GHASP: an H{\alpha} kinematic survey of spiral and irregular galaxies -- IX. The NIR, stellar and baryonic Tully-Fisher relations

Abstract

We studied, for the first time, the near infrared, stellar and baryonic
Tully-Fisher relations for a sample of field galaxies taken from an homogeneous
Fabry-Perot sample of galaxies (the GHASP survey). The main advantage of GHASP
over other samples is that maximum rotational velocities were estimated from 2D
velocity fields, avoiding assumptions about the inclination and position angle
of the galaxies. By combining these data with 2MASS photometry, optical colors,
HI masses and different mass-to-light ratio estimators, we found a slope of
4.48\pm0.38 and 3.64\pm0.28 for the stellar and baryonic Tully-Fisher relation,
respectively. We found that these values do not change significantly when
different mass-to-light ratios recipes were used. We also point out, for the
first time, that rising rotation curves as well as asymmetric rotation curves
show a larger dispersion in the Tully-Fisher relation than flat ones or than
symmetric ones. Using the baryonic mass and the optical radius of galaxies, we
found that the surface baryonic mass density is almost constant for all the
galaxies of this sample. In this study we also emphasize the presence of a
break in the NIR Tully-Fisher relation at M(H,K)\sim-20 and we confirm that
late-type galaxies present higher total-to-baryonic mass ratios than early-type
spirals, suggesting that supernova feedback is actually an important issue in
late-type spirals. Due to the well defined sample selection criteria and the
homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies
can be used as a reference for the study of this relation in other environments
and at higher redshifts.

Full text

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arXiv:1106.0505v1 [astro-ph.CO] 2 Jun 2011
Mon. Not. R. Astron. Soc. 000, 1–13 (2011) Printed 6 June 2011(MN LATEX style file v2.2)
GHASP: an Hα kinematic survey of spiral and irregular
galaxies – IX. The NIR, stellar and baryonic Tully-Fisher
relations.⋆
S. Torres-Flores1,2,3†, B. Epinat1,4, P. Amram1, H. Plana1,5, C. Mendes de Oliveira2
1Laboratoire d’Astrophysique de Marseille, Universit´ e de Provence & CNRS,
38 rue F. Joliot–Curie, 13388 Marseille, Cedex 13, France
2Departamento de Astronomia, Instituto de Astronomia, Geof´ ısica e Ciˆ encias Atmosf´ ericas da USP,
Rua do Mat˜ ao 1226, Cidade Universit´ aria, 05508-090, S˜ ao Paulo, Brazil
3Departamento de F´ ısica, Universidad de La Serena, Av. Cisternas 1200 Norte, La Serena, Chile
4Institut de Recherche en Astrophysique et Plan´ etologie, Universit´ e de Toulouse & CNRS,
14 avenue Edouard Belin, 31400 Toulouse, France
5Laborat´ orio de Astrof´ ısica Te´ orica e Observacional, Universidade Estadual de Santa Cruz, Ilh´ eus, Brazil
ABSTRACT
We studied, for the first time, the near infrared, stellar and baryonic Tully-Fisher
relations for a sample of field galaxies taken from an homogeneous Fabry-Perot sample
of galaxies (the GHASP survey). The main advantage of GHASP over other samples
is that maximum rotational velocities were estimated from 2D velocity fields, avoiding
assumptions about the inclination and position angle of the galaxies. By combining
these data with 2MASS photometry, optical colors, HI masses and different mass-to-
light ratio estimators, we found a slope of 4.48±0.38 and 3.64±0.28 for the stellar and
baryonic Tully-Fisher relation, respectively. We found that these values do not change
significantly when different mass-to-light ratios recipes were used. We also point out,
for the first time, that rising rotation curves as well as asymmetric rotation curves
show a larger dispersion in the Tully-Fisher relation than flat ones or than symmetric
ones. Using the baryonic mass and the optical radius of galaxies, we found that the
surface baryonic mass density is almost constant for all the galaxies of this sample.
In this study we also emphasize the presence of a break in the NIR Tully-Fisher
relation at MH,K ∼–20 and we confirm that late-type galaxies present higher total-
to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback
is actually an important issue in late-type spirals. Due to the well defined sample
selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation
for GHASP galaxies can be used as a reference for the study of this relation in other
environments and at higher redshifts.
