virial radius R200
which is assumed 160 kpc for C09 and R200
200 kpc for C10, cis the concentration parameter
of the halo which is defined as c=R200 /Rhand
xis r/R200 . According to C09 and C10, the total
dark halo mass at the respective virial radius is
2
M200 1012 M. Our free parameters are V200
and c. Values from C09 are c= 20.1±2.0 and
V200 = 146.2±3.9km/s. Values from C10 are
c= 12 and V200 140 km/s.
2.3. The regular magnetic field of M31
The first measurements of the magnetic field of
M31 were obtained by Beck (1982) using the po-
larized synchrotron emission at 2700 MHz, show-
ing that a magnetic pattern was aligned with HI
structures and formed a ring at r10 kpc.
They obtained a strength of Breg = 4.5±1.2µG.
Berkhuijsen et al. (2003) used observations of po-
larized emission to show that M31 hosts an ax-
isymmetric field. Han et al. (1998) used Faraday
rotation measurements to show that the regular
field could extend at least up to galactocentric
distances of r25 kpc without significant de-
crease of the strength and at least with a z1
kpc of height above the galactic plane. However,
recently, Stepanov et al. (2008) have shown that
these results contained a significant contribution
of Galactic foregrounds and so, it is difficult to in-
fer the model from these measurements. In any
case, as we show below, the detailed structure of
the field is not relevant for the rotation curve.
Fletcher et al. (2004) presented a detailed
study of the regular field of M31 based on multi-
wavelength polarized radio observations in the re-
gion between 6 and 14 kpc. By fitting the observed
azimuthal distribution of polarization angles, they
found that the regular magnetic field follows an
axisymmetric pattern in the radial range from 8 to
14 kpc. The pitch angle decreases with the radial
distance, being p∼ −16for distances r < 8 kpc,
and p∼ −7for r < 14 kpc. This fact implies
that the field becomes more tightly wound with
increasing galactocentric distance. They found
a total field strength (i.e. regular and turbulent
components) of 5µG. For the regular field they
found that it became slowly lower, reaching at
r14 kpc a strength of 4.6µG.
In this paper, our basic assumption is that the
regular magnetic field of M31 is described by an
axisymmetric model, that extends up to 38 kpc.
For this model, the components in cylindrical co-
ordinates are given by
Br=B0(r) sin(p) (5)
Bφ=B0(r) cos(p),(6)
where pis the pitch angle and B0(r) is the field
strength as a function of the radial distance. As
shown below, from the point of view of the descrip-
tion of the rotation curve, the relevant component
is Bφ. Here, we will assume that p= 0, as we
are mostly interested in the outer region where p
is very low. Several previous probes also indicates
low values of p. In any case, this is not a strong
assumption in the sense that a non-zero pvalue
can be absorbed into the field strength (B1) as a
different amplitude. For the field strength, as a
baseline computation, we shall consider a radial
dependence of B0(r) or equivalently Bφgiven by
Bφ(r) = B1
1 + r
r1
,(7)
where r1represents the characteristic scale at
which B0(r) decreases to half its value at the galac-
tic centre and B1is an amplitude in which we
are absorbing the cos(p) factor. This expression
has an appropriate asymptotic behaviour, in the
sense that we obtain a finite value when ris close
to the galactic center (r0), and asymptoti-
cally tends to 1/r when r→ ∞, as suggested
Battaner & Florido (2007). Observations carried
out by Fletcher et al. (2004) established that
Bφ(r= 14kpc)4.6µG. (8)
This observational value at this radius was con-
sidered as fixed in our baseline computation. By
substituting into Equation (7), we can find a rela-
tion between B1and r1that allows us to re-write
Equation (7) in terms of a single free-parameter
(r1)
Bφ(r) = 4.6r1+ 64.4
r1+r,(9)
where ris given in kpc and Bφ(r) in µG.
3. Methodology
3.1. Observational rotation curve of M31
We have considered the two datasets from C09
and C10. They consist on a set of 98 and 29 mea-
surements of the circular velocity (and their as-
sociated error bars) respectively, which were ob-
tained with the high-resolution observations per-
formed with the Synthesis Telescope and the 26-
m antenna at the Dominion Radio Astrophys-
ical Observatory (C09) and with the wide-field
3
and high-resolution HI mosaic survey done with
the help of the Westerbork Synthesis Radiotele-
scope and the Robert C. Byrd Green Bank Tele-
scope (GBT) (Braun et al. 2009). For our pur-
poses, we consider only distances higher than
r > 10 kpc to illustrate the effects of the mag-
netic field. The actual data points on the rota-
tion curve were obtained after fitting a tilted ring
model to the data, and assuming a distance to
M31 of 785 kpc. C09 derived a value of the incli-
nation angle of i74, which is lower than that
derived from optical surface photometry measure-
ments (Walterbos & Kennicutt 1987) and by C10
(i77). The data points are plotted in Figure 1,
in two separate panels.
