Single-peaked Profile Research Articles

MOSEL Survey: Spatially Offset Lyman-continuum Emission in a New Emitter at z = 3.088 Can Explain the Low Number Density of Observed LyC Leakers

We present the discovery of a unique Lyman-continuum (LyC) emitter at z = 3.088. The LyC emission was detected using the Hubble Space Telescope WFC3/UVIS F336W filter, covering a rest-frame wavelength range of 760–900 Å. The peak signal-to-noise ratio of LyC emission is 3.9 in an r = 0.″24 aperture and is spatially offset by 0.″29 ± 0.″04 (∼2.2 ± 0.3 kpc) from the peak of rest-UV emission (F606W). By combining imaging and spectroscopic data from the James Webb Space Telescope (JWST) JADES, FRESCO, and JEMS surveys, along with VLT/MUSE data from the MXDF survey, we estimate that the probability of random alignment with an interloper galaxy causing the LyC emission is less than 6 × 10−5. The interstellar medium (ISM) conditions in the galaxy are similar to those in other LyC emitters at high redshift ( 12+log(O/H)=7.79−0.05+0.06 , logU=−3.27−0.12+0.14 , O32 = 0.63 ± 0.03), although the single-peaked Lyα profile and lack of rest-UV emission lines suggest an optically thick ISM. Our observations indicate that LyC photons are leaking through a narrow cone of optically thin neutral ISM, most likely created by a past merger (as evidenced by medium-band F210M and F182M images). Using the constraints on escape fraction from individual leakers and a simple model, we estimate that the opening half-angle of ionization cones can be as small as 16° (2% ionized fraction) to reproduce some of the theoretical constraints on the average escape fraction for galaxies. The narrow opening angle required can explain the low number density of confirmed LyC leakers.

Probing the origin of the two-component structure of broad-line region by reverberation mapping of an extremely variable quasar

ABSTRACT The physical origins of quasar components, such as the broad-line region (BLR) and dust torus, remain under debate. To gain insights into them, we focused on changing-state quasars (CSQs) which provide a unique perspective through structural changes associated with accretion disc state transitions. We targeted SDSS J125809.31+351943.0, an extremely variable CSQ, to study its central core structure and kinematics. We conducted reverberation mapping with optical spectroscopy to explore the structure of the BLR and estimate the black hole mass. The results from Hβ reverberation mapping indicated a black hole mass of $10^{9.64^{+0.11}_{-0.20}}\rm {M_\odot }$. Additionally, we analysed variations in the optical to X-ray spectral indices, αox, before and after the state transition, to investigate the accretion disc. These variations in αox and the Eddington ratio (from 0.4 per cent to 2.4 per cent) exhibitied behaviour similar to state transitions observed in X-ray binary systems. Spectral analysis of Hβ revealed a predominantly double-peaked profile during dim periods, transitioning to include a single-peaked component as the quasar brightened, suggesting that Hβ contains a mixture of two components. Each of these components has its distinct characteristics: the first is a double-peaked profile that remains stable despite changes in the accretion rate, while the second is a variable single-peaked profile. Using time-lags from reverberation mapping, we estimated the spatial relationships between these BLR components, the accretion disc, and the dust torus. Our results suggest that the BLR consists of two distinct components, each differing in location and origin.

Optical and X-ray studies of Be/X-ray binary 1A 0535+262 during its 2020 giant outburst

ABSTRACT We report results obtained from the optical and X-ray studies of the Be/X-ray binary 1A 0535+262/HD 245770 during the 2020 October giant X-ray outburst, using the 1.2-m telescope at Mount Abu Infrared observatory and AstroSat, respectively. The peak flux of the outburst was recorded to be ∼11 Crab in the 15–50 keV range, the highest ever observed from the pulsar. We performed optical observations in the 6000–7200 Å band before, during, and after the outburst to investigate the evolution of the circumstellar disc of the Be star between 2020 February and 2022 February. Our optical spectra exhibit prominent emission lines at 6563 Å (H i), 6678 Å (He i), and 7065 Å (He i). We found a significantly variable H α line in the spectra. The single-peaked line profile appeared asymmetric with broad red- and blue-wings in the data before and during the outburst. The post-outburst observations, however, resulted in a double-peaked profile with asymmetry in the blue-wing. Our observations before the outburst confirmed a larger Be disc that decreased in size as the outburst progressed. Furthermore, the observed variabilities in the H α line profile and parameters suggest the presence of a highly misaligned, precessing, and warped Be disc. AstroSat observation of the pulsar detected pulsations at ∼103.55 s in the light curve up to 110 keV. We found strongly energy-dependent pulse profiles with increasing contribution of the pulsing component in hard X-rays. The broad-band spectral fitting in the 0.7–90.0 keV range confirmed the presence of the known cyclotron resonance scattering feature at ∼46.3 keV.

