J/MNRAS/505/4048 WISDOM Project IX study of GMCs in NGC 4429 (Liu+, 2021)
WISDOM Project. IX. Giant molecular clouds in the lenticular galaxy NGC 4429:
effects of shear and tidal forces on clouds
Liu L., Bureau M., Blitz L., Davis T.A., Onishi K., Smith M., North E.,
Iguchi S.
<Mon. Not. R. Astron. Soc., 505, 4048-4085 (2021)>
=2021MNRAS.505.4048L 2021MNRAS.505.4048L (SIMBAD/NED BibCode)
ADC_Keywords: Galaxies, radio ; Interstellar medium ; H II regions ;
Molecular clouds; Molecular data ; CO ; Line Profiles ;
Millimetric/submm sources ; Photometry, millimetric/submm
Keywords: ISM: clouds - galaxies: elliptical and lenticular, cD -
galaxies: individual: NGC 4429 - galaxies: ISM - galaxies: nuclei -
submillimetre: ISM
Abstract:
We present high spatial resolution (~= 12 pc) Atacama Large
Millimeter/submillimeter Array 12CO(J = 3-2) observations of the
nearby lenticular galaxy NGC 4429. We identify 217 giant molecular
clouds within the 450 pc radius molecular gas disc. The clouds
generally have smaller sizes and masses but higher surface densities
and observed linewidths than those of Milky Way disc clouds. An
unusually steep size-linewidth relation
(σ∝Rc0.8) and large cloud internal velocity
gradients (0.05-0.91 km/s/pc) and observed virial parameters
(<αobs,vir> ~= 4.0) are found, which appear due to internal
rotation driven by the background galactic gravitational potential.
Removing this rotation, an internal virial equilibrium appears to be
established between the self-gravitational (Usg) and turbulent kinetic
(Eturb) energies of each cloud, i.e.
<αsg,vir> ∼ 2Eturb/|Usg| ∼ 1.3.
However, to properly account for both self and external gravity (shear
and tidal forces), we formulate a modified virial theorem and define
an effective virial parameter
αeff,vir ∼ αsg,vir+Eext/|Usg|
(and associated effective velocity dispersion).
The NGC 4429 clouds then appear to be in a critical state in which the
self-gravitational energy and the contribution of external gravity to
the cloud's energy budget (Eext) are approximately equal, i.e.
Eext/|Usg| ~= 1. As such,
<αeff,vir> ~= 2.2 and most clouds are not virialized but remain
marginally gravitationally bound. We show this is consistent with the
clouds having sizes similar to their tidal radii and being generally
radially elongated. External gravity is thus as important as
self-gravity to regulate the clouds of NGC 4429.
Description:
This paper is the first of a series studying the GMCs in WISDOM
galaxies, and it introduces many of the methods and tools we will use
to identify GMCs and analyse their properties and dynamics.
The mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) aims
to use the high angular resolution of the Atacama Large
Millimeter/submillimeter Array (ALMA) to study the masses and
properties of the supermassive black holes (SMBHs) lurking at the
centres of galaxies and the physical properties and dynamics of GMCs
in the central parts of the same galaxies. As part of WISDOM, we
analyse here the properties and dynamics of individual GMCs in the
bulge of NGC 4429, an SA0-type galaxy located in the centre of the
Virgo cluster, with a bar and stellar inner ring morphology (Alatalo
et al. 2013MNRAS.432.1796A 2013MNRAS.432.1796A).
NGC 4429 was observed in the 12CO(3-2) line (345 GHz). The data were
calibrated and reduced in a standard manner (Davis et al.
2018MNRAS.473.3818D 2018MNRAS.473.3818D), and the final 12CO(3-2) data cube we adopt has a
synthesized beam covers a region of 17.5 arcsec * 17.5 arcsec (1400 *
1400 pc2), thus comprising the entire nuclear dust and molecular gas
disc. Our spatial and spectral resolutions allow for reliable
estimates of the radii and velocity dispersions of individual GMCs,
which have a typical size of ~= 50 pc (Blitz 1993 , eds, Protostars
and Planets III. University of Arizona Press, Tucson, Arizona, p. 125)
and a typical linewidth of several km/s (e.g. Solomon et al.