3.2. Influence of the magnetic field on the
gas distribution
The presence of a regular magnetic field af-
fects the gas distribution (Battaner et al. 1992;
Battaner & Florido 1995, 2000). The fluid mo-
tion equation can be written as (see e.g. Battaner
1996)
ρ∂~v0
∂t +ρ~v0·~
~v0+~
P=n~
F+1
4π~
B·~
~
B−∇ B2
8π,
(10)
where ρis the gas density; ~v0, the velocity of the
fluid; P, the pressure; ~
F, the total force due to
gravity and ~
B, the magnetic field. We assume
standard MHD conditions i.e. infinite conduc-
tivity. Equation (10) is simplified by assuming
axisymmetry and assuming pure rotation, where
~v0= (v0r, v0φ, v0z) = (0, θ, 0) even if these condi-
tions are not necessary regarding the dynamic ef-
fects in the radial direction. Taking into account
all these facts, the motion equation in the radial
cylindrical coordinate is
ρdΦ(r)
dr +θ2
rdP
dr Fmag
r= 0,(11)
where Φ(r) is the gravitational potential; Fmag
r,
the radial component of the magnetic force, and
Pthe pressure of the fluid. We can assume that
pressure gradients in the radial direction are neg-
ligible (Battaner & Florido 2000). In this case,
then the radial component of the magnetic force
is given by
Fmag
r=1
4π B2
φ
r+1
2
dB2
φ
dr !,(12)
and the contribution of the magnetic field to the
circular velocity is given by
v2
mag =r
4πρ B2
φ
r+1
2
dB2
φ
dr !.(13)
3.3. Modelling the rotation curve
The rotation curve is obtained, as usual, by
quadratic summation of the different contributions
θ(r)2=vb(r)2+vd(r)2+vh(r)2+vmag(r)2,(14)
where we explicitly set vb(r) = 0 as mentioned
above.
3.4. Model selection
For the luminous mass models, the different pa-
rameters are considered as fixed values in our anal-
ysis (see Table 1). For the NFW dark halo, we
constrain the V200 and cparameters, allowing a
range for V200 between 100 and 220 km/s with
steps of 0.5 km/s and c[5,30] with steps of 0.3.
The contribution of the magnetic field to the ro-
tation curve is fitted through one free parameter,
r1, that we are considering which is equivalent to
fit Bφas we discussed above. For this parameter,
we have explored values in the range from 1 to
1000 kpc. Our analysis is based on a reduced-χ2
as the goodness-of-fit statistic. Thus, the best-fit
parameters are obtained by minimizing this func-
tion
χ2=1
NM
n
X
i=1
(θobs
iθmodel
i)2
σ2
i
,(15)
where Nis the total number of points to which
we have measured the rotational velocity and de-
pends on the considered dataset (N= 74 for C09
and N= 27 for C10) and Mis the number of free
parameters. The sum runs over the observational
data points, being θobs
ithe observed velocity and
θmodel
ithe modelled velocity, which depends on
the particular model. We shall consider two mod-
els: one without magnetic contribution (DM) and
another with the magnetic field (DM+MAG). Fi-
nally, σiis the observational error bar associated
to each data point.
4. Results and discussion
Our main results are summarized in Figure 1.
The dotted line shows our best-fit rotation curve
4
Dataset Disc parameters
C09 Rd= 5.6 kpc
Md= 7.1×1010 M
Mgas 6.6×109M
C10 Rd= 4.5 kpc
Md= 8.0×1010 M
Mgas 7.7×109M
Table 1: Fixed parameters for bulge and disc.
for C09 and C10 when considering only the usual
dynamical components (the stellar component and
the dark halo at this range of distances), while the
solid line shows the result when adding up also the
magnetic contribution.
The most important result is that, as shown
in Battaner & Florido (2000), the effects of mag-
netism on the rotation curve are only relevant at
large radii (in this case of M31, at distances larger
than about 25 kpc). In this sense, the radial range
of the datasets of C09 and C10 are optimal to ob-
serve the magnetic effects.
Table 2 summarizes our results for the best-
fit solutions without (labelled as DM model)
and with magnetic field influence (DM + MAG
model). As shown, magnetic effects on the gaseous
disc significantly decrease the value of the reduced
χ2statistic for both datasets. Specially for C09,
the fit is significantly improved when taking into
account a new parameter (∆χ2= 6.5). The radial
scale factor of the magnetic field (r1) is uncon-
strained in both cases, but shows clear preference
for high values, which means that the best-fit so-
lution for the field slowly decreases with the radial
distance in the considered interval (i.e. between
10 and 38 kpc). For example, at r38 kpc, the
field is found to be Bφ&4.4µG for C09 and
Bφ&4.0µG for C10 for this best-fit solution.
Both values are compatible with the strength of
the field obtained by Fletcher et al. (2004) who
found a nearly constant strength of the regular
field of about 5µG between 6 kpc and 14 kpc.
Moreover, when no radial variation of the strength
is considered, (i.e. if r1→ ∞), and we fit for the
amplitude Bφ, we obtain that Bφ= 4.7+0.6
0.7µG
which it is again compatible with results discussed
above. This suggests that the data do not require
an important radial variation of the strength of the
field for the considered range of distances, or in
other words, the contribution of the second term
in the r.h.s. of Equation (12) is negligible (i.e.
dB2
φ/dr B2
φ/r). Therefore, if we had consid-
ered another radial profile (e.g. exponential), we
would have found a large radial scale factor too.
