(Abridged) We performed a spectroscopic galaxy survey, complete to m<20.3 (L_B>0.15L_B* at z=0.3), within 100x100" of the quasar Q1127-145 (z=1.18). The VLT/UVES quasar spectrum contains three z<0.33 MgII absorption systems. We obtained eight new galaxy redshifts, adding to the four previously known, and galaxy star formation rates and metallicities were computed where possible. A strong MgII system [W_r(2796)=1.8A], which is a known DLA, had three previously identified galaxies; we found two additional galaxies associated with this system. These five galaxies form a group with diverse properties, such as a luminosity range of 0.04<L_B<0.63L_B*, an impact parameter range of 17<D<241kpc and velocity dispersion of 115km/s. The DLA group galaxy redshifts span beyond the 350km/s velocity spread of the metallic absorption lines of the DLA itself. The two brightest group galaxies have SFRs of a few Msun/yr and should not have strong winds. We have sufficient spectroscopic information to directly compare three of the five group galaxies' (emission-line) metallicities with the DLA (absorption) metallicity: the DLA metallicity is 1/10th solar, substantially lower than the three galaxies' which range between less than 1/2 solar to solar metallicity. HST/WFPC-2 imaging shows perturbed morphologies for the three brightest group galaxies, with tidal tails extending 25kpc. We favor a scenario where the DLA absorption originates from tidal debris in the group environment. Another absorber exhibits weak MgII absorption [W_r(2796)=0.03A] and had a previously identified galaxy at a similar redshift. We have identified a second galaxy associated with this system. Both galaxies have solar metallicities and unperturbed morphologies. The SFR of one galaxy is much lower than expected for strong outflows. Finally, we have identified five galaxies at large impact parameters with no associated MgII absorption.
Physical properties of Damped Lyman-alpha absorbers and their evolution are closely related to galaxy formation and evolution theories, and have important cosmological implications. H I 21 cm absorption study is one useful way of measuring the temperature of these systems. In this work, very strong constraints on the temperature of two Damped Lyman-alpha absorbers at z > 3 are derived from low radio frequency observations. The H I spin temperature is found to be greater than 2000 K for both the absorbers. The high spin temperature of these high-redshift systems is in agreement with the trend f…
By comparing the widths of absorption lines from OI, SiII and FeII in the redshift z=2.076 single-component damped Lyman alpha absorption system in the spectrum of Q2206-199 we establish that these absorption lines arise in Warm Neutral Medium gas at ~12000 +/- 3000K. This is consistent with thermal equilibrium model estimates of ~ 8000K for the Warm Neutral Medium in galaxies, but not with the presence of a significant cold component. It is also consistent with, but not required by, the absence of CII* fine structure absorption in this system. Some possible implications concerning abundance e…
We demonstrate that the Lyman alpha emission in the absorption troughs of a large sample of stacked damped Lyman alpha absorption systems (DLAS) presented by Rahmani et al (2010) is consistent with the spectral profiles and luminosities of a recently detected population of faint Lyman alpha emitters at z ~ 3. This result supports the suggestion that the faint emitters are to be identified with the host galaxies of DLAS at these redshifts.
