Hydrogen Number Density Research Articles

Prediction and Distribution of Supernovae in the Epoch of Reionization Universal Model

The distribution of SNe during the epoch of reionization is usually determined by the Schmidt-kennicutt law, but the values and specific impact of different SNe types have been ambiguous. This study delves into the impact of Type Ia, Type Ib/Ic, & Type 2 Supernovae (SNe) effect on galaxy formation and distribution during the epoch of reionization, which in turn significantly influences and determines the symmetry and spread of elements, stars, galaxies, and even the cosmic microwave background radiation. The first phase determines the estimated amount of the SNe with neutral (hydrogen) fractions, photo-ionization rate for the H1 region, escape fraction with respect to redshift, and relative distribution of hydrogen number density all predicted by the THESAN simulations. The second phase determines the powers and scale of SNe in the reionization period using PDEs. The last phase calibrates the data on current SN remnants and progenitors such as mass, redshift, and composition to predict the evolution of SNE behavior since the epoch of reionization to contemporary astronomy. Then, using the provided data on SNe, this study will form a constructive model layering all three phases to determine the effect of different types of SNe during the ionization period and their patterns leading to today. Further research using the Nancy Grace Roman Telescope and telescopes specifically built to study redshift (like HERA and JWST) to have smaller error margins and more reliable data to determine a better fit for the distribution and impact of SNe in the Epoch.

Constraints on the narrow-line region of the X-ray quasi-periodic eruption source GSN 069

ABSTRACT The origins of quasi-periodic eruptions (QPEs) are poorly understood, although most theoretical explanations invoke an accretion disc around a supermassive black hole. The gas and stellar environments in the galactic nuclei of these sources are also poorly constrained. In this paper, we present an analysis of archival Hubble Space Telescope (HST) images to study the narrow-line [O iii] emission in the QPE source GSN 069. We find strong evidence for a compact nuclear [O iii] emission region of size ≲ 35 pc, overlaid on top of extended [O iii] emission up to 1 kpc away from the nucleus. The age of the accretion system is estimated to be between 10 and 100 yr. The [O iii] luminosity of the compact region was measured to be $(2.1 \pm 0.3) \times 10^{40}\, \rm erg\, s^{-1}$. Based on cloudy simulations, we constrain that the [O iii] emitting gas has a hydrogen number density in the range $2 \times 10^{3} \lt n_{\rm H} \lesssim 10^{8}\, \rm cm^{-3}$ and volume filling factor fV < 4 × 10−3. We suggest that the dense gas in the nuclear region of GSN 069 originates from molecular clouds (with total mass $\gtrsim 3 \times 10^{3}\, {\rm M}_{\odot }$), which are freshly ionized by the soft X-ray photons from the accretion disc. We predict possible evolution of the compact narrow-line region on emission-line diagnostic diagrams, and hence future HST or integral-field unit observations can be used to further pin down the age of this puzzling system.

[C ii] Emission in a Self-regulated Interstellar Medium

The [C ii] 157.74 μm fine-structure transition is one of the brightest and most well-studied emission lines in the far-infrared, produced in the interstellar medium (ISM) of galaxies. We study its properties in subparsec-resolution hydrodynamical simulations for an ISM patch with gas surface density of Σ g = 10 M ⊙ pc−2, coupled with time-dependent chemistry, far-ultraviolet dust and gas shielding, star formation, photoionization and supernova feedback, and full line radiative transfer. We find a [C ii]-to-H2 conversion factor that scales weakly with metallicity X[CII]=6.31×1019Z′0.17cm−2(Kkms−1)−1 , where Z′ is the normalized metallicity relative to solar. The majority of [C ii] originates from atomic gas with hydrogen number density n ∼ 10 cm−3. The [C ii] line intensity positively correlates with the star formation rate (SFR), with a normalization factor that scales linearly with metallicity. We find that this is broadly consistent with z ∼ 0 observations. As such, [C ii] is a good SFR tracer even in metal-poor environments where molecular lines might be undetectable. Resolving the clumpy structure of the dense (n = 10−103 cm−3) ISM is important, as it dominates [C ii] 157.74 μm emission. We compare our full radiative transfer computation with the optically thin limit and find that the [C ii] line becomes marginally optically thick only at supersolar metallicity for our assumed gas surface density.

