Category: Astrophysics

The Universe, on a resized-scale perspective, is composed of billions of objects such as stars, black holes, pulsars, white dwarfs whose study of chemical-physical properties and dynamics is really interesting!

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An Explanation about the Primordial Black Holes Genesis


Cosmic Strings [1] can emerge from symmetry-breaking [2] phase transitions in the early Universe (further information in here). These one-dimensional structures have been proposed as catalysts for large-scale cosmic structures, such as Galaxy(ies) (Figure 1) and galaxy clusters. Theoretical investigations often require cosmic strings to have substantial linear mass densities to effectively influence matter. A key parameter, [math]\small{G\mu/c^2}[/math], where [math]\small{G}[/math] is the gravitational constant (for further information upgrade here), is typically expected to be of the order of 10-6.


However, a critical aspect of cosmic string dynamics involves the formation of black holes (further information in here, section 3) from cosmic-string loops [3] As a loop contracts, it may cross its own gravitational horizon, leading to the creation of a black hole. Hawking Radiation from these black holes could then emit energy, primarily in the form of gamma rays, with implications for the observable gamma-ray background [4] (Figure 2). However, it's possible to set an upper limit on [math]\normalsize{\mu}[/math], considering the potential creation and evaporation of black holes from cosmic strings and their impact on gamma-ray observations.


Black Hole Formation from Cosmic-String Loops


A cosmic-string loop possesses energy [math]\small{E}[/math], and its gravitational radius (also known as the Schwarzschild Radius, further information in here, section 1) is given by:


[math]\LARGE{R_g = 2GE = 2G\mu l,}[/math]


[math]\Large{R_g = 2GE = 2G\mu l,}[/math]

Equation 1.   Schwarzschild Radius form for a string loop


where [math]\small{l}[/math] is the Length of the String Loop, and [math]\normalsize{\mu}[/math] is the Linear Mass Density of the cosmic string. If the loop contracts to within this gravitational radius, it can form a black hole. This black hole could then evaporate due to the Hawking radiation mechanism, emitting energy primarily in the form of gamma rays. The density of primordial black holes created by cosmic-string loops would then be a significant factor in understanding the gamma-ray background.


The condition for black hole formation is therefore met when the loop's radius becomes less than or equal to the Schwarzschild radius. This condition is a basic criterion and represents a lower bound for black hole formation. The interesting point about this criterion is that it depends on the one-dimensional nature of the string. The ratio of the Schwarzschild radius to the loop length is given by:


[math]\LARGE{f = \frac{R_g}{l} = 2G\mu}[/math]


[math]\Large{f = \frac{R_g}{l} = 2G\mu}[/math]

Equation 2.   Relation between the Schwarzschild Radius and the loop length


which does not depend on the fundamental length, [math]\small{l}[/math] of the loop.


craiyon_180439_milky_way_galaxy (1)

Figure 1.   The Milky Way in a Dark Night Sky


Parameterization and Probability of Black Hole Formation


The formation probability of black holes from cosmic-string loops depends on several factors, including the loop's energy and its shape. The probability, [math]\normalsize{p}[/math], is related to the ratio [math]\small{R_g/l}[/math], which is proportional to [math]\small{2G\mu}[/math]. This relationship can be expressed as:


[math]\LARGE{p = \kappa (G\mu)^{2 + q}}[/math]


[math]\Large{p = \kappa (G\mu)^{2 + q}}[/math]

Equation 3.   The equation for Black Holes Formation Probability


in which [math]\normalsize{\kappa}[/math] and [math]\normalsize{q}[/math] are coefficients to be determined. The parameter [math]\normalsize{q}[/math] represents the uncertainty in the parametrization of the loop's shape and evolution. This uncertainty is critical in estimating the upper limit for [math]\small{G\mu/c^2}[/math], as it influences the probability of black-hole formation from cosmic-string loops.