Key words: galaxies: evolution – galaxies: kinematics and dynamics
1 INTRODUCTION
The Tully-Fisher relation (Tully & Fisher, 1977) is a di-
rect indication of a close relationship between the detected
baryons and the total mass in spiral galaxies. The detected
baryons consist of the stellar and gaseous content, i.e. the
visible mass, and this sets the luminosity profile of the galaxy
while the total gravitational mass, which includes the dark
matter content (and possibly a component of baryonic dark
⋆GHASP
http://fabryperot.oamp.fr
† Current address. E-mail: storres@dfuls.cl
Fabry-Perotdata are availableat
matter), sets its rotation velocity. Numerous studies have
been carried out to investigate this relation, crucial in de-
termining extragalactic distances (e. g. Pierce & Tully 1988,
Tully & Pierce 2000), in the study of evolution of galax-
ies (e.g. Puech et al. 2008) and also in giving constraints
on cosmological galaxy formation models (e. g. Portinari &
Sommer-Larsen 2007).
The Tully-Fisher relation is undoubtedly a crucial test
for galaxy evolution models and although it has been the
focus of a number of studies, its origin is still being debated.
A few authors argue a cosmological origin (e. g. Avila-Reese,
Firmani & Hern´ andez 1998) while others suggest that this

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2S. Torres–Flores et al.
relation is regulated by star forming processes (e. g. Silk
1997). On the other hand, the Tully-Fisher relation is related
to the stellar populations of galaxies as it is suggested by its
steeper slope when the luminosity is measured in the near
infrared (NIR) bands, when compared to the slope measured
in the optical (e.g. Tully & Pierce, 2000). The use of NIR
bands in the Tully-Fisher relation has shown to be extremely
useful, because NIR bands present lower internal extinction
than optical bands (Verheijen 2001) and the mass-to-light
ratio is less contaminated by younger stellar populations,
giving a better reflection of the stellar mass of the galaxies.
Luminosities can be converted into stellar masses by
scaling them by a given mass-to-light ratio. Thus, instead
of linking rotation velocities to luminosities, a few authors
have chosen to show the correlation of rotation velocities
to stellar masses. This relation is called stellar Tully-Fisher
relation (e.g. Bell & de Jong 2001). In order to estimate
the whole baryonic mass, the gaseous component should be
added to the stellar mass. The relation between luminosities
and baryonic masses is called the baryonic Tully-Fisher re-
lation. This relation has been studied by several authors (e.
g. McGaugh 2000, Verheijen 2001, Geha et al. 2006, Bell &
de Jong 2001). The slope of the baryonic TF relation is an
important test for galaxy formation models. A steeper slope
indicates that the baryonic mass of massive galaxies tends
to approximately match the total mass of the galaxy.
To date, most of the works devoted to study the Tully-
Fisher relation have used compilations of several galaxy sur-
veys, observed in different ways (HI line profiles and rotation
curves) adding factors of uncertainties due to sample non-
homogeneity. Beside the problems of using different samples,
the use of certain observational techniques may add other
uncertainties in the study of the Tully-Fisher relation. For
example, an over or under prediction of the position angle
in long-slit observation could produce an erroneous estimate
of the maximum velocity of a galaxy, which will be reflected
in the Tully-Fisher relation.
In order to avoid the problems listed in the previous
paragraph, we have made use of the homogeneous galaxy
survey Gassendi HAlpha survey of SPirals (GHASP) to
study the NIR, stellar and baryonic Tully-Fisher relations
and their implications for the total mass of galaxies. The
GHASP survey represents a large effort to constitute a sam-
ple of field galaxies in an homogeneous way. First, a strict
isolation criterion has been used to insure the isolation of the
galaxies. Rather close galaxies have been chosen in order to
guarantee a high spatial resolution, compared to HI surveys.
High and low inclination objects have been excluded in order
to minimize uncertainties in the de-projected rotation curve.
Second, all GHASP galaxies have been observed using the
same instrument; a scanning Fabry-Perot attached to a focal
reducer at the 193 cm at Observatoire de Haute Provence
(OHP). In addition to obtaining data for the whole sample
with the same instrument, which is a great advantage to in-
sure homogeneity, the scanning Fabry-Perot is certainly the
most adapted instrument to obtain rotation curves in the
most proper way. Because it gives a 2D velocity field, we
can obtain the rotation curve (and the maximum velocity)
without any previous assumptions about the position angle
or the inclination like it is the case for long-slit observations.
