Envelope Density Research Articles

TeV–PeV NEUTRINO OSCILLATION OF LOW-LUMINOSITY GAMMA-RAY BURSTS

There is a sign that long-duration gamma-ray bursts (GRBs) originate from the core collapse of massive stars. During a jet puncturing through the progenitor envelope, high energy neutrinos can be produced by the reverse shock formed at the jet head. It is suggested that low-luminosity GRBs (LL-GRBs) are possible candidates of this high energy neutrino precursor up to $\sim {\rm PeV}$. Before leaving the progenitor, these high energy neutrinos must oscillate from one flavor to another with matter effect in the envelope. Under the assumption of a power-law stellar envelope density profile $\rho \propto r^{-\alpha}$ with an index $\alpha$, we study the properties of ${\rm TeV-PeV}$ neutrino oscillation. We find that adiabatic conversion is violated for these neutrinos so we do certain calibration of level crossing effect. The resonance condition is reached for different energies at different radii. We notice that the effective mixing angles in matter for ${\rm PeV}$ neutrinos are close to zero so the transition probabilities from one flavor to another are almost invariant for ${\rm PeV}$ neutrinos. We plot all the transition probabilities versus energy of ${\rm TeV-PeV}$ neutrinos from the birth place to the surface of the progenitor. With an initial flavor ratio $\phi_{\nu_e}^0:\phi_{\nu_\mu}^0:\phi_{\nu_\tau}^0=1:2:0$, we plot how the flavor ratio evolves with energy and distance when neutrinos are still in the envelope, and further get the ratio when they reach the Earth. For ${\rm PeV}$ neutrinos, the ratio is always $\phi_{\nu_e}:\phi_{\nu_\mu}:\phi_{\nu_\tau}\simeq0.30:0.37:0.33$ on Earth. In addition, we discuss the dependence of the flavor ratio on energy and $\alpha$ and get a pretty good result. This dependence may provide a promising probe of the progenitor structure.

Effect of Coating and Particle Properties on the Cycling Stability of Li-Ion Conductor (LIC) Coated Sulfur Cathodes

Introduction Among the available energy-storage technologies, lithium batteries will play an increasingly important role because of their high specific energy and energy density. Since their introduction in 1991, Li-ion batteries have transformed portable electronic devices. New generations of such batteries will transform transport and find use in stationary electricity storage. Extensive research in lithium-ion anode technologies have made it possible to obtain 1,950 mAh/g anode capacities with stable performance (1-3). However the current cathodes plays a limiting role with a maximum achieved capacity five folds lower than that of the anode (4). Reaching beyond the horizon of Li-ion batteries is a serious challenge and requires the exploration of new chemistries, especially related to the electrochemistry, and new materials development. Li-S battery which works on the ‘conversion’ principle is a promising candidate for this purpose. Sulfur has a theoretical capacity of 1672 mAh/g, representing to nearly 6, 11 and 10 fold improvement in capacity as compared to LiCoO2, LiMn2O4 and LiFePO4respectively. Since the first demonstration of LiS batteries, research has burgeoned at an alarming rate in this exciting field. However, this technology still has many challenges due to the poor conductivity of sulfur and more importantly, the polysulfide dissolution. Polysulfide originally dissolves as short chain and grows into a longer chain, eventually resulting in the loss of active material and capacity fade. Polysulfide dissolution is a serious issue yet to be addressed economically. Previous work from our group(5) demonstrates a very effective method to prevent polysulfide dissolution by coating a thin layer of Lithium Ion Conductor (LIC) over nano-sulfur anode in a multilayer architecture. This approach resulted in a stable capacity of ~600mAh/g for over 60 cycles with minimal fade. In this work, we attempt to enhance the capacity and stability by altering the size of the active sulfur nanomaterials and engineering the porosity of LIC layer on the performance of the battery. Figure 1 depicts an LIC coated sulfur electrode with tailored porosity and pore volume. Using dynamic light scattering the size of nanoparticles is analyzed and porosity and pore volume are studied using mercury porosimetry, envelope density measurement and BET surface area analysis. Results of these studies will be presented and discussed. Captions Figure 1: SEM image of the LIC coated sulfur electrodes(5).

