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DOE OSTI2013

THE MASS DISTRIBUTION OF SUBGIANT PLANET HOSTS

High mass stars are hostile to Doppler measurements due to rotation and activity on the main-sequence, so RV searches for planets around massive stars have relied on evolved stars. A large number of planets have been found around evolved stars with M > 1.5 M{sub Sun }. To test the robustness of mass determinations, Lloyd compared mass distributions of planet hosting subgiants with distributions from integrating isochrones and concluded that it is unlikely the subgiant planet hosts are this massive, but rather that the mass inferences are systematically in error. The conclusions of Lloyd have been called in to question by Johnson et al., who show TRILEGAL-based mass distributions that disagree with the mass distributions in Lloyd, which they attribute to Malmquist bias. Johnson et al. argue that the very small spectroscopic observational uncertainties favor high masses, and there are a large number of high mass sub giants in RV surveys. However, in this Letter, it is shown that Malmquist bias does not impact the mass distributions, but the mass distribution is sensitive to Galaxy model. The relationship needed to reconcile the subgiant planet host masses with any model of the Galactic stellar population is implausible, and the conclusion of Lloyd that spectroscopic mass determinations of subgiants are likely to have been overestimated is robust.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Mass of 101 Sn and Bayesian extrapolations to the proton drip line

The favorable energy configurations of nuclei at magic numbers of 𝑁 neutrons and 𝑍 protons are fundamental for understanding the evolution of nuclear structure. The 𝑍 = 50 (tin) isotopic chain is a frontier for such studies, with particular interest at and around the doubly magic 100 Sn isotope, for which the mass is a topic of debate. Precise mass values for neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies remain out of reach. In this work, we report a Penning trap mass measurement of 101 Sn . The determined mass excess of −59889.89⁢(96) keV for 101 Sn represents a factor-of-300 improvement over the current precision and indicates that 101 Sn is less bound than previously thought. Mass predictions from a recently developed Bayesian model combination framework employing statistical machine learning and nuclear masses computed within seven global models based on nuclear density functional theory agree within 1⁢𝜎 with experimental masses from the 48 ≤ 𝑍 ≤ 52 isotopic chains. The framework's resilience to new mass data gave confidence in the extrapolation of tin masses down to 𝑁 = 46. Our calculations suggest that 96 Sn is a two-proton drip line nucleus and predict a mass excess of −58090⁢(800) keV for 100 Sn , showing a preference within 1⁢𝜎 for the mass of 100 Sn derived from the 𝛽-delayed 𝑄 value measured at GSI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Explaining the stellar initial mass function with the theory of spatial networks

The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) are among the key factors regulating star formation and are the subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale-free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars, and on the scaling relation between the amplitude and mass of a fluctuation. Here we propose a new approach exploiting techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. We effectively combine gravoturbulent and competitive accretion approaches and predict the accretion rate to be proportional to the dense core mass: dM/dt∝M. Then we describe the dense core growth and demonstrate that the power-law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low-mass cut-off, it reproduces observations over three decades in mass. We also rule out a low-mass star dominated “bottom-heavy” IMF in a single star-forming region.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Unification of the fundamental plane and super massive black hole masses

