Day 1 Discussion

Theory

Observations

Stella Offner & Alycia Weinberger

Synthetic Observations

syn・the・tic ob・ser・va・tion (noun) \sin-ˈthe-tik\ \ˌäb-sər-ˈvā-shən

: a quantitative prediction for the emission produced by a model and detected assuming the model is a real astronomical object at some point in the sky

- should include noise, resolution limits, instrumental effects

M*, 𝜌, v, x, T, t

Photons:TA(K), ∆v, mJy

Radiative Transfer

“Observe”

Simulation or Observation

Polaris FlareHerschel

Pop Quiz

✓

time

Dense cores and clumps, protostars, accretion disks

Today’s topics

exoplanet statistics

young binaries, brown dwarfs

0 Myr

+100 Myr

0.1 Myr

1 Myr

Discusion Theme

•What important physics is missing? •What (unnecessary) assumptions are being made? •What open problems need more theory support and/or synthetic observations?

• What observables can best discriminate between models?

• What problems require more statistics? More resolution?

Theory:

Observations:

time

Dense cores and clumps, protostars, accretion disks

Today’s topics

exoplanet statistics

young binaries, brown dwarfs

0 Myr

+100 Myr

0.1 Myr

1 Myr

time

Dense cores and clumps, protostars, accretion disks

Today’s topics

exoplanet statistics

young binaries, brown dwarfs

0 Myr

+100 Myr

1. What simulations would best further constrain core fragmentation? (HC)

2. Should low- and high-mass SF be considered separately? (HC)

4. How much of a stars mass is assembled in bursts? (WF)

3. What physics sets the IMF & stellar multiplicity? (SO)

7. Do the properties of disks we measure in the protostar phase have a direct relationship with what is observed in the later phases? (JT)8. How do we calibrate stellar ages and determine observationally when various planet formation processes happen? (AW)

5. How can we test how BDs form observationally and can formation be linked to compositional measurements? (KW-D)

6. How can we tell that planetesimals are forming? (AW)

G. A. Feiden: Magnetic inhibition of convection and the fundamental properties of low-mass stars. III.

(a)

Isochrone Ages: 5, 10, 15 Myr

(top to bottom)

log

10(L

/ L

�)

Teff (K)

10.0 Myr: ⟨Βƒ⟩ = Beq (0.00)

(0.18)

(0.36)

(0.53)

(0.70)

(0.85)

(0.98)

(1.00)

−2.00

−1.00

0.00

1.00

2.00

4000 6000 8000 10000

(b)log

10(L

/ L

�)

Teff (K)

0.0

1.0

2.0

5000 6000 7000 8000 9000 10000

(c)log

10(L

/ L

�)

Teff (K)

−2.0

−1.0

0.0

3000 3500 4000 4500 5000

Fig. 2. a) Comparison of theoretical Hertzsprung-Russell (HR) diagram predictions to the observational locus of Upper Scorpius. The medianempirical locus calculated in Sect. 3 is shown by the light gray shaded region. Black points signify HR diagram positions of eclipsing binarymembers for which masses and radii are known. Over-plotted are predictions from Dartmouth stellar evolution isochrones. Standard (i.e., non-magnetic) isochrones at 5 Myr, 10 Myr, and 15 Myr are shown as short-dashed, dash-dotted, and long-dashed lines, respectively. A single magneticisochrone at 10 Myr is plotted as a solid yellow line. Values in parentheses along the magnetic isochrone are predicted radiative core mass fractions(Mrad. core/M?) at the circled points. All models are computed with a solar metallicity. b) Zoom-in on the high-mass region of the HR diagram.c) Zoom-in on the low-mass region.

note that this age is inconsistent with the HR diagram age of5 Myr for UScoCTIO5.

Both eclipsing systems exhibit a disagreement between theirHR and mass-radius diagram age. However, the disagreementsdo not immediately appear to be systematic. HD 144548 appearsyounger in the mass-radius plane than it does in the HR dia-gram by roughly a factor of two. In contrast, UScoCTIO5 ap-pears older in the mass-radius plane than it does in the HR di-agram – also by about a factor of two. Slopes of the theoreticalTe↵-luminosity and mass-radius relationships must be altered indi↵erent directions to produce an overall agreement.

