Measuring a black hole mass - you're doing it right

1.  The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Kepler's laws are among the most fundamental laws of astronomy.
Basically, they describe the orbits of planets around the Sun (or any "small" object around a much more massive central object), under the assumption that the gravitational field can be considered Newtonian (even if historically quite the opposite happened, with Newton using Kepler's orbits to derive his laws of gravity).
The orbits of all planets in the Solar system are very well described, to first order, by these laws. Only after centuries of observations of Mercury, the closest to the Sun, it was possible to notice post-Keplerian deviations due to relativistic effects.
When Kepler's laws say "proportional", the proportionality factor involves the masses of the objects (this was found by Newton). For example, in this approximation the third law is actually

where a is the semi-major axis of the orbit (the radius if the orbit is circular), G (=6.67384 × 10^-11 m³ kg^-1 s^-2) the gravitational constant, M the mass of the central object, and T the orbital period.

It is therefore possible to use the orbit of the small object to infer the mass of the big one, if we have an idea of the size of the orbit.

One nice example? The measurement of our Galaxy's central supermassive black hole.
Several groups have been able to measure accurately the mass of this black hole by tracking the movement of several stars around it.
In the animated GIF above, a nice illustration of the procedure. Every orbit is an ellipse having in one of its foci, marked by the red cross in the center of the picture, an "invisible" object. This object, in order to describe the orbits of all the tracked orbiting points, must have a mass of about 4 million solar masses.
Here is a quite complete description of the work done by several groups to obtain this result. 
Enjoy!

Medium-sized black holes? Probably not.

Ultraluminous X-ray sources (ULXs) are accreting black holes, i.e. black holes that are "eating" matter from a companion star. They are called ultraluminous because their luminosity is too high to be explained by "normal" accretion on stellar-mass black holes, i.e. black holes formed by the collapse of a single big star (from 8 up to ~100 masses of the Sun).
A step behind. During accretion, matter falls towards a central object. This matter heats up in the process, and this heat is freed in form of radiation. This radiation in turn "pushes" on the matter that keeps falling in, and a point is reached when the luminosity produced is comparable to the push by the infalling matter and so no higher luminosity can be achieved. This is called the Eddington luminosity and is a well known quantity in accretion studies. This luminosity scales with the mass of the central object, so that supermassive black holes (billions of times the mass of the Sun) will be able to radiate at much larger luminosities than stellar-mass black holes (mass several times the Sun)
Well, ULXs radiate at much more than the Eddington luminosity for stellar-mass black holes, so the first things that comes to mind is that they are bigger than stellar-mass black holes, and so they are members of the evasive class of Intermediate-mass black holes. Right?
Not so fast, my friend. People like these japanese researchers have done a great deal of simulations to show that it is possible to overcome the Eddington limit some extent.
Only problem: it was impossible to tell which of the two hypotheses was more right until 2012, since the few X-ray satellites capable of observing ULXs were sensitive only up to 10 keV, where the models started to really give incompatible predictions.
In this old post we talked about the launch of the NuSTAR satellite. Well, that was the turning point.
NuSTAR observed several ULXs and was able to finally strongly point in one direction. See the animated GIF above: the blue points are NuSTAR data, and they clearly follow better two models (the ones cutting off above 10 keV) than the others, while data from the XMM satellite weren't able to make a difference. This cutoff is considered a signature of super-Eddington accretion and permitted to estimate the mass of these ULXs to be in the high-end of the stellar-mass range.

Here is a press release of these studies. Enjoy!

Enrico Fermi on Einstein's theory of special relativity

Yesterday I came across some fantastic notes by a young Enrico Fermi on Einstein's special relativity, which were included in "Asimmetrie", an outreach magazine issued by the Italian Institute for Nuclear Physics (INFN). After some search I found an English translation (by Robert Jantzen, I think).

The reading is really mind-blowing (well, at least for me...) and even more so considering Fermi was 21 at the time...

Enjoy!

Apparently, there are no pictures of Fermi and Einstein together, so I turned down to this one...

Recommended by us: "MicroBooNE, in 3-D"

Tingjun Yang (left) and Wesley Ketchum lead the effort to develop new 3-D reconstruction 
software for the MicroBooNE experiment. Here they stand inside the MicroBooNE 
time projection chamber.Photo: Reidar Hahn

“ 

Imagine your job is to analyze the data coming from Fermilab's MicroBooNE experiment. 