This technique avoids, in this way, a great factor of uncer-
tainty that is common to not be taken into account using
other techniques. Third, the data reduction has been per-
formed in an homogeneous way, in order to derive the rota-
tion curves from the velocity fields in the cleanest and most
rigorous possible way (see Epinat et al. 2008a,b for details).
These three points allowed eliminating (or at least greatly
minimizing) several problems that previous studies have en-
countered. Using rotation curves to obtain the maximum
rotation velocity is a more precise way compared to the HI
line width profile technique, used by several others studies.
The higher spatial resolution of optical velocity maps, com-
pared to HI, avoids the problem of missing the maximum
velocity because of lack of resolution (beam smearing).
Together with the kinematic information, we have used
H and K-band photometry from 2MASS survey, mass-to-
light ratios derived from stellar population models, HI fluxes
and H2 masses from the literature to perform, for the first
time, the NIR, stellar and baryonic Tully-Fisher relations
for the GHASP sample.
In §2 we describe the data, including the method used
to compute the stellar, gaseous and baryonic masses. In §3,
we present the results. In §4 we discuss and compare our
results with previous works. Finally, we summarize our main
findings in §5.
2 DATA
2.1 Rotational velocities
GHASP is the largest sample of spiral and irregular galax-
ies observed to date using Fabry-Perot techniques. It con-
sists of 3D Hα data cubes for 203 galaxies, covering a large
range in morphological types and absolute magnitudes. All
the GHASP galaxies have been recently reanalyzed in a ho-
mogeneous way in Epinat et al. (2008a,b). These authors
published velocity fields, monochromatic Hα images, disper-
sion velocity maps, rotation curves and maximum rotation
velocities (Vmax) for each galaxy.
A sub-sample of 93 galaxies has been selected by remov-
ing from the sample: 1) galaxies with radial systemic veloci-
ties lower than 3000 km s−1(to avoid the effect of the Local
Group infall) for which no other individual measurements
of distances were available (the references are indicated in
Epinat et al. 2008b) and 2) galaxies with inclinations lower
than 25 degrees for which the uncertainties on the rotational
velocity is comparatively high.
Rotation curves shown in Epinat et al. (2008a,b) present
a large variety of shapes (from falling to rising) and degrees
of asymmetry. In order to study the influence of the shape
of the rotation curves in the Tully-Fisher relation, we have
made a classification of our sample in three subsamples, i.
e. rising, flat and decreasing rotation curves, which will be
described with the letters “R”, “F” and “D”, respectively.
An “+” or ‘–” sign has been added if the rotation curve is
respectively more or less extended than the optical radius
of the galaxy (R25). No symbol is added if the radius of the
observed rotation curve is barely equal to R25.
A decreasing or flat rotation curve displays a clear
Vmax. This is not the case for a rotation curve which rises
up to the very last observed radius, for which Vmax is possi-
bly underestimated. This is even worse if the rising rotation
curve does not reach the optical radius. In this case, Vmax

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GHASP: The baryonic Tully-Fisher relation for field galaxies3
was computed at R25 by extrapolating an arctan function
(V (r) = V0×(2/π)×arctan(2r/rt), where rt is the core ra-
dius) to the rotation curves. If observed rotational velocities
at R<R25 are higher than the modeled value, the observed
values have been used. This could be the case if large scale
bumps in the inner parts of rotation curves are present. Ta-
ble A1 (column 8) presents the results of the rotation curve
quality assessments.
The main assumption necessary to derive a rotation
curve from the observed velocity field is that rotation mo-
tions are dominant and non circular motions are not part
of a large-scale pattern. Thus, by construction, a rotation
curve provides a measurement, for each radius, of the axi-
symmetric component of the gravitational potential well of
the galaxy. By consequence, if the motions in the galaxy disk
are purely circular, the receding and the approaching sides
of a rotation curve should match and the residual velocity
field should not display any structure. Once the parame-
ters of the rotation curves are properly computed by mini-
mizing the velocity dispersion in the residual velocity field
(Epinat et al. 2008), the remaining residuals are the signa-
ture of non-circular motions in or out the plane of the disk (e.
g. bars, oval distortions, spiral arms, local inflows and out-
flows, warps), including the intrinsic turbulences of the gas.
