Everything is a Simple Harmonic Oscillator

Posted in mathematics, The Universe and Stuff with tags , , , on December 13, 2025 by telescoper

Anyone who has studied theoretical physics for any time will be familiar with the simple harmonic oscillator, which I will call the SHO for short. This is a system that can be solved exactly and its solutions can be applied in a wide range of situations where it holds approximately, e.g. when looking at small oscillations around equilibrium. I’ve often remarked in lectures that we spend much of our lives solving the SHO problem in various guises, often pretending that the difficult system we have in front of us can, if looked at in the right way, and with sufficient optimism, be approximated by the much simpler SHO. Cue the old joke that if all you have is a hammer, everything looks like nail…

That rambling prelude occurred to me when I found this little problem in some old notes. It is a cute mathematical result that shows that the Friedman equations that underpin our standard cosmological model can in fact be written in the same form as those describing a Simple Harmonic Oscillator. In what follows we take the cosmological constant term to be zero.

The resulting equation is the SHO equation if k>0. I’m not sure whether this result is very useful for anything, but it is cute. It also goes to to show that, if looked at in the right way, the whole Universe is a Simple Harmonic Oscillator!

Weekly Update from the Open Journal of Astrophysics – 13/12/2025

Posted in OJAp Papers, Open Access, The Universe and Stuff with tags , , , , , , , , , , , , , , , , , , , , , , , , , , on December 13, 2025 by telescoper

It’s time once again for the usual Saturday morning update of the week’s new papers at the Open Journal of Astrophysics. Since the last update we have published a further five papers, which brings the number in Volume 8 (2025) up to 195, and the total so far published by OJAp up to 430.

The first paper this week is “Cosmic Rays Masquerading as Cool Cores: An Inverse-Compton Origin for Cool Core Cluster Emission” by Philip F. Hopkins (Caltech), Eliot Quataert (Princeton), Emily M. Silich, Jack Sayers, Sam B. Ponnada and Isabel S. Sands (Caltech).  This was published on Tuesday 9th December 2025 in the folder marked High-Energy Astrophysical Phenomena. It presents an argument  that cosmic-ray inverse-compton emission could contribute significantly to the X-ray surface brightness (SB) in cool-corre clusters, implying that gas densities may have been overestimated therein.

The overlay is here:

You can find the officially accepted version on arXiv here and the Fediverse announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Cosmic Rays Masquerading as Cool Cores: An Inverse-Compton Origin for Cool Core Cluster Emission" by

Philip F. Hopkins (Caltech), Eliot Quataert (Princeton), Emily M. Silich, Jack Sayers, Sam B. Ponnada and Isabel S. Sands (Caltech)

doi.org/10.33232/001c.154053

December 9, 2025, 7:22 am 1 boosts 0 favorites

The second paper of the week is “Detecting False Positives With Derived Planetary Parameters: Experimenting with the KEPLER Dataset” by Ayan Bin Rafaih (Aitchison College, Lahore, Pakistan) and Zachary Murray (Université Côte d’Azur, France). This one was published on 9th December 2025 in the folder Earth and Planetary Astrophysics. It is an investigation into the performance of a range of machine-learning algorithms on the KEPLER dataset, using precision-recall trade-off and accuracy metrics.

The overlay is here:

You can find the official version of this one on arXiv here. The federated announcement on Mastodon is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Detecting False Positives With Derived Planetary Parameters: Experimenting with the KEPLER Dataset" by Ayan Bin Rafaih (Aitchison College, Lahore, Pakistan) and Zachary Murray (Université Côte d’Azur, France)

doi.org/10.33232/001c.154054

December 9, 2025, 7:34 am 1 boosts 0 favorites

Next one up is “The role of peculiar velocity uncertainties in standard siren cosmology” by Chris Blake and Ryan J. Turner (Swinburne, Australia). This paper discusses the impact of peculiar velocities on the error in H0 determinations from local distance indicators with observed redshifts, incorporating the effect of bulk flows. It was published on Tuesday 9th December in the folder Cosmology and Nongalactic Astrophysics.

