Power-law Density Distribution Research Articles

Quantitative spectroscopy of photospheric-phase type II supernovae

We present first results on the quantitative spectroscopic analysis of the photospheric-phase of Type II supernovae (SN). The analyses are based on the non-LTE model atmosphere code, CMFGEN, of Hillier & Miller (1998). A key asset of CMFGEN is its thorough treatment of line-blanketing due to metal species. From its applicability to hot star environments, the main modifications to the source code were to allow a linear velocity law, a power-law density distribution, an adaptive grid to handle the steep H recombination/ionization front occurring in cooler SN models, and a routine to compute the gray temperature structure in the presence of large velocities. In this first paper we demonstrate the ability of CMFGEN to reproduce, with a high level of accuracy, the UV and optical observations of a sample of well observed Type II SN, i.e. SN1987A and SN1999em, at representative stages of their photospheric evolution. Two principal stages of SN are modeled - that where hydrogen is fully ionized, and that in which H is only partially ionized. We provide detailed and accurate line identifications for our sample of epochs. We discuss the impact on the SED of varying the density exponent, the spatial scale of the SN, the value of Rmax and the metallicity; we illustrate the formation sites for selected lines. Both Hydrogen Balmer and Helium lines (when present) are very well reproduced, even for our adopted CNO-equilibrium abundance values adequate for a massive supergiant progenitor star. NII lines are also predicted in the blue-wing of both Hbeta and HeI 5875A, and thus not associated with peculiar absorption/emission far above the photosphere. We finally present a pedagogical discussion of P-Cygni profile formation and explain, e.g., the noticeable blue-shift of Halpha in early time spectra (much abridged abstract).

COJ= 2–1 and 4–3 Observations of Proto–planetary Nebulae: Time‐variable Mass Loss

Observations made with the Heinrich Hertz Telescope of CO millimeter and submillimeter emission toward a sample of 22 proto-planetary nebula (PPN) candidates resulted in detections of 12 sources in the CO J = 2-1 line. Of these 12, seven sources were also detected in the J = 4-3 line. These 4-3 transitions are the highest yet observed in all but one of these PPNs. Statistical equilibrium/radiative transfer models were calculated for the CO emission in the circumstellar envelopes (CSEs), assuming various power-law density distributions. These models were compared with the intensity and profile shape of the observed spectra. For the region of the CSE probed by CO emission, the density laws must be steeper than inverse squared and are consistent with power laws between ρ ∝ r-3 and r-4. These radial density distributions imply that the mass loss was not constant but increased during the last part of the asymptotic giant branch (AGB) phase. Mass-loss rates at the end of the AGB for the three best-constrained sources are found to be 7.7 × 10-5 M☉ yr-1 (IRAS 22272+5435), 2.3 × 10-5 M☉ yr-1 (IRAS 07134+1005), and 1.3 × 10-5 M☉ yr-1 (IRAS 17436+5003) for the case of ρ ∝ r-3. These time-varying mass-loss rates can be integrated to calculate the enclosed envelope masses ejected in the past ~10,000 yr. The ejected envelope masses close to the star lie in the range 0.02-0.30 M☉; these values are consistent with theoretical models, which indicate that <20% of the stellar mass loss occurs in the last 10,000 years of the AGB. These results are in contrast to some recent dust studies based on infrared emission, however, in which much higher envelope masses are determined. The density laws, mass-loss rates, and enclosed envelope masses that we derive furnish important constraints for evolutionary models of stars in the late AGB and during the transition to the planetary nebula phase.

