Recent HST-ACS observations revealed the presence of a double subgiant branch (SGB) in the core of the Galactic globular cluster NGC 1851. This peculiarity was tentatively explained by the presence of a second population with either an age difference of about 1 Gyr, or a higher C+N+O abundance, probably due to pollution by the first generation of stars.
In the present Letter, we analyze VLT-FORS V,I images, covering 12.7x12.7 arcmin, in the southwest quadrant of the cluster, allowing us to probe the extent of the double SGB from ~1.4 to ~13 arcmin from the cluster center. Our study reveals, for the first time, that the "peculiar" population is the one associated to the fainter SGB. Indeed, while the percentage of stars in this sequence is about 45% in the cluster core (as previously found on the basis of HST-ACS data), we find that it drops sharply, to a level consistent with zero in our data, at ~2.4 arcmin from the cluster center, where the brighter SGB, in our sample, still contains ~100 stars. Implications for the proposed scenarios are discussed.
We present the first chemical analysis of stars on the double subgiant branch (SGB) of the globular cluster NGC 1851. We obtained 48 Magellan IMACS spectra of subgiants and fainter stars covering the spectral region between 3650-6750Å, to derive C and N abundances from the spectral features at 4300Å(G-band) and at ~ 3883Å(CN). We added to our sample ~ 45 unvevolved stars previously observed with FORS2 at the VLT. These two datasets were homogeneously reduced and analyzed. We derived abundances of C and N for a total of 64 stars and found considerable star-to-star variations in both [C/H] and […
The color magnitude diagram (CMD) of NGC 1851 presents two subgiant branches (SGB), probably due the presence of two populations differing in total CNO content. We test the idea that a difference in total CNO may simulate an age difference when comparing the CMD of clusters to derive relative ages. We compare NGC 1851 with NGC 6121 (M4), a cluster of very similar [Fe/H]. We find that, with a suitable shift of the CMDs that brings the two red horizontal branches at the same magnitude level, the unevolved main sequence and red giant branch match, but the SGB of NGC 6121 and its red giant branch …
NGC 6388 and NGC 6441 are two massive Galactic bulge globular clusters which share many properties, including the presence of an extended horizontal branch (HB), quite unexpected because of their high metal content. In this paper we use HST's WFPC2, ACS, and WFC3 images and present a broad multicolor study of their stellar content, covering all main evolutionary branches. The color-magnitude diagrams (CMDs) give compelling evidence that both clusters host at least two stellar populations, which manifest themselves in different ways. NGC 6388 has a broadened main sequence (MS), a split sub-gian…
The presence of extended main-sequence turn-off (eMSTO) regions in intermediate-age star clusters in the Large and Small Magellanic Clouds is often interpreted as resulting from extended star-formation histories (SFHs), lasting $\geq$ 300 Myr. This strongly conflicts with the traditional view of the dominant star-formation mode in stellar clusters, which are thought of as single-aged stellar populations. Here we present a test of this interpretation by exploring the morphology of the subgiant branch (SGB) of NGC 411, which hosts possibly the most extended eMSTO among all known intermediate-age…
Recent high-quality photometry of many star clusters in the Magellanic Clouds with ages of 1$\,-\,$2 Gyr revealed main sequence turnoffs (MSTOs) that are significantly wider than can be accounted for by a simple stellar population (SSP). Such extended MSTOs (eMSTOs) are often interpreted in terms of an age spread of several $10^8$ yr, challenging the traditional view of star clusters as being formed in a single star formation episode. Li et al. and Bastian & Niederhofer recently investigated the sub-giant branches (SGBs) of NGC 1651, NGC 1806, and NGC 1846, three star clusters in the Large Mag…
While the extended main-sequence turn-offs (eMSTOs) found in almost all 1--2 Gyr-old star clusters in the Magellanic Clouds are often explained by postulating extended star-formation histories, the tight subgiant branches (SGBs) seen in some clusters challenge this popular scenario. Puzzlingly, the SGB of the eMSTO cluster NGC 419 is significantly broader at bluer than at redder colors. We carefully assess and confirm the reality of this observational trend. If we would assume that the widths of the features in color--magnitude space were entirely owing to a range in stellar ages, the star-for…