The overlay is here:

You can find the official accepted version on arXiv here. The fediverse announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "The role of peculiar velocity uncertainties in standard siren cosmology" by Chris Blake and Ryan J. Turner (Swinburne, Australia)

doi.org/10.33232/001c.154055

December 9, 2025, 7:47 am 1 boosts 0 favorites

The fourth article of the week is “Transient QPOs of Fermi-LAT blazars with Linearly Multiplicative Oscillations” by P. Penil (Clemson University, USA) and 7 others based in the USA, Italy and Germany. This was published on Thursday 10th December in the folder High-Energy Astrophysical Phenomena. This paper presents an investigation of patterns of quasi-periodic oscillations in observed blazar systems characterized by periodic multiplicative amplitudes including both the periodicities and long-term variations.  The overlay is here:

You can find the official published version on arXiv here. The Fediverse announcement follows:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Transient QPOs of Fermi-LAT blazars with Linearly Multiplicative Oscillations" by P. Penil (Clemson University, USA) and 7 others based in the USA, Italy and Germany

doi.org/10.33232/001c.154123

December 10, 2025, 12:22 pm 0 boosts 1 favorites

The last paper for this week is “Tidally Delayed Spin-Down of Very Low Mass Stars” by Ketevan Kotorashvili and Eric G. Blackman (U. Rochester, USA). This was published on Friday 12th December (yesterday) in the folder Solar and Stellar Astrophysics. It discusses the effect of tides from sub-stellar companions on rotational evolution of very low-mass stars, suggesting that these may explain the dearth of field, late-type M dwarfs with intermediate rotation periods.

The overlay is here:

 

You can find the officially-accepted version on arXiv here, and the Mastodon announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Tidally Delayed Spin-Down of Very Low Mass Stars" by Ketevan Kotorashvili and Eric G. Blackman (U. Rochester, USA)

doi.org/10.33232/001c.154268

December 12, 2025, 10:31 am 1 boosts 0 favorites

 

And that concludes the update for this week. I will do another of these regular announcements next Saturday, which will be the last such update for 2025. Will we make it past 200 for the year? Tune in next week to find out!

Blue Christmas Again

Posted in Jazz with tags , , , on December 12, 2025 by telescoper

I’ve had a very busy penultimate week of term and am out of energy so instead of attempting a new post I thought I’d repost this “festive” classic. I posted this one during the “festive” season” in 2013 and haven’t posted it since. Until now. The band is led by none other than Miles Davis; the other members are Frank Rehak (trombone), Wayne Shorter (tenor sax), Paul Chambers (bass), Jimmy Cobb (drums), and Willie Bobo (bongos); the arrangement is unmistakably by Gil Evans. The vocalist is the legendary Bob Dorough who also wrote the lyrics.

“Bah Humbug” never sounded so cool!

 P.S. I’m not particularly blue myself, just tired…

An Introduction to Philosophy

Posted in Uncategorized with tags , on December 11, 2025 by telescoper
Cartoon from Private Eye

Around the Circle – Wassily Kandinsky

Posted in Art with tags , , on December 10, 2025 by telescoper

by Wassily Kandinsky (1940; oil and enamel on canvas. 96.8 x 146 cm Guggenheim, New York)

Storm Bram Approaches…

Posted in Biographical, Maynooth with tags , , on December 9, 2025 by telescoper

The weather is rather strange today, as a result of Storm Bram which is approaching from the South. The storm is bringing warm air with it, so the temperature is around 15°C which is very mild for December. The prevailing winds are usually westerly or south-westerly.

Heavy rain fell overnight, especially in the South. It’s clearer now and the winds are starting to pick up. Although Maynooth is relatively sheltered we’re still expecting gusts up to 100 km/h. As a precaution, the large tent which is usually situated outside the John Hume building has been dismantled to stop it blowing away.

Campus remains open and lectures are going ahead as normal.

At least mine are…

UPDATE: 4.25pm. I spoke to soon. I have a teaching session between 2pm and 4pm on Tuesdays; I usually take a break halfway through, as I did this afternoon. Chatting with some students in the interval we noted the wind was picking up and discussed the possibility of a power cut. We obviously tempted fate, as no sooner had we resumed for the second half when all the power went off. It came on intermittently a few times, but at 3.30pm I called off the lecture. It was too dark to see the blackboard and no other AV equipment was working. When I got back to the Physics Department, where the power was also off, as it appeared to be for the whole campus, a colleague who lives nearby told me that our area of Maynooth still had power. So I headed home, via Dunnes (which has a generator) to buy a few things. As I walked through Maynooth some lights were on, some were off. The worst affected area seemed to be to the north-west and around campus. Anyway, I’m home safely and can continue working here as long as the power stays on.

P.S. The storm is named after Bram Stoker, author of Dracula, who was born in Dublin.