The azimuthal component of the field is practi-
cally constant between 10 and 38 kpc.
Our results imply large magnetic fields at large
radii. How these are produced lies beyond our
scope. On the other hand, we would expect the
extragalactic field to be also of this order of mag-
nitude. Theoretical predictions (Dar & de R´ujula
2005) suggest values of the level of few µG for the
intergalactic magnetic fields (hereafter IGMF).
Kronberg (1994); Govoni & Feretti (2004); Kronberg
(2005) have reviewed observations of µG level in
rich clusters, though no direct measurements have
been reported for the IGMF in the Local Group
near M31. The observational evidence for IGMF
is still weak, but quite strong IGMF near galaxies
cannot be disregarded.
We finally note the apparent discrepancy be-
tween our derived parameters for the DM model
and those obtained by C09 and C10 (see Sect. 2.2).
However, it is important to stress that we are re-
stricting the fit to the outer region of M31 (r >
10 kpc). In this outer range, there is a weaker de-
pendence of the shape of the rotation curve on the
concentration parameter c, and thus lower values
of care found because the fit tries to compensate
the rising behaviour in the outer part. The inclu-
sion of the magnetic field corrects this apparent
discrepancy, and in this case the values of care
now compatible with those obtained by C09 and
C10.
5
5. Conclusions
The rotation curve of M31 (Chemin et al. 2009;
Corbelli et al. 2010) is rather representative of the
standard rotation curves of spirals for r < 30 kpc,
but it seems to rise out to, at least 38 kpc, the
limiting distance of the observations. Indeed, this
behaviour is not restricted to M31, and we are
probably dealing with a common dynamical fea-
ture of many other spirals. Therefore, the out-
ermost rising rotation curve is a very important
theoretical challenge.
It is certainly a challenge as the standard dark
matter halo models, in particular the universal
NFW profiles, do not account for this dynamical
unexpected behaviour.
A conventional galactic model, with bulge, disc
and dark matter halo, has been shown to provide
good fit to the data in the range r < 20 kpc (C09,
C10). Here, we take advantage of these results
and we do not fit any of the luminous components,
which are taken to be exactly the same as those
proposed by C09 and C10. We have restricted our
study to the region r > 10 kpc, and we only fitted
the parameters describing the dark matter halo,
and the magnetic field contribution. Our main
conclusion is that magnetic fields are not ignor-
able for explaining large-scale dynamic phenom-
ena in M31, producing a significant improvement
of the fit of the rotation curve at large distances.
Moreover, the required field strength of the reg-
ular component (Bφ4µG) is fully consistent
with the measured magnetic field in M31 at least
up to r15 kpc.
This conclusion seems very reasonable, as mag-
Model Parameters C09 C10
DM V200 (km/s) 160.2±2.0 132.1+5.7
5.4
c12.3±0.6 19.1+2.4
2.2
χ219.8 1.1
DM + MAG V200 (km/s) 133.8+1.7
1.3120.0+4.7
4.0
c22.7+1.2
1.125.0+2.8
2.9
r1(kpc) >888.0>185.0
χ213.3 0.6
Table 2: Best-fit for the rotation curve with and
without the contribution of magnetic fields for r&
10 kpc.
netic fields are amplified and act “in situ”, and
therefore they become increasingly important at
the rim, where gravity becomes weaker.
The best-fit model of the magnetic fields re-
quires a field strength slowly decreasing with
radius. This slow decrease is compatible with
present values of the strength derived from ob-
servations of the polarized synchrotron emission
of the disc, but clearly we need measurements of
Faraday rotation of extragalactic sources at this
large radii to confirm that the magnetic field is
present up to this distance and to trace unam-
biguously the regular component. Hence, future
experiments such as LOFAR1and SKA2(Beck
2009), will be extremely important, allowing a de-
tailed explorations on the galactic edge as well as
in the intergalactic medium.
This work was partially supported by projects
AYA2007-68058-C03-01 of Spanish Ministry of
Science and Innovation (MICINN), by Junta de
Andaluc´ıa Grant FQM108 and by Spanish MEC
Grant AYA 2007-67625-C02-02. JAR-M is a
Ram´on y Cajal fellow of the MICINN.
REFERENCES
Battaner, E., Garrido, J. L., Membrado, M., &
Florido, E. 1992, Nature, 360, 652
Battaner, E. & Florido, E. 1995, MNRAS, 277,
1129
Battaner, E. 1996, Astrophysical Fluid Dy-
namics, by E. Battaner, pp. 256. ISBN
0521431662. Cambridge, UK: Cambridge Uni-
versity Press, March 1996.