Herschel Hi-GAL imaging of massive young stellar objects

We used Herschel Hi-GAL survey data to determine whether massive young stellar objects (MYSOs) are resolved at 70$\mu$m and to study their envelope density distribution. Our analysis of three relatively isolated sources in the l=30{\deg} and l=59{\deg} Galactic fields show that the objects are partially resolved at 70$\mu$m. The Herschel Hi-GAL survey data have a high scan velocity which makes unresolved and partially resolved sources appear elongated in the 70$\mu$m images. We analysed the two scan directions separately and examine the intensity profile perpendicular to the scan direction. Spherically symmetric radiative transfer models with a power law density distribution were used to study the circumstellar matter distribution. Single dish sub-mm data were also included to study how different spatial information affects the fitted density distribution. The density distribution which best fits both the 70$\mu$m intensity profile and SED has an average index of ~0.5. This index is shallower than expected and is probably due to the dust emission from bipolar outflow cavity walls not accounted for in the spherical models. We conclude that 2D axisymmetric models and Herschel images at low scan speeds are needed to better constrain the matter distribution around MYSOs.

Water in star-forming regions withHerschel(WISH)(Corrigendum)

Context. Outflows are an important part of the star formation process as both the result of ongoing active accretion and one of the main sources of mechanical feedback on small scales. Water is the ideal tracer of these effects because it is present in high abundance for the conditions expected in various parts of the protostar, particularly the outflow. Aims. We constrain and quantify the physical conditions probed by water in the outflow-jet system for Class 0 and I sources. Methods. We present velocity-resolved Herschel HIFI spectra of multiple water-transitions observed towards 29 nearby Class 0/ Ip rotostars as part of the WISH guaranteed time key programme. The lines are decomposed into different Gaussian components, with each component related to one of three parts of the protostellar system; quiescent envelope, cavity shock and spot shocks in the jet and at the base of the outflow. We then use non-LTE radex models to constrain the excitation conditions present in the two outflow-related components. Results. Water emission at the source position is optically thick but effectively thin, with line ratios that do not vary with velocity, in contrast to CO. The physical conditions of the cavity and spot shocks are similar, with post-shock H2 densities of order 10 5 −10 8 cm −3 and H2O column densities of order 10 16 −10 18 cm −2 .H 2O emission originates in compact emitting regions: for the spot shocks these correspond to point sources with radii of order 10−200 AU, while for the cavity shocks these come from a thin layer along the outflow cavity wall with thickness of order 1−30 AU. Conclusions. Water emission at the source position traces two distinct kinematic components in the outflow; J shocks at the base of the outflow or in the jet, and C shocks in a thin layer in the cavity wall. The similarity of the physical conditions is in contrast to off-source determinations which show similar densities but lower column densities and larger filling factors. We propose that this is due to the differences in shock properties and geometry between these positions. Class I sources have similar excitation conditions to Class 0 sources, but generally smaller line-widths and emitting region sizes. We suggest that it is the velocity of the wind driving the outflow, rather than the decrease in envelope density or mass, that is the cause of the decrease in H2O intensity between Class 0 and I sources.