To quantify the effects of these non-circular motions on the
Tully-Fisher relations we have computed, for each galaxy,
two indicators. The first one is based on the asymmetries
between both sides of the rotation curves, it quantifies the
mean difference of amplitude between the receding and ap-
proaching sides of the rotation curve. For each ring centered
on the galaxy center, the weighted (absolute) velocity differ-
ence between both sides is computed. The weight is provided
by the number of bins in each ring. Each bin is an indepen-
dent velocity measurement on the velocity field, it may be
constituted by ∼50 pixels for low signal-to-noise region of
the galaxy. Depending of the spatial resolution, each ring
contains from two to several hundreds bins. Due to the fact
that their radius are smaller, the central rings contains a
number of pixels lower than the outer ones, their weights
is thus smaller. The second indicator is based on the mean
velocity dispersion extracted from the residual velocity field.
This parameter is quantified by computing the average lo-
cal velocity dispersion on the whole residual velocity field.
To not overestimate the weight of non circular motion in
slowly rotating systems with respect to high rotators, both
indicators have been normalized by the maximum rotation
velocity. We found that both indicators show the same trend
on the Tully-Fisher relation, thus we will only illustrate the
results using the indicator related to the asymmetries in the
rotation curve.
2.2 Photometry
We computed the near-infrared magnitudes using 2MASS
data (Skrutskie et al. 2006). 2MASS H and K-band data
were available for 83 galaxies of the GHASP sub-sample de-
fined in section §2.1. Absolute magnitudes were obtained
using:
MH,K = mH,K+ (kH,K− AH,K) − 5 × log(D) − 25(1)
Distances (D) were taken from Epinat et al. (2008b).
They are computed from the systemic velocities (from the
NED database) corrected from Virgo infall and assuming
H0=75 km s−1Mpc−1, except when accurate distance mea-
surements where available (references are listed in Epinat et
al. 2008b). The magnitudes mH,K have been computed us-
ing the flux within the isophote of 20 mag arcsec−1(where
uncertainties were taken from 2MASS). We corrected the
magnitude for Galactic extinction using the Schlegel maps
(Schlegel et al. 1998). k-corrections (kH,K), extinction due
to the inclinations (AH,K) and seeing were applied using the
method given in Masters et al. (2003). Columns 1, 2 and 3
in Table A1 list the name, H and K-band absolute magni-
tudes for the sample. K-band luminosities were estimated
using LK=10−0.4(MK−3.41), where the K-band absolute So-
lar magnitude of 3.41 was taken from Allen (1973).
Given the homogeneity of the Sloan Digital Sky Survey
(SDSS), g and r-band optical magnitudes were extracted
from this database. Moreover, most of the mass-to-light ra-
tio recipes use B-V colors as an input parameter. For this
reason, we have converted g and r-band data into B and
V-band magnitudes by using the recipes given in Lupton
(2000). We have extracted the optical size for each galaxy
from the SDSS. In this case, we used the parameter isoA
(in the r-band), which corresponds to the diameter of the
isophote where the disk surface brightness profile drops to
25 mag arcsec−2. These values were converted in radii (in
kpc) by using the distance to each galaxy.
In order to compute the mass-to-light ratio for GHASP
galaxies, g-r colors were corrected by Galactic extinction
using the values given in the SDSS database and then con-
verted into B-V colors. SDSS colors were available for 45
galaxies from which we removed five objects for which their
magnitudes and optical radius are obviously incorrect (com-
pared with the optical radius, and magnitudes, given in Hy-
perLeda). For other six galaxies, there were no radius mea-
surement. All the analysis including the radius of the galax-
ies were thus performed with 34 objects.
