today in astronomy 142: standard...

Astronomy 142 1

Today in Astronomy 142: Standard candles

! Standard candles and standard rulers.

! Cepheids, and Henrietta Leavitt’s invention of standard candles.

! The extragalactic nature of the spiral nebulae and the Shapley-Curtis debate.

! Type Ia supernovae as standard candles.

! The extragalactic distance scale.

The Small Magellanic Cloud, site of the discovery of Leavitt’s Law. (Photograph by Weihao Wang (NRAO).)

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Standard candles and standard rulers

There’s only one direct distance measurement method for individual objects – trig parallax – and it only works on objects within a few hundred parsecs (until GAIA mission). Thus astronomers have often sought standard candles or rulers to aid in distance determinations. ! Standard candle: an object with a well determined

luminosity L known a priori, whose distance is therefore

! Standard ruler: an object with length d perpendicular to the line of sight is known a priori, whose distance is

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Introducing Cepheid variable stars

Discovered in 1784 by 21-year-old John Goodricke. Periods of variations are measured in days or weeks, brightness variations (at V) are typically of order one magnitude. !  δ Cep (archetype):

!  α UMi (Polaris), a prominent but peculiar Cepheid:

Today about 20000 are known, about 2400 of which were discovered around the turn of the century by Henrietta Leavitt. Most of those she found were in the Small Magellanic Cloud, and therefore all about the same distance (~60 kpc) from us.

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Henrietta Leavitt and standard candles

! The Bruce telescope itself was built with a $50k donation to Harvard from Catherine W. Bruce of New York; the site in Peru was upgraded for it by another of Miss Bruce’s bequests. (Pickering was a friend of Miss Bruce’s.) Leavitt never observed with it; women were not allowed.

! Leavitt noted in the first few sets of Bruce photographic plates on the SMC and LMC that there were many variables among the brightest stars, and that the brighter variables had longer periods (Leavitt 1908).

(AIP photo)

Henrietta Leavitt: one of the women who worked as “computers” in Edward Pickering’s group at Harvard College Observatory.

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WW Cyg, a classical Cepheid

Composite photograph at maximum (left) and minimum (right) brightness

Light curve

(Chaisson and McMillan, Astronomy Today)

Henrietta Leavitt and standard candles (continued)

Period-apparent magnitude relation for bright variables in the SMC (“Pickering” 1912). The upper (lower) curve represents each star’s maximum (minimum) brightness. The linear fits have the same slope, 1 mag per 0.48 in the logarithm of period in days.

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In modern terms: we know that Leavitt’s stars are classical Cepheids (not RR Lyraes) and the period-average magnitude relation for her LMC stars is

(Monson et al. 2012). Since the absolute and apparent magnitudes differ only by the constant distance modulus and the V extinction – 18.48 and 0.39 mag for LMC – we have a relation between period and absolute magnitude:

and the distance to a new Cepheid with period Π is given by

Leavitt’s law


The Leavitt law, measured at λ = 3.6 µm with Spitzer/IRAC, for ten Galactic Cepheids with trigonometric parallax, and 80 LMC Cepheids. ! At this wavelength,

extinction is very small. ! Also the 3.6 µm magni-

tude difference between Cepheids with different metallicity is small. (LMC has much lower metal-licity than the Galaxy).

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Freedman et al. 2012

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Cepheid variable stars (continued)

As first suggested by Harlow Shapley in 1914, Cepheids owe their variability to radial pulsation. During the cycle the stellar radius and effective temperature change by some 10-20% of their average values. Cepheids turn out to be the highest-luminosity versions of a class of variable stars lying in a small part of the HR diagram called the instability strip. The other inhabitants of the instability strip: W Virginis stars (“Population II Cepheids”), RR Lyrae stars (lower-mass stars on the horizontal branch), δ Scuti stars (just above the main sequence) and ZZ Ceti stars (pulsating white dwarfs). Mistaken identification of one type as another led to a lot of confusion in the early days of their use as standard candles.

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The instability strip in the HR diagram

(From Carroll and Ostlie, Modern Astrophysics)

Period of oscillation approximately that for a sound wave to travel from surface to center and back.


The Leavitt law measured with HST/WFC3 at λ = 1.6 µm for 120 Cepheids in M106. ! Orbital parallax has been

measured by VLBI for M106’s circumnuclear water masers, giving r = 7.28 Mpc, (Herrnstein et al. 1999).

! The metallicity of M106 is close to that of the Milky Way; systematic effects from metallicity are small.

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Riess et al. 2011

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The extragalactic distance scale

Here is the “ladder” by which distances to celestial objects are currently determined. Each rung uses the previous result, inheriting its uncertainty and adding its own. 1.  Measure the AU, using radar reflection from Venus.

! It would be tempting to try to measure stellar distances by radar, but the reflected signal decreases with distance to the object according to 1/r4, so it turns out not to work for objects more than a few light-hours away.