According to the virial theorem, all gravitational systems in equilibrium sit on a plane in the three-dimensional parameter space defined by their mass, size, and second moment of the velocity tensor. While these quantities cannot be directly observed, there are suitable proxies: the luminosity L {sub k}, half-light radius R {sub e}, and dispersion σ{sub e}. These proxies indeed lie on a very tight fundamental plane (FP). How do the black holes (BHs) in the centers of galaxies relate to the FP? Their masses are known to exhibit no strong correlation with total galaxy mass, but they do correlate weakly with bulge mass (when present), and extremely well with the velocity dispersion through the M{sub ∙}∝σ{sub e}{sup 5.4} relation. These facts together imply that a tight plane must also exist defined by BH mass, total galaxy mass, and size. Here, I show that this is indeed the case using a heterogeneous set of 230 BHs. The sample includes BHs from zero to 10 billion solar masses and host galaxies ranging from low surface brightness dwarfs, through bulgeless disks, to brightest cluster galaxies. The resulting BH–size–luminosity relation M{sub ∙}∝(L{sub k}/R{sub e}){sup 3.8} has the same amount of scatter as the M {sub •}–σ relation and is aligned with the galaxy FP, such that it is just a reprojection of σ{sub e}. The inferred BH–size–mass relation is M{sub ∙}∝(M{sub ⋆}/R{sub e}){sup 2.9}. These relationships are universal and extend to galaxies without bulges. This implies that the BH is primarily correlated with its global velocity dispersion and not with the properties of the bulge. I show that the classical bulge–mass relation is a projection of the M {sub •}–σ relation. When the velocity dispersion cannot be measured (at high z or low dispersions), the BH–size–mass relation should be used as a proxy for BH mass in favor of just galaxy or bulge mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A Massive Prestellar Clump Hosting No High-mass Cores

The infrared dark cloud (IRDC) G028.23-00.19 hosts a massive (1500 M {sub ⊙}), cold (12 K), and 3.6–70 μ m IR dark clump (MM1) that has the potential to form high-mass stars. We observed this prestellar clump candidate with the Submillimeter Array (∼3.″5 resolution) and Jansky Very Large Array (∼2.″1 resolution) in order to characterize the early stages of high-mass star formation and to constrain theoretical models. Dust emission at 1.3 mm wavelength reveals five cores with masses ≤15 M {sub ⊙}. None of the cores currently have the mass reservoir to form a high-mass star in the prestellar phase. If the MM1 clump will ultimately form high-mass stars, its embedded cores must gather a significant amount of additional mass over time. No molecular outflows are detected in the CO (2-1) and SiO (5-4) transitions, suggesting that the SMA cores are starless. By using the NH{sub 3} (1, 1) line, the velocity dispersion of the gas is determined to be transonic or mildly supersonic (Δ V {sub nt}/Δ V {sub th} ∼ 1.1–1.8). The cores are not highly supersonic as some theories of high-mass star formation predict. The embedded cores are four to seven times more massive than the clump thermal Jeans mass and the most massive core (SMA1) is nine times less massive than the clump turbulent Jeans mass. These values indicate that neither thermal pressure nor turbulent pressure dominates the fragmentation of MM1. The low virial parameters of the cores (0.1–0.5) suggest that they are not in virial equilibrium, unless strong magnetic fields of ∼1–2 mG are present. We discuss high-mass star formation scenarios in a context based on IRDC G028.23-00.19, a study case believed to represent the initial fragmentation of molecular clouds that will form high-mass stars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Optical and Near-infrared Spectra of σ Orionis Isolated Planetary-mass Objects

We have obtained low-resolution optical (0.7–0.98 μ m) and near-infrared (1.11–1.34 μ m and 0.8–2.5 μ m) spectra of 12 isolated planetary-mass candidates ( J = 18.2–19.9 mag) of the 3 Myr σ Orionis star cluster with the aim of determining the spectroscopic properties of very young, substellar dwarfs and assembling a complete cluster mass function. We have classified our targets by visual comparison with high- and low-gravity standards and by measuring newly defined spectroscopic indices. We derived L0–L4.5 and M9–L2.5 using high- and low-gravity standards, respectively. Our targets reveal clear signposts of youth, thus corroborating their cluster membership and planetary masses (6–13 M {sub Jup}). These observations complete the σ Orionis mass function by spectroscopically confirming the planetary-mass domain to a confidence level of ∼75%. The comparison of our spectra with BT-Settl solar metallicity model atmospheres yields a temperature scale of 2350–1800 K and a low surface gravity of log g ≈ 4.0 [cm s{sup −2}], as would be expected for young planetary-mass objects. We discuss the properties of the cluster’s least-massive population as a function of spectral type. We have also obtained the first optical spectrum of S Ori 70, a T dwarf in the direction of σ Orionis. Our data provide reference optical and near-infrared spectra of very young L dwarfs and a mass function that may be used as templates for future studies of low-mass substellar objects and exoplanets. The extrapolation of the σ Orionis mass function to the solar neighborhood may indicate that isolated planetary-mass objects with temperatures of ∼200–300 K and masses in the interval 6–13 M {sub Jup} may be as numerous as very low-mass stars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Dependence of X-Ray Burst Models on Nuclear Masses