We investigate the new and still poorly studied matter of so-called multiple stellar populations (MSPs) in Galactic globular clusters (GGCs). Studying MSPs and their accumulated data can shed more light on the formation and evolution of GGCs and other closely related fundamental problems. We focus on the strong relation between the radial distribution of evolutionary homogeneous stars and their U-based photometric characteristics in the nearby GGC NGC 6752 and compare this with a similar relation we found in NGC 3201 and NGC 1261. We use our new multi-color photometry in a fairly wide field of…
We have recently shown that the $\sim2$ Gyr old Large Magellanic Cloud star cluster NGC 1978 hosts multiple populations in terms of star-to-star abundance variations in [N/Fe]. These can be seen as a splitting or spread in the sub-giant and red giant branches (SGB and RGB) when certain photometric filter combinations are used. Due to its relative youth, NGC 1978 can be used to place stringent limits on whether multiple bursts of star-formation have taken place within the cluster, as predicted by some models for the origin of multiple populations. We carry out two distinct analyses to test whet…
The Hubble Space Telescope photometric survey of Galactic globular clusters (GCs) has revealed a peculiar "chromosome map" for NGC6934. Besides a typical sequence, similar to that observed in Type I GCs, NGC 6934 displays additional stars on the red side, analogous to the anomalous, Type II GCs, as defined in our previous work. We present a chemical abundance analysis of four red giants in this GC. Two stars are located on the chromosome map sequence common to all GCs, and another two on the additional sequence. We find: (i) star-to-star Fe variations, with the two anomalous stars being enrich…
We report on evidence of the inhomogeneity (multiplicity) of the stellar population in the Galactic globular cluster (GC) NGC 3201, which is irregularly reddened across its face. We carried out a more detailed and careful analysis of our recently published new multi-color photometry in a wide field of the cluster with particular emphasis on the U band. Using the photometric data corrected for differential reddening, we found for the first time two key signs of the inhomogeneity in the cluster's stellar population and of its radial variation in the GC. These are (1) an obvious trend in the colo…
Archival [3.6] and [4.5] images are used to identify and characterize variable stars in the Magellanic-type galaxies Holmberg II, NGC 2366, and IC 2574. Using parametric and non-parametric detection methods, 74 confirmed or suspected long period variables (LPVs) are found. The period distributions of the LPVs in NGC 2366 and IC 2574 are similar. While the period distribution of LPVs in Ho II is uncertain due to small number statistics there appears to be a deficiency of LPVs with periods between 550 and 650 days when compared with NGC 2366 and IC 2574. The LPVs are diffusely distributed on the…
(Abriged)This work studies in more detail the stellar population, including its photometric properties and characteristics, in the rarely studied southern Galactic globular cluster NGC 1261. We focus on the brighter sequences of the cluster's color-magnitude diagram (CMD). Like in our previous works, we rely upon photometry in several passbands to achieve more reliable results and conclusions. We carried out and analyzed new multi-color photometry of NGC 1261 in UBVI reaching below the turnoff point in all passbands in a fairly extended cluster field, about 14'x14'. We found several signs of t…
The analysis of multiple populations (MPs) in globular clusters, both spectroscopically and photometrically, is key in understanding their formation and evolution. The relatively narrow Johnson U, F336W, and Stromgren and Sloan u filters have been crucial in exhibiting these MPs photometrically, but in Paper I we showed that the broader Washington C filter can more efficiently detect MPs in the test case globular cluster NGC 1851. In Paper I we also detected a double MS that has not been detected in previous observations of NGC 1851. We now match this photometry to NGC 1851's published RGB abu…
Using a combination of high-resolution Hubble Space Telescope/WFPC2 observations, we explore the physical properties of the stellar populations in two intermediate-age star clusters in the Large Magellanic Cloud, NGC 1831 and NGC 1868, based on their color-magnitude diagrams. We show that both clusters exhibit extended main-sequence turn-offs. To explain the observations, we consider variations in helium abundance, binarity, age dispersions, and fast rotation of the clusters' member stars. The observed narrow main sequence excludes significant variations in helium abundance in both clusters. W…