Constraining the structure of the non-spherical pre-protostellar core L1544

We present a study of the pre-protostellar core L1544. A series of self-consistent, three-dimensional continuum radiative transfer models is constructed. The outputs of these models are convolved with appropriate telescope beam responses, and compared with existing SCUBA data. The resulting comparison allows us to constrain the structure of L1544. We find that the source is well-fitted by a prolate spheroid, having an ellipsoidal power-law density distribution of index m ∼ 2(1.75 < m < 2.25) in to at least r ∼ 1600 au. For r < 1600 au, the data are consistent with either an extension of the power law to smaller radii, or a flattened (Bonner-Ebert-like) density distribution. Furthermore, we find an optical depth along the short axis at 1300 μm of τ 1300,short = 5 x 10 -3 (2 x 10 -3 < τ 1300,short < 8 x 10 -3 ), a central luminosity L* =0(<10 -3 L ○. ), a long-axis diameter D = 0.1 pc [0.08 < D(pc) < 0.16; 16000 < D(au) < 32 000], an axis ratio q = 2 (1.7 < q < 2.5), and an external interstellar radiation field (ISRF) defined by Mathis et al. to within 50 per cent. The outer diameter and axis ratio may each be somewhat larger due to potential on-source chopping in the observations, and the projection of the long axis on to the plane of the sky. While these results are similar to those inferred directly from observations or spherical modelling due to the source transparency at submillimetre wavelengths, we infer a smaller size, lower mass, and higher optical depth/column density, exposed to a stronger external radiation field than previously assumed. Finally, we find that both the spectral energy distribution (SED) and surface brightness distribution are necessary to constrain the source properties in this way, and even a modest variation in X 2 can significantly alter the fit quality.

A Redshift Survey of Nearby Galaxy Groups: The Shape of the Mass Density Profile

We constrain the mass profile and orbital structure of nearby groups and clusters of galaxies. Our method yields the joint probability distribution of the density slope n, the velocity anisotropy β, and the turnover radius r0 for these systems. The measurement technique does not use results from N-body simulations as priors. We incorporate 2419 new redshifts (included here) in the fields of 41 systems of galaxies with z < 0.04. The new groups have median velocity dispersion σ = 360 km s-1. We also use 979 archived redshifts in the fields of eight nearly relaxed clusters with z < 0.1. Within R ≲ 2r200, the data are consistent with a single power-law matter density distribution with slope n = 1.8-2.2 for systems with σ < 470 km s-1 and n = 1.6-2.0 for those with σ > 470 (95% confidence). We show that a simple, scale-free phase-space distribution function (DF) f(E,L2) ∝ (-E)α-1/2L-2β is consistent with the data as long as the matter density has a cusp. Using this DF, matter density profiles with constant-density cores (n = 0) are ruled out with better than 99.7% confidence.

Hubble Space TelescopeObservations of High‐Velocity Lyα and Hα Emission from Supernova Remnant 1987A: The Structure and Development of the Reverse Shock

We present two-dimensional line profiles of high-velocity (~+/-12,000 km s-1) Lyα and Hα emission from supernova remnant 1987A obtained with the Space Telescope Imaging Spectrograph between 1997 September and 2001 September (days 3869-5327 after the explosion). This emission comes from hydrogen in the debris that is excited and ionized as it passes through the remnant's reverse shock. We use these profiles to measure the geometry and development of the reverse-shock surface. The observed emission is confined within ~+/-30° about the remnant's equatorial plane. At the equator, the reverse shock has a radius of ~75% of the distance to the equatorial ring. We detect marginal differences (6%+/-3%) between the location of the reverse-shock front in the northeast and southwest parts of the remnant. The radius of the reverse shock surface increases for latitudes above the equator, a geometry consistent with a model in which the supernova debris expands into a bipolar nebula. Assuming that the outer supernova debris has a power-law density distribution, we can infer from the reverse-shock emission light curve an expansion rate (in the northeast part of the remnant) of 3700+/-900kms-1, consistent with the expansion velocities determined from observations in radio (Manchester et al.) and X-ray (Park et al.; Michael et al.) wavelengths. However, our most recent observation (at day 5327) suggests that the rate of increase of mass flux across the northeast sector of the reverse shock has accelerated, perhaps because of deceleration of the reverse shock caused by the arrival of a reflected shock created when the blast wave struck the inner ring. Resonant scattering within the supernova debris causes Lyα photons created at the reverse shock to be directed preferentially outward, resulting in a factor of ~5 difference in the observed brightness of the reverse shock in Lyα between the near and far sides of the remnant. Accounting for this effect, we compare the observed reverse-shock Lyα and Hα fluxes to infer the amount of interstellar extinction by dust as E(B-V)=0.17+/-0.01 mag. We also notice extinction by dust in the equatorial ring with E(B-V)~0.02-0.08 mag, which implies dust-to-gas ratios similar to that of the LMC. Since Hα photons are optically thin to scattering, the observed asymmetry in brightness of Hα from the near and far sides of the remnant represents a real asymmetry in the mass flux through the reverse shock of ~30%. We discuss future observational strategies that will permit us to further investigate the reverse-shock dynamics and resonant scattering of the Lyα line and to constrain better the extinction by dust within and in front of the remnant.

