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{{Use dmy dates|date=September 2014}}
In [[mathematics]], a [[partially ordered set]] P is said to have '''Knaster's condition upwards''' (sometimes '''property (K)''') if any [[uncountable]] subset ''A'' of ''P'' has an [[linked set|upwards-linked]] uncountable subset. Anologous definition applies to '''Knaster's condition downwards'''.
{{Starbox begin
| name = PSR J1719-1438
}}
{{Starbox image
| image = <!--image location (i.e. "Sunspots.png")-->
| caption = <!--caption (optional)-->
| credit = <!--credit for image if the image's use requires them (optional)-->
}}
{{Starbox observe
| epoch = [[Julian day#Alternatives|MJD]] 55411.0<ref name=bailes/><!--Epoch of observation-->
| equinox = [[J2000]]
| constell = [[Serpens]]
| pronounce = <!--Pronunciation guide-->
| ra = 17:19:10.0730(1)<ref name=bailes/> <!--Right Ascension-->
| dec = −14:38:00.96(2)<ref name=bailes/> <!--Declination-->
| appmag_v = <!--Apparent magnitude (Johnson-Cousins V system)-->
}}
{{Starbox character
| class = [[millisecond pulsar]]<ref name=bailes/> <!--Stellar class-->
| appmag_1_passband = R<!-- Passband for first apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_1 = >25.4<ref name=bailes/><!-- Value of first apparent magnitude  -->
| appmag_2_passband = g<!-- Passband for second apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_2 = >24.1<ref name=bailes/><!-- Value of second apparent magnitude  -->
| appmag_3_passband = I<!-- Passband for third apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_3 = >22.5<ref name=bailes/><!-- Value of third apparent magnitude  -->
| appmag_4_passband = <!-- Passband for fourth apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_4 = <!-- Value of fourth apparent magnitude  -->
| appmag_5_passband = <!-- Passband for fifth apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_5 = <!-- Value of fifth apparent magnitude  -->
| appmag_6_passband = <!-- Passband for sixth apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_6 = <!-- Value of sixth apparent magnitude  -->
| appmag_7_passband = <!-- Passband for seventh apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_7 = <!-- Value of seventh apparent magnitude  -->
| appmag_8_passband = <!-- Passband for eighth apparent magnitude (e.g., H, J, K, etc.) -->
| appmag_8 = <!-- Value of eighth apparent magnitude  -->
| r-i = <!--R-I color-->
| v-r = <!--V-R color-->
| b-v = <!--B-V color-->
| u-b = <!--U-B color-->
| j-h = <!--J-H color-->
| j-k = <!--J-K color-->
| variable = <!--Variability type-->
}}
{{Starbox astrometry
| radial_v = <!--Radial velocity (in km/sec)-->
| prop_mo_ra = <!--Proper motion (RA), μ<sub>α</sub> cos δ (in milliarcsec/yr)-->
| prop_mo_dec = <!--Proper motion (dec), μ<sub>δ</sub> (in milliarcsec/yr)-->
| parallax =  <!--Parallax (in milliarcsec)-->
| p_error = <!--Parallax error (in milliarcsec)-->
| parallax_footnote = <!--Parallax footnote-->
| dist_ly = <!--Distance (in light years)-->
| dist_pc = ~1,200<ref name=bailes/><!--Distance (in parsecs)-->
| absmag_v = <!--Absolute magnitude ([[UBV photometric system|Johnson-Cousins V system]])-->
}}
{{Starbox orbit
| reference =<ref name=bailes/><!--Reference-->
| primary = PSR J1719-1438<!--Primary name -->
| name = [[PSR J1719-1438b]]<!--Companion name-->
| period = <!--Period (in years)-->
| period_unitless = 0.090706293(2) days<!--Period (no units provided by template)-->
| axis = <!--Semimajor axis (in arcseconds)-->
| axis_unitless = <math>a_P\sin i=</math>0.001819(1) [[light second]]s<!--Semimajor axis (no units provided by template)-->
| eccentricity = <0.06 <!--Eccentricity-->
| inclination = <!--Inclination (in degrees)-->
| node = <!--Longitude of node (in degrees)-->
| periastron = [[Julian day#Alternatives|MJD]] 55411.0<!--Periastron epoch-->
| periarg = <!--Argument of periastron (in degrees), secondary -->
| periarg_primary = <!--Argument of periastron (in degrees), primary -->
| k1 = <!-- Velocity semi-amplitude (SB1, or primary in SB2), in km/s -->
| k2 = <!-- Velocity semi-amplitude (secondary in SB2), in km/s -->
}}
{{Starbox detail
| source              =  <!--[source url]-->
| mass                =  <!--Mass (in solar masses)-->
| radius              =  <!--Radius (in solar radii)-->
| gravity            =  <!--Surface gravity (given as the base 10 logarithm expressed in cgs units)-->
| luminosity          =  <!--Luminosity (in solar luminosities); prefer luminosity_bolometric or luminosity_visual-->
| luminosity_bolometric = <!--Luminosity (in solar luminosities), bolometric-->
| luminosity_visual  =  <!--Luminosity (in solar luminosities), visual (V)-->
| temperature        =  <!--Temperature (in kelvins)-->
| metal              =  <!--Metallicity (no units provided by template)-->
| rotation            =  <!--Rotation (no units provided by template)-->
| rotational_velocity =  <!--Rotational velocity (v sin i, in km/s)-->
| age                =  <!--Age (in years)-->
| age_gyr            =  <!--Age (in billions of years)-->
}}
{{Starbox catalog
| names = <!--Other catalog designations-->
}}
{{Starbox reference
| Simbad = <!--Search String-->
}}
{{Starbox end}}


'''PSR J1719-1438''' is a [[millisecond pulsar]] with a spin period of 5.8 ms located about 4000 [[light year|ly]] from Earth in the direction of [[Serpens]] Cauda,<ref name=bailes/><ref name=UniverseToday /> one minute from the border with Ophiuchus. Millisecond pulsars are generally thought to begin as normal pulsars and then spin up by accreting matter from a [[Binary star|binary]] companion.
The property is named after [[Poles|Polish]] [[mathematician]] [[Bronisław Knaster]].


==Diamond planet==
Knaster's condition implies [[ccc]], and it is sometimes used in conjunction with a weaker form of [[Martin's axiom]], where the ccc requirement is replaced with Knaster's condition. Not unlike ccc, Knaster's condition is also sometimes used as a property of a [[topological space]], in which case it means that the topology (as in, the family of all open sets) with [[inclusion]]{{Disambiguation needed|date=February 2012}} satisfies the condition.
{{main|PSR J1719-1438 b}}
PSR J1719-1438 was discovered in 2011 by the High Time Resolution Survey, a [[radio astronomy]] search for astronomical objects that rapidly vary in radio brightness, such as pulsars.<ref name=bailes/> Timing measurements using the [[Parkes Telescope]] and [[Lovell Telescope]] showed that it has a low-mass companion: [[PSR J1719-1438 b]].<ref name=bailes/> The companion has a mass similar to that of [[Jupiter]], but 40% of the diameter. It orbits the pulsar with a period of 2 hours 10 minutes and 37 seconds, at a distance of around 600,000&nbsp;km (0.89 [[Solar radius|solar radii]]).<ref name=bailes/> The companion is likely the remnant of a star whose outer layers were siphoned off by the more massive pulsar. Calculations show the companion has a minimum density of 23 grams per cubic centimeter and is probably an ultra-low-mass carbon–oxygen [[white dwarf]].<ref name=bailes/>


Because the companion to PSR J1719-1438 is planet-sized, made primarily of carbon (with an unknown amount of oxygen), and very dense, it may be similar to a large diamond. In the science press, the object has been called the [[Carbon planet|"Diamond Planet"]].<ref name=UniverseToday>{{cite web|title=Star Transforms into A Diamond Planet|url=http://www.universetoday.com/88449/star-transforms-into-a-diamond-planet|work=Universe Today|accessdate=2011-08-26}}</ref><ref name=Space.com>{{cite web|title=Surprise! Alien Planet Made of Diamond Discovered|url=http://www.space.com/12731-diamond-alien-planet-discovered-neutron-star.html|work=Space.com|accessdate=2011-08-25}}</ref><ref name= MaxPlanck>{{cite web|title=A Planet made of Diamond|url=http://www.mpifr-bonn.mpg.de/public/pr/pr-pulsar-august2011-en.html|work=Max Planck Institut for Radio Astronomy|accessdate=2011-08-26}}</ref>
Furthermore, assuming [[Martin's axiom|MA]](<math>\omega_1</math>), ccc implies Knaster's condition, making the two equivalent.


==A lump of QCD matter==
== References ==
It has been suggested in 2012 that PSR J1719-1438 b may not be the remmant of a white dwarf, but a lump of [[QCD matter|quark matter]] with a size of just 1 kilometer and the mass of Jupiter,<ref name=horvath>
*{{cite book | last=Fremlin | first=David H. | title=Consequences of Martin's axiom | publisher=[[Cambridge University Press]]| location=Cambridge | year=1984 | isbn=0-521-25091-9 | others=Cambridge tracts in mathematics, no. 84}}
{{cite journal|doi=10.1088/1674-4527/12/7/009|title=The nature of the companion of PSR J1719-1438: a white dwarf or an exotic object?|year=2012|last1=Horvath|first1=J. E.|journal=Research in Astronomy and Astrophysics|bibcode = 2012RAA....12..813H|volume=12|number=7|pp=813–816}}
</ref> that would have been born in the collision and merger of two previous [[quark star]]s, part of the ejected matter ending orbiting the merger remmant we see as the pulsar PSR J1719-1438.<ref name=bauswein>
{{cite journal|doi=10.1103/PhysRevLett.103.011101|title=Mass Ejection by Strange Star Mergers and Observational Implications|year=2009|last1=Bauswein|first1=A.|last2=Janka|first2=H. -T.|last3=Oechslin|first3=R.|last4=Pagliara|first4=G.|last5=Sagert|first5=I.|last6=Schaffner-Bielich|first6=J.|last7=Hohle|first7=M. M.|last8=Neuhäuser|first8=R.|journal=Physical Review Letters|bibcode = 2009PhRvL.103a1101B|volume=103|issue=1|id=011101}}
</ref>


==See also==
[[Category:Order theory]]
* [[EF Eridani]], a star system with a compact star and a degraded planetary-mass former star


==References==
{{reflist|colwidth=25em|refs=


<ref name=bailes>
{{Mathlogic-stub}}
{{cite journal|doi=10.1126/science.1208890|title=Transformation of a Star into a Planet in a Millisecond Pulsar Binary|year=2011|last1=Bailes|first1=M.|last2=Bates|first2=S. D.|last3=Bhalerao|first3=V.|last4=Bhat|first4=N. D. R.|last5=Burgay|first5=M.|last6=Burke-Spolaor|first6=S.|last7=d'Amico|first7=N.|last8=Johnston|first8=S.|last9=Keith|first9=M. J.|last10=Kramer|first10=M.|last11=Kulkarni|first11=S. R.|last12=Levin|first12=L.|last13=Lyne|first13=A. G.|last14=Milia|first14=S.|last15=Possenti|first15=A.|last16=Spitler|first16=L.|last17=Stappers|first17=B.|last18=Van Straten|first18=W.|journal=Science|bibcode = 2011Sci...333.1717B|pmid=21868629|volume=333|issue=6050|pages=1717–20|arxiv = 1108.5201 |display-authors=8}}
</ref>
 
}}
 
{{Stars of Serpens}}
 
[[Category:Astronomical objects discovered in 2010]]
[[Category:Millisecond pulsars]]
[[Category:Planetary systems]]
[[Category:Serpens (constellation)]]

Revision as of 15:48, 18 August 2014

In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. Anologous definition applies to Knaster's condition downwards.

The property is named after Polish mathematician Bronisław Knaster.

Knaster's condition implies ccc, and it is sometimes used in conjunction with a weaker form of Martin's axiom, where the ccc requirement is replaced with Knaster's condition. Not unlike ccc, Knaster's condition is also sometimes used as a property of a topological space, in which case it means that the topology (as in, the family of all open sets) with inclusionTemplate:Disambiguation needed satisfies the condition.

Furthermore, assuming MA(ω1), ccc implies Knaster's condition, making the two equivalent.

References

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