2.  Use trigonometric parallax to determine the distances to the nearest stars, and an “absolute main sequence.” ! A few open clusters, notably the Hyades and the

Pleiades, are close enough for accurate parallax measurements on all of their members.

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The extragalactic distance scale (continued)

3.  With the absolute main sequence as a calibration, use main-sequence fitting to determine the distances to open clusters that contain Cepheids, and thus the distance to the Cepheids themselves. Sound familiar? !  Hopefully soon to be rendered unnecessary by Gaia.

4.  Observe Cepheid periods and fluxes in galaxies, get their luminosities from their periods, and determine their distance (and that to their host galaxy) by using

! This works until it is impossible to separate Cepheids from nearby stars in the galaxy disks. The Hubble Space Telescope allowed this technique to be extended from 3 Mpc (all you can get with ground-based measurements) to about 40 Mpc.

The next standard candle

In the 20-40 Mpc distance range we begin to find significant numbers of galaxies in which both Cepheids and Type Ia supernovae have been observed. ! SNe Ia differ observationally

from core-collapse supernovae (SNe II) by the shape of their light curves and their spectra when near maximum light, and a different explosive process has been inferred.

! SNe Ia appear to happen in close binary systems with C-O white dwarfs which are accreting mass from their main-sequence or giant companions.

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NGC 3370 (Cepheids and SN Ia)

The next standard candle (continued)

! Accretion adds heat and hydrogen, but the degeneracy-pressure- supported WD does not expand in response.

! So a very hot surface region can develop in which fusion and a thermonuclear explosion can be touched off.

! This is called a dwarf nova; it can result in a month long, 3-magnitude brightening of the system.

! Despite punctuation by nova outbursts, the accretion process can keep the WDs increasing in mass, which eventually may approach the SAC limit.

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Tim Pyle (SSC/JPL/NASA)

The next standard candle (continued)

! As MSAC is approached, the temperature of the nondegenerate nuclei increases, along with the that of the accreted hydrogen at the surface.

! Eventually, at about C-C fusion can be touched off. ! This becomes a runaway thermonuclear deflagration that

consumes the whole star; it explodes violently and leaves no remnant. The explosion is very bright, brighter than a SN II at its peak, and can outshine the rest of its galaxy.

! Because of the constancy of MSAC , the WDs all have very nearly the same mass when they explode, and the same “yield”: SNe Ia are standard bombs.

! And thus the integral over the SN Ia light curve should vary little from SN Ia to SN Ia, for given distance.

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Reminder: supernova light curves

! SNe Ia reach peak absolute magnitude of about MV = -19, and then decline in brightness by about 0.1 mag/day.

! SNe II have smaller peak luminosities (MV ~-16 – -17 ) and decline more slowly ( 0.05 mag/day) than SNe Ia. The average integrated light is about the same as that of SNe Ia but there is considerably more variation about the average – they’re not such good standard candles as SNe Ia.

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Wikimedia Commons SN Ia

The extragalactic distance scale (continued)

So, continuing up the ladder, 6.  Observe galaxies that have

both Cepheids and SNe Ia, measuring the distance to the supernovae with the Cepheids. This calibrates the SNe Ia as standard candles, as in the figure at right.

7.  Then the distance is known to any galaxy in which an SN Ia is seen.

8.  Cosmological indicators: Hubble constant, cosmic microwave background oscillations.

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Riess et al. 2011

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Pulsating stars and the 1918 size of the Galaxy

Shapley recognized the importance of Leavitt’s discovery of the Cepheid period-luminosity relationship, and set about applying it as a standard candle in distance measurements of globular clusters. He could not have known at the time, despite a grasp of the physics of pulsation that turned out to be correct, that there were so many different types of pulsating stars. The regular variable stars in globular clusters are actually RR Lyrae stars, much less luminous than Cepheids. ! Nor did he know about interstellar extinction…

Thus he determined the shape of the GC distribution correctly, and found our offset from the center of the galaxy, but his Milky-way sizes were way too large (100 kpc diameter).

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Spiral nebulae and the Shapley-Curtis Debate

The Galactic diameter seemed so enormous to Shapley that he began to think his work also ruled out the longstanding (as far back as Kant, 1793) “island universe” description of the spiral nebulae, and that they must be Galactic objects. Spiral nebulae are what we now call spiral galaxies. At the time they knew the following about them: ! They come in the shapes and sizes we already know and

love; some (the edge-on ones) bear an uncanny resemblance to the Milky Way.

! They were not resolved into individual stars. ! They “avoid” the Galactic plane: only observed at

relatively high Galactic latitude.