B-bandluminosities were
LB=10−0.4(MB−5.48), where the B-band absolute Solar
magnitude of 5.48 was taken from Binney & Merrifield
(1998).
estimated byusing
2.3Mass-to-light ratios and stellar masses
The main uncertainty in the study of the stellar and baryonic
Tully-Fisher relations states in the stellar mass-to-light disk
ratio Υ⋆. Two main methods to estimate this parameter are
used. Spano et al. (2008) have modeled the stellar mass dis-
tribution of rotation curves, by scaling the R-band surface
brightness profile to the rotation curve, obtaining an esti-
mation of Υ⋆. Bell & de Jong (2001) have used stellar pop-
ulations synthesis models to predict a relation between the
colors of galaxies and their Υ⋆. Although both approaches
attempt to compute the same physical parameter, several
authors have shown that surprisingly there seems to be no
clear correlation between the Υ⋆ obtained from these two
methods (e.g. Barnes et al. 2004). Other authors have in-
voked the modified Newton dynamics (MOND) to obtain the
Υ⋆and study its implication on the baryonic Tully-Fisher re-
lation (McGaugh 2005). In this work, we have estimated Υ⋆
and stellar masses using stellar population synthesis models
recipes. One of them consists of simply fixing the value of
Υ⋆. We have compared our results with other works available

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4 S. Torres–Flores et al.
in the literature following the stellar populations synthesis
models given by Bell & de Jong (2001, B&J), Bell et al.
(2003, BE) and Portinari et al. (2004, PO) (equations 2 and
3, 4 and 5 and 6 respectively).
MB&J
⋆
= 10−0.692+0.652(B−V )LK
(2)
MB&J
⋆
= 10−0.994+1.804(B−V )LB
(3)
MBE
⋆
= 10−0.206+0.135(B−V )LK
(4)
MBE
⋆
= 10−0.942+1.737(B−V )LB
(5)
MPO
⋆
= 100.730[(B−V )−0.600]−0.115LK
(6)
B&J and BE suggested an uncertainty of 0.1 dex in the
Υ⋆estimation. The adopted uncertainty in Υ⋆is larger than
the uncertainties of the optical colors. We have adopted the
same uncertainty for the PO relation. B&J used a scaled
Salpeter initial mass function (IMF). PO used a Salpeter
IMF, with masses ranging between 0.1 and 100 M⊙. These
models are available for several colors (to estimate Υ⋆) and
also for the luminosity in several bands (to estimate the
stellar mass). We have converted SDSS g-r colors into B-
V colors to obtain the Υ⋆ parameter by using the recipes
listed above. Stellar masses were calculated using the K-
band luminosities. This band is more likely to be reflective
of the stellar mass of galaxies. In order to compare stel-
lar masses derived from the K-band luminosities, we have
also used the B-band luminosity, despite the fact that this
photometric band could be contaminated with the emission
of young stars. We removed from this analysis galaxies for
which no SDSS colors were available in the literature. There-
fore, in the stellar and baryonic analysis, we were left with 45
galaxies in total. K-band luminosities were estimated using
LK=10−0.4(MK−3.41)(see section 2.2).
Stellar masses were also estimated using a fixed mass-
to-light ratio following McGaugh et al. (2000, MG). These
authors defined the mass-to-light ratio in the K-band as
Υ⋆ = 0.8M⊙/L⊙. In this case, the stellar mass is simply:
MMG
⋆
= Υ⋆LK
(7)
It is interesting to note that Gurovich et al. (2010) esti-
mated the Υ⋆for a sample of local galaxies by modeling their
stellar population histories. These authors did not find dif-
ferences in the Tully-Fisher relation when the stellar masses
were computed by using the modeled Υ⋆ or when this pa-
rameter was fixed to Υ⋆=0.8 (McGaugh et al. 2000).
2.4 Baryonic masses
The mass of a galaxy is constituted of its content in stars and
stellar remnants, gas (neutral, molecular and a negligible
component of ionized gas), dust (usually negligible) and dark
matter. The baryonic mass is the sum of the stellar and gas
contents. The total mass in gas, Mgas, is:
Mgas = MHI + MHe+ MH2+ (MHII) (8)
where MHI is the neutral gas, MHeis the mass in helium
and metals, MH2is the mass in molecular hydrogen and
MHII is the (negligible) mass in ionized hydrogen.
In order to obtain the baryonic mass for the GHASP
sample we have calculated the observed HI mass for each
galaxy using the corrected 21-cm line flux taken from Hy-
perLeda (Paturel et al. 2003). Fluxes were converted into
mass using the relation:
MHI = 2.356 × 105FHID2
(9)
where D is the distance to the galaxy in Mpc, and FHI
is the HI flux in Jy km−1.