Neutral carbon in diffuse interstellar medium: abundance matching with H2 for damped Lyman alpha systems at high redshifts

ABSTRACT We present a study of C i/H2 relative abundance in the diffuse cold neutral medium (CNM). Using the chemical and thermal balance model, we calculate the dependence of C i/H2 on the main parameters of the medium: hydrogen number density, metallicity, strength of the UV field, and cosmic ray ionization rate (CRIR). We show that the observed relative C i and H2 column densities in damped Lyman alpha systems (DLAs) at high redshifts can be reproduced within our model assuming the typically expected conditions in the diffuse CNM. Using additional observed information on metallicity, H i column density, and excitation of C i fine-structure levels, as well as temperature, we estimated for a wide range metallicities in the CNM at high redshifts that CRIRs are in the range from ∼10−16 to a $\rm few \times 10^{-15}\, \rm s^{-1}$, hydrogen number densities are in the range ∼10−103 cm−3, and the UV field is in the range from 10−2 to a $\rm few \times 10^2$ of the Mathis field. We argue that because the observed quantities used in this work are quite homogeneous and much less affected by radiative transfer effects (in comparison with, for example, the dissociation of HD and UV pumping of H2 rotational levels), our estimates are quite robust against the assumption of the exact geometrical model of the cloud and local sources of the UV field.

Circumnuclear Multiphase Gas in the Circinus Galaxy. V. The Origin of the X-Ray Polarization in the Circinus Galaxy

The Imaging X-ray Polarimetry Explorer (IXPE) detected X-ray polarization in the nearest Seyfert 2 galaxy, the Circinus galaxy, for the first time. To reproduce the IXPE results, we computed the degree of polarization based on two types of radiative hydrodynamic simulations: a parsec-scale three-dimensional model and a sub-parsec-scale axisymmetric model with a higher spatial resolution. In a series of papers, we confirmed that these models naturally explain the multiwavelength observations of the Circinus galaxy from radio to X-rays. We used a Monte Carlo Simulation for Astrophysics and Cosmology code to compute the linear polarization of continuum emission. We found that the degree of polarization based on the parsec-scale radiation-driven fountain model was smaller than that observed with the IXPE. The degree of polarization based on the sub-parsec-scale model depends on the hydrogen number density of the disk (d), and the degree of polarization obtained from our simulation is consistent with that observed with the IXPE in the case of . We investigate where the photons are Compton scattered and imply that the origin of the X-ray polarization in the Circinus galaxy is the outflow inside 0.01 pc. In this case, the degree of polarization may change over a timescale of approximately 10 yr.

Magnetic Evidence for an Extended Hydrogen Exosphere at Mercury

AbstractRemote observations by the Mariner 10 and MErcury Surface, Space ENvironment, GEophysics, and Ranging (MESSENGER) spacecraft have shown the existence of hydrogen in the exosphere of Mercury. However, to date the hydrogen number densities could only be estimated indirectly from exospheric models, based on the remotely observed Lyman‐α radiances for atomic H, and the detection threshold of the Mariner 10 occultation experiment for molecular H2. Here, we show the first on‐site determined altitude‐density profile of atomic H, derived from in situ magnetic field observations by MESSENGER. The results reveal an extended H exosphere with densities that are ∼1–2 orders of magnitude larger than previously predicted. Using an exospheric model that reproduces the H altitude‐density profile allows us to constrain the so far unknown H2 density at the surface, which is ∼2–3 orders of magnitude smaller than previously assumed. These findings demonstrate the importance of (a) in situ measurements supporting remote observations of Mercury's exosphere that will be realized in the near future by the BepiColombo mission and (b) that dissociation processes play a crucial role in Mercury's exosphere.

