An Affine-Invariant Sampler for Exoplanet Fitting and Discovery in Radial Velocity Data

Hou, Fengji; Goodman, Joel W.; Hogg, David W.; Weare, Jonathan; Schwab, Christian

doi:10.1088/0004-637x/745/2/198

Cited by 72 publications

(55 citation statements)

References 28 publications

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“…The individual thermal observations were obtained when the object was at different heliocentric and geocentric distances, so, although the differences are small, each flux density is modeled for the individual distance that the observation was made at. We use the Python package emcee (Foreman-Mackey et al 2013), which provides a convenient and parallel implementation of the Hou et al (2012) affine invariant ensemble sampler for MCMC. In each of the modeling cases that we discuss below, we assign uniform priors to the parameters and run an ensemble of 100 chains through 10 4 steps after a 10 3 step initialization ("burn-in") period.…”

Section: Multi-parameter Markov Chain Monte Carlo Thermal Modelingmentioning

confidence: 99%

The Density of Mid-sized Kuiper Belt Objects from ALMA Thermal Observations

Brown

Butler

2017

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The densities of mid-sized Kuiper Belt objects (KBOs) are a key constraint in understanding the assembly of objects in the outer solar system. These objects are critical for understanding the currently unexplained transition from the smallest KBOs with densities lower than that of water, to the largest objects with significant rock content. Mapping this transition is made difficult by the uncertainties in the diameters of these objects, which maps into an even larger uncertainty in volume and thus density. The substantial collecting area of the Atacama Large Millimeter Array allows significantly more precise measurements of thermal emission from outer solar system objects and could potentially greatly improve the density measurements. Here we use new thermal observations of four objects with satellites to explore the improvements possible with millimeter data. We find that effects due to effective emissivity at millimeter wavelengths make it difficult to use the millimeter data directly to find diameters and thus volumes for these bodies. In addition, we find that when including the effects of model uncertainty, the true uncertainties on the sizes of outer solar system objects measured with radiometry are likely larger than those previously published. Substantial improvement in object sizes will likely require precise occultation measurements.

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Section: Multi-parameter Markov Chain Monte Carlo Thermal Modelingmentioning

confidence: 99%

The Density of Mid-sized Kuiper Belt Objects from ALMA Thermal Observations

Brown

Butler

2017

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“…We display the results both as a PDF and a cumulative density function (CDF) fit to the data (see Figure 8). The plotted 11 We perform the sampling with a modified C version of the original Python implementation (Foreman-Mackey et al 2013) of an affine-invariant ensemble sampler (Hou et al 2012) using an ensemble of 1000 walkers. with the best fit model PDF (solid red line) surrounded by a ±1σ error region (gray shading).…”

Section: Black Hole Mass Function For Local Spiral Galaxiesmentioning

confidence: 99%

The Black Hole Mass Function Derived From Local Spiral Galaxies

Davis

Berrier

Johns

et al. 2014

ApJ

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We present our determination of the nuclear supermassive black hole mass (SMBH) function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0 • ) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. A limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M B = −19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t L ≤ 82.1 h . We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ = 5.54 . Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω BH = 4.35 of the universal baryonic inventory (Ω BH /ω b ) is confined within nuclear SMBHs at the center of spiral galaxies.

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“…The posterior is approximated using the affine invariant MCMC sampler emcee (Foreman-Mackey et al 2013; see also Hou et al 2012). Using the emcee routine, the posterior distribution is mapped, after which parameter estimates are evaluated as the median of the respective marginalised distributions (see Sect.…”

Section: A1 Modelling the Power Spectrummentioning

confidence: 99%

Asteroseismic inference on the spin-orbit misalignment and stellar parameters of HAT-P-7

Lund

Lundkvist

Aguirre

et al. 2014

A&A

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Context. The measurement of obliquities -the angle between the orbital and stellar rotation -in star-planet systems is of great importance for understanding planet system formation and evolution. The bright and well-studied HAT-P-7 (Kepler-2) system is intriguing because several Rossiter-McLaughlin (RM) measurements found a high projected obliquity in this system, but it was not possible so far to determine whether the orbit is polar and/or retrograde. Aims. The goal of this study is to measure the stellar inclination and hereby the full 3D obliquity of the HAT-P-7 system instead of only the 2D projection as measured by the RM effect. In addition, we provide an updated set of stellar parameters for the star. Methods. We used the full set of available observations from Kepler spanning Q0-Q17 to produce the power spectrum of HAT-P-7. We extracted oscillation-mode frequencies via an Markov chain Monte Carlo peak-bagging routine and used the results from this to estimate the stellar inclination angle. Combining this with the projected obliquity from RM and the inclination of the orbital plane allowed us to determine the stellar obliquity. Furthermore, we used asteroseismology to model the star from the extracted frequencies using two different approaches to the modelling, for which either the stellar evolution codes MESA or GARSTEC were adopted. Results. Our updated asteroseismic modelling shows, i.a., the following stellar parameters for HAT-P-7: M = 1.51+0.01 −0.02 R , and age = 2.07 +0.28 −0.23 Gyr. The modelling offers a high precision on the stellar parameters, the uncertainty on age, for instance, is of the order ∼11%. For the stellar inclination we estimate i < 36.5• , which translates into an obliquity of 83 • < ψ < 111• . The planet HAT-P-7b is likely retrograde in its orbit, and the orbit is close to being polar. The new parameters for the star give an updated planetary density of ρ p = 0.65 ± 0.03 g cm −3 , which is lower than previous estimates.

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An Affine-Invariant Sampler for Exoplanet Fitting and Discovery in Radial Velocity Data

Cited by 72 publications

References 28 publications

The Density of Mid-sized Kuiper Belt Objects from ALMA Thermal Observations

The Density of Mid-sized Kuiper Belt Objects from ALMA Thermal Observations

The Black Hole Mass Function Derived From Local Spiral Galaxies

Asteroseismic inference on the spin-orbit misalignment and stellar parameters of HAT-P-7

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