Distant luminous quasars provide important information on the growth of the first supermassive black holes, their host galaxies and the epoch of reionization. The identification of quasars is usually performed through detection of their Lyman-$α$ line redshifted to $\sim$ 0.9 microns at z>6.5. Here, we report the discovery of a very Lyman-$α$ luminous quasar, PSO J006.1240+39.2219 at redshift z=6.618, selected based on its red colour and multi-epoch detection of the Lyman-$α$ emission in a single near-infrared band. The Lyman-$α$-line luminosity of PSO J006.1240+39.2219 is unusually high and e…
In this work we report deep MUSE observations of a Broad Absorption Line (BAL) quasar at z ~ 5, revealing a Lyman alpha nebula with a maximum projected linear size of ~ 60 kpc around the quasar (down to our 2-sigma SB limit per layer of ~ 9e-19 erg/s/cm^2/arcsec^2 for a 1 arcsec^2 aperture). After correcting for the cosmological surface brightness dimming, we find that our nebula, at z ~ 5, has an intrinsically less extended Lyman alpha emission than nebulae at lower redshift. However, such a discrepancy is greatly reduced when referring to comoving distances, which take into account the cosmo…
We investigate the large-scale structure of Lyman-alpha emission intensity in the Universe at redshifts z=2-3.5 using cross-correlation techniques. Our Lya emission samples are spectra of BOSS Luminous Red Galaxies from Data Release 12 with the best fit model galaxies subtracted. We cross-correlate the residual flux in these spectra with BOSS quasars, and detect a positive signal on scales 1-15 Mpc/h. We identify and remove a source of contamination not previously accounted for, due to the effects of quasar clustering on cross-fibre light. Corrected, our quasar-Lya emission cross-correlation i…
We study the H2 molecular content in high redshift damped Lyman-alpha systems (DLAs) as a function of the HI column density. We find a significant increase of the H2 molecular content around log N(HI) (cm^-2)~21.5-22, a regime unprobed until now in intervening DLAs, beyond which the majority of systems have log N(H2) > 17. This is in contrast with lines of sight towards nearby stars, where such H2 column densities are always detected as soon as log N(HI)>20.7. This can qualitatively be explained by the lower average metallicity and possibly higher surrounding UV radiation in DLAs. However, unl…
Damped Ly-alpha absorbers (DLAs) are a well-studied class of absorption line systems, and yet the properties of their host galaxies remain largely unknown. To investigate the origin of these systems, we have conducted an imaging survey of 32 quasar fields with intervening DLAs between z~1.9-3.8, leveraging a technique that allows us to image galaxies at any small angular separation from the background quasars. In this paper, we present the properties of the targeted DLA sample, new imaging observations of the quasar fields, and the analysis of new and archival spectra of the background quasars…
We examine the kinematic structure of Damped Lyman-alpha Systems (DLAs) in a series of cosmological hydrodynamic simulations using the AREPO code. We are able to match the distribution of velocity widths of associated low ionisation metal absorbers substantially better than earlier work. Our simulations produce a population of DLAs dominated by halos with virial velocities around 70 km/s, consistent with a picture of relatively small, faint objects. In addition, we reproduce the observed correlation between velocity width and metallicity and the equivalent width distribution of SiII. Some disc…
We report a deep search for redshifted HI 21 cm emission from three damped and sub-damped Lyman-$α$ absorbers (DLAs) at $z \approx 0.1$ with the Green Bank Telescope (GBT). No evidence for a redshifted HI 21 cm emission signal was obtained in the GBT spectra of two absorbers, with the data on the third rendered unusable by terrestrial interference. The non-detections of HI 21 cm emission yield strong constraints on the HI masses of the associated galaxies, M$_{\rm HI} < 2.3 \times 10^9 \times (ΔV/100)^{1/2}$ M$_\odot$ for the sub-DLA at $z = 0.0830$ towards J1553+3548, and M$_{\rm HI} < 2.7 \t…
We present a comprehensive analysis of the spin temperature/covering factor degeneracy, T/f, in damped Lyman-alpha absorption systems. By normalising the upper limits and including these via a survival analysis, there is, as previously claimed, an apparent increase in T/f with redshift at z > 1. However, when we account for the geometry effects of an expanding Universe, neglected by the previous studies, this increase in T/f at z > 1 is preceded by a decrease at z < 1. Using high resolution radio images of the background continuum sources, we can transform the T/f degeneracy to T/d^2, where d …
We present new estimates for the statistical properties of damped Lyman-$α$ absorbers (DLAs). We compute the column density distribution function at $z>2$, the line density, $\mathrm{d}N/\mathrm{d}X$, and the neutral hydrogen density, $Ω_\mathrm{DLA}$. Our estimates are derived from the DLA catalogue of Garnett 2016, which uses the SDSS-III DR12 quasar spectroscopic survey. This catalogue provides a probability that a given spectrum contains a DLA, allowing us to use even the noisiest data without biasing our results and thus substantially increase our sample size. We measure a non-zero column…
The relative abundances of the Fe-peak elements (Ti-Zn) at the lowest metallicities are intimately linked to the physics of core-collapse supernova explosions. With a sample of 25 very metal-poor damped Lyman-alpha systems, we investigate the trends of the Fe-peak element ratios with metallicity. For nine of the 25 DLAs, a direct measurement (or useful upper limit) of one or more of the Ti,Cr,Co,Ni,Zn/Fe abundance ratios could be determined from detected absorption lines. For the remaining systems (without detections), we devised a new form of spectral stacking to estimate the typical Fe-peak …
Reconstruction techniques for intrinsic quasar continua are crucial for the precision study of Lyman-$α$ (Ly-$α$) and Lyman-$β$ (Ly-$β$) transmission at $z>5.0$, where the $λ<1215 A$ emission of quasars is nearly completely absorbed. While the number and quality of spectroscopic observations has become theoretically sufficient to quantify Ly-$α$ transmission at $5.0<z<6.0$ to better than $1\%$, the biases and uncertainties arising from predicting the unabsorbed continuum are not known to the same level. In this paper, we systematically evaluate eight reconstruction techniques on a unified test…
We present a study of ~100 high redshift (z~2-4) extremely strong damped Lyman-alpha systems (ESDLA, with N(HI)>0.5x10^22 cm^-2) detected in quasar spectra from the Baryon Oscillation Spectroscopic Survey SDSS-III DR11. We study the neutral hydrogen, metal, and dust content of this elusive population of absorbers and confirm our previous finding that the high column density end of the N(HI) frequency distribution has a relatively shallow slope with power-law index -3.6, similar to what is seen from 21-cm maps in nearby galaxies. The stacked absorption spectrum indicates a typical metallicity ~…
We estimate the abundance of dust in damped Lyman-α absorbers (DLAs) by statistically measuring the excess reddening they induce on their background quasars. We detect systematic reddening behind DLA consistent with the SMC type reddening curve, but it is inconsistent with the Milky Way type reddening. We find that the derived dust-to-gas ratio is, on average, inversely proportional to the column density of neutral hydrogen, implying that the amount of dust is constant, irrespective of the column density of hydrogen. It means that the average metallicity is inversely proportional to the column…
We argue that the lack of observed damped Lyman alpha (DLA) systems that simultaneously have high HI columns densities and high metallicities results naturally from the formation of molecules in the cold phase of a two-phase atomic medium in pressure balance. Our result applies equally well in diffuse systems where the ultraviolet radiation field is dominated by the extragalactic background and in dense star-forming ones, where the local radiation field is likely to be orders of magnitude higher. We point out that such a radiation-insensitive model is required to explain the absence of high co…
Simulations of structure formation in the Universe predict that galaxies are embedded in a "cosmic web", where the majority of baryons reside as rarefied and highly ionized gas. This material has been studied for decades in absorption against background sources, but the sparseness of these inherently one-dimensional probes preclude direct constraints on the three-dimensional morphology of the underlying web. Here we report observations of a cosmic web filament in Lyman-alpha emission, discovered during a survey for cosmic gas fluorescently "illuminated" by bright quasars at z=2.3. With a proje…
We present chemical abundance measurements for 47 damped Lyman-alpha systems (DLAs), 30 at z>4, observed with the Echellette Spectrograph and Imager and the High Resolution Echelle Spectrometer on the Keck telescopes. HI column densities of the DLAs are measured with Voigt profile fits to the Lyman-alpha profiles, and we find an increased number of false DLA identifications with SDSS at z>4 due to the increased density of the Lyman-alpha forest. Ionic column densities are determined using the apparent optical depth method, and we combine our new metallicity measurements with 195 from previous …
