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NASA NTRS2013

Optimization of the Orbiting Wide-Angle Light Collectors (OWL) Mission for Charged-Particle and Neutrino Astronomy

OWL [1] uses the Earth's atmosphere as a vast calorimeter to fully enable the emerging field of charged-particle astronomy with high-statistics measurements of ultra-high-energy cosmic rays (UHECR) and a search for sources of UHE neutrinos and photons. Confirmation of the Greisen-Zatsepin-Kuzmin (GZK) suppression above approx. 4 x 10(exp 19) eV suggests that most UHECR originate in astrophysical objects. Higher energy particles must come from sources within about 100 Mpc and are deflected by approx. 1 degree by predicted intergalactic/galactic magnetic fields. The Pierre Auger Array, Telescope Array and the future JEM-EUSO ISS mission will open charged-particle astronomy, but much greater exposure will be required to fully identify and measure the spectra of individual sources. OWL uses two large telescopes with 3 m optical apertures and 45 degree FOV in near-equatorial orbits. Simulations of a five-year OWL mission indicate approx. 10(exp 6) sq km/ sr/ yr of exposure with full aperture at approx. 6 x 10(exp 19) eV. Observations at different altitudes and spacecraft separations optimize sensitivity to UHECRs and neutrinos. OWL's stereo event reconstruction is nearly independent of track inclination and very tolerant of atmospheric conditions. An optional monocular mode gives increased reliability and can increase the instantaneous aperture. OWL can fully reconstruct horizontal and upward-moving showers and so has high sensitivity to UHE neutrinos. New capabilities in inflatable structures optics and silicon photomultipliers can greatly increase photon sensitivity, reducing the energy threshold for n detection or increasing viewed area using a higher orbit. Design trades between the original and optimized OWL missions and the enhanced science capabilities are described.

Optimization↗
NASA NTRS2016

A Giant Radio Halo in a Low-Mass SZ-Selected Galaxy Cluster: ACT-CL J0256.5+0006

We present the detection of a giant radio halo (GRH) in the Sunyaev-Zel'dovich (SZ)-selected merging galaxy cluster ACT-CL J0256.5+0006 (zeta = 0.363), observed with the Giant Metrewave Radio Telescope at 325 MHz and 610 MHz. We find this cluster to host a faint (S(sub 610) = 5.6 +/- 1.4 mJy) radio halo with an angular extent of 2.6 arcmin, corresponding to 0.8 Mpc at the cluster redshift, qualifying it as a GRH. J0256 is one of the lowest-mass systems, M(sub 500,SZ) = (5.0 +/- 1.2) x 10(sup14) solar mass foud to host a GRH. We measure the GRH at lower significance at 325 MHz (S(sub 325) = 10.3 +/- 5.3 mJy), obtaining a spectral index measurement of alpha sup 610 sub 325 = 1.0(sup +0.7)(sub 0.9). This result is consistent with the mean spectral index of the population of typical radio halos, alpha = 1.2 +/- 0.2. Adopting the latter value, we determine a 1.4 GHz radio power of P(sub 1.4GHz) = (1.0 +/- 03) x 10(sup 24) W Hz(sup -1), placing this cluster within the scatter of known scaling relations. Various lines of evidence, including the ICM morphology, suggest that ACT-CL J0256.5+0006 is composed of two subclusters. We determine a merger mass ratio of 7:4, and a line-of-sight velocity difference of perpendicular = 1880 +/- 210 km s(sup -1). We construct a simple merger model of infer relevant time-scales in the merger. From its location on the P1.4GHz-L(sub x) scaling relation, we infer that we observe ACT-CL J0256.5+0006 just before first core crossing.

core crossing↗
NASA NTRS2017

Spitzer Photometry of Approximately 1 Million Stars in M31 and 15 Other Galaxies

We present Spitzer IRAC 3.6-8 micrometer and Multiband Imaging Photometer 24 micrometer point-source catalogs for M31 and 15 other mostly large, star-forming galaxies at distances approximately 3.5-14 Mpc, including M51, M83, M101, and NGC 6946. These catalogs contain approximately 1 million sources including approximately 859,000 in M31 and approximately 116,000 in the other galaxies. They were created following the procedures described in Khan et al. through a combination of pointspread function (PSF) fitting and aperture photometry. These data products constitute a resource to improve our understanding of the IR-bright (3.6-24 micrometer) point-source populations in crowded extragalactic stellar fields and to plan observations with the James Webb Space Telescope.

