# Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

Gan Liu  Xinran Ma  Kuanyu He  Qing Li  National Laboratory of Solid State
Microstructures and Department of Physics, Nanjing University, Nanjing 210093,
China  Hengxin Tan  Yizhou Liu  Department of Condensed Matter Physics,
Weizmann Institute of Science, Rehovot 7610001, Israel  Jie Xu  Wenna Tang
National Laboratory of Solid State Microstructures and Department of Physics,
Nanjing University, Nanjing 210093, China  Kenji Watanabe  Research Center for
Functional Materials, National Institute for Materials Science, 1-1 Namiki,
Tsukuba 305-0044, Japan  Takashi Taniguchi  International Center for Materials
Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki,
Tsukuba 305-0044, Japan  Libo Gao  Yaomin Dai  Hai-Hu Wen  National Laboratory
of Solid State Microstructures and Department of Physics, Nanjing University,
Nanjing 210093, China  Collaborative Innovation Center of Advanced
Microstructures, Nanjing University, Nanjing 210093, China  Binghai Yan
<EMAIL_ADDRESS>Department of Condensed Matter Physics, Weizmann
Institute of Science, Rehovot 7610001, Israel  Xiaoxiang Xi<EMAIL_ADDRESS>National Laboratory of Solid State Microstructures and Department of Physics,
Nanjing University, Nanjing 210093, China  Collaborative Innovation Center of
Advanced Microstructures, Nanjing University, Nanjing 210093, China

Abstract

The charge-density wave (CDW) phase is often accompanied by the condensation
of a soft acoustic phonon mode, giving rise to lattice distortion and charge
density modulation. This picture was challenged for the recently discovered
kagome metal CsV3Sb5, based on the evidence of absence of soft phonons. Here
we report the observation of Raman-active CDW amplitude modes in this
material, which are collective excitations typically thought to emerge out of
frozen soft phonons. The amplitude modes strongly hybridize with other
superlattice modes, imparting them with clear temperature-dependent frequency
shift and broadening, rarely seen in other known CDW materials. Both the mode
mixing and the large amplitude mode frequencies suggest that the CDW exhibits
the character of strong electron-phonon coupling, a regime in which acoustic
phonon softening can cease to exist. The observation of amplitude modes in the
absence of soft phonons highlights the unconventional nature of the CDW in
CsV3Sb5.

Introduction

Materials with a kagome lattice can host rich phenomena encompassing quantum
magnetism [1, 2], Dirac fermions [3, 4], nontrivial topology [5, 6, 7],
density waves, and superconductivity [8, 9, 10]. The recently discovered
kagome metals $A$V3Sb5 ($A=\mathrm{K,Rb,or~{}Cs}$) [11, 12] offer a new
platform to study the interplay of these phenomena. These compounds have Fermi
levels close to Dirac points or van Hove singularities [12, 13, 14], leading
to a plethora of possible intriguing ground states. Indeed, charge-density
waves and superconductivity have been discovered [12, 15, 16], with ample
evidence showing that both types of orders are exotic. For example, the CDW
transition is accompanied possibly by a large anomalous Hall effect [17, 18],
and the superconductivity features a pair-density wave state [19].

The nature of the CDW state and the mechanism for its formation have been
under close scrutiny. In this work, we focus on CsV3Sb5, which has a CDW
transition temperature $T_{\mathrm{CDW}}=94$ K [12]. Both hard-x-ray and
neutron scattering showed the lack of soft acoustic phonons [20, 21], although
density functional theory (DFT) calculations found two phonon instabilities at
the $M$ and $L$ points of the Brillouin zone [22, 23, 24]. Considering that a
$2\times 2$ modulation of the crystal lattice is well established [12, 19, 25,
26, 27], the absence of soft modes apparently breaks a pattern proven generic
to many known CDW systems — a soft acoustic phonon freezes to zero frequency
and triggers the formation of a distorted lattice [28]. Currently, there is
still no consensus on the form of the in-plane structure and the $c$-axis
periodicity [27, 29]. The roles of Fermi-surface nesting and electron-phonon
coupling are also debated. Because the period of the $2\times 2$ superlattice
matches perfectly with the Fermiology of the van Hove singularity, it is
natural to ascribe the CDW transition to Fermi surface nesting [22], supported
by the appreciable partial gapping of the Fermi surface observed
experimentally [30, 31, 32, 33, 34]. However, the calculated electronic
susceptibility lacks the expected divergence [35, 36], and the effect of
electron-phonon coupling may not be dismissed [36, 21].

Because the CDW features lattice distortions, studies of the lattice degree of
freedom can offer insight into the mechanism. Raman scattering is a valuable
tool in this respect. In well-studied CDW systems, such as the transition
metal dichalcogenides, as a soft acoustic phonon mode condenses to form a
distorted lattice, new Raman-active collective excitations, known as amplitude
modes, emerge, providing a direct probe of the CDW order parameter [37, 38,
39] (see Fig. 1a). Conversely, the observation of amplitude modes is typically
considered as evidence for the soft mode. The temperature dependence of the
amplitude modes as well as the zone-folded modes, which become Raman-active
due to zone folding induced by the superlattice, can both reflect the CDW
transition [40, 41, 42, 43, 44]. Combined with symmetry information from
polarization-resolved measurements, constraints can be set on the possible CDW
ground state.

Here, we report Raman scattering measurements on CsV3Sb5. We observe a
multitude of CDW-induced modes, whose symmetries and frequencies are in good
agreement with DFT calculations for a single layer CsV3Sb5 under inverse Star
of David distortion. The observed temperature dependence of these modes and
their calculated evolutions with varying lattice distortion allow us to
identify two of them as amplitude modes, emerging from the predicted soft
modes, although the soft modes are elusive experimentally. In contrast to
mostly independent amplitude modes and zone-folded modes in well-known CDW
materials [41, 42, 43], we show that they hybridize strongly in CsV3Sb5,
causing spectral weight redistribution to the latter and rendering them
amplitude-mode-like. The anomalous hybridization and the large values of the
amplitude mode frequencies provide evidence of strong-coupling CDW, offering a
possible explanation for the lack of soft acoustic modes. These results stress
the importance of the lattice degree of freedom and electron-phonon coupling
in the CDW formation in CsV3Sb5.

Results
Raman-active modes in CsV3Sb5

CsV3Sb5 crystallizes in a hexagonal lattice with the $P6/mmm$ space group
[11]. Fig. 1b shows the unit cell of its crystal structure. The V atoms form a
kagome net interspersed by Sb atoms (labeled Sb1), all within the ab-plane.
The V atoms are further bonded by Sb atoms above and below the kagome plane
(labeled Sb2). These V3Sb5 slabs are separated by Cs layers, with weak
coupling between them to form a quasi-two-dimensional (quasi-2D) structure.
Factor group analysis yields three Raman-active phonon modes,
$\Gamma_{\mathrm{Raman}}=A_{1g}+E_{2g}+E_{1g}$. The former two can be detected
when the photons are polarized in the $ab$-plane, satisfied by the back-
scattering geometry used in our experiment. These intense modes are marked by
dashed lines in Figs. 1c, d. They involve only the Sb2 atoms, with their
atomic vibrations along the $c$-axis and within the $ab$-plane for the
$A_{1g}$ and $E_{2g}$ modes, respectively; see Fig. 1b. The $E_{2g}$ modes are
a pair of degenerate vibrations with opposite circling directions, i.e.,
opposite chiralities (see Supplementary Note 1). These two types of symmetries
can be distinguished by polarization-resolved measurements. Specifically, the
$A_{1g}$ modes can be detected in the XX and LL polarization configurations,
whereas the $E_{2g}$ modes appear in the XX, XY, and LR configurations. Here,
XX and XY represent collinear and cross-linear polarization for the incident
and scattered photons, and LL and LR involve circularly polarized light with
left (L) and right (R) helicity. A comparison of data in all four
configurations is included in Supplementary Fig. 1.

Below $T_{\mathrm{CDW}}$, multiple peaks emerge, highlighted by the dotted
lines in Figs. 1c, d. Their origin will be discussed in the next sections.
These modes are rather weak compared to the main lattice phonons. Their
disappearance at 100 K suggests a close correlation with CDW formation. In
contrast, many weak peak-like structures below 100 cm-1 lack temperature
dependence, whose origin is unclear.

Fig. 1e compares the observed Raman mode frequencies with those from DFT
calculations for a single layer of CsV3Sb5 [22], considering two possible
forms of lattice distortion, the Star of David (SD) and inverse Star of David
(ISD, also referred to as tri-hexagonal) structures. Both of them show the
same number of $A_{1g}$ and $E_{2g}$ modes, but with different ordering.
Overall, the calculated ISD phonons agree much better with the experimental
results, as shown in the figure and in Supplementary Tab. 1. All the five
predicted $A_{1g}$ modes and five out of the eight predicted $E_{2g}$ modes
are observed. The observed $A_{1g}$ mode below 50 cm-1 is unaccounted for by
our calculations. This mode was also observed by pump-probe time-resolved
spectroscopy, which, when compared with calculations taking into account
interlayer coupling, was assigned as a Cs-mode due to CDW modulation along the
$c$-axis [23]. Except for this mode and the three missing $E_{2g}$ modes due
to their weak scattering cross section, the symmetry ordering of all the other
modes is in exact agreement between the experiment and theory. These results
suggest that the CDW ground state consists of weakly coupled layers with ISD-
type distortion, but CDW modulation along the $c$-axis is also indispensable.
Since the single-layer CsV3Sb5 holds the key to unraveling the CDW mechanism,
we attempted creating atomically thin CsV3Sb5 by mechanical exfoliation.
However, the loss of crystallinity impeded further investigation
(Supplementary Figs. 2 and 3).