We investigate the multiple stellar populations in one of peculiar globular clusters (GCs) M22 using new ground-based wide-field Ca by and HST/WFC3 photometry with equivalent passbands, confirming our previous result that M22 has a distinctive red-giant branch (RGB) split mainly due to difference in metal abundances. We also make use of radial velocity measurements of the large number of cluster membership stars by other. Our main results are followings. (i) The RGB and the subgiant branch (SGB) number ratios show that the calcium-weak (Ca-w) group is the dominant population of the cluster. Ho…
Stars in massive star clusters exhibit intrinsic variations in some light elements (MPs) that are difficult to explain in a coherent formation scenario. In recent years, HST photometry has led to the characterisation of the global properties of th MPs in an unparalleled level of detail. In particular, the colour-colour diagrams known as chromosome maps have been proven to be very efficient at separating cluster stars with field-like metal abundance distribution (1P) from object with distinctive light-element abundance anti-correlations (2P). The unexpected wide colour ranges covered by the 1P …
High-precision astrometry requires accurate point-spread function modeling and accurate geometric-distortion corrections. This paper demonstrates that it is possible to achieve both requirements with data collected at the high acuity wide-field K-band imager (HAWK-I), a wide-field imager installed at the Nasmyth focus of UT4/VLT ESO 8m telescope. Our final astrometric precision reaches ~3 mas per coordinate for a well-exposed star in a single image with a systematic error less than 0.1 mas. We constructed calibrated astro-photometric catalogs and atlases of seven fields: the Baade's Window, NG…
We study the near-infrared properties of the super star cluster NGC1750-1 in order to constrain its spatial extent, its stellar population and its age. We use adaptive optics assisted integral field spectroscopy with SINFONI on the VLT. We estimate the spatial extent of the cluster and extract its K-band spectrum from which we constrain the age of the dominant stellar population. Our observations have an angular resolution of about 0.11", providing an upper limit on the cluster radius of 2.85+/-0.50 pc depending on the assumed distance. The K-band spectrum is dominated by strong CO absorption …
Understanding the exact extent and content of tidal tails of open clusters provide useful clues on how field stars populate the Milky Way. We reanalyse, using Gaia EDR3 data, the tails around the open cluster NGC 752. Compared to previous analyses, we look at a much wider region around the cluster and use first the convergent point method, coupled with a clustering analysis using DBSCAN. We find that the cluster, located 433 pc away and well described by a Plummer profile, has very long and asymmetric tails, extending more than 260 pc on the sky (from tip to tip) - four times larger than previ…
The discovery of faint FR~I radio jets in the nearby elliptical galaxy NGC 5322 is reported here using 144 MHz LOFAR image. The jets have an angular extent of $\sim40$ arcmin or a projected physical extent of $\sim350$ kpc. The faint jets remain well collimated and disappear in the intergalactic medium, without any visible hotspot or radio lobes. The jets detected up to $\sim20$ kpc extent at higher frequencies are relatively bright within the optical extent of the galaxy but become faint abruptly outside, where detection is made only in the LOFAR image. The total radio luminosity of the galax…
NGC 7538 IRS2 is a compact HII region and recent star formation source, with a shell morphology, lying on the border of the visible HII region NGC 7538. We present a spectral cube of the [NeII] 12.8 micron emission line obtained with the TEXES spectrometer on Gemini North with velocity resolution approximately 4 km/s and angular resolution 0.3". The kinematics of the data cube show ionized gas flowing along multiple cavity walls. We have simulated the kinematics and structure of IRS2 with a model of superimposed cavities created by outflows from embedded stars in a cloud with density gradients…
He has been proposed as a key element to interpret the observed multiple MS, SGB, and RGB, as well as the complex horizontal branch (HB) morphology. Stars belonging to the bluer part of the HB, are thought to be more He rich (ΔY=0.03 or more) and more Na-rich/O-poor than those located in the redder part. This hypothesis was only partially confirmed in NGC 6752, where stars of the redder zero-age HB showed a He content of Y=0.25+-0.01, fully compatible with the primordial He content of the Universe, and were all Na-poor/O-rich. Here we study hot blue HB (BHB) stars in the GC NGC 6121 (M4) to me…