Photometry↗
NASA NTRS2016

A Giant Radio Halo in a Low-Mass Sz-selected Galaxy Cluster: ACT-CLJ0256.5+0006

We present the detection of a giant radio halo (GRH) in the Sunyaev-Zel'dovich (SZ)- selected merging galaxy cluster ACT-CL J0256.5+ 0006 (z = 0.363), observed with the Giant Metrewave Radio Telescope at 325 and 610 MHz. We find this cluster to host a faint (S610 = 5.6 +/- 1.4mJy) radio halo with an angular extent of 2.6 arcmin, corresponding to 0.8 Mpc at the cluster redshift, qualifying it as a GRH. J0256 is one of the lowest mass systems, M500, SZ = (5.0 +/- 1.2) × 10(exp14) M, found to host a GRH. We measure the GRH at lower significance at 325 MHz (S325 = 10.3 +/- 5.3mJy), obtaining a spectral index measurement of α610 325 = 1.0+ 0.7 − 0.9. This result is consistent with the mean spectral index of the population of typical radio haloes, alpha = 1.2 +/- 0.2. Adopting the latter value, we determine a 1.4 GHz radio power of P1.4 GHz = (1.0 +/- 0.3) × 10(exp 24)W/Hz, placing this cluster within the scatter of known scaling relations. Various lines of evidence, including the intracluster medium morphology, suggest that ACT-CL J0256.5+ 0006 is composed of two subclusters. We determine a merger mass ratio of 7:4, and a line-of-sight velocity difference of v⊥ = 1880 +/- 210 km/s. We construct a simple merger model to infer relevant time-scales in the merger. From its location on the P1.4GHz-LX scaling relation, we infer that we observe ACT-CL J0256.5+ 0006 just before first core crossing.

Knowles, Kendra↗
NASA NTRS2016

Exploring the Overabundance of ULXs in Metal- and Dust-Poor Local Lyman Break Analogs

We have studied high-mass X-ray binary (HMXB) populations within two low-metallicity, starburst galaxies, Haro 11 and VV 114. These galaxies serve as analogs to high-redshift (z greater than 2) Lyman break galaxies and, within the larger sample of Lyman break analogs (LBAs), they are sufficiently nearby (less than 87 Mpc) to be spatially resolved by Chandra. Previous studies of the X-ray emission in LBAs have found that the 2-10 keV luminosity per star formation rate (SFR) in these galaxies is elevated, potentially because of their low metallicities (12 + log[O/H] = 8.3-8.4). Theoretically, the progenitors of XRBs forming in lower metallicity environments lose less mass from stellar winds over their lifetimes, producing more massive compact objects (i.e., neutron stars and black holes), and thus resulting in more numerous and luminous HMXBs per SFR. In this paper, we have performed an in-depth study of the only two LBAs that have spatially resolved 2-10 keV emission with Chandra to present the bright end of the X-ray luminosity distribution of HMXBs (L(sub X) approximately greater than 10(exp 39) erg s(exp −1); ultraluminous X-ray sources, ULXs) in these low-metallicity galaxies, based on eight detected ULXs. Compared with the star-forming galaxy X-ray luminosity function (XLF) presented by Mineo et al., Haro 11 and VV 114 host approximately equal to 4 times more L(sub X) greater than 10(exp 40) erg s(exp −1) sources than expected given their SFRs. We simulate the effects of source blending from crowded lower-luminosity HMXBs using the star-forming galaxy XLF and then vary the XLF normalizations and bright-end slopes until we reproduce the observed point source luminosity distributions. We find that these LBAs have a shallower bright-end slope (gamma(sub 2) = 1.90) than the standard XLF (gamma(sub 2) 2.73). If we conservatively assume that the brightest X-ray source from each galaxy is powered by an accreting supermassive black hole rather than an HMXB and eliminate these sources from consideration, the luminosity distribution becomes poorly constrained but does appear to be consistent with a standard XLF.

galaxies: evolution aEuro" galaxies: individual↗
NASA NTRS2015

Optimization of the Swift X-Ray Follow-Up of Advanced LIGO and Virgo Gravitational Wave Triggers in 2015-16

One of the most exciting near-term prospects in physics is the potential discovery of gravitational waves by the Advanced LIGO and Virgo detectors. To maximize both the confidence of the detection and the science return, it is essential to identify an electromagnetic counterpart.This is not trivial, as the events are expected to be poorly localized, particularly in the near-term, with error regions covering hundreds or even thousands of square degrees. In this paper, we discuss the prospects for finding an X-ray counterpart to a gravitational wave trigger with the Swift X-ray Telescope, using the assumption that the trigger is caused by a binary neutron star merger which also produces a short gamma-ray burst. We show that it is beneficial to target galaxies within the GW error region, highlighting the need for substantially complete galaxy catalogues out to distances of 300 Mpc. We also show that nearby, on-axis short GRBs are either extremely rare, or are systematically less luminous than those detected to date. We consider the prospects for detecting afterglow emission from an off-axis GRB which triggered the GW facilities, finding that the detectability, and the best time to look,are strongly dependent on the characteristics of the burst such as circumburst density and our viewing angle.

gravitational waves – methods: observational –↗
NASA NTRS2016

Hard X-Ray Emission from SH 2-104: A NuSTAR Search for Gamma-Ray Counterparts

We present NuSTAR hard X-ray observations of Sh 2-104, a compact H II region containing several young massive stellar clusters (YMSCs). We have detected distinct hard X-ray sources coincident with localized VERITAS TeV emission recently resolved from the giant gamma-ray complex MGRO J2019+37 in the Cygnus region. Fainter, diffuse X-rays coincident with the eastern YMSC in Sh2-104 likely result from the colliding winds of a component star. Just outside the radio shell of Sh 2-104 lies 3XMM J201744.7+365045 and a nearby nebula, NuSTAR J201744.3+364812, whose properties are most consistent with extragalactic objects. The combined XMM-Newton and NuSTAR spectrum of 3XMM J201744.7+365045 is well-fit to an absorbed power-law model with N(sub H) = (3.1 +/- 1.0) x 10(exp 22) cm(exp -2) and a photon index gamma = 2.1 +/- 0.1. Based on possible long-term flux variation and the lack of detected pulsations (less than or equal to 43% modulation), this object is likely a background active galactic nucleus rather than a Galactic pulsar. The spectrum of the NuSTAR nebula shows evidence of an emission line at E = 5.6 keV, suggesting an optically obscured galaxy cluster at z = 0.19 +/- 0.02 (d = 800 Mpc) and L(sub X) = 1.2 x 10(exp 44) erg s(exp -1). Follow-up Chandra observations of Sh 2-104 will help identify the nature of the X-ray sources and their relation to MGRO J2019+37. We also show that the putative VERITAS excess south of Sh 2-104, is most likely associated with the newly discovered Fermi pulsar PSR J2017+3625 and not the H II region.

SM: individual objects↗
NASA NTRS2016

Observation of Gravitational Waves from a Binary Black Hole Merger

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 x 10(exp -21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ring down of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 Sigma. The source lies at a luminosity distance of 410(+160/-180) Mpc corresponding to a redshift z = 0.09(+0.03/-0.04). In the source frame, the initial black hole masses are 36(+5/-4) Mass compared to the sun, and 29(+4/-4) Mass compared to the sun, and the final black hole mass is 62(+4/-4) Mass compared to the sun, with 3.0(+0.5/-0.5)sq c radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

gravitational waves↗
NASA NTRS2016

Properties of the Binary Black Hole Merger GW150914

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of masses 36(+5/-4) solar mass and 29(+4/-4) solar mass; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be less than 0.7 (at 90% probability). The luminosity distance to the source is 410(+160/-180) Mpc, corresponding to a redshift 0.09(+0.03/−0.04) assuming standard cosmology. The source location is constrained to an annulus section of 610 sq deg, primarily in the southern hemisphere. The binary merges into a black hole of mass 62(+4/−4) solar mass and spin 0.67(+0.05/−0.07). This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.

Abbott, B. P.↗
NASA NTRS2016

GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5(sigma). The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of 3.4(+0.7/-0.9) x 10(exp -22). The inferred source-frame initial black hole masses are 14.2(+8.3/-3.7 Stellar Mass and 7.5(+2.3/-2.3) Stellar Mass, and the final black hole mass is 20.8(+6.1/-1.7) Stellar Mass. We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of 440(+180/-190) Mpc corresponding to a redshift of 0.090(+.030/-0.04). All uncertainties define a 90% credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

Abbott, B. P.↗
NASA NTRS2014

Extreme Blazars Studied with Fermi-Lat and Suzaku: 1ES 0347-121 and Blazar Candidate HESS J1943+213

We report on our study of high-energy properties of two peculiar TeV emitters: the "extreme blazar" 1ES 0347-121 and the "extreme blazar candidate" HESS J1943+213 located near the Galactic plane. Both objects are characterized by quiescent synchrotron emission with flat spectra extending up to the hard X-ray range, and both were reported to be missing GeV (gigaelectronvolt) counterparts in the Fermi Large Area Telescope (LAT) two-year Source Catalog. We analyze a 4.5 year accumulation of the Fermi-LAT data, resulting in the detection of 1ES 0347-121 in the GeV band, as well as in improved upper limits for HESS J1943+213. We also present the analysis results of newly acquired Suzaku data for HESS J1943+213. The X-ray spectrum is well represented by a single power law extending up to 25 keV (kiloelectronvolts) with photon index 2.00 plus or minus 0.02 and a moderate absorption in excess of the Galactic value, which is in agreement with previous X-ray observations. No short-term X-ray variability was found over the 80 kilosecond duration of the Suzaku exposure. Under the blazar hypothesis, we modeled the spectral energy distributions of 1ES 0347-121 and HESS J1943+213, and we derived constraints on the intergalactic magnetic field strength and source energetics. We conclude that although the classification of HESS J1943+213 has not yet been determined, the blazar hypothesis remains the most plausible option since, in particular, the broadband spectra of the two analyzed sources along with the source model parameters closely resemble each other, and the newly available Wide-field Infrared Survey Explorer (WISE) and UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey data for HESS J1943+213 are consistent with the presence of an elliptical host at the distance of approximately 600 Mpc (megaparsecs).

blazar↗
NASA NTRS2018

Black Holes and Neutron Stars in Nearby Galaxies: Insights from NuSTAR

Nearby galaxy surveys have long classified X-ray binaries (XRBs) by the mass category of their donor stars (high-mass and low-mass). The NuSTAR (Nuclear Spectroscopic Telescope Array) observatory, which provides imaging data at E greater than 10 keV (kiloelectronvolts), has enabled the classification of extragalactic XRBs by their compact object type: neutron star (NS) or black hole (BH). We analyzed NuSTAR/Chandra/XMM-Newton observations from a NuSTAR-selected sample of 12 galaxies within 5 Mpc (megaparsecs) having stellar masses (M (sub asterisk)) 10 (sup 7-11) solar masses and star formation rates (SFRs) approximately 0.01-15 solar masses per year. We detected 128 NuSTAR sources to a sensitivity of 10 (sup 38) ergs per second. Using NuSTAR color-intensity and color-color diagrams we classified 43 of these sources as candidate NSs and 47 as candidate BHs. We further subdivide BHs by accretion states (soft, intermediate, and hard) and NSs by weak (Z/Atoll) and strong (accreting pulsar) magnetic field. Using eight normal (Milky Way-type) galaxies in the sample, we confirm the relation between the SFR and galaxy X-ray point source luminosity in the 4-25 and 12-25 keV energy bands. We also constrained galaxy X-ray point source luminosity using the relation L (sub X) equals M (sub asterisk) plus Beta SFR, finding agreement with previous work. The X-ray luminosity function (XLF) of all sources in the 4-25 and 12-25 keV energy bands matches the alpha = 1.6 slope for high-mass XRBs. We find that NS XLFs suggest a decline beginning at the Eddington limit for a 1.4 solar mass NS, whereas the BH fraction shows an approximate monotonic increase in the 4-25 and 12-25 keV energy bands. We calculate the overall ratio of BH to NS to be approximately 1 for 4-25 keV and approximately 2 for 12-25 keV.

Vulic, N.↗
NASA NTRS2019

Cosmic Pathways for Compact Groups in the Milli-Millennium Simulation

We detected 10 compact galaxy groups (CGs) at z=0 in the semianalytic galaxy catalog of Guo et al. for themilli-Millennium Cosmological Simulation (sCGs in mGuo2010a). We aimed to identify potential canonicalpathways for compact group evolution and thus illuminate the history of observed nearby CGs. By constructingmerger trees for z=0 sCG galaxies, we studied the cosmological evolution of key properties and compared themwith z=0 Hickson CGs (HCGs). We found that, once sCG galaxies come within 1 (0.5) Mpc of their mostmassive galaxy, they remain within that distance until z=0, suggesting sCG "birth redshifts." At z=0 stellarmasses of sCG most massive galaxies are within 1010M*/Me1011. In several cases, especially in the twofour- and five-member systems, the amount of cold gas mass anticorrelates with stellar mass, which in turncorrelates with hot gas mass. We define the angular difference between group members' 3D velocity vectors,vel, and note that many of the groups are long-lived because their small values of vel indicate a significantparallel component. For triplets in particular, vel values range between 20° and 40° so that galaxies are comingtogether along roughly parallel paths, and pairwise separations do not show large pronounced changes after closeencounters. The best agreement between sCG and HCG physical properties is for M* galaxy values, but HCGvalues are higher overall, including for star formation rates (SFRs). Unlike HCGs, due to a tail at low SFR and M*and a lack of M*1011Me galaxies, only a few sCG galaxies are on the star-forming main sequence

Tzanavaris, Panayiotis↗
NASA NTRS2017

Neutral Gas Properties of Extremely Isolated Early-Type Galaxies

We present the results of single-dish atomic hydrogen (H I) observations of six highly isolated early-type galaxies. These objects are a representative subset of galaxies previously studied at optical wavelengths and selected to be separated by at least 2.5Mpc from companions brighter than M(sub V) =−16.5 mag. Each galaxy was observed with a single pointing using the NRAO Green Bank Telescope L-band receiver. Five of these systems were strongly detected in H I. These five galaxies exhibit H I profiles with a range of properties: single Gaussian-like peaks, separate double peaks, and double horn-like profiles. The four bluest galaxies (B−V<0.54) all contain significant gas with H I masses ranging from 1.1 × 10(exp 8) to 1.4 × 10(exp 9).

Ashley, Trisha L.↗
NASA NTRS2015

High Precision Focal Plane Astrometry… and possibilities for the HDST

The calibration techniques we are developing for WFIRST can be also used on HDST, turning it into a revolutionary astrometric instrument. Estimated astrometric accuracy is 10’s of nano arcseconds.Two examples of what such a capability allows us to do: 1)Parallaxes of galactic neighborhood out to 100 Mpc 2) Astrometric characterization of sun like stars out to 50 p.

Shao, Mike↗
NASA NTRS2019

The NANOGrav 11 Yr Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Observations indicate that nearly all galaxies contain supermassive black holes at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays. We have searched the North American Nanohertz Observatory for Gravitational Waves 11 yr data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95% upper limits on the strength of GWs from such sources. At f(gw) = 8 nHz, we placed a sky-averaged upper limit of h(0) < 7.3(3) × 10(exp −15). We also developed a technique to determine the significance of a particular signal in each pulsar using "dropout" parameters as a way of identifying spurious signals. From these upper limits, we ruled out SMBHBs emitting GWs f(gw) = 8 nHz within 120 Mpc for M = 10(exp 9) Solar Mass, and within 5.5 Gpc for M= 10(exp 10) Solar Mass at our most sensitive sky location. We also determined that there are no SMBHBs with M > 1.6 x 10(exp 9) Solar Mass emitting GWs with f(gw) = 2.8–317.8 nHz in the Virgo Cluster. Finally, we compared our strain upper limits to simulated populations of SMBHBs, based on galaxies in the Two Micron All-Sky Survey and merger rates from the Illustris cosmological simulation project, and found that only 34 out of 75,000 realizations of the local universe contained a detectable source.

Aggarwal, K.↗
NASA NTRS2020

Nuclear X-Ray Activity in Low-surface-brightness Galaxies: Prospects for Constraining the Local Black Hole Occupation Fraction with a Chandra Successor Mission

About half of nearby galaxies have a central surface brightness>1 mag below that of the sky. The overall properties of these low-surface-brightness galaxies(LSBGs)remain understudied, and in particular we know very little about their massive black hole population. This gap must be closed to determine the frequency of massive black holes at z=0 as well as to understand their role in regulating galaxy evolution. Here we investigate the incidence and intensity of nuclear, accretion-powered X-ray emission in a sample of 32 nearby LSBGs with the Chandra X-ray Observatory. A nuclear X-ray source is detected in four galaxies(12.5%). Based on an X-ray binary contamination assessment technique developed for normal galaxies, we conclude that the detected X-ray nuclei indicate low-level accretion from massive black holes. The active fraction is consistent with that expected from the stellar mass distribution of the LSBGs, but not their total baryonic mass, when using a scaling relation from an unbiased X-ray survey of normal galaxies. This suggests that their black holes co-evolved with their stellar population. In addition, the apparent agreement nearly doubles the number of galaxies available within∼100 Mpc for which a measurement of nuclear activity can efficiently constrain the frequency of black holes as a function of stellar mass. We conclude by discussing the feasibility of measuring this occupation fraction to a few percent precision below ≲ 10^10 M(ʘ) with high-resolution, wide-field X-ray missions currently under consideration.

Edmund J. Hodges-Kluck↗
NASA NTRS2019

Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control

For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efficient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.

Bayard, David S.↗