Signs of damping wing absorption attenuating the Lyman-$α$ emission line of the first known $z \sim 7$ quasar, ULAS J1120+0641, recently provided exciting evidence of a significantly neutral IGM. This long-awaited signature of reionization was inferred, in part, from a deficit of flux in the quasar's Lyman-$α$ emission line based on predictions from a composite of lower-redshift quasars. The composite sample was chosen based on its C IV emission line properties; however, as the original study by Mortlock et al. noted, the composite contained a slight velocity offset in C IV compared to ULAS J1…
The XQ-100 survey provides optical and near infrared coverage of 36 blindly selected, intervening damped Lyman alpha systems (DLAs) at 2 < z < 4, simultaneously covering the MgII doublet at 2796A, 2803A, and the Ly-alpha transition. Using the XQ-100 DLA sample, we investigate the completeness of selecting DLA absorbers based on their MgII rest-frame equivalent width (W2796) at these redshifts. Of the 29 DLAs with clean MgII profiles, we find that six (20% of DLAs) have W2796 < 0.6A. The DLA incidence rate of W2796 < 0.6A absorbers is a factor of ~5 higher than what is seen in z~1 samples, indi…
We present long-slit spectroscopic data which reveals extended Lyman alpha emission around the z=6.417 radio-quiet quasar CFHQS J2329-0301. The Lyman alpha emission is extended over 15 kpc and has a luminosity of > 8 x 10^36 W, comparable to the most luminous Lyman alpha halos known. The emission has complex kinematics, in part due to foreground absorption which only partly covers the extended nebula. The velocity ranges from -500 km/s to +500 km/s, with a peak remarkably close to the systemic velocity identified by broad MgII emission of the quasar. There is no evidence for infall or outflow …
We present the characteristics of the Damped Lyman-$α$ (DLA) systems found in the data release DR16 of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) of the Sloan Digital Sky Survey (SDSS). DLAs were identified using the convolutional neural network (CNN) of~\cite{Parks2018}. A total of 117,458 absorber candidates were found with $2 \leq \zdla \leq 5.5$ and $19.7 \leq \lognhi \leq 22$, including 57,136 DLA candidates with $\lognhi \geq 20.3$. Mock quasar spectra were used to estimate DLA detection efficiency and the purity of the resulting catalog. Restricting the quasar sample t…
We present high resolution observations of an extremely metal-poor damped Lyman-alpha system, at z_abs = 2.3400972 in the spectrum of the QSO J0035-0918, exhibiting an abundance pattern consistent with model predictions for the supernova yields of Population III stars. Specifically, this DLA has [Fe/H] = -3.04, shows a clear `odd-even' effect, and is C-rich with [C/Fe] = +1.53, a factor of about 20 greater than reported in any other damped Lyman-alpha system. In analogy to the carbon-enhanced metal-poor stars in the Galactic halo (with [C/Fe] > +1.0), this is the first reported case of a carbo…
We cross-correlate the positions of damped Lyman-$α$ systems (DLAs) and their parent quasar catalog with a convergence map derived from the Planck cosmic microwave background (CMB) temperature data. We make consistent measurements of the lensing signal of both samples in both Fourier and configuration space. By interpreting the excess signal present in the DLA catalog with respect to the parent quasar catalog as caused by the large scale structure traced by DLAs, we are able to infer the bias of these objects: $b_{\rm DLA}=2.6\pm0.9$. These results are consistent with previous measurements mad…
We present the results of a survey for damped (DLA, log N(H I) > 20.3) and sub-damped Lyman-? systems (19.5 < log N(H I) < 20.3) at z > 2.55 along the lines-of-sight to 77 quasars with emission redshifts in the range 4 < zem < 6.3. Intermediate resolution (R ? 4300) spectra have been obtained with the Echellette Spectrograph and Imager (ESI) mounted on the Keck telescope. A total of 100 systems with log N(H I) > 19.5 are detected of which 40 systems are damped Lyman-? systems for an absorption length of ?X = 378. About half of the lines of sight of this homogeneous survey have never been inves…
We develop an automated technique for detecting damped Lyman-$α$ absorbers (DLAs) along spectroscopic lines of sight to quasi-stellar objects (QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys such as SDSS-III sheds light on galaxy formation at high redshift, showing the nucleation of galaxies from diffuse gas. We use nearly 50 000 QSO spectra to learn a novel tailored Gaussian process model for quasar emission spectra, which we apply to the DLA detection problem via Bayesian model selection. We propose models for identifying an arbitrary number of DLAs along a given…
We measure the large-scale cross-correlation of quasars with the Lyman α forest absorption in redshift space, using ~ 60000 quasar spectra from Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS). The cross-correlation is detected over a wide range of scales, up to comoving separations r of 80 Mpc/h. For r > 15 Mpc/h, we show that the cross-correlation is well fitted by the linear theory prediction for the mean overdensity around a quasar host halo in the standard ΛCDM model, with the redshift distortions indicative of gravitational evolution detected at high confidence.…
