# Alan Aversa

"For he hath given me the true knowledge of the things that are: to know the disposition of the whole world, and the virtues of the elements, the beginning, and ending, and midst of the times, the alterations of their courses, and the changes of seasons, the revolutions of the year, and the dispositions of the stars, the natures of living creatures, and rage of wild beasts, the force of winds, and reasonings of men, the diversities of plants, and the virtues of roots, and all such things as are hid and not foreseen, I have learned: for wisdom, which is the worker of all things, taught me. For in her is the spirit of understanding: holy, one, manifold, subtile, eloquent, active, undefiled, sure, sweet, loving that which is good, quick, which nothing hindereth, beneficent, gentle, kind, steadfast, assured, secure, having all power, overseeing all things, and containing all spirits, intelligible, pure, subtile." —Wisdom of Solomon 7:17-23

"La più sublime, la più nobile tra le Fisiche scienze ella è senza dubbio l'Astronomia. L'uomo s'innalza per mezzo di essa come al di sopra di se medesimo, e giunge a conoscere la causa dei fenomeni più straordinari." ("The most sublime, the most noble among the Physical sciences is without doubt Astronomy. Man raises himself through being beyond himself and arrives at understanding the cause of the most extraordinary phenomena.") —Giacomo Leopardi, Storia dell'Astronomia

## Research

### Writings

#### Books

Ganfornina, Raúl M. Falcón, and Juan Núñez Valdés. “Mathematical Foundations of Santilli Isotopies.” Translated by Alan Aversa. Algebras, Groups, and Geometries 32 (2015): 135–308.

Duhem, Pierre Maurice Marie. The Electric Theories of J. Clerk Maxwell. Translated from French by Alan Aversa. Boston Studies in the Philosophy of Science. Springer, September 2015. ISBN: 978-3-319-18514-9.

Pierre Maurice Marie Duhem: Les Théories électriques de J. Clerk Maxwell: Étude Historique et Critique. 2nd edition re-typeset by Alan Aversa, 08/2014.

Réginald Garrigou-Lagrange, O.P.: The Essence & Topicality of Thomism. first edition translated from Italian and Latin by Alan Aversa, 09/2013; ISBN: 9781304416186.

#### Journal Publications

Alan G. Aversa: The Two Uses of Reason, accepted for publication in the first volume of The Romish Papist. (cf. its excellent history-of-logic article: "The Scholastics' Neglected Heritage")

Alan G. Aversa: review of Francisco J. Romero Carrasquillo’s translation of Édouard Hugon, O.P.’s Cosmology manual, Nova et Vetera Vol. 13, No. 1 (2015): 297.

Alan G. Aversa: Limits on the Gas Disk Content of Two "Evolved" T Tauri Stars. 12/2011. (undergrad. thesis)

Alan G. Aversa, Kelsey E. Johnson, Crystal L. Brogan, W. M. Goss, and D. J. Pisano: Very Large Array and ATCA Search for Natal Star Clusters in Nearby Star-forming Galaxies. The Astronomical Journal 03/2011; 141(4):125.

M. Andersen, M. R. Meyer, J. Greissl, A. Aversa: Evidence for a Turnover in the IMF of Low Mass Stars and Sub-stellar Objects: Analysis from an Ensemble of Young Clusters. The Astrophysical Journal Letters 07/2008; 683:L183.

### Previous Research

#### T Tauri Gas Circumstellar Disks

T Tauri stars are young, nascent, sunlike stars which often have circumstellar disks of gas and dust revolving around them. It is not known, however, how long the gas persists in circumstellar disks before it accretes onto the T Tauri star or perhaps becomes locked up in newly formed gaseous planets. To assess the gas disk lifetime of T Tauri stars, we observed the $^{12}\mathrm{CO~}J=2-1$ rotational transition emission line of two T Tauri stars with the Heinrich Hertz Sub-Millimeter Telescope (HHT) on Mt. Graham, Arizona. We did not detect any gas around our two sources, RX J0432 and the circum-binary disk of St 34. The upper limits of these two objects are shown in the plot of stellar age versus circumstellar disk mass. Also plotted are circumstellar gas disk masses of other T Tauri stars.

See our proposal and arXiv:1112.4581 for more information.

#### Super Star Clusters (SSCs)

Super Star Clusters (SSCs) are massive, dense star formation regions where generally $\ge10^4$ nascent O7.5 stars ionize a cocoon of gas and dust. Due to the large amounts of obscuring gas and dust, SSCs are only observable in the IR or radio. IR detects the warm poly-aromatic hydrocarbons (PAHs) while radio detects thermal free-free emission due to the Lyman continuum flux of the embedded O stars. Measuring the thermal luminosity $L_\mathrm{thermal}$ at a frequency $\nu$ and assuming an HII temperature of $10^4\mathrm{~K}$, one can put a lower limit on the Lyman continuum flux $Q_\mathrm{Lyc}$. Since an O7.5 star has a Lyman continuum of $Q_\mathrm{Lyc}=1.0\times10^{49}\mathrm{~s}^{-1}$, we can estimate how many stars are embedded in a SSC. To detect thermal free-free emission, we observed 27 galaxies in the northern and southern hemispheres with the Australia Telescope Compact Array (ATCA) and Very Large Array (VLA) radio telescopes at 3.5 cm and 6.2 cm and at 1.3 cm and 3.6 cm, respectively. We use the spectral index $\alpha$, where $S_\nu \propto \nu^\alpha$, to determine if a source is thermal, which we define as $\alpha>0.2$. Only 9 of the 27 galaxies selected based upon their likelihood of harboring nascent star formation actually showed evidence of thermal emission. This suggests that SSCs form quickly.

The radio map shows 3 cm contours overlaid on an SDSS z-band optical image of Arp 233, a galaxy harboring SSCs.

We used this relation to compute our $Q_\mathrm{Lyc}$ lower limits:$Q_\mathrm{Lyc}\ge 6.3\times 10^{52}\,\mathrm{s}^{-1} \left(\frac{T_e}{10^4\,\mathrm{ K}}\right)^{-0.45}\left(\frac{\nu}{\mathrm{GHz}}\right)^{0.1} \left(\frac{L_\mathrm{thermal}}{10^{27}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{ Hz}^{-1}}\right).$See this presentation and Aversa et al. for more information.

#### Initial Mass Function (IMF) of Brown Dwarfs

An IMF $\xi(m)$ describes how many zero age main sequence (ZAMS) stars $\xi$ of a given mass $m$ form per unit volume. For stars greater than the sun's mass ($>1\mathrm{~M}_\odot=1.988\times10^{30}\mathrm{~kg}$), the IMF is nearly the same in all star clusters, i.e., it is nearly independent of the physical conditions of a particular star formation environment. It follows a power-law developed by Edwin Salpeter in the '50s: $\frac{d\xi(m)}{dm}\propto m^{-\alpha},$ where $\alpha$ is a constant roughly equal to $2.35$. For stars with masses $<1\mathrm{~M}_\odot$, the IMF is not so well-determined. It is unknown whether the IMF peaks, presumably somewhere around $\sim0.1\mathrm{~M}_\odot$, or whether it flattens off toward low masses or even increases. To investigate this question, we ran Monte Carlo simulations of clusters with various IMFs and analyzed the distribution of the ratio $\frac{N(0.08-0.1)}{N(0.03-0.08)},$ where $N(a-b)$ represents the number of stars with a mass in the range $[a,b]$. We then compared the distribution of these ratios for 7 observed clusters (top panel) to the theoretical distributions (bottom panel) with a $\chi^2$ test. The theoretical distributions arise from clusters obeying Salpeter IMFs with different slopes $\alpha$ in the low mass regime. The solid line represents the distribution of clusters obeying a Chabrier IMF. We were able to constrain strongly that the brown dwarf or sub-stellar IMF does turn over.

See Andersen et al. for more information.

## Interests

### Philosophy

St. Thomas Aquinas's philosophy opposes the relativism of truth and recognizes that both faith and reason are legitimate means to knowledge and wisdom. Sententiæ Deo addresses how I see science progressing with the aid of the true philosophy of St. Thomas Aquinas, which the Society of Scholastics and the Institute for Advanced Physics promote. Works like St. Thomas's Division and Methods of the Sciences and commentary on the Posterior Analytics and Physics of Aristotle, Aristotle's Posterior Analytics and Physics themselves, the 24 Thomistic Theses, and especially all the works on which I have commented here continue to influence me. Read also my "Scholasticism in Empiriological Sciences" reading list.

I have become interested in Pierre Duhem's history and philosophy of physics. See, e.g., the quantum mechanics, space and time, and statistical physics Stanford Encyclopedia of Philosophy articles.

### Ideas

Mathematics can be applied in physics in various ways. A physical theory's equations are often identical in form but interpreted depending on the context and in which field one uses them. The diagram here shows how I think the various physics fields might be related.

### Proving There is No Largest Prime

I like mathematics, so here is Euclid's classic proof that there is no largest prime number.
1. Suppose $p_\mathrm{largest}$ is the largest prime.
2. Then form a new integer $n=p_1\times p_2\times p_3\times\cdots\times p_\mathrm{largest}+1$.
3. Observe that every prime divides $n$ with a remainder of 1.
4. The Fundamental Theorem of Arithmetic says that any integer can be expressed as a product of prime number(s) and $1$, thus if an integer is not divisible by any primes, then that integer itself must be a prime. So $n$ is a prime.
5. $n$ being a prime is a contradiction because $n>p_\mathrm{largest}$ and we assumed $p_\mathrm{largest}$ to be the largest prime; therefore, there is no largest prime number.

## Miscellanea

#### Biographies

From Fr. Alban Butler's The Lives of the Saints: Click below to download scanned PDFs of all the volumes of The Lives of the Saints online, organized by their feast days: