Black Holes in Pesachim

This week, many Jews all over the world who follow the Daf Yomi (Daily Page/Folio) cycle of Talmud study began studying the Talmudic Tractate Pesachim, which deals primarily with Passover. Its very first line, however, focuses attention on one of astronomers’ favorite topics: light! Or does it?

אוֹר לְאַרְבָּעָה עָשָׂר בּוֹדְקִין אֶת הֶחָמֵץ לְאוֹר הַנֵּר.

[The Mishnah:] On the evening [“or”] of the fourteenth [of the month of Nisan] one searches for leaven [bread] by the light of a lamp. (Pesachim 2a)

The Gemara, analyzing the phraseology of the Mishnah, immediately questions:

מַאי ״אוֹר״? רַב הוּנָא אָמַר: נַגְהֵי, וְרַב יְהוּדָה אָמַר: לֵילֵי

What is “OR”? — R. Huna said: Light [naghe]; while Rab Judah said: Night [lele].

Now, this is a little odd, since it seems a given that bedikat chametz – the searching for leaven – is in practice done on the night of the fourteenth. In Aramaic, the word אוּרְתָּא – “ourta” – which seems very close to אוֹר – “or” – does mean night. In fact, ultimately, the Gemara concludes that there’s no real disagreement between Rav Huna and Rav Judah, just a difference in common usage of words in different locales.

However, before reaching that conclusion, the Gemara proceeds to bring multiple proofs and refutations for the meaning of  ״אוֹר״ – “OR.” Among them, one stands out for particular astronomical interest:

מֵיתִיבִי: ״הַלְלוּהוּ כׇּל כּוֹכְבֵי אוֹר״ — אַלְמָא ״אוֹר״ אוּרְתָּא הוּא. הָכִי קָאָמַר: הַלְלוּהוּ כׇּל כּוֹכָבִים הַמְּאִירִים. אֶלָּא מֵעַתָּה, כּוֹכָבִים הַמְּאִירִים הוּא דְּבָעוּ שַׁבּוֹחֵי, שֶׁאֵינָן מְאִירִין לָא בָּעוּ שַׁבּוֹחֵי?! וְהָא כְּתִיב: ״הַלְלוּהוּ כָּל צְבָאָיו״

אֶלָּא הָא קָא מַשְׁמַע לַן — דְּאוֹר דְּכוֹכָבִים נָמֵי אוֹר הוּא. לְמַאי נָפְקָא מִינַּהּ? לְנוֹדֵר מִן הָאוֹר. (דִּתְנַן:) הַנּוֹדֵר מִן הָאוֹר — אָסוּר בְּאוֹרָן שֶׁל כּוֹכָבִים.

An objection is raised: “Praise Him all ye stars of light” (Psalms 148:3) [“or”; here, there is an initial assumption that כּוֹכְבֵי אוֹר means “stars of night”], which proves that ‘or’ is evening? — This is its meaning: praise him all ye stars which give light. If so, are only the stars that give light to praise [Him], while those which do not give light need not praise — yet surely it is written, “Praise ye Him, all His host?” Rather he [the Psalmist] tells us this: the light of the stars too is [designated] light. What is its practical bearing? In respect of one who vows [not to benefit] from light. For it was taught: If one vows [not to benefit] from light, he is prohibited the light of stars.

A few astronomical ideas jumped out of this passage.

First, notice the rabbis’ understanding in the latter part of the passage that starlight is the same stuff as other light, i.e. sunlight. In modern times, we take it for granted that stars are like our Sun, but appear less bright to us because they are much farther away from us. However, that idea was not commonly found in the ancient world. It is interesting that the rabbis, at least from a practical point of view, seem to have focused on the commonality between light sources, and not differentiated between them.

Another astronomical question arises from this passage: what were the talmudic rabbis thinking when they spoke of stars “which do not give light”?

Modern astronomers know of several types of stars that do not emit light – at least not visible light. Black holes, neutron stars (or pulsars), and (some might include) brown dwarfs are all stages of stellar evolution in which stars do not “shine.”

Black holes and neutron stars are the remains of stars after they have used up all of their fuel available for nuclear fusion. Without the energy of fusion, they can no longer support themselves against gravity and they collapse or “go supernova.”

Depending on their mass, their collapse may be halted by “neutron degeneracy” pressure, in which case they end up as a super-dense neutron star, with the density of the star like the density of neutrons. Neutron stars are about the size of a small city, with a radius of around 10km.

For more massive stars, neutron degeneracy pressure is not enough to halt the collapse, and they collapse down to a black hole.

Black holes are called “black holes” because they are so massive that their gravitational pull is so great that even light cannot escape.

These are “stars” that do not radiate. Although, they often do accrete a “disk” surrounding them of highly energized matter, which is being pulled into them, that does (brightly) radiate.

Some neutron stars do radiate in the radio part of the electromagnetic spectrum – but not in the same way as visible stars. Because they have a magnetic field, they are like spinning magnets that emit radio waves, but in narrow beams. A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis.

Due to their spinning (often at very high speeds), these beams are only in the direction of Earth periodically, and they are called “Pulsars” because they appear to be “pulsing.”

The radiation beams sweep through space like rotating lighthouse beams as the neutron star rotates.

Neutron stars were discovered using a radio telescope in 1967. Jocelyn Bell noticed very regular pulses of radio emission coming from a single part of the sky. The pulses were coming from a spinning neutron star—a pulsar.

Yet another type of “not-quite star” could perhaps also be called a “star that does not radiate”: brown dwarfs, although technically they are not actually stars, but “almost stars.”

Brown dwarfs are massive objects, bigger than Jupiter or other giant planets, but not massive enough to become stars with nuclear fusion going on in them.

When brown dwarfs form, in a process that is initially similar to the stellar formation process, (electron) degeneracy pressure halts the gravitational contraction of any objects with less than about 0.08 times the mass of the Sun. This occurs before the core temperature becomes hot enough to cause fusion. These starlike objects not massive enough to start fusion are called brown dwarfs.

A brown dwarf emits infrared light because of heat left over from contraction, but it does not shine in the same way as actual stars do. Its luminosity gradually declines with time as it loses thermal energy.

These are a few types of “stars that do not shine” that have been discovered by modern astronomy. But obviously, the talmudic rabbis would not have known of them.

Perhaps they were thinking in terms of ideas known in ancient astronomy.

One simple explanation might be that since stars on the “celestial sphere” remain in their locations as the Earth rotates, those stars that would be in the daytime sky, which are not visible due to the much greater intensity of the Sun’s light lighting up the daytime sky were thought of as “stars that do not shine” – at least not enough to be seen in the daytime!

Another possibility is that they were thinking about stars’ brightness, as described by the ancient Greek astronomer Hipparchus. He classified visible stars as 1st through 6th “magnitude,” with 1st being the brightest and 6th the dimmest.

Modern astronomers “jury rigged” a formula for magnitude to (approximately) match ancient magnitude for visible stars, and extended it to brighter and dimmer stars not necessarily visible with the naked eye.

It would not be too much of a “reach” to suggest that ancients might have considered the idea that there exist even dimmer stars than the 6th magnitude that are not shining strongly enough to be visible, simply based on the continuation of the scale downwards.

Yet another possibility to understand this in an ancient context could be that they were referring to the (visible) planets, which do not shine with their own light, but just reflect light from the Sun.

Ancient Greek astronomers, starting with Anaxagoras (467 BCE) and those who followed in his footsteps, knew that the Moon does not shine with its own light but only reflected sunlight. In the 5th century CE – roughly contemporaneous with later generations of the talmudic rabbis – the Indian astronomer Aryabhata wrote that the planets also do not shine with their own light but only reflected Sunlight. It is hypothetically possible, though unproven, that talmudic rabbis might have been clued in to such contemporary ideas and been referring to the visible planets as “stars that do give light.”

From a modern point of view, if we posit that the “giving praise” to God from astronomical bodies equates to the wonder they instill and their display of the awesomeness of God’s creations, it seems to me that the wonders of these “non-shining stars” certainly give praise to God as much as the “regular” shining stars. In fact, if we ponder the wondrousness and awesomeness of black holes and super-dense super-fast spinning neutron stars, they might be giving even more praise!

One Comment Add yours

  1. Dan Epstein says:

    Amazing!!! I am not going to pretend I understand everything but the last paragraph was amazing and was so well put!!!

    Chazak Ve Amatz, I can’t wait to read next week’s post!!! -Dan

    On Sun, Nov 29, 2020 at 10:23 PM AstroRav: Torah & Astronomy wrote:

    > astrorav posted: “This week, many Jews all over the world who follow the > Daf Yomi (Daily Page/Folio) cycle of Talmud study began studying the > Talmudic Tractate Pesachim, which deals primarily with Passover. Its very > first line, however, focuses attention on one of astronom” >


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