The Physical Conditions for Massive Star Formation: Dust Continuum Maps and Modeling

Fifty-one dense cores associated with water masers were mapped at 350 micron. These cores are very luminous, 10^3 < Lbol/Lsun < 10^6, indicative of the formation of massive stars. Dust continuum contour maps and photometry are presented for these sources. The spectral energy distributions and normalized radial profiles of dust continuum emission were modeled for 31 sources using a one-dimensional dust radiative transfer code, assuming a power law density distribution in the envelope, n = n_f (r/r_f)^{-p}. The best fit density power law exponent, p, ranged from 0.75 to 2.5 with = 1.8 +/- 0.4. The mean value of p is comparable to that found in regions forming only low mass stars. The mean p is incompatible with a logatropic sphere (p = 1), but other star formation models cannot be ruled out. Different mass estimates are compared and mean masses of gas and dust are reported within a half-power radius determined from the dust emission and within a radius where the total density exceeds 10^4 cm^3. Evolutionary indicators commonly used for low mass star formation may have some utility for regions forming massive stars. For comparison with extragalactic star formation studies, the luminosity to dust mass ratio is calculated for these sources with a method most parallel to that used in studies of distant galaxies and is found to be similar to that seen in high redshift starburst galaxies.

Self‐similar Champagne Flows in HiiRegions

We consider the idealized expansion of an initially self-gravitating, static, singular, isothermal cloud core. For t ≥ 0, the gas is ionized and heated to a higher uniform temperature by the formation of a luminous but massless star in its center. The approximation that the mass and gravity of the central star are negligible for the subsequent motion of the H II region holds for distances r much greater than ~100 AU and for the massive cloud cores that give rise to high-mass stars. If the initial ionization and heating are approximated to occur instantaneously at t = 0, then the subsequent flow (for r ≫ 100 AU) caused by the resulting imbalance between self-gravity and thermal pressure is self-similar. Because of the steep density profile (ρ ∝ r-2), pressure gradients produce a shock front that travels into the cloud, accelerating the gas to supersonic velocities in what has been called the "champagne phase." The expansion of the inner region at t > 0 is connected to the outer envelope of the now ionized cloud core through this shock, whose strength depends on the temperature of the H II gas. In particular, we find a modified Larson-Penston (L-P) type of solution as part of the linear sequence of self-similar champagne outflows. The modification involves the proper insertion of a shock and produces the right behavior at infinity (v → 0) for an outflow of finite duration, reconciling the long-standing conflict on the correct (inflow or outflow) interpretation for the original L-P solution. For realistic heating due to a massive young central star that ionizes and heats the gas to ~104 K, we show that even the self-gravity of the ionized gas of the massive molecular cloud core can be neglected. We then study the self-similar solutions of the expansion of H II regions embedded in molecular clouds characterized by more general power-law density distributions: ρ ∝ r-n with 3/2 < n < 3. In these cases, the shock velocity is an increasing function of the exponent n and diverges as n → 3. We show that this happens because the model includes an origin where the pressure driving the shock diverges because the enclosed heated mass is infinite. Our results imply that the continued photoevaporation of massive reservoirs of neutral gas (e.g., surrounding disks and/or globules) near the embedded ionizing source is required in order to maintain over a significant timescale the emission measure observed in champagne flows.

Numerical methods for non-LTE line radiative transfer: Performance and convergence characteristics

Comparison is made between a number of independent computer programs for radiative transfer in molecular rota- tional lines. The test models are spherically symmetric circumstellar envelopes with a given density and temperature profile. The first two test models have a simple power law density distribution, constant temperature and a fictive 2-level molecule, while the other two test models consist of an inside-out collapsing envelope observed in rotational transitions of HCO + .F or the 2-level molecule test problems all codes agree well to within 0.2%, comparable to the accuracy of the individual codes, for low optical depth and up to 2% for high optical depths (τ = 4800). The problem of the collapsing cloud in HCO + has a larger spread in results, ranging up to 12% for the J = 4 population. The spread is largest at the radius where the transition from collisional to radiative excitation occurs. The resulting line profiles for the HCO + J = 4-3 transition agree to within 10%, i.e., within the calibration accuracy of most current telescopes. The comparison project and the results described in this paper provide a benchmark for future code development, and give an indication of the typical accuracy of present day calculations of molecular line transfer.