We present ALFALFA HI observations of a well studied region of the Leo Cloud, which includes the NGC 3227 group and the NGC 3190 group. We detect optically dark HI tails and plumes with extents potentially exceeding 600 kpc, well beyond the field of view of previous observations. These HI features contain approximately 40% of the total HI mass in the NGC~3227 group and 10% in the NGC~3190 group. We also present WSRT maps which show the complex morphology of the extended emission in the NGC~3227 group. We comment on previously proposed models of the interactions in these groups and the implicat…
The statistical analysis of gathered of astronomical objects (such as open cluster) are excellent tools to compute its parameters and to constrain the theory of its evolution. Here, we are represented detailed structural and membership analysis of an open cluster NGC 1960 through various statistical formulas and approaches. King empirical methods provide the information about the cluster extent as 5.2 +/- 0.4 pc. The exact identification of members of cluster is needed to precise estimation of its age, reddening, metallicity etc., therefore, to identify most probable members (MPMs), we adopted…
We present a comprehensive photometric study of the old open cluster, NGC 6819 using 1x1 degree field VI MOSAIC CCD imaging taken with the WIYN 0.9m telescope. The resultant color-magnitude diagram (CMD) shows a well developed main sequence (MS) extending from V~14.5 mag down to our photometric limit of V~21 mag. Fitting theoretical isochrones with adopted values of the reddening and metallicity (E(B-V)=0.14, [Fe/H]=+0.09 dex) to the observed CMD yields a distance modulus of (m-M)_{0}=11.93+/-0.10 and an age of ~2.6 Gyr for NGC 6819. Our wide-field imaging reveals that NGC 6819 is larger in ar…
Studies of outer regions of spirals disks are fundamental to our understanding of both the process of galaxy assembly and the subsequent secular evolution of galaxies. In an earlier series of papers we explored the extent and abundance gradient in the outer disk of NGC 300 and found an extended purely exponential disk with a metallicity gradient which flattens off in the outermost regions. We now continue the study of outskirts of pure disk spirals with another Sculptor Group spiral, NGC 7793. Using Gemini Multi Object Spectrograph camera at Gemini South, we trace the disk of NGC 7793 with sta…
We present an analysis of the relatively low mass ($\sim2400$~M$_{\odot}$), $\sim800$~Myr, Galactic open cluster, NGC~2818, using Gaia DR2 results combined with VLT/FLAMES spectroscopy. Using Gaia DR2 proper motions and parallax measurements we are able to select a clean sample of cluster members. This cluster displays a clear extended main sequence turn-off (eMSTO), a phenomenon previously studied mainly in young and intermediate age massive clusters in the Magellanic clouds. The main sequence of NGC~2818 is extremely narrow, with a width of $\sim0.01$ magnitudes (G$_{\rm BP} - $ G$_{\rm RP}$…
We present a multi-wavelength observational study of the NGC 2024 filament using infrared to sub-millimeter continuum and the NH$_3$ $(1,1)$ and $(2,2)$ inversion transitions centered on FIR-3, the most massive core therein. FIR-3 is found to have no significant infrared point sources in the Spitzer/IRAC bands. But the NH$_3$ kinetic temperature map shows a peak value at the core center with $T_{\rm k}=25$ K which is significantly higher than the surrounding level ($T_{\rm k}=15-19$ K). Such internal heating signature without an infrared source suggests an ongoing core collapse possibly at a t…
We present a photometric study of the prototype merger remnant NGC 3610 and its globular cluster (GC) system, based on new GEMINI/GMOS and ACS/HST archival images. Thanks to the large FOV of our GMOS data, larger than previous studies, we are able to detect a `classical' bimodal GC colour distribution, corresponding to metal-poor and metal-rich GCs, at intermediate radii and a small subsample of likely young clusters of intermediate colours, mainly located in the outskirts. The extent of the whole GC system is settled as about 40 kpc. The GC population is quite poor, about 500 +/- 110 members,…
Recent work has shown that the properties of multiple populations within massive stellar clusters (i.e., in the extent of their abundance variations as well as the fraction of stars that show the anomalous chemistry) depend on the mass as well as the age of the host cluster. Such correlations are largely unexpected in current models for the formation of multiple populations and hence provide essential insight into their origin. Here we extend or previous study into the presence or absence of multiple populations using integrated light spectroscopy of the $\sim600$~Myr, massive ($\sim10^7 - 10^…