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The Shapley-Curtis debate (continued)

Astronomers immediately split into two armed camps over the issue of Galaxy membership of the spiral nebulae, with one camp led by Shapley and the other by Heber Curtis. Other late-breaking spiral news in the 1918-1921 time frame: ! “Flares” were observed in a few spiral nebulae that were

immediately compared with novae. (SN, AGNs not known)

! Von Maanen reported observations of proper motion of the spiral arms of the big Sc galaxy M101. The corresponding rotation period was 105 years; if it were extragalactic the rotation speeds would be relativistic.

! All but a few spiral nebulae recede from the LSR at speeds much larger than typical of Galactic stars (Slipher, 1919).

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Shapley’s main points in support of his assertion that spiral nebulae lie within our Galaxy: ! If the “flare stars” were novae, then their

brightness is consistent with Galactic membership. (Use of novae as standard candles…)

! The observed proper motion of the arms of M 101, taken with relativity (no speed can exceed c), indicate that M 101 must lie within the Galaxy.

! If they lie within the Galaxy, the Galaxy can presumably influence them; Shapley postulated a hitherto unobserved force by which the Galactic plane repels the spiral nebulae, producing thereby the observed restriction to high Galactic latitude.

Shapley

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Curtis’ main points in claiming that the spiral nebulae are extra-Galactic, and in fact are “island universes”: ! The range of shapes of spirals looks like a

population seen at different orientations ranging from face on to edge on, and the latter bear a strong resemblance to the Milky Way.

! That they aren’t seen in the plane, are essentially all receding, and have such large radial velocities, indicates that they comprise a different population from Galactic stars; there is thus no a priori reason for taking them to be Galactic members.

! To consider them to be extragalactic involves no assumption of hitherto unobserved physical forces.

Curtis

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Resolution of the Shapley-Curtis debate

In the first of several huge contributions to astronomy, Edwin Hubble (1923) settled the whole matter by detecting variable stars in the Andromeda Nebula, M 31 (which we now call an Sb I galaxy); assuming them to be Cepheids, he showed M 31 to be ten times further away than the distance to the center of the Galaxy, derived in the same way by Shapley. ! This distance was too large, too, compared to modern

measurements, because Hubble took some stars that turned out to be W Virginis stars (which he didn’t know about) as Cepheids. W Virginis stars are fainter leading to a larger, wrong distance estimated.

! Regardless of precise distance, though, the results proved a large ratio for the M 31/Galactic center distance, far too large for M 31 to lie within the Milky Way.

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Resolution of the Shapley-Curtis debate (cont’d)

What about the novae, M 101’s rotation, Galactic plane avoidance, and high recession speeds? ! The “flares” in spirals turned out to be supernovae: a

hitherto unsuspected class of astronomical object, but one that required no new physics for its explanation.

! Van Maanen’s proper motion measurements were shown by Hubble and by van Maanen himself to be in error; more accurate measurements were consistent with no proper motion.

! When Trumpler discovered interstellar extinction, the reason that other galaxies are not seen in the plane of the Milky Way became obvious.

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Resolution of the Shapley-Curtis debate (cont’d)

! Slipher’s measurements held up, though: the galaxies are nearly all receding from the Galaxy, and are doing so at high speed. These results were used to great effect by Hubble in the late 1920s, as we will discuss in a few lectures.

Thus Shapley’s reasoning is seen to have been flawless, but based upon flawed data. Curtis’s instinct that one should try to explain phenomena in the physically simplest possible way (i.e. without invoking “new physics” unless one absolutely has to) led him to distrust data that indeed turned out to be flawed.

For further information, see the Shapley-Curtis debate itself (Bull. N.R.C. 2, 171 [1921].

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The extragalactic distance scale, version 1 (distances less than about 30 Mpc)

Here are the first few rungs of the “ladder” by which distances to celestial objects are determined. Each rung uses the previous result, inheriting its uncertainty and adding its own. 1. Measure the AU, using radar reflection from Venus. ! It would be tempting to try to measure stellar distances by

radar, but the reflected signal decreases with distance to the object according to 1/r4, so it turns out not to work for objects more than a few light-hours away.

2. Use trig parallax to determine the distances to the nearest stars, and an “absolute main sequence.” 3. Use trig parallax and moving-cluster parallax to determine the distance to the nearest open clusters, checking to see that their main sequences match that of the trig-parallax stars.

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The extragalactic distance scale, version 1 (distances less than about 30 Mpc), continued

4. With the open clusters as a calibration, use main-sequence fitting to determine the distances to open clusters that contain Cepheids, and thus the distance to the Cepheids themselves. This allows the measurement of luminosities for a sample of Cepheids, and thus a calibration of the Cepheid period-luminosity relation. 5. Observe Cepheid periods and fluxes in galaxies, get their luminosities from their periods, and determine their distance (and that to their host galaxy) by using ! This works until it is impossible to resolve Cepheids from

nearby stars in the galaxy disks; the Hubble Space Telescope allows this technique to be extended from 3 Mpc (all you can get with ground-based measurements) to about 30 Mpc.

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