CHARACTERIZING THE YOUNGESTHERSCHEL-DETECTED PROTOSTARS. I. ENVELOPE STRUCTURE REVEALED BY CARMA DUST CONTINUUM OBSERVATIONS

We present CARMA 2.9 mm dust continuum emission observations of a sample of 14 Herschel-detected Class 0 protostars in the Orion A and B molecular clouds, drawn from the PACS Bright Red Sources (PBRS) sample (Stutz et al.). These objects are characterized by very red 24 \micron\ to 70 \micron\ colors and prominent submillimeter emission, suggesting that they are very young Class 0 protostars embedded in dense envelopes. We detect all of the PBRS in 2.9 mm continuum emission and emission from 4 protostars and 1 starless core in the fields toward the PBRS; we also report 1 new PBRS source. The ratio of 2.9 mm luminosity to bolometric luminosity is higher by a factor of $\sim$5 on average, compared to other well-studied protostars in the Perseus and Ophiuchus clouds. The 2.9 mm visibility amplitudes for 6 of the 14 PBRS are very flat as a function of uv-distance, with more than 50\% of the source emission arising from radii $<$ 1500 AU. These flat visibility amplitudes are most consistent with spherically symmetric envelope density profiles with $\rho$~$\propto$~R$^{-2.5}$. Alternatively, there could be a massive unresolved structure like a disk or a high-density inner envelope departing from a smooth power-law. The large amount of mass on scales $<$ 1500 AU (implying high average central densities) leads us to suggest that that the PBRS with flat visibility amplitude profiles are the youngest PBRS and may be undergoing a brief phase of high mass infall/accretion and are possibly among the youngest Class 0 protostars. The PBRS with more rapidly declining visibility amplitudes still have large envelope masses, but could be slightly more evolved.

A Model of Foam Density Prediction for Expanded Perlite Composites

Multiple sets of variables associated with expanded perlite particle consolidation in foam manufacturing were analyzed to develop a model for predicting perlite foam density. The consolidation of perlite particles based on the flotation method and compaction involves numerous variables leading to the final perlite foam density. The variables include binder content, compaction ratio, perlite particle size, various perlite particle densities and porosities, and various volumes of perlite at different stages of process. The developed model was found to be useful not only for prediction of foam density but also for optimization between compaction ratio and binder content to achieve a desired density. Experimental verification was conducted using a range of foam densities (0.15 - 0.5 g/cm 3 ) produced with a range of compaction ratios (1.5 - 3.5), a range of sodium silicate contents (0.05 - 0.35 g/ml) in dilution, a range of expanded perlite particle sizes (1 - 4 mm), and various perlite densities (such as skeletal, material, bulk, and envelope densities). A close agreement between predictions and experimental results was found.

Water in star-forming regions withHerschel(WISH)

Context: Outflows are an important part of the star formation process as both the result of ongoing active accretion and one of the main sources of mechanical feedback on small scales. Water is the ideal tracer of these effects because it is present in high abundance in various parts of the protostar. Method: We present \textit{Herschel} HIFI spectra of multiple water-transitions towards 29 nearby Class 0/I protostars as part of the WISH Survey. These are decomposed into different Gaussian components, with each related to one of three parts of the protostellar system; quiescent envelope, cavity shock and spot shocks in the jet and at the base of the outflow. We then constrain the excitation conditions present in the two outflow-related components. Results: Water emission is optically thick but effectively thin, with line ratios that do not vary with velocity, in contrast to CO. The physical conditions of the cavity and spot shocks are similar, with post-shock H$_{2}$ densities of order 10$^{5}-$10$^{8}$\,cm$^{-3}$ and H$_{2}$O column densities of order 10$^{16}-$10$^{18}$\,cm$^{-2}$. H$_{2}$O emission originates in compact emitting regions: for the spot shocks these correspond to point sources with radii of order 10-200\,AU, while for the cavity shocks these come from a thin layer along the outflow cavity wall with thickness of order 1-30\,AU. Conclusions: Water emission at the source position traces two distinct kinematic components in the outflow; J shocks at the base of the outflow or in the jet, and C shocks in a thin layer in the cavity wall. Class I sources have similar excitation conditions to Class 0 sources, but generally smaller line-widths and emitting region sizes. We suggest that it is the velocity of the wind driving the outflow, rather than the decrease in envelope density or mass, that is the cause of the decrease in H$_{2}$O intensity between Class 0 and I.