Even after decades of research, the origin of multiple stellar populations in globular clusters remains enigmatic. The question as to whether the galaxy environment plays a role in their formation remains unanswered. To that extent, we analysed two classical (> 10 Gyr old) Large Magellanic Cloud globular clusters namely, NGC 1786 and NGC 1898, using imaging data from Hubble Space Telescope to compare and contrast them with ancient Galactic globular clusters to assess systematic differences that might exist between their abundance variations. We calculated their Red Giant Branch width, subtract…
We present a photometric study of the isolated elliptical NGC 6411 and its globular cluster (GC) system, based on Gemini/GMOS g', r', i' photometry. This galaxy has been the host of a SNIa. Spectral studies indicate an intermediate-age and very metal-rich stellar population in its inner region. The extent of the globular cluster system is about 65 kpc. Its population contains $700\pm45$ members, implying a rather poor system, as normally found for isolated ellipticals. The colour bimodality and luminosity distribution are typical of old GC systems. An excess of bright GCs with intermediate col…
Observations that span a broad range of wavelengths are used to examine asymmetries in the disk of the nearby late-type spiral galaxy NGC 247. The northern spiral arm is over-luminous at all wavelengths when compared with other parts of the galaxy at similar galactocentric radii, while the density of very luminous red stars in the void that is immediately south of this arm matches that in other parts of the disk at the same galactocentric radius. Two bubbles with spatial extents of many kpc are identified in the disk, and many of the young stars in the southern disk of NGC 247 are located in t…
NGC 6872, hereafter the Condor, is a large spiral galaxy that is interacting with its closest companion, the S0 galaxy IC 4970. The extent of the Condor provides an opportunity for detailed investigation of the impact of the interaction on the current star formation rate and its history across the galaxy, on the age and spatial distribution of its stellar population, and on the mechanism that drive the star formation activity. To address these issues we analyzed the far-ultraviolet (FUV) to near-infrared (near-IR) spectral energy distribution (SED) of 17, 10 kpc diameter, regions across the ga…
We report the identification of extended tidal debris potentially associated with the globular cluster NGC 3201, using the RAVE catalogue. We find the debris stars are located at a distance range of 1-7 kpc based on the forthcoming RAVE distance estimates. The derived space velocities and integrals of motion show interesting connections to NGC 3201, modulo uncertainties in the proper motions. Three stars, which are among the 4 most likely candidates for NGC 3201 tidal debris, are separated by 80 degrees on the sky yet are well matched by the 12 Gyr, [Fe/H] = -1.5 isochrone appropriate for the …
We carried out new CO ($J=$1-0, 2-1 and 3-2) observations with NANTEN2 and ASTE in the region of the twin Galactic mini-starbursts NGC 6334 and NGC 6357. We detected two velocity molecular components of 12 km s$^{-1}$ velocity separation, which is continuous over 3 degrees along the plane. In NGC 6334 the two components show similar two-peaked intensity distributions toward the young HII regions and are linked by a bridge feature. In NGC 6357 we found spatially complementary distribution between the two velocity components as well as a bridge feature in velocity. Based on these results we hypo…
We present Mon-735, a detached double-lined eclipsing binary (EB) member of the $\sim$3 Myr old NGC 2264 star forming region, detected by Spitzer. We simultaneously model the Spitzer light curves, follow-up Keck/HIRES radial velocities, and the system's spectral energy distribution to determine self-consistent masses, radii and effective temperatures for both stars. We find that Mon-735 comprises two pre-main sequence M dwarfs with component masses of $M = 0.2918 \pm 0.0099$ and $0.2661 \pm 0.0095$ $\rm{M}_{\odot}$, radii of $R = 0.762 \pm 0.022$ and $0.748 \pm 0.023$ $\rm{R}_{\odot}$, and eff…
We have used a combination of high-resolution Hubble Space Telescope WFPC2 and wide-field ground-based observations, in ultraviolet and optical bands, to study the blue straggler star population of the massive outer-halo globular cluster NGC 5824, over its entire radial extent. We have computed the center of gravity of the cluster and constructed the radial density profile, from detailed star counts. The profile is well reproduced by a Wilson model with a small core (r_c \simeq 4.4 arcsec) and a concentration parameter c \simeq 2.74. We also present the first age determination for this cluster…