Impact on Gamma-Ray Background


When black holes evaporate [5] through Hawking radiation, they emit energy across the electromagnetic spectrum (further information in here, section 2), with a significant contribution to gamma rays. The density of these black holes, [math]\normalsize{n_{BH}}[/math], is dependent on the cosmic-string loop density, [math]\normalsize{n_{loop}}[/math], and the probability of black-hole formation:


[math]\LARGE{n_{BH} = p \cdot n_{loop}}[/math]


[math]\Large{n_{BH} = p \cdot n_{loop}}[/math]

Equation 4.   Black holes density - loop density expression


As the Universe expands [6], the energy density of black holes, [math]\normalsize{\rho_{BH}}[/math] decreases at a slower rate than the energy density of radiation (Equation 5), implying that even a low initial density of primordial black holes could lead to a measurable gamma-ray background. The observation of this background, along with gamma-ray bursts, allows for setting upper limits on [math]\small{G\mu/c^2}[/math].



[math]\LARGE{\frac{\rho_{BH}}{\rho_{matter}} = \frac{(G\mu)^{2 + q}\cdot \nu \kappa \cdot \mu^3 + M^{-2}}{\rho_{matter}|_{t \ = \ t_{BH}}}}[/math]


[math]\Large{\frac{\rho_{BH}}{\rho_{matter}} = \frac{(G\mu)^{2 + q}\cdot \nu \kappa \cdot \mu^3 + M^{-2}}{\rho_{matter}|_{t \ = \ t_{BH}}}}[/math]

Equation 5.   Ratio between black hole energy density and the matter density


[math]\small{M}[/math] is the Black Hole Mass, [math]\small{t_{BH}}[/math] is the Black Hole Formation Time and [math]\normalsize{\rho_{matter}}[/math] is the Matter Density.


unnamed

Figure 2.   A pictorical Represention of the Gamma-Ray Background


Constraints on Cosmic-String Linear Mass Density


Combining theoretical predictions with observational constraints from gamma-ray background and gamma-ray bursts, we can derive an upper bound for the linear mass density of cosmic strings (Equation 6). This upper bound depends on the value of [math]\normalsize{q}[/math], which represents the uncertainty in the parameterization of the loop's shape and evolution. If [math]\normalsize{q \approx 0}[/math], then the upper bound for [math]\small{G\mu/c^2}[/math] aligns with theoretical expectations of the order of 10-6. However, variations in [math]\normalsize{q}[/math] could significantly alter this bound.



[math]\LARGE{G\mu \leq [(G\mu)_{max, \ q \ = \ 0}]^{(\frac{7}{7 + 2q})}}[/math]


[math]\Large{G\mu \leq [(G\mu)_{max, \ q \ = \ 0}]^{(\frac{7}{7 + 2q})}}[/math]

Equation 6.   The upper bound equation: the maximal value for [math]\normalsize{G\mu}[/math]


as [math]\normalsize{[(G\mu)_{max, \ q \ = \ 0}]}[/math] represents the Maximum Value for [math]\normalsize{G\mu}[/math] corresponding to [math]\normalsize{q = 0}[/math].


A "String" Cosmological Structure


The study of cosmic strings and their potential to form black holes has significant implications for cosmic structure formation and observational cosmology. By considering the gamma-ray background and gamma-ray bursts, one can derive an upper limit for the linear mass density of cosmic strings. The uncertainty in the parameter [math]\normalsize{q}[/math], representing the choice of parameterization and the dynamics of loop formation, is a critical factor in refining this upper limit. Further research into this parameterization and the evolution of cosmic strings is necessary to provide more accurate constraints on [math]\normalsize{G\mu/c^2}[/math].