Battaner, E. & Florido, E. 2000, Fundamentals of
Cosmic Physics, 21, 1
Battaner, E. & Florido, E. 2007, Astronomische
Nachrichten, 328, 92
Beck, R. 1982, A&A, 106, 121
Beck, R., Brandenburg, A., Moss, D., Shukurov,
A., & Sokoloff, D. 1996, ARA&A, 34, 155
Beck, R. 2001, Space Science Reviews, 99, 243
1http://www.lofar.org
2http://www.skatelescope.org/
6
Beck, R. 2004, Ap&SS, 289, 293
Beck, R. 2005, Cosmic Magnetic Fields, 664, 41
Beck, R. 2007, A&A, 470, 539
Beck, R. 2009, IAU Symposium, 259, 3
Beck, R. 2009, Revista Mexicana de Astronomia
y Astrofisica Conference Series, 36, 1
Berkhuijsen, E. M., Beck, R., & Hoernes, P. 2003,
A&A, 398, 937
Binney, J., & Tremaine, S. 1987, Princeton, NJ,
Princeton University Press, 1987, 747 p.
Braun, R. 1991, ApJ, 372, 54
Braun, R., Thilker, D. A., Walterbos, R. A. M., &
Corbelli, E. 2009, ApJ, 695, 937
Chemin, L., Carignan, C., & Foster, T. 2009, ApJ,
705, 1395
Corbelli, E., Lorenzoni, S., Walterbos, R., Braun,
R., & Thilker, D. 2010, A&A, 511, A89 (C10)
Dar, A., & de R´ujula, A. 2005, Phys. Rev. D, 72,
123002
de Blok, W. J. G., Walter, F., Brinks, E., Tra-
chternach, C., Oh, S.-H., & Kennicutt, R. C.
2008, AJ, 136, 2648
Fardal, M. A., Babul, A., Geehan, J. J., &
Guhathakurta, P. 2006, MNRAS, 366, 1012
Fletcher, A., Berkhuijsen, E. M., Beck, R., &
Shukurov, A. 2004, A&A, 414, 53
Freeman, K. C. 1970, ApJ, 160, 811
Geehan, J. J., Fardal, M. A., Babul, A., &
Guhathakurta, P. 2006, MNRAS, 366, 996
Govoni, F., & Feretti, L. 2004, International Jour-
nal of Modern Physics D, 13, 1549
Han, J. L., Beck, R., & Berkhuijsen, E. M. 1998,
A&A, 335, 1117
Hernquist, L. 1990, ApJ, 356, 359
Howley, K. M., Geha, M., Guhathakurta, P.,
Montgomery, R. M., Laughlin, G., & Johnston,
K. V. 2008, ApJ, 683, 722
Ibata, R., Irwin, M., Lewis, G., Ferguson,
A. M. N., & Tanvir, N. 2001, Nature, 412, 49
Kassin, S. A., de Jong, R. S., & Weiner, B. J. 2006,
ApJ, 643, 804
Kronberg, P. P. 1994, Reports on Progress in
Physics, 57, 325
Kronberg, P. P. 2005, Cosmic Magnetic Fields,
664, 9
Kutschera, M., & Jalocha, J. 2004, Acta Physica
Polonica B, 35, 2493
Navarro, J. F., Frenk, C. S., & White, S. D. M.
1996, ApJ, 462, 563
Navarro, J. F., Frenk, C. S., & White, S. D. M.
1997, ApJ, 490, 493
Nelson, A. H. 1988, MNRAS, 233, 115
Noordermeer, E., van der Hulst, J. M., Sancisi,
R., Swaters, R. S., & van Albada, T. S. 2007,
MNRAS, 376, 1513
Ruiz-Granados, B., Rubino-Martin, J. A., & Bat-
taner, E. 2010, arXiv:1006.5573
Seigar, M. S., Block, D. L., Puerari, I., Chorney,
N. E., & James, P. A. 2005, MNRAS, 359, 1065
Spano, M., Marcelin, M., Amram, P., Carignan,
C., Epinat, B., & Hernandez, O. 2008, MNRAS,
383, 297
Stepanov, R., Arshakian, T. G., Beck, R., Frick,
P., & Krause, M. 2008, A&A, 480, 45
Tsiklauri, D. 2008, arXiv:0806.1513
Walterbos, R. A. M., & Kennicutt, R. C., Jr. 1987,
A&AS, 69, 311
This 2-column preprint was prepared with the AAS L
A
T
E
X
macros v5.2.
7
Fig. 1.— Best-fit solutions for the rotation curve
of M31, with and without including the contri-
bution of a regular magnetic field component.
Top shows the C09 dataset and bottom the C10
dataset. Asterisks and rombhus represent the ob-
servational data with the associated error bars.
The solid line is the best fit derived in this paper,
including the contribution of the regular magnetic
field over the gaseous disc. The dotted line is the
best-fit model obtained without the contribution
of the magnetic field.
8
... Magnetic fields in galaxies are strong enough to turn a significant amount of kinetic energy into magnetic energy, driving gas mass inflows into the galactic core (Kim & Stone 2012). Magnetic fields have even been considered as a hidden contributor to flattening rotation curves (Battaner & Florido 2007;Ruiz-Granados et al. 2010;Tsiklauri 2011;Ruiz-Granados et al. 2012;Jałocha et al. 2012a,b). However, various studies have posited that the local conditions of magnetic fields might be too turbulent to add a significant kinematic support to the gas disk or to create a systematic stellar migration (Sánchez-Salcedo & Santillán 2013;Elstner et al. 2014). ...