Magnetic fields on FIRE: Comparing B-fields in the multiphase ISM and CGM of simulated L* galaxies to observations

ABSTRACT The physics of magnetic fields (B) and cosmic rays (CRs) have recently been included in simulations of galaxy formation. However, significant uncertainties remain in how these components affect galaxy evolution. To understand their common observational tracers, we analyse the magnetic fields in a set of high-resolution, magnetohydrodynamic, cosmological simulations of Milky-Way-like galaxies from the FIRE-2 project. We compare mock observables of magnetic field tracers for simulations with and without CRs to observations of Zeeman splitting and rotation/dispersion measures. We find reasonable agreement between simulations and observations in both the neutral and the ionized interstellar medium (ISM). We find that the simulated galaxies with CRs show weaker ISM |B| fields on average compared to their magnetic-field-only counterparts. This is a manifestation of the effects of CRs in the diffuse, low density inner circumgalactic medium (CGM). We find that equipartition between magnetic and cosmic ray energy densities may be valid at large (> 1 kpc) scales for typical ISM densities of Milky-Way-like galaxies, but not in their haloes. Within the ISM, the magnetic fields in our simulated galaxies follow a power-law scaling with gas density. The scaling extends down to neutral hydrogen number densities < 300 cm−3, in contrast to observationally derived models, but consistent with the observational measurements. Finally, we generate synthetic rotation measure (RM) profiles for projections of the simulated galaxies and compare to observational constraints in the CGM. While consistent with upper limits, improved data are needed to detect the predicted CGM RMs at 10–200 kpc and better constrain theoretical predictions.

Inhomogeneity within Local Interstellar Clouds* *All of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via https://doi.org/10.17909/gabn-m136. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support to MAST for these

Analysis of interstellar absorption lines observed in high-resolution Hubble Space Telescope spectra of nearby stars provides temperatures, turbulent velocities, and kinetic properties of warm interstellar clouds. A new analysis of 97 interstellar-velocity components reveals a wide range of temperatures and turbulent velocities within the Local Interstellar Cloud (LIC) and the nearby Cluster of Interstellar Clouds (CLIC). These variations appear to be random with Gaussian distributions. We find no trends of these properties with stellar distance or angles from the Galactic Center, magnetic field, the main source of extreme-UV radiation (the star ϵ CMa), the center of the LIC, or the direction of inflowing interstellar matter into the heliosphere. The spatial scale for temperature variations in the LIC is likely smaller than 5100 au, a distance that the Sun will traverse in 1000 yr. Essentially all velocity components align with known warm clouds. We find that within 4 pc of the Sun, space is completely filled with partially ionized clouds, but at larger distances space is only partially filled with partially ionized clouds. We find that the neutral hydrogen number density in the LIC and likely other warm clouds in the CLIC is about 0.10 cm−3 rather than the 0.20 cm−3 density that may be representative of only the immediate environment of the LIC. The ≤3000–12,000 K temperature range for the gas is wider than the predictions of thermal equilibrium theoretical models of the warm neutral medium and warm ionized medium, and the high degree of inhomogeneity within clouds argues against simple theoretical models.