X-ray burst model predictions of light curves and the final composition of the nuclear ashes are affected by uncertain nuclear masses. However, not all of these masses are determined experimentally with sufficient accuracy. Here we identify the remaining nuclear mass uncertainties in X-ray burst models using a one-zone model that takes into account the changes in temperature and density evolution caused by changes in the nuclear physics. Two types of bursts are investigated—a typical mixed H/He burst with a limited rapid proton capture process (rp-process) and an extreme mixed H/He burst with an extended rp-process. When allowing for a 3 σ variation, only three remaining nuclear mass uncertainties affect the light-curve predictions of a typical H/He burst ({sup 27}P, {sup 61}Ga, and {sup 65}As), and only three additional masses affect the composition strongly ({sup 80}Zr, {sup 81}Zr, and {sup 82}Nb). A larger number of mass uncertainties remain to be addressed for the extreme H/He burst, with the most important being {sup 58}Zn, {sup 61}Ga, {sup 62}Ge, {sup 65}As, {sup 66}Se, {sup 78}Y, {sup 79}Y, {sup 79}Zr, {sup 80}Zr, {sup 81}Zr, {sup 82}Zr, {sup 82}Nb, {sup 83}Nb, {sup 86}Tc, {sup 91}Rh, {sup 95}Ag, {sup 98}Cd, {sup 99}In, {sup 100}In, and {sup 101}In. The smallest mass uncertainty that still impacts composition significantly when varied by 3 σ is {sup 85}Mo with 16 keV uncertainty. For one of the identified masses, {sup 27}P, we use the isobaric mass multiplet equation to improve the mass uncertainty, obtaining an atomic mass excess of −716(7) keV. The results provide a roadmap for future experiments at advanced rare isotope beam facilities, where all the identified nuclides are expected to be within reach for precision mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Why are we still using 3D masses for cluster cosmology?

ABSTRACT The abundance of clusters of galaxies is highly sensitive to the late-time evolution of the matter distribution, since clusters form at the highest density peaks. However, the 3D cluster mass cannot be inferred without deprojecting the observations, introducing model-dependent biases and uncertainties due to the mismatch between the assumed and the true cluster density profile and the neglected matter along the sightline. Since projected aperture masses can be measured directly in simulations and observationally through weak lensing, we argue that they are better suited for cluster cosmology. Using the Mira–Titan suite of gravity-only simulations, we show that aperture masses correlate strongly with 3D halo masses, albeit with large intrinsic scatter due to the varying matter distribution along the sightline. Nonetheless, aperture masses can be measured ≈2–3 times more precisely from observations, since they do not require assumptions about the density profile and are only affected by the shape noise in the weak lensing measurements. We emulate the cosmology dependence of the aperture mass function directly with a Gaussian process. Comparing the cosmology sensitivity of the aperture mass function and the 3D halo mass function for a fixed survey solid angle and redshift interval, we find the aperture mass sensitivity is higher for Ωm and $w_a$, similar for σ8, ns, and $w_0$, and slightly lower for h. With a carefully calibrated aperture mass function emulator, cluster cosmology analyses can use cluster aperture masses directly, reducing the sensitivity to model-dependent mass calibration biases and uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The mass profiles of dwarf galaxies from Dark Energy Survey lensing