... One of the most important and unexplored questions in galaxy evolution is Can magnetic fields shape galaxies? (Battaner & Florido 2007;Ruiz-Granados et al. 2010;Tsiklauri 2011;Ruiz-Granados et al. 2012;Jałocha et al. 2012a,b;Elstner et al. 2014). Previous analysis on this topic based their conclusions on the structure of the radio polarization magnetic field, corresponding to the diffuse ISM. ...
Preprint
Full-text available
The recent availability of high-resolution far-infrared (FIR) polarization observations of galaxies using HAWC+/SOFIA has facilitated studies of extragalactic magnetic fields in the cold and dense molecular disks.We investigate if any significant structural differences are detectable in the kpc-scale magnetic field of the grand design face-on spiral galaxy M51 when traced within the diffuse (radio) and the dense and cold (FIR) interstellar medium (ISM). Our analysis reveals a complex scenario where radio and FIR polarization observations do not necessarily trace the same magnetic field structure. We find that the magnetic field in the arms is wrapped tighter at 154um than at 3 and 6 cm; statistically significant lower values for the magnetic pitch angle are measured at FIR in the outskirts (R > 7 kpc) of the galaxy. This difference is not detected in the interarm region. We find strong correlations of the polarization fraction and total intensity at FIR and radio with the gas column density and 12CO(1-0) velocity dispersion. We conclude that the arms show a relative increase of small-scale turbulent B-fields at regions with increasing column density and dispersion velocities of the molecular gas. No correlations are found with HI neutral gas. The star formation rate shows a clear correlation with the radio polarized intensity, which is not found in FIR, pointing to a small-scale dynamo-driven B-field amplification scenario. This work shows that multi-wavelength polarization observations are key to disentangling the interlocked relation between star formation, magnetic fields, and gas kinematics in the multi-phase ISM.
... Indeed, through magnetic braking and angular momentum transport, they could reduce galactic rotation and establish inward gas flows (Sparke 1982;Beck 2015). Alternatively, Ruiz-Granados et al. (2010) suggest that magnetic fields could boost galactic circular velocities at large radii. ...
... It is also interesting to note that maFgnetic acceleration takes place during a significant fraction of time in the outskirts of the galaxy for all the magnetized MBz runs apart from MB14z. This could boost orbital velocities at large distances through a different mechanism to that proposed by Ruiz-Granados et al. (2010), i.e. a rise of the circular velocity produced by the radial decrease of toroidal magnetic field strength. However, we remark that for the galaxy mass and physical distances studied here, we found that the presence of magnetic fields decreases rather than increases orbital velocities. ...
Article
As one of the prime contributors to the interstellar medium energy budget, magnetic fields naturally play a part in shaping the evolution of galaxies. Galactic magnetic fields can originate from strong primordial magnetic fields provided these latter remain below current observational upper limits. To understand how such magnetic fields would affect the global morphological and dynamical properties of galaxies, we use a suite of high-resolution constrained transport magnetohydrodynamic cosmological zoom simulations where we vary the initial magnetic field strength and configuration along with the prescription for stellar feedback. We find that strong primordial magnetic fields delay the onset of star formation and drain the rotational support of the galaxy, diminishing the radial size of the galactic disc and driving a higher amount of gas towards the centre. This is also reflected in mock UVJ observations by an increase in the light profile concentration of the galaxy. We explore the possible mechanisms behind such a reduction in angular momentum, focusing on magnetic braking. Finally, noticing that the effects of primordial magnetic fields are amplified in the presence of stellar feedback, we briefly discuss whether the changes we measure would also be expected for galactic magnetic fields of non-primordial origin.
... This becomes a conversion rate, Γ conv , when dividing by the average time required to follow the path considered (this being l σv where l is the path length). We will use M31 as a test case, as there is data on the gas and magnetic field distributions available [60] where ρ M31 is drawn from [61]. We will assume the magnetic field is turbulent with a coherence length of 0.1 kpc and a power-spectral index of 5/3. ...
Preprint
Full-text available
In the past few years, the search for axion-like particles (ALPs) has grown significantly as very promising candidates to form the total abundance of the cold dark matter (CDM) content in the universe. It has been recently pointed out that ALPs may form a Bose-Einstein condensate (BEC) and, through their gravitational attraction and self-interactions, they can thermalize to spatially localized clumps. The coupling between ALPs and photons allows the spontaneous decay of ALPs into pairs of photons. For ALP condensates with very high occupation numbers, the stimulated decay of ALPs into photons is also possible, and thus the photon occupation number can receive Bose enhancement and grows exponentially. In this work, we study the evolution of the ALPs field due to their stimulated decays in the presence of an electromagnetic background, which exhibits an exponential increase in the photon occupation number by taking into account the role of the cosmic plasma in modifying the photon growth profile. Then, we focus on investigating the plasma effects in modifying the early-universe stability of ALPs, as this may have consequences for attempts to detect their decay by the forthcoming radio telescopes such as the Square Kilometer Array (SKA) telescopes with the intention of detecting the CDM ALPs. We find the radio signal produced via the stimulated decay of ALPs in the range $10^{-6} \text{--} 10^{-4} \; \text{eV}$ mass range to be within the reach of the next-generation of the SKA radio telescopes.