Temperature dependence of Raman modes

Figs. 2a, b show the temperature dependent Raman intensity color plot for
CsV3Sb5, obtained in the LL and LR configurations, respectively. The intense
$A_{1g}$ and $E_{2g}$ main lattice modes are the most conspicuous features.
Figs. 2e–g show the frequency (with the corresponding value at 200 K
subtracted), linewidth (full width at half maximum), and normalized integrated
area for both modes, extracted from Lorentzian fits of the peaks. The $A_{1g}$
frequency sharply increases below $T_{\mathrm{CDW}}$, whereas the $E_{2g}$
frequency exhibits a subtle kink across the CDW transition. This is consistent
with the planar ISD lattice distortion mainly involving V atoms, forcing the
Sb2 atoms to displace along the $c$-axis, hence affecting the out-of-plane
vibration of the $A_{1g}$ mode more effectively. The calculated phonon
vibration patterns and frequencies confirm this picture (see Supplementary
Fig. 4 and Supplementary Tab. 1). The CDW transition also causes a faster
decrease in the linewidths below $T_{\mathrm{CDW}}$. This can be understood as
being due to the CDW-induced partial gapping of the Fermi surface [30, 31, 32,
33, 34], which reduces the electron-phonon interaction. The integrated peak
intensity for both phonons increases upon warming, in line with increased
thermal phonon populations. The rate of increase is faster when approaching
$T_{\mathrm{CDW}}$ from below, and interestingly, the value saturates below
approximately 50 K. The renormalization of the phonon parameters across the
CDW transition evidences sizable electron-phonon coupling.

CDW-induced modes are labeled in Figs. 2a, b. Except for the $A_{1}$ mode,
there appears to be two types of modes, represented by $A_{2}$ and $E_{3}$.
$A_{2}$ exhibits appreciable softening and broadening upon warming toward
$T_{\mathrm{CDW}}$. It is overdamped before disappearing, visualized in the
color plot in Fig. 2a as the streak of signal below 100 cm-1 between 60–90 K.
These are signatures of a CDW amplitude mode [40, 41, 42, 43, 44], caused by
the collapse of coherent CDW order near $T_{\mathrm{CDW}}$. $E_{3}$ shows a
smaller change of frequency and much less broadening, more consistent with the
characteristics of a zone-folded mode [41], as this type of mode arises from
folding a zone-boundary phonon to the zone center, making its temperature
dependence of the frequency as weak as that of normal phonons. Figs. 2c, d
compare the distinct temperature dependence of these two types of modes. While
$A_{2}$ broadens significantly above 40 K, $E_{3}$ maintains its linewidth and
suddenly vanishes above $\sim$80 K. The dramatic difference in the linewidth
broadening is quantified in Fig. 2i. Fig. 2h shows the frequencies of all the
observed Raman modes on the same scale. Upon warming, the CDW-induced modes
($A_{1}$ excluded) soften more dramatically than the main lattice modes. While
it is tempting to assign most of them as amplitude modes because of the
apparent softening behavior, we show below that they are in fact zone-folded
modes, mixed with the amplitude modes to partially inherit their properties.

Nature of CDW-induced modes

Although soft acoustic phonons were not detected experimentally, our DFT
results show that the formation of CDW in CsV3Sb5 is similar to that in other
well-known systems [40, 41, 42, 43, 44], in the sense that a soft acoustic
phonon mode at the CDW wavevector condenses and gives rise to a distorted
lattice [38]. The imaginary phonon modes of pristine CsV3Sb5 at three $M$
points (see Supplementary Fig. 5) transform as irreducible representation
$M_{1}^{+}$ ($A_{g}$) of the space group $P6/mmm$ (little co-group $D_{2h}$).
Fig. 3a shows that after the $2\times 2\times 1$ CDW transition, they are
folded to $\Gamma$ and form triply degenerate modes. With lattice distortion,
they decompose to a singlet $A_{1g}$ mode and a doublet $E_{2g}$ mode under
the point group $D_{6h}$:

$3M^{+}_{1}\rightarrow A_{1g}\oplus E_{2g}.$ (1)

As the lattice distorts from the pristine phase to the stable ISD pattern, the
imaginary $A_{1g}$ and $E_{2g}$ modes turn real with positive frequencies,
expected to be observable as two Raman-active amplitude modes. The phonon
wavefunctions of the soft $A_{1g}$ and $E_{2g}$ modes are shown in Figs. 4a,
b, dominated by vibrations of V atoms. The $A_{1g}$ mode is fully symmetric,
involving breathing-type motion for the V triangles, V hexagons, and Sb2
atoms. The $E_{2g}$ mode involves circling motion for the atoms forming the V
hexagons, while the amplitude for the Sb2 vibration is almost ten times
smaller.

DFT calculations further reveal that the amplitude modes strongly hybridize
with the other CDW-induced Raman modes (i.e. the zone-folded modes always at
positive frequencies at the $\Gamma$ point in Fig. 3a), rendering them
amplitude-mode-like, hence their apparent temperature-dependent frequencies.
Figs. 4c, d show the real space wavefunctions of all the CDW-induced modes in
the $2\times 2\times 1$ ISD phase. $A_{2-5}$ and $E_{1-4}$ correspond to those
in Fig. 2, and $E^{\prime}_{1-3}$ are undetected experimentally. Comparison
with Figs. 4a, b shows that $A_{2-5}$ ($E_{1-4}$) all resemble the $A_{1g}$
($E_{2g}$) soft mode, but the difference is also apparent. The similarity
results from hybridization of phonon wavefunctions.

To quantify the mode mixing, we calculated the overlap between the soft modes
and all the real modes of the stable ISD phase by projecting the phonon
wavefunctions, $P_{f}=|\langle\bm{u}_{f}|\bm{u}_{\mathrm{SM}}\rangle|^{2}$,
where $|\bm{u}_{\mathrm{SM}}\rangle$ refers to the wavefunction of the soft
modes shown in Figs. 4a, b and $|\bm{u}_{f}\rangle$ refers to the wavefunction
of the mode at frequency $f$ in the ISD phase. The results in Fig. 3b show
that as the soft $A_{1g}$ and $E_{2g}$ modes shift from negative to positive
frequencies and turn into amplitude modes, they hybridize with most of the
zone-folded modes belonging to the same irreducible representation. The amount
of calculated projection in the stable ISD phase correlates reasonably well
with the observed mode intensity in Fig. 1c, d. $A_{2}$ and $E_{1}$ are
residual amplitude modes after mode mixing. $E^{\prime}_{1-3}$ show minor
projection from the $E_{2g}$ soft mode because of negligible wavefunction
overlap, and accordingly their scattering cross section is weak. $E_{2-4}$ all
involve V triangles (Fig. 4d), indicating that they have contributions
unrelated with the $E_{2g}$ soft mode. Indeed, as discussed earlier, $E_{3}$
shows clear experimental signatures of a zone-folded mode.

The $A_{2}$ mode was also observed by Wulferding et al. in their Raman study
[45] and by time-resolved pump-probe spectroscopy [23, 46]. However, in these
works, it was suggested to emerge below $\sim$60 K [23, 46, 45], hence
ascribed to another phase transition associated with a unidirectional order
[19, 25, 26]. According to our data (Fig. 2a), the $A_{2}$ mode survives above
60 K, and there is no clear evidence for two distinct phase transitions. Its
vibration pattern shown in Fig. 4c confirms no relation with the
unidirectional order. Another Raman study by Wu et al. [47] reported a similar
set of modes as ours, but with different relative intensities. They also
observed extra modes that are possibly due to stronger $c$-axis modulation in
their sample.

Discussion

The anomalously large hybridization between the amplitude modes and zone-
folded modes is rare, because they are mostly decoupled in the canonical CDW
materials, with the amplitude modes dominating the spectral intensity [41, 42,
43]. The hybridization is highly unusual, because the $A_{2}$ and $E_{1}$
amplitude modes and the zone-folded Raman modes span a wide frequency range,
and they do not overlap in energy (except for $E_{1}$ and $E^{\prime}_{1}$) to
exhibit the typical anti-crossing [48, 49]. Their strong coupling suggests
that the hybridization occurs indirectly, through interaction with the common
electronic system. As the Fermi surface instability associated with the van
Hove singularity is from the V bands [22], modes mainly involving V (including
$A_{2-5}$ and $E_{1-4}$) naturally mix with the amplitude modes, whereas those
mainly involving Sb (including $E^{\prime}_{1-2}$ and the $A_{1g}$ and
$E_{2g}$ main lattice modes) do not. Similar mode mixing was also observed in
the quasi-one-dimensional (quasi-1D) K0.3MoO3 using time-resolved pump-probe
spectroscopy [50], and a simple model based on Ginzburg-Landau theory can well
describe the entanglement of the electronic and lattice parts of the CDW order
parameter. The similar phenomena observed in two systems with different
dimensionality suggest the importance of electron-phonon coupling in both
materials.

However, a soft acoustic phonon is well established in K0.3MoO3 [51], but
shown to be absent in CsV3Sb5 [20, 21]. In the mean field weak-coupling theory
[38, 28], the acoustic phonon softening, known as Kohn anomaly [52], is a
direct consequence of the divergent electronic susceptibility, which screens
the phonon vibration at the CDW wavevector. In reality, the singular
electronic susceptibility is smeared out, especially at dimensions higher than
one, and momentum dependent electron-phonon coupling dictates the phonon
renormalization in certain systems such as 2$H$-NbSe2 [53, 54]. The lack of
soft acoustic phonons in CsV3Sb5 clearly rules out both mechanisms. Instead,
CsV3Sb5 may fall into the strong electron-phonon coupling regime [55], in
which the non-detection of Kohn anomaly in the quasi-1D (TaSe4)2I, NbSe3, and
BaVS3 has also been reported [56, 57, 58]. In all these materials, strong
electron-phonon coupling tends to localize electrons, violating the adiabatic
Born-Oppenheimer approximation [55] used in DFT. Failure of the conduction
electrons to screen the phonon vibration can naturally explain the absence of
phonon softening [59].

The strong-coupling nature of the CDW in CsV3Sb5 is indeed supported by
multiple facts, according to the qualitative criteria discussed in Ref. [28].
The CDW-induced gap $\Delta_{\mathrm{CDW}}$ is large, with
$2\Delta_{\mathrm{CDW}}/k_{B}T_{\mathrm{CDW}}\approx 22$ according to infrared
spectroscopy [30], where $k_{B}$ is the Boltzmann constant. The lattice
distortion is substantial (amounting to about 5% of the lattice constant
[22]), the distorted lattice exhibits clustering of V atoms to form trimers
and hexamers, and the CDW locks with the pristine lattice to form a
commensurate structure, all indicating local chemical bonding [22, 35].
Moreover, DFT shows that the elastic potential for the ions in the pristine
structure features double minima deeper than the thermal energy
$k_{B}T_{\mathrm{CDW}}$ at the transition [22], a defining feature of the
strong-coupling theory proposed by Gor’kov [55]. Such potential well traps the
ions in one of its minima, precluding soft phonon condensation. From the
perspective of Raman scattering, the electron-phonon coupling constant
$\lambda$ can be estimated from the amplitude mode frequency
$\omega_{\mathrm{AM}}$ and the unscreened soft mode frequency
$\omega_{\mathrm{SM}}^{0}$ as
$\lambda=(\omega_{\mathrm{AM}}/\omega_{\mathrm{SM}}^{0})^{2}$, valid on the
mean-field level [38]. The results for CsV3Sb5 and a variety of other CDW
materials are complied in Fig. 5. Notably, the four quasi-2D compounds
2$H$-NbSe2, 2$H$-TaSe2, CsV3Sb5, and 1$T$-TaS2 are roughly located in the
expected order according to their $T_{\mathrm{CDW}}$, $\Delta_{\mathrm{CDW}}$,
and commensurability. The frequencies of the amplitude modes in CsV3Sb5 are
large, only lower than that of the higher one in 1$T$-TiSe2. Although the
exact value of $\lambda$ may not be meaningful beyond the weak-coupling limit,
these results clearly indicate the strong-coupling nature of the CDW in
CsV3Sb5.

Our Raman results offer informative insights into the CDW phase in CsV3Sb5,
suggesting the dominance of the single layer in driving the transition and
evidencing strong electron-phonon coupling. CsV3Sb5 represents a unique case
in which the amplitude modes emerge in the absence of soft acoustic phonons.
As important collective excitations of the CDW ground state, how they forms
without being driven by folding of a soft acoustic phonon warrants further
investigation. Although DFT accurately predicts the CDW-induced Raman modes in
the zero-temperature limit, in good agreement with our experiment, to
understand how the amplitude modes emerge below $T_{\mathrm{CDW}}$ apparently
requires models and computational methods working at finite temperature.

Methods

Sample preparation
CsV3Sb5 single crystals were synthesized using the flux method [11]. The
freshly cleaved surface of the samples was used in the study of bulk crystals.
Raman scattering spectroscopy was performed using home-built confocal
microscopy setups in the back-scattering geometry with 532 nm laser
excitation. The normally incident light was focused on the sample to a micron-
sized spot, and the scattered light was directed through Bragg notch filters
to access the low-wavenumber region. The Raman signal was collected using a
grating spectrograph and a liquid-nitrogen-cooled charge-coupled device. The
samples were mounted in a vacuum chamber during data acquisition. Temperature
control was achieved using a Montana Instrument Cryostation.

Calculations
The DFT calculation results by Tan et al. [22] are used to compare with the
experiment. Details of the calculations can be found therein. In addition, we
calculated the force constants by Vienna ab-initio Simulation Package (VASP)
[60] and computed the phonon dispersion relation by Phonopy [61]. For the DFT
calculation, a $5\times 5\times 5$ $\bm{k}$ mesh and an energy cutoff of 400
eV were used.

Data availability
The data in Figure 1e are available in Supplementary Table 1. Other data are
available from the corresponding authors upon request.

References

## References

  * [1] Sachdev, S.  Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons.  _Phys. Rev. B_ 45, 12377–12396 (1992).  URL https://link.aps.org/doi/10.1103/PhysRevB.45.12377.
  * [2] Han, T.-H. _et al._ Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet.  _Nature_ 492, 406–410 (2012).  URL https://doi.org/10.1038/nature11659.
  * [3] Mazin, I. I. _et al._ Theoretical prediction of a strongly correlated Dirac metal.  _Nat. Commun._ 5, 4261 (2014).  URL https://doi.org/10.1038/ncomms5261.
  * [4] Ye, L. _et al._ Massive Dirac fermions in a ferromagnetic kagome metal.  _Nature_ 555, 638–642 (2018).  URL https://doi.org/10.1038/nature25987.
  * [5] Tang, E., Mei, J.-W. & Wen, X.-G.  High-temperature fractional quantum Hall states.  _Phys. Rev. Lett._ 106, 236802 (2011).  URL https://link.aps.org/doi/10.1103/PhysRevLett.106.236802.
  * [6] Xu, G., Lian, B. & Zhang, S.-C.  Intrinsic quantum anomalous Hall effect in the kagome lattice ${\mathrm{Cs}}_{2}{\mathrm{LiMn}}_{3}{\mathrm{F}}_{12}$.  _Phys. Rev. Lett._ 115, 186802 (2015).  URL https://link.aps.org/doi/10.1103/PhysRevLett.115.186802.
  * [7] Kang, M. _et al._ Topological flat bands in frustrated kagome lattice CoSn.  _Nat. Commun._ 11, 4004 (2020).  URL https://doi.org/10.1038/s41467-020-17465-1.
  * [8] Yu, S.-L. & Li, J.-X.  Chiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome lattice.  _Phys. Rev. B_ 85, 144402 (2012).  URL https://link.aps.org/doi/10.1103/PhysRevB.85.144402.
  * [9] Kiesel, M. L., Platt, C. & Thomale, R.  Unconventional Fermi surface instabilities in the kagome Hubbard model.  _Phys. Rev. Lett._ 110, 126405 (2013).  URL https://link.aps.org/doi/10.1103/PhysRevLett.110.126405.
  * [10] Wang, W.-S., Li, Z.-Z., Xiang, Y.-Y. & Wang, Q.-H.  Competing electronic orders on kagome lattices at van Hove filling.  _Phys. Rev. B_ 87, 115135 (2013).  URL https://link.aps.org/doi/10.1103/PhysRevB.87.115135.
  * [11] Ortiz, B. R. _et al._ New kagome prototype materials: discovery of ${\mathrm{KV}_{3}\mathrm{Sb}_{5}}$, ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$, and ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. Mater._ 3, 094407 (2019).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.3.094407.
  * [12] Ortiz, B. R. _et al._ $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$: A ${\mathbb{Z}}_{2}$ Topological Kagome Metal with a Superconducting Ground State.  _Phys. Rev. Lett._ 125, 247002 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevLett.125.247002.
  * [13] Liu, Z. _et al._ Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. X_ 11, 041010 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevX.11.041010.
  * [14] Kang, M. _et al._ Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5.  _Nature Physics_ (2022).  URL https://doi.org/10.1038/s41567-021-01451-5.
  * [15] Ortiz, B. R. _et al._ Superconductivity in the ${\mathbb{Z}}_{2}$ kagome metal ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. Mater._ 5, 034801 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.5.034801.
  * [16] Yin, Q. _et al._ Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals.  _Chin. Phys. Lett._ 38, 037403 (2021).  URL https://doi.org/10.1088/0256-307x/38/3/037403.
  * [17] Yang, S.-Y. _et al._ Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5.  _Sci. Adv._ 6, eabb6003 (2020).  URL https://advances.sciencemag.org/content/advances/6/31/eabb6003.full.pdf.
  * [18] Yu, F. H. _et al._ Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal.  _Phys. Rev. B_ 104, L041103 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.L041103.
  * [19] Chen, H. _et al._ Roton pair density wave in a strong-coupling kagome superconductor.  _Nature_ 599, 222–228 (2021).  URL https://doi.org/10.1038/s41586-021-03983-5.
  * [20] Li, H. _et al._ Observation of unconventional charge density wave without acoustic phonon anomaly in kagome superconductors ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{Rb}$, Cs).  _Phys. Rev. X_ 11, 031050 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevX.11.031050.
  * [21] Xie, Y. _et al._ Electron-phonon coupling in the charge density wave state of CsV3Sb5 (2021).  URL https://arxiv.org/abs/2111.00654.  eprint 2111.00654.
  * [22] Tan, H., Liu, Y., Wang, Z. & Yan, B.  Charge density waves and electronic properties of superconducting kagome metals.  _Phys. Rev. Lett._ 127, 046401 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevLett.127.046401.
  * [23] Ratcliff, N., Hallett, L., Ortiz, B. R., Wilson, S. D. & Harter, J. W.  Coherent phonon spectroscopy and interlayer modulation of charge density wave order in the kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. Mater._ 5, L111801 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.5.L111801.
  * [24] Christensen, M. H., Birol, T., Andersen, B. M. & Fernandes, R. M.  Theory of the charge density wave in $A$V3Sb5 kagome metals.  _Phys. Rev. B_ 104, 214513 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.214513.
  * [25] Zhao, H. _et al._ Cascade of correlated electron states in the kagome superconductor $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$.  _Nature_ 599, 216–221 (2021).  URL https://doi.org/10.1038/s41586-021-03946-w.
  * [26] Wang, Z. _et al._ Electronic nature of chiral charge order in the kagome superconductor $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. B_ 104, 075148 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.075148.
  * [27] Liang, Z. _et al._ Three-dimensional charge density wave and surface-dependent vortex-core states in a kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. X_ 11, 031026 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevX.11.031026.
  * [28] Rossnagel, K.  On the origin of charge-density waves in select layered transition-metal dichalcogenides.  _Journal of Physics: Condensed Matter_ 23, 213001 (2011).  URL https://doi.org/10.1088/0953-8984/23/21/213001.
  * [29] Ortiz, B. R. _et al._ Fermi surface mapping and the nature of charge-density-wave order in the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. X_ 11, 041030 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevX.11.041030.
  * [30] Zhou, X. _et al._ Origin of charge density wave in the kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ as revealed by optical spectroscopy.  _Phys. Rev. B_ 104, L041101 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.L041101.
  * [31] Uykur, E. _et al._ Low-energy optical properties of the nonmagnetic kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. B_ 104, 045130 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.045130.
  * [32] Nakayama, K. _et al._ Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. B_ 104, L161112 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.L161112.
  * [33] Lou, R. _et al._ Charge-density-wave-induced peak-dip-hump structure and the multiband superconductivity in a kagome superconductor CsV3Sb5.  _Phys. Rev. Lett._ 128, 036402 (2022).  URL https://link.aps.org/doi/10.1103/PhysRevLett.128.036402.
  * [34] Luo, Y. _et al._ Distinct band reconstructions in kagome superconductor CsV3Sb5 (2021).  URL https://arxiv.org/abs/2106.01248.  eprint 2106.01248.
  * [35] Wang, C., Liu, S., Jeon, H. & Cho, J.-H.  Origin of charge density wave in the layered kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.  _Phys. Rev. B_ 105, 045135 (2022).  URL https://link.aps.org/doi/10.1103/PhysRevB.105.045135.
  * [36] Ye, Z., Luo, A., Yin, J.-X., Zahid Hasan, M. & Xu, G.  Structural instability and charge modulations in the Kagome superconductor $A$V3Sb5 (2021).  URL https://arxiv.org/abs/2111.07314.  eprint 2111.07314.
  * [37] Rice, M. & Strässler, S.  Theory of the soft phonon mode and dielectric constant below the Peierls transition temperature.  _Solid State Communications_ 13, 1931–1933 (1973).  URL https://www.sciencedirect.com/science/article/pii/0038109873900033.
  * [38] Grüner, G.  _Density Waves in Solids_.  Advanced book program: Addison-Wesley (Perseus Books Group, 2000).
  * [39] Sugai, S.  Lattice vibrations in the charge-density-wave states of layered transition metal dichalcogenides.  _phys. stat. sol. (b)_ 129, 13–39 (1985).  URL http://dx.doi.org/10.1002/pssb.2221290103.
  * [40] Travaglini, G., Mörke, I. & Wachter, P.  CDW evidence in one-dimensional K0.3MoO3 by means of Raman scattering.  _Solid State Commun_ 45, 289–292 (1983).  URL https://www.sciencedirect.com/science/article/pii/0038109883904830.
  * [41] Joshi, J. _et al._ Short-range charge density wave order in $2H$-TaS2.  _Phys. Rev. B_ 99, 245144 (2019).  URL https://link.aps.org/doi/10.1103/PhysRevB.99.245144.
  * [42] Hill, H. M. _et al._ Phonon origin and lattice evolution in charge density wave states.  _Phys. Rev. B_ 99, 174110 (2019).  URL https://link.aps.org/doi/10.1103/PhysRevB.99.174110.
  * [43] Lin, D. _et al._ Patterns and driving forces of dimensionality-dependent charge density waves in 2$H$-type transition metal dichalcogenides.  _Nature Commun._ 11, 2406 (2020).  URL https://doi.org/10.1038/s41467-020-15715-w.
  * [44] Barath, H. _et al._ Quantum and classical mode softening near the charge-density-wave–superconductor transition of ${\mathrm{Cu}}_{x}{\mathrm{TiSe}}_{2}$.  _Phys. Rev. Lett._ 100, 106402 (2008).  URL https://link.aps.org/doi/10.1103/PhysRevLett.100.106402.
  * [45] Wulferding, D. _et al._ Fermi surface instabilities in electronic Raman scattering of the metallic kagome lattice CsV3Sb5 (2021).  URL https://arxiv.org/abs/2108.11690.  eprint 2108.11690.
  * [46] Wang, Z. X. _et al._ Unconventional charge density wave and photoinduced lattice symmetry change in the kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ probed by time-resolved spectroscopy.  _Phys. Rev. B_ 104, 165110 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.165110.
  * [47] Wu, S. _et al._ Charge density wave order in kagome metal $A$V3Sb5 ($A$=Cs, Rb, K) (2022).  URL https://arxiv.org/abs/2201.05188.  eprint 2201.05188.
  * [48] Yusupov, R. V., Mertelj, T., Chu, J.-H., Fisher, I. R. & Mihailovic, D.  Single-particle and collective mode couplings associated with 1- and 2-directional electronic ordering in metallic $R{\mathrm{Te}}_{3}$ ($R=\mathrm{Ho},\mathrm{Dy},\mathrm{Tb}$).  _Phys. Rev. Lett._ 101, 246402 (2008).  URL https://link.aps.org/doi/10.1103/PhysRevLett.101.246402.
  * [49] Lavagnini, M. _et al._ Raman scattering evidence for a cascade evolution of the charge-density-wave collective amplitude mode.  _Phys. Rev. B_ 81, 081101 (2010).  URL https://link.aps.org/doi/10.1103/PhysRevB.81.081101.
  * [50] Schäfer, H., Kabanov, V. V., Beyer, M., Biljakovic, K. & Demsar, J.  Disentanglement of the electronic and lattice parts of the order parameter in a 1D charge density wave system probed by femtosecond spectroscopy.  _Phys. Rev. Lett._ 105, 066402 (2010).  URL https://link.aps.org/doi/10.1103/PhysRevLett.105.066402.
  * [51] Pouget, J. P., Hennion, B., Escribe-Filippini, C. & Sato, M.  Neutron-scattering investigations of the Kohn anomaly and of the phase and amplitude charge-density-wave excitations of the blue bronze K0.3MoO3.  _Phys. Rev. B_ 43, 8421–8430 (1991).  URL https://link.aps.org/doi/10.1103/PhysRevB.43.8421.
  * [52] Kohn, W.  Image of the Fermi surface in the vibration spectrum of a metal.  _Phys. Rev. Lett._ 2, 393–394 (1959).  URL https://link.aps.org/doi/10.1103/PhysRevLett.2.393.
  * [53] Johannes, M. D. & Mazin, I. I.  Fermi surface nesting and the origin of charge density waves in metals.  _Phys. Rev. B_ 77, 165135 (2008).  URL https://link.aps.org/doi/10.1103/PhysRevB.77.165135.
  * [54] Zhu, X., Cao, Y., Zhang, J., Plummer, E. W. & Guo, J.  Classification of charge density waves based on their nature.  _Proceedings of the National Academy of Sciences_ 112, 2367–2371 (2015).  URL https://www.pnas.org/content/112/8/2367.
  * [55] Gor’kov, L. P.  Strong electron-lattice coupling as the mechanism behind charge density wave transformations in transition-metal dichalcogenides.  _Phys. Rev. B_ 85, 165142 (2012).  URL https://link.aps.org/doi/10.1103/PhysRevB.85.165142.
  * [56] Lorenzo, J. E. _et al._ A neutron scattering study of the quasi-one-dimensional conductor (TaSe4)2I.  _Journal of Physics: Condensed Matter_ 10, 5039–5068 (1998).  URL https://doi.org/10.1088/0953-8984/10/23/010.
  * [57] Requardt, H., Lorenzo, J. E., Monceau, P., Currat, R. & Krisch, M.  Dynamics in the charge-density-wave system ${\mathrm{NbSe}}_{3}$ using inelastic x-ray scattering with mev energy resolution.  _Phys. Rev. B_ 66, 214303 (2002).  URL https://link.aps.org/doi/10.1103/PhysRevB.66.214303.
  * [58] Ilakovac, V. _et al._ Order-disorder type of peierls instability in ${\mathrm{BaVS}}_{3}$.  _Phys. Rev. B_ 103, 014306 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.103.014306.
  * [59] Pouget, J.-P.  The Peierls instability and charge density wave in one-dimensional electronic conductors.  _Comptes Rendus Physique_ 17, 332–356 (2016).  URL https://www.sciencedirect.com/science/article/pii/S163107051500225X.
  * [60] Kresse, G. & Furthmüller, J.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.  _Phys. Rev. B_ 54, 11169–11186 (1996).  URL https://link.aps.org/doi/10.1103/PhysRevB.54.11169.
  * [61] Togo, A. & Tanaka, I.  First principles phonon calculations in materials science.  _Scr. Mater._ 108, 1–5 (2015).  URL https://doi.org/10.1016/j.scriptamat.2015.07.021.
  * [62] Hu, Y., Zheng, F., Ren, X., Feng, J. & Li, Y.  Charge density waves and phonon-electron coupling in ${\mathrm{ZrTe}}_{3}$.  _Phys. Rev. B_ 91, 144502 (2015).  URL https://link.aps.org/doi/10.1103/PhysRevB.91.144502.
  * [63] Hoesch, M., Bosak, A., Chernyshov, D., Berger, H. & Krisch, M.  Giant Kohn anomaly and the phase transition in charge density wave ${\mathrm{ZrTe}}_{3}$.  _Phys. Rev. Lett._ 102, 086402 (2009).  URL https://link.aps.org/doi/10.1103/PhysRevLett.102.086402.
  * [64] Maschek, M. _et al._ Wave-vector-dependent electron-phonon coupling and the charge-density-wave transition in $\mathrm{TbT}{\mathrm{e}}_{3}$.  _Phys. Rev. B_ 91, 235146 (2015).  URL https://link.aps.org/doi/10.1103/PhysRevB.91.235146.
  * [65] Weber, F. _et al._ Electron-phonon coupling and the soft phonon mode in ${\mathrm{TiSe}}_{2}$.  _Phys. Rev. Lett._ 107, 266401 (2011).  URL https://link.aps.org/doi/10.1103/PhysRevLett.107.266401.
  * [66] Moncton, D. E., Axe, J. D. & DiSalvo, F. J.  Study of superlattice formation in 2$H$-NbSe2 and 2$H$-TaSe2 by neutron scattering.  _Phys. Rev. Lett._ 34, 734–737 (1975).  URL https://link.aps.org/doi/10.1103/PhysRevLett.34.734.
  * [67] Weber, F. _et al._ Extended phonon collapse and the origin of the charge-density wave in 2$H$-NbSe2.  _Phys. Rev. Lett._ 107, 107403 (2011).  URL https://link.aps.org/doi/10.1103/PhysRevLett.107.107403.
  * [68] Tsang, J. C., Smith, J. E. & Shafer, M. W.  Raman spectroscopy of soft modes at the charge-density-wave phase transition in 2$H$-NbSe2.  _Phys. Rev. Lett._ 37, 1407–1410 (1976).  URL https://link.aps.org/doi/10.1103/PhysRevLett.37.1407.

Acknowledgements
This work was supported by the National Key Research and Development Program
of China (Grant Nos. 2018YFA0307000 and 2017YFA0303201) and the National
Natural Science Foundation of China (Grant Nos. 11774151). Growth of hexagonal
boron nitride crystals was supported by the Elemental Strategy Initiative
conducted by the MEXT, Japan (Grant No. JPMXP0112101001), JSPS KAKENHI (Grant
No. JP20H00354), and A3 Foresight by JSPS. B.Y. acknowledges the financial
support by the European Research Council (ERC Consolidator Grant
“NonlinearTopo”, No. 815869) and the ISF - Quantum Science and Technology (No.
1251/19).

Author information
Contributions
X.X. conceived the project. G.L., X.M., and K.H. performed the Raman
experiments. Q.L., Y.D., and H.-H.W. grew the CsV3Sb5 crystals. K.W. and T.T.
grew the h-BN crystals. G.L. and X.X. analysed the experimental data. H.T.,
Y.L., and B.Y performed the DFT calculations. J.X., W.T., and L.G. performed
atomic force microscopy measurements. X.X. and B.Y. interpreted the results
and co-wrote the paper, with comments from all authors.
Corresponding authors
Correspondences should be sent to Binghai Yan<EMAIL_ADDRESS>or
Xiaoxiang Xi (xxi@nju.edu.cn).

Competing interests
The authors declare no competing interests.

Figure 1: Raman-active phonon modes in CsV3Sb5. a Schematic illustration of
the relation between the soft mode and amplitude mode in typical CDW
materials, showing the latter emerges after the former freezes below
$T_{\mathrm{CDW}}$. b Crystal structure of CsV3Sb5. Sb sites with different
Wyckoff positions are labeled as Sb1 and Sb2. The arrows illustrate the
vibration patterns of the main lattice $A_{1g}$ and $E_{2g}$ modes. The
$E_{2g}$ mode is doubly degenerate, and only one form is shown. c, d Raman
spectra measured on the $ab$-plane at 100 K and 4 K in the LL and LR
polarization configurations. The dashed lines denote the main lattice phonons,
and the dotted lines indicate the CDW-induced modes. e Comparison of the
measured (Expt.) and the calculated Raman mode frequencies for the inverse
Star of David (ISD) and Star of David (SD) lattice distortions. The thick
lines denote the main lattice phonons. The dots indicate modes undetected in
our experiment.

Figure 2: Evolution of the Raman modes in CsV3Sb5 across the CDW transition.
a, b Temperature-dependent Raman intensity color plot for CsV3Sb5, measured in
the LL and LR configurations. The normal phonon modes are labeled in black and
the CDW-induced modes in white. The dashed lines mark $T_{\mathrm{CDW}}$. c, d
Temperature-dependent spectra for the $A_{2}$ and $E_{3}$ modes. e–g
Frequency, linewidth, and amplitude for the $E_{2g}$ and $A_{1g}$ main lattice
phonons. The frequency and amplitude are compared to the corresponding values
at 200 K. h Temperature dependence of the Raman mode frequencies. i
Temperature dependence of the linewidth of the $A_{2}$ and $E_{3}$ modes.

Figure 3: Phonon band structures and mode mixing in the process of CDW
distortion. a Phonon band structures. Here, 100% (0%) refers to the fully
stable ISD ($2\times 2$ pristine) structure. 10% refers to the intermediate
structure with 10% distortion from the pristine to ISD phases. After $2\times
2\times 1$ band folding with no distortion, the imaginary triply-degenerate
modes form at $\Gamma$. A weak ISD-type distortion lifts the degeneracy and
leads to $A_{1g}$ and $E_{2g}$ modes. The ISD distortion gradually transforms
imaginary modes to real. b Projections of the imaginary $A_{1g}$ ($E_{2g}$)
mode with 10% distortion to all the other phonon modes at $\Gamma$, as
evolving into the stable ISD phase (100%). We highlight all $A_{1g}$ and
$E_{2g}$ modes by orange and blue dots, respectively, at the $\Gamma$ point.
The dashed orange (blue) curve in b guides eyes to show the evolution of the
imaginary $A_{2}$ ($E_{1}$) modes in the CDW distortion.

Figure 4: Real space wavefunctions of the imaginary soft modes and the stable
CDW-induced Raman modes in the $2\times 2\times 1$ ISD phase. a, b Soft modes
with $A_{1g}$ and $E_{2g}$ symmetries, respectively. c, d CDW-induced $A_{1g}$
and $E_{2g}$ stable modes. The $E_{2g}$ modes are pairs of chiral phonons and
only one chiral mode is shown. The radius of the circles represents the
amplitude of the vibration, and the arrow on the circles stands for the
initial phase of the wavefunction. Cs atoms are omitted in the crystal
structure for clarity, because they do not contribute to lattice vibrations.

Figure 5: Evidence of strong-coupling CDW in CsV3Sb5. Frequency of the
amplitude mode $\omega_{\mathrm{AM}}$ in the zero-temperature limit and the
unscreened frequency of the soft mode $\omega_{\mathrm{SM}}^{0}$ far above
$T_{\mathrm{CDW}}$ for a collection of CDW materials. Some of the materials
feature two amplitude modes, hence two data points connected by a vertical
line. Since no soft mode is observed in CsV3Sb5, $\omega_{\mathrm{SM}}^{0}$ is
taken to be its acoustic phonon frequency at 300 K [21]. Open (filled) symbols
indicate the material is quasi-1D (quasi-2D). The dashed lines mark electron-
phonon coupling constant $\lambda=1$ and 3 according to mean-field theory.
Source of data: ZrTe3 [62, 63], TbTe3 [48, 64], K0.3MoO3 [51, 40], 1$T$-TiSe2
[65, 44], 2$H$-TaSe2 [66, 42, 43], 2$H$-NbSe2 [66, 67, 68].


# First detection of $c$-C3H2 in a circumstellar disk

Chunhua Qi  Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138, USA  Karin I. Öberg  Departments of Chemistry and
Astronomy, University of Virginia, Charlottesville, VA 22904, USA  David J.
Wilner, Katherine A. Rosenfeld  Harvard-Smithsonian Center for Astrophysics,
60 Garden Street, Cambridge, MA 02138, USA

###### Abstract

We report the first detection of $c$-C3H2 in a circumstellar disk. The
$c$-C3H2 J=$6-5$ line (217.882 GHz) is detected and imaged through Atacama
Large Millimeter Array (ALMA) Science Verification observations toward the
disk around the Herbig Ae star HD 163296 at 0.8′′ resolution. The emission is
consistent with that arising from a Keplerian rotating disk. Two additional
$c$-C3H2 transitions are also tentatively detected, bolstering the
identification of this species, but with insufficient signal-to-noise ratio to
constrain the spatial distribution. Using a previously developed model for the
physical structure of this disk, we fit a radial power-law distribution model
to the $c$-C3H2 $6-5$ emission and find that $c$-C3H2 is present in a ring
structure from an inner radius of about 30 AU to an outer radius of about 165
AU. The column density is estimated to be 1012–1013 cm-2. The clear detection
and intriguing ring structure suggest that $c$-C3H2 has the potential to
become a useful probe of radiation penetration in disks.

protoplanetary disks; astrochemistry; stars: formation; ISM: molecules;
techniques: high angular resolution; radio lines: ISM

##  1 Introduction

Pre-main sequence stars are commonly surrounded by disks, which serve the dual
purpose of funneling accretion onto the central star and transporting away
angular momentum. These disks are also the formation sites of planets and
connect protostars and planets physically and chemically. The main component
of gas-rich circumstellar disks, cold H2, cannot be observed directly because
of a lack of transitions at suitable energy levels. Instead, constraints on
disk mass, density and temperature structures depend on observations of trace
species, most commonly dust and CO gas (e.g. Qi et al., 2006; Piétu et al.,
2007; Andrews et al., 2009). To access other disk properties, such as
ionization levels, X-ray and UV radiation fields, turbulent mixing, chemical
age and bulk composition requires the development of additional molecular
probes whose formation and destruction depend critically on one or several of
these properties.

The past decade has witnessed significant progress on disk chemistry theory,
resulting in large numbers of predictions on how molecular abundance
structures should depend on different disk properties (e.g. Aikawa & Nomura,
2006; Willacy, 2007; Semenov & Wiebe, 2011; Fogel et al., 2011; Walsh et al.,
2012). A lack of observational sensitivity has however limited detections to
the simplest molecules in the millimeter/submillimeter range which
characterizes the bulk of the gas disk, including CO, HCO+, DCO+, CN, HCN,
DCN, C2H, H2CO, CS, SO, CH2, N2H+ and HC3N (Dutrey et al., 1997; Aikawa et
al., 2003; Thi et al., 2004; Semenov et al., 2005; Dutrey et al., 2007; Qi et
al., 2008; Fuente et al., 2010; Henning et al., 2010; Öberg et al., 2010,
2011). This list is expected to expand with the arrival of ALMA and its
unprecedented sensitivity and spatial resolution, which will enable the
development of a more diverse set of molecular probes. In this Letter, we use
ALMA Science Verification observations of HD 163296 to report the first
detection of cyclopropenylidene, $c$-C3H2, in a circumstellar disk. At a
distance of $\sim$122 pc (Perryman et al., 1997), this Herbig Ae star (stellar
mass 2.3 M⊙; spectral type A1; age $\sim$4 Myr) harbors a large disk (a
scattered light pattern extending out to a radius of $\sim$500 AU, Grady et
al., 2000) with strong millimeter continuum and molecular line emission
(Mannings & Sargent, 1997; Thi et al., 2004; Natta et al., 2004; Isella et
al., 2007; Qi et al., 2011). The large disk size and strong molecular emission
make this system an ideal target to search for new molecules.

The $c$-C3H2 molecule is a small cyclic hydrocarbon, which was first detected
in space by Thaddeus et al. (1985) towards Sgr B2. Since then, $c$-C3H2 has
been detected in a wide range of astrophysical environments, including diffuse
and dense clouds, protostars, planetary nebulae and extragalactic sources
(e.g., Matthews & Irvine, 1985; Cox et al., 1988, 1989; Madden et al., 1989;
Benson et al., 1998; Menten et al., 1999; Fossé et al., 2001; Sakai et al.,
2008; Tenenbaum et al., 2009; Liszt et al., 2012), and is one of the most
abundant molecules with 3 carbon atoms in the interstellar medium (Teyssier et
al., 2004). In the context of disks, $c$-C3H2 has some favorable
characteristics that may make it a powerful molecular probe, especially when
observed in combination with isotopologues and chemically related molecules:

  1. 1.

$c$-C3H2 has two equivalent H nuclei, which couple to generate ortho (nuclear
spin of 1) and para (nuclear spin of 0) states. Deviations from the
statistical weights of 3 to 1 may be used to constrain the formation
conditions of the molecule (Park et al., 2006).

  2. 2.

$c$-C3H2 is also one of two isomers; the other is the linear molecule
$l$-C3H2. The isomer ratio can be used to assess the fractional ionization in
clouds (Fossé et al., 2001) and may provide similar constraints on disks.

  3. 3.

The formation and destruction chemistry of $c$-C3H2 (and carbon chains) are
sensitive to high energy radiation. The vertical and radial abundance
structure should provide strong constraints on the penetration depth of X-rays
and UV photons (Semenov & Wiebe, 2011).

  4. 4.

Within the family of hydrocarbons, the sensitivity to turbulent mixing
increases dramatically from C2 to C3H2, and from C3H2 to larger hydrocarbons.
Observed ratios and limits have the potential to constrain transport in disks
(Semenov & Wiebe, 2011).

Finally, the chemistry that produces $c$-C3H2 is important to constrain in its
own right, since $c$-C3H2 shares precursors with other, more complex carbon
chains, which may be an important source of carbon during planet formation. In
light of these possibilities, we aim to provide first constraints on the
abundance, distribution and $o/p$ ratio of $c$-C3H2 in the HD 163296 disk.

##  2 Observations

HD 163296 (RA: 17h56m21$\fs$287, DEC: $-$21°57′22$\farcs$39; J2000.0) was
observed on 2012 June 9, June 23 and July 7 as part of the ALMA Science
Verification (SV) program in band 6. At the time of observations, 25 12-m
antennae were used (2 7-m ACA antennae were present in the dataset but
flagged) in the array with a resulting synthesized beam size of
0.9$\times$0.7$\arcsec$ (PA=84°). The source was observed with a total
integration time of 84 minutes. The ALMA correlator was configured to
simultaneously observe four spectral windows (two in each sideband). One of
those windows (SpwID #1) covered both 13CO and C18O $2-1$ lines (220.399 and
219.560 GHz, respectively). The data were calibrated in the CASA software
package (v3.4), following the detailed calibration and imaging scripts
provided by the ALMA science verification team. Since those scripts, along
with fully calibrated measurement sets, are publicly available
online111https://almascience.nrao.edu/almadata/sciver/HD163296Band6, we do not
repeat the details here. The 218 GHz (1.37mm) continuum was generated from the
line-free channels in the two spectral windows (SpWID #0 and #1) of the lower
sideband, and the flux is determined to be 608.5$\pm$2.5 mJy, which agrees
with the SMA observations (Qi et al., 2011). Excellent agreement is also seen
between the SMA and ALMA spectra for the 13CO and C18O $2-1$ lines with fluxes
within 10% (Qi et al., 2011).

All of the $c$-C3H2 lines are continuum-subtracted and retrieved from SpwID #0
with a channel width of 0.488 MHz (0.67 km s-1) covering the total 1.875 GHz
bandwidth from 216.167 to 218.042 GHz. We have binned the lines in channels of
1 km s-1 to achieve higher signal-to-noise ratios and still keep the key
kinematic features of the disk. The resulting line rms noise level is
estimated to be 2.2 mJy beam-1 per 1 km s-1 channel in line free channels.

##  3 Results and Analysis

###  3.1 $c$-C3H2 detection

Figure 1 shows that the $c$-C3H2 $6-5$ line is clearly detected towards HD
163296 and that the position angle of its resolved velocity field is
consistent with that of 13CO from the same data set, which shows a clear
pattern of Keplerian rotation. Interestingly, the $c$-C3H2 $6-5$ moment map
displays a double-peaked morphology, indicative of an inner hole. The $c$-C3H2
$3-2$ and $5-4$ lines are only tentatively detected, insufficient to resolve
the velocity field or any spatial structure. To improve the sensitivity in
imaging these lines, we applied a Gaussian taper to the visibility data that
corresponds to 1″ FWHM in the image domain, which resulted in a beam of
1.3$\times$1.2$\arcsec$ (PA=78°).

Because the line emission changes position with channels, using a single mask
for all channels to extract spectra will lead to a degradation of the signal.
Instead, we create separate masks to cover the $c$-C3H2 $6-5$ line emission at
each channel and use these masks to extract the line spectra. The same masks
are also used for other $c$-C3H2 lines. Figure 2 shows the resulting spectra
of all three $c$-C3H2 $3-2$ lines together with 13CO $2-1$ line (with its own
masks covering the 13CO $2-1$ emission at each channel). The $6-5$ line is
clearly detected with the expected line shape and Vlsr consistent with 13CO.
The $5-4$ line presents a consistent spectral profile, at lower signal-to-
noise ratio. In contrast, the $3-2$ line is both narrower and clearly blue-
shifted, suggestive of a different physical origin, perhaps in a disk wind.
However, both the $3-2$ and $5-4$ lines are observed at the edge of the
spectral window, so this apparent asymmetry should be confirmed by independent
observations before any strong conclusions are drawn.

The integrated fluxes are reported in Table 1. These are just below the upper
limits reported in two previous failed searches of $c$-C3H2 in disks (Fuente
et al., 2010; Öberg et al., 2010).

###  3.2 Ring structure model

We explore the distributions of $c$-C3H2 in HD 163296 based on a previously
developed accretion disk model with well-defined temperature and density
structures (Qi et al., 2011). To simulate and compare with the data, we assume
the disk material orbits the central star in Keplerian motion, and fix the
disk geometric and kinematic parameters that affect the observed spatio-
kinematic behavior of the disk. The details of the stellar and accretion
properties and the disk geometric and kinematic parameters are summarized in
Table 3 of Qi et al. (2011). We have developed a physically self-consistent
accretion disk model with an exponentially tapered edge that matches the
spectral energy distribution and spatially resolved millimeter dust continuum
emission. The disk temperature and density structures are further constrained
by multiple CO and CO isotopologue line observations. Such analysis provides
the essential framework for constraining the distribution of molecular
abundances in protoplanetary disks.

Within this model framework, we assume that $c$-C3H2 is present with a
constant abundance in a layer with boundaries toward the midplane and toward
the surface of the disk (Qi et al., 2008; Öberg et al., 2012). This assumption
is motivated by chemical models (e.g. Aikawa & Nomura, 2006) that predict a
three-layered structure where most molecules are photodissociated in the
surface layer, frozen out in the midplane, and have an abundance that peaks at
intermediate disk heights. The surface ($\sigma_{s}$) and midplane
($\sigma_{m}$) boundaries are presented in terms of
$\Sigma_{21}=\Sigma_{H}/(1.59\times 10^{21}cm^{-2})$, where $\Sigma_{H}$ is
the hydrogen column density measured from the disk surface in the adopted
physical model. This simple model approach approximates the vertical location
where $c$-C3H2 is most abundant. Due to the limited signal-to-noise of the
multiple $c$-C3H2 line detections, we cannot constrain the location of this
vertical layer based on the $c$-C3H2 data. We therefore fix the vertical
surface boundary $\sigma_{s}$ as 0.32 ($\log_{10}(\sigma_{s})=-0.5$) and the
midplane boundary $\sigma_{m}$ as 3.2 ($\log_{10}(\sigma_{m})=0.5$), between
which lies the expected location of most molecules with peak abundances in the
warm molecular layer (Aikawa & Nomura, 2006).

We model the radial column density distribution of $c$-C3H2 as a power law
N${}_{100}\times(r/100)^{p}$, where N100 is the column density at 100 AU in
cm-2, $r$ is the distance from the star in AU, and $p$ is the power-law index.
Since the emission shows a clear indication of a central hole, we fit for both
an inner radius Rin and outer radius Rout together with the power-law
parameters (N100 and $p$). Using the structure model and the fixed vertical
distributions, we compute a grid of synthetic $c$-C3H2 J=$6-5$ visibility
datasets over a range of Rout, Rin, $p$ and N100 values and compare with the
observations. The best-fit model is obtained by minimizing $\chi^{2}$, the
weighted difference between the real and imaginary part of the complex
visibility measured in the ($u,v$)-plane sampled by the ALMA observations. We
use the two-dimensional Monte Carlo model RATRAN (Hogerheijde & van der Tak,
2000) to calculate the radiative transfer and molecular excitation. The
collisional rates are taken from Chandra & Kegel (2000) and the molecular data
file is retrieved from the Leiden Atomic and Molecular Database (Schöier et
al., 2005).

Figure 3 shows the $\chi^{2}$ surfaces for the Rin and $R_{out}$ versus the
power law index $p$. We find the $p$ is constrained between -2.5 and -1.5, Rin
15–40 AU and Rout 150–200 AU (within 1$\sigma$) with best-fit values at -2, 30
and 165 AU, respectively (reduced $\chi^{2}=1.07$). By fixing the above
parameters at their best-fit values, N($c$-C3H2) is determined to be
2.2$\pm$0.2 $\times$1012 cm-2 at 100 AU. Figure 4 presents comparisons between
the observed channel maps and the best-fit model. The residual image doesn’t
show any significant emission, which indicates that the $c$-C3H2 emission is
consistent with that arising from a Keplerian rotating disk. The $6-5$ line is
actually blended with the $6_{1,6}-5_{0,5}$ (ortho) and $6_{0,6}-5_{1,5}$
(para) lines at the same frequency. Since the Einstein $A$-coefficients for
both ortho and para lines are the same, 5.393$\times$10-4 s-1 (Schöier et al.,
2005), we fit the data with the ortho line only and the resulting column
density can be accounted as the sum of both ortho and para forms of the
molecule.

For the weaker $5-4$ ortho line, the signal-to-noise ratio is too low to
provide any constraints on the $c$-C3H2 the distribution. By assuming the
$c$-C3H2 distribution derived from the $6-5$ line, however, we can use the
unresolved line flux to constrain the $o/p$ ratio. The resulting best-fit
N(C3H2-($o$))=1.6$\pm$0.3 $\times$1012 and N(C3H2-($o+p$)=2.2$\pm$0.2
$\times$1012 cm-2 at 100 AU (as shown above). Hence $o/p$=2.7$\pm$1.7, which
is close to the statistical value of 3, but the large uncertainty implies that
better data are required to use this ratio as a probe of formation conditions.

##  4 Discussion

We have clearly detected $c$-C3H2 in the disk around HD 163296. This is one of
the two largest molecules detected in disks so far, the other being HC3N, also
a carbon-chain molecule, detected recently using deep single-dish observations
(Chapillon et al., 2012).

Using the spatially and spectrally resolved line emission, we have constrained
the radial distribution of $c$-C3H2 in the HD 163296 disk as a ring structure
ranging from $\sim$30 to $\sim$165 AU. The outer edge of $<$250 AU (2$\sigma$
limit) is much smaller than the gas disk size which extends to 500 AU (Qi et
al., 2011), which suggests that $c$-C3H2 formation is slow or that $c$-C3H2
destruction is fast in the outer disk. In terms of formation, the best-fit
outer radius coincides with the previously determined location of the CO
midplane snow line, and it is possible that CO freeze-out limits the carbon
available in the gas phase to form hydrocarbons in general and $c$-C3H2 in
particular. A second characteristic of the outer disk is that it is rather
tenuous because of a rapidly decreasing column density outside of 200 AU (Qi
et al., 2011). This may result in efficient penetration of radiation and thus
destruction of the easily dissociated $c$-C3H2. Explicit model predictions are
required to resolve which effect drives the disappearance of $c$-C3H2 in the
outer disk.

No existing disk chemistry model in the literature contains predictions for
the radial distribution of $c$-C3H2. Based on strong correlations found
between $c$-C3H2 and CCH in several astrophysical environments (Lucas & Liszt,
2000; Pety et al., 2005; Gerin et al., 2011), predictions on CCH in disks can
be used to shed further light on the origins of $c$-C3H2. Aikawa & Herbst
(2001) predicts a CCH central cavity in the absence of X-ray radiation; when
X-rays are present, and HD 163296 is a known X-ray emitter (Swartz et al.,
2005; Günther & Schmitt, 2009), the CCH column is instead centrally peaked.
Despite the presence of X-rays, the central cavity could be due to a UV
dominated radiation field. This may be tested by observing $c$-C3H2 towards T
Tauri stars with weak UV fields and strong X-rays, and towards additional
Herbig Ae stars with weak X-rays.

The inner cavity could also be a product of the main formation pathway of
$c$-C3H2. Carbon chains can form through at least three different pathways:
(1) ion-neutral reactions at low temperatures, (2) photo-erosion of larger
carbonaceous compounds, and (3) neutral-neutral reactions at luke-warm
temperatures following CH4 ice evaporation at $\sim$30 K (Herbst et al., 1984;
Teyssier et al., 2004; Sakai et al., 2008; Gerin et al., 2011). Detailed
modeling of $c$-C3H2 radial distributions in each of these formation scenarios
are clearly needed to use $c$-C3H2 rings as tracers of the radiation field and
other disk characteristics.

In addition to more detailed modeling, additional observations are needed to
constrain whether different hydrocarbons, especially CCH and $c$-C3H2, are
correlated in disk environments, and to constrain the vertical distribution of
these molecules. The latter requires multiple lines with a range of excitation
energies. With the combined advance in theory and observations, $c$-C3H2 may
become one of the more useful probes of penetration of the radiation fields in
disks.