Magnetic Fields in Massive Star-forming Regions (MagMaR). II. Tomography through Dust and Molecular Line Polarization in NGC 6334I(N)

Abstract Here, we report ALMA detections of polarized emission from dust, CS(J = 5 → 4), and C33S(J = 5 → 4) toward the high-mass star-forming region NGC 6334I(N). A clear “hourglass” magnetic field morphology was inferred from the polarized dust emission, which is also directly seen from the polarized CS emission across velocity, where the polarization appears to be parallel to the field. By considering previous findings, the field retains a pinched shape that can be traced to clump length scales from the envelope scales traced by ALMA, suggesting that the field is dynamically important across multiple length scales in this region. The CS total intensity emission is found to be optically thick (τ CS = 32 ± 12) while the C33S emission appears to be optically thin ( τ C 33 S = 0.1 ± 0.01 ). This suggests that sources of anisotropy other than large velocity gradients, i.e., anisotropies in the radiation field, are required to explain the polarized emission from CS seen by ALMA. By using four variants of the Davis–Chandrasekhar–Fermi technique and the angle dispersion function methods (ADF), we obtain an average of the estimates for the magnetic field strength on the plane of the sky of B pos = 16 mG from the dust and B pos ∼ 2 mG from the CS emission, where each emission traces different molecular hydrogen number densities. This effectively enables a tomographic view of the magnetic field within a single ALMA observation.

Impact of the ERF on the structure and evolution of SNRs

ABSTRACT We carry out 1D hydrodynamical simulations of the evolution of a spherically symmetric supernova remnant (SNR) subject to an external radiation field (ERF) that influences the cooling and heating rates of the gas. We consider homogeneous media with ambient hydrogen number densities nH, 0 of 0.1 and 1 cm−3 permeated by an average radiation field including the cosmic microwave, extragalactic, and Galactic backgrounds, attenuated by an effective column density NH, eff from 1018 to 1021 cm−2. Our results may be classified into two broad categories: at low NH, eff, the ERF presents little absorption in the ultraviolet (ionizing) regime, and all the ’unshielded’ cases feature an equilibrium temperature Teq ∼ 7000 K below which the ambient gas cannot cool further. In this scenario, the SNR develops a nearly isothermal shock profile whose shell becomes thicker over time. At higher NH, eff, the ERF is heavily absorbed in the UV range, yielding a roughly constant heating function for temperatures ≲ 104 K. These ‘shielded’ cases develop a thin, cold and dense shell throughout their evolution. Energy and momentum injection to the medium do not change significantly between both scenarios, albeit luminosity is higher and more uniformly distributed over the shell for unshielded SNR.

Ultradense Gas Tracked by Unshifted Broad Absorption Lines in a Quasar

Abstract We present a detailed analysis of the broad absorption line system in the quasar SDSS J122017.06+454941.1, which are clearly detected in hydrogen Lyman series and metal lines, such as C iv, Si iv, Si iii, Al iii, and C ii, with a similar velocity as that of the broad emission lines. We reliably measured the column densities of H i, Al iii, and C ii, and obtained a low limit to Si iv and Si iii. With the help of the photoionization simulations, we found that the absorption gas has a hydrogen number density n H ≈ 1011.03 cm−3 and a hydrogen column density N H ≈ 1021.0 cm−2, and is exposed to the radiation with an ionization parameter U ≈ 10−1.25, and thus located the absorber at ∼0.3 pc from the central supermassive black hole, remarkably similar to the radius of the broad-line region (BLR; 0.17–0.84 pc as estimated by the luminosity–radius relation) of the quasar. It is likely that our line of sight may happen to intercept the low-column part of the BLR with a high density similar to that of the inferred value of the absorber. We suggest that detection of Al iii absorption line doublet in moderate quality quasar spectra could be a good indicator of dense gases, provided that the neutral hydrogen column density of the absorber is .