  1. ResearchForLife7 (revisited from Canadian Science Publishing). "Solutions of the Schrödinger equation for pseudo-Coulomb potential plus a new improved ring-shaped potential in the cosmic string space–time" https://httpsresearchforlife7.com/wp-content/uploads/2024/12/Solutions_of_the_Schrodinger_equation_for_pseudo_Coulomb_potential_plus_a_new_improved_ring_shaped_potential_in_the_cosmic_string_space_time.pdf

  2. Physical Review Letter. "Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking" https://journals.aps.org/prd/abstract/10.1103/PhysRevD.74.063527

  3. Physical Review D. "Scaling of cosmic string loops" https://journals.aps.org/prd/pdf/10.1103/PhysRevD.74.063527

  4. IOPscience. "Measurements of the Galactic X-Ray/Gamma-Ray Background Radiation: Contribution of Discrete Sources" https://iopscience.iop.org/article/10.1086/308755/pdf

  5. Physical Review D. "Information loss in black holes" https://journals.aps.org/prd/pdf/10.1103/PhysRevD.72.084013

  6. arXiv. "Is the Expansion of the Universe Accelarating? All Signs Point to yes" https://arxiv.org/pdf/1610.08972


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Traveling the Heart of a Supernova Explosion via a Dynamic Stream of Neutrinos


What is a Supernova?


Type II Supernovae (SN), triggered by the Gravitational Collapse of Massive Stars, emit a substantial portion of their energy in the form of Neutrinos (Figure 1). These elusive particles, constituting what is known as the Supernova Relic Neutrino (SRN) background [1], could potentially be detected by large underground neutrino detectors, such as the Super - Kamiokande and Sudbury Neutrino Observatory (SNO) detectors.


The primary objective of these detectors is to capture traces of this elusive SRN background. The SN II Rate Evolution [2], coupled with the Metal Enrichment History [3], forms the basis of predicting the SRN Flux. By relating observations of Star Formation and metallicity enrichment, one establishes a robust framework for estimating the supernova rate and, consequently, the SRN flux.


craiyon_174809_supernova_explosion

Figure 1.   Representation of an Exploiting Supernova


The Photophysical Fingerprint of Neutrinos


The composition of neutrinos reaching Earth, originating from past supernovae, relies on several factors. First, it hinges on the differential flux of neutrinos per unit energy interval emitted by each supernova. Secondly, it is influenced by the distribution of supernova rates with respect to Redshift. Additionally, it's contingent upon a Friedmann-Robertson-Walker Cosmology, typically characterized by parameters such as the Hubble Parameter, H0 and the Matter Density Parameter, [math]\small{\Omega_{0}}[/math] (further information in here, Section 4).


The Spectrum (Figure 2) of neutrinos emitted from a supernova is characterized by a Fermi-Dirac Distribution with zero Chemical Potential, normalized to the total energy emitted by the supernova. For each Neutrino Species, [math]\small{\nu}[/math], the Neutrino Luminosity, L [math]\small{{_{\nu}}^{S}}[/math]([math]\small{\epsilon}[/math]) can be defined as:


L [math]\LARGE{{_{\nu}}^{S} (\epsilon) = E_{\nu} {120 \over 7{\pi}^4} {{\epsilon}^2 \over T_{\nu}^{4}} \Biggl[e^{\epsilon \over T_{\nu}} + 1 \Biggr]^{-1}}[/math]


L [math]\large{{_{\nu}}^{S} (\epsilon) = E_{\nu} {120 \over 7{\pi}^4} {{\epsilon}^2 \over T_{\nu}^{4}} \Biggl[e^{\epsilon \over T_{\nu}} + 1 \Biggr]^{-1}}[/math]

Equation 1.   Neutrinos Luminosity Equation



where the apex [math]\small{S}[/math] stands for "Spectrum"; [math]\small{\epsilon}[/math] is the Neutrino Species Energy for a singluar neutrino; [math]\small{E_{\nu}}[/math] and [math]\small{T_{\nu}}[/math] are, in the order, the Neutrino Species Total Energy and the Temperature Parameter derived by the neutrinosphere during the collapse, and both dependent on the Progenitor Mass of the supernova. However, obtaining the Initial Mass Function (IMF)-averaged neutrino flux is simplified because [math]\small{T_{\nu}}[/math] doesn't vary significantly with the progenitor mass.