Bullets in a Core‐Collapse Supernova Remnant: The Vela Remnant

We use two-dimensional hydrodynamical simulations to investigate the properties of dense ejecta clumps (bullets) in a core-collapse supernova remnant, motivated by the observation of protrusions probably caused by clumps in the Vela supernova remnant. The ejecta, with an inner flat and an outer steep power-law density distribution, were assumed to freely expand into an ambient medium with a constant density, ~0.1 H atoms cm-3 for the case of Vela. At an age of 104 yr, the reverse shock front is expected to have moved back to the center of the remnant. Ejecta clumps with an initial density contrast χ ~ 100 relative to their surroundings are found to be rapidly fragmented and decelerated. In order to cause a pronounced protrusion on the blast wave, as observed in the Vela remnant, χ ~ 1000 may be required. In this case, the clump should be near the inflection point in the ejecta density profile, at an ejecta velocity ~3000 km s-1. These results apply to moderately large clumps; smaller clumps would require an even larger density contrast. Clumps can create ring structure in the shell of the Vela remnant, and we investigate the possibility that RX J0852-4622, an apparent supernova remnant superposed on Vela, is actually part of the Vela shell. Radio observations support this picture, but the possible presence of a compact object argues against it. The Ni bubble effect or compression in a pulsar wind nebula are possible mechanisms to produce the clumping.

The Beaming Pattern and Spectrum of Radiation from Inverse Compton Scattering in Blazars

By including Klein-Nishina effects, we generalize previous calculations of the beaming pattern of photons produced by inverse Compton scattering. For an isotropic distribution of soft photons upscattered by nonthermal electrons with a power-law density distribution n(γ) ∝ γ-p, embedded in a plasma moving with relativistic bulk speed, we show that the observed radiation intensity is proportional to D3+p, where D is the Doppler boosting factor. This agrees with previous computations performed in the Thomson limit, where the observed spectral index is α = (p - 1)/2 and the beaming pattern is D4+2α. Independent of D, Klein-Nishina effects limit the location of the peak energy peakmec2 of the observed spectral energy distribution such that peak ≲ 1/0, where 0 is the energy of the seed photons in units of mec2. Assuming that the seed photons originate in the broad-line region, we demonstrate that the GeV emission of blazars is significantly modified by Klein-Nishina effects, the spectrum being softer than that calculated in the Thomson limit. We further show that the change in the spectral index of the inverse Compton emission across peak can exceed the value of 0.5 predicted by computations performed in the Thomson limit. The model spectra agree with OSSE and COMPTEL limits on this break without invoking the effects of differential absorption at the edge of a gamma-ray photosphere.

Dense cores in the L1630 molecular cloud: discovering new protostars with SCUBA

Maps of the 450 micron and 850 micron dust continuum emission from three star-forming condensations within the Lynds 1630 molecular cloud, made with the SCUBA bolometer array, reveal the presence of four new submillimetre sources, each of a few solar masses, two of which are probably Class I, two Class 0, as well as several sources whose existence was previously known. The sources are located in filaments and appear elongated when observed at 450 microns. They likely have dust temperatures in the range 10 to 20 K, in good agreement with previous ammonia temperature estimates. Attempts to fit their structures with power-law and Gaussian density distributions suggest that the central distribution is flatter than expected for a simple singular isothermal sphere. Although the statistics are poor, our results suggest that the ratio of `protostellar core' mass to total virial mass may be similar for both large and small condensations.

Tracing the Mass during Low‐Mass Star Formation. II. Modeling the Submillimeter Emission from Preprotostellar Cores

We have modeled the emission from dust in preprotostellar cores, including a self-consistent calculation of the temperature distribution for each input density distribution. Model density distributions include Bonnor-Ebert spheres and power laws. The Bonnor-Ebert spheres fit the data well for all three cores that we have modeled. The dust temperatures decline to very low values (Td ~ 7 K) in the centers of these cores, strongly affecting the dust emission. Compared to earlier models that assume constant dust temperatures, our models indicate higher central densities and smaller regions of relatively constant density. Indeed, for L1544, a power-law density distribution, similar to that of a singular, isothermal sphere, cannot be ruled out. For the three sources modeled herein, there seems to be a sequence of increasing central condensation, from L1512 to L1689B to L1544. The two denser cores, L1689B and L1544, have spectroscopic evidence for contraction, suggesting an evolutionary sequence for preprotostellar cores.

