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The mass dependence of dwarf satellite galaxy quenching

We combine observations of the Local Group with data from the NASA-Sloan Atlas to show the variation in the quenched fraction of satellite galaxies from low-mass dwarf spheroidals and dwarf irregulars to more massive dwarfs similar to the Magellanic Clouds. While almost all of the low-mass (M {sub *} ≲ 10{sup 7} M {sub ☉}) dwarfs are quenched, at higher masses the quenched fraction decreases to approximately 40%-50%. This change in the quenched fraction is large and suggests a sudden change in the effectiveness of quenching that correlates with satellite mass. We combine this observation with models of satellite infall and ram pressure stripping to show that the low-mass satellites must quench within 1-2 Gyr of pericenter passage to maintain a high quenched fraction, but that many more massive dwarfs must continue to form stars today even though they likely fell into their host >5 Gyr ago. We also characterize how the susceptibility of dwarfs to ram pressure must vary as a function of mass if it is to account for the change in quenched fractions. Though neither model predicts the quenching effectiveness a priori, this modeling illustrates the physical requirements that the observed quenched fractions place on possible quenching mechanisms.

79 ASTRONOMY AND ASTROPHYSICS↗

Wideband very large array observations of A2256. I. Continuum, rotation measure, and spectral imaging

We report new observations of A2256 with the Karl G. Jansky Very Large Array (VLA) at frequencies between 1 and 8 GHz. These observations take advantage of the 2:1 bandwidths available during a single observation to study the spectral index, polarization, and rotation measure as well as using the associated higher sensitivity per unit time to image total intensity features down to ∼0.''5 resolution. We find that the Large Relic, which dominates the cluster, is made up of a complex of filaments that show correlated distributions in intensity, spectral index, and fractional polarization. The rotation measure varies across the face of the Large Relic but is not well correlated with the other properties of the source. The shape of individual filaments suggests that the Large Relic is at least 25 kpc thick. We detect a low surface brightness arc connecting the Large Relic to the Halo and other radio structures, suggesting a physical connection between these features. The center of the F-complex is dominated by a very steep-spectrum, polarized, ring-like structure, F2, without an obvious optical identification, but the entire F-complex does have interesting morphological similarities to the radio structure of NGC 1265. Source C, the Long Tail, is unresolved in width near the galaxy core and is ≲ 100 pc in diameter there. This morphology suggests either that C is a one-sided jet or that the bending of the tails takes place very near the core, consistent with the parent galaxy having undergone extreme stripping. Overall it seems that many of the unusual phenomena can be understood in the context of A2256 being near the pericenter of a slightly off-axis merger between a cluster and a smaller group. Given the lack of evidence for a strong shock associated with the Large Relic, other models should be considered, such as reconnection between two large-scale magnetic domains.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding the unique assembly history of central group galaxies

Central galaxies (CGs) in massive halos live in unique environments with formation histories closely linked to that of the host halo. In local clusters, they have larger sizes (R{sub e} ) and lower velocity dispersions (σ) at fixed stellar mass M {sub *}, and much larger R{sub e} at a fixed σ than field and satellite galaxies (non-CGs). Using spectroscopic observations of group galaxies selected from the COSMOS survey, we compare the dynamical scaling relations of early-type CGs and non-CGs at z ∼ 0.6 to distinguish possible mechanisms that produce the required evolution. CGs are systematically offset toward larger R{sub e} at fixed σ compared to non-CGs with similar M {sub *}. The CG R{sub e} -M {sub *} relation also shows differences, primarily driven by a subpopulation (∼15%) of galaxies with large R{sub e} , while the M {sub *}-σ relations are indistinguishable. These results are accentuated when double Sérsic profiles, which better fit light in the outer regions of galaxies, are adopted. They suggest that even group-scale CGs can develop extended components by these redshifts that can increase total R{sub e} and M {sub *} estimates by factors of ∼2. To probe the evolutionary link between our sample and cluster CGs, we also analyze two cluster samples at z ∼ 0.6 and z ∼ 0. We find similar results for the more massive halos at comparable z, but much more distinct CG scaling relations at low-z. Thus, the rapid, late-time accretion of outer components, perhaps via the stripping and accretion of satellites, would appear to be a key feature that distinguishes the evolutionary history of CGs.