To take into account the correction for helium and met-
als in the gas content (e. g. McGaugh et al. 2000), MHe is
related to the HI mass through:
MHe = 0.4MHI
(10)
The H2 mass has been computed following the formula
given by McGaugh & de Blok (1997), using the morpholog-
ical type of the galaxies (Young & Knesek, 1989).
MH2= MHI(3.7 − 0.8T + 0.043T2)(11)
Nevertheless, to avoid uncertainties linked to our bad
knowledge in the H2 content, the baryonic mass studied in
this paper does not include H2, except when it is explicitly
mentioned. The baryonic mass, Mbar, is defined as:
Mbar= M⋆+ Mgas
(12)
where M⋆ is the total stellar mass. Uncertainties in the
baryonic mass are the results of the quadratic sum of the
uncertainties in stellar masses and uncertainties in the H I
masses, which were taken from HyperLeda.
We have compared the baryonic mass to the total dy-
namical mass for each galaxy of our sample. Although al-
most the whole baryonic mass is approximately within the
optical radius, the total dark matter content is not, thus we
compute the dynamical total mass only within the optical
radius. To estimate the total dynamical mass, we assumed
the mass has a spherical distribution, which is likely the
case for the dark halo component, as supported by observa-
tions (e.g. Ibata et al. 2001) and N-body simulations (e.g.
Kazantzidis et al. 2010) by using:
M(R) = αR × V2
max/G(13)
where α is a parameter depending on the mass profile
distribution (equal to one for an uniform distribution). To
compute M(R) we have used the r-band optical radius from
SDSS, as tabulated in the Appendix. In order to obtain an
estimation of the dark matter content at the optical radius,
we have subtracted the baryonic mass (as estimated in §2.5)
from the dynamical total mass within the optical radius.
2.5 Fitting method
Galaxies having the same rotational velocity do not neces-
sarily have the same luminosity (or reciprocally), thus the
observed Tully-Fisher relation presents a dispersion which
may be produced by intrinsic properties of galaxies. Beside
this dispersion, uncertainties in magnitudes/masses and ro-
tational velocities should be taken into account when the
slope and zeropoint of this relation are computed (see Hogg
et al. 2010 for details about fitting straight lines). Several
efforts have be performed to fit straight lines to fundamen-
tal relations, taken into account together the uncertainties
in both axis and the intrinsic dispersion of the relation (e.
g. Tremaine et al. 2002, Weiner et al. 2006). In this paper,

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GHASP: The baryonic Tully-Fisher relation for field galaxies5
we have followed the prescription given by Tremaine et al.
(2002), by adding (in quadrature) a dispersion factor to the
uncertainties estimation of the NIR magnitudes, stellar and
baryonic masses. The value of the dispersion factor is cho-
sen in order to reach a χ2of unity per degree of freedom. To
fit the Tully-Fisher relation, we used linear relation of the
form:
y = αx + β (14)
where, y = MH,K and y = log(M/M⊙), for the NIR
and stellar/baryonic Tully-Fisher relation, respectively, and
x = log(Vmax/kms−1). To obtain the slope and the zerpoint
of this relation, we used the task FITEXY (Press et al. 1992).
3 RESULTS
In Table A1 we list the NIR magnitudes and the different
rotational velocities that we obtained, from the observations
and from the arctan model (see §2.1). Columns 1, 2 and 3
list the name, H and K-band magnitudes. Column 4 shows
the observed maximum rotational velocity for each galaxy.
Column 5 gives the modeled velocity at R25. Column 6 cor-
responds to the rotational velocity used in the TF relation.
Finally, in column 7 we classify the shape of rotation curves
of the GHASP sample as shown in §2.1.
In Table A3 we list the different determinations of mass-
to-light ratios (Υ⋆) and masses for each galaxy. Columns 1, 2
and 3 indicate respectively the name, the radius of the galax-
ies (taken from SDSS) and the B-V colors (transformed from
g-r colors). In columns 4, 5 and 6 we list the mass-to-light
ratios calculated from equations 2, 4 and 6, respectively.