Using a spectral stacking technique we searched for the average \lya emission from high-z Damped \lya (DLA) galaxies detected in the Sloan Digital Sky Survey QSO spectra. We used a sample of 341 DLAs of mean redshift <z>= 2.86 and log N(HI) > 20.62 to place a 3$σ$ upper limit of 3.0 \times 10^{-18} erg s^{-1} cm^{-2} on the \lya flux emitted within $\sim$1.5 arcsec (or 12 kpc) from the QSO line of sight. This corresponds to an average \lya luminosity of < 2 \times 10^{41} erg s^{-1} or 0.03 $L_\star$(\lya). This limit is deeper than the limit of most surveys for faint \lya emitters. The lack o…
We show that the recently observed elemental abundance pattern of the carbon-rich metal-poor Damped Lyman $α$ (DLA) system is in excellent agreement with the nucleosynthesis yields of faint core-collapse supernovae of primordial stars. The observed abundance pattern is not consistent with the nucleosynthesis yields of pair-instability supernovae. The DLA abundance pattern is very similar to that of carbon-rich extremely metal-poor (EMP) stars, and the contributions from low-mass stars and/or binary effects should be very small in DLAs. This suggests that chemical enrichment by the first stars …
We show that comparisons of HeII Lyman-alpha forest lines of sight to nearby quasar populations can strongly constrain the lifetimes and emission geometry of quasars. By comparing the HeII and HI Lyman-alpha forests along a particular line of sight, one can trace fluctuations in the hardness of the radiation field (which are driven by fluctuations in the HeII ionization rate). Because this high-energy background is highly variable - thanks to the rarity of the bright quasars that dominate it and the relatively short attenuation lengths of these photons - it is straightforward to associate feat…
We present the first measurement of the large-scale cross-correlation of Lyman alpha forest absorption and Damped Lyman alpha systems (DLA), using the 9th Data Release of the Baryon Oscillation Spectroscopic Survey (BOSS). The cross-correlation is clearly detected on scales up to 40 Mpc/h and is well fitted by the linear theory prediction of the standard Cold Dark Matter model of structure formation with the expected redshift distortions, confirming its origin in the gravitational evolution of structure. The amplitude of the DLA-Lyman alpha cross-correlation depends on only one free parameter,…
We report the identification of a very metal-poor damped Lyman-alpha system (DLA) at z_abs = 3.067295 that is modestly carbon-enhanced, with an iron abundance of ~1/700 solar ([Fe/H] = -2.84) and [C,O/Fe] ~ +0.6. Such an abundance pattern is likely to be the result of nucleosynthesis by massive stars. On the basis of 17 metal absorption lines, we derive a 2 sigma upper limit on the DLA's kinetic temperature of T_DLA <= 4700 K, which is broadly consistent with the range of spin temperature estimates for DLAs at this redshift and metallicity. While the best-fitting abundance pattern shows the ex…
For around 100 years, hydrogen spectral modelling has been based on Voigt profile fitting. The semi-classical Voigt profile is based on a 2-level atom approximation. Whilst the Voigt profile is excellent for many circumstances, the accuracy is insufficient for very high column density damped Lyman-$α$ absorption systems. We have adapted the quantum-mechanical Kramers-Heisenberg model to include thermal broadening, producing a new profile, the KHT profile. Interactions involving multiple discrete atomic levels and continuum terms, not accounted for in the Voigt model, generate asymmetries in th…
Recently, the number of detected galaxy counterparts of z > 2 Damped Lyman-alpha Absorbers in QSO spectra has increased substantially so that we today have a sample of 10 detections. Møller et al. in 2004 made the prediction, based on a hint of a luminosity-metallicity relation for DLAs, that HI size should increase with increasing metallicity. In this paper we investigate the distribution of impact parameter and metallicity that would result from the correlation between galaxy size and metallicity. We compare our observations with simulated data sets given the relation of size and metallicity…
Arguably the best hope of understanding the tail end of the reionization of the intergalactic medium (IGM) at redshift z > 6 is through the detection and characterization of the Gunn-Peterson (GP) damping wing absorption of the IGM in bright quasar spectra. However, the use of quasar spectra to measure the IGM damping wing requires a model of the quasar's intrinsic Lyman-alpha emission line. Here we quantify the uncertainties in the intrinsic line shapes, and how those uncertainties affect the determination of the IGM neutral fraction. We have assembled a catalog of high-resolution HST spectra…