79 ASTRONOMY AND ASTROPHYSICS↗

STELLAR KINEMATICS AND STRUCTURAL PROPERTIES OF VIRGO CLUSTER DWARF EARLY-TYPE GALAXIES FROM THE SMAKCED PROJECT. III. ANGULAR MOMENTUM AND CONSTRAINTS ON FORMATION SCENARIOS

We analyze the stellar kinematics of 39 dwarf early-type galaxies (dEs) in the Virgo Cluster. Based on the specific stellar angular momentum λ{sub Re} and the ellipticity, we find 11 slow rotators and 28 fast rotators. The fast rotators in the outer parts of the Virgo Cluster rotate significantly faster than fast rotators in the inner parts of the cluster. Moreover, 10 out of the 11 slow rotators are located in the inner 3° (D < 1 Mpc) of the cluster. The fast rotators contain subtle disk-like structures that are visible in high-pass filtered optical images, while the slow rotators do not exhibit these structures. In addition, two of the dEs have kinematically decoupled cores and four more have emission partially filling in the Balmer absorption lines. These properties suggest that Virgo Cluster dEs may have originated from late-type star-forming galaxies that were transformed by the environment after their infall into the cluster. The correlation between λ{sub Re} and the clustercentric distance can be explained by a scenario where low luminosity star-forming galaxies fall into the cluster, their gas is rapidly removed by ram-pressure stripping, although some of it can be retained in their core, their star formation is quenched but their stellar kinematics are preserved. After a long time in the cluster and several passes through its center, the galaxies are heated up and transformed into slow rotating dEs.

79 ASTRONOMY AND ASTROPHYSICS↗

WEAK GRAVITATIONAL LENSING AS A PROBE OF PHYSICAL PROPERTIES OF SUBSTRUCTURES IN DARK MATTER HALOS

We propose a novel method to select satellite galaxies in outer regions of galaxy groups or clusters using weak gravitational lensing. The method is based on the theoretical expectation that the tangential shear pattern around satellite galaxies would appear with negative values at an offset distance from the center of the main halo. We can thus locate the satellite galaxies statistically with an offset distance of several lensing smoothing scales by using the standard reconstruction of surface mass density maps from weak lensing observation. We test the idea using high-resolution cosmological simulations. We show that subhalos separated from the center of the host halo are successfully located even without assuming the position of the center. For a number of such subhalos, the characteristic mass and offset length can be also estimated on a statistical basis. We perform a Fisher analysis to show how well upcoming weak lensing surveys can constrain the mass density profile of satellite galaxies. In the case of the Large Synoptic Survey Telescope with a sky coverage of 20,000 deg{sup 2}, the mass of the member galaxies in the outer region of galaxy clusters can be constrained with an accuracy of ∼0.1 dex for galaxy clusters with mass 10{sup 14} h {sup –1} M {sub ☉} at z = 0.15. Finally we explore the detectability of tidal stripping features for subhalos having a wide range of masses of 10{sup 11}-10{sup 13} h {sup –1} M {sub ☉}.

79 ASTRONOMY AND ASTROPHYSICS↗

The next generation Virgo Cluster Survey. XII. Stellar populations and kinematics of compact, Low-mass early-type galaxies from Gemini GMOS-IFU Spectroscopy