Effects of magnetic field strength on the microwave discharge cusped field thruster

The microwave discharge cusped field thruster is a novel electric propulsion concept developed for the space-borne Gravitational Wave detection mission. It is an effective combination of the cusped magnetic field and the ECR microwave plasma source, which provide the thruster strong confinement for the plasma and the ability to operate on low mass flow rate conditions. To meet the requirements on the high accuracy, low noise thrust over a wide range, a series of studies are carried out on the microwave discharge cusped field thruster. Since the magnetic field strength is one of the critical factors with a significant impact on the thruster, a plume plasma diagnosis is performed to analyze the discharge performance and plasma characteristics with different magnetic field strength conditions. A Faraday probe, a retarding potential analyzer, and an emissive probe are employed to characterize the plume. The results show that the variation of the magnetic field strength performs strong effects on the plume structure, the ion acceleration, and the electron conduction process. As the magnetic field strength weakens, the single-peaked plume profile transforms to a hollow cone structure, which is attributed to the conversion of acceleration mechanism. The thruster prototype performs a continuous thrust of 2–26.9 μN and a highest specific impulse of 248s with superior reproducibility in a low mass flow rate of 0.1sccm.

Radial characterization of an ion beam in a deflected magnetic nozzle

The radial characterization of an ion beam generated in a magnetically steered radio-frequency (RF) plasma source is presented. In the symmetrical magnetic nozzle (MN) configuration, radial profiles of the ion saturation current obtained with a planar Langmuir probe show a double-peaked profile. The same behaviour is confirmed by the radial measurements of the total ion current and the ion energy distribution functions (IEDFs) obtained with a retarding field energy analyzer. The IEDFs also show the presence of an ion beam centred at r = -2 cm. On the contrary, radial measurements taken with a magnetic nozzle deflected on the r - z plane exhibit a single-peaked profile with both the local ion population and the ion beam centred at r = -5 cm, in the direction of the MN orientation. It is shown that the ion beam location is changed as a result of a deflected magnetic nozzle, and that it follows the direction of increasing radial magnetic field.

Controlling Resonance Fluorescence Spectra and Photon Statistics in a Driven V-Type Quantum Emitter—Metal Nanoparticle Coupled Structure

We study the resonant fluorescence emission spectrum and the intensity-intensity correlations of the emitted fluorescent field by a V-type quantum emitter (QE) which is located near a metal nanosphere. For the description of the studied phenomena, we use the density matrix equations methodology combined with electromagnetic calculations and obtain results for the profile of the resonant fluorescence spectrum and the second-order correlation functions associated with the fluorescent photons. The decay rates and the coupling term exhibit a strong dependence on the distance that separates the QE from the metal nanoparticle. This distance also influences the resonance fluorescence of the V-type QE. We find that, in the general case, the resonant fluorescence spectrum is composed of five Lorentzian-type peaks, for high interparticle distances, while, when the QE is located very close to the surface of the nanosphere, the central resonance becomes dominant, and a single-peaked spectral profile appears. The two-time correlation functions of the fluorescent photons evolve in an oscillatory manner around unity, for non-zero time delay, with a period that decreases with the increase of the field intensity. In the strong driving field regime, the antibunching to bunching crossing time does not depend on the interparticle distance, contrary to the results found in the weak driving field regime. We also find that, for a weak laser field and under specific conditions, the second-order correlation functions constantly remain in the antibunching region.

SRG/ART-XC, Swift, NICER, and NuSTAR study of different states of the transient X-ray pulsar MAXI J0903–531

The results of the broadband spectral and timing study of the recently discovered transient X-ray pulsar MAXI J0903–531 in a wide range of luminosities that differ by a factor of ~30 are reported. The observed X-ray spectrum in both states can be described as a classical pulsar-like spectrum consisting of a power law with a high-energy cutoff. We argue that the absence of the spectrum transformation to the two-hump structure that is expected at low fluxes indicates that the magnetic field of the neutron star is relatively weak below (2–3) × 1012 G. This estimate is consistent with other indirect constraints and non-detection of any absorption features that might be interpreted as a cyclotron absorption line. The timing analysis of the NuSTAR data revealed only slight variations of a single-peaked pulse profile of the source as a function of the energy band and mass accretion rate. In both intensity states, the pulsed fraction increases from 40% to roughly 80% with the energy. Finally, we were also able to obtain the orbital solution for the binary system using data from the Fermi/GBM, NICER, and NuSTAR instruments.