The characterisation of the stellar population toward young high-mass star-forming regions allows to constrain fundamental cluster properties like distance and age. These are essential when using high-mass clusters as probes to conduct Galactic studies. NGC 7538 is a star-forming region with an embedded stellar population only unearthed in the near-infrared. We present the first near-infrared spectro-photometric study of the candidate high-mass stellar content in NGC 7538. We obtained H and K spectra of 21 sources with both the multi-object and long-slit modes of LIRIS at the WHT, and compleme…
We report on observational evidence of an extra-tidal clumpy structure around NGC 288 from an homogeneous coverage of a large area with the Pan-STARRS PS1 database. The extra-tidal star population has been disentangled from that of the Milky Way field by using a cleaning technique that successfully reproduced the stellar density, luminosity function and colour distributions of MW field stars. We have produced the cluster stellar density radial profile and a stellar density map from independent approaches, from which we found results in excellent agreement : the feature extends up to 3.5 times …
We analyse Gaia EDR3 and re-calibrated HST proper motion data from the core-collapsed and non core-collapsed globular clusters NGC 6397 and NGC 3201, respectively, with the Bayesian mass-orbit modelling code MAMPOSSt-PM. We use Bayesian evidence and realistic mock data sets constructed with AGAMA to select between different mass models. In both clusters, the velocities are consistent with isotropy within the extent of our data. We robustly detect a dark central mass (DCM) of roughly 1000 solar masses in both clusters. Our MAMPOSSt-PM fits strongly prefer an extended DCM in NGC 6397, while only…
We present Gemini South GMOS g,i photometry of 14 intermediate-age Large Magellanic Cloud (LMC) star clusters, namely: NGC 2155, 2161, 2162, 2173, 2203, 2209, 2213, 2231, 2249, Hodge 6, SL 244, 505, 674, and 769, as part of a continuing project to investigate the extended Main Sequence Turnoff (EMSTO) phenomenon. Extensive artificial star tests were made over the observed field of view. These tests reveal the observed behaviour of photometric errors with magnitude and crowding. The cluster stellar density radial profiles were traced from star counts over the extent of the observed field. We ad…
The case of NGC 5824, a cluster possibly embedded in a dark matter halo
Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究所）；Institute for Astronomy, University of Edimburgh（爱丁堡大学天文研究所）；Departamento de Astronomía, Universidad de Chile（智利大学天文学系）
We have used a combination of high-resolution Hubble Space Telescope WFPC2 and wide-field ground-based observations in ultraviolet and optical bands to study the blue straggler star (BSS) population of the outer-halo globular cluster NGC 6229, over its entire radial extent. A total of 64 bright BSS (with m255 6 21.30, corresponding to m555 6 20.75) has been identified. The BSS projected radial distribution is found to be bimodal, with a high central peak, a well defined minimum at intermediate radii (r \sim 40"), and an upturn in the outskirts. From detailed star counts even in the very inner …
The discovery of the ultra-diffuse galaxy NGC 1052-DF2 and its peculiar population of star clusters has raised new questions about the connections between galaxies and dark matter halos at the extremes of galaxy formation. In light of debates over the measured velocity dispersion of its star clusters and the associated mass estimate, we constrain mass models of DF2 using its observed kinematics with a range of priors on the halo mass. Models in which the galaxy obeys a standard stellar-halo mass relation are in tension with the data and also require a large central density core. Better fits ar…
We performed a Chandra X-ray study of three giant H II regions (GHRs), NGC 5461, NGC 5462, and NGC 5471, in the spiral galaxy M101. The X-ray spectra of the three GHRs all contain a prominent thermal component with a temperature of ~0.2 keV. In NGC 5461, the spatial distribution of the soft (< 1.5 keV) X-ray emission is generally in agreement with the extent of H1105, the most luminous H II region therein, but extends beyond its southern boundary, which could be attributed to outflows from the star cloud between H1105 and H1098. In NGC 5462, the X-ray emission is displaced from the H II region…
We report a 3.4$σ$ detection of the warm-hot, massive, extended circumgalactic medium (CGM) around an L$^\star$ star-forming spiral galaxy NGC 3221, using deep Suzaku observations. The temperature of the gas is $10^{6.1}$ K, comparable to that of the Milky Way CGM. The spatial extent of the gas is at least $150$ kpc. For a $β$-model of density profile with solar abundance, the central emission measure is EM = $3\pm 1 \times 10^{-5}$ cm$^{-6}$ kpc and the central electron density is $n_{eo} = 4\pm 1 \times10^{-4}$ cm$^{-3}$, with a slope of $β= 0.56$. We investigate a range of $β$ values, and f…