4.2. Magnetic models

Introducing a magnetic perturbation as described in Sect. 2, a10 Myr isochrone is computed and overlaid in the HR and mass-radius diagrams in Figs. 2 and 3 (thick yellow solid line). An ageof 10 Myr was chosen as a starting point based on the approxi-mate median age of the A-, F-, and G-type stars determined fromstandard stellar evolution models.

A 10 Myr magnetic isochrone naturally explains the fac-tor of two age di↵erence observed between high- and low-massstars, provided the high-mass stars are not appreciably a↵ectedby additional non-standard physics (e.g., rotation). Figures 2aand 2c (HR diagrams) show that a 10 Myr isochrone computedwith equipartition magnetic fields is shifted toward cooler tem-peratures and higher luminosities compared to a 10 Myr non-magnetic isochrone. Inhibition of convection by magnetic fieldscools the stellar surface temperature thereby slowing the con-traction rate of young stars. Stars have a larger radius and ahigher luminosity at a given age, as a result. The combinationof cooler surface temperatures and higher luminosities makes a10 Myr magnetic isochrone look nearly identical to a 5 Myr non-magnetic isochrone for stars with e↵ective temperatures below

about 5000 K. The magnetic stellar model isochrone lies on topof the 5 Myr standard model isochrone in Figs. 2a and 2c andentirely within the empirical stellar locus for low-mass stars inUpper Scorpius.

The magnetic model isochrone also correctly converges to-ward the 10 Myr standard model isochrone at warmer e↵ectivetemperatures. To some degree, this convergence reproduces anobserved transition in the empirical HR diagram where the ageinferred from standard model isochrones shifts from 5 Myr to10 Myr. Below Te↵ ⇠ 5000 K, the magnetic isochrone closelymatches predictions from a 5 Myr standard model isochrone.Compare this to the small segment of the magnetic isochroneabove Te↵ ⇠ 6000 K. Here, the magnetic isochrone traces the10 Myr standard model isochrone. Although the model pre-dicted transition appears to occur over approximately the cor-rect e↵ective temperature domain, Fig. 2a shows a sharper tran-sition from a magnetic to a non-magnetic sequence between4500 < Te↵ /K < 6000 compared to model predictions. This ismore clearly seen in Fig. 1, where the empirical median stellarlocus exhibits a knee around Te↵ ⇠ 4500 K that roughly corre-sponds to the beginning of the transition region in Fig. 2a. A dis-tinct knee feature is absent from the magnetic model isochrone.

Moreover, inspection of the mass-radius diagram in Fig. 3shows a 10 Myr magnetic isochrone provides reasonable agree-ment with the two low-mass eclipsing binary systems. It is ap-parent that magnetic inhibition of convection leads to more sig-nificant radius “inflation” at higher masses compared to at lowermasses. This e↵ect leads to a change in slope of the model pre-dicted mass-radius relationship that is consistent with observa-tions. Although agreement is good, it is not perfect. Depend-ing on whether mass and radius estimates are adopted fromKraus et al. (2015) or David et al. (2016), at 10 Myr the radiiof the primary and secondary in UScoCTIO5 are either 3.2%and 2.1% (Kraus et al.) larger than model predictions or 5.7%

A99, page 5 of 11

Stellar Ages and Planet Formation Processes Figure 6. Absolute H magnitude vs. effective temperature for the Upper Sco stars in our sample. The stars are separated into those with circumstellar disks (blue xsymbols) and those without disks (black circles). The orange diamonds represent stars where the presence of a disk is not known. The models of Baraffe et al. (2015)are displayed as colored lines. The gray dashed lines represent the constant masses. From left to right they are 1.0, 0.8, 0.6, 0.5, 0.4, 0.3 0.2, and 0.06 :M . SeeSection 4.1 for more details.

Figure 7. Histogram of the ages of the individual stars, split into those with circumstellar disks (dashed line) and those without disks (solid line). The groups appear tobe two different populations. See Section 4.2 for more details.

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The Astrophysical Journal, 850:11 (13pp), 2017 November 20 Donaldson et al.

Howwillweinves+gatethe+mescalesforearlyplanetformingprocesses?

Feiden,2016,A&A

Donaldson,Weinbergeretal.2017