Study of Guest Molecules in Metal–Organic Frameworks by Powder X-ray Diffraction: Analysis of Difference Envelope Density

The structural characterization of metal–organic frameworks (MOFs) by powder X-ray diffraction can be challenging. Even more difficult are studies of guest solvent or gas molecules inside the MOF pores. Hence, recently we successfully designed several new approaches for structural investigations of porous MOFs. These methods use structure envelopes, which can be easily generated from the structure factors of a few (1–10) of the most intense low index reflections. However, the most interesting results have been found by using difference envelope density (DED) analysis. DED can be produced by taking the difference between observed and calculated structure envelope densities. The generation and analysis of DED maps are straightforward but allow studying guest molecules in the pores of MOFs by using routine powder X-ray diffraction data. Examples of DED used for studies of solvent molecule location, porosity activation, and gas loading are presented herein. We show that DED analysis is an important technique in the study of host–guest properties in MOFs by providing position, shape, and approximate occupancy of molecules in the MOF pores.

Hydrogen cryo-adsorption by hexagonal prism monoliths of MIL-101

Hexagonal prism shaped monoliths of envelope density 0.40–0.467 g/cm3 and remarkable mechanical stability were obtained from MIL-101 powder. The hydrogen adsorption isotherms within an extended pressure range show that the excess adsorption decreases with the increasing density of the pellets. At 77 K and 150 bar, the total volumetric capacity is 46.5 g/L; the discharge to 159 K and 5 bar leads to 45 g/L (38.8 g/L referring to the outer tank volume) supporting MIL-101 as a promising candidate for applications in the 77–160 K range of interest for cryo-adsorption hydrogen storage method. The isosteric adsorption enthalpy evaluated from the experimental data with the van't Hoff equation, using fugacity, is in agreement with the calorimetric heat of adsorption reported in literature. Monoliths of this shape allow the best possible packing density of any sorbent in a container and the primary data reported here on MIL-101 could serve as material engineering properties required for modeling hydrogen storage tanks.

The Use of PAT and Off-line Methods for Monitoring of Roller Compacted Ribbon and Granule Properties with a View to Continuous Processing

Real-time process monitoring using process analytical technology (PAT) tools can augment process understanding, enable improved process control, and hence facilitate the production of high-quality pharmaceutical products. While beneficial for batch processes, the availability of PAT tools to monitor continuous processes in real time is required to ensure product quality. This paper presents the application of novel process analytical technology (PAT) tools in combination with off-line analytical techniques for the study of a laboratory-scale roller compaction dry granulation process. An experiment whereby roll pressure was linearly increased and the effects thereof on roller compacted ribbon and granule properties of a placebo formulation is described. Analysis of the ribbons and granules was performed using both in-line and off-line techniques. Ribbon envelope density was measured using the GeoPyc, and the results were compared to off-line near-infrared (NIR) measurements and a novel in-line NIR tool, the Multieye. Particle size analysis of roller compacted granules was assessed with traditional sieve analysis, Camsizer and a novel technique, the Eyecon. Both Camsizer and Eyecon have the potential of being used as PAT tools in-line. Additionally the compressibility of the granules was determined using in-die Heckle analysis and the hardness of the resultant compacts was assessed. The compacts were subsequently analysed using off-line Raman spectroscopy to investigate the surface smoothness which was shown to indicate crushing strength for compacts prepared. The results of this initial study demonstrate a good relationship between in-line and off-line measurement of key in-process material attributes. The findings thus support the further exploitation of these new in-line PAT methods in monitoring of continuous unit operations at a commercial scale.