Pulse Peak Migration during the Outburst Decay of the Magnetar SGR 1830-0645: Crustal Motion and Magnetospheric Untwisting

Abstract Magnetars, isolated neutron stars with magnetic-field strengths typically ≳1014 G, exhibit distinctive months-long outburst epochs during which strong evolution of soft X-ray pulse profiles, along with nonthermal magnetospheric emission components, is often observed. Using near-daily NICER observations of the magnetar SGR 1830-0645 during the first 37 days of a recent outburst decay, a pulse peak migration in phase is clearly observed, transforming the pulse shape from an initially triple-peaked to a single-peaked profile. Such peak merging has not been seen before for a magnetar. Our high-resolution phase-resolved spectroscopic analysis reveals no significant evolution of temperature despite the complex initial pulse shape, yet the inferred surface hot spots shrink during peak migration and outburst decay. We suggest two possible origins for this evolution. For internal heating of the surface, tectonic motion of the crust may be its underlying cause. The inferred speed of this crustal motion is ≲100 m day−1, constraining the density of the driving region to ρ ∼ 1010 g cm−3, at a depth of ∼200 m. Alternatively, the hot spots could be heated by particle bombardment from a twisted magnetosphere possessing flux tubes or ropes, somewhat resembling solar coronal loops, that untwist and dissipate on the 30–40 day timescale. The peak migration may then be due to a combination of field-line footpoint motion (necessarily driven by crustal motion) and evolving surface radiation beaming. This novel data set paints a vivid picture of the dynamics associated with magnetar outbursts, yet it also highlights the need for a more generic theoretical picture where magnetosphere and crust are considered in tandem.

An episodically variable stellar wind in the planetary nebula IC 4997

IC 4997 is a planetary nebula well known by its variability. We present high-resolution spectra of IC 4997 obtained in 1993, 2019, and 2020 that reveal changes in the Hα and [N II] emission line profiles, which had never been reported for this object. The Hα P Cygni emission profile observed in 1993 changed to a single-peaked profile in 2019−2020, implying that the stellar wind has largely weakened. The very broad Hα emission wings narrowed by a factor of ∼2 between 1993 and 2019−2020, indicating that the efficiency of the Rayleigh–Raman scattering has noticeably decreased. A high-velocity [N II] nebular component detected in 1993 is missing in 2019 and 2020, probably due to a decrease in its electron density. A correlation exists between the strength of the stellar wind and the episodic (∼50−60 yr) variation in the [O III]λ4363/Hγ line intensity ratio, suggesting that an episodic, smoothly variable stellar wind is the main cause of the variability of IC 4997. Monitoring of that intensity ratio and of the Hα emission line profile in the coming years and new multiwavelength observations are key to unveiling the ongoing processes in IC 4997 and constraining the origin of the wind variability.

Parametric assessment of pore pressure dynamics in hydrocarbon contaminated Guwahati sand using shake table test

This paper presents a series of systematic shake table investigations to study the influence of hydrocarbon compounds on the pore pressure response of silty sand. The effect of degree of contamination in terms of crude oil content, ω (0, 2, 4, 6, 8 and 10% crude oil v/w), depth of contamination by varying the contamination depth ratio (β) from 0 to 1, and shaking history were extensively evaluated. A uniaxial scaled down model was subjected to three sequential horizontal base shaking (at a defined time interval) of peak ground acceleration 0.35 g. The results revealed a substantial improvement in the liquefaction resistance of the sand with an initial increase in crude oil content up to ω = 6%. With further increase in ω, the liquefaction resistance falloff sharply, resulting into a single-peaked profile with the highest resistance observed at ω = 6%, which has been regarded as threshold point. The microstructural mechanism believed to be responsible for such a behavior has also been discussed. Coupled effect of degree of contamination and depth of contamination has also been discussed in viewpoint of zero change point where no net change in the behavior was recorded.