The Fundamental Plane as a consequence of Clausius’ virial minimum

In order to explain the main features of the Fundamental Plane for pressure-supported, elliptical galaxies, we analysed the virialized state, at Clausius’ virial minimum, of a bright component which is completely embedded inside a dark halo. It was assumed that the two subsystems are concentric and coaxial, similar, heterogeneous spheroids, with two different, power-law density distributions. The peculiarities of Clausius’ virial minimum are: (i) it provides an induced scale length for the luminous structure, which, at given mass distributions, corresponds to the maximum virial dimension with minimal random kinetic energy; (ii) it shares in almost equal amounts, tidal-potential energy due to a dark halo, and self-potential energy. These properties and the structure of dark matter halo, which allows the existence of the virial minimum, turn out to be the key for understanding the observed properties of FP. A universal, dark matter distribution of exponent d≃0.5 inside the luminous subsystem, seems to be required when comparing with the observed tilt of FP.

Tracing the Mass during Low‐Mass Star Formation. I. Submillimeter Continuum Observations

We have obtained 850 and 450 micron continuum maps of 21 low mass cores with SED's ranging from pre-protostellar to Class I (18K < Tbol < 370K), using SCUBA at the JCMT. In this paper we present the maps, radial intensity profiles, and photometry. Pre-protostellar cores do not have power-law intensity profiles, whereas the intensity profiles of Class 0 and Class I sources can be fitted with power laws over a large range of radii. A substantial number of sources have companion sources within a few arcminutes (2 out of 5 pre-protostellar cores, 9 out of 16 Class 0/I sources). The mean separation between sources is 10800 AU. The median separation is 18000 AU including sources without companions as a lower limit. The mean value of the spectral index between 450 and 850 microns is 2.8 +- 0.4, with PPCs having slightly lower spectral indices (2.5 +- 0.4). The mean mass of the sample, based on the dust emission in a 120 arcsecond aperture, is 1.1 +- 0.9 solar masses. For the sources fitted by power-law intensity distributions (I_nu(b)/I_nu(0) = (b/b_0) ^ m), the mean value of m is 1.52 +- 0.45 for Class 0 and I sources at 850 microns and 1.44 +- 0.25 at 450 microns. Based on a simple analysis, assuming the emission is in the Rayleigh-Jeans limit and that T_d(r) ~ r ^ {-0.4}, these values of m translate into power-law density distributions (n ~ r ^ {-p}) with p ~ 2.1. However, we show that this result may be changed by more careful consideration of effects such as beam size and shape, finite outer radii, more realistic T_d(r), and failure of the Rayleigh-Jeans approximation.

The Density Structure of Highly Compact H [CSC]ii[/CSC] Regions

We report the density structure of the ultracompact (UC) H ii regions G35.2021.74, G9.6210.19-E, and G75.7810.34-H O. The density profiles are derived from radio continuum emission at wavelengths from 6 to 2 0.3 cm. In the case of G35.2021.74, a cometary UC H ii region with a core and a tail, the spectrum of the core varies as , implying that the density structure is . The emission from the tail has a flatter spectrum, 0.6 22 S / n n / r n e indicating that the density gradient is also negative but shallower. For the case of G9.62 10.19, which is an H ii region complex with several components, the spectrum of the region designated component E is , cor0.95 S / n n responding to . The steepest spectral index, , is for the super UC H ii region G75.7810.34-H O; 22.5 1.4 n / rS / n e n 2 its density stratification may be as steep as . The actual density gradient may be smaller, owing to an 24 n / r e exponential (rather than a power-law) density distribution or to the effects of finite spatial extent. The contribution from dust emission and some of the possible implications of these density distributions are briefly discussed. Stellar groups form in the dense cores of molecular clouds. The structure of these clouds has been unveiled with optical, infrared, and radio observations over the last three decades, and a great effort has been made to understand the connections between cloud properties and star-forming activity. In particular, knowledge of the gas density structure is required to determine fundamental properties, such as the mass and stability of star-forming cores. Extinction studies can be used to derive the density profiles of clouds, but given the large opacities involved, they can only probe the outermost gas layers. Tracers occurring at radio frequencies, on the other hand, can penetrate deeper into the cloud and can reveal the density stratification of dark clouds and cloud cores. The information obtained from extinction and molecular-line studies shows that molecular clouds are centrally condensed. For instance, moderate-density (10 3 ‐10 5 cm ) envelopes sur23 rounding higher density (10 7 cm ) cores suggest the existence 23