Assuming that the Supernova Rate, [math]\small{N_{SN}}[/math]([math]\small{z}[/math]) follows the Metal Enrichment Rate, it can be expressed like below.


[math]\LARGE{N_{SN} (z) = {\dot{\rho}_{Z} (z) \over \langle M_{Z} \rangle}}[/math]




[math]\large{N_{SN} (z) = {\dot{\rho}_{Z} (z) \over \langle M_{Z} \rangle}}[/math]



Equation 2.   The form of Supernova Rate



[math]\Large{z}[/math] is the Redshift value; [math]\large{Z}[/math] is Atomic Number of a chemical element; [math]\large{\dot{\rho}_{Z} (z)}[/math] represents the Metal Enrichment Rate per unit comoving volume and [math]\large{\langle M_{Z} \rangle}[/math] denotes the Average Yield of Heavy Elements per supernova.


To track the metal enrichment rate, one can assume a constant supernova rate at higher redshifts ([math]\small{z > 1} [/math]) due to the limited knowledge of high-redshift evolution. This assumption is supported by various independent studies showing consistent evolutionary patterns.


Looking for Elusive Particles!


Detecting relic neutrinos from supernovae poses significant challenges, particularly across various energy ranges. SuperKamiokande, for instance, has an observable energy window estimated to span from 19 to 35 MeV. However, below 10 MeV, the contribution from neutrinos generated by reactors and those from Earth is expected to overshadow any relic neutrino signal. Beyond 10 MeV but still below the observable window, background sources include solar neutrinos, external radiation, and events induced by Cosmic - Ray Muons [4] within the detector.


Atmospheric neutrinos become the primary background above 19 MeV. As energy surpasses approximately 35 MeV, the rapidly diminishing flux of relic neutrinos becomes less significant compared to atmospheric neutrinos. The Efficiency [5] of this detector within the observable energy window is assumed to be 100%.


Given the detector's specifications, the predicted event rate at SuperKamiokande for SN relic neutrinos can be calculated, and it is suggested being a peaked distribution. The flux at the detector is assessed across various energy ranges, with considerations for background sources and detector capabilities.


Figure 3.   Statistical and figurative Entropy Concept: the Order and Combinations Number of a small balls group


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Figure 2.   The Rainbow is an example of Electromagnetic Spectrum including Radiation in the Visible Energy Window

A Troublesome Research


One can present conservative upper bounds on the expected SRN event rates, indicating challenges in detecting these elusive particles. Despite advancements in detector technology, the Signal - to - Background Ratio remains a significant obstacle. Future research directions, including refining metal enrichment history models and exploring alternative detection strategies will be discussed.






  1. ScienceDirect. "Discovery potential for supernova relic neutrinos with slow liquid scintillator detectors "https://www.sciencedirect.com/science/article/pii/S0370269317302629

  2. STScl. "The Evolution of the Cosmic Supernova Rates" https://www.stsci.edu/files/live/sites/www/files/home/jwst/about/history/design-reference-mission-drm/_documents/drm11.pdf

  3. Springer. "Metal enrichment history of the proto-galactic interstellar medium" https://link.springer.com/article/10.1023/A:1019527307631

  4. PhysicsOpenLab.org. "Cosmic Ray Muons & Muon Lifetime " https://physicsopenlab.org/2016/01/10/cosmic-muons-decay/

  5. KNS.org. "Detection Efficiency Calculation and Evaluation for Condenser Off-gas Radiation Monitoring System " https://www.kns.org/files/pre_paper/45/21S-123-%EA%B9%80%EC%9B%90%EA%B5%AC.pdf


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Many types of Fuels for Space-Time Travels


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Figure 1.  A Spaceship refueling with liquid Hydrogen (LH2) in deep Space


Overview of different Fuel types for Space-Time Travel

You'll need different fuels for different things. LH2 is really too bulky for most air-breathing aircraft, but it's a waste to operate nuclear rockets on anything else, and spaceplanes almost require it for cooling and combustion speed (Figure 1). Methane is a much better launch vehicle fuel due to its density, which makes tanks far smaller and improves thrust density. And any decently developed industrial base will allow production of heavier hydrocarbons, for example by the Fischer-Tropsch process. And then there's various room-temperature chemical fuels and ion thruster propellants [1].