Values for the stellar masses are shown in columns 7, 8 and
9, following B&J, BE and PO, respectively. In column 10,
we list the MHI+MHe, where MHI is calculated using the
observed HI mass for the GHASP sample. Column 11 cor-
responds to the baryonic masses excluding the H2 content
(M⋆+MHI+MHe), M⋆ is here calculated following BE given
in column 8.
3.1H and K-band TF relations
In Fig. 1 (upper panels) we plot the Tully-Fisher relations
for the H and K-band (left and right panels, respectively).
In both panels, flat, decreasing and rising rotation curves
are indicated by black dots, green triangles and red stars,
respectively. Galaxies having a rising rotation curve show a
large dispersion on the Tully-Fisher relation, while most of
the flat rotation curves lie on the relation. This may simply
reflect the scatter in the determination of Vmax for rising
rotation curves, for which Vmax may be uncertain. Alterna-
tively, this might indicated that rising rotation curves, that
are usually dark matter dominated galaxies, show an intrin-
sic scatter in the Tully-Fisher relation. In the bottom panel
of Fig. 1 we plot the K-band Tully-Fisher relation in which
we divided the sample by their asymmetries in the rotation
curve. Galaxies displaying the largest non-circular motions
(red stars) lie preferentially in the low velocity/luminosity
region of the plot and present a larger scatter than galaxies
less affected by non circular motion (black dots). The conclu-
sion is that non-circular motions contribute to the scatter in
the NIR Tully-Fisher relation, at least in the low luminosity
(and mass) region of the plot.
Inspecting Fig. 1, we observe a break in the Tully-Fisher
relation at MH,K ∼-20. This effect has already been noted by
McGaugh et al. (2000), Gurovich et al. (2004) and Amor´ ın
et al. (2009). In order to quantify this break, we have applied
a fit (as discusses in §2.5) to all galaxies (black dashed line)
and to the galaxies with MK <-20 (red dotted-dashed lines).
For the first case, we have derived the followings equations:
MH = (1.97 ± 1.36) − (10.84 ± 0.61)[log(Vmax)] (15)
where we use a dispersion factor of 0.75 in the H-band
magnitude.
MK = (2.27 ± 1.39) − (11.07 ± 0.63)[log(Vmax)] (16)
where we use a dispersion factor of 0.76 in the K-band
magnitude.
For galaxies with MK <–20, we have derived:
MH = (−4.29 ± 1.14) − (8.18 ± 0.50)[log(Vmax)] (17)
where we use a dispersion factor of 0.47 in the H-band
magnitude.
MK = (−4.02 ± 1.17) − (8.39 ± 0.52)[log(Vmax)](18)
where we use a dispersion factor of 0.49 in the K-band
magnitude.
In the equations above we have included the one-sigma
uncertainties in the slope and zero point. Three galaxies
(∼4% of the sample) are 1σ off the Tully-Fisher relation.
These galaxies could have slightly too high magnitudes for
their rotational velocities or too low rotational velocities for
their magnitudes (upper left region in each panel of Fig. 1).
In spite of the rotation curves of these objects reach the
optical radius R25, two of them have rising rotation curves
(red stars in the left panels of Fig. 1). In this sense, we can
not exclude that both galaxies could have higher rotational
velocities than the observed values, placing both galaxies on
the TF relation. On the other hand, one galaxy has a flat
rotation curve (black dot in Fig. 1), meaning that this ob-
ject already reached its maximum rotational velocity. Two
possible scenarios could explain the high near-infrared mag-
nitude of this galaxy. AGN activity, that could enhance the
near-infrared magnitude of Seyfert 1 galaxies (Riffel et al.
2009) and/or the contribution of TP-AGB stars into the K-
band luminosity (Maraston 1998). TP-AGB stars are often
not taken into account in the models and they are quite im-
portant specially for stellar populations with ages below 1
Gyr. A detailed study of this galaxy is out of the scope of
this paper.
Taking into account the dispersions, the slopes of the H
and K-band TF relations are similar, being slightly steeper
in the K-band. Table 1 summarizes the fit parameters (de-
noted by α for slopes and β for the zero points) found for
the TF relation in H and K-bands. In the same table we list
values of α and β found in the literature.
3.2The stellar TF relation
In order to compare different estimators of the stellar mass
available in the literature, we have calculated the slope and
zero points of the stellar TF relations of our GHASP sample