Black hole shadows, photon rings, and lensing rings

The presence of a bright "photon ring" surrounding a dark "black hole shadow" has been discussed as an important feature of the observational appearance of emission originating near a black hole. We clarify the meaning and relevance of these heuristics with analytic calculations and numerical toy models. The standard usage of the term "shadow" describes the appearance of a black hole illuminated from all directions, including from behind the observer. A backlit black hole casts a somewhat larger shadow. Neither "shadow" heuristic is particularly relevant to understanding the appearance of emission originating near the black hole, where the emission profile and gravitational redshift play the dominant roles in determining the observed size of the central dark area. A photon ring results from light rays that orbit around the black hole in the near-field region before escaping to infinity, where they arrive near a ring-shaped "critical curve" on the image plane. Although the brightness can become arbitrarily large near this critical curve in the case of optically thin emitting matter near the black hole, we show that the enhancement is only logarithmic, and hence is of no relevance to present observations. For optically thin emission from a geometrically thin or thick disk, photons that make only a fraction of an orbit will generically give rise to a much wider "lensing ring," which is a demagnified image of the back of the disk, superimposed on top of the direct emission. For nearly face-on viewing, the lensing ring is centered at a radius similar to 5% larger than the photon ring and, depending on the details of the emission, its width is similar to 0.5-1M (where M is the mass of the black hole). It can be relatively brighter by a factor of 2-3, as compared to the surrounding parts of the image, and thus could provide a significant feature in high-resolution images. Nevertheless, the characteristic features of the observed image are dominated by the location and properties of the emitting matter near the black hole. We comment on the recent M87* Event Horizon Telescope observations and mass measurement.NSF [PHY-1505124, PHY-1804216, PHY-1752809, PHY-1708081]; Kavli Institute for Cosmological Physics at the University of Chicago through an endowment from the Kavli Foundation; Marion and Stuart Rice AwardThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A Rigorous Derivation of Electromagnetic Self-force

During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit. The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(\lambda=0)$. We then obtain self-force, dipole forces, and spin force as first order perturbative corrections to the center of mass motion of the body. We believe that this is the first rigorous derivation of the complete first order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the "reduction of order" procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. There is no corresponding justification for the non-reduced-order equations.Comment: 52 pages, minor correction

Lateral one-third gland resection in Cushing patients with failed adenoma identification leads to low remission rates: long-term observations from a small, single-center cohort.

BACKGROUND Currently, there are no guidelines for neurosurgeons treating patients with Cushing's disease (CD) when intraoperative adenoma identification is negative. Under these circumstances, a total hypophysectomy or hemi-hypophysectomy on the side indicated by inferior petrosal sinus sampling (IPSS) is the approach being used, although there is a subsequent risk of hypopituitarism. Data on whether one-third lateral pituitary gland resection results in cure of hypercortisolism and low rates of hypopituitarism remain inconclusive. METHODS Retrospective single-center study of CD patients with failed intraoperative adenoma identification and subsequent resection of the lateral one-third of the pituitary gland as predicted by IPSS. We assessed (i) histopathological findings, (ii) early and long-term remission rates, and (iii) rates of additional pituitary hormone insufficiency. RESULTS Ten women and three men met the inclusion criteria. At 3 months, remission was noted in six (46%) patients: three (23%) had histologically confirmed adenomas, two (15%) had ACTH hyperplasia, and one patient (8%) was positive for Crooke's hyaline degeneration. New pituitary hormone deficits were noted in two patients (15%). After a median (±SD) follow-up of 14±4 years, recurrence was noted in two (15%) patients. Long-term control of hypercortisolism was attained by 10 patients (77%), with additional therapies required in nine (69%) of them. CONCLUSIONS In CD patients with failed intraoperative adenoma visualization, lateral one-third gland resection resulted in low morbidity and long-term remission in 31% of patients without the need for additional therapies. Bearing in mind the sample size of this audit, the indication for lateral one-third-gland resection has to be critically appraised and discussed with the patients before surgery

Selective inferior petrosal sinus sampling without venous outflow diversion in the detection of a pituitary adenoma in Cushing's syndrome

Introduction: Conventional MRI may still be an inaccurate method for the non-invasive detection of a microadenoma in adrenocorticotropin (ACTH)-dependent Cushing's syndrome (CS). Bilateral inferior petrosal sinus sampling (BIPSS) with ovine corticotropin-releasing hormone (oCRH) stimulation is an invasive, but accurate, intervention in the diagnostic armamentarium surrounding CS. Until now, there is a continuous controversial debate regarding lateralization data in detecting a microadenoma. Using BIPSS, we evaluated whether a highly selective placement of microcatheters without diversion of venous outflow might improve detection of pituitary microadenoma. Methods: We performed BIPSS in 23 patients that met clinical and biochemical criteria of CS and with equivocal MRI findings. For BIPSS, the femoral veins were catheterized bilaterally with a 6-F catheter and the inferior petrosal sinus bilaterally with a 2.7-F microcatheter. A third catheter was placed in the right femoral vein. Blood samples were collected from each catheter to determine ACTH blood concentration before and after oCRH stimulation. Results: In 21 patients, a central-to-peripheral ACTH gradient was found and the affected side determined. In 18 of 20 patients where transsphenoidal partial hypophysectomy was performed based on BIPSS findings, microadenoma was histologically confirmed. BIPSS had a sensitivity of 94% and a specificity of 67% after oCRH stimulation in detecting a microadenoma. Correct localization of the adenoma was achieved in all Cushing's disease patients. Conclusion: BIPSS remains the gold standard in the detection of a microadenoma in CS. Our findings show that the selective placement of microcatheters without venous outflow diversion might further enhance better recognition to localize the pituitary tumo

Programming gene expression with combinatorial promoters

Promoters control the expression of genes in response to one or more transcription factors (TFs). The architecture of a promoter is the arrangement and type of binding sites within it. To understand natural genetic circuits and to design promoters for synthetic biology, it is essential to understand the relationship between promoter function and architecture. We constructed a combinatorial library of random promoter architectures. We characterized 288 promoters in Escherichia coli, each containing up to three inputs from four different TFs. The library design allowed for multiple −10 and −35 boxes, and we observed varied promoter strength over five decades. To further analyze the functional repertoire, we defined a representation of promoter function in terms of regulatory range, logic type, and symmetry. Using these results, we identified heuristic rules for programming gene expression with combinatorial promoters

Prediction of Long-Term Restenosis After Carotid Endarterectomy Using Quantitative Magnetic Resonance Angiography.

Background To detect restenosis after carotid endarterectomy (CEA), long-term monitoring is required. However, non-selective follow-up is controversial and can be limited by costs and logistical considerations. Objective To examine the value of immediate perioperative vessel flow measurements after CEA using quantitative magnetic resonance angiography (QMRA) to detect patients at risk of long-term restenosis. Methods A prospective cohort study with long-term sonographic follow-up after CEA for symptomatic internal carotid artery stenosis (ICAs) > 50%. In all patients, vessel flow has been assessed both pre- and postoperatively using QMRA within ±3 days of surgery. Data on QMRA assessment were analyzed to identify patients at risk of restenosis for up to 10 years. Results Restenosis was recorded in 4 of 24 patients (17%) at a median follow-up of 6.8 ± 2.6 years. None of them experienced an ischemic event. Perioperative flow differences were significantly greater in patients without long-term restenosis, both for the ipsilateral ICA (p < 0.001) and MCA (p = 0.03), compared to those with restenosis (p = 0.22 and p = 0.3, respectively). The ICA mean flow ratio (p = 0.05) tended to be more effective than the MCA ratio in predicting restenosis over the long term (p = 0.35). Conclusion Our preliminary findings suggest that QMRA-based mean flow increases after CEA may be predictive of restenosis over the long term. Perioperative QMRA assessment could become an operator-independent screening tool to identify a subgroup of patients at risk for restenosis, in whom long-term monitoring is advised