It wouldn't be an easy task. MicroBooNE has been designed specifically to follow up on the MiniBooNE experiment, which may have seen hints of a fourth type of neutrino, one that does not interact with matter in the same way as the three types we know about. The big clue to the possible existence of these particles is low-energy electrons.

But that experiment could not adequately separate the production of electrons from the production of photons, which would not indicate a new particle. MicroBooNE's detector, an 89-ton active volume liquid-argon time projection chamber, will be able to. To take advantage of this, every neutrino interaction in the chamber will have to be examined to determine if it created an electron or a photon.

And there will be a lot of interactions to study — the MicroBooNE collaboration expects to see activity in their detector once every 20 seconds, including nearly 150 neutrino interactions each day.

If all goes to plan, human operators won't have to worry about any of that. When MicroBooNE switches on next summer, it will sport one of the most sophisticated 3-D reconstruction software programs ever designed for a neutrino experiment.

According to Wesley Ketchum and Tingjun Yang, two postdocs leading the software development team at Fermilab, MicroBooNE's computers will be able to accurately reconstruct neutrino interactions and automatically filter the ones that create electrons. The key to accomplishing this lies in the design of the time projection chamber.

Continue to read on Fermilab Today 

                                                                                                                                                                                        ”       

La sezione d'urto "plettro-bicchiere"

In questo post volevo parlarvi di un fatto curioso capitatomi questo fine settimana durante un concerto del gruppo scozzese dei Biffy Clyro al Live Music Club di Trezzo sull'Adda (MI). 

Naturalmente il fatto accaduto ha un rilevanza, seppur marginale, con la fisica nel raccontarvelo c’è quindi l’intento di comunicare come, la quasi totalità dei fenomeni che ci accadono, possono essere analizzati con un approccio scientifico e razionale. Ma entriamo nel vivo del racconto: durante l’esibizione del “gruppo spalla” i Walking papers, io e il mio amico ci siamo recati al bancone del bar, situato su un lato del locale, per acquistare da bere. Appena ricevute le bevande, un bicchiere di birra da 0.40L (e un bicchiere di Montenegro), ci siamo apprestati a ritornare approssimativamente al centro del locale dove ci aspettavano gli altri nostri due amici. Contemporaneamente all’atto dell’acquisto delle bevande il gruppo spalla finiva la sua esibizione e procedeva ai classici saluti e all’usuale lancio dei plettri per la chitarra* quando ad un certo punto sentiamo un rumore nelle nostre vicinanze e riceviamo alcuni schizzi di birra o qualche altro liquido.  Un po’ confusi ci guardiamo e ci chiediamo che cosa mai fosse accaduto, personalmente non avevo compreso la situazione, avevo sentito un colpo nel mio bicchiere di plastica** (di Montenegro) e poi avevo ricevuto degli schizzi ed ho pensato subito che esso fosse attribuibile al quel “balzetto” indotto da un bicchiere deformato che  ritorna nella sua configurazione originale e produce uno schizzo a seguito della agitazione della superficie del liquido contenuto al suo interno. Ho comunicato tempestivamente la mia interpretazione del fenomeno al mio amico il quale tuttavia mi ha guardato e mi ha riferito: “no! ti dico che è entrato un plettro nel mio bicchiere”; io l’ho guardato stranito e un po’ incredulo perché avevo sentito una botta nel mio bicchiere ed ero convinto dipendesse quindi dal mio e non che gli schizzi provenissero dal suo bicchiere o da un altro, quando però egli ha recuperato con le sue stesse mani il plettro all’interno del suo bicchiere mi son dovuto “arrendere” all’evidenza. Ebbene si, un plettro lanciato dal palco da alcuni componenti del gruppo, aveva dapprima colpito il mio bicchiere per poi dirigersi all’interno del bicchiere di birra del mio amico producendo degli schizzi. Tutto questo ci ha lasciato abbastanza perplessi e abbiamo riso dell’accaduto, passando subito al vaglio i parametri coinvolti per valutare una prima stima della probabilità del fatto e classificandolo in maniere affrettata quantomeno come “poco probabile”, ma dal momento che la situazione non permetteva un approfondimento “serio”, mi son ripromesso di valutare meglio la questione in separata sede, ed eccomi qui a fare un po’ di stime :)