We present Gemini Multi Object Spectrograph integral-field unit (GMOS-IFU) data of eight compact, low-mass early-type galaxies (ETGs) in the Virgo cluster. We analyze their stellar kinematics and stellar population and present two-dimensional maps of these properties covering the central 5″ × 7″ region. We find a large variety of kinematics, from nonrotating to highly rotating objects, often associated with underlying disky isophotes revealed by deep images from the Next Generation Virgo Cluster Survey. In half of our objects, we find a centrally concentrated younger and more metal-rich stellar population. We analyze the specific stellar angular momentum through the λ{sub R} parameter and find six fast rotators and two slow rotators, one having a thin counterrotating disk. We compare the local galaxy density and stellar populations of our objects with those of 39 more extended low-mass Virgo ETGs from the SMAKCED survey and 260 massive (M > 10{sup 10} M{sub ⊙}) ETGs from the ATLAS{sup 3D} sample. The compact low-mass ETGs in our sample are located in high-density regions, often close to a massive galaxy, and have, on average, older and more metal-rich stellar populations than less compact low-mass galaxies. We find that the stellar population parameters follow lines of constant velocity dispersion in the mass–size plane, smoothly extending the comparable trends found for massive ETGs. Our study supports a scenario where low-mass compact ETGs have experienced long-lived interactions with their environment, including ram-pressure stripping and gravitational tidal forces, that may be responsible for their compact nature.

79 ASTRONOMY AND ASTROPHYSICS↗

A DEEP STUDY OF THE DWARF SATELLITES ANDROMEDA XXVIII AND ANDROMEDA XXIX

We present the results of a deep study of the isolated dwarf galaxies Andromeda XXVIII and Andromeda XXIX with Gemini/GMOS and Keck/DEIMOS. Both galaxies are shown to host old, metal-poor stellar populations with no detectable recent star formation, conclusively identifying both of them as dwarf spheroidal galaxies (dSphs). And XXVIII exhibits a complex horizontal branch morphology, which is suggestive of metallicity enrichment and thus an extended period of star formation in the past. Decomposing the horizontal branch into blue (metal-poor, assumed to be older) and red (relatively more metal-rich, assumed to be younger) populations shows that the metal-rich are also more spatially concentrated in the center of the galaxy. We use spectroscopic measurements of the calcium triplet, combined with the improved precision of the Gemini photometry, to measure the metallicity of the galaxies, confirming the metallicity spread and showing that they both lie on the luminosity–metallicity relation for dwarf satellites. Taken together, the galaxies exhibit largely typical properties for dSphs despite their significant distances from M31. These dwarfs thus place particularly significant constraints on models of dSph formation involving environmental processes such as tidal or ram pressure stripping. Such models must be able to completely transform the two galaxies into dSphs in no more than two pericentric passages around M31, while maintaining a significant stellar population gradient. Reproducing these features is a prime requirement for models of dSph formation to demonstrate not just the plausibility of environmental transformation but the capability of accurately recreating real dSphs.

79 ASTRONOMY AND ASTROPHYSICS↗

The effect of halo mass on the H i content of galaxies in groups and clusters

We combine data from the Sloan Digital Sky Survey (SDSS) and the Arecibo Legacy Fast ALFA Survey (ALFALFA) to study the cold atomic gas content of galaxies in groups and clusters in the local universe. A careful cross-matching of galaxies in the SDSS, ALFALFA, and SDSS group catalogs provides a sample of group galaxies with stellar masses 10{sup 8.4}M{sub ⊙}⩽M{sub ∗}⩽10{sup 10.6}M{sub ⊙} and group halo masses 10{sup 12.5}h{sup −1}M{sub ⊙}⩽M{sub h}⩽10{sup 15.0}h{sup −1}M{sub ⊙}. Controlling our sample in stellar mass and redshift, we find no significant radial variation in the galaxy H i gas-to-stellar mass ratio for the halo mass range in our sample. However, the fraction of galaxies detected in ALFALFA declines steadily toward the centers of groups, with the effect being most prominent in the most massive halos. In the outskirts of massive halos a hint of a depressed detection fraction for low-mass galaxies suggests pre-processing that decreases the H i in these galaxies before they fall into massive clusters. We interpret the decline in the ALFALFA detection of galaxies in the context of a threshold halo mass for ram pressure stripping for a given galaxy stellar mass. The lack of an observable decrease in the galaxy H i gas-to-stellar mass ratio with the position of galaxies within groups and clusters highlights the difficulty of detecting the impact of environment on the galaxy H i content in a shallow H i survey.