Using synthetic Lyman-$α$ forests from the Dark Energy Spectroscopic Instrument (DESI) survey, we present a study of the impact of errors in the estimation of quasar redshift on the Lyman-$α$ correlation functions. Estimates of quasar redshift have large uncertainties of a few hundred $\text{km s}^{-1}\,$ due to the broadness of the emission lines and the intrinsic shifts from other emission lines. We inject Gaussian random redshift errors into the mock quasar catalogues, and measure the auto-correlation and the Lyman-$α$-quasar cross-correlation functions. We find a smearing of the BAO featur…
Sub-damped Lyman-alpha systems (sub-DLAs) have previously been found to exhibit a steeper metallicity evolution than the classical damped Lyman-alpha systems (DLAs), evolving to close to solar metallicity by z~1. From new high-resolution spectra of 17 sub-DLAs we have increased the number of measurements of [Fe/H] at z<1.7 by 25% and compiled the most complete literature sample of sub-DLA and DLA abundances to date. We find that sub-DLAs are indeed significantly more metal-rich than DLAs, but only at z<1.7; the metallicity distributions of sub-DLAs and DLAs at z>1.7 are statistically consisten…
Using a sample of 100 H I - selected damped Lyman alpha (DLA) systems, observed with the High Resolution Echelle Spectrometer on the Keck I telescope, we present evidence that the scatter in the well-studied correlation between the redshift and metallicity of a DLA is largely due to the existence of a mass-metallicity relationship at each redshift. To describe the fundamental relations that exist between redshift, metallicity and mass, we use a fundamental plane description, which is described by the following equation: [M/H]=(-1.9+-0.5)+(0.74+-0.21)logdv_90-(0.32+-0.06)z. Here, we assert that…
We compute the z = 3 neutral hydrogen column density distribution function f(NHI) for 19 simulations drawn from the OWLS project using a post-processing correction for self-shielding calculated with full radiative transfer of the ionising background radiation. We investigate how different physical processes and parameters affect the abundance of Lyman-limit systems (LLSs) and damped Lyman-alpha absorbers (DLAs) including: i) metal-line cooling; ii) the efficiency of feedback from SNe and AGN; iii) the effective equation of state for the ISM; iv) cosmological parameters; v) the assumed star for…
The squeezed-limit bispectrum, which is generated by nonlinear gravitational evolution as well as inflationary physics, measures the correlation of three wavenumbers, in the configuration where one wavenumber is much smaller than the other two. Since the squeezed-limit bispectrum encodes the impact of a large-scale fluctuation on the small-scale power spectrum, it can be understood as how the small-scale power spectrum "responds" to the large-scale fluctuation. Viewed in this way, the squeezed-limit bispectrum can be calculated using the response approach even in the cases which do not submit …
Correlations in and with the flux transmission of the Lyman$-α$ (Ly$α$) forest in the spectra of high-redshift quasars are powerful cosmological tools, yet these measurements can be compromised if the intrinsic quasar continuum is significantly uncertain. One particularly problematic case is broad absorption line (BAL) quasars, which exhibit blueshifted absorption associated with many spectral features that are consistent with outflows of up to $\sim0.1c$. As these absorption features can both fall in the forest region and be difficult to distinguish from Ly$α$ absorption, cosmological analyse…
In order to characterize Damped Lyman Alpha systems (DLAs) potentially hosting first stars, we present a novel approach to investigate DLAs in the context of Milky Way (MW) formation, along with their connection with the most metal-poor stars and local dwarf spheroidal (dSph) galaxies. The merger tree method previously developed is extended to include inhomogeneous reionization and metal mixing, and it is validated by matching both the Metallicity Distribution Function of Galactic halo stars and the Fe-Luminosity relation of dSph galaxies. The model explains the observed NHI-Fe relation of DLA…
Details of processes through which galaxies convert their gas into stars need to be studied in order to obtain a complete picture of galaxy formation. One way to tackle these phenomena is to relate the HI gas and the stars in galaxies. Here, we present dynamical properties of Damped and sub-Damped Lyman-alpha Systems identified in H-alpha emission with VLT/SINFONI at near infra-red wavelengths. While the DLA towards Q0302-223 is found to be dispersion-dominated, the sub-DLA towards Q1009-0026 shows clear signatures of rotation. We use a proxy to circular velocity to estimate the mass of the ha…