1987ApJ...319..730S 1987ApJ...319..730S). As CO(3-2) is excited in denser and warmer gas
than CO(1-0), we are likely to identify a cloud population that is
associated with H II regions and thus ongoing star formation at the
centre of NGC 4429 only.
The resulting sample of GMCs in NGC 4429 contains 217 GMCs, 141 of
which are spatially resolved, shown in Fig. 3. The majority of the
resolved clouds have a single-peaked Gaussian-like spatially
integrated line profile, although a few do reveal a double-peaked line
profile possibly indicating significant rotation. We calculate the
physical properties of the clouds by following the standard
cpropstoo/cprops definitions (Rosolowsky & Leroy 2006PASP..118..590R 2006PASP..118..590R).
The cpropstoo algorithm applies moment methods to derive the size,
linewidth, and flux of a cloud from its distribution within a
position-position-velocity data cube.
The table1.dat contains the positions and properties of the 217 GMCs
identified in our work. Around 65 percents of the GMCs identified are
resolved spatiallyand all are resolved spectrally. As our primary beam
covers all the CO emission in NGC 4429, our derived GMC catalogue is
complete at 12CO(3-2). The table1.dat lists each cloud's
identification number, central position in both RA and Dec., local
standard of rest velocity VLSR, radius Rc, observed velocity
dispersion σobs,los and gradient-subtracted velocity dispersion
σgs,los, the total CO(3-2) luminosity LCO(3-2), gaseous mass
Mgas, peak intensity Tmax, angular velocity ω , position angle of
the rotation axis φrot (see Section 4.1), and deprojected distance
from the centre of the galaxy Rgal.
Further in our study, we focused on cloud kinematics and dynamical
state of the GMCs clouds (see section 4 and 5). In section 5, we
derived properties (from our gas dynamical model see Section 4.2 and
Fig. 10) of the clouds in NGC 4429 such as Ω0 the circular
orbital angular velocity at the cloud's centre of mass (CoM), T0 the
tidal acceleration parameter at cloud's CoM, σeff,los the
effective linewidth or velocity dispersion of each cloud measured for
the 141 spatially resolved clouds of NGC 4429 and logarithm of
ρ*,0) which is the stellar mass volume density at the
cloud's CoM calculated with the MGE formalism (see appendix c :
stellar density calculation). All these 4 variables constitute the
table3.dat.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 111 217 *Observed properties of the clouds in NGC 4429
table3.dat 41 217 *Derived properties of the clouds in NGC 4429
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Note on table1.dat: All uncertainties are quoted at the 1 sigma level.
As noted in the text, the uncertainty of the adopted distance D to NGC 4429
was not propagated through the tabulated uncertainties of the measured
quantities. This is because an error on the distance to NGC 4429 translates to
a systematic (rather than random) scaling of some of the measured quantities
(no effect on the others), i.e. Rc ∝ D, LCO(3-2) ∝ D2,
Mgas ∝ D2, ω ∝ D-1, and Rgal ∝ D.
Note on table3.dat: All uncertainties are quoted at the 1 σ level, and
those of σeff,los have been propagated from the uncertainties of both
observed and modelled quantities (see equation 38 section 5.5.3
Effective parameters). As noted in the text, the uncertainty of the adopted
distance D to NGC 4429 was not propagated through the tabulated uncertainties
of the quantity σeff,los. This is because an error on the distance
to NGC 4429 translates to a systematic (rather than random) scaling of some
of the measured quantities (no effect on the others), here Rc ∝ D,
Ω0 ∝ D-1 and T0 ∝ D-2 in equation (38).
Oort's constants A and B can be derived using respectively A = T/4Ω
and B = T/4Ω - Ω.