That’s good for planet Earth, especially when compared with rocket launches that rely on a popular alternative: Kerosene-based propellant. In the case of SpaceX, a single Falcon 9 flight emits about 336 tons of Carbon Dioxide—the equivalent of a car traveling around the World 70 times—according to John Cumbers, a former NASA synthetic biologist and CEO of SynBioBeta [2].


Advantages and Disadvantages of each Fuel Type

Whilst liquid fuels present disadvantages such as the potential for hazardous spills or leaks, one of the biggest issues discovered with such fuels is the relatively complex design, with an increased likelihood of things going wrong. If the liquid substance is cryogenic the fuel cannot be stored for long, and so the foundations for cryogenic storage facilities must be set up at the launch site. This is an area where Skyrora stands out from market competitors, with the propellants of our Skyrora XL vehicle designed to be stored for a longer launch window which is crucial for UK launches where weather conditions make go-for-launch difficult [3].

Pros: Thirty-percent better fuel economy than an equivalent gasoline vehicle, widely available, lower cost premium than for hybrid vehicles, engines deliver lots of torque for a given displacement, and any Diesel car can run on a blend of renewable Biodiesel fuel. With effort and investment, older diesel engines can be converted to run on pure waste vegetable oil (Figure 2).

Cons: Traditionally more engine noise and vibration. Additional emissions equipement drives up vehicle prices, which along with currently higher cost of Diesel fuel takes a big bite out of any savings. Most clean diesels require refills of Urea solution. Manufacturers won't warranty Biodiesel blends of more than five-percent of Biodiesel [4].


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Figure 2.  A Solar Sail in a Space-Time Travel


Current research and development in Alternative Fuel Sources for Space-Time Travel

Picking up fuel along the way — the Ramjet approach — will lose efficiency as the Space craft's speed increases relative to the planetary reference (Figure 3). This happens because the fuel must be accelerated to the spaceship's velocity before its energy can be extracted, and that will cut the fuel efficiency dramatically [5].

Whilst reusability of rockets benefits science, exploration and human spaceflight – one of the greatest drivers for stakeholders in the global launch segment is the scale and demand for in-orbit assets by industry and economy, fuelled in tandem by the plummeting costs and size of satellites (e.g. CubeSats), instrumentation, and even ride-sharing platform services [6].


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Figure 3.  A futuristic Warp Drive spaceship slicing through the Galaxy with neon blue lights






  1. Headed For Space. "Using Liquid Methane As Rocket Fuel – Advantages & Drawbacks" https://headedforspace.com/using-liquid-methane-as-rocket-fuel/

  2. Fortune.com. "Space travel is heating up—and so are rocket fuel emissions. These companies are developing cleaner alternatives to protect earth first." https://fortune.com/2022/12/05/space-travel-is-heating-up-and-so-are-rocket-fuel-emissions-these-companies-are-developing-cleaner-alternatives-to-protect-earth-first/

  3. Skyrora. "Rocket fuel: is it rocket science?." https://www.skyrora.com/rocket-fuel-is-it-rocket-science/

  4. Consumer Reports. "The Pros and Cons on Alternative Fuels." https://www.consumerreports.org/cro/2011/05/pros-and-cons-a-reality-check-on-alternative-fuels/index.htm

  5. Wikipedia. "Spacetravel under constant acceleration" https://en.wikipedia.org/wiki/Space_travel_under_constant_acceleration

  6. Spaceaustralia. "Renewable Rocket Fuels – Going Green and Into Space" https://spaceaustralia.com/feature/renewable-rocket-fuels-going-green-and-space


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The Extraordinary Frontier: A Glimpse into Life on Asteroids



Only Rock Pieces of Scientific Interest...