79 ASTRONOMY AND ASTROPHYSICS↗

A unified solution to the small scale problems of the ΛCDM model II: introducing parent-satellite interaction

We continue the study of the impact of baryon physics on the small scale problems of the ΛCDM model, based on a semi-analytical model (Del Popolo, 2009). With such model, we show how the cusp/core, missing satellite (MSP), Too Big to Fail (TBTF) problems and the angular momentum catastrophe can be reconciled with observations, adding parent-satellite interaction. Such interaction between dark matter (DM) and baryons through dynamical friction (DF) can sufficiently flatten the inner cusp of the density profiles to solve the cusp/core problem. Combining, in our model, a Zolotov et al. (2012)-like correction, similarly to Brooks et al. (2013), and effects of UV heating and tidal stripping, the number of massive, luminous satellites, as seen in the Via Lactea 2 (VL2) subhaloes, is in agreement with the numbers observed in the MW, thus resolving the MSP and TBTF problems. The model also produces a distribution of the angular spin parameter and angular momentum in agreement with observations of the dwarfs studied by van den Bosch, Burkert, and Swaters (2001)

79 ASTRONOMY AND ASTROPHYSICS↗

An Open-Source Frequency-Domain Model for Floating Wind Turbine Design Optimization

A new frequency-domain dynamics model has been developed that uses open-source components to efficiently represent a complete floating wind turbine system. The model, called RAFT (Response Amplitudes of Floating Turbines), incorporates quasi-static mooring reactions, strip-theory and potential-flow hydrodynamics, blade-element-momentum aerodynamics, and linear turbine control. The formulation is compatible with a wide variety of support structure configurations and no manual or time-domain preprocessing steps are required, making RAFT very practical in design and optimization workflows. The model is applied to three reference floating wind turbine designs and its predictions are compared with results from time-domain OpenFAST simulations. There is good agreement in mean offsets as well the statistics and spectra of the dynamic response, verifying RAFT’s general suitability for floating wind analysis. Follow-on work will include verification of potential-flow and turbine-control features and application to optimization problems.

17 WIND ENERGY↗

STELLAR MASS VERSUS STELLAR VELOCITY DISPERSION: WHICH IS BETTER FOR LINKING GALAXIES TO THEIR DARK MATTER HALOS?

It was recently suggested that compared to its stellar mass (M{sub *}), the central stellar velocity dispersion ({sigma}{sub *}) of a galaxy might be a better indicator for its host dark matter halo mass. Here we test this hypothesis by estimating the dark matter halo mass for central galaxies in groups as a function of M{sub *} and {sigma}{sub *}. For this we have estimated the redshift-space cross-correlation function (CCF) between the central galaxies at given M{sub *} and {sigma}{sub *} and a reference galaxy sample, from which we determine both the projected CCF, w{sub p} (r{sub p} ), and the velocity dispersion profile. A halo mass is then obtained from the average velocity dispersion within the virial radius. At fixed M{sub *}, we find very weak or no correlation between halo mass and {sigma}{sub *}. In contrast, strong mass dependence is clearly seen even when {sigma}{sub *} is limited to a narrow range. Our results thus firmly demonstrate that the stellar mass of central galaxies is still a good (if not the best) indicator for dark matter halo mass, better than the stellar velocity dispersion. The dependence of galaxy clustering on {sigma}{sub *} at fixed M{sub *}, as recently discovered by Wake et al., may be attributed to satellite galaxies, for which the tidal stripping occurring within halos has stronger effect on stellar mass than on central stellar velocity dispersion.

