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    Eddington luminosity

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    sunloops575.jpg.8f0e597dfa11cbf7c2671096

    The Eddington luminosity, also referred to as the Eddington limit, is the maximum luminosity a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called hydrostatic equilibrium. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are mostly driven by the less intense line absorption.[1] The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars.

    Originally, Sir Arthur Stanley Eddington took only the electron scattering into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also counts on other radiation processes such as bound-free and free-free radiation (see Bremsstrahlung) interaction.

    Derivation

    The limit is obtained by setting the outward radiation pressure equal to the inward gravitational force. Both forces decrease by inverse square laws, so once equality is reached, the hydrodynamic flow is different throughout the star.

    From Euler's equation in hydrostatic equilibrium, the mean acceleration is zero,

    \frac{d u}{d t} = - \frac{\nabla p}{\rho} - \nabla \Phi = 0

    where u is the velocity, p is the pressure, \rho is the density, and \Phi is the gravitational potential. If the pressure is dominated by radiation pressure associated with a radiation flux F_{\rm rad},

     
    -\frac{\nabla p}{\rho} = \frac{\kappa}{c} F_{\rm rad}\,.

    Here \kappa is the opacity of the stellar material. For ionized hydrogen \kappa=\sigma_{\rm T}/m_{\rm p}, where \sigma_{\rm T} is the Thomson scattering cross-section for the electron and m_{\rm p} is the mass of a proton.

    The luminosity of a source bounded by a surface S is

    L = \int_S F_{\rm rad} \cdot dS = \int_S \frac{c}{\kappa} \nabla \Phi \cdot dS\,.

    Now assuming that the opacity is a constant, it can be brought outside of the integral. Using Gauss's theorem and Poisson's equation gives

    L = \frac{c}{\kappa} \int_S \nabla \Phi \cdot dS = \frac{c}{\kappa} \int_V \nabla^2 \Phi \, dV = \frac{4 \pi G c}{\kappa} \int_V \rho \, dV = \frac{4 \pi G M c}{\kappa}

    where M is the mass of the central object. This is called the Eddington Luminosity.[2] For pure ionized hydrogen

    \begin{align}L_{\rm Edd}&=\frac{4\pi G M m_{\rm p} c} {\sigma_{\rm T}}\\ &\cong 1.26\times10^{31}\left(\frac{M}{M_\bigodot}\right){\rm W} = 3.2\times10^4\left(\frac{M}{M_\bigodot}\right) L_\bigodot \end{align}

    where M☉ the mass of the Sun and L☉ the luminosity of the Sun.

    The maximum luminosity of a source in hydrostatic equilibrium is the Eddington luminosity. If the luminosity exceeds the Eddington limit, then the radiation pressure drives an outflow.

    The mass of the proton appears because, in the typical environment for the outer layers of a star, the radiation pressure acts on electrons, which are driven away from the center. Because protons are negligibly pressured by the analog of Thomson scattering, due to their larger mass, the result is to create a slight charge separation and therefore a radially directed electric field, acting to lift the positive charges, which are typically free protons under the conditions in stellar atmospheres. When the outward electric field is sufficient to levitate the protons against gravity, both electrons and protons are expelled together.

    Different limits for different materials

    The derivation above for the outward light pressure assumes a hydrogen plasma. In other circumstances the pressure balance can be different from what it is for hydrogen.

    In an evolved star with a pure helium atmosphere, the electric field would have to lift a helium nucleus (an alpha particle), with nearly 4 times the mass of a proton, while the radiation pressure would act on 2 free electrons. Thus twice the usual Eddington luminosity would be needed to drive off an atmosphere of pure helium.

    At very high temperatures, as in the environment of a black hole or neutron star, high energy photon interactions with nuclei or even with other photons, can create an electron-positron plasma. In that situation the mass of the neutralizing positive charge carriers is nearly 1836 times smaller (the proton to electron mass ratio), while the radiation pressure on the positrons doubles the effective upward force per unit mass, so the limiting luminosity needed is reduced by a factor of ≈1836*2.

    The exact value of the Eddington luminosity depends on the chemical composition of the gas layer and the spectral energy distribution of the emission. A gas with cosmological abundances of hydrogen and helium is much more transparent than gas with solar abundance ratios. Atomic line transitions can greatly increase the effects of radiation pressure, and line driven winds exist in some bright stars.