Measuring angular diameters of extended sources

When measuring diameters of partially resolved sources like planetary nebulae, H ii regions or galaxies, often a technique called Gaussian deconvolution is used. This technique yields a Gaussian diameter, which subsequently has to be multiplied by a conversion factor to obtain the true angular diameter of the source. This conversion factor is a function of the FWHM of the beam or point spread function, and also depends on the intrinsic surface brightness distribution of the source. In this paper, conversion factors are presented for a number of simple geometries: a circular constant surface brightness disc and a spherical constant emissivity shell, using a range of values for the inner radius. Also, more realistic geometries are studied, based on a spherically symmetric photoionization model of a planetary nebula. This enables a study of optical depth effects, a comparison between images in various emission lines, and the use of power-law density distributions. It is found that the conversion factor depends quite critically on the intrinsic surface brightness distribution, which is usually unknown. The uncertainty is particularly large if extended regions of low surface brightness are present in the nebula. In such cases the use of Gaussian or second-moment deconvolution is not recommended. As an alternative, a new algorithm is presented which allows the determination of the intrinsic FWHM of the source using only the observed surface brightness distribution and the FWHM of the beam. Hence no assumptions concerning the intrinsic surface brightness distribution are needed. Tests show that this implicit deconvolution method works well in realistic conditions, even when the signal-to-noise ratio is low, provided that the beamsize is less than roughly 2/3 of the observed FWHM and the beam profile can be approximated by a Gaussian. A code implementing this algorithm is available.

The origin and formation of cuspy density profiles through violent relaxation of stellar systems

It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ρ∝r−1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n, of the density profiles, defined as ρ∝r−n, changes from n≈2.1 at intermediate radii to a shallower power than n≈2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.

The Jeans-Buneman Instability in the Presence of an Ion Beam in a Dusty Plasma and the Influence of Dust-Size Distribution

The fluid dispersion relation for the Jeans-Buneman instability is solved for a three component plasma consisting of warm electrons and ions, and cold dust grains. In our model the electrons are assumed to be in electrostatic equilibrium, merely providing Debye shielding. The Buneman instability is driven by the free energy of the ions drifting relative to the dust grains. The transition from the purely Jeans to the Buneman instability is studied as a function of the ion beam speed, ion to electron temperature ratio and the wave number. The effect of the magnitude of the Jeans frequency in comparison to the dust plasma frequency is also examined. Initially the dust grains are assumed to be of uniform charge and mass. Thereafter, the influence of dust-size distributions following a power law density distribution is investigated.

A point explosion within a cavity with power-law density distribution

A point explosion within a cavity with power-law density distribution

A Very Dense Low-Mass Molecular Condensation in Taurus: Evidence for the Moment of Protostellar Core Formation

We present evidence for a protostellar condensation that is very close to the moment of the formation of a protostellar core within a time scale of ∼ 104 yr. This starless condensation, named MC 27 in complete surveyed molecular condensations in Taurus, is ∼ 0.1 pc in size and ∼ 3M® in mass. It exhibits fairly strong and narrow H13CO+ emission of the J = 4–3, 3–2, and 1–0 transitions, as well as self-reversed profiles of HCO+ J = 4–3 and 3–2. MC 27 has a density of – 106 cm″3 within – 1000 AU at the center, which is the highest value among the ∼ 40 starless condensations in Taurus. MC 27 shows a sharply peaked density distribution; the molecular intensity is well fitted by a power-law density distribution of $\textrm r\sim\sim^2$ over 0.02 pc &amp;lt; r &amp;lt; 0.2 pc. A statistical analysis indicates a very short time scale of ∼ 104 yr, which is consistent with a free-fall time scale for a density of ∼ 106 cm−3. These properties strongly suggest that MC 27 is in a very early stage of star formation. A Monte Carlo simulation of the present profiles indicates that the infall velocity at 2000–3000 AU should be 0.2–0.3 km s″1 while it is less than 0.3 km s−1 at &amp;lt; 1000 AU. This derived infall velocity profile can be explained by a dynamical-collapse model of supercritical condensation prior to formation of the first protostellar core by ∼ 103−4 yr.