79 ASTRONOMY AND ASTROPHYSICS↗

DISCOVERY OF A POSSIBLY SINGLE BLUE SUPERGIANT STAR IN THE INTRA-CLUSTER REGION OF VIRGO CLUSTER OF GALAXIES

IC 3418 is a dwarf irregular galaxy falling into the Virgo cluster, and a 17 kpc long trail is seen behind the galaxy, which is considered to have formed due to ram pressure stripping. The trail contains compact knots and diffuse blobs of ultraviolet and blue optical emission and, thus, it is a clear site of recent star formation but in an unusual environment, surrounded by a million degree intra-cluster medium. We report on our optical spectroscopy of a compact source in the trail, SDSS J122952.66+112227.8, and show that the optical spectrum is dominated by emission from a massive blue supergiant star. If confirmed, our report would mark the farthest star with spectroscopic observation. We interpret that a massive O-type star formed in situ in the trail has evolved recently out of the main sequence into this blue supergiant phase, and now lacks any detectable spectral sign of its associated H II region. We argue that turbulence within the ram pressure striped gaseous trail may play a dominant role for the star formation within such trails.

79 ASTRONOMY AND ASTROPHYSICS↗

SIGNATURES OF THE M31-M32 GALACTIC COLLISION

The unusual morphologies of the Andromeda spiral galaxy (M31) and its dwarf companion M32 have been characterized observationally in great detail. The two galaxies' apparent proximity suggests that Andromeda's prominent star-forming ring as well as M32's compact elliptical (cE) structure may result from a recent collision. Here we present the first self-consistent model of the M31-M32 interaction that simultaneously reproduces observed positions, velocities, and morphologies for both galaxies. Andromeda's spiral structure is resolved in unprecedented detail, showing that a rare head-on orbit is not necessary to match Andromeda's ring-like morphology. The passage of M32 through Andromeda's disk perturbs the disk velocity structure. We find tidal stripping of M32's stars to be inefficient during the interaction, suggesting that some cEs are intrinsically compact. Additionally, the orbital solution implies that M32 is currently closer to the Milky Way than models have typically assumed, a prediction that may be testable with upcoming observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DEEP IMAGING OF M51: A NEW VIEW OF THE WHIRLPOOL’S EXTENDED TIDAL DEBRIS

We present deep, wide-field imaging of the M51 system using CWRU’s Burrell Schmidt Telescope at KPNO to study the faint tidal features that constrain its interaction history. Our images trace M51's tidal morphology down to a limiting surface brightness of μ{sub B,lim} ∼ 30 mag arcsec{sup −2} and provide accurate colors (σ{sub B−V}<0.1) down to μ{sub B} ∼ 28. We identify two new tidal streams in the system (the south and northeast plumes) with surface brightnesses of μ{sub B} = 29 and luminosities of ∼10{sup 6}L{sub ⊙,B}. While the northeast plume may be a faint outer extension of the tidal “crown” north of NGC 5195 (M51b), the south plume has no analog in any existing M51 simulation and may represent a distinct tidal stream or disrupted dwarf galaxy. We also trace the extremely diffuse northwest plume out to a total extent of 20′ (43 kpc) from NGC 5194 (M51a) and show it to be physically distinct from the overlapping bright tidal streams from M51b. The northwest plume’s morphology and red color (B−V=0.8) instead argue that it originated from tidal stripping of M51a’s extreme outer disk. Finally, we confirm the strong segregation of gas and stars in the southeast tail and do not detect any diffuse stellar component in the H i portion of the tail. Extant simulations of M51 have difficulty matching both the wealth of tidal structure in the system and the lack of stars in the H i tail, motivating new modeling campaigns to study the dynamical evolution of this classic interacting system.