Small one-dimensional Euclidean preference profiles

We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. We show that every single-peaked preference profile with two voters is one-dimensional Euclidean, and that every preference profile with up to five alternatives is one-dimensional Euclidean if and only if it is both single-peaked and single-crossing. By the work of Chen et al. (Social Choice and Welfare 48(2):409–432, 2017), we thus obtain that the smallest single-peaked and single-crossing preference profiles that are not one-dimensional Euclidean consist of three voters and six alternatives.

Space Telescope and Optical Reverberation Mapping Project. IX. Velocity–Delay Maps for Broad Emission Lines in NGC 5548

Abstract In this contribution, we achieve the primary goal of the active galactic nucleus (AGN) STORM campaign by recovering velocity–delay maps for the prominent broad emission lines (Lyα, C iv, He ii, and Hβ) in the spectrum of NGC 5548. These are the most detailed velocity–delay maps ever obtained for an AGN, providing unprecedented information on the geometry, ionization structure, and kinematics of the broad-line region. Virial envelopes enclosing the emission-line responses show that the reverberating gas is bound to the black hole. A stratified ionization structure is evident. The He ii response inside 5–10 lt-day has a broad single-peaked velocity profile. The Lyα, C iv, and Hβ responses extend from inside 2 to outside 20 lt-day, with double peaks at ±2500 km s−1 in the 10–20 lt-day delay range. An incomplete ellipse in the velocity–delay plane is evident in Hβ. We interpret the maps in terms of a Keplerian disk with a well-defined outer rim at R = 20 lt-day. The far-side response is weaker than that from the near side. The line-center delay τ = ( R / c ) ( 1 − sin i ) ≈ 5 days gives the inclination i ≈ 45°. The inferred black hole mass is M BH ≈ 7 × 107 M ⊙. In addition to reverberations, the fit residuals confirm that emission-line fluxes are depressed during the “BLR Holiday” identified in previous work. Moreover, a helical “Barber-Pole” pattern, with stripes moving from red to blue across the C iv and Lyα line profiles, suggests azimuthal structure rotating with a 2 yr period that may represent precession or orbital motion of inner-disk structures casting shadows on the emission-line region farther out.

Cyclic degradation and pore pressure dynamics of EICP treated hydrocarbon contaminated sands

Enzyme-induced carbonate precipitation (EICP) is an innovative bio-inspired approach that has emerged in recent years, offering a more environmentally sustainable option for soil improvement. The present article aims at extensively examining the effect of EICP treatment on the cyclic response of silty sands containing petroleum hydrocarbon compounds. Strain-controlled cyclic triaxial tests have been carried out on hydrocarbon contaminated sand with and without EICP treatment. Several independent variables such as hydrocarbon content (2, 4, 6, 8, and 10%), shear strain amplitudes (0.5% and 1%), and curing period (7 days and 14 days) were considered in the study. Prior to this, a baseline analysis was conducted to determine the effect of EICP treatment solution composition on the efficiency of carbonate precipitation. The effectiveness of the treatment was systematically investigated based on cyclic pore pressure response and degradation of cyclic shear modulus. The results revealed that petroleum contamination moderately increases the cyclic resistance up to a transition point beyond which it falls off sharply. The coupled effect of increasing oil content and curing time of EICP treatment has also been assessed. The variation of cyclic strength with crude oil content results in a single-peaked profile for both untreated and treated specimens. EICP treatment increases the cyclic resistance of oil-contaminated sand up to 1.5 times by suppressing the excess pore pressure build-up. A signification recovery in the degradation parameter, as high as 80%, was also observed. However, with increasing oil content and shear strain levels, the efficacy of EICP treatment exhibited a remarkable decline. The microstructural mechanism believed to be responsible for such a behavior has also been discussed.