New approaches to measuring biochar density and porosity

It is clear that the density and porosity of biochar will impact its mobility in the environment, its interaction with the soil hydrologic cycle, and its suitability as an ecological niche for soil microorganisms. However, the wide range of biochar pore sizes complicates biochar porosity characterization, making it challenging to find methods appropriate to connect the fundamental physical properties of density and porosity to environmental outcomes. Here, we report the use of two fast, simple density measurement techniques to characterize biochar density and porosity. We measured biochar skeletal density by helium pycnometry and envelope density by displacement of a dry granular suspension. We found that biochar skeletal density ranged from 1.34 g cm−3 to 1.96 g cm−3, and increased with pyrolysis temperature. Biochar envelope density ranged from 0.25 g cm−3 to 0.60 g cm−3, and was higher for wood biochars than grass biochars—a difference we attribute to plant cell structures preserved during pyrolysis. We compared the pore volumes measured by pycnometry with those measured by nitrogen gas sorption and mercury porosimetry. We show that biochar pore volumes measured by pycnometry are comparable to the values obtained by mercury porosimetry, the current benchmark method. We also show that the majority of biochar pore volume is in macropores, and thus, is not measured by gas sorption analysis. These fast, simple techniques can now be used to study the relationship between biochar's physical properties and its environmental behaviors.

Facile preparation of monolithic κ-carrageenan aerogels

To the best of our knowledge, it is the first study reporting the synthesis of monolithic κ-carrageenan aerogels with meso- and macroporous structures, being unique in physical and chemical properties. We demonstrate a novel method to synthesize κ-carrageenan aerogels in which potassium thiocyanate was used as the source of specific ions. Aerogels were characterized by envelope density analysis, scanning electron microscopy, nitrogen adsorption-desorption analysis, X-ray powder diffractometry and IR spectroscopy. By varying the concentration of κ-carrageenan between 0.5 and 3 wt%, the envelope density can be linearly increased from 40 to 160 kg m⁻³. The sulphate functional groups in the wet gel and the specific ions are the key factors controlling the volume shrinkage of aerogels which average about 66%. The aerogels exhibit a fibrillar structure similar to cellulose aerogels. The fibril thickness was observed to be 10-15 nm and the specific surface area was about 230 m² g⁻¹. The existing meso- and macroporous structures were confirmed by nitrogen adsorption-desorption isotherm analysis and scanning electron microscopy. The aerogels were completely pure, free of specific ions and confirmed to be amorphous by powder X-ray diffraction. Hence, these porous materials can provide a matrix with a chelating function which can be used as a host in many applications.

An assessment of powder pycnometry as a means of determining granule porosity

A powder pycnometry method, using a commercially available instrument (GeoPyc® with DryFlo® displacement media), was evaluated as a means of measuring the envelope density of hydroxyapatite (HA) granules in the size range of 75–8000 µm. The aims of this study were to (1) investigate the reproducibility of the DryFlo® powder particle size and consolidation properties, (2) determine the number of preparation cycles required before test measurements should be taken, (3) compare the powder pycnometry method to the reference mercury porosimetry method and (4) investigate the effect of granule size on envelope density measurement. DryFlo® was shown to have a reproducible particle size when sampled at multiple locations across three separate containers. A minimum of 1 preparation cycle should be used to ensure consistent packing of the DryFlo® and HA granules. DryFlo® density was found to be insensitive to consolidation forces in the range of 10–100 N. The powder pycnometry method could be linearly calibrated against the reference mercury porosimetry method when considering polydisperse HA granule samples. However, when analyzing narrow particle size fractions limitations in the powder pycnometry method were noted resulting in a reduced particle size range of 1850–4050 µm that could be linearly calibrated against the mercury porosimetry method.

PHOTOMETRIC REDSHIFTS OF SUBMILLIMETER GALAXIES

We use the photometric redshift method of Chakrabarti & McKee (2008) to infer photometric redshifts of submillimeter galaxies with far-IR (FIR) $\it{Herschel}$ data obtained as part of the PACS Evolutionary Probe (PEP) program. For the sample with spectroscopic redshifts, we demonstrate the validity of this method over a large range of redshifts ($ 4 \ga z \ga 0.3$) and luminosities, finding an average accuracy in $(1+z_{\rm phot})/(1+z_{\rm spec})$ of 10%. Thus, this method is more accurate than other FIR photometric redshift methods. This method is different from typical FIR photometric methods in deriving redshifts from the light-to-gas mass ($L/M$) ratio of infrared-bright galaxies inferred from the FIR spectral energy distribution (SED), rather than dust temperatures. Once the redshift is derived, we can determine physical properties of infrared bright galaxies, including the temperature variation within the dust envelope, luminosity, mass, and surface density. We use data from the GOODS-S field to calculate the star formation rate density (SFRD) of sub-mm bright sources detected by AzTEC and PACS. The AzTEC-PACS sources, which have a threshold $850 \micron$ flux $\ga 5 \rm mJy$, contribute 15% of the SFRD from all ULIRGs ($L_{\rm IR} \ga 10^{12} L_{\odot}$), and 3% of the total SFRD at $z \sim 2$.

The Use of Near-Infrared and Microwave Resonance Sensing to Monitor a Continuous Roller Compaction Process

Roller compaction is commonly used in the pharmaceutical and nutraceutical industries to increase and narrow the size distribution of a particulate material, making it easier to process. Both the moisture content of the material and the density of the roller compacted ribbon affect the uniformity and physical properties of the resultant granules. Without process analytical technologies, these parameters cannot be determined on-line or in real time. In this study, the more commonly used near-infrared (NIR) spectroscopy was compared and contrasted with microwave resonance for the determination of roller-compacted ribbons' envelope density and moisture content. Results indicate that microwave resonance can offer improved accuracy, robustness, and ease-of-use compared with NIR spectroscopy for these property measurements.

Modelling and simulation of a generalised vehicle‐to‐vehicle fading channel

This study presents statistical properties of the vehicle-to-vehicle Nakagami–Hoyt channel model with diffused line of sight (LOS) under isotropic condition. The envelope and phase probability density functions, spatial-time autocorrelation function, the power spectral density, level crossing rate, the average duration of fade, squared time autocorrelation function and mean-square error of time autocorrelation function of the Nakagami–Hoyt channel have been derived under the assumption that both the transmitter and receiver are mobile having omnidirectional antennas and a diffused LOS component is present. The model has been validated using the inverse fast Fourier transform-based simulator. The simulator and analytical results corroborate.

Laser hosing in relativistically hot plasmas.

Electron response in an intense laser is studied in the regime where the electron temperature is relativistic. Equations for laser envelope and plasma density evolution, both in the electron plasma wave and ion acoustic wave regimes, are rederived from the relativistic fluid equations to include relativistic plasma temperature effect. These equations are used to study short-pulse and long-pulse laser hosing instabilities using a variational method approach. The analysis shows that relativistic electron temperatures reduce the hosing growth rates and shift the fastest-growing modes to longer wavelengths. These results resolve a long-standing discrepancy between previous nonrelativistic theory and simulations or experiments on hosing.

AHERSCHELAND APEX CENSUS OF THE REDDEST SOURCES IN ORION: SEARCHING FOR THE YOUNGEST PROTOSTARS

We perform a census of the reddest, and potentially youngest, protostars in the Orion molecular clouds using data obtained with the PACS instrument on board the Herschel Space Observatory and the LABOCA and SABOCA instruments on APEX as part of the Herschel Orion Protostar Survey (HOPS). A total of 55 new protostar candidates are detected at 70 μm and 160 μm that are either too faint (m24 > 7 mag) to be reliably classified as protostars or undetected in the Spitzer/MIPS 24 μm band. We find that the 11 reddest protostar candidates with log λFλ70/λFλ24 > 1.65 are free of contamination and can thus be reliably explained as protostars. The remaining 44 sources have less extreme 70/24 colors, fainter 70 μm fluxes, and higher levels of contamination. Taking the previously known sample of Spitzer protostars and the new sample together, we find 18 sources that have log λFλ70/λFλ24 > 1.65; we name these sources "PACS Bright Red sources," or PBRs. Our analysis reveals that the PBR sample is composed of Class 0 like sources characterized by very red spectral energy distributions (SEDs; Tbol < 45 K) and large values of sub-millimeter fluxes (Lsmm/Lbol > 0.6%). Modified blackbody fits to the SEDs provide lower limits to the envelope masses of 0.2–2 M☉ and luminosities of 0.7–10 L☉. Based on these properties, and a comparison of the SEDs with radiative transfer models of protostars, we conclude that the PBRs are most likely extreme Class 0 objects distinguished by higher than typical envelope densities and hence, high mass infall rates.

Results from HOPS: A multiwavelength census of Orion protostars

AbstractSurveys with the Spitzer and Herschel space observatories are now enabling the discovery and characterization of large samples of protostars in nearby molecular clouds, providing the observational basis for a detailed understanding of star formation in diverse environments. We are pursuing this goal with the Herschel Orion Protostar Survey (HOPS), which targets 328 Spitzer ‐identified protostars in the Orion molecular clouds, the largest star‐forming region in the nearest 500 pc. The sample encompasses all phases of protostellar evolution and a wide range of formation environments, from dense clusters to relative isolation. With a grid of radiative transfer models, we fit the 1–870 µm spectral energy distributions (SEDs) of the protostars to estimate their envelope densities, cavity opening angles, inclinations, and total luminosities. After correcting the bolometric luminosities and temperatures of the sources for foreground extinction and inclination, we find a spread of several orders of magnitude in luminosity at all evolutionary states, a constant median luminosity over the more evolved stages, and a possible deficit of high‐inclination, rapidly infalling envelopes among the Spitzer ‐identified sample. We have detected over 100 new sources in the Herschel images; some of them may fill this deficit. We also report results from modeling the pre‐ and post‐outburst 1–870 µm SEDs of V2775 Ori (HOPS 223), a known FU Orionis outburster in the sample. It is the least luminous FU Ori star with a protostellar envelope. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

HERSCHEL/PACS SPECTROSCOPIC SURVEY OF PROTOSTARS IN ORION: THE ORIGIN OF FAR-INFRARED CO EMISSION

We present far-IR (57-196 mu) spectra of 21 protostars in the Orion molecular clouds, obtained with the Photodetector Array Camera and Spectrometer (PACS) onboard the Herschel Space observatory, as part of the Herschel Orion Protostar Survey (HOPS) program. We analyzed the CO emission lines (J_up = 14-46) in the PACS spectra, extracted within a projected distance of <= 2000 AU centered on the protostar. The total luminosity of the CO lines observed with PACS (L(CO)) is found to increase with increasing L_bol. The CO rotational temperature implied by the line ratios increases with J, and at least 3-4 rotational temperature components are required to fit the observed rotational diagram. The rotational temperature components are remarkably invariant between protostars and show no dependence on L_bol, T_bol or envelope density, implying that if the emitting gas is in LTE, the CO emission must arise in multiple temperature components that remain independent of L_bol over two orders of magnitudes. The observed CO emission can also be modeled as arising from a single temperature gas component or from a medium with a power-law temperature distribution; both of these require sub-thermally excited molecular gas at low densities (n(H_2) <= 10^6 cm^-3) and high temperatures (T >= 2000 K). Our results suggest that the contribution from PDRs along the envelope cavity walls is unlikely to be the dominant component of the CO emission observed with PACS. Instead, the "universality" of the rotational temperatures and the observed correlation between L(CO) and L_bol can most easily be explained if the observed CO emission originates in shock-heated, hot (T >= 2000 K), sub-thermally excited (n(H_2) <= 10^6 cm^-3) molecular gas. Post-shock gas at these densities is more likely to be found within the outflow cavities along the molecular outflow or along the cavity walls at radii >= several 100-1000 AU.