We present a novel approach to extracting dwarf galaxies from photometric data to measure their average halo mass profile with weak lensing. We characterize their stellar mass and redshift distributions with a spectroscopic calibration sample. By combining the ${\sim} 5000\,\mathrm{deg}^2$ multiband photometry from the Dark Energy Survey and redshifts from the Satellites Around Galactic Analogs Survey with an unsupervised machine learning method, we select a low-mass galaxy sample spanning redshifts $z\lt 0.3$ and divide it into three mass bins. From low to high median mass, the bins contain [146 420, 330 146, 275 028] galaxies and have median stellar masses of $\log _{10}(M_*/\text{M}_\odot)=\left[8.52\substack{+0.57 -0.76},\, 9.02\substack{+0.50 -0.64},\, 9.49\substack{+0.50 -0.58}\right]$ . We measure the stacked excess surface mass density profiles, $\Delta \Sigma (R)$, of these galaxies using galaxy–galaxy lensing with a signal-to-noise ratio of [14, 23, 28]. Through a simulation-based forward-modelling approach, we fit the measurements to constrain the stellar-to-halo mass relation and find the median halo mass of these samples to be $\log _{10}(M_{\rm halo}/\text{M}_\odot)$ = [$10.67\substack{+0.2 -0.4}$, $11.01\substack{+0.14 -0.27}$, $11.40\substack{+0.08 -0.15}$]. The cold dark matter profiles are consistent with NFW (Navarro, Frenk, and White) profiles over scales ${\lesssim} 0.15 \, {h}^{-1}$ Mpc. We find that ${\sim} 20$ per cent of the dwarf galaxy sample are satellites. This is the first measurement of the halo profiles and masses of such a comprehensive, low-mass galaxy sample. The techniques presented here pave the way for extracting and analysing even lower mass dwarf galaxies and for more finely splitting galaxies by their properties with future photometric and spectroscopic survey data.

dark matter↗

DOE OSTI2015

Charm and strange quark masses and f D s from overlap fermions

We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the 2 + 1 -flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates O($a^2$) and O($m^4a^4$) corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of D s , D$^*_s$ and J/ψ as inputs, Sommer's scale parameter r 0 and the masses of charm quark and strange quark in the $\overline{MS}$ scheme are determined to be r 0 = 0.465 (4) (9) fm, $m^{\overline{MS}}_c$ (2 GeV ) = 1.118 (6) (24) GeV (or $m^{\overline{MS}}_c(m_c)$ = 1.304 (5) (20) GeV), and $m^{\overline{MS}}_s$ (2 GeV ) = 0.101 (3) (6) GeV, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, M J/ψ -$M_{η_c}$, is determined o be 119(2)(7) MeV, which is in good agreement with the experimental value. Finally, we also predict the decay constant of D s to be $f_{D_S}$ = 254 (2) (4) MeV. The masses of charmonium P-wave states χ c0 , χ c1 and $h_c$ are also in good agreement with experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Test for the Origin of Solar Mass Black Holes

Solar-mass black holes with masses in the range of ~1–2.5 M ⊙ are not expected from conventional stellar evolution, but can be produced naturally via neutron star (NS) implosions induced by capture of small primordial black holes (PBHs) or from accumulation of some varieties of particle dark matter. We argue that a unique signature of such “transmuted” solar-mass BHs is that their mass distribution would follow that of the NSs. This would be distinct from the mass function of black holes in the solar-mass range predicted either by conventional stellar evolution or early Universe PBH production. We propose that analysis of the solar-mass BH population mass distribution in a narrow mass window of ~1–2.5 M ⊙ can provide a simple yet powerful test of the origin of these BHs. Recent LIGO/VIRGO gravitational wave (GW) observations of the binary merger events GW190425 and GW190814 are consistent with a BH mass in the range ~1.5–2.6 M ⊙ . Though these results have fueled speculation on dark matter-transmuted solar-mass BHs, we demonstrate that it is unlikely that the origin of these particular events stems from NS implosions. Data from upcoming GW observations will be able to distinguish between solar-mass BHs and NSs with high confidence. This capability will facilitate and enhance the efficacy of our proposed test.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Understanding the Origin of the Hadron Mass within the Standard Model