Broad-band X-ray characteristics of the transient pulsar GRO J2058+42

ABSTRACT The Be X-ray binary GRO J2058+42 recently went through a Type-II outburst during 2019 March–April lasting for about 50 d. This outburst was detected with the operating all sky X-ray monitors like the Fermi-GBM, Swift-BAT, and MAXI-GSC. Two Nuclear Spectroscopic Telescope Array(NuSTAR) observations were also made, one during the rise and other during the decay of the outburst. It gave us the unique opportunity to analyse the broad-band characteristics of the pulsar for the first time and accretion torque characteristics of the pulsar over a range of X-ray luminosity. The pulse profiles are strongly energy-dependent, with at least four different pulse components at low energy (< 20 keV), which evolves to a single-peaked profile at high energy (> 30 keV). In each of the narrow energy bands, the pulse profiles are nearly identical in the two NuSTAR observations. The spectra from both the observations are fitted well to a power-law with a Fermi–Dirac-type high-energy cutoff. We ruled out presence of a cyclotron line in the pulse phase averaged X-ray spectrum in the NuSTAR band with an optical depth greater than 0.15. An iron emission line is detected in both the NuSTAR spectra with an equivalent width of about 125 eV. We looked at the dependence of the spin-up rate on the luminosity and estimated the magnetic field strength from that, which came out to be much higher compared to other known BeXRB pulsars. Lastly, we discussed the inadequacy of the torque–luminosity relation for determination of magnetic field strength of neutron stars.

A systematic study of soft X-ray pulse profiles of magnetars in quiescence

Abstract Magnetars are neutron stars with extremely high surface magnetic fields. They show diverse X-ray pulse profiles in the quiescent state. We perform a systematic Fourier analysis of their soft X-ray pulse profiles. We find that most magnetars have a single-peaked profile and hence have low amplitudes of the second Fourier harmonics (A2). On the other hand, the pulsed fraction (PF) spreads over a wide range. We compared the results with theoretical profiles assuming various surface hotspot asymmetries, viewing geometries, and beaming functions. We found that a single value of the intensity ratio r between two antipodal hotspots is unable to reproduce the observed distribution of A2 and PF for all magnetars. The inferred r is probably anticorrelated with the thermal luminosity, implying that high-luminosity magnetars tend to have two symmetric hotspots. Our results are consistent with theoretical predictions, for which the existence of an evolving toroidal magnetic field breaks the symmetry of the surface temperature.

Occurrence of Single- and Double-Peaked Emission Profiles of Synthetic Chemicals.

This work aims to elucidate the circumstances that can lead to two peaks in the temporal emission profile of synthetic chemicals. Using a simplified substance flow model, we explore how emission factors, product lifespan, and degradation half-life in waste stock influence the (i) relative importance of emissions from three lifecycle stages (industrial processes, use phase, and waste disposal), and (ii) the resulting composite emission profile. A double-peaked emission profile occurs if the lifespan of products containing the chemical is longer than its production history, and the gross emission factor from waste disposal exceeds that from the use phase. Since most chemicals fail to meet these two conditions, it is reasonable to use single-peaked emission profile as the default in environmental studies. On the basis of their emission profiles and contributions from individual lifecycle stages, we can categorize chemicals into "simple single-peakers", "composite single-peakers", and "double-peakers". Our simplified model derived emission profiles for five real chemicals that agree well with earlier, more sophisticated calculations, indicating the model's ability to capture the essential features of actual emissions. It is hoped that the model and conclusions in this work will benefit both environmental modelers and decision makers.

Weak metallic emission lines in early B-type stars

Abstract Previously unrecognized weak emission lines originating from high excitation states of Si ii (12.84 eV) and Al ii (13.08 eV) are detected in the red-region spectra of slowly rotating early B-type stars. We surveyed high-resolution spectra of 35 B-type stars covering spectral sub-types between B1 and B7 near the main sequence and found the emission line of Si ii at 6239.6 Å in all of the 13 stars that have spectral sub-types B2 and B2.5. There are 17 stars belonging to sub-type B3 among which seven stars are found to show the emission line of Si ii. The emission line of Al ii at 6243.4 Å is detected in a narrower temperature range (Teff between 19000 K and 23000 K) in nine of the stars. Both emission lines are not detected in cooler (Teff < 16000 K) stars in our sample. The emission line of Si ii at 6239.6 Å shows a single-peaked and symmetrical profile, and the line center has no shift in wavelength with respect to line centers of low excitation absorption lines of Si ii. The measured half-width of the emission line is the same as those of rotationally broadened, low-excitation absorption lines of Si ii. These observations imply that the emitting gas is not of circumstellar origin, but it is located at the outermost layer of the atmosphere covering the whole stellar surface, and corotates with the star.