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Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 3 I3 --- ID GMC Cloud identifier number (ID)
5- 6 I2 h RAh Right ascension (RAh) (J2000)
8- 9 I2 min RAm Right ascension (RAm) (J2000)
11- 14 F4.1 s RAs Right ascension (RAs) (J2000)
16- 17 I2 deg DEd Declination (DEd) (J2000)
19- 20 I2 arcmin DEm Declination (DEm) (J2000)
22- 25 F4.1 arcsec DEs Declination (DEs) (J2000)
27- 32 F6.1 km/s Vlsr Local standard of rest velocity (Vlsr)
34- 38 F5.2 pc Rc ? Cloud radius computed with equation 2
section 3.1.2 (R)
40- 43 F4.2 pc e_Rc ? Mean error of Rc (d_R)
45- 49 F5.2 km/s sigma Observed velocity dispersion computed
with equation 3 section 3.1.3
(sigmaobs,los)
51- 54 F4.2 km/s e_sigma Mean error of sigma (d_sigmaobs,los)
56- 59 F4.2 km/s sigmags Gradient-subtracted velocity dispersion
derived via the same bootstrapping
technique see section 3.1.8
(sigmags,los)
61- 64 F4.2 km/s e_sigmags Mean error of sigmags (d_sigmags,los)
66- 70 F5.2 10+4K.km/s.pc2 LCO The CO(3-2) luminosity of each cloud
computed with the equation 4 section
3.1.4 (LCO3-2)
72- 75 F4.2 10+4K.km/s.pc2 e_LCO Mean error of LCO (d_LCO3-2)
77- 80 F4.2 10+5Msun Mgas Cloud gaseous mass of each cloud
computed with the equation 6 section
3.1.5 (Mgas) (1)
82- 85 F4.2 10+5Msun e_Mgas Mean error of Mgas (d_Mgas)
87- 89 F3.1 K Tmax Peak intensity temperature (Tmax)
91- 94 F4.2 km/s/pc omega ? Measured angular velocity (omega)
96- 99 F4.2 km/s/pc e_omega ? Mean error of omega (d_omega)
101-103 I3 deg PA ? Position angle of the rotation axis
(phirot)
105-107 I3 deg e_PA ? Mean error on PA (d_phirot)
109-111 I3 pc Rgal The deprojected distance of a cloud
from the centre of the galaxy see
section 3.1.7 (Rgal)
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Note (1): Measurements of Mgas assume a CO(3-2)/CO(1-0) line ratio of
1.06 ± 0.15 (in beam temperature units,
Davis et al. 2018MNRAS.473.3818D 2018MNRAS.473.3818D) and a standard Galactic conversion
factor XCO = 2 * 1020 cm-2/(K.km/s) (including the mass
contribution from helium).
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Byte-by-byte Description of file: table3.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- ID GMC Cloud identifier number (ID)
5- 8 F4.2 km/s/pc Omega0 The circular orbital angular velocity at
the cloud's CoM (Omega0)
10- 13 F4.2 km/s/pc e_Omega0 Mean error of Omega0 (d_Omega0)
15- 18 F4.2 km2/s2/pc2 T0 The tidal acceleration parameter at
cloud's CoM (T0) (1)
20- 24 F5.2 km2/s2/pc2 e_T0 Mean error of T0 (d_T0)
26- 30 F5.2 km/s sigmaeff ? The effective linewidth or velocity
dispersion (sigmaeff,los) (2)
32- 36 F5.2 km/s e_sigmaeff ? Mean error on sigmaeff (d_sigmaeff,los)
38- 41 F4.2 [Msun/pc3] log(rho) The stellar mass volume density
at the cloud's CoM (3)
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Note (1): T0 = -R.dΩ(R)2/dR|R=R0 is the tidal acceleration per unit
length in the radial direction T (e.g. Stark & Blitz
1978ApJ...225L..15S 1978ApJ...225L..15S) evaluated at the cloud's CoM (R is the
galactocentric distance in the plane of the disc and R0 that of the
cloud's CoM). We note that here and throughout, Ω(R) is a
theoretical quantity see section 5.2 basic framework.
Note (2): Linewidth or velocity dispersion of each cloud measured for
the 141 spatially resolved clouds of NGC 4429.
Clouds with no σeff,los entry are unresolved spatially.
Calculations of σeff,los assume be = 1/5
(spherical homogeneous clouds).
Note (3): Calculated with the MGE formalism (see appendix c:
stellar density calculation).
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History:
From electronic version of the journal
(End) Luc Trabelsi [CDS] 03-Jun-2024