Shattering as a source of small grains in the circum-galactic medium

ABSTRACT Observed reddening in the circum-galactic medium (CGM) indicates a significant abundance of small grains, of which the origin is still to be clarified. We examine a possible path of small-grain production through shattering of pre-existing large grains in the CGM. Possible sites where shattering occurs on a reasonable time-scale are cool clumps with hydrogen number density nH ∼ 0.1 cm−3 and gas temperature Tgas ∼ 104 K, which are shown to exist through observations of Mg ii absorbers. We calculate the evolution of grain size distribution in physical conditions appropriate for cool clumps in the CGM, starting from a large-grain-dominated distribution suggested from theoretical studies. With an appropriate gas turbulence model expected from the physical condition of cold clumps (maximum eddy size and velocity of ∼100 pc and 10 km s−1, respectively), together with the above gas density and temperature and the dust-to-gas mass ratio inferred from observations (0.006), we find that small-grain production occurs on a time-scale (a few × 108 yr) comparable to the lifetime of cool clumps derived in the literature. Thus, the physical conditions of the cool clouds are favourable for small-grain production. We also confirm that the reddening becomes significant on the above time-scale. Therefore, we conclude that small-grain production by shattering is a probable cause for the observed reddening in the CGM. We also mention the effect of grain materials (or their mixtures) on the reddening at different redshifts (1 and 2).

The warm-up phase in massive star-forming cores around RCW 120

ABSTRACT We study molecular emission in a massive condensation at the border of the H ii region RCW 120, paying particular attention to the Core 1 and 2 objects, the most massive fragments of the condensation found previously by ALMA. The latter fragment was previously suggested to host a high-mass analogue of Class 0 young stellar object. We present spectra of molecular emission in the 1 mm range made with the APEX telescope. We detect CH3OH and C34S lines in Cores 1 and 2. The CH3CN series and the SO2 lines are only found in Core 2. We estimate gas physical parameters using methanol lines and obtain gas temperature less than 100 K in both regions. Molecular hydrogen number density in Core 2 is in the range of 105−107 cm−3 and is more uncertain in Core 1. However, the detection of the CH3CN lines corresponding to highly excited transitions (Eu > 400 K) in Core 2 indicates that the region contains hot gas, while the abundances of CH3OH, CS, SO2, and CH3CN are quite low for a hot core stage. We propose that Core 2 is in the warm-up phase prior to the establishing of the hot gas chemistry. We suggest that Core 2 is in the beginning of the hot core stage. There are no detected CH3CN lines in Core 1; therefore, it might be on an even less evolved evolutionary stage.

Spatially resolved X-ray spectroscopy of the archetype type 2 active galactic nucleus NGC 1068 with Chandra

Abstract We investigate spatial distributions of iron Kα (Fe-Kα) lines in the cental 100 pc of the Seyfert 2 galaxy NGC 1068 observed with Chandra. The spatial distributions of Fe-Kα lines, neutral and highly ionized, around the center of the galactic nucleus are not isotropic, as consistently confirmed in both image and spectral analyses. The hydrogen number density of the gas clouds responsible for the neutral Fe-Kα line emission is estimated to be 102–103 cm−3 for the sampled regions near the galactic core. The photo-ionization model, where iron is assumed to be ionized by X-rays from the galactic nucleus, yields ionization parameters lower than 19 for these clouds. The range of this ionization parameter is two or three orders of magnitude lower than the theoretically expected value to produce the observed helium-like Fe-Kα line intensities. Therefore, the photo-ionization model is excluded from the explanation of the amount of highly ionized iron that is responsible for the observed Fe-Kα lines. Also, we find anti-correlation in the spatial distributions between the molecular cloud in the area observed with ALMA and that of the Fe-Kα lines, including that from neutral iron. We suggest that X-ray iron-line and radio molecular cloud observations are complementary to probe the distribution of matters in the central regions around the cores of active galactic nuclei.

Galactopause Formation and Gas Precipitation during Strong Galactic Outflows

Abstract Using X-ray constrained β-models for the radial distribution of gas in the outskirts of galaxies, we analyze the termination of galactic winds and the formation and evolution of halo clouds by thermal instability. At low mass-loss rates ( ) galactic winds are trapped within the halo, but they burst into the intergalactic medium during intermittent strong outflows with . We develop analytic models of halo clouds as they cool radiatively over condensation timescales for hydrogen number densities , gas temperatures T ≈ (106 K)T 6, and metallicities (Z/Z ⊙). Halo gas can form kiloparsec-scale clouds out to galactocentric distances r ≈ 30–65 kpc, where efficient radiative cooling from 106 K down to T ≈ 104–5 K occurs at Z ≥ 0.3 Z ⊙ on timescales less than 1 Gyr. After condensing to column densities N H ≥ 4 × 1016 cm−2, these clouds lose hydrostatic pressure support and fall inward on dynamical timescales of ∼200 Myr. Our baseline analysis will be followed by numerical calculations to understand the governing principles of halo cloud formation and transport of gas to the galactic disk.