As humanity's curiosity extends beyond Earth, the possibility of life on asteroids becomes an intriguing subject of exploration. While asteroids are traditionally viewed as barren rocks floating in Space, recent scientific discoveries and advancements in Space exploration have opened up new possibilities. This article delves into the potential for life on asteroids and the exciting prospects that lie ahead.

The Microbial Universe

Scientists have long believed that life may exist in the most extreme conditions, and asteroids are no exception. Recent studies suggest that microbial life forms could potentially survive on asteroids, adapting to the harsh cosmic environment. Microorganisms (Figure 1), known for their resilience, might find a way to thrive in the microgravity and extreme temperatures of these Space rocks. [1]

Asteroid Mining and Its Implications

The growing interest in asteroid mining (Figure 2) has further fueled discussions about life beyond Earth. As Space agencies and private companies eye asteroids for their rich mineral resources, the possibility of encountering extraterrestrial life during mining operations raises ethical and scientific questions. Researchers are actively exploring methods to minimize the impact on potential life forms while extracting valuable resources. [2]



craiyon_174157_a_close_up_view_of_a_microbial_cell_attached_to_a_mineralized_polymer_matrix

Figure 1.  Close up view of a microbial cell attached to a mineralized polymer matrix


The Trojan Asteroids: Potential Havens for Life?

Trojan Asteroids (Figure 3), which share an orbit with a larger celestial body, could offer unique conditions for sustaining life. Scientists hypothesize that these asteroids might have stable environments with consistent temperatures, making them potential havens for microbial life. Future missions aim to study Trojan asteroids to uncover more clues about the potential existence of life in our cosmic neighborhood. [3]

The Water-Rich Asteroids

Water, a fundamental requirement for life as we know it, has been discovered on certain asteroids. These Water-rich asteroids could serve as crucial stepping stones for future human exploration and colonization efforts. The presence of water raises the possibility of sustaining plant life, opening up the potential for a self-sustaining ecosystem. [4]



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Figure 2.  Futuristic space station situated in the asteroid belt


Challenges and Future Prospects

While the concept of life on asteroids is fascinating, numerous challenges must be addressed before confirming its existence. The harsh conditions of Space, radiation exposure, and the lack of a protective atmosphere pose significant hurdles. Nonetheless, advancements in astrobiology, robotics, and Space exploration technologies offer hope for overcoming these challenges in the future. [5]

The Dream Perspective: Living by Floating!

The exploration of life on asteroids represents a thrilling frontier in Space science. As researchers delve into the mysteries of these celestial bodies, the possibilities of finding microbial life, water sources, and stable environments continue to capture our imagination. Whether through scientific missions or the pursuit of asteroid mining, the quest for life beyond Earth is an exciting journey that may redefine our understanding of the Cosmos.



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Figure 3.  A Trojan Asteroid orbiting near a planet






  1. Scientific American. "Hardy Microbes Hint at Possibilities for Extraterrestrial Life." https://www.scientificamerican.com/article/hardy-microbes-hint-at-possibilities-for-extraterrestrial-life/

  2. Space.com. "NASA's OSIRIS-REx lands samples of asteroid Bennu to Earth after historic 4-billion-mile journey." https://www.space.com/nasa-osiris-rex-success-recovery-asteroid-sample

  3. The Planetary Society. "NASA’s Lucy mission: an odyssey to the Trojan asteroids." https://www.planetary.org/articles/what-can-nasa-learn-from-the-trojans

  4. NASA. "NASA’s Bennu Asteroid Sample Contains Carbon, Water." https://www.nasa.gov/news-release/nasas-bennu-asteroid-sample-contains-carbon-water/

  5. SciTechDaily. "NASA’s Psyche Gets Huge Solar Arrays for 1.5-Billion-Mile Journey to Metal-Rich Asteroid." https://scitechdaily.com/nasa-psyche-gets-huge-solar-arrays-for-1-5-billion-mile-journey-to-metal-rich-asteroid/



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