Nine Teaching Days to Christmas

Posted in Biographical, mathematics, Maynooth, Television with tags , , , on December 8, 2025 by telescoper

This week is the penultimate week of teaching term at Maynooth and, as usual at this stage of the Semester, we’re getting busier and busier. The examinations for January have been sent off for printing and are (presumably) ready to go, and I’m up to date with all my coursework gradin so I am, miraculously, on schedule as far as teaching is concerned. I should finish covering the respective syllabuses by Tuesday 16th, with the remaining teaching sessions devoted to revision. I don’t have any lectures on Fridays this term, so my teaching ends, a day before the end of term, on Thursday 18th December. To celebrate the end of term I’ll be presenting the students in the last session of my Engineering Mathematics module the gift of a final Class Test. I’m not sure when I’ll get to correct it. Oh, and our Department Christmas Dinner is on Wednesday 17th.

I’ll soon have to decide when to pause the publication of new papers at the Open Journal of Astrophysics and prepared for next year’s Volume 9. A certain person is insisting that I take a complete break for at least a week, so I think we’ll probably stop on Christmas Eve and begin again in the New Year.

In the meantime, term goes on. I have three lectures to get ready for tomorrow. Incidentally, my mid-Semester feedback suggested that I start each lecture with an introduction to say what I’m going to be covering. Here are some examples of what I’ve been doing in response:

Black Holes, Hawking Radiation (and AI…)

Posted in Artificial Intelligence, The Universe and Stuff with tags , , , , , on December 7, 2025 by telescoper

It seems to be a common misapprehension that the energy released by the supermassive black holes in, for example, active galactic nuclei is in the form of Hawking radiation. It isn’t. Hawking radiation is only significant for black holes of very low mass. The radiation produced around supermassive black holes is due to the extremely high density and temperate of matter falling into the black hole through an accretion disk not due to the evaporation of the black hole itself. Hawking radiation has never been experimentally detected.

Hawking showed that the a black hole will produce black-body radiation with a temperature, the Hawking Temperature, given by TH in a beautiful formula below that brings together constants relating to gravity, statistical mechanics, quantum theory and relativity:

You can see that the Hawking Temperature is inversely proportional to the mass of the black hole M so is largest for very small black holes. In fact for a black hole with mass of order that of the Moon, the Hawking Temperature is just 3 Kelvin. Since the Universe is bathed in cosmic radiation with this temperature, such a black hole would not evaporate at all because it would absorb as much radiation as it emits by the Hawking mechanism as would any black hole of mass greater than this. The Hawking temperature for a supermassive black hole is many orders of magnitude lower than this, so Hawking radiation is completely irrelevant.

Notice that if a black hole does start to evaporate then its mass begins to decrease. Its Hawking temperature therefore increases so its mass decreases even more quickly. In the end the mass gets so low and the temperature so high that the black hole effectively explodes. Nobody really knows how to describe the final stage as it relies on physics we don’t understand.

Anyway, this all reminds that years ago I set an examination question that involved applying the Hawking formula above to calculate the lifetime of a black hole of mass M. It’s not too hard to show that it scales as M-3. Another part of the question asked: what is the mass of a black hole whose Hawking Temperature is room temperature (say 300 K), what would be the Schwarzschild radius of such a black hole, and what would be its lifetime?

I’ll leave it to my readers to plug the numbers into the Hawking formula above to derive the mass, etc. Please submit your answers through the comments box below. The first correct entry does not win a prize, not even a joke Peace Prize.

For a laugh I asked Google for the answer. Here is the AI summary:

Bonus marks for pointing out everything that’s wrong in this summary.

Mozart and Bruckner at the National Concert Hall

Posted in Biographical, Music, Uncategorized with tags , , , , , , , on December 6, 2025 by telescoper

I was worried I might have to miss last night’s concert by National Symphony Orchestra Ireland conducted by Anja Bihlmaier at the National Concert Hall. I bought the ticket some weeks ago and was looking forward to it, but I had been a bit unwell earlier in the week and didn’t want to go only to cough all the way through, possibly infecting others on the way. By Friday afternoon, however, I felt a lot better and took the decision to go for it. I’m very glad I did because I enjoyed the music enormously and didn’t cough or sneeze once!

There were only two items on the menu, another pairing of Mozart and Bruckner.

In the first half we heard the Piano Concerto No. 15 by Wolfgang Amadeus Mozart played by Boris Giltberg. This piece was written in 1784 when the composer had reached the ripe old age of 28. It’s an enjoyable and entertaining piece, not perhaps as profound as some of the later piano concertos (Mozart wrote 27 altogether), but well worth listening to. It’s also regarded as one of the most difficult to play, though Boris Giltberg made it look easy enough and was clearly enjoying himself while he played it as I’m sure did the composer when he performed it for the first time in Vienna. The three movements follow a standard fast-slow-fast pattern; the last being a sprightly Rondo, part of which features in the soundtrack of an episode of Inspector Morse: Who Killed Harry Field?

After generous applause, Giltberg returned to the stage to play a very solo encore piece. I didn’t recognize it, but someone I know who was there told me it was by Robert Schumann but didn’t know the name. When I got home I spent a good half-hour going through recordings until I finally identified it as the Arabeske in C Major. Anyway, it was a very nice way to send us into the wine break.

After the interval we had Anton Bruckner‘s monumental Symphony No. 9, which was unfinished at Bruckner’s death in 1896. Insufficient material was recovered after the composer’s death to enable a reconstruction of the missing 4th movement, so this work is generally performed in its incomplete state with only three movements. Even so, it’s an immense work in both length and ambition, lasting over an hour in performance and calling for a large orchestra.

The majestic first movement (marked FeierlichMisterioso; solemn & mysterious) with its soaring themes and thunderous climaxes always puts me in mind of a mountaineering expedition, with wonderful vistas to experience but with danger lurking at every step. At times it’s rapturously beautiful, at times terrifying. It’s not actually about mountaineering, of course – Bruckner meant this symphony to be an expression of his religious faith, which, in the latter years of his life must have been pretty shaky if the music is anything to go by.

The second movement (Scherzo) is all juddering rhythms, jagged themes and harsh dissonances reminiscent (to me) of Shostakovich. It alternates between menacing, playful and cryptic; the frenzied animation of central Trio section is especially disconcerting.

The last movement  (Adagio)  begins restlessly, with an unaccompanied violin theme and then becomes more obviously religious in character in various passages of hymn-like quality, still punctuated by stark crescendi. In this movement Bruckner doffs his cap in the direction of Richard Wagner,  especially when the four Wagner tubas appear, and the movement reaches yet another climax with the brass bellowing out the initial violin theme. This dies away and the movement comes to an unresolved, poignant conclusion. With a long pause in silence as if to say “that’s all he wrote”, the concert came to an end.

Although I’ve loved this work for many years I’ve only ever heard it once before in concert.  The live performance definitely adds other dimensions you will miss on a recording and I enjoyed it enormously. For one thing you can see how hard the musicians – especially the cellos and basses – have to work. The sight of a large symphony orchestra working together to produce amazing sounds is quite something.

The National Symphony Orchestra Ireland may not be the Berlin Philharmonic but I was generally very impressed, there was split note in the brass section near the end, but this was a minor blemish. The performance was very warmly received by the audience. The NCH wasn’t full, but it was quite a good attendance.

That’s not quite the end of my concert-going for 2025. I’m off to Messiah next week. Well, you have to, don’t you? It’s Christmas..

Weekly Update from the Open Journal of Astrophysics – 06/12/2025

Posted in OJAp Papers, Open Access, The Universe and Stuff with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , on December 6, 2025 by telescoper

Once again it’s time for the usual Saturday morning update of the week’s new papers at the Open Journal of Astrophysics. Since the last update we have published a further six papers, which brings the number in Volume 8 (2025) up to 190, and the total so far published by OJAp up to 425. I blogged about the significance of the latter figure here.

The first paper this week is “The galaxy-IGM connection in THESAN: observability and information content of the galaxy-Lyman-alpha cross-correlation at z>6” by Enrico Garaldi (U. Tokyo, Japan), Verena Bellscheidt (Tech. U. Munich, Germany), Aaron Smith (U. Texas Austin, USA) and Rahul Kannan (York U. Canada). This paper was published on Monday 1st December 2025 in the folder Cosmology and Nongalactic Astrophysics. It describes an investigation of the impact of observational limitations on the ability to retrieve the intrinsic galaxy-Lyman-alpha cross correlation from line-of-sight observations.

The overlay is here:

 

 

You can find the officially accepted version on arXiv here and the Fediverse announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "The galaxy-IGM connection in THESAN: observability and information content of the galaxy-Lyman-alpha cross-correlation at z>6" by Enrico Garaldi (U. Tokyo, Japan), Verena Bellscheidt (Tech. U. Munich, Germany), Aaron Smith (U. Texas Austin, USA) and Rahul Kannan (York U. Canada)

doi.org/10.33232/001c.151666

December 1, 2025, 8:37 am 1 boosts 0 favorites

The second paper of the week is “A Less Terrifying Universe? Mundanity as an Explanation for the Fermi Paradox” by Robin H.D. Corbet (U. Maryland, USA). This paper was published on 1st December 2025 in the folder Instrumentation and Methods for Astrophysics. It presents a discussion of possible explanations for the lack of s evidence for the presence of technology-using extraterrestrial civilizations in the Galaxy (usually called the Fermi paradox). The overlay is here:

 

 

You can find the official version of this one on arXiv here. The federated announcement on Mastodon is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "A Less Terrifying Universe? Mundanity as an Explanation for the Fermi Paradox" by Robin H.D. Corbet (U. Maryland, USA)

doi.org/10.33232/001c.151454

December 1, 2025, 8:50 am 2 boosts 2 favorites

 

Next one up is “Sulphur abundances in star-forming regions from optical emission lines: A new approach based on photoionization models consistent with the direct method” by Enrique Pérez-Montero, Borja Pérez-Díaz, & José M. Vílchez ( (Instituto de Astrofísica de Andalucía, Spain), Igor A. Zinchenko (LMU, Germany), Asier Castrillo, Marta Gavilán, Sandra Zamora & Ángeles I. Díaz (Universidad Autonoma de Madrid, Spain). This was published on 1st December 2025 in the folder Astrophysics of Galaxies. This study uses the emission lines produced in the optical part of the spectrum and with photoionization models to derive sulphur chemical abundances in the gas-phase of star-forming galaxies.

The overlay is here:

 

 

You can find the official accepted version on arXiv here. The fediverse announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Sulphur abundances in star-forming regions from optical emission lines: A new approach based on photoionization models consistent with the direct method" by Enrique Pérez-Montero, Borja Pérez-Díaz, & José M. Vílchez ( (Instituto de Astrofísica de Andalucía, Spain), Igor A. Zinchenko (LMU, Germany), Asier Castrillo, Marta Gavilán, Sandra Zamora & Ángeles I. Díaz (Universidad Autonoma de Madrid , Spain)

doi.org/10.33232/001c.151253

December 1, 2025, 9:12 am 0 boosts 0 favorites

The fourth article of the week is “Bayesian Posteriors with Stellar Population Synthesis on GPUs” by Georgios Zacharegkas & Andrew Hearin (Argonne National Laboratory, USA) and Andrew Benson (Carnegie Observatories, USA). This is an exploration of a range of computational techniques aimed at accelerating Stellar Population Synthesis predictions of galaxy photometry using the JAX library to target GPUs (Graphics Processing Units, in case you didn’t know). This paper was published on Tuesday December 2nd 2025 in the folder Astrophysics of Galaxies.

The overlay is here:

 

You can find the official published version on arXiv here. The Fediverse announcement follows:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Bayesian Posteriors with Stellar Population Synthesis on GPUs" by Georgios Zacharegkas & Andrew Hearin (Argonne National Laboratory, USA) and Andrew Benson (Carnegie Observatories, USA)

doi.org/10.33232/001c.151255

December 2, 2025, 7:38 am 3 boosts 1 favorites

Next one up is “IAEmu: Learning Galaxy Intrinsic Alignment Correlations” by Sneh Pandya Yuanyuan Yang, Nicholas Van Alfen, Jonathan Blazek and Robin Walters (Northeastern University, Boston, USA). This presents a neural-network-based emulator that predicts the galaxy position-position, position-orientation, and orientation-orientation, correlation functions and their uncertainties using mock catalogs based on the halo occupation distribution (HOD) framework. It was published on December 2nd 2025 in the folder Cosmology and Nongalactic Astrophysics. The overlay is here:

The official accepted version can be found on arXiv here. The Mastodon announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "IAEmu: Learning Galaxy Intrinsic Alignment Correlations" by Sneh Pandya Yuanyuan Yang, Nicholas Van Alfen, Jonathan Blazek and Robin Walters (Northeastern University, Boston, USA)

doi.org/10.33232/001c.151749

December 2, 2025, 7:52 am 1 boosts 0 favorites

The last paper for this weel is “Unraveling the Nature of the Nuclear Transient AT2020adpi” by Paarmita Pandey (Ohio State University, USA) and a team of 15 others based in the USA, UK and Australia. This was published on Thursday December 4th 2025 in the folder High-Energy Astrophysical Phenomena. It is an investigation into a particular transient event AT2020adpi and a discussion of whether it is an extreme example of AGN variability or a Tidal Disruption Event (TDE). The overlay is here:

You can find the officially-accepted version on arXiv here, and the Mastodon announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Unraveling the Nature of the Nuclear Transient AT2020adpi" by Paarmita Pandey (Ohio State University, USA) and 15 others based in the USA, UK and Australia

doi.org/10.33232/001c.151453

December 4, 2025, 8:48 am 1 boosts 0 favorites

And that concludes the update for this week. I will do another next Saturday.