Understanding the origin of the hadron mass, which constitutes 99% of our visible universe, is one of the central goals of nuclear physics. Although the Higgs mechanism provides mass for the fundamental building blocks of matter, it can only contribute less than 2% of the proton mass. The vast majority of the proton mass is believed to come from the strong force that tightly binds quarks and gluons (collectively called partons) together as described by Quantum Chromodynamics (QCD). The mass that emerges as a consequence of the strong interactions within QCD is commonly denoted as Emergent Hadronic Mass (EHM). Understanding how the nucleon mass emerges in QCD is a prerequisite to an explanation of how the Universe came into being, therefore it is of utmost importance and one of the key questions to be addressed by the future Electron-Ion Collider (EIC). When it comes to light mesons, particularly pions, the mass decomposition is drastically different. Since the pion is naturally massless in the chiral limit, the majority of its observed mass needs to come from other mechanisms within QCD. Any successful explanation for the EHM needs to be able to reconcile both the heavy proton mass and the very light pion mass (~15% of proton mass) simultaneously. The EHM theories have direct measurable implications on the description of the internal structure of the hadron, i.e., how the partons distribute inside the hadron. Precise measurement of the parton distribution functions (PDFs) will provide necessary experimental verifications and constraints of potential EHM mechanisms. We propose to carry out a comprehensive study of the poorly known pion PDFs at the AMBER experiment at CERN. The measurement will provide vital input to constrain the global analysis of the pion PDFs, which are still based on limited data obtained more than 30 years ago. The proposed pion measurement is the only direct measurement achievable within this decade, which could lead to a future major meson structure program parallel to the EIC’s proton structure measurement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe

Profiles of dark matter-dominated halos at the group and cluster scales play an important role in modern cosmology. Using results from two very large cosmological N-body simulations, which increase the available volume at their mass resolution by roughly two orders of magnitude, we robustly determine the halo concentration-mass (c-M) relation over a wide range of masses, employing multiple methods of concentration measurement. We then characterize individual halo profiles, as well as stacked profiles, relevant for galaxy-galaxy lensing and next-generation cluster surveys; the redshift range covered is 0 ≤ z ≤ 4, with a minimum halo mass of M 200c ~ 2 x 10 11 M ⊙ . Despite the complexity of a proper description of a halo (environmental effects, merger history, nonsphericity, relaxation state), when the mass is scaled by the nonlinear mass scale M * (z), we find that a simple non-power-law form for the c-M/M * relation provides an excellent description of our simulation results across eight decades in M/M * and for 0 ≤ z ≤ 4. Over the mass range covered, the c-M relation has two asymptotic forms: an approximate power law below a mass threshold M/M * ~500-1000, transitioning to a constant value, c 0 ~ 3 at higher masses. The relaxed halo fraction decreases with mass, transitioning to a constant value of ~0.5 above the same mass threshold. We compare Navarro-Frenk-White (NFW) and Einasto fits to stacked profiles in narrow mass bins at different redshifts; as expected, the Einasto profile provides a better description of the simulation results. At cluster scales at low redshift, however, both NFW and Einasto profiles are in very good agreement with the simulation results, consistent with recent weak lensing observations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1979

Stellar evolution at high mass including the effect of a stellar wind

The effect of a stellar wind on the evolution of stars in the mass range from 15 to 120 solar masses is investigated. All the stellar models are constructed with the use of Cox-Stewart opacities. Four possible cases of mass loss are considered: (1) no mass loss at all; (2) substantial mass loss from stars in all stages of evolution; (3) heavy mass loss from red supergiants only; and (4) sudden and very heavy mass loss from luminous yellow supergiants. The assumption of mass loss during the main-sequence phase of evolution is found to lead to a lowering of the luminosity and, unless the mass loss is extremely heavy, of the effective temperature as well. A comparison of the adopted mass-loss rates with observed rates suggests that stellar winds are probably not an important factor in the evolution of main-sequence stars and supergiants unless the initial masses are greater than about 30 solar masses.

Stothers, R.↗

NASA NTRS1986

The Cepheid mass problem and Cepheid binaries

Existing mass determinations for Cepheids with different periods are examined. Wesselink masses are independent of the adopted distance scale. For short periods (less than 6 days) they follow the sequence of evolutionary masses. For periods longer than 10 days they are lower by up to a factor of 2. The lower mass branch joins up with the bump masses. The new pulsational masses agree with the Wesselink masses for periods longer than 6 days. Cepheid masses determined by means of their giant companions also agree with the Wesselink masses and the new pulsational masses. While the error bars are large, the derived dynamical masses determined for S Mus and V636 Sco also agree with the low Wesselink and giant companion masses.

Bohm-Vitense, E.↗

NASA NTRS1993

Luminosity functions for very low mass stars and brown dwarfs

A theoretical investigation of the luminosity function for low-mass objects to constrain the stellar initial mass function at the low-mass end is reported. The ways in which luminosity functions for low-mass stars are affected by star formation histories, brown dwarf and premain-sequence cooling rates and main-sequence mass luminosity relations, and the IMF are examined. Cooling rates and the mass-luminosity relation are determined through a new series of evolutionary calculations for very low mass stars and brown dwarfs in the range 0.05-0.50 solar mass. Model luminosity functions are constructed for specific comparison with the results of four recent observational surveys. The likelihood that the stellar mass function in the solar neighborhood is increasing at masses near the bottom of the main sequence and perhaps at lower masses is confirmed. In the most optimistic case, brown dwarfs contribute half of the local missing disk mass. The actual contribution is likely to be considerably less.

Laughlin, Gregory↗

NASA NTRS1993

The evolution of massive stars including mass loss - Presupernova models and explosion

The evolution of massive stars of 35, 40, 60, and 85 solar masses is followed through all stages of nuclear burning to the point of Fe core collapse. Critical nuclear reaction and mass-loss rates are varied. Efficient mass loss during the Wolf-Rayet (WR) stage is likely to lead to final masses as small as 4 solar masses. For a reasonable parameterization of the mass loss, there may be convergence of all WR stars, both single and in binaries, to a narrow band of small final masses. Our representative model, a 4.25 solar-mass WR presupernova derived from a 60 solar mass star, is followed through a simulated explosion, and its explosive nucleosynthesis and light curve are determined. Its properties are similar to those observed in Type Ib supernovae. The effects of the initial mass and mass loss on the presupernova structure of small mass WR models is also explored. Important properties of the presupernova star and its explosion can only be obtained by following the complete evolution starting on the main sequence.

Woosley, S. E.↗

NASA NTRS2009

Evidence for an Intermediate Mass Black Hole in NGC 5408 X-1

We report the discovery with XMM-Newton of correlated spectral and timing behavior in the ultraluminous X-ray source (ULX) NGC 5408 X-1. An approx. 100 ksec pointing with XMM/Newton obtained in January, 2008 reveals a strong 10 mHz QPO in the > 1 keV flux, as well as flat-topped, band limited noise breaking to a power law. The energy spectrum is again dominated by two components, a 0.16 keV thermal disk and a power-law with an index of approx. 2.5. These new measurements, combined with results from our previous January 2006 pointing in which we first detected QPOs, show for the first time in a ULX a pattern of spectral and temporal correlations strongly analogous to that seen in Galactic black hole sources, but at much higher X-ray luminosity and longer characteristic time-scales. We find that the QPO frequency is proportional to the inferred disk flux, while the QPO and broad-band noise amplitude (root mean squared, rms) are inversely proportional to the disk flux. Assuming that QPO frequency scales inversely with black hole mass at a given power-law spectral index we derive mass estimates using the observed QPO frequency - spectral index relations from five stellar-mass black hole systems with dynamical mass constraints. The results from all sources are consistent with a mass range for NGC 5408 X-1 from 1000 - 9000 Stellar mass. We argue that these are conservative limits, and a more likely range is from 2000 - 5000 Stellar mass. Moreover, the recent relation from Gierlinski et al. that relates black hole mass to the strength of variability at high frequencies (above the break in the power spectrum), and the variability plane results of McHardy et al. and Koerding et al., are also suggestive of such a. high mass for NGC 5408 X-1. Importantly, none of the above estimates appears consistent with a black hole mass less than approx. 1000 Stellar mass for NGC 5408 X-1. We argue that these new findings strongly support the conclusion that NGC 5408 X-1 harbors an intermediate mass black hole.

Strohmayer, Tod E.↗