Exploring the Possibility of Identifying Hydride and Hydroxyl Cations of Noble Gas Species in the Crab Nebula Filament

Abstract The first identification of the argonium ion ( ) toward the Crab Nebula supernova remnant was proclaimed by Herschel in the submillimeter and far-infrared domains. Very recently, the discovery of the hydro-helium cation ( ) in the planetary nebula (NGC 7027) by SOFIA has been reported. The elemental abundance of neon is much higher than that of argon. However, the presence of neonium ions ( ) is yet to be confirmed in space. Though the hydroxyl radicals (−OH) are very abundant in both neutral and cationic forms, hydroxyl cations of such noble gases (i.e., ArOH+, NeOH+, and HeOH+) are yet to be identified in space. Here, we employ a spectral synthesis code to examine the chemical evolution of the hydride and hydroxyl cations of the various isotopes of Ar, Ne, and He in the Crab Nebula filament and calculate their line emissivity and intrinsic line surface brightness. We successfully explain the observed surface brightness of two transitions of ArH+ (617 and 1234 GHz), one transition of OH+ (971 GHz), and one transition of H2 (2.12 μm). We also explain the observed surface brightness ratios between various molecular and atomic transitions. We find that our model reproduces the overall observed features when a hydrogen number density of ∼(104–106) cm−3 and a cosmic-ray ionization rate per H2 of ∼(10−11–10−10) s−1 are chosen. We discuss the possibility of detecting some hydride and hydroxyl cations in the Crab and diffuse cloud environment. Some transitions of these molecules are highlighted for future astronomical detection.

The Downwind Solar Wind: Model Comparison with Pioneer 10 Observations

Abstract The solar wind in the upwind region has been well modeled using a pickup ion (PUI) mediated MHD model (Zank et al.). It suggests that PUIs have an important role in heating the solar wind in the outer heliosphere. However, the solar wind in the downwind region is not as well understood. Here, we compare the Zank et al. model with Pioneer 10 observations, which allows us to investigate the downwind solar wind out to 60 au. We use a model in which the hydrogen temperature is finite to obtain a proper hydrogen number density distribution in the downwind region and incorporate it into the model. Our results explain Pioneer 10 observations well and indicate that the heating due to PUIs is less effective than in the upwind region since the density of PUIs in the downwind region is less than the upwind PUIs density. We also derive parameters at several possible locations of the downwind termination shock.

Nature of the DLA towards Q 0528−250: High pressure and strong UV field revealed by excitation of C i, H2, and Si ii

ABSTRACT We present the detection of excited fine-structure energy levels of singly ionized silicon and neutral carbon associated with the proximate damped Lyman-α system at zabs = 2.811 towards Q 0528−250. This absorber has an apparent relative velocity that is inconsistent with the Hubble flow indicating motion along the line-of-sight towards the quasar, i.e. zabs > zem. We measure the metallicity of the system to be [Zn/H] = −0.68 ± 0.02. Using the relative populations of the fine-structure levels of Si ii and C i, as well as the populations of H2 rotational levels, we constrain the physical conditions of the gas. We derive hydrogen number densities of $n_{\rm H}=190^{+70}_{-50}$ cm−3 and $260^{+30}_{-20}$ cm−3 in two velocity components where both C i and H2 are detected. Taking into account the kinetic temperature in each component, ∼150 K, we infer high values of thermal pressure in the cold neutral medium probed by the observations. The strengths of the UV field in Draine’s unit are $I_{\rm UV} = 10^{+5}_{-3}$ and $14^{+3}_{-3}$ in each of these two components, respectively. Such enhanced UV fluxes and thermal pressure compared to intervening DLAs are likely due to the proximity of the quasar. The typical size of the absorber is ∼104 au. Assuming the UV flux is dominated by the quasar, we constrain the distance between the quasar and the absorber to be ∼150−200 kpc. This favours a scenario where the absorption occurs in a companion galaxy located in the group where the quasar-host galaxy resides. This is in line with studies in emission that revealed the presence of several galaxies around the quasar.