... Indeed, through magnetic braking and angular momentum transport, they could reduce galactic rotation and establish inward gas flows (Sparke 1982;Beck 2015). Alternatively, Ruiz-Granados et al. (2010) suggest that magnetic fields could boost galactic circular velocities at large radii. ...
Preprint
As one of the prime contributors to the interstellar medium energy budget, magnetic fields naturally play a part in shaping the evolution of galaxies. Galactic magnetic fields can originate from strong primordial magnetic fields provided these latter remain below current observational upper limits. To understand how such magnetic fields would affect the global morphological and dynamical properties of galaxies, we use a suite of high-resolution constrained transport magneto-hydrodynamic cosmological zoom simulations where we vary the initial magnetic field strength and configuration along with the prescription for stellar feedback. We find that strong primordial magnetic fields delay the onset of star formation and drain the rotational support of the galaxy, diminishing the radial size of the galactic disk and driving a higher amount of gas towards the centre. This is also reflected in mock UVJ observations by an increase in the light profile concentration of the galaxy. We explore the possible mechanisms behind such a reduction in angular momentum, focusing on magnetic braking. Finally, noticing that the effects of primordial magnetic fields are amplified in the presence of stellar feedback, we briefly discuss whether the changes we measure would also be expected for galactic magnetic fields of non-primordial origin.
Preprint
Full-text available
The observational high-resolution data on the $HI$ gas disk rotation curve of the spiral galaxy $NGC\;6946$ at large radii and the recent increased amount and quality of data on linearly polarized radio continuum emission for this galaxy provide us to re-investigate the role of the regular magnetic fields in the rotation of gas and to test whether disk magnetic fields should be considered as a non-negligible dynamical ingredient. The spiral galaxy $NGC\;6946$ hosts two symmetric bright magnetic spiral arms which have been revealed in the radio polarization map. By taking into account the dynamical effect of the regular magnetic fields caused by two main magnetic arms, on the circular gas rotation and considering two dark matter mass density models, ISO and the universal NFW profile, the shape of the $HI$ gas rotation curve of this galaxy is fitted better, especially in the outer part. The contribution of the regular magnetic fields in the rotation velocity of the gas has a positive value and shows an ascending curve with a typical amplitude of about $ 7 - 14 \; km s^{-1}$ in the outer gaseous disc of the galaxy $NGC\;6946$. We also generate the map of the modeled regular magnetic field strength for the spiral galaxy $NGC\;6946$, which clearly shows two main inner contours with the spiral pattern and the highest magnetic field strength, with the field directed towards the galaxy's center in both, almost compatible with two inner main magnetic arms detected in the polarized synchrotron intensity map.
Article
In the past few years, the search for axion-like particles (ALPs) has grown significantly due to their potential to account for the total abundance of the cold dark matter (CDM) in the universe. The coupling between ALPs and photons allows the spontaneous decay of ALPs into pairs of photons. For ALPs condensed in CDM halos around galaxies, the stimulated decay of ALPs is also possible. In this work, we examine the detectability of the radio emissions produced from this process with forthcoming radio telescopes such as the Square Kilometer Array (SKA) and MeerKAT. Our results, using recent more realistic sensitivity estimates, show that previous non-observation upper-limits projected for the SKA were highly optimistic, with the limits from dwarf galaxy observations being weakened by an order of magnitude at least. Notably, our results also depend far more strongly on ALP mass than previously, due to the inclusion of frequency dependent degradation effects. We show that the strongest potential environment to probe ALPs is nearby radio galaxies (due to the strong photon enhancement factor). In addition, with the use of a visibility taper, ALPs in the mass range of 4.96 × 10 ⁻⁷ − 1.04 × 10 ⁻⁴ eV would have non-observation upper limits on the ALP-photon g aγ in the range of 1.83 × 10 ⁻¹² − 7.69 × 10 ⁻¹⁰ GeV ⁻¹ with SKA. MeerKAT can only produce limits similar to the CAST experiment within 50 hours of observation. Finally, we demonstrate that magnetic conversion of CDM ALPs to photons, in galactic magnetic fields, is highly sub-dominant, even to spontaneous decay.