79 ASTRONOMY AND ASTROPHYSICS↗

A Study of a Mini-Drift GEM Tracking Detector

In this paper, a GEM tracking detector with an extended drift region has been studied as part of an effort to develop new tracking detectors for future experiments at RHIC and for the Electron Ion Collider that is being planned for BNL or JLAB. The detector consists of a triple GEM stack with a 1.6 cm drift region that was operated in a mini TPC type configuration. Both the position and arrival time of the charge deposited in the drift region were measured on the readout plane which allowed the reconstruction of a short vector for the track traversing the chamber. The resulting position and angle information from the vector could then be used to improve the position resolution of the detector for larger angle tracks, which deteriorates rapidly with increasing angle for conventional GEM tracking detectors using only charge centroid information. Two types of readout planes were studied. One was a COMPASS style readout plane with 400 μm pitch XY strips and the other consisted of 2 × 10 mm 2 chevron pads. The detector was studied in test beams at Fermilab and CERN, along with additional measurements in the lab, in order to determine its position and angular resolution for incident track angles up to 45 degrees. Several algorithms were studied for reconstructing the vector using the position and timing information in order to optimize the position and angular resolution of the detector for the different readout planes. Finally, applications for large angle tracking detectors at RHIC and EIC are also discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Roles of plasma-generated vacuum-ultraviolet photons and oxygen radicals in damaging nanoporous low-k films

One important class of low-k materials used as interconnect dielectrics employs methyl groups added to nanoporous SiO{sub 2} matrices. These carbon-doped oxide materials are known to be susceptible to damage from plasma species during various stages of plasma processing. Two key active species generated in O{sub 2} plasma are oxygen (O) radicals and vacuum-ultraviolet (VUV) photons. These species are known to cause carbon loss, resulting in damaging increases in dielectric constant throughout the film. However, the mechanisms through which this damage is incurred are poorly understood. By capping the substrate in different ways during plasma exposure, it is possible to expose films to either photons alone or O atoms alone. The authors report measurements of damage induced by VUV photons only, O radicals only, and the combination of O radicals and photons. Through HF stripping, they note that carbon extraction from photons and from radicals yields different outcomes; the profile of carbon concentration within the modified region is different for each case. Damage from photons alone can be modeled and model predictions are in good agreement with measurements. Damage from O atoms alone can only be modeled if it is assumed that the near-surface region has a significantly reduced diffusivity compared to the bulk of the film. Experiment and model agree that both photons alone and O radicals alone damage the material by removing carbon. When radicals and photons are present simultaneously during plasma exposure, however, more C removal appears to be occurring in the model than experimentally observed. Remarkably, if only radicals are exposed to the film after short (10-30 s) plasma exposures, very little additional damage is incurred during this radical-only exposure. The most straightforward interpretation of these results appears to be that photons combine synergistically with radicals in the pores to narrow the pores, thereby reducing film diffusivity in the C-poor, plasma-damaged regions.

36 MATERIALS SCIENCE↗

Atomic layer deposition synthesis and evaluation of core–shell Pt-WC electrocatalysts

Pt-WC core shell particles were produced using atomic layer deposition (ALD) to deposit Pt layers onto WC particle substrates. A range of Pt depositions were used to determine the growth mechanism for the Pt-WC powder system. TEM imaging and Cu stripping voltammetry found that Pt ALD growth on WC powder substrates was similar to that on WC thin films. However, excess free carbon was found to affect Pt ALD by blocking adsorption sites on WC. The Pt-WC samples were evaluated for the oxygen reduction reaction using a rotating disk electrode to obtain quantitative activity information. The mass and specific activities for the 30 and 50 ALD cycle samples were found to be comparable to a 10 wt. % Pt/C catalyst. However, higher overpotentials and lower limiting currents were observed with ALD Pt-WC compared to Pt/C catalysts, indicating that the oxygen reduction mechanism is not as efficient on Pt-WC as on bulk Pt. Additionally, these Pt-WC catalysts were used to demonstrate hydrogen evolution reaction activity and were found to perform as well as bulk Pt catalyst but with a fraction of the Pt loading, in agreement with the previous work on Pt-WC thin film catalysts.

36 MATERIALS SCIENCE↗

Molecular radiotherapy: The NUKFIT software for calculating the time-integrated activity coefficient

Purpose: Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error.Methods: The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB.Results: To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples.Conclusions: The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.

61 RADIATION PROTECTION AND DOSIMETRY↗