Multimission observations of the old nova GK Per during the 2015 outburst

GK Per, a classical nova of 1901, is thought to undergo variable mass accretion on to a magnetized white dwarf (WD) in an intermediate polar system (IP). We organized a multi-mission observational campaign in the X-ray and ultraviolet (UV) energy ranges during its dwarf nova (DN) outburst in 2015 March-April. Comparing data from quiescence and near outburst, we have found that the maximum plasma temperature decreased from about 26 to 16.2+/-0.4 keV. This is consistent with the previously proposed scenario of increase in mass accretion rate while the inner radius of the magnetically disrupted accretion disc shrinks, thereby lowering the shock temperature. A NuSTAR observation also revealed a high-amplitude WD spin modulation of the very hard X-rays with a single-peaked profile, suggesting an obscuration of the lower accretion pole and an extended shock region on the WD surface. The X-ray spectrum of GK Per measured with the Swift X-Ray Telescope varied on time-scales of days and also showed a gradual increase of the soft X-ray flux below 2 keV, accompanied by a decrease of the hard flux above 2 keV. In the Chandra observation with the High Energy Transmission Gratings, we detected prominent emission lines, especially of Ne, Mg and Si, where the ratios of H-like to He-like transition for each element indicate a much lower temperature than the underlying continuum. We suggest that the X-ray emission in the 0.8-2 keV range originates from the magnetospheric boundary.

Extensive photometry of the intermediate polar MU Cam: detection of a spin period change

Intermediate polars with known rates of spin period changes are not numerous because such tasks require measurements performed for a long time. To measure a spin period change, MU Cam is a good candidate because it has a spin oscillation with a large amplitude enabling measurements with high precision. Fortunately, in the past the spin period of MU Cam was measured with high precision. To measure the spin period anew, in 2014-2015 we performed extensive photometric observations of MU Cam, spanning a total duration of 208 h within 46 nights. We found that the spin, sideband and orbital periods are equal to 1187.16245+/-0.00047 s, 1276.3424+/-0.0022 s and 4.71942+/-0.00016 h, respectively. Comparing the measured spin period with the spin period of MU Cam in the past, we detected the spin period change with dP/dt=-(2.17+/-0.10) X 10^(-10). This rate of the spin period change was not stable and varied in a time scale of years. During four nights in 2014 April-May MU Cam was fainter than usual by 0.8 mag, and the amplitude of the sideband oscillation was five times larger, denoting significant fraction of disc-overflow accretion. The sideband oscillation showed a double-peaked pulse profile in the normal brightness state. When the star brightness was decreased by 0.8 mag, the sideband oscillation showed a single-peaked pulse profile. In contrast, the spin pulse, which was quasi-sinusoidal, remained remarkably stable both in profile and in amplitude. Moreover, the spin pulse was also remarkably stable in a time scale of years and even decades. MU Cam is of great interest because it represents a distinctive object with a large and unstable rate of the spin period change and exhibits a distinctive behaviour of the pulse profiles.

Probing the 2D temperature structure of protoplanetary disks withHerschelobservations of high-JCO lines

The gas temperature structure of protoplanetary disks is a key ingredient for interpreting various disk observations and for quantifying the subsequent evolution of these systems. The comparison of low- and mid-$J$ CO rotational lines is a powerful tool to assess the temperature gradient in the warm molecular layer of disks. Spectrally resolved high-$J$ ($J_{\rm u} > 14$) CO lines probe intermediate distances and heights from the star that are not sampled by (sub-)millimeter CO spectroscopy. This paper presents new {\it Herschel}/HIFI and archival PACS observations of $^{12}$CO, $^{13}$CO and \cii \ emission in 4 Herbig AeBe (HD 100546, HD 97048, IRS 48, HD 163296) and 3 T Tauri (AS 205, S CrA, TW Hya) disks. In the case of the T Tauri systems AS 205 and S CrA, the CO emission has a single-peaked profile, likely due to a slow wind. For all other systems, the {\it Herschel} CO spectra are consistent with pure disk emission and the spectrally-resolved lines (HIFI) and the CO rotational ladder (PACS) are analyzed simultaneously assuming power-law temperature and column density profiles, using the velocity profile to locate the emission in the disk. The temperature profile varies substantially from disk to disk. In particular, $T_{\rm gas}$ in the disk surface layers can differ by up to an order of magnitude among the 4 Herbig AeBe systems with HD 100546 being the hottest and HD 163296 the coldest disk of the sample. Clear evidence of a warm disk layer where $T_{\rm gas} > T_{\rm dust}$ is found in all the Herbig Ae disks. The observed CO fluxes and line profiles are compared to predictions of physical-chemical models. The primary parameters affecting the disk temperature structure are the flaring angle, the gas-to-dust mass ratio the scale height and the dust settling.