Article
Mixing between photons and low-mass bosons is well considered in the literature. The particular case of interest here is with hypothetical gravitons, as we are concerned with the direct conversion of gravitons into photons in the presence of an external magnetic field. We examine whether such a process could produce direct low-frequency radio counterparts to gravitational-wave events. Our work differs from previous work in the literature in that we use the results of numerical simulations to demonstrate that, although a single such event may be undetectable without at least 105 dipoles, an unresolved gravitational wave background from neutron star mergers could be potentially detectable with a lunar telescope composed of 103 elements. This is provided the gravitational wave spectrum only experiences exponential damping above 80 kHz, a full order of magnitude above the limit achieved by present simulation results. In addition, the extrapolation cannot have a power-law slope ≲−2 (for 100 hours of observation time) and background and foregrounds must be effectively subtracted to obtain the signal. This does not make detection impossible, but suggests it may be unlikely. Furthermore, assuming a potentially detectable spectral scenario we show that, for the case when no detection is made by a lunar array, a lower bound, competitive with those from Lorentz-invariance violation, may be placed on the energy-scale of quantum gravitational effects. The SKA is shown to have very limited prospects for the detection of either a single merger or a background.
Chapter
Magnetic fields are a major agent in the interstellar medium. They contribute significantly to the total pressure which balances the gas disk against gravitation. They affect the gas flows in spiral arms (Gómez and Cox, 2002). The effective sound speed of the gas is increased by the presence of strong fields which reduce the shock strength. The interstellar fields are closely connected to gas clouds. They affect the dynamics of the gas clouds (Elmegreen, 1981; de Avillez and Breitschwerdt, 2004). The stability and evolution of gas clouds are also influenced by magnetic fields, but it is not understood how (Crutcher, 1999; see Chap. 7). Magnetic fields are essential for the onset of star formation as they enable the removal of angular momentum from the protostellar cloud during its collapse (magnetic braking, Mouschovias, 1990). Strong fields may shift the stellar mass spectrum towards the more massive stars (Mestel, 1990). MHD turbulence distributes energy from supernova explosions within the ISM (Subramanian, 1998) and regenerates the field via the dynamo process (Wielebinski, R., Krause, 1993, Beck et al., 1996; Sect. 6). Magnetic reconnection is a possible heating source for the ISM and halo gas (Birk et al., 1998). Magnetic fields also control the density and distribution of cosmic rays in the ISM. A realistic model for any process in the ISM needs basic information about the magnetic field which has to be provided by observations.
Article
We present a radio continuum survey of M 31 at λ6.2 cm with high sensitivity in total power and polarization, observed with the 100-m Effelsberg dish with an angular resolution of 2′.4. (1) Combination with the VLA + Effelsberg map at λ20.5 cm in total power yielded a spectral index map at 3′ resolution. Both the spectrum of the integrated emission and the spectral index distribution across M 31 indicate a nonthermal spectral index αn = 1.0 ± 0.2. We derived maps of thermal and nonthermal emission at λ6.2 cm. Radial profiles of the various emission components north and south of the minor axis revealed that the stronger total emission in the northern part of M 31 is entirely due to stronger thermal emission, whereas the profiles of nonthermal and polarized emission are nearly identical on either side of the minor axis. This suggests that recent star formation does not lead to a local increase of the number of relativistic electrons and/or magnetic field strength. (2) We discuss several properties of the polarized emission from M 31 and their implications for the magnetic field. At λ6.2 cm the polarized intensity systematically varies along the bright "ring" of emission which shows that the regular magnetic field, Breg, is nearly aligned with the spiral arms forming this "ring". The variation of the rotation measures between λ11.1 cm and λ6.2 cm, RM(11, 6), across the galaxy confirms this alignment. The nonthermal degree of polarization reaches values >50% near the polarization maxima, implying that the magnetic field in M 31 is exceptionally regular. (3) We derived the distribution of the nonthermal depolarization between λ11.1 cm and λ6.2 cm, DPn(11, 6), which is a measure of Faraday depolarization. Gradients in RM(11, 6) may be an important cause of Faraday depolarization in M 31. The lack of anticorrelation between the thermal emission, which comes mainly from dense H n regions with small filling factors, and RM(11, 6) and DPn(11, 6) indicates that rotation measures and Faraday depolarization originate in the extended diffuse ionized gas.
Article
The existence of magnetic fields associated with the intracluster medium in clusters of galaxies is now well established through different methods of analysis. Magnetic fields are investigated in the radio band from studies of the rotation measure of polarized radio galaxies and the synchrotron emission of cluster-wide diffuse sources. Other techniques include X-ray studies of the inverse Compton emission and of cold fronts and magneto hydrodynamic simulations. We review the main issues that have led to our knowledge on magnetic fields in clusters of galaxies. Observations show that cluster fields are at the muG level, with values up to tens of muG at the center of cooling core clusters. Estimates obtained from different observational approaches may differ by about an order of magnitude. However, the discrepancy may be alleviated by considering that the magnetic field is not constant throughout the cluster, and shows a complex structure. In particular, the magnetic field intensity declines with the cluster radius with a rough dependence on the thermal gas density. Moreover, cluster magnetic fields are likely to fluctuate over a wide range of spatial scales with values from a few kpc up to hundreds kpc. Important information on the cluster field axe obtained by comparing the observational results with the prediction from numerical simulations. The origin of cluster magnetic fields is still debated. They might originate in the early Universe, either before or after the recombination, or they could have been deposited in the intracluster medium by normal galaxies, starburst galaxies, or AGN. In either case, magnetic fields undergo significant amplification during the cluster merger processes.