Comparison of the Intensity of the Nighttime Scattered Atmospheric Radiation in the Lyman-Alpha Line from OGO-4 Satellite Measurements and Calculations

A theoretical model has been developed for the calculation of the intensity and flux of nighttime Lyman-alpha solar radiation at altitudes of the atmosphere that takes into account the multiple scatterings of this radiation by atmospheric atomic hydrogen. At heights of more than two Earth radii, the number density of atomic hydrogen is calculated by an empirical model based on the agreement of the results of calculations of the Lyman-alpha radiation intensity with the results of measurements of this intensity by TWINS 1 and 2 satellites instruments. At lower heights, it is calculated according to the NRLMSISE-00 empirical model. The temperature of neutral atmospheric components and the O2 number density are taken according to the NRLMSISE-00 model, and the absorption of Lyman-alpha radiation by molecular oxygen is taken into account. The results of measurements of the integral intensity of the Lyman-alpha radiation intensity by the wavelength instruments of the OGO-4 satellite at an height of 650 km are compared at night on January 31, 1968, at high solar activity with the results of model calculations of this intensity. It is shown that the 1.2-fold decrease in [H] in the NRLMSISE-00 model at heights of less than two Earth radii allows satisfactory agreement between the calculated and measured intensities of the radiation in question.

Mass-loss rate and local thermodynamic state of the KELT-9 b thermosphere from the hydrogen Balmer series

KELT-9 b, the hottest known exoplanet, withTeq~ 4400 K, is the archetype of a new planet class known as ultra-hot Jupiters. These exoplanets are presumed to have an atmosphere dominated by neutral and ionized atomic species. In particular, Hαand HβBalmer lines have been detected in the KELT-9 b upper atmosphere, suggesting that hydrogen is filling the planetary Roche lobe and escaping from the planet. In this work, we detectedδScuti-type stellar pulsation (with a periodPpuls= 7.54 ± 0.12 h) and studied the Rossiter-McLaughlin effect (finding a spin-orbit angleλ= −85.01° ± 0.23°) prior to focussing on the Balmer lines (Hαto Hζ) in the optical transmission spectrum of KELT-9 b. Our HARPS-N data show significant absorption for Hαto Hδ. The precise line shapes of the Hα, Hβ, and Hγabsorptions allow us to put constraints on the thermospheric temperature. Moreover, the mass loss rate, and the excited hydrogen population of KELT-9 b are also constrained, thanks to a retrieval analysis performed with a new atmospheric model. We retrieved a thermospheric temperature ofT= 13 200−720+800K and a mass loss rate ofṀ= 1012.8±0.3g s−1when the atmosphere was assumed to be in hydrodynamical expansion and in local thermodynamic equilibrium (LTE). Since the thermospheres of hot Jupiters are not expected to be in LTE, we explored atmospheric structures with non-Boltzmann equilibrium for the population of the excited hydrogen. We do not find strong statistical evidence in favor of a departure from LTE. However, our non-LTE scenario suggests that a departure from the Boltzmann equilibrium may not be sufficient to explain the retrieved low number densities of the excited hydrogen. In non-LTE, Saha equilibrium departure via photo-ionization, is also likely to be necessary to explain the data.