Facility: ALMA

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00010.SV.
ALMA is a partnership of ESO (representing its member states), NSF (USA) and
NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in
cooperation with the Republic of Chile. The Joint ALMA Observatory is operated
by ESO, AUI/NRAO and NAOJ.
We would like to thank an anonymous referee for thoughtful suggestions for the
paper. We also acknowledge NASA Origins of Solar Systems grant No. NNX11AK63.

## References

  * Aikawa & Herbst (2001) Aikawa, Y. & Herbst, E. 2001, A&A, 371, 1107
  * Aikawa et al. (2003) Aikawa, Y., Momose, M., Thi, W., et al. 2003, PASJ, 55, 11
  * Aikawa & Nomura (2006) Aikawa, Y. & Nomura, H. 2006, ApJ, 642, 1152
  * Andrews et al. (2009) Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700, 1502
  * Benson et al. (1998) Benson, P. J., Caselli, P., & Myers, P. C. 1998, ApJ, 506, 743
  * Chandra & Kegel (2000) Chandra, S., & Kegel, W. H. 2000, A&AS, 142, 113
  * Chapillon et al. (2012) Chapillon, E., Dutrey, A., Guilloteau, S., et al. 2012, ApJ, 756, 58
  * Cox et al. (1988) Cox, P., Guesten, R., & Henkel, C. 1988, A&A, 206, 108
  * Cox et al. (1989) Cox, P., Walmsley, C. M., & Guesten, R. 1989, A&A, 209, 382
  * Dutrey et al. (1997) Dutrey, A., Guilloteau, S., & Guelin, M. 1997, A&A, 317, L55
  * Dutrey et al. (2007) Dutrey, A., Henning, T., Guilloteau, S., et al. 2007, A&A, 464, 615
  * Fogel et al. (2011) Fogel, J. K. J., Bethell, T. J., Bergin, E. A., Calvet, N., & Semenov, D. 2011, ApJ, 726, 29
  * Fossé et al. (2001) Fossé, D., Cernicharo, J., Gerin, M., & Cox, P. 2001, ApJ, 552, 168
  * Fuente et al. (2010) Fuente, A., Cernicharo, J., Agúndez, M., et al. 2010, A&A, 524, A19
  * Gerin et al. (2011) Gerin, M., Kaźmierczak, M., Jastrzebska, M., et al. 2011, A&A, 525, A116
  * Grady et al. (2000) Grady, C. A., et al. 2000, ApJ, 544, 895
  * Günther & Schmitt (2009) Günther, H. M., & Schmitt, J. H. M. M. 2009, A&A, 494, 1041
  * Henning et al. (2010) Henning, T., Semenov, D., Guilloteau, S., et al. 2010, ApJ, 714, 1511
  * Herbst et al. (1984) Herbst, E., Adams, N. G., & Smith, D. 1984, ApJ, 285, 618
  * Hogerheijde & van der Tak (2000) Hogerheijde, M. R. & van der Tak, F. F. S. 2000, A&A, 362, 697
  * Isella et al. (2007) Isella, A., Testi, L., Natta, A., Neri, R., Wilner, D., & Qi, C. 2007, A&A, 469, 213
  * Liszt et al. (2012) Liszt, H., Sonnentrucker, P., Cordiner, M., & Gerin, M. 2012, ApJ, 753, L28
  * Lucas & Liszt (2000) Lucas, R. & Liszt, H. S. 2000, A&A, 358, 1069
  * Mannings & Sargent (1997) Mannings, V., & Sargent, A. I. 1997, ApJ, 490, 792
  * Matthews & Irvine (1985) Matthews, H. E. & Irvine, W. M. 1985, ApJ, 298, L61
  * Madden et al. (1989) Madden, S. C., Irvine, W. M., Swade, D. A., Matthews, H. E., & Friberg, P. 1989, AJ, 97, 1403
  * Menten et al. (1999) Menten, K. M., Carilli, C. L., & Reid, M. J. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 156, Highly Redshifted Radio Lines, ed. C. L. Carilli, S. J. E. Radford, K. M. Menten, & G. I. Langston, 218
  * Natta et al. (2004) Natta, A., Testi, L., Neri, R., Shepherd, D. S., & Wilner, D. J. 2004, A&A, 416, 179
  * Öberg et al. (2010) Öberg, K. I., Qi, C., Fogel, J. K. J., et al. 2010, ApJ, 720, 480
  * Öberg et al. (2011) Öberg, K. I., Qi, C., Fogel, J. K. J., et al. 2011, ApJ, 734, 98
  * Öberg et al. (2012) Öberg, K. I., Qi, C., Wilner, D. J., & Hogerheijde, M. R. 2012, ApJ, 749, 162
  * Perryman et al. (1997) Perryman, M. A. C., et al. 1997, A&A, 323, L49
  * Park et al. (2006) Park, I. H., Wakelam, V., & Herbst, E. 2006, A&A, 449, 631
  * Pety et al. (2005) Pety, J., Teyssier, D., Fossé, D., et al. 2005, A&A, 435, 885
  * Piétu et al. (2007) Piétu, V., Dutrey, A., & Guilloteau, S. 2007, A&A, 467, 163
  * Qi et al. (2011) Qi, C., D’Alessio, P., Öberg, K. I., et al. 2011, ApJ, 740, 84
  * Qi et al. (2008) Qi, C., Wilner, D. J., Aikawa, Y., Blake, G. A., & Hogerheijde, M. R. 2008, ApJ, 681, 1396
  * Qi et al. (2006) Qi, C., Wilner, D. J., Calvet, N., et al. 2006, ApJ, 636, L157
  * Sakai et al. (2008) Sakai, N., Sakai, T., & Yamamoto, S. 2008, Ap&SS, 313, 153
  * Schöier et al. (2005) Schöier, F. L., van der Tak, F. F. S., van Dishoeck, E. F., & Black, J. H. 2005, A&A, 432, 369
  * Semenov et al. (2005) Semenov, D., Pavlyuchenkov, Y., Schreyer, K., et al. 2005, ApJ, 621, 853
  * Semenov & Wiebe (2011) Semenov, D. & Wiebe, D. 2011, ApJS, 196, 25
  * Swartz et al. (2005) Swartz, D. A., Drake, J. J., Elsner, R. F., et al. 2005, ApJ, 628, 811
  * Tenenbaum et al. (2009) Tenenbaum, E. D., Milam, S. N., Woolf, N. J., & Ziurys, L. M. 2009, ApJ, 704, L108
  * Teyssier et al. (2004) Teyssier, D., Fossé, D., Gerin, M., et al. 2004, A&A, 417, 135
  * Thaddeus et al. (1985) Thaddeus, P., Vrtilek, J. M., & Gottlieb, C. A. 1985, ApJ, 299, L63
  * Thi et al. (2004) Thi, W., van Zadelhoff, G., & van Dishoeck, E. F. 2004, A&A, 425, 955
  * Walsh et al. (2012) Walsh, C., Nomura, H., Millar, T. J., & Aikawa, Y. 2012, ApJ, 747, 114
  * Willacy (2007) Willacy, K. 2007, ApJ, 660, 441

Table 1: $c$-C3H2 line results. Transition | Frequency (GHz) | Eu (K) | Beam |  $\int Fdv$ (mJy km s-1)
---|---|---|---|---
$3_{3,0}-2_{2,1}$ | 216.279 | 19 |  $1\farcs 3\times 1\farcs 2$(76°) | 53[9]
$6_{1,6}-5_{0,5}/6_{0,6}-5_{1,5}$ | 217.822 | 39 |  $0\farcs 9\times 0\farcs 7$(83°) | 185[10]
$5_{1,4}-4_{2,3}$ | 217.940 | 35 |  $1\farcs 3\times 1\farcs 2$(78°) | 74[9]

Figure 1: The integrated intensity maps summed between 0 and 11 km s-1) and
intensity-weighted mean velocity fields of 13CO $2-1$ and $c$-C3H2 $6-5$ lines
(left panel), $c$-C3H2 $5-4$ and $3-2$ lines (right panel) toward HD 163296.
The resolved velocity field of the $c$-C3H2 $6-5$ line agrees with the CO
kinematics. In the $c$-C3H2 maps, the first contour marks 3$\sigma$ followed
by 1$\sigma$ contour increases. The rms varies between 6 and 9 mJy km s-1 per
beam. Synthesized beams are presented in the lower left corners. The star
symbol indicates the continuum (stellar) position. The axes are offsets from
the pointing center in arcseconds. Figure 2: Extracted spectra of the three
$c$-C3H2 transitions toward HD 163296, plotted together with 13CO $2-1$. The
dashed line marks VLSR toward HD 163296.  Figure 3: Iso-$\chi^{2}$ surfaces of
$R_{\rm out}$ and $R_{\rm in}$ versus $p$. Contours correspond to the 1–5
$\sigma$ errors.  Figure 4: The top panel shows the velocity channel map of
the $c$-C3H2 $6-5$ emission toward HD 163296 (velocities binned in 1 km s-1).
Contours are 0.0022 Jy Beam-1 (1$\sigma$) $\times[3,4,5,6,7,8,9]$. The middle
and bottom panels show the best-fit model and the difference between the best-
fit model and data on the same contour scale. The star symbol indicates the
continuum (stellar) position. The axes are offsets from the pointing center in
arcseconds.