Article
This textbook is a general introduction to the dynamics of astrophysical fluids for students with a knowledge of basic physics at the undergraduate level. No previous knowledge of fluid dynamics or astrophysics is required because the author develops all new concepts in context. The first four chapters cover classical fluids, relativistic fluids, photon fluids and plasma fluids, with many cosmic examples being included. The remaining six chapters deal with astrophysical applications: stars, stellar systems, astrophysical plasmas, cosmological applications, and large scale structure of the universe. Astrophysical fluid dynamics is a promising branch of astronomy, with wide applicability. This textbook considers the role of plasma and magnetism in planets, stars, galaxies, the interplanetary, interstellar and intergalactic media, as well as the universe at large.
Article
The results obtained from a study of the mass distribution of 36 spiral galaxies are presented. The galaxies were observed using Fabry-Perot interferometry as part of the GHASP survey. The main aim of obtaining high-resolution Halpha 2D velocity fields is to define more accurately the rising part of the rotation curves which should allow to better constrain the parameters of the mass distribution. The Halpha velocities were combined with low resolution HI data from the literature, when available. Combining the kinematical data with photometric data, mass models were derived from these rotation curves using two different functional forms for the halo: an isothermal sphere (ISO) and a Navarro-Frenk-White (NFW) profile. For the galaxies already modelled by other authors, the results tend to agree. Our results point at the existence of a constant density core in the centre of the dark matter haloes rather than a cuspy core, whatever the type of the galaxy from Sab to Im. This extends to all types the result already obtained by other authors studying dwarf and low surface brightness galaxies but would necessitate a larger sample of galaxies to conclude more strongly. Whatever model is used (ISO or NFW), small core radius haloes have higher central densities, again for all morphological types. We confirm different halo scaling laws, such as the correlations between the core radius and the central density of the halo with the absolute magnitude of a galaxy: low-luminosity galaxies have small core radius and high central density. We find that the product of the central density with the core radius of the dark matter halo is nearly constant, whatever the model and whatever the absolute magnitude of the galaxy. This suggests that the halo surface density is independent from the galaxy type.
Article
We present a radio continuum survey of M 31 at lambda 6.2 cm with high sensitivity in total power and polarization, observed with the 100-m Effelsberg dish with an angular resolution of 2\farcm 4. (1) Combination with the VLA + Effelsberg map at lambda 20.5 cm in total power yielded a spectral index map at 3arcmin resolution. Both the spectrum of the integrated emission and the spectral index distribution across M 31 indicate a nonthermal spectral index alphan = 1.0+/- 0.2. We derived maps of thermal and nonthermal emission at lambda 6.2 cm. Radial profiles of the various emission components north and south of the minor axis revealed that the stronger total emission in the northern part of M 31 is entirely due to stronger thermal emission, whereas the profiles of nonthermal and polarized emission are nearly identical on either side of the minor axis. This suggests that recent star formation does not lead to a local increase of the number of relativistic electrons and/or magnetic field strength. (2) We discuss several properties of the polarized emission from M 31 and their implications for the magnetic field. At lambda 6.2 cm the polarized intensity systematically varies along the bright ``ring'' of emission which shows that the regular magnetic field, Breg, is nearly aligned with the spiral arms forming this ``ring''. The variation of the rotation measures between lambda 11.1 cm and lambda 6.2 cm, RM(11, 6), across the galaxy confirms this alignment. The nonthermal degree of polarization reaches values >50% near the polarization maxima, implying that the magnetic field in M 31 is exceptionally regular. (3) We derived the distribution of the nonthermal depolarization between lambda 11.1 cm and lambda 6.2 cm, DPn(11,6), which is a measure of Faraday depolarization. Gradients in RM(11, 6) may be an important cause of Faraday depolarization in M 31. The lack of anticorrelation between the thermal emission, which comes mainly from dense H Ii regions with small filling factors, and RM(11, 6) and DPn(11,6) indicates that rotation measures and Faraday depolarization originate in the extended diffuse ionized gas.
Article
The origin of magnetic fields in space is one of the outstanding problems in astrophysics. The possible origin from neutron creation, alignment in the intergalactic field, and decay is suggested. It is shown that only a small proportion of the neutron decay energy is needed to create the field. The aligned-neutron hypothesis is compared with the possible creation of magnetic fields by cosmic radio sources, and a laboratory experiment on aligned radioactive ions is suggested. (D.J.C.)
Article
A steady-state two-dimensional model of the outermost region of a spiral galaxy is presented. The magnetic field, which is able to explain the flat rotation curve, is calculated, without the existence of any kind of dark matter. The vertical and radial distributions of the density are calculated, as well as the radial and vertical velocities. The magnetic field strength is noticeably constant in the peripheral disc, at about 7x10^-7 gauss, much more moderate than that obtained in our previous model (Battaner et al.). The vertical velocities are driven by Parker's instabilities and induce a moderate escape of gas of about 0.1 M_solar yr^-1 which prevents excessive flaring.