    Super-Eddington luminosities

    The role of the Eddington limit in today’s research lies in explaining the very high mass loss rates seen in for example the series of outbursts of η Carinae in 1840–1860.[3] The regular, line driven stellar winds can only stand for a mass loss rate of around 10−4–10−3 solar masses per year, whereas mass loss rates of up to 0.5 solar masses per year are needed to understand the η Carinae outbursts. This can be done with the help of the super-Eddington broad spectrum radiation driven winds.

    Gamma-ray bursts, novae and supernovae are examples of systems exceeding their Eddington luminosity by a large factor for very short times, resulting in short and highly intensive mass loss rates. Some X-ray binaries and active galaxies are able to maintain luminosities close to the Eddington limit for very long times. For accretion-powered sources such as accreting neutron stars or cataclysmic variables (accreting white dwarfs), the limit may act to reduce or cut off the accretion flow, imposing an Eddington limit on accretion corresponding to that on luminosity. Super-Eddington accretion onto stellar-mass black holes is one possible model for ultraluminous X-ray sources (ULXs).

    For accreting black holes, all the energy released by accretion does not have to appear as outgoing luminosity, since energy can be lost through the event horizon, down the hole. Such sources effectively may not conserve energy. Then the accretion efficiency, or the fraction of energy actually radiated of that theoretically available from the gravitational energy release of accreting material, enters in an essential way.

    Other factors

    The Eddington limit is not a strict limit on the luminosity of a stellar object. The limit does not consider several potentially important factors, and super-Eddington objects have been observed that do not seem to have the predicted high mass-loss rate. Other factors that might affect the maximum luminosity of a star include:

    • Porosity. A problem with steady winds driven by broad-spectrum radiation is that both the radiative flux and gravitational acceleration scale with r −2. The ratio between these factors is constant, and in a super-Eddington star, the whole envelope would become gravitationally unbound at the same time. This is not observed. A possible solution is introducing an atmospheric porosity, where we imagine the stellar atmosphere to consist of denser regions surrounded by lower density gas regions. This would reduce the coupling between radiation and matter, and the full force of the radiation field would only be seen in the more homogeneous outer, lower density layers of the atmosphere.
    • Turbulence. A possible destabilizing factor might be the turbulent pressure arising when energy in the convection zones builds up a field of supersonic turbulence. The importance of turbulence is being debated, however.[4]
    • Photon bubbles. Another factor that might explain some stable super-Eddington objects is the photon bubble effect. Photon bubbles would develop spontaneously in radiation-dominated atmospheres when the magnetic pressure exceeds the gas pressure. We can imagine a region in the stellar atmosphere with a density lower than the surroundings, but with a higher radiation pressure. Such a region would rise through the atmosphere, with radiation diffusing in from the sides, leading to an even higher radiation pressure. This effect could transport radiation more efficiently than a homogeneous atmosphere, increasing the allowed total radiation rate. In accretion discs, luminosities may be as high as 10–100 times the Eddington limit without experiencing instabilities.[5]

    References

    1.  A. J. van Marle; S. P. Owocki; N. J. Shaviv (2008). "Continuum driven winds from super-Eddington stars. A tale of two limits". AIP Conference Proceedings 990: 250–253. arXiv:0708.4207. Bibcode:2008AIPC..990..250V. doi:10.1063/1.2905555.
    2. Rybicki, G.B., Lightman, A.P.: Radiative Processes in Astrophysics, New York: J. Wiley & Sons 1979.
    3. N. Smith; S. P. Owocki (2006). "On the role of continuum driven eruptions in the evolution of very massive stars and population III stars". Astrophysical Journal 645 (1): L45–L48. arXiv:astro-ph/0606174. Bibcode:2006ApJ...645L..45S. doi:10.1086/506523.
    4. R. B. Stothers (2003). "Turbulent pressure in the envelopes of yellow hypergiants and luminous blue variables". Astrophysical Journal 589 (2): 960–967. Bibcode:2003ApJ...589..960S. doi:10.1086/374713.
    5. J. Arons (1992). "Photon bubbles: Overstability in a magnetized atmosphere". Astrophysical Journal 388: 561–578. Bibcode:1992ApJ...388..561A. doi:10.1086/171174.
    6. Juhan Frank; Andrew King; Derek Raine (2002). Accretion Power in Astrophysics (Third ed.). Cambridge University Press. ISBN 0-521-62957-8.
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    GN-z11, the remotest galaxy yet discovered.

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    Posted

    Astronomers use the Hubble Space Telescope to discover GN-z11, the remotest galaxy yet discovered. 

    Distant_galaxy_GN-z11_in_GOODS-N_image_b

    GN-z11 is a high-redshift galaxy found at the constellation Ursa Major. GN-z11 has a spectroscopic redshift ofz = 11.1, an age of 13.4 billion years, and is observed as it existed 400 million years after the Big Bang that occurred 13.8 billion years ago.

    As of March 3, 2016, GN-z11 is the most distant known galaxy in the Universe. GN-z11 was identified by a team studying data from the Hubble Space Telescope's CANDELS and GOODS-North surveys.

    “Right now, we expect this galaxy to be about 32 billion light-years away from us in distance,” per study coauthor Pascal Oesch of Yale University.

    The research team used Hubble’s Wide Field Camera 3 to measure the distance to GN-z11 spectroscopically, by splitting the light into its component colors to measure the redshift caused by the expansion of the universe.

    GN-z11 is 25 times smaller than the Milky Way and has 1% of the Milky Way galaxy’s mass in stars. GN-z11 is growing forming stars at a rate about 20 times faster than the Milky Way galaxy does today.

    The study authors said: “It’s amazing that a galaxy so massive existed only 200 to 300 million years after the very first stars started to form”, “It takes really fast growth, producing stars at a huge rate, to have formed a galaxy that is a billion solar masses (one solar mass is equal to the mass of the Sun) so soon.”

    “The discovery of this unexpectedly bright galaxy at such a great distance challenges some of our current theoretical models for the build-up of galaxies,” “Larger area datasets are now needed to measure how common such bright galaxies really are so early in the history of the universe.”

    North Korean leader Kim Jong-un orders the country's nuclear weapons to be made ready for use

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    Posted

    SEOUL, March 4 (Yonhap) -- North Korean leader Kim Jong-un on Friday ordered the country's nuclear weapons to be made ready for use at a moment's notice.

    He also said the communist country will revise its military posture so it can be ready to carry out pre-emptive attacks, stressing that the current situation has become very precarious, according to the Korean Central News Agency.

    The announcement comes more than a day after the United Nations Security Council passed a new sanctions resolution penalizing the country for its fourth nuclear test and long-range missile launch earlier in the year.

    yonngong@yna.co.kr

    http://english.yonhapnews.co.kr/news/2016/03/04/0200000000AEN20160304001100315.html

    The one sentence your LinkedIn profile must have

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    Posted

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    Once upon a time, someone wiser than I am told me a marketing truth I never forgot: A confused prospect never buys.

    In sales and marketing, clarity is king.

    This is especially true in the 21st century, when our ultra-connected, always on, stream-of-consciousness lives as we scroll through one social media profile and update after another gives marketers precious few seconds to grab our attention.

    Is Your LinkedIn Summary Scaring Prospects Away?

    Today, I want to focus on the first sentence of your LinkedIn Summary.

    The way LinkedIn lays out a profile page, your Summary area is the first text area visitors come across after seeing your headshot and professional title.

    Needless to say, the first sentence of your LinkedIn Summary is critical.

    Let me ask: What do you have in there right now? Don't lie! Are you talking about yourself in the third person, like a professional athlete? Are you telling us where you work and what your job title or duties are?

    If you are, it's okay.

    Blame it on LinkedIn!

    You're far from alone. In fact, LinkedIn has trained us to think that way — to treat our profile page like a virtual résumé, listing our employers, job titles, duties, and so on.

    If you're trying to use LinkedIn to generate business for yourself, however, that approach is a huge mistake.

    Here's why: Your clients don't care about you.

    I hate to burst your bubble, but your clients do not care what your job title is, where you attended college, what awards you've won or anything else. What they do care about is quite simple.

    “Your clients care about themselves – morning, noon, and after supper!”

    Dale Carnegie penned those words all the way back in 1936, but they ring just as true in 2016, don't they?

    The Secret to a Successful LinkedIn Summary

    Which leads us to the all-important first sentence of your LinkedIn Summary.

    Take the template I'm going to share below and copy it, filling in the blanks to personalize it for you and your business.

    Here it is:

    WHAT I DO: I help [MY TARGET AUDIENCE] achieve [THEIR GOAL] by providing [MY PRODUCT/SERVICE].

    See how simple and clear that is?

    Using that approach, the first sentence of your LinkedIn Summary instantly identifies your target audience, tells that audience how you help them achieve their goals or solve their problems, and it explains how you do it (the service or product you provide).

    It's that simple.

    Make sure you watch this video to see how some of my LinkedIn Riches students have applied the formula above to their profiles.

    You’ll see how they’re able to take the template I shared above and simply fill in the blanks in a way that helps them appeal to their target audiences in a fast, efficient and clear manner.

    Go watch the video, and then give it a shot yourself!

    John Nemo is the author of the Amazon #1 Bestseller “LinkedIn Riches.” Register here for his free webinar on generating more business with LinkedIn!

    John Nemo

    http://www.bizjournals.com/portland/how-to/marketing/2016/02/the-one-sentence-your-linkedin-profile-must-have.html?page=all

    Scott Kelly grew two inches during year-long space flight

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    When astronaut Scott Kelly arrived in Houston on Thursday morning (March 3), he was about two inches taller than when he left for the International Space Station a year before, according to NASA representatives. That's pretty normal for an astronaut, for without the full strength of gravity pressing down on gel-filled discs between the vertebrae, they expand and lengthen the spine. It's a weird but temporary side effect of spaceflight.

    But even if Kelly hadn't had his vitals checked immediately upon landing, he might have noticed the slight height change. One of the first earthlings he saw was his identical twin, retired astronaut Mark Kelly, a man now notably, if only temporarily, shorter.

    NASA scientists already knew that Kelly would walk a little taller when he emerged from the Soyuz capsule. But he'll have changed in other, less obvious ways, too, and that's the whole point of his record-breaking mission. Kelly and Russian cosmonaut Mikhail Kornienko spent 342 days on the space station to help scientists measure the effects of long-term spaceflight on the human body.

    http://www.nola.com/science/index.ssf/2016/03/scott_kelly_grew_two_inches_in.html

    Apple launches ‘Support’ Twitter account, allowing people to tweet at it

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    Posted

     

    The company doesn’t have an official account, instead preferring to send updates out through its executives or profiles dedicated to specific services

    Apple has launched an official Twitter account to allow people to tweet at it with their problems.

    The company doesn’t run an official Twitter feed, instead offering individual ones for each service. But the new account might be the closest that it comes to offering a central account.

    The @AppleSupport account is tweeting tips and tricks for Apple devices, as well as responding to questions from users. People can tweet at the account publicly, or it offers private direct message conversations.

    Apple has long offered live online chat with its support staff, through its own website. But the new account brings it in line with a range of other companies by offering a way for people to get in touch over the social network.

    Apple has never had an official Twitter account, but still uses the service heavily. Most of its important tweets have gone out from the @AppStore account, though executives including Tim Cook also send out a combination of personal and company-related posts.

    The account with the @Apple name is held by an unknown person and has never posted. Its owner joined in September 2011, it has nearly 40,000 followers but has never tweeted and only has a default egg picture.

    http://www.independent.co.uk/life-style/gadgets-and-tech/news/apple-launches-support-twitter-account-allowing-people-to-tweet-at-it-a6909536.html

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    Mysterious Fast Radio Bursts Detected Outside Milky Way Galaxy

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    Scientists want to know what is causing a mysterious, rapid burst of radio waves that appear to be coming from a source located beyond the Milky Way galaxy.

    What makes these waves so special is the fact they appear to be repeating, scientists said. Fast radio bursts are uncommon -- just 17 have been detected by scientists in the past eight years -- and they're often viewed as isolated events, according to researchers at Cornell University.

    Understanding these bursts can help scientists learn more about the origins of the universe. The particular fast radio bursts in this study lasted 10 milliseconds and were found in archived Cornell data. The bursts were observed from the enormous Arecibo telescope in Puerto Rico.

    Astronomers from Cornell published a paper last week in "Nature" regarding the 17th discovered FRB. Noting an afterglow, researchers argued in the paper this particular FRB cannot have an explosive origin.

    The latest discoveries upend previous theories that the fast radio bursts were the result of explosive events, such as the smashing together of neutron stars.

    Shami Chatterjee, a senior researcher at Cornell, said the perplexing fast radio burst didn't have an explosive origin.

    "So, either there's an odd coincidence, or maybe there are different types of FRBs," Chatterjee said. "Either way, it seems we've broken this enigmatic phenomenon wide open."

    http://abcnews.go.com/Technology/mysterious-fast-radio-bursts-detected-milky-galaxy/story?id=37370758

    Dronebox could allow UAVs to work for months

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    Posted

    DRONEBOX is a drone nesting solution that helps automate professional drone operations in numerous industrial applications.
    It's also a grid-independent drone battery charging system that removes costly or dangerous tasks, remote area travel and operations. Finally - it's a networked and movable surveillance and inspection sensor